Lecture 3 By Tom Wilson. Summary of Lecture 1 Noise in a Receiver time on source Receiver itself,...

Lecture 3Lecture 3

By Tom Wilson

Summary of Lecture 1Summary of Lecture 1

Noise in a ReceiverNoise in a Receiver

timetime

on sourceon source

TT

R M SSY S

Receiver itself,Receiver itself,

atmosphere,atmosphere,

ground ground

and sourceand source

Analying bandwidth (for lines, need 3 resolution Analying bandwidth (for lines, need 3 resolution

elements on the line above the ½ power point)elements on the line above the ½ power point)

Temperatures from thermal hot and cold Temperatures from thermal hot and cold load measurements using the receiver. load measurements using the receiver.

Hot-cold load measurementsHot-cold load measurements

Absorber at a given temperature

Input to receiver

(to determine receiver noise contribution)

OK for heterodyne receivers, but OK for heterodyne receivers, but not for Bolometers for Bolometers

Current Receiver Noise TemperaturesCurrent Receiver Noise Temperatures

Tmin=h/kfor coherentreceivers

TTSYSSYS=T=TRXRX e e Atmospheric optical depthAtmospheric optical depth

ReceiversReceivers

Heterodyne for spectral linesHeterodyne for spectral lines High velocity resolutionHigh velocity resolution flexibility, but not multi-pixel receivers in the mm/sub-mmflexibility, but not multi-pixel receivers in the mm/sub-mm

Bolometers for continuumBolometers for continuum Multi-pixel camerasMulti-pixel cameras

k

NEPATAT SYS

RMS2

NoiseNoise

Equivalent Equivalent

powerpower(about (about 1)1)

Types of Receivers

Fractional R

esolution

Lecture 3 page 7Lecture 3 page 7

BOLOMETERS VS COHERENT RECEIVERS

JCMT: 15 m sub mm dish,A = 0.5 at = 0.87 mm, = 345 GHz= 345 GHz

With SCUBA, can detect a source with 0.16 Jy in With SCUBA, can detect a source with 0.16 Jy in 11 secondsecond. So RMS is ¼ . So RMS is ¼ of this peak value or of this peak value or SS0.04 Jy in 1 sec.0.04 Jy in 1 sec.

Compare to a coherent receiver:Compare to a coherent receiver:

TTSYSSYS = 50 K, = 50 K, = 2 GHz, integration time= 2 GHz, integration time= 1 sec

In antenna temperature.In antenna temperature.

From Lecture 2: From Lecture 2:

For JCMT, For JCMT,

Or Or

So comparable for 1 beam, but SCUBA has 37 beams & MAMBO has 117 So comparable for 1 beam, but SCUBA has 37 beams & MAMBO has 117 beams. beams.

TK

KR M S

5 0

2 1 01 2 1 0

9

3.

ST

DA

a m 3 5 2 0 2

S Ta

A

1 6

S JyR M S 4 1 0 2

(arc sec)=(arc sec)=kkmm)mm)/D(m)/D(m)

of order 1.2 for single dishesof order 1.2 for single dishes

SS=3520 T=3520 TAA /( /(AA D D22))

ST

DP A S k T A AA

ae A e a g

3 5 2 01

22

Rayleigh-Jeans

ST

cm

TM B M B

cm

2 6 5 2 6 50

2

20

2

2.( ' )

( ).

( ' )

Or

S

T

m m

M B

0 0 7 4 0

2

2.( ' ' )

( )

Gaussian beams:

Summary of Lecture 2Summary of Lecture 2

(Show that these(Show that these

are consistent)are consistent)

In JyIn Jy

22

2

222

22

Beams

ssMB

sBeamobs

ssobsMB

TT

TT

True source size True source size

and temperatureand temperature

apparent source size apparent source size

and temperatureand temperature

Can make a relation for flux density similar to that for Can make a relation for flux density similar to that for

Main Beam Brightness temperature:Main Beam Brightness temperature:

S(total)=S(peak) S(total)=S(peak) .. ( (SS 22 + + BB 22 )/ )/ BB 22

Example: Orion A is an HII region with a total flux Example: Orion A is an HII region with a total flux

density of 380 Jy at 1.3 cm. The size is 2.5’ (FWHP). If the radiodensity of 380 Jy at 1.3 cm. The size is 2.5’ (FWHP). If the radio

telescope beam size is 40” (FWHP), what is the peak flux density?telescope beam size is 40” (FWHP), what is the peak flux density?

Use the R-J relation to find the peak main beam brightnessUse the R-J relation to find the peak main beam brightness

temperature. temperature. Solution: peak Jy/beam=9.5; TSolution: peak Jy/beam=9.5; TAA=8.8K, T=8.8K, TBB=24 K=24 K

Far FieldFar Field Diffraction and Fourier Transforms Diffraction and Fourier Transforms

(Exact calculations require programs such as GRASP)(Exact calculations require programs such as GRASP)

(radiation passing through an opening)(radiation passing through an opening)


Grading Across the Aperture and Far E FieldGrading Across the Aperture and Far E FieldLecture 3 page 2Lecture 3 page 2

ALMA ALMA

Front-End

DigitizerClock

Local Oscillator

ANTENNA

Data Encoder12*10Gb/s

12 Optical Transmitters

12->1 DWD Optical Mux

Digitizer8* 4Gs/s -3bit ADC

8* 250 MHz, 48bit out

IF-Processing(8 * 2-4GHz sub-bands)

Fiber Patch-PanelFrom 270 stations to 64 DTS Inputs

Optical De-Mux& Amplifier

Digital De-Formatter

Correlator

Technical Building

Tunable Filter Bank

Fiber

Lecture 3, page 3Lecture 3, page 3

Sketch of 2 element Sketch of 2 element interferometerinterferometer

((u,vu,v) plane and image plane ) plane and image plane

These are related by Fourier transformsThese are related by Fourier transformsThe distance between antennas varies, so The distance between antennas varies, so we sample different source structureswe sample different source structuresOn the next overheads, we indicate how On the next overheads, we indicate how structures are sampled. Following structures are sampled. Following tradition, tradition, u u represents one dimension represents one dimension distributions, with x as the separtion in distributions, with x as the separtion in wavelenghts wavelenghts uu=2=2xxandandv=2v=2yy

Earth Rotation Aperture SynthesisEarth Rotation Aperture Synthesis

Above: the 2antennas onthe earth’s surface have a different orientation as a function of time.

Below: the ordering of correlated data in (u,v) plane.

Gridding and sampling in (Gridding and sampling in (u,vu,v) ) planeplane

Sensitivity: http://www.eso.org/projects/alma/science/bin/sensitivity.htmlSensitivity: http://www.eso.org/projects/alma/science/bin/sensitivity.html

VLA VLA uvuv plane response plane response

Dataas taken

Datawith MEM

with MEMand Self-Calibration

The radiogalaxy Cygnus Aas measured with all configurations of the VLA

From W. D. Cotton (in ‘The Role of VLBI in Astrophysics, Astrometry, From W. D. Cotton (in ‘The Role of VLBI in Astrophysics, Astrometry,

And Geodesy, ed Mantovani & Kus, Kluwer 2004)And Geodesy, ed Mantovani & Kus, Kluwer 2004)


BROADBAND RADIATION

• Black body (Moon, planets, 3K background)

• Dust thermal emission

• Bremsstrahlung (free-free)

• Synchrotron (relativistic electrons in magnetic fields)

• Inverse Compton Scattering (S-Z)

Dust: Mostly carbon, silicon with ice mantles “ground up planets”

From Hildebrand (1983)

D U STSun

H

z

zb N

7 1 0 2 1 2

22

2

:

:

:

:

min

cmindensitycolumnN

datathefittoaccounttofactorb

mmin

H

DUST


For warm grains

Use R-J

get

T TD U ST D U ST

S k TD U ST D U ST 2 2

NS m Jy

zz

b TH

m m

SunD U ST

1 9 3 1 0 2 42

4

.( )

(" )

EXAMPLE: Dust emission from Orion KL

The Orion “hot core” has the following properties:

1 0

1 6 0

1 0

1 5 1 0 5 0 0

27 3

2 1

"

( )

. ( )

T K

n H cm

D ist cm pc

D U ST


Calculate the column density N(H2) = n L and the 1.3 mm dust flux density, S, ,

if z = zif z = zSunSun, b = 1.9 , b = 1.9

If the value of L = diameter, use L (diameter in cm) x (size in radians) =

= 7.5 1016 cm

Them N(cm-2) = 7.5 1016 cm x 107 cm-3 = 7.5 1023 cm-2 for H2

N(H) = 2 N(H N(H22) = 1.5 ) = 1.5 1024 cm-2

So

1 5 1 0 1 9 3 1 01 3 0 0

1 0 1 9 1 6 0

1 0

1 0

2 4 2 44

2

4

. .( ) ( )

( ) ( . ) ( )

( )

S m Jy

S m Jy

S Jy

At 4 mm, S S is 81 times smaller or 120 mJy. At 0.39 mm, Sis 81 times smaller or 120 mJy. At 0.39 mm, S is 81 times is 81 times

larger or 810 Jylarger or 810 Jy


BREMSSTRAHLUNG (FREE-FREE)

Hydrogen is ionized by O, B, electron and protons interact, electrons radiate. Classically:

P t ev t

cL arm or( )

( )( )

2

32

2

3

Power radiated during encounter:W

e

cv t d t

2

3

2

32 ( )

Find

4

3

22 6

3 22

1

z e

c

N N

m

m

k T

p

pi e

e

ln

From the Kirchhoff relation, get

B T k Tc

k Tso

N N L

Te e

i e

e( ) 2 2

2

2

2 3

22

velocityvelocity

‘ ‘ pp’ is impact parameter’ is impact parameter

frequencyfrequency


T T eB e 1

When = 1: = 1: 0

0 6 4 3

6

0 4 7 6

0 3 0 4 5

..

.

TE M

pc cmB

For Orion A, 00 = 1 GHz, or 30 cm.

1 8 0 0 0

1

5 4 0 0

2 3 2 4

2

G H z T T K

G H z T TT

at G H z T K

at G H z T K

B e

B ee

B

B

But

SkT kT

E M constB e

2 22 2 2

8 2 3 5 1 0 2 1 3 5 2

..

T E Me G H z

--

What is the What is the

Relation forRelation for

TTBB??


Orion A HII Region

Te = 8500 K, = 2.5’ (FWHP), so use

is much less than 1, at = 23 GHz so T = T = 23 GHz so T = Tee

From 100-m, TMB (main beam) = 24 K in a 40” beam, so TMB (main beam) == T(true)

24 = (8500) (8.235 10(8.235 10-2-2) ) (8500)(8500)-1.35-1.35 (23)(23)-2.1-2.1 EMEM

so EM = 4 so EM = 4 101066 cm cm-6-6 pc = N pc = Nee N Ni i

LL

If L = 25’ = 0.33 pc converted to radians @ 500 pc get NIf L = 25’ = 0.33 pc converted to radians @ 500 pc get Nee = N = Nii = 3.5 = 3.5 101033 cm cm-3-3

This is the RMS density. Calculate the mass of ionized gas. This is the RMS density. Calculate the mass of ionized gas.

Rough number since know Orion A is not spherical. From spectral lines know Ne = 10= 1044 cm cm-3-3, so L = 0.03 pc. Then M = 0.6 M, so L = 0.03 pc. Then M = 0.6 MSunSun in ionized gas in ionized gas

Free-Free Intensity and Flux Density as function of FrequencyFree-Free Intensity and Flux Density as function of Frequency

(Problem: Use the (Problem: Use the

exampleexample

of Orion to of Orion to

check thesecheck these

Curves)Curves)



Free-Free Emission from Planetary Nebulae

NGC7027 (a PNe) has SS = 5.4 Jy at 1.3 cm. What is the T= 5.4 Jy at 1.3 cm. What is the TMBMB (main beam (main beam

brightness temperature) if the 100-m FWHP beam size is 43”?brightness temperature) if the 100-m FWHP beam size is 43”?

UseUse

Where Where 0 is the telescope beam size in are min.

Suppose the “true” gaussian source size is 10”, what is TB (true brightness temperature). Could use

ST

cm

T

T K

M B

M B

M B

2 6 5

5 4 2 6 5

4 36 0

1 3

6 7

02

2

2

2

.( )

. ..

.

STM B

5 4 2 6 5

1 06 0

1 3

2

2. ..

(Problem: Repeat for the (Problem: Repeat for the

30-m, with beam 30-m, with beam

27’’, wavelength 27’’, wavelength

3.5 mm, flux density3.5 mm, flux density

4.7 Jy)4.7 Jy)


Or

And get

We know that the electron temperature of NGC7027 is Te = 14000 K. Use equation of radiative transfer:

To get 0 0 0 9.

This is a source which is thermal, so the radiation is free-free or Bremsstrahlung

2

22

10

1043MBB TT

KTB 124

eTT eB 1


SYNCHROTON RADIATION (NON-THERMAL)

Highly relativistic electrons spiraling in a B field with a frequency

B

e B

m

1

P: Power radiated by electron (lab)

P’: Power radiated by electron (rest frame)

so P = P’

Pd

dtP

d

d td t d t

''

'' '

Transformation of acceleration

So

a a' 2

Pe

ca a v

e B

mvB

2

3

2

34 2

Radiation patterns of an electron in a B fieldRadiation patterns of an electron in a B field

B Field,B Field,

V about 0V about 0

VelocityVelocity

B Field,B Field,

V about 0.2 cV about 0.2 c



Then

E: Particle energy

Is difficult to separate energy of electron from B field strength

To get spectral distribution, use

Find a synchrotron spectrum ::

dN

dEk E

1

21 0 7 2 4. .

Synchