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Modern Cosmology Introduction

Cosmology is the study of the evolution, current state, and future of the

universe. Since the earliest history humans have pondered and studied the universe.

The oldest of known societies have had creation/evolution myths of the universe.

Even today some of the simplest possible questions one could ask about the universe

are still unknown. How old is the universe? How large is the universe? What is the

fate of the universe? We have been asking these questions for thousands of years

with little success, until very recently. We live in a very interesting time for

cosmological study. Technology has finally started to catch up with our questions.

Within the last 50 years we can actually start trying to answer these questions.

Cosmology is one of the sciences where we can not repeat, tweak, or even

attempt to change variables in a controlled way, we can only merely observe. The

experiment was started long ago. Instead, using the laws of physics we attempt to

make models that have attributes matching those we can observe in the universe.

Therefore, almost any prediction made in cosmology is a model dependant one.

Luckily, our models are starting to match the observable universe quite well.

There are several modern theories of the evolution of the universe. Currently the two

most popular models are probably the Steady State Universe and the Big Bang

Universe. Neither of these theories perfectly predict the universe we observe, but are

both constantly being revised as new data and ideas strengthen them. Of the two, the

Big Bang theory is certainly the most accepted and popular.

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The steady state theory proposes that the universe will always be and has always

been. Old stars die to simply have new ones born in their place. The universe

remains, and has always has maintained an equilibrium.

The Big Bang theory proposes that the universe is expanding. The theory states that

galaxies are moving further from each other and the energy density of the universe is

falling. A logical consequence of the Big Bang theory is an eventual heat death of the

universe where photons will continually redshift to longer and longer wavelengths

and matter with grow to sparse to form any structure as we know it today. Since it is

expanding now if we go back in time the universe would have to have been a very

dense, hot place. There are three pillars of modern cosmology, or more formerly the

Big Bang theory: 1) Hubble Expansion 2) Big Bang Nucleosynthysis 3) Cosmic

Microwave Background.

In 1929 Edwin Hubble first discovered that almost all of the nearby galaxies were

moving away from us with velocities proportional to their distance away. Since that

time, this observation has been confirmed and more accurately measured. One of the

most recent

)( LawHubbleDHV o=

Equation 1. V is the velocity of a receding galaxy in km/sec. D is the distance away in Mpc. And Ho is called the Hubble Constant with units of km/sec/Mpc.

measurements of the Hubble Constant is 67 ± 5 km/s/Mpc, measured by the 2dF

Galaxy Redshift Survey. (Hubblecon, 2003) Luckily, we have several independent

ways to measure the Hubble expansion, galaxy distribution surveys, super nova

surveys, and Quasar surveys, to name a few. As more data comes in and technology

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improves these measurements are quickly converging to similar values. The Hubble

constant is a measure of the velocity of this observed expansion; in addition there is

also evidence at a slight acceleration that has been detected. Assuming that we do not

occupy a special place in the universe, we conclude that everywhere in the universe it

also appears that the surrounding galaxies are receding, or that the entire universe is

expanding everywhere, not just around us. This universal expansion is a fundamental

foundation to modern cosmology, or one of the pillars to modern cosmology.

Astrophysicist Fred Hoyle who was actually against the idea of an expanding

universe and in favor of a “Steady State” universe sarcastically coined the expansion

the “Big Bang” (Hoyle, 2001). He coined the term on his BBC radio series The

Nature of the Universe, in 1950. The name ended up being catchy and was adopted

by the scientific community for the expanding universe theory.

If we attempt to trace the laws of physics backwards in time to understand the

early universe we find the universe must have been a much denser, hotter place than it

is now. It was once so hot that matter, as we know it, could not exist and the universe

was at one time a dense sea of quarks and fundamental particles. At these energy

levels the four fundamental physical forces (strong, weak, electro-magnetic, and

gravity) merged into a Grand Unified Force. Currently we think we understand the

physics of the unification of two, and possibly three of the fundamental forces, strong,

weak, and electro-magnetism. However, we do not yet know how to unify gravity as

well. The energy levels required are far beyond the levels our particle accelerators

can probe and thus beyond our current understanding. Trying to push further back in

time from this point becomes a religious question rather than a scientific one.

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In the 1930’s Dr. Hans Bethe and others worked out the nuclear reactions that

powered the stars in the universe. It was discovered that heavier elements could be

created fusing lighter elements together through nuclear reactions. It was predicted

that all of the elements we see were created in the nuclear fires of stars. From these

calculations the abundances of elements was predicted in the universe, but were

found to quite off from observations. In 1948 Gamow, Alpher and Herman (Gamow,

1948) predicted that all of the elements could have been created in the big bang

itself. It was later shown by Fermi and Turkevich that coulomb barriers and lack of

stable nuclei with mass 5 and 8 precluded the formation of elements beyond 7Li in the

Big Bang. The most popular theory presently is that most of the universe’s hydrogen

and helium (and lithium) was created from the big bang during Recombination (see

below), and then all of the heavier elements up to iron were created by the nuclear

cores within stars. It is believed the heaviest elements, those heavier then iron were

created during supernova. Current theory predictions and actual observed

abundances of elements match very well, so well that Big Bang Nucleosynthysis

(BBN) is considered second fundamental pillar of modern cosmology.

Now starting with the hot, dense quark soup and letting time again run

forward the universe starts to cool and expand. At this point the mean free path of

any given particle is tiny and the entire universe is within thermodynamic

equilibrium. However, as it cools enough eventually particles start freezing out of

equilibrium when the energy density of the universe roughly approaches their rest

mass energy or chemical potential. The first major component to freeze out are the

neutrinos. If we had sensitive enough telescopes to view them, we should be able to

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see a uniform cosmological neutrino flux seemingly coming from everywhere in the

sky. The second major components to freeze-out were the photons. The photons

maintained thermal equilibrium amongst the charged particles, and when they

dropped from the reactions the first atoms could be formed. This process is called

“Recombination” but is really a misnomer since it was actually the first time, we

believe, for atoms to have formed. The now mostly-neutral atoms lost several ways

to interact with the photons and thermal equilibrium was lost. These high energy

photons broke free from the matter and except for a gravitational redshift down to

microwave energies have remained untouched and unaltered since the time of

recombination. This Cosmic Microwave Background (CMB) is thus the farthest

away and oldest thing we will ever be able to observe in the universe. (With the

possible exception of the neutrino background, or a gravitational wave background)

Today, we detect these cosmic microwaves uniformly over the entire sky.

Photons from one direction of the sky, thus one edge of the universe, have nearly the

same temperature as those coming from the completely opposite spot in the sky, the

other side of the universe. And in addition, if we take a power spectrum of the

photon distribution, (a plot of the number of photons at a given energy) we fine the

spectrum nearly exactly matches a perfect blackbody distribution of 2.728 K. The

CMB power spectrum is in fact the most perfect example of a blackbody curve ever

to be discovered in nature. This is very strong evidence that the whole universe was

at one time in thermal equilibrium. The Cosmic Microwave Radiation forms the third

pillar of modern cosmology.

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It would be a useful aside to discuss what is meant by a photon distribution's

temperature. Let us assume we are viewing a photon distribution with a radio

antenna that has an equivalent light collecting area of Ae. The antenna's normalized

power pattern on the sky is given as, Pn(θ, φ). In simpler terms we expect the antenna

to be more sensitive to light directly in front of it, as opposed to light coming from its

side, Pn(θ, φ) quantifies this sensitivity pattern. And finally we need to quantify the

brightness distribution of the photon field itself relative to the center of the antenna

beam, Bν(θ, φ). The total power collected by the antenna per unit bandwidth would

be:

( ) ( )∫∫ Ω= dPBAW ne φθφθν ,,2

1

Equation 2. The total power delivered to an antenna from an incoming photon field.

To then gain the antenna temperature of the distribution, Ta, we simply divide by

Boltzmann's constant kb.

abTkW =

Equation 3. The equivalent antenna temperature.

This relationship is derived by imagining a matched resistor attatched to the antenna

output. Equilibrium would eventually take place heating the resistor to Ta to match

the incoming antenna power.

George Gamow, Ralph Alpher, and Robert Herman first postulated the

existence of the CMB in 1948. (Gamow, 1948) However, they predicted its

blackbody temperature to be 5 K rather then 2.7 K. Later the theory was refined by

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others including Robert Dicke and James Peebles of Princeton. (Dicke, 1965)

Although a few groups had detected excess background radiation earlier, the

discovery of the CMB is usually credited to Arno Penzias and Robert Wilson of Bell

Telephone Laboratories in 1965. (Penzias, 1965)

The CMB is a near perfectly uniform 2.7253 K ± 0.66 mK (COBE, 1999)

blackbody distribution on the sky after foreground effects like the galactic plane and

the dipole effect are removed. A dipole field is created across the sky due to the earth

motion through the rest frame of the CMB itself. One half of the microwave sky

viewed from the earth is slightly “Hotter”, or blue-shifted, then the other half, red-

shifted. It is believed this is a Doppler shift due to the earths apparent velocity of 370

km/s with respect to the CMB’s rest frame. (Doppler, 1996) The CMB does,

however, have anisotropies on the level of about one part in 105. These anisotropies

were first discovered by the Cosmic Background Explorer satellite (COBE) in 1992.

(COBE, 1999) These deviations are thought to be caused by density fluctuations in

the early universe, possibly quantum fluctuations. In a process known as the Sachs-

Wolfe Mechanism (Sachs-Wolfe, 1967) photons coming from over-dense regions will

be slightly red-shifted relative to those coming from under dense pockets due to the

stronger gravitational fields. These early density fluctuations are also thought to lead

to the matter distribution we see today including the great walls and voids in galaxy

spatial distributions.

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Figure 1. All sky Maps based on 53 GHz (5.7 mm wavelength) observations made with the DMR over the entire 4-year mission (top) on a scale from 0 - 4 K, showing the near-uniformity of the CMB brightness, (middle) on a scale intended to enhance the contrast due to the dipole, and (bottom) following subtraction of the dipole component. Emission from the Milky Way Galaxy is evident in the bottom image. (COBE images, ref)

Figure 2. CMB power spectrum measured by the COBE experiment. The solid curve shows the expected intensity from a single temperature blackbody spectrum, as predicted by the hot Big Bang theory. The FIRAS/COBE data were taken at 34 positions equally spaced along this curve. The FIRAS data match the curve so exactly, with error uncertainties less than the width of the blackbody curve, that it is impossible to distinguish the data from the theoretical curve. (COBE images, 2003)

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Studying the anisotropies of the CMB can teach us a great deal of the universe

as most cosmological models can be constrained by them. If the scatter in the

anisotropy distribution is gaussian, then all of the anisotropy information can be

represented with a two-point autocorrelation function. All of the anisotropy

information can be represented simply by the angular separation between fractional

temperature deviations upon the celestial sphere. (Novikov, 1996)

( ) ( ) ( )cmbcmb T

xT

T

xTC

'rr ∆∆≡Θ

Equation 4. Two-point autocorrelation function. For each angular scale ΘΘΘΘ, , , , we average over all vectors on the sky, x and x’ such that x · x’= cosΘ.

When dealing with distributions upon a sphere it is often useful to expand things

using Legendre polynomials. The useful information is now encoded within the Cl

coefficients.

( ) ( )∑ Θ=Θl ll PCC cos

4

1

π

Equation 5. Two-point autocorrelation function expanded in terms of Legendre polynomials.

This ensemble of Cl coefficients are known as the angular power spectrum of the

CMB anisotropy. Cosmologists often refer to this angular power spectrum when

comparing and constraining various theories. The angular power spectrum for a

given theory often relies heavily upon the fundamental cosmological parameters used,

such as the Hubble Constant: Ho, Critical density: Ωo, etc.

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Figure 3. This is a sample CMB angular power spectrum. The actual positions and magnitudes of the wiggles (called acoustic peaks) are model dependant on various cosmological parameters. The blue boxes are predicted error bars from the upcoming PLANCK satellite mission. A multipole l of ~200 is close to a 1°°°° scale upon the sky. This has been taken from Wayne Hu’s CMB tutorial web page. (Huweb, 2003)

So far we have spoken of the CMB power spectrum and its angular power

spectrum. There is a third aspect of the CMB that also provides a good deal of

scientific information, namely its Polarization. Thomson Scattering at the last

scattering surface is theorized to cause CMB Polarization.

Polarization levels, however, are thought to be only 10% or less then the

anisotropy levels themselves and thus it is a very daunting task to detect such a weak

signal. The first experiment to look for CMB Polarization was realized by Lubin and

Smoot in the late 70’s. (Lubin, 1979) Very recently, the first reported detection of the

CMB Polarization was made by the DASI Collaboration. (DASI, 2002) DASI stands

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for the Degree Angular Scale Interferometer. DASI is compact microwave

interferometer optimized to detect CMB anisotropy at multipoles l ≅ 140 – 900. The

telescope has operated at the Amundsen-Scott South Pole research station since 2000

January.

Before we continue with Polarization it is important that we review Stokes

parameters. Electro-magnetic radiation can have magnitude and Polarization. Since

the Polarizations of the fields are not scalar quantities, it can be mathematically

difficult to keep track of the Polarizations of interacting fields. In 1852

mathematician George Stokes developed scalar quantities called the Stokes

Parameters in which electromagnetic fields could be represented, and thus easily

mathematically manipulated. The stokes parameters are commonly labeled I, Q, U,

and V. I represents the total intensity of the field. Q and U represent the two linear

Polarization states and V represents the circular Polarization.

We may represent and electro magnetic field as follows:

( )( )22

11

cos

cos

:

ˆˆ

δωδω

+−=+−=

+=→

tkzEE

tkzEE

where

yExEE

y

x

yx

Equation 6. The equation of an electromagnetic wave traveling in the positive z direction.

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We can then define the stokes parameters as follows:

22

21 EEI +=

22

21 EEQ −=

( )2121 cos2 δδ −= EEU

( )2121 sin2 δδ −= EEV

Equation 7. The four scalar Stokes parameters. The < > braces represent time averaging of the electromagnetic fields.

So the total intensity of an electro-magnetic field is I. The total Polarized intensity is

the quadrature sum of Q, U and V. We can define a fractional Polarized intensity as

well.

( )

( )onpolarizatifractionalI

P

ensitypolarizedVUQP

ensitytotalI

≡Π

++≡

=

int

int222

Equation 8. Total intensity, total Polarized intensity, and fractional Polarization defined.

Now it is useful to point out that Polarization is not a vector quantity, but rather a

spinor quantity. A 180° rotation to the direction of a vector is a new vector, however

the same rotation to a Polarization state is again the same state. A useful formula

when transforming between rotated coordinate systems becomes:

( ) ( )( ) ( )θθ

θθ2cos2sin

2sin2cos

UQU

UQQ

+−=′+=′

Equation 9. Transformation of linear Polarizations from one coordinate system into another rotated by an angle θθθθ.

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Although the stokes parameters are scalar quantities it is still useful to be able to

define or represent the Polarization axis of the field. The Polarization angle α, is

defined as follows:

( )rotationundertiontransforma

Q

U

θαα

α

−⇒

≡ −1tan

2

1

Equation 10. A definition of the Polarization axis and the axis defined after a coordinate rotation by the angle θθθθ. Note, regardless of a rotational coordinate transformation the Polarization axis remains fixed to the sky as one would expect.

Another non-intuitive feature of stokes parameters is that the Q and U “orientations”

are not perpendicular to each other, in contrast to the x and y Polarization states. Q

and U are offset by 45° as opposed to 90°. For example around a circle Q and U

could have these relative positions.

Figure 4. Arbitrary U and Q values around a circle.

Q

U

-Q

-U

-Q

U

Q

-U

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Thompson Scattering of Polarization

Polarization in the CMB is theorized to be caused by Thompson scattering in the early universe. Thompson scattering can only lead to polarization when the incident radiation has a quadruple distribution about the scatterer. We now follow the notation of Kosowsky, (Kosowsky, 1999) in defining the total Thomson scattering cross section. It is defined as the radiated intensity per unit solid angle divided by the incoming intensity per unit area.

εεπ

σσˆˆ

8

3 •′=Ω

T

d

d

Equation 11. Total Thomson scattering cross-section, defined as the radiated intensity per unit solid angle divided by the incoming intensity per unit area. σσσσT is the total Thomson cross section, εεεε’ and εεεε are the unit vectors perpendicular to the electric fields, and perpendicular to the propagation of the incoming and outgoing fields.

Figure 5. Diagrammatical representation of Thompson scattering. A low energy photon field with no net polarization is incident upon an electron from the left. (blue lines) The electric fields cause the electron to vibrate in all directions ⊥⊥⊥⊥ to the incoming photon field. An observer looking at the process from a 90°°°° angle will only see the electron radiate in one dimension since the other is along their plane of sight. If we then add another incident field of a higher energy from the top. (red lines) the observer would then detect a net polarization in the scattered photons. Diagram taken from (Hu, 1997).

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Following Kosowsky, we will attempt to derive how only an incoming quadrupole distribution can lead to a net polarization.

Consider a nearly monochromatic, unpolarized plane wave of intensity I’ and cross sectional area σB scattered into the Z direction by a single electron.

I ≡ <ax2> + < ay

2> Q ≡ <ax

2> - < ay2>

U ≡ <2axay Cos[θx - θy] V ≡ <2axay Sin[θx - θy]

It is easiest to break down the resulting scattered radiation into its x, and y components. We define both an incoming and outgoing coordinate system. The incoming system is the primed system, the outgoing system will be the unprimed system. In both the incoming and outgoing coordinate systems the fields will travel in the z direction so the x, and y axis will be perpendicular to the radiation fields. For the outgoing, scattered radiation we define:

( ) ( ) normalizedd

daa

d

daaaaI

yyxxyx Ω′+

Ω′→+≡ σσ 2222

222I

IIQI

IQI

Iyxyx

′=′=′−=+=

Z

Y X

ε’

ε

θ

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For now lets assume the incoming field, I’ is a single photon. Later we will integrate all the incoming radiation, from all directions upon the scattering electrons. Now we apply Eqn, 11. to both the Ix and Iy outgoing (scattered) components.

( ) ( )[ ] θπσσ

πσσ 222

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3ˆˆˆˆ8

3CosIjjIjiII

B

Tyx

B

Ty ′=•′′+•′′=

We note that V=0 means Thompson scattering never produces circularly polarized radiation. In our particular choice of coordinates we have also found U=0, but

caution needs to be applied because Q and U can easily rotate into one another depending on the orientations of coordinate systems involved, etc. Now we wish to intergrate over the entire incoming field. It is important to remember that when rotating Q or U into another reference frame a correction factor must be applied in the rotation. The I stokes field needs no such rotation.

Q’ = Q Cos(2φ) + U Sin(2φ) These are used when switching U’ = -Q Sin(2φ) + U Cos(2φ) to another coordinate system.

( ) ( )[ ] IijIiiIIB

T

yx

B

T

x′=•′′+•′′=

πσσ

πσσ

163ˆˆˆˆ

83 22

( )θπσσ 21

163

CosIIIIB

T

yx+′=+=

θπσσ 2

16

3SinIIIQ

B

Tyx ′=−=

0==VU

( ) ( ) Ω′+= ∫ dICosIB

T φθθπσσ

,116

3 2

( ) Ω′= ∫ dICosSinQB

T φθφθπσσ

,)2()(16

3 2

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To perform this integration we will expand the incoming field in terms of spherical harmonics.

Figure 6. This is a small table detailing the structure of spherical harmonics as well as generation rules. This was taken from the web site: (Nave, 2003) which in turn had taken the information from (Krane, 1987).

To be complete the associated Legendre polynomials equations are as follows:

( ) ( )xPdx

dxxP lm

mmm

l221)( −=

Where the Pl(x)’s are known as the Legendre polynomials. We can also represent the Legendre polynomials easily using the Rodrigues formula:

( ) ( )l

l

l

ll xdx

d

lxP 1

!2

1 2 −=

( ) ( )φθφθ ,,lm

lmlm

YaI ∑=′

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Now theoretically we have an infinite number of integrations to make since l can run from 0 to ∞ and m can run from –l to l. (both integers) However, there exists a well know relationship that we may apply.

( ) ( ) ( )∫ ∫ =π π

δδφθθφθφθ2

0 0 ''

'*' sin,, llmm

m

lm

l ddYY Where δ is a kronecker delta function. Applying these limits we find only the quadripole terms result in a non-zero solution:

+=

2000 53

4

3

8

16

3aaI

B

Tππ

πσσ

[ ]22

Re152

43

aQB

Tπ

πσσ=

[ ]22

Im152

43

aUB

Tπ

πσσ−=

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Foreground Contamination

Normally in scientific experiments we are worried about background noise

sources that may obscure, confuse, or limit the data. Study of the Cosmic Microwave

Background also has its share of noise to deal with. However, since the CMB is the

furthest known signal away, all forms of noise are really in the foreground, hence

cosmologists have adopted the term foreground contaminations. For COMPASS, we

are interested especially in polarized foregrounds. Possible contaminants include the

Earth’s atmosphere, synchrotron radiation, free-free radiation, dust emission, and

point sources.

Clouds can be major absorbers and emitters at microwave frequencies. To

really observe the CMB in a ground based experiment it must be done in nearly clear

weather. It is possible to observe during light, overcast conditions as long as the

cloud cover is fairly uniform, but these are far from ideal conditions. Cloud edges

can create polarization effects due to scattering.

In clear skies the greatest contribution to polarization is Zeeman splitting of

oxygen lines within the earths magnetic field. It has been shown that this effect leads

to less then 10-8 fractional polarizations. (Keating, 2000) This results in negligible

contributions at the COMPASS observing frequencies. There is also the possibility

of a Faraday rotation of incoming polarized signals due to the Earth’s magnetic field.

This results in less then a 0.01° rotation at frequencies above 25 GHz, (Keating,

1998) and thus is negligible for the most CMB observations.

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Of the major polarized foregrounds synchrotron is most likely to be dominant

in the Ka radio band. (26-36 GHz) (Cortiglioni, 1995) Synchrotron radiation is

caused by charged, relativistic particles traveling through a magnetic field.

Synchrotron, like most foregrounds is concentrated along the galactic plane. At high

galactic latitudes synchrotron radiation seems to follow a power law distribution. α

is the spectral index, and ν is the frequency.

αν∝antT

Synchrotron radiation is naturally strongly polarized. It can be up to 75%

polarized and a relationship has been found relating the total polarization percentage

to its spectral index. (Cortiglioni, 1995)

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33

++=Π

αα

Equation 12. Relationship between the total polarized percentage and spectral index for synchrotron radiation. (Cortiglioni, 1995)

Free-free emission, is also known as Bremsstrahlung emission, which in German

means braking radiation. High energy electrons passing protons are forced to slow

down, or “brake”, this deceleration of charged particles releases photons.

Bremsstrahlung, like synchrotron also follows a power law, T ∝ ν-α, with α = 2.15 ±

0.02 is large portions of the sky. (Tegmark, 2000) Free-free emission creation is an

unpolarized process, but often occurs in regions where Thompson scattering may

induce up to 10% polarization. (Keating, 2000) (Davies, 1999)

There seems to be two main sources of dust emission, thermal emission and

spinning dust emission. COBE DIRBE and IRAS data support the thermal model for

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the dust emission. The theory states that most of the dust lies at 20 K. (Kogut, 1996)

The spectrum is shown as thermal dust in fig. 5.

In 1995, excess emission was discovered at 14.5 and 32 GHz that was

inconsistent with synchrotron radiation and highly correlated with the 14.5 GHz

IRAS far-infrared data. (Leitch, 1997) Draine & Lazarian have proposed an emission

mechanism where thermal fluctuations of individual dust grains lead to magnetic

dipole emission, (Draine, 1999) and electric dipole emission (Draine2, 1998) The

excess emission discovered by Leitch et. al. (Leitch, 1997) can be explained by the

Draine & Lazarian models if the interstellar dust holds more then 5% of the available

iron. As further support for the Draine & Lazarian model (Draine2, 1998),

Finkbeiner. et. al. had discovered what appeared to be dust emission with a rising

spectrum that strongly matched spinning dust model predictions. Specifically,

evidence of spinning dust emission at 5, 8, and 10 GHz. was explored. They found

two very promising detections in two particularly dusty regions known as LPH

201.663+1.643, and L 1622.

In particular, the brightest Finkbeiner source, LPH was predicted to peak in the Ka

band, and COMPASS should have had a good chance to confirm its spectral

dependence along with the Finkbeiner data. During the second observing season both

LPH and L 1622 were scanned with the COMPASS telescope. Neither dust region

was detected by COMPASS, and sadly, mechanical pointing problems would not let

us confidently place limits on the detection either because we can not confirm we

properly scanned the regions.

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The contamination of COMPASS data due to point sources was still an unknown

quantity. The closest current limits on point sources had been set by the NVSS 1.4

GHz sky survey. NVSS stands for the NRAO VLA sky survey. (NVSS, 1998) The

NVSS sky survey was completed in 1998. The survey covers the entire sky north of

declination -40°, or ~10.3 steradians of the sky. The survey included flux density and

10 100 1000Frequency (GHz)

0.01

0.10

1.00

10.00

100.00B

righ

tne

ss T

em

pe

ratu

re (µ K

) Synchrotron

ThermalDust

CMB E-POL

Brem.

DW

CMB B-POLSpinningDust

Ka

Figure 7. Estimated Spectra of Polarized Microwave Foregrounds. The synchrotron spectrum is normalized to the rms brightness temperature of synchrotron at 19 GHz (de Oliveira-Costa, 1999) and assumes 30% polarization. The Bremsstrahlung spectrum is normalized to 30 µµµµK at 10 GHz. (Davies, 1999) and assumes 10% polarization. The spinning dust emission proposed by Draine & Lazarian (Draine2, 1998) is shifted by 2/3 to lower frequencies as prescribed by (de Oliveira-Costa, 1999) and assumes 3% polarization. The thermal dust spectrum assumes 5% polarization (Prunet, 1999), a dust temperature of 18 K, an emissivity index of 1.8 (Kogut, 1996) and uses 3 µµµµK/MJy/sr to scale typical degree scale rms values of ( 0.5 MJy/sr) at 100 microns to 90 GHz. The CMB E-polarization is assumed to be 0.1 of the E-polarization spectrum. Three frequency bands (Ka, W, D) are shown above the spectra. This plot has been taken from Chris O’Dell’s thesis. (O’Dell, 2000)

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both Stokes Q and U information. The NVSS 1.4 GHz survey has catalogued close to

two million radio sources down to a flux level of 2.5 mJy/beam. (NVSS, 1998) Other

surveys, although far les complete in terms of sky coverage, did add some

information on specific sources up to ~15 GHz. Combining data from the NVSS and

the Green Bank 4.85 GHz survey (Gregory, ref.) gives us some information on the

spectral dependence of many of the brightest sources. For a good review see Tucci

et. al. (Tucci, 2003)

We enlisted the service of the Effelsberg 100m radio telescope to scan the

same region of the sky as COMPASS in a search for potential Polarized point

sources. Dr. Wolfgang Reich of the Max Planck Institute of Radio Astronomy, Bonn,

took the scans over several nights between May 5, 2001 and August 8, 2002.

Unfortunately, the data was taken, but there was little help available to analyze the

data. It was decided that this would be a good project for me to undertake, and it

coordinated well with the COMPASS project.

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COMPASS Overview

The COMPASS telescope (Cosmic Microwave Polarization At Small Scales) is a

dedicated Polarimeter, built to put limits upon the cosmic microwave Polarization

signal and possible foregrounds. The telescope operates in the Ka band. (26-36 GHz)

COMPASS is located in Pine Bluff Wisconsin. Pine Bluff is a small community

about 20 minutes west of the state capitol, Madison. COMPASS was placed at the

University of Wisconsin’s off campus Pine Bluff Observatory.

COMPASS was the next generation of the POLAR (Polarization Of Large

Angular Regions) experiment that was also located at the Pine Bluff Observatory.

POLAR was a large scale (7° beam) instrument. It rotated about its own zenith axis,

and simply looked straight up. The Pine Bluff Observatory lies at a latitude of 43° 4'

41.88'' N., and a longitude of 89° 51' 54'' W. The latitude gives POLAR (~36) pixels

upon the sky. (O'Dell, 2002) There are several differences between the two

telescopes. Firstly, we took the POLAR 7° beam and added optics shrinking the

beam size to nearly 24 arc minutes. We also mounted the experiment on an azimuth-

elevation rotation base allowing the flexibility of pointing. COMPASS’s new

observing strategy was to create variously sized caps about the north celestial pole by

scanning back and forth in azimuth across the pole. A new building was created at

the observatory specifically for COMPASS. A unique rolling building design was

implemented to shield COMPASS from the elements and allow it to remain fixed and

aligned at all times. And finally we improved nearly all of the telescope subsystems

from cryogenics to the electrical systems.

25

COMPASS has taken data for two observing seasons. A typical observing season

for COMPASS was late fall through late spring. The first season’s data allowed us to

put interesting upper limits on various Polarized foregrounds in the NCP region, as

well as an upper limit on the CMB Polarization. (Farese, 2003) The Second season

unfortunately ran into several problems. Windy weather during the second season

badly damaged the telescopes motion systems, as well as ruined our ability to read

out our azimuthal position.

We noticed during the first season we were having wind loading problems on the

telescopes Azimuth base. Smooth metal drive rollers had a tendency to slip in under

windy conditions. As an improvement for the second observing season we

introduced a direct gear drive system. The new drive system ended up working

perfectly, however the telescope azimuth table itself ended up breaking early in the

season due to this excess torque. The table broke in a way that we could no longer

read the telescopes true position out with our azimuth encoders, and ultimately ruined

our second season of data.

Dr. Phil Farese, my fellow graduate student collaborator on the COMPASS

project, has analyzed the first season of data. (Farese, 2003) The second season's

analysis was to be the data for my thesis. Despite the wind loading problems that

ruined the second season of data, I was able to analyze related data from the

Effelsberg 100m radio telescope near Bonn Germany. We commissioned the

Effelsberg telescope to scan the north celestial POLAR region with its 25” beam to

look for potential point sources in the same sky positions that COMPASS had

covered and at the same frequencies. Point sources are a possible foreground for any

26

CMB experiment, and knowledge of their magnitude and distribution are crucial for

and CMB analysis.

COMPASS Front End I will now describe the COMPASS telescope in some detail from the front-end

optics to the data acquisition and telescope drive systems. The COMPASS telescope

is an on-axis Cassegrain Telescope. COMPASS’s primary mirror is a 2.6m concave

aluminum mirror donated to the COMPASS collaboration by fellow collaborator, Dr.

Giorgio Dall’Oglio at the University of Roma III. The secondary mirror of the

COMPASS telescope is a 26 cm convex aluminum mirror designed and created at the

University of California, Santa Barbara. The secondary mirror had been mounted on

a specially made expanded polystyrene (Styrofoam) cone support structure. We felt

the Styrofoam cone was a necessary technology in order to lessen sidelobe effects

which plague typical aluminum strut mounted mirrors common on radio telescopes.

Overall the Styrofoam cone seemed a grand success to the experiment. It did

however, poses some problems of its own. The first problem of the cone was that it

increased our system temperature by ~1.6 K, but it induced no noticeable scattering

or Polarization offsets. Another problem the cone presented was the dew that

collected upon it. On average we would loose several hours of data each day due to

the excess loading of the dew until it would evaporate away. In order to lesson this

harmful effect each morning the cone was manually cleaned, and if needed, the

telescope was positioned to sit facing the sun in order to speed the drying process.

27

Precautions were taken to waterproof the foam cone. A sealant was sprayed upon the

cone surfaces to prevent retention of water.

The next optical element in the chain would be the polypropylene window on the

COMPASS Dewar. COMPASS’s window consists of a 20-mil polypropylene

window of ~6 inches in diameter. The plastic window was backed by a microwave-

transparent Gore-tex window for structural support. The window marks the border

between the cryogenic inside of the dewar and the ~300 K outside temperatures,

needles to say we needed to take measures to avoid frost condensing upon the

window. In order to prevent water vapor from condensing upon the window an extra

microwave transparent layer of Volara (Reilly, 1999) was added above the window

with a slightly less the air-tight seal. Volara is a fine-cell crosslinked polyethylene

foam, waterproof and virtually transparent to microwaves. Dry nitrogen from the boil

off of a liquid nitrogen dewar was blown into this region in an attempt to slightly over

pressure the space keeping water vapor out. A power resistor was lowered into the

boiling dewar and an electric current was applied in order to increase the boil off rate.

In additionally the nitrogen blow off was heated. In order to warm the blow off it was

passed via a rubber tube into a metal sheath containing the heating element of a hair

dryer. And finally the metal ring mount of the polypropylene window itself was

wrapped with heater tape and kept warm.

Behind the dewar’s window lies the next optical element of the COMPASS

telescope, the Teflon microwave lens and the microwave feed horn. The COMPASS

telescope is the second stage of the POLAR microwave telescope. POLAR had a 7°

beam upon the sky. The POLAR beam was defined by its feed horn, a near exact

28

copy of the COBE (Cosmic Microwave Background Explorer satellite mission) feed

horn. COMPASS actually also used the same 7° feed horn and in order to integrate it

with the cassegrain system a lens was required. The Teflon lens was also designed at

the University of California at Santa Barbara. It is a convex lens machined with anti-

refractive gratings to prevent standing waves between the horn and the lens. In the

Ka band Teflon has a refractive index, n of 1.429. The lens was slightly offset from

the microwave horn to keep it thermally isolated. The Horn itself sits upon our inner

cold plate at (~20K). There was concern that although the lens is mostly transparent

to microwaves it could absorb infra-red radiation and provide a great heat load on our

cold plate itself. Instead a brace was made to hold the lens slightly off the horn and

heat sunk to our outer, (70K) cryogenic stage.

The COMPASS horn was designed by Dr. Joshua Gundersen, based off of the

COBE horn design. (Cobehorn, 1979) The horn is a conical, corrugated feedhorn with

a circular waveguide output. Then a circular to square transition is introduced and

then we have our Orthomode Transducer (OMT) (OMT, 2003) that separates the

power into its two linear Polarization components. The Orthomode Transducer is a

critical part of the Polarimeter as it alone separates the separate Polarization

components.

29

On each output arm of the Orthomode transducer we have a ~22dB cryogenic isolator

(Isolator, ref). The isolators help prevent cross talk between each signal chain. After

the isolators we then have our main amplifiers. COMPASS uses 26-36 GHz

cryogenic HEMT (High Electron Mobility) amplifiers. The amplifiers were

borrowed from Dr. John Carlstrom of the University of Chicago, and are also some of

the same amplifiers used on the DASI instrument. The HEMTs themselves were built

by NRAO. During the first season of data taking we used HEMTs with NRAO serial

numbers A31 and A32. During the second season we used HEMTs A24 and A27.

Figure 8. COMPASS window, lens and dewar. The light purple is the Volara window. Next sits the polypropylene window in black. The corrugated, Teflon lens is shown in blue. The top of the horn is shown in purple. Red represents the Dewar’s outer shell as well the 70K and 20K heat shields. The window extension is shown in gold and allows more room for the Teflon lens.

30

The HEMTs boost the signal by a factor of (~25dB) and retransmit the signal through

waveguide out of the dewar into our back-end optics.

The Back End

The back end optics of the COMPASS telescope consist of a full correlation

POLARimeter and total power sensitive diode detectors. The back end optics reside

in a RF shielded aluminum box we call the radiometer box or Radbox. Due to

mechanical constraints the Radbox was forced to sit along side of the COMPASS

dewar, as opposed to being in a linear position below it. (It was originally designed

to sit linearly below the dewar in the POLAR experiment.) This forced a careful

examination of our waveguide plumbing between the two entities. Waveguide bends,

both E and H plane, can cause some dispersion to the transmitted signals and

therefore are avoided if at all possible. Perhaps more importantly in our case was the

desire to treat each signal chain identically. We sought to have a similar number of E

plane and H plane bends in each of the two waveguide paths to make them as similar

as possible. In the end we were forced to introduce two additional E plane bends and

two additional H plane bends in each of the two waveguide paths in addition to one

90° twist along each path. In addition flexibility was needed to allow the radiometer

box to slide up and back parallel to the dewar (7 inches). Depending on what

Polarization Stokes parameter we wished to view upon the sky, Q, U, -Q, etc.

mechanical constraints forced us to be able to slide the radiometer box up and back

between two positions for clearance. This was simply solved by adding or removing

two,7 inch, straight pieces of waveguide.

31

Inside the radiometer box are another pair of 22 dB isolators (Isolators, ref) and

then the wave guide pathways are converted into semi-flexible coaxial cables. (Storm,

2003) Next the signals are again amplified approximately 20dB by a set of room

temperature amplifiers. (Amplifiers, 2003) The signals are then down converted to

2-12 GHz. The down conversion was achieved by use of a 38 GHz local oscillator

and a pair of IF mixers. The oscillator signal is split by use of a magic tee. One

branch of the tee’s output has an adjustable phase shifter used for phase matching.

The second branch of the tee has an electronically switched phase adjuster that

switches 0° to 180° at 1 kHz. (967 Hz) This electronic phase shift is later used with a

lock-in amplifier to lock into the true signal.

The now IF signals are amplified one more time via commercial IF amplifiers and

then each of the two arms is split. One half of the split goes directly to a diode

detector, these DC voltages will eventually become our total power channels TP0 and

TP1. The second half of the split signals are multiplexed into three sub-bands: J1 (2-

6 GHz), J2 (6-9 GHz), and J3 (9-12 GHz). Finally these three sub-bands are sent into

correlators (double balanced mixers) (Correlators, 2003) Because of our electronic

180° phase shift introduced earlier, the output of the correlators will be a square wave

modulated at 1 KHz. There will be a DC offset to the correlator output proportional

to the input power into the two polarized states. The correlator and total power diode

outputs are both voltage outputs. From here on we will treat the signals

electronically.

After the total power diode detector and the correlators comes yet another stage of

signal amplification. All 5 data channels, (J1, J2, J3, Tp0, Tp1) enter our pre-

32

amplifier. The COMPASS pre-amplifier circuit is actually the 3rd generation of

amplifier starting back during the POLAR experiment. We found that strong

measures were necessary in order to keep as much noise as possible from entering our

pre-amplifier. The final form of the COMPASS pre-amplifier was contained in its

own aluminum box within the radiometer box itself. The amplifier has SMA cables

as both the inputs and outputs. The correlator outputs themselves are already SMA

cable so it was natural for SMA inputs to our pre-amplifier. The coaxial inputs also

helped to reduce any inductive noise pick up that normal wires could receive.

One drawback to using the SMA cables however was that the outer conductor was

not electrically shielded. The outer conductor is a bare metal shield. We found that

contact between SMA cables or to the other metallic microwave components could

produce excess noise in the signal chains. (Most likely small grounding loop

problems.) To alleviate this problem we simply wrapped the SMA cables in black

electrical tape. This simple fix seemed to solve a great deal of our electrical pick up

problems.

In a further attempt to lesson ground loop problems we also decided to make the

amplifier use differential inputs. To accomplish the differential inputs, the first

component in the amplifier is an AD620 instrumentation amplifier. In the two total

power line chains the next component is an OP 27 operational amplifier. The

correlator chains first have a simple resistor/capacitor high pass filter to kill a dc

component and then the OP 27. The AD620’s gains were individually set on each of

the five signal chains by resistor values. The OP 27’s gains were also set by resistor

values, however one of two resistors could be chosen via the use of an electronic

33

switch circuit, DG201. In this way one of two gains could be chosen, our high and

low gain. This was useful because often times calibration sources were orders of

magnitude brighter then the sky itself and without a separate gain setting could rail

the system.

Channel First Stage Gain Second Stage

Low Gain Second Stage High Gain

TP0 19.4 1.0 94.6 Tp1 19.4 1.0 94.7 J1 38.0 1.0 5.8 J2 38.0 1.0 5.8 J3 38.0 1.0 5.8

Table 1. Pre-amplifier gain stages.

After the second gain stage, the OP 27, the total power channels then entered a 20

Hz low pass elliptical filter, a D74L4L. The correlator channels were also given the

flexibility to enter a 2-stage, four-pole Butterworth filter. However, during our

normal operations we decided to bypass this part of the circuitry, and this stage was

actually shorted.

The entire pre-amplifier was built upon integrated circuit chip sockets. This

proved helpful in the early troubleshooting stage because components could easily be

remove/replaced. In addition, gain resistors could easily be changed or modified

easily without having to re-solder any components.

In the beginning of the observing season we were experiencing several electrical

ground-loop issues. As an attempt to break a possible ground path the front and the

rear of our pre-amplifier are actually referenced from different grounds. Since the

AD620 is a differential input chip no current is allowed to flow past it through the

input leads. The output of the AD620 however has a separate ground reference pin,

and we chose to use a separate ground at this point. The back half of the pre-

34

amplifier and our entire lock-in amplifier up to our data acquisition system was held

at a separate ground then the rest of the telescope. So the pre-amplifier circuit

actually used two separate DC power supplies, one for the front and one for the rear

half of the circuit. This ground separation trick works as long as the two individual

grounds do not float to far away from one another.

Figure 9. A Circuit diagram of a total power chain within the pre-amplifier.

35

Figure 10. A circuit diagram of one of the correlator channel paths through the pre-amplifier.

Ultimately, a 10Ω resistor was used to connect “lock-in ground” (back half of

the pre-amplifier) to the rest of the system through the lock-in amplifier. We choose

to use a star grounding system centered on the actual telescope frame itself. The

radiometer box components were all case grounded, and thus directly grounded to the

center of our star ground, except one component, the 180° phase-shifter. The 180°

phase shifter was isolated from the rest of the case-grounded microwave components

using capton tape. This was necessary because the phase shifter was fed a square

wave signal, and this same signal was also sent to the lock-in amplifier. Since the

lock-in was separated on its own “ground island” the phase shifter needed to remain

on the island as well.

The lock-in amplifier was also located in the radiometer box in a connected but

separate compartment. The 5 signal channels out of our pre-amplifier were directly

fed into the lock-in amplifier. The total power signals actually passed directly

through and were not modified by the lock-in until the very end where we had

36

installed line drivers. On a separate board, outside the radiometer box, a square wave

sine and cosine signal were created. The square wave generator circuit was also held

to the same ground as our lock-in amplifier. The sine signal was sent to the 180°

phase shifter and both the sine and cosine signals were sent to the lock-in board. For

each correlator channel we then attempted to lock into its in-phase and out-of-phase

signal. So now we had 8 main data channels coming out of the lock-in amplifier,

Tp0, Tp1, J1i, J2i, J3i, J1o, J2o, J3o. (In phase and out of phase correlators) Next the

6 correlator channels went through a 20 Hz elliptical filter chip similar to the ones the

total power channels entered in the pre-amplifier. Finally we installed balanced line

drivers for each of the 8 signal channels before they are passed on to our data

acquisition system.

37

Figure 11. COMPASS optical, and back-end electronics diagram. Diagram created by Chris O'dell (O’Dell, 2000).

During the second season we installed one more processing step in our total power

channels between the lock-in amplifier and the data acquisition system. From the

lock-in we once again split the total power channels, one ran straight to the data

acquisition as previously, the second ran into a high pass filter. We call these data

channels TP0_HP, TP1_HP. We also took the difference between the two total

power channels and we both AC and DC coupled this difference. These channels are

named TPQ_DC, and TPQ_AC respectively. All four of these channels are an

38

attempt to get more stable data from our total power channels. The total power

channels suffer greatly from 1/f noise due to sky drifts, clouds, long-term electronic

drifts, etc.

All of the data and housekeeping channels were recorded via a custom-built data

acquisition system created in Santa Barbara. All signal inputs to the data acquisition

system were coaxial BNC inputs. All of the data channels were recorded

differentially, through differential input amplifiers. Other channels including the

telescope position encoders and the tilt meters were also recorded differentially. This

was another attempt to further shield us from potential ground loops. Most of the

other channels we recorded, including mostly housekeeping thermometers, were

recorded single-endedly, meaning they all shared a common ground. The custom-

built data acquisition system was operated via a Toshiba Satellite laptop running

Windows 2000. Both the data acquisition and telescope motion was controlled using

Labview, a software package created by National Instruments. (National Instruments,

2003) For the second season we then had 13 channels, Tp0, Tp1, J1i, J2i, J3i, J1o,

J2o, J3o, Tp0_HP, Tp1_HP, TpQ_DC, TpQ_AC, and our azimuth encoder that we

recorded at 90 Hz. The rest of the channels were sampled a factor of 18 slower (5

Hz), simply because we did not need the other channels so highly sampled, and to

save disk space. The data was recorded to the laptop itself which rested directly upon

the telescope at all times, and was also written to a secondary desk top computer for

back-up purposes. Every 15 minutes a new file was created. We chose 15 minute

long files for the convenience of size and the ease of working with them.

39

Housekeeping and Thermometry

The COMPASS telescope had several thermometers placed around its subsystems

for monitoring purposes. Firstly, there were three thermometers within the dewar

itself. One was placed directly upon one of the HEMT amplifiers, one upon the 20K

cold plate, and one upon the top of our 70K shield very near the Teflon lens in order

to get a handle on its temperature. Inside the dewar we chose to use silicon diodes

created by Lakeshore Cryogenics Incorporated, serial number DT-470. We

positioned 8 thermometers around the back of the primary mirror. As the temperature

of the primary mirror changed during the diurnal cycle and through the season this

could have affected the total loading upon the telescope. We felt it was important to

be able to monitor the various sections of the mirror independently. Uneven solar

heating might possibly be able to set up dipole and quadripole temperature gradients

along the mirror possibly mimicking a polarization signal. Finally we placed one

thermometer on each of 4 quadrants that made up our inner ground screens. Again,

uneven solar heating was a possibility we sought to monitor lest it lead to mock

signals. The external mirror and ground shield thermometers were all National

Instruments LM235 diodes.

Telescope Base and Drive systems

The COMPASS telescope was given an azimuth-elevation pointing system. A

small azimuth rotation table, used in previous UC Santa Barbara South Pole

experiments, was taken and the frame rebuilt in Santa Barbara. During the first

season the azimuth table drive system consisted of 4 evenly spaced, frustum shaped

smooth aluminum rollers that supported the rotation table itself on a large anodized

40

aluminum cone. One of these rollers was attached to an elliptical gear reduction drive

and then to an electric stepper motor. With this system COMPASS could rotate in

either direction, with potentially 360° of motion. The roller to cone size ratio gave a

factor of 6 in mechanical advantage. The elliptical drive granted us a factor of 72 in

mechanical advantage. The stepper motor we were using gave us up to 200 N-m of

holding torque. A central shaft extended below the rotation stage to the underside of

the table. We attached a rotation encoder directly to this shaft in order to find the

position the telescope was pointing at all times. This system was employed during

the entire first season of data taking.

One large drawback of this drive was slippage of the smooth rollers on the smooth

cone during windy conditions. Fortunately, any time the telescope was blown off of

its proper azimuth we could get an accurate reading of its position due to the rotation

encoder at the bottom of the telescope. During strong windy gusts the wind had the

ability to turn the telescope greatly, greatly enough that there was a danger of pulling

out wires and cables that hung off the rotation frame to the ground itself. To fix this

danger we simply inserted hard stops for the telescope using Unistrut. (Unistrut,

2003) This resulted in the telescope periodically being pinned to one side or the other

of the hard stops until the wind died down.

Before the second season of observations we decided to replace the smooth cone

drive system by a direct gear drive system through the central shaft of the telescope.

We ultimately decided to go with a low backlash worm gear drive system. We chose

to use a Series-W "zero backlash" 60:1 right-angle worm gear reducer from Textron.

(Wormgear, 2003) On front of the zero backlash worm reducer we had another

41

(12:1) gear reducer (Gearreducer, ref.) before going to a new powerful stepper motor.

(Superstepper, 2003) The new stepper motor was one of the highest holding torque

steppers we could find.

Our decision was based on the following criteria: For the first season we had

a stepper motor with 1592 oz. -in. of holding torque. Our elliptical gear drive gave us

a mechanical advantage of x60, and the tables roller to cone size ratio gave us an

additional advantage of x6. In order to have an educated guess at the wind loading

torque the telescope actually faced during windy conditions we used force gauges

with a lever arm distance of the telescope frame width during actual windy

conditions. Our best estimate ended up being 33600 oz.-in. This number was

multiplied by a factor of three for safety to 100800 oz.-in. So we found our system

had 1592 oz.-in. x 360 = 573120 oz.-in. of available torque, more then enough as long

as the cone-roller system would not have slid. We decided to look into a direct gear

drive system that could not slide.

When dealing with gears two issues are important, compliance and backlash.

Compliance is motion the system undertakes under stress due to the actual physical

deformation of its components (elastic deformations unless the system is pushed

beyond its elastic limit). Gear axles can bend, soft gear teeth can deform, etc.

Backlash is "slop" between gear teeth where one tooth can slightly move between two

of the opposing gears teeth. Unfortunately, in high performance gear systems one is

often sacrificed for the other. In our particular case we choose to minimize the

backlash. In order to gain the mechanical advantage we would need, we needed at

least two components involved. The backlash in each thus can affect the total

42

backlash. Most commercial gear reduction packages had difficulty meeting our

pointing requirements (A fraction of our 20' beam) with the torque loads required.

Textron did have a worm gear drive system with extremely low backlash and

a 60:1 mechanical advantage. Another important consideration that needed attention

was the efficiency of the gearing systems. Gear systems also have their own internal

friction, and they are usually less efficient at slower speeds. Our particular worm

reducer was only ~62% efficient at transferring torque under 9 r.p.m. 1592 oz.-in. x

60 X .62 = 59222 oz.-in. This still was not enough driving torque to suit our needs.

In actuality things were even worse then they appear since we sought to

actually scan under the windy conditions, as opposed to just holding position against

them. Another important consideration with stepper motors is that the moving torque

is usually only 40-70% of the holding torque.

To solve this problem we decided to do two things, add more gear reduction

and use a more powerful stepper motor. We decided to add a standard 12:1 gear

reducer between the worm gear and the stepper motor. Although this additional gear

reducer was not a low backlash set up, luckily any backlash it did have was reduced

by a factor of 60 due to the worm gear ahead of it. We chose to use a new, stronger

stepper motor made by Pacific Scientific. (Superstepper, 2003)

Serial number/Company K43/Pacific Scientific Holding Torque: 5700 oz.-in. Working Torque: (Under 9 r.p.m.)

~4000 oz.-in.

Rotor Inertia .2293 oz.-in.-s2

Power Requirements: 66-120 Volt, 5 Amp.

Table 2. New stepper motor specifications.

43

In actuality, the x12 gear reducer alone could have handled the telescope

loading but there was once last factor we tried to account for. In talking to stepper

motor engineers there seemed to be a rule of thumb that was followed when designing

stepper motor drive systems. The moment of inertial of the load was not supposed to

exceed the motor "Rotor inertia" by a factor of 10. Unfortunately, several different

engineers swore by the rule but none could derive it or really explain it to me. Taking

into account the various components of the telescope, such as the dewar, radbox,

mirror, etc., I estimated the telescope moment of inertia to be. ~169.044 Kg-m2. The

rule of thumb was to divide this by 9.8 m/s2 and compare it to 10 times the rotor

inertia times any mechanical advantage. For the new stepper motor we had: .2293

oz.-in.-s2 x 720 x 10 = 1651 oz.-in.-s2. For the load: 169.044 kg.-m2 / 9.8 m/s2 =

17.249 Kg-m-s2 = 23953.9 oz.-in.-s2. It is clear we were not even close to fulfilling

this rule of thumb. Obtaining more mechanical advantage was both cost and spatially

difficult. The new stepper motor was the largest we found in production at the time.

Ultimately, we simply decided to try it. We found that the system worked

beautifully. The azimuth turn around points did not seem to cause the drive system

any particular troubles. I believe two things ended up helping us, first, the telescope

always moved quite slowly, and secondly it is significantly harder to back-drive a

worm gear then to front-drive a worm gear. It can take hundreds of times the torque

to back-drive a worm gear even when accounting for its given mechanical advantage.

I believe this aspect softened the turning points and aided the motor in stopping the

momentum of the telescope.

44

Sadly, however, our attempts to push the telescope to running in stronger

winds eventually lead to its failure. The new worm gear drive system attached to the

lower end of the central rotation shaft of the azimuth table. The rotation readout

encoders were then on the bottom end of this shaft. Around mid February the upper

parts of the rotation shaft began loosening due to the constant wind loading

experienced in the Spring winds. Since our rotation encoder was attached below the

drive system, and the break occurred above the driving system we unfortunately

could no longer accurately read out the telescopes azimuthal position. We first

noticed this problem in March 1999, but did not totally understand the initial cause.

We simply re-pointed the telescope using the radio tower and Polaris. Gradually we

became aware of the pointing “looseness” and that it was slowly getting worse as the

season wore on.

We saw two options at the time. We could have taken the telescope apart and

attempted to re-tighten the upper central shaft of the table. Unfortunately this would

have taken a heroic effort. The entire telescope would have had to be disassembled

and brought back to campus. This process would have easily taken us a month worth

of time to remedy. In addition when the worm gear, low-backlash reducer was

attached to the telescope a key pin was tightly driven in to secure it tightly to the main

shaft. Removing this key would be no easy task since driving it in took two graduate

students, two hours and a sledgehammer to insert it. Once fixed the telescope would

need to be taken back out the observatory and reassembled, re-leveled, pointed, etc.

Our second option was to attempt to vigilantly check and correct the pointing as often

as possible and hope that we had several non-windy days left. We decided on the

45

second route at the time. In hindsight the second never actually worked for us, but we

really didn’t have time to implement the first either.

In an attempt to put better checks on our pointing we increased our pointings off of

Polaris, the radio tower, and TAU A. In addition at the very end of the season we

installed a sighting scope mounted to the elevation frame, yet fixed horizontally.

Using the sighting scope and marks we placed on buildings downrange of the

telescope we were able to see if the azimuth pointing was still on in real time without

having to break observations and point off of a celestial source. Also the sighting

scope could be used day or night and even if the sky was cloudy. For a pointing

scope we ended up choosing a simple deer rifle sighting scope. The scope easily had

enough magnification for our needs, was built to be weatherproof, shockproof, and

was relatively inexpensive.

The elevation mount was custom designed in Santa Barbara by Phil Farese. The

elevation mount consisted of a simple swivel with the primary mirror and the dewar

counterbalancing the torque of each other. A linear actuator (Actuator, ref) was

attached to this shaft by using an extending arm. With this arrangement we were able

to swing from ~70° in elevation down to ~ -2° degrees below the horizontal. The

linear actuator did a wonderful job of keeping the elevation locked in place due to a

worm gear reducing box. Our scan strategy involved scanning back and forth in

Azimuth while holding at a constant elevation, so the actuator worked very well.

Upon the end of the shaft another rotation encoder was attached to measure

telescopes elevation.

46

During the second season we did have some troubles with this system. During

the windier days of early February, the persistent wind loading upon the elevation

mount eventually stripped the drive gears within the actuator itself. This incident

unfortunately caused us many headaches. As the gears first began to strip the

motions resulting resembled electrical noise problems we were having in the

elevation control system earlier. Noise glitches in the driving circuitry of the

elevation stepper motor was causing us strange lurching behavior earlier in the season

and we spent some time pursuing this idea again. Eventually the stripped gears were

found and we repaired the actuator arm.

Calibration and Pointing

One of the largest differences between the COMPASS and POLAR experiments

was the ability to point the COMPASS telescope. Finding the true pointing of the

radio telescope could have been a difficult task. There are few sources we can

observe in the night sky that we can see in the real time, time stream, namely the Sun,

Moon, Venus, and Jupiter. (Arguably TAU A as well, Phil claimed he could see it in

real time but I could never confidently say the same) When finding a pointing

solution it is usually easiest to get accurate pointing for one region of the sky and the

farther you look from the region the more of an offset one finds. Since the

COMPASS main scanning strategy was to make a polar cap of the NCP, we

obviously wished to have the pointing offsets best known in this region.

Unfortunately, none of the above radio/visible sources came within (30°) of the NCP

so accurate pointing would have proven difficult. Luckily we had another tool in

47

which we could point the telescope. Approximately 1.2 km from the observation site

a commercial radio tower just peaked over the tree line and was visible to the

telescope, (~120° west of true north) We were able to rent space enough upon the

tower to place our own microwave transmitter. The transmitter was a simple

microwave oscillator (31 GHz) coupled to a wide angle ( 60°) microwave horn. The

oscillator was driven by a square wave chopping power supply running at 5.8 Hz.

The tower source was chopped simply so we would have an easier time picking out

its transmitted signal over that of the tree line, which was unfortunately close. The

tower made it possible four us to accurately align the radio telescope and a small

~100X power optical telescope that we mounted on the side of the primary mirror for

this exact purpose. Theoretically this would have been possible to do with Jupiter

since it was visible to us in both the optical and radio, however the tracking issues

would have made alignment much more difficult. We found ourselves able to co-

align the radio and the optical telescopes within <4'. With confidence in our

alignment we were then able to point off of any star we were able to see visibly in the

night sky. The final pointing offsets were then chosen by taking the pointing data

from the brightest 10 stars near the NCP. A program written by Jon Goldstein of

UCSB was used to calculate our pointing offsets, as well as information such as the

tilt of the telescopes azimuthal axis, angle of misalignment to true north, etc. For a

check of the pointing at various times throughout the season pointings were made of

the star Polaris who’s proximity to the NCP made it very convenient.

COMPASS First Season Observations

48

We started to take the first season of COMPASS data during March of 2001 and

stopped the observing season mid-May. Phil Farese was given the task of analyzing

the first season's data. Of the 1776 total potential hours, 409 were considered good-

weather hours. 72 hours were lost due to strong winds, and 28 hours were lost to

equipment failures. We were left with a total of 309 hours of data. Next, various

noise tests were applied to the data, de-spiking, white noise tests, 1/f tests and the ς

test. (Keating, 2001) After all the final noise cuts, we were left with 144, 123, and

164 good hours in the J1, J2 and J3 correlators respectively.

The first season of data was broken down into sub-seasons called BIGS, BOGS,

SIGS, and BIGS. These stood for (big/small) (inner/outer) ground screens. The

(big/small) referred to the scan size we chose. During different times of the season

we scanned back and forth in azimuth by both .8° and 1.6°. A large portion of the

first half of the season was taken with our outer ground screens in place. (Outer)

refers to the times in which we were using the outer ground screens, and (inner) at the

times we did not.

The outer ground screens were created from construction scaffolding frames. A

wooden frame was built upon the scaffolding and sheet metal pieces were bent to

cover the frame. The entire structure was quite large, nearly 20 ft. tall, and with a

foot-print of 20’x30’ feet on the ground. Luckily the outer ground screens were

designed to still fit within the rolling canvas building. The outer ground screens were

fixed to the ground and did not move with the telescope, as did the inner ground

screens. It was discovered later in the season that the outer ground screens were

creating a rather large offset within the data. The offset had linear, quadratic, and

49

higher order components and the decision was made to remove them. The entire

second season of data was taken without the outer ground screens at all. Zach Lewis,

a former undergraduate in the lab, created the design of the outer ground screens.

COMPASS First Season Analysis and Results A lion’s share of the first season analysis was undertaken by Phil Farese, and was

the bulk of his thesis work. The main analysis I contributed to the first year data was

determination of the beam size and mapping the telescope side-lobes. The

determination of our beam shape ended up being a fairly difficult task. Once the

second season observations were begun the analysis expanded into determination of

the second years beam as well. We had two main tools to probe the beam shape,

Figure 12. A side view of the COMPASS telescope showing the outer ground screens.

50

scans of TAU A and scans of the radio tower. Although we did scan other potential

sources like Jupiter, Venus, and CAS A the signal to noise of these scans made beam

determination rather difficult.

Analysis of the TAU A scans, both calibration and beam size determination, was

undertaken by Dr. Josh Gundersen, another COMPASS collaborator. For beam size

determination TAU A had some good points and some negative points. First, TAU A

gave us an opportunity to get beam sizes for all three of the correlators as well as the

total power channels. The biggest downside to TAU A scans were the low signal to

noise and tricky offsets that needed removal. It was found that two scans of TAU A

in the first season and two scans of TAU A during season two were of a quality to

attempt full-width extractions. Unfortunately, several second season TAU A scans

had to be discarded because of pointing errors. TAU A was not bright enough to see

real time in the data stream and we simply missed it often with second season

pointing issues. The COMPASS total power channels were less sensitive overall and

more susceptible to elevation dependant offsets. The low sensitivity made beam size

determinations with the total power channels near useless with TAU A. However,

after a great deal of work the correlator results converged into an answer.

51

Figure 13. Beam width determinations from First season TAU A scans. Note there is a great deal of scatter within the total power results and this data was ignored. These x and y FWHM values are measured along the azimuth and elevation axis and not necessarily the maximum and minimum values.

The second main tool for beam analysis was scanning of the radio tower. The

radio tower also had some positive and negative aspects. The radio tower had a much

greater signal to noise ratio and allowed us to push much deeper into the side-lobes,

and it could be pointed at, at any time of the day since it sat stationary and did not

rotate with the sky. The radio tower did, however, have some disadvantages as well.

52

It was a single frequency transmitter, and thus was detectable in only one of the three

correlators. In addition it’s location placed it right at the top of the tree line, making

side lobe determination more difficult, especially below the tower in elevation. Some

of the far sidelobe structure we found may very well be from tree scattered signal.

The radio tower sat 1895.3 meters away from the COMPASS telescope. It was

located at an azimuth position of 278.78°, with 0° straight north (a slightly different

value first season).

The source we mounted on the tower sat ~580 feet above the ground and it was

located at an elevation of 3.596° placing it right at the tree line. In order to weather-

proof the microwave transmitter we decided to encase it within a 6” diameter PVC

water pipe. Both ends of the tube were sealed with Zotefoam. (Zotefoam, 2003)

Zotefoam is cross-linked polyolefin foam that was nearly transparent to microwaves

yet water-tight. An AC power cable was strung the 580 foot length of the tower and

made accessible to us near the bottom. Thus to turn the tower off and on a drive to

the tower was necessary. Inside the PVC tube was an AC to DC power converter, a

DC power square-wave chopping circuit, a 100 mW Gunn microwave oscillator, a

large attenuator, and finally a 60° rectangular horn. In addition a simple temperature

control circuit was added to help remove temperature dependant effects with the

Gunn oscillator output power, and to ensure the system had an easier time turning on

in the dead of winter.

53

Figure 14. Tower mounted, microwave source COMPASS used for pointing and beam size analysis. This tube was mounted to a local radio tower with a simple bracket system. This

diagram has been borrowed from Phil Farese’s thesis.

The DC power to the oscillator was chopped at 5.8 Hz in a square-wave pattern.

This was done so that it would be easier to recognize the tower signal out further into

the side lobes, and this proved crucial. Ideally we would have had some sort of

separate signal line that ran from the chopping tower source directly to the telescope

in which we could use to lock directly into the chopping source. Considering the

distance between the tower source and the telescope this would have proven difficult,

not to mention the need to string a cable across a local farmers potato field. This

forced us to attempt locking into the signal indirectly, decoding the pattern from the

data rather then from knowing the chopping state A priori, and limited how far into

the side-lobes we could push. Luckily for us the chopping frequency of the DC

power supply was very stable. This allowed us to lock into the signal through the

time stream via software written in IDL. Knowing the incoming microwave power

from the transmitter chopped on and off allowed us to simply take the difference.

54

Differencing allowed us to ignore the vastly drifting background due to the 300 K tree

line down range between the telescope and the tower. Some cleaning of the

differenced data was needed, specifically an in phase square wave was multiplied by

the data effectively multiplying the tower off data by zero. Applying this technique

to the correlator channels was also possible and fruitful, however, since the

correlators could have both positive and negative signal (correlation and anti-

correlation) locking in was much harder.

Figure 15. This is a small example of the software lock-in procedure. The black represents the raw data. The red represents the differenced signal after a slight cleaning procedure. Note, the slight baseline drift in the original data has been removed.

The tower source power was set high enough to send the J2 correlator channel

to its positive rail (Only the J2 correlator since the tower source was monochromatic.

During the first season we had a different oscillator in the tower source with a

different frequency and only J3 detected signal instead.) near the center of the beam,

however, it was not strong enough to rail the TP0 and TP1 channels. This was a large

advantage since it gave us a beam mapping ability with a much higher dynamic

range. The only catch to this method was properly patching the two channels of data

55

together. This was done by visually matching the slopes of the two beam patterns.

The resulting beam pattern was compiled from the best second season tower scan.

Note the elevation is only mapped above -1° elevation. We could not physically map

lower due to the inner ground screens touching the ground.

Figure 16. The COMPASS composite beam map. (Second season) Red values are 4-42dB down from the positive peak value. Blue areas are 12-40 dB down from an “inverted” peak. White

areas are >41 dB down from either peak. Axis are in degrees from the main beam center.

Another important effect was also examined with the tower scans. The tower

distance was obviously not infinity and we needed to explore the possibility of a near

field distortion in observed beam size. The distance between the near and far field of

a telescope is defined by Eqn. 11. Z is the distance away from the telescope. D is the

diameter of the telescope and λ is the wavelength.

56

λ

22DZ >

Equation 13. The cut off distance between the near and far field of a telescope.

In COMPASS’s case D=160cm., and λ=.967 cm. This leads us to a far field cut off

at: 1.398^105 cm. The distance to the tower was 1.8953^105 cm so the tower was

within the far field of the telescope, but not well into the far field. A calculation of

the near field effect was necessary. The method of calculation of the beam width at

the tower distance was taken from Goldsmith, Quasioptical Systems. (Goldsmith,

2001)

λ=.967 cm. (31 GHz.) Z=1.8953^105 cm. Distance to the tower θo=Angle of beam at z=∞, center to edge, not the full angle. θ=Angle of beam at z=z, center to edge, not the full angle. ωo= beam waist at z=0. ω = beam waist at z=z.

( )( )2

oω

r

2e2

0,

−

==o

zrEπω

Equation 14. Goldsmith's definition of the electric field at the telescope.

If we assume a far field beam width of 18’: θo fwhm = 1.18 θo

'627.718.12

'18

=

=oθ

For the far field limit Goldsmith states:

57

= −

oo πω

λθ 1tan

Solving for ωo we get 138.256 cm. Now the general form of the beam width at an arbitrary distance, z, away from the telescope is given as:

( )

+= −

22

221 1tan

o

o z

z πωλωθ

Equation 15. Beam width at an arbitrary distance, z, from the telescope.

Solving we get θ = 8.0327’ θfwhm = 1.18 θ θfwhm = 9.4782’ Our resulting beam-width is actually 2 times this value: 18.957’

%04.5957.18

00.18957.18 =−

So we found that the beam size from the tower scan is actually 5.04% larger then the true beam width. Compiling the above numbers we find:

fwhm(max) (arcmin.)

fwhm(min) (arcmin.)

Rot. (Deg.)

fwhm(max) Corrected

fwhm(min) Corrected

1st. Season Tower 23.28 ± 2.25 20.60 ± 1.18 0° ± 1.0 22.11 ± 2.13 19.56 ± 1.12 2nd. Season Tower 21.57 ± .25 18.55 ± .20 45° ± .50 20.48 ± .24 17.62 ± .19 1st. Season TAU A 22.2 ± .70 21.5 ± .70 NA NA NA

Table 3. Beam width calculations from tower scans, as well as, TAU A scans in both first and second season. The rotation column refers to the position of the semi-major axis relative to the horizon. The TAU A data axis are not the major and minor axis of the beam pattern, but rather the values along the elevation and azimuth directions.

We found that for the first season data, the radio tower scans and the TAU A scans

were in agreement. It is important to point out the radio tower scans were fit allowing

the routine to fit the semi-major and semi-minor axis, while the TAU A results were

the values along the elevation and azimuth axis. Due to pointing issues, the second

58

season TAU A scans were not fully analyzed. The Rotation column refers to the

orientation of the semi-major axis to the horizon. It is interesting because between

the end of the first season and the start of the second season we decided to rotate the

dewar exactly 45° to switch from observing Stokes U polarization to Stokes Q

polarization. This 45° rotation was directly mirrored in the beam scans.

The POLAR experiment was originally calibrated by the use of a copper wire

grid oriented at a 45° to the optical axis. Two blackbody (Eccosorb CV-3) (Eccosorb,

2003) loads would then be placed, one beyond the grid and one along side, 90° out of

the optical axis.

One load is partially transmitted through the grid into the horn with a portion

reflected out of the beam. The other blackbody load is reflected into the beam, with a

portion of its power transmitted away. This process ends up creating a calculable

Composite View of POLAR WINDOW

POLAR adaptor plate

Upper Window Plate

Volera Plate

Dewar SurfaceLower Window Plate

Figure 17. The calibration method used in the POLAR experiment, and the early testing stages of COMPASS. Shown is the plastic frame that held a piece of polypropylene at 45º with respect to the horn axis. On the right, the 300 K piece of Eccosorb (Eccosorb, 2003) is shown, above the Eccosorb is shown submerged in a Styrofoam container filled with liquid nitrogen. The dewar face and horn are shown below.

59

polarized signal. A simple rotation of this known polarized source about the axis of

the beam was all that was necessary for a calibration of the polarization sensitivity.

For blackbody loads we would use room temperature Eccosorb, and Eccosorb dunked

within a liquid nitrogen Styrofoam container. (Eccosorb, ref.) This setup allowed us

two temperatures, room temperature and 77 K. We could also use the sky itself as

one “blackbody” On a clear day the sky in Madison Wisconsin was found to be

within a couple of degrees from 15° F. For more detail see (O'Dell, 2002).

For COMPASS naturally extending this proved to be difficult mainly due to our

foam cone secondary support. Once the telescope was focused we were unable to

open the secondary cone and thus could not have access to the mirror or window.

The POLAR calibration rig was designed to rotate upon the window itself. In the

early testing stages we did indeed calibrate COMPASS in the above-described

manner, during the season however, we solely had to calibrate off of celestial sources.

We attempted calibration off of Cassiopeia A and Taurus A. Additionally, to be

complete there is also Cygnus A, but it was certainly too weak to calibrate the

COMPASS telescope. Taurus A is probably better known as the Crab Nebula. Both

CAS A and TAU A are supernova remnants that tend to emit some Polarized

microwave radiation. We found CAS A to be to weak as a calibration source and

decided to solely calibrate off of TAU A observations throughout the season. In

addition to the measured intensity found by Johnston and Hobbs (Hobbs, 1969), a

further correction for the decay rate over time (Allers, 1985), and spectral index

(Baar, 1977) was applied to the TAU A calibration. Additional corrections were

60

added for atmospheric absorption, and the conversion from the Raleigh-Jeans to

thermodynamic temperature. For further details see (Farese, 2003).

Source RA Dec Intensity at 30 GHz (Polarized)

References

TAU A 05h 34m 32s 22º 00' 52" 23.5 Jy (Hobbs, 1969)*

CAS A 23h 23m 24s 58º 48' 54" 1.94 Jy (Mason, 1999) CYG A 19h 59m 29s 40º 44' 02" 1.1 Jy (Melhuish, 1999)

Table 4. The three potential polarized calibrators for the COMPASS telescope. Ultimately we only calibrated off of TAU A. *Additional correction factors applied, see text.

An excerpt of the final calibration information for COMPASS as taken from

(Farese, 2003):

Factors J3i J2i J1i Ant. Temperature (K) 1.25 ± 0.20 0.98 ± 0.16 0.79 ± 0.13

Signal (mV) 12.4 ± 0.37 5.15 ± 0.14 3.59 ± 0.16 Gain (K/V) 6.4 ± 1.1 5.01 ± 0.9 4.0 ± 1.6

Table 5. Calibration results for the first season data. Calibration was based soley on Tau A scans. This table is an excerpt from (Farese, 2003)

COMPASS Second Season Observations

The Pine Bluff observatory is situated at the top of a small bluff and therefore

is a fairly windy place. The months of February through March unfortunately are

some of the worst. One of the goals of the second season observation was to push

observations into some of the windier days to obtain more integration time. We

found that even though the new direct gear drive system itself had little trouble with

the wind, winds greater the 20 mph did shake the telescope with its sail-like inner

ground screens rather violently. A decision was made to abort observations if wind

61

conditions rose above ~20 mph. In hindsight observations should have been aborted

earlier.

For the next few months the telescope was in operation 24 hours a day, seven

days a week. Observations were paused, however, on days of precipitation,

particularly windy days, and times where maintenance was required. Unfortunately,

this cut out a considerable chunk of the observing season. On nights where weather

forecasts predicted a greater then ~10-15% chance of precipitation, for example,

operation was shut down. During daylight hours the telescope was near constantly

"baby sat" by either Zak Staniszewski or myself. Zak was also a former

undergraduate of the lab, and a vital part of the second season observational efforts.

Our first observing day in the second season began on Thursday, January 17.

During the remaining month of January we managed to log 73.25 hours of CMB data.

Additionally 59.05 hours of maintenance were recorded. By maintenance hours, I

mean hours where the data acquisition system recorded, but actual CMB data was not

being taken. This included things such as, repair, trouble-shooting problems, pointing

checks, beam maps of the tower, etc. The season is broken down in table #6.

Table 6. Hour break-down of the second observing season.

Month CMB Hours Maint. Hours

Total CMB Hours

Total Maint. Hours

January 73.25 59.05 73.25 59.05 February 159.5 39.86 232.75 98.91 March 227.5 23.75 460.25 122.66 April 33.25 59.02 493.5 181.68 May 19.5 17.9 513 199.58

62

On February 16 after a relatively gusty evening of observations we visually

noticed the telescope pointing to be off by .5 degrees in the azimuth. At the time we

thought it was a simple miss-entered telescope offset, as it was almost exactly .5

degrees off in azimuth. This was the first time we noticed major pointing problems

with the system. It was later found that the pointing slightly before this time was also

untrustworthy. The first two weeks in February had been unusually windy, and with

our new telescope drive system we were determined to push the limits on what winds

we could observe in.

It was discovered by some simple azimuth push tests that there was some new

backlash in the upper sections of the azimuth table. When a fairly large torque was

applied to the telescope frame, (close to what a strong wind gust would apply) we

noticed the backlash. Smaller applied torques did not seem to effect the positioning

however. We concluded that during early February the COMPASS telescope had

suffered sever wind damage. From February 14th on through the rest of the season

care was taken to run the telescope in the lowest winds possible. (<12 mph) The

wind also managed to wreak havoc with our elevation pointing system, but since our

scan strategy was not really dependant on elevation motion to any real extent the

damage done to the observing season was much less extreme.

Once the backlash in the azimuth table was found we had two options on

how to continue: first, we could take the telescope apart, fix problem, and reassemble

to continue the season, and second, we could try to continue the season as we were,

but only observing in low wind conditions. Unfortunately the problem was not with

the newly added drive system, it appeared to be up higher in the table itself. The

63

central shaft of the azimuth table was loosening. To gain access to this central shaft

we would have had to completely remove everything above the azimuth table

including the elevation mount, the dewar, mirror, and foam cone. Then to continue

observations the telescope we would have had to be re-assembled, re-focused, and re-

leveled, and re-pointed, a process that alone could have taken several weeks.

We decided to continue with the observations for the rest of the season

checking the status of the pointing as often as we were able. It was found that as the

season wore on the backlash continued to get worse, both the distance the table was

off position increased, and the amount of torque to misalign it decreased.

At the end of the season I then made an extensive search through the data for

all of the sources that the telescope scanned through the season. It was important to

try to determine exactly when our pointing errors began and to see how much of the

data was potentially salvageable. The criteria I sought were back-to-back pointing of

the same object, be it TAU A, the radio tower, Jupiter, etc. For objects such as

planets it was important that the planet sighting be in similar portions of the sky since

our global pointing solution was most accurate at the NCP and varied to different

degrees away from it. If an object were found to be in the same position, with

pointing offsets small compared to our beam size we decided the data in between

would be usable data. Our telescopes beam pattern ended up being roughly 24

arcminutes in diameter and so I looked for pointing position offsets no larger then 8

arcminutes. After all was said and done I found only 22 hours of our 513-hour

observing season that we could demonstrate had trustable pointing. In addition there

were 135 hours of data taken before the incident that should have been "innocent",

64

but its innocence could not be directly proven. We decided that this small amount of

data would not be significant enough to analyze for cosmological purposes and sadly

choose to abandon the second season observations.

During the observing season we scanned several other objects for calibration,

pointing, or troubleshooting. A breakdown by month is shown in Table #7.

Sightings of Polaris were actually made using our optical spotting scope.

They were done at various times throughout the year to confirm our pointing offsets

were correct. Sightings of TAU A were purely radio in nature since there is no

optical counterpart for the supernova remnant. TAU A served as our primary

calibrator. CAS A, another supernova remnant, was also a potential calibration

source, and was scanned a few times during the beginning of the season. Jupiter,

Saturn, and Mars could be seen both optically and in the radio, therefore they were

excellent pointing confirmation tools. The Tower, referred to our tower mounted

microwave transmitter. The tower was used for several reasons such as radio/optical

alignment, pointing, and it was also used early on to aid in focusing the secondary

mirror.

Month Polaris TAU A CAS A Jupiter Saturn Mars Tower Dust December 1 0 0 1 1 1 1 0 January 3 2 4 2 0 0 4 5 February 1 2 1 0 0 0 1 0 March 2 2 0 0 0 0 3 0 April 2 1 0 0 0 0 1 0 May 5 3 0 1 0 0 0 3

Table 7. These were the second season attempts to scan sources other then the NCP region.

65

The dust sources referred to in table 5 refer to the findings of Finkbeiner, et.

al. (Finkbeiner, 2001) The paper outlines a search of 10 dust regions using the Green

Bank 140 ft. telescope. Specifically, evidence of spinning dust emission at 5, 8, and

10 GHz. was explored. They found two very promising detections in two particularly

dusty regions known as LPH 201.663+1.643, and L 1622. Draine and Lazarian

theorized the "Spinning Dust" emission mechanism. (Lazarian, 2000) The spinning

dust theory predicts the strongest dust emission for the above sources to fall very

close to the COMPASS observing frequency. We sought to place limits, if not detect

the dust emission out-right. Scaling the Finkbeiner results we expected LPH to have

a temperature of ~3.5 mK. This was close to what we should have been able to see.

Ultimately, we did not detect either of these dust regions with the COMPASS

telescope. Even more regrettably, we were unable to even place upper limits to the

dust clouds brightness due to our pointing problems. It was very possible our scan

pattern did not even contain the dust regions.

Effelsberg Analysis

The contamination of COMPASS data due to point sources was still an unknown

quantity, especially point source contamination. The closest current limits on point

sources had been set by the NVSS 1.4 GHz sky survey. NVSS stands for the NRAO

VLA sky survey. (NVSS, 1998) The NVSS sky survey was completed in 1998. The

survey covers the entire sky north of declination -40°, or ~10.3 steradians of the sky.

The survey included flux density and both Stokes Q and U information. The NVSS

1.4 GHz survey has catalogued close to two million radio sources down to a flux level

of 2.5 mJy/beam. (NVSS, 1998) Other surveys, although far les complete in terms of

66

sky coverage, did add some information on specific sources up to ~15 GHz.

Combining data from the NVSS and the Green Bank 4.85 GHz survey (Gregory, ref.)

gives us some information on the spectral dependence of many of the brightest

sources. For a good review see Tucci et. al. (Tucci, 2003)

We enlisted the service of the Effelsberg 100m radio telescope to scan the same

region of the sky as COMPASS in a search for potential Polarized point sources. Dr.

Wolfgang Reich of the Max Planck Institute of Radio Astronomy, Bonn, took the

scans over several nights between May 5, 2001 and August 8, 2002. Unfortunately,

the data was taken, but there was little help available to analyze the data. It was

decided that this would be a good project for me to undertake, and it coordinated well

with the COMPASS project.

I traveled to Germany for two weeks, in order to learn about the Effelsberg data

and begin the analysis process. I was able to stay in guest housing at the Max Planck

Institute for Radio Astronomy in Bonn, as well as tour the Effelsberg telescope

facility itself. While in Germany I was greatly helped into the project by Dr.

Wolfgang and Dr. Patricia Reich. My time was spent learning about how the data

was taken, but mostly learning the analysis software, Ozmapax. Ozmapax was a

multi-purpose Fortran script created on sight at the Max Planck Institute for analyzing

the Effelsberg data. Ozmapax was only designed to run upon a Sun workstation, and

thus much of the analysis was thought to need be done at the Institute. At the end of

my two weeks stay I still had a great deal of the analysis process to complete.

Luckily, I found that I was able to run the program via telneting to the institute from

my home computer in the US.

67

Figure 6. Effelsberg 100m radio telescope near Bonn Germany

Figure 19. Effelsberg telescope support structure and elevation gear. Note the staircase winding up the structure for a scale reference.

68

Effelsberg Telescope and Observation

The North celestial POLAR region was observed at 32 GHz with the Effelsberg

100-m telescope on several nights between May 5, 2001 and August 8, 2002. Quasar

3C286 served as the primary calibrator. We believe the calibration to be accurate

within 10% of the true value. Details of the telescope performance are displayed in

table 1. (See Table 1) In this configuration, the telescope was designed to have a half

power beam width of 25". We estimate, however, slight pointing uncertainty and

small focal differences between individual horn fields reduced the angular resolution

to about 26".

Telescope Beam Width: 26”

Maximum Aperture efficiency: 23%

First Sidelobe maxima/minima: -12 dB/-17 dB

Instrumental Polarization: ≤ 1%

Center Frequency: 32 GHz

Bandwidth: 2 GHz

TB/S [K/Jy]: 1.8

MOD1: Intensity/Polarization 12/2.4 mJy/beam

MOD2: Intensity 4 mJy/beam

Table 8. Basic Observational parameters.

69

Main Calibration Source: Quasar 3C286

Quasar Flux: 2.1 Jy

Percent Polarization: 10%

Polarization Angle 33°

Table 9. Effelsberg Calibration information

The Effelsberg 100m radio telescope was equipped with its 32 GHz set of

receivers in the secondary focus of the telescope. Two separate modules, named

MOD1 and MOD2, allowed for sensitive Polarization and total power measurements.

MOD1 is sensitive to Polarization and, to a lesser degree, to total power signals.

MOD2 is insensitive to Polarization, but is better suited to detect total power signal.

(See Table 1) Both modules are arranged in two linear rows of three horns each. The

horn row orientations were linear and parallel to the ground. The feeds were thus

aligned along the azimuth direction with spacings of 2', 4.3', and 6.3' respectively.

The two rows we offset by 153" on the sky.

Figure 19. This is the horn arrangement for the Effelsberg 32 GHz system used.

The telescope scanning was done in azimuth while holding the elevation constant.

This strategy granted the advantage of constant atmospheric loading for each pass.

We broke the NCP cap into 54 sub regions, and observed all them over the course of

70

several months. This strategy was designed to give fairly even coverage time per

pixel, however, we are still slightly over-sampled nearer the NCP. The physical

scanning rate of the telescope was ~1°/min. We originally planned to do a 1.5°

diameter cap to compliment the COMPASS scan region. Due to improper pointing

corrections our scan region was slightly enlarged to a radius of ~1.25°.

Figure 20. The shows the area of coverage of the Effelsberg scans. The mean has already been removed. Negative areas are blue and positive areas are red. White areas are close to zero. There are 36 total contour levels from -12 dB to +12 dB.

Each horn produced two circularly Polarized signals. The two circularly Polarized

components of each feed were connected by waveguides into a magic-T. The signal

71

difference between two feeds was obtained by a correlation of the magic-T outputs.

The data channels were recorded at 8 ms sampling including the 6 feed horns as well

as the various hardware-differenced channels between horns. Each of the three horns

within a module looks through nearly the same column of air. By differencing the

horn outputs we are able to remove a great deal of atmospheric effects from the data.

We decided to analyze the MOD2 data first. If no sources were detected in total

power then analysis of the MOD1 Polarization data wouldn't likely detect signal

either since we don't expect sources to be almost completely Polarized. After careful

visual inspection and cleaning we applied the Emerson algorithm (Emerson, ref.)

upon these differenced data sets. The Emerson algorithm takes a set of horn-

differenced data and transforms it into the equivalent output of a single horn with

better noise properties. This technique works best if the radio source is smaller then

the distance between the horns. Since three horns have three possible spacings

between them, we had three difference channels per module. Application of the

above algorithm left us with a clean, noise reduced 6 arc second, pixelized "map" of

the sky. It is important to point out that for each azimuthal pass a linear fit was

removed. The azimuthal width of the sub-scans varied from roughly 20' to 51' across

the sky. Therefore our "map" no longer includes any large-scale information > 20'.

The data was then smoothed to a pixel resolution of 24" to be roughly the same

size as our beam upon the sky. Unfortunately we found that a power spectrum of the

24" data did not closely resemble a Gaussian distribution. A good deal of excess

noise was discovered at the tail ends of the distribution. It did however start to

become fairly gaussian when we smoothed the data up to 1' scales. From this point

72

we found 8 pixels that seemed to deviate from the gaussian distribution and thus had

the potential to be possible detections. Inspection of these regions however found

them to be noise glitches rather then actual detections.

In addition we searched for the 5 brightest NVSS 1.4 GHz detections within our

scan region. (See Table 10.) We found no evidence of any of the NVSS sources

within our data.

Name RA (hours) Dec. (degrees) Flux (mJy)

RN 03 ♣ 19.3867 89.48011 2060.1 8C 0029+892 ♥ 11.2102 89.4910 270.1

RN 84 ♣ 335.4623 89.1465 123.4 8C 2241+890 ♥ 334.3781 89.3166 80.3 8C 2152+888 ♥ 320.3999 89.0379 60.6

Table 10. Five brightest point sources detected within our scanning region (>88.75) by the NVSS 1.4 GHz survey. ♣♣♣♣ (Ryle, 1962) ♥♥♥♥(Hales, 1995)

Effelsberg Results We have detected no sources at 32 GHz with the Effelsberg telescope. The noise

floor that we reached had a standard deviation of 6.69 mJy/26" beam in total power

across the entire map. It is important to examine how the noise varies across the map

as well. Since the map was composed of several separate observations taken over

many months, and with slightly non-uniform coverage, it is informative to break the

region into smaller sections for comparison.

Region Standard Deviation mJy/26” beam

Full Cap Map 6.69 Declination > 89.75° 5.24

89.50° ≤ Dec. < 89.75° 5.73 89.25° ≤ Dec. < 89.50° 6.61 89.00° ≤ Dec. < 89.25° 8.17

0° ≤ RA < 45° 5.71

73

45° ≤ RA < 90° 6.46 90° ≤ RA < 135° 7.64 135° ≤ RA < 180° 8.27 180° ≤ RA < 225° 7.55 225° ≤ RA < 270° 6.00 270° ≤ RA < 315° 6.30 315° ≤ RA < 360° 6.96

Table 11. Noise scatter across various sections of the cap map. Note, all of these values have a ±±±± 10% calibration uncertainty.

It is curious that we did not detect the brightest source (RN 03), in our field,

detected by the NVSS 1.4 GHz survey. From this we are able to put a limit on the

sources spectral index, α.

α

=

off f

fFluxFlux

o

Equation 16. Definition of the Spectral index, αααα.

If the flux at a given frequency, f, is known and the spectral index of the source, α, is

also known then we can calculate the flux at another frequency, fo (See Equation #9)

If we then ask how our non-detection limits the spectral index of RN 03 we find α ≥

1.63 assuming that the source would need to be greater then 2α to be detectable.

(95% confidence limit.) As another sanity check we note that the WMAP point

source catalog also did not detect RN 03. The weakest source listed in the WMAP

catalog is .3 ± .1 Jy. (Bennett ref.)

It is useful to convert our flux limit to temperature units so we can see how our

results constrain point source contamination of the Cosmic Microwave Background.

We follow the steps outlined by Taylor, et. al.(Taylor, 2001) We start with the

74

Rayleigh Jeans approximation for the flux density of an unresolved source. (See Eqn.

#17)

2

2

λΩ

=Tk

S b

Equation 17. The Rayleigh Jeans approximation for the flux density of an unresolved source.

S is the flux density, kb is Boltzmann's constant, Ω is the beam solid angle, λ is the

observing wavelength and T is the resulting antenna temperature. Arranging for

temperature and applying the conversion factor between solid angle and multipole

moment (See Eqn. #18) we come up with (See Eqn. #19).

2

24

l

π≅Ω

Equation 18. The conversion factor between solid angle and multipole moment.

2

22

8 πλ

bk

SlT =

Equation 19. Temperature to flux relationship derived above.

If we enter our 1σ flux limit of 6.69 mJy/(26" beam) ± .67 mJy/(26" beam)

and calculate the ∆T point source contamination limits, we find: 12.85 mK ± 1.29

mK for Effelsberg and 4.20 µK ± .422 µK in total power for the COMPASS

angular scales.

COMPASS was designed to measure Polarization and not total power signal.

Although COMPASS did not detect any Polarization it did set an upper limit of E-

mode Polarized anisotropies of 33.5 µK (95\% confidence limit) in the l-range

200-600. (Farese, 2003) In both steep and flat/inverted spectrum sources

75

compiled by Mesa, et. al. (Mesa, 2002) the mean Polarization degree Π,

Π=(U2+Q2)1/2/I was not found to be greater then 1.84 %. Thus if this relationship

holds into the 30 GHz regime we expect little contamination to the COMPASS

data due to point sources and the Effelsberg results concur.

Pine Bluff Observatory

The Pine Bluff Observatory is UW Madison’s own off campus observatory.

The observatory was built in 1958 and is located about 15 miles west of the main

campus. It sits at E. Longitude: -89 28 and a Latitude: 43 04. The facilities include a

36-inch optical reflector, a 16-inch optical reflector, and a dedicated hydrogen

interferometer dedicated to mapping hydrogen in the upper atmosphere. (Reference

here?) In addition the site now contains a new facility that was designed and built for

the COMPASS telescope.

The observatory itself is set in a cleared area on the top of a small bluff

allowing a more commanding view of its surroundings. Unfortunately, this also made

the site fairly windy at times. The roads were well kept around the observatory and in

the two winters we operated in I only failed to make it up the hill in a car once. (An

interesting and scary experience)

It took a bit of searching to come up with the final design for the COMPASS

building. Because of the foam cone and various electrical components the telescope

needed to be sheltered during times of foul weather. Rain, snow, and strong winds

could have harmed the telescope. We also wished the telescope to have full access to

the sky so in addition to the NCP CMB scans we could also scan various point

76

sources and access to our calibration/alignment source mounted near the western

horizon. Precise and repeatable pointing made any scenarios of rolling the telescope

in and out of a building difficult to implement within our budget requirements.

We decided to go with the novel idea of moving the building itself, rather then

the telescope. This allowed us to cover the telescope easily and quickly in times of

bad weather without having to sacrifice the telescope alignment at all. We ended up

using a rolling canvas building created by a company called Bigtop Manufacturing.

(Bigtop, ref) The building consisted of an approximately 30 x 60 foot concrete pad,

the rail mounted canvas shelter, and a separate control room.

Since the building itself moved outlets were built within the concrete slab

itself and extended up from the floor. The receptacles were mounted with in the path

of the front and back doors of the building with the doors open would clear. Iron rails

were mounted to the pad and extended off of the southern side of the pad. Off the

pad, the rails were supported by concrete pillars. The rails themselves extended ~80

feet beyond the pad in order to get the building well away from the telescope during

observations. Since the canvas building was supported by a metal aluminum frame

caution was taken to try to keep it back as far as possible during the observations.

The canvas cover of the building itself was mounted to a large aluminum

skeleton. The UW Physical Plant Engineering department then designed how to

attach the wheels in which the frame could roll upon the rails. For quite a time the

building needed to be opened buy truck winches that were temporarily mounted to the

track until a permanent opening system could be implemented. To close the building

the same winches were used with a set of pulleys to reverse the direction. This

77

temporary system caused many headaches throughout the first season. The building

needed to be pulled straight back otherwise it would bind against the rails. It proved

very difficult to get the two winches to pull at the same speed and it cost us a great

many pulleys and steel cable. During the second season a centrally powered chain

drive mechanism was added and allowed us to open and close the building buy a

touch of a button. Until all the bugs were routed out of the system even the new drive

system broke a few drive chains on one side or the other. The canvas building that

housed the telescope was never really heated, and if open was the equivalent of being

totally outside in a field. The often proved troublesome when repairs were needed

during the cold winter months. Luckily two kerosene heaters were available to roll in

when repairs were needed and managed to warm the building to tolerable levels.

Another problem with the white canvas material was that it was not totally opaque to

light. If repairs were needed during the night and we turned on lights within the

canvas building it would glow like a Chinese lantern. Since we were positioned right

next to an optical observatory this obviously caused some additional problems.

It was, however, necessary to have a heated room where we could work and

place several of the data computers. A company named ???????? (Seabox, ref.)

designs remote heated buildings from sea cargo containers. One of these “rooms”

was set next ro the concrete pad and became our operations center, the Sea Box. The

Sea Box had both heat and air conditioning and made a suitable working

environment.

78

Figure 21. The COMPASS rolling building set back upon its tracks.

79

Appendix A: Vacuum System Design

During the year of 1998 I sent a good deal of time designing and building a 4He

pumping system for our lab and a neighboring lab. Our two labs often deal with

scientific dewars that need be cooled to cryogenic temperatures, < 1 K. To

accomplish this we often use a two-cryogen system, liquid nitrogen and liquid

helium. The liquid nitrogen, which is about 77 K, acts as a heat shield and surrounds

the liquid helium stage that sits at 4 K. Often from the helium stage we attach an

ADR (adiabatic demagnetization refrigerator) which can cool the most sensitive

devices to the mK level. Often the liquid helium stages are pumped on, reducing the

vapor pressure and decreasing the boiling point of the helium. This has the effect of

lowering the helium bath temperature below the normal 4 K.

Liquid helium vapor pumping is a much different operation then normal lab

vacuum applications that simply seek low pressures within various vessels. The two

main differences are, the fact we are pumping helium and not air, and we are often

pumping under relatively high pressure, high flow situations. A third but different

difference is that when pumping cryogenic fluids/vapors ice plugs and Teconis

oscillations (Teconis, 1992) are potential hazards. Ice plugs are formed when water

vapor in the surrounding air is frozen within a pipe or choke point leading to potential

explosive situations. Teconis oscillations are a super-fluid phenomenon in which

violent fluid oscillations can build upon themselves in a cryogenically pumped

system.

In our case we sought to connect two labs on the sixth floor of the physics

building to two large vacuum pumps in the basement. We sought to place the pumps

80

far away for several reasons: The farther downstream the pumps were the less micro-

phonics they would introduce into the lab dewars, the pumps were loud and obtrusive,

and the pumps simply took up a good deal of space. This required us to run piping

straight up for 6 stories and ended up being a large job. To accomplish the task a

climbing harness was acquired and I was chosen to climb up the maintenance shaft in

order to guide and fasten the pipes. We chose to use household pvc pipes for the job

due to cost, availability, and the ability to do the job.

The remaining parts of this appendix are excerpts from a presentation presented

about vacuum system design, and basic vacuum pump and gauge information.

81

Vacuum System Design Considerations

Slade Klawikowski Nov. 9 1998

Outline:

I. Definitions

A. Throughput B. Conductance C. Mean free D. Knudsen Number (flow regimes)

1. What do we use in the lab? II. Electrical Circuit Analogy III. Leaks, Outgassing, other bad guys

A. Ultimate pressure calculation IV. Equations in Molecular Flow Regime V. Types and Ranges of Vacuum Pumps VI. Types and ranges of vacuum gauges

82

Throughput: The amount of gas in pressure-volume units flowing per unit time across some specified cross section. (Temperature must be defined)

-Normally symbolized by: Q Units = (Pressure*Volume) / time = Energy Also: QD = Throughput due to outgassing.

QL = Throughput due to leaks

Conductance: Inverse of the flow Impedance

-Normally symbolized by time

Pumping Speed: The volumetric rate at which a gas is transported across a plane.

- Symbol: S Units: = Volume / time -Note* Same units as conductance, but not quite the same thing!!

Cp

=−

Q

p1 2

p

QS =

83

Mean Free Path:

The average distance a particle travels between successive collisions with other particles:

In reality there is extra factor due to motion of all the molecules:

Collisions of Numbertravelled Distance

Path Free Mean ==λ

)V

N( d

1 =

)/(t) V(

t V =

olume

2elocity2

elocity

ππ olumeVNd ∆∆

λπ

= 1

2 d (N / V)2

P/(RT)= (N/V) T N R = PV

R = d

V ∆t

84

So….

T in Kelvin P in Torr d in cm (Air: d = 3.76*10^-8 cm) (Helium: d = 2.2*10^-8 cm)

Knudsen Number: Kn The Knudsen number is a dimensionless number that determines what regime your vacuum system is in.

λ = mean free path D = characteristic length of vacuum component, (Tube diameter, etc.)

λ = 2.330 *10 T

d-20

2P

KnD

= λ

85

3 Flow Regimes for gasses:

Regime Gas State

Gas Density

Knudsen #

Viscous

Laminar/ Turbulent

High

Kn < .01

Knudsen

Transition

Medium

1 ≥ Κn ≥ .01

Molecular

Tenuous

Low

Kn > 1

1. Viscous Regime: I. Most difficult to deal with II. We need to worry about this in Helium pumping III. Turbulence/ Chaos makes calculation difficult IV. Need Knowledge of pressures 2. Molecular: V. Most understood regime VI. Less pressure dependent VII. We fall in this regime with Turbo pumps etc. 3. Knudsen Regime: VIII. This is just the middle ground between the two extremes. IX. Also difficult to calculate values

86

Typical Lab Values?

Gas Type

Temp. (K)

Pressure (Torr)

Pipe/hose Dia. (in.)

Knudsen # Regime

Air

300

.0001

1.5

12.99 Molecular

Helium

300

.01

1.5

0.379 Knudsen

Air

300

.0001

4.0

4.87 Molecular

Helium

300

.1

6.0

.0095 Viscous

Helium

300

.1

3.0

.019 Knudsen

Electrical / Vacuum Analog: One way to think about vacuum calculations: V= I * R 1/R = I / V C = Q / (p1-p2) Where: V is analogous to the pressure difference

87

I is analogous to the current 1/C is analogous to the resistance

88

For items in series: For items in parallel:

321Total

321Total

321Total

321Total

C C C C C1

C1

C1

C1

R1

R1

R1

R1

R R R R

++=++=

++=++=

C7

Vacuum Chamber

Vacuum Pump

C2

C1

C3

C5

Sn

Sp

1 1 1

S S Cn p Total

= +

: Never let Sn < 80% Sp If it is in your design, get bigger pipes.

C6 C8

C4

89

Unfortunately, Real Life Has Leaks: Leaks, out-gassing etc. provide positive loads on vacuum systems. -They raise the ultimate pressure limit. -To a lesser degree they slow down pump down time. QBad = QD + QE + QL+ QPer Where: QD = Load due to outgassing QE= Load due to evaporation

QL = Load due to Leaks QPer = Load due to permeation

Out-gassing: QD = qD A qD= temp. and material dependent constant A=Surface Area

Evaporation: QE = 3.639 ( T / M)1/2 (pE – p) A M= grams/mole of specific gas pE = vapor pressure of gas

Leaks:

90

QL = ? for most systems… = Massively huge values for 70 ft. PVC runs…

Permeation:

Where: KPer = material dependent constant ∆p= pressure gradient across material (Atmosphere to inside) L= thickness of wall.

Ultimate Pressure possible:

Calculation of Conductances:

QA

Perp=

K

LPer ∆

nUltimate S

P BadQ=

91

Molecular Region: Conductance of a thin aperture:

Conductance of a long pipe (uniform cross section): (long if L > 20 d)

Conductance of short pipes:

P1 P2

2cm in A

grams/mole M

Kelvinin T

) sliters( A 64.3 ==

M

TCma

molegramsM

cmlengthLM

TCmp

/

)(

(cm)diameter inner d

)sliters(

Ld

81.33

==

==

92

Note* Pr is an experimentally determined number. Conductance of Elbows: Conductance of a diaphragm:

L

d

Rule of Thumb:

Treat elbows as straight pipes using an effective length: Leff ≤ (L + 1.33 d)

( )grams/mole M

(K) .

(cm)area A

PA 64.3

2

r

===

= tempTsliters

M

TCmsp

!!!radius! r *Note

8

31

1 =

+≈

r

LPr

93

Ao A

2

2

o

cm s

cm is A )s

liters( )

AA

-(1

A 6.11

iAC

o

md =

94

Conductance’s in the Viscous Region: Complications: Choked Flow: When the flow of a gas in a viscous region reaches the speed of sound. -Usually only need to worry about this in transient behavior and positive pressure systems. -All the equations below have choked counter parts. Conduction of a thin aperture:

Where γ = (Cp / Cv) -Note* This ugly boy is pressure dependent unlike its molecular flow cousin.

γγ

γ

γγ

1

1

2

1

1

2

1

2 1 p

p-1

p

p

1

2

)1(

1

−

−

−=

M

TR

p

pApC Inc

95

Conduction of a long pipe (circular cross section): (L > 20 d)

X. Note* This equation is assuming Room temperature. Conduction for short pipes (Viscous flow region):

CLS = Ugly!!!!! ???? Knudsen Regime:

(Torr) pres. p

(cm) length. L

(cm) Dia.d

2

184 214

+

=

pp

L

dCL

Rule of Thumb: When dealing with short pipes in the viscous regime, treat the pipe as a pipe (as normal) in series with its aperture: CLS = CL + CInc

96

-This is the transition region between the other two extremes. -Most books gloss over it, being beyond the scope of their pages. -Many suggest just using the equations of the closest regime to your system as a rough estimate. -As you can guess it gets ugly as well. Conductance for a long pipe (circular cross section):

( )

+

+

+

= −

η

ηη d

T

M0.1811

d

T

M0.1471

81.3d

10*269.3 23

p

p

M

Tp

L

dC KL

grams/mole M

(Torr) pipe along press. average p

(poise) in viscosity

(cm) in , =

=η

Ld

97

Types of Vacuum Pumps: Mechanical, Piston Pumps: In One Stroke the volume of gas VA is expanded to VA + VB, So our pressure is reduced:

P= initial pressure P’= pressure after one cycle. The minimum obtainable pressure is limited by the dead space below the piston (Our tube connecting the two chambers)

A B

( )BA

A

BV

V

P

P

+=

'

98

Rotary-Vane Pumps:

99

Sliding Vane Pumps:

The two large Helium pumps we have in the basement are of this type.

100

Theoretical Limits of mechanical pumps: -Dead space ruining volume compression. (Volume Suckers) -External pressure against exhaust valve.

Pumping speed curves (Ex. Rotary Vane):

101

Root Pumps:

These pumps are designed to be only loosely-sealed. They can maintain a good vacuum by spinning at very high velocities. (1000-4000+ rpm.)

102

Root Pump pumping Curve:

Root Pumps are limited at the high-pressure end

due to the short mean free path of gas particles flowing in both directions. Also drag prevents them from reach higher operating speeds. Root Pumps need to be operated with a fore pump for best use.

They are limited by the loose sealing at the low pressures, which allow back streaming.

103

Molecular Drag Pumps: (Turbo Pumps) Gas molecules randomly float into the pump where they are physically scattered preferentially due to angled rotating blades. These pumps can spin Very rapidly, (can be faster than 90,000 rpm!) This is why after you turn these off you should not move them right away to let them spin down. Example Turbo Pump Speed Curve

104

Diffusion Pumps: A diffusion pump uses an oil shower to trap gas molecules and pull them out of the system. -Mean Free path of the gas is greater then the throat the gas interacts with the oil through diffusion.

The oil is boiled by a heater at the bottom and forced up through umbrella shaped baffles. These oil “walls” keep forcing the gas molecules to the outport.

105

Typical Diffusion Pump Speed

Area #1: Low pressure limited by the vapor pressure of the oil used. Cooled baffles allow pressures ~10-10 Torr or greater. Area #2: Consistent pumping speed over many decades. Area#3: Mass transfer limit of the pump has been reached. Area #4: Diffusion pump does nothing. (Only roughing pump is effective) -Critical point determines the size of rough pump needed.

106

Other types of vacuum pumps: -Ion pumps: Gas molecules can be ionized by a high temperature filament and removed from the system by a charged cathode. -Vapor Ejector Pumps: These are similar to diffusion pumps in using an oil spray to collect the residual gas. They differ in that the mean free path of the gas is smaller then the throat so the interaction is not diffusion but viscous drag. -Sorption Pumps: Cryogenic temperature pumps that absorb gas molecules into porous crystalline materials. -Cryo-pumps: Cryogenic temperature “bottles” that trap gas by either liquefying it or solidifying it to a surface, thus removed from the rest of the system.

107

Pump Type Pressure

Range Pumping

Speed Comments

Mechanical Piston

High Atm. - ~102 Torr

Low <200 cfm?

Sliding-Vane High Atm. - ~10-3 Torr

Low 5-200 cfm

(Large pumps in basement)

Root Pumps Medium 102 - ~10-4 Torr

Medium 50-500 cfm

Turbo Molecular

Low 10-3 – 10-10 Torr

High 15-2000 cfm

Let spin down. Beware oil damage.

Oil Diffusion Pumps

Low 10-3 – 10-11 Torr

High at least 7,839 cfm. (Varian)

Beware oil mess.

Cryogenic Pumps

Low 10-3 – <10-11 Torr

Low ?

must refill LN trap

Ion Pumps Low 10-3 - <10-11 Torr

Medium (up to ~600 cfm.) (Torr)

Can be delicate, like light bulbs.

108

Vacuum Measuring Devices: Bourdon Gauge: Simple gauge, based on a small tube of oval cross section bent into a coil. One end is sealed and the other is set to the vacuum chamber. As the pressure decreases, the tube flattens and this registers on a calibrated needle. -Depends on atmospheric pressure (which can vary ~40 Torr) -Independent of the gas species being measured. Diaphragm Gauge: measure pressure differences by measuring the deflection of a diaphragm. -Physical indentation may be magnified mechanically, optically or electrically. -Measurement is absolute and does not depend on atmospheric pressure. -Independent of gas species being measured. -Balzer makes baritrons with range:

Atm. 10-5 Torr. -Our lab baritrons can display:

Atm. 10-2 Torr.

109

Thermal Conductivity Gauges: A fixed electrical energy is sent through a filament. Its temperature depends on the thermal conductivity of the gas around it and thus the pressure of the surrounding gas. The temperature may be measured in two ways: -Directly through a thermocouple. -By measuring the resistance of the filament through an electrical bridge circuit. (Like high-pressure sensor on our orange pump.) (called Pirani gauges) -Orange pump gauges Range: Atm. 10-4 Torr -Convectron Vacuum gauges: Similar to the Pirani gauge at low temp, but extends its range by using gravitational convection to get more accurate readings. -Must be held horizontally!! -Cart Pump Gauges. -Range: Atm. 1 mTorr. Ionization Gauges: Hot Cathode Ionization Gauges: Hot electrons created in a wire filament ionize the surrounding gas. These ions then are collected on the anode as a positive current proportional to the pressure present. (Note different gasses have

110

different ionization potentials.) Has the draw back of filaments burning out quickly (like a light bulb) Range: (10-3 - < 10-8) Cold Cathode Ionization Gauges (Penning): Emits electrons from a relatively cold cathode and using magnetic fields bends the flight path of the electron into a helical path. This increased flight-time of the electrons greatly increases their ionization potential. Range: 10-2 – 10-9 Torr. (Like the low pressure gauge on the orange pump.) -Nice thing about ionization gauges is that they can act like pumps themselves. (speed = a few liters/sec)

111

(From Balzers Catalog)

112

Appendix Bibliography:

Handbook of Vacuum Engineering, Steinherz, H. A. Reinhold Publishing Corp. Copyright: 1963 Scientific Foundations of Vacuum Technique, Dushman, Saul John Wiley & Sons Copyright: 1949 A Users Guide to Vacuum Technology, O’Hanlon, John. John Wiley & Sons. Copyright: 1980 Vacuum Engineering calculations, Formulas, and Solved Exercises, Berman, Armand. Academic Press Inc. Copyright: 1992 Vacuum Physics and Techniques, Delchar, T. A. Chapman & Hall Copyright: 1993 “Vacuum Pumps – Diffusion”, World Wide Web Page. http://www.capovani.com/cat/VacuumPumps--Diffusion.html Web Master: CBI@CAPOVANI.COM June 6. 1999. “Torr International Inc.”, World Wide Web Page. http://www.torr.com/ Web Master: torr.intl@juno.com June 6, 1999.

113

Acronym/Abbreviation Glossary -ADR (Adiabatic Demagnetization Refrigerator) A cryogenic refrigerator able to cool small loads using a strong magnetic field and a paramagnetic salt crystal. The magnetic moments of the salt is aligned via the magnetic field, and while the field is removed heat energy from the load is removed to redistribute the spin states to a higher entropy level.

-BNC (Bayonet Neill Concelman) Invented by and named after Amphenol Engineer Carl Concelman and Bell Labs Engineer Paul Neill and was developed in the late 1940's. A coaxial connector with a bayonet coupling mechanism. This connector is available in 50 Ohm and 75 Ohm versions. This connector has a frequency range of DC (0 HZ) through 4 GHz (50 Ohm version) and DC (0 HZ) through 1 GHz (75 Ohm version).

-CMB Cosmic Microwave Background -COBE Comic Microwave Background Explorer, a satellite experiment launched in (1986) to observe the CMB. -COMPASS (Cosmic Microwave Polarization At Small angular Scales) -Correlators Double balanced mixers made by the Miteq Corporation. -DASI (Degree Angular Scale Interferometer) A compact microwave interferometer optimized to detect CMB anisotropy at multipoles l ≅ 140 – 900. The telescope has operated at the Amundsen-Scott South Pole research station since 2000 January. The telescope was retrofit as a POLARimeter during the 2000 – 2001 austral summer, and throughout the 2001 and 2002 austral winters has made observations of the CMB with sensitivity to all four Stokes parameters. -HEMT (High Electron Mobility Transistors) The main cryogenic amplifiers of the COMPASS experiment. -IDL (Interactive Data Language) A software language that is used frequently in Astronomical data analysis due to its strengths in plotting and displaying. -IF (Intermediate Frequency) In COMPASS’s case this is 2-12 GHz. -Last Scattering Surface, See Recombination. -NRAO (National Radio Astronomy Organization?) (Location?) -NVSS. (NRAO VLA sky survey) A large sky survey made at 1.4 GHz buy the VLA radio telescope in 1998. Before the Effelsberg Polarized point source search the NVSS

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probably held the best limits on Polarized point sources in the NCP region. (NVSS, 1998) -OMT (Orthomode Transducer) A waveguide device that accepts either circular or square waveguide input. There are two output ports that separate the incoming signal into the x- and y- components of the electric field. -POLAR. (Polarization of Large Angular Regions) A large scale Polarization experiment with roots at the University of Wisconsin at Madison. It was the thesis project of Dr. Brian Keating and Dr. Chris O’Dell both graduates of Wisconsin. COMPASS is the next generation of the POLAR experiment. -PVC sewer pipe. A common house hold plastic plumbing pipe that gains its name from the type of plastic: Polyvinyl Chloride. -Recombination. The time in the early universe when photons dropped from thermal equilibrium and atoms were first allowed to form. Note it is a misnomer, since this the first time atoms were able to form to our knowledge. A related term is the Last Scattering Surface. This refers to the last scattering process the CMB photons had undertaken before dropping out of equilibrium and free streaming away. -Radbox (Radiometer Box). The aluminum box on the COMPASS telescope that contains the back end optical systems. -RF Radio Frequency pertaining to the shielding of electronics from external radio waves that could introduce noise via inductive and capacitive pick up.

-SMA Cables: (Subminiature Version A) A subminiature coaxial connector with screw type coupling mechanism. This connector has a 50 Ohm Impedance. This connector has a frequency range of DC (0 HZ) through 18 GHz.

-VLA (Very Large Array radio telescope) Large radio telescope array located in New Mexico.

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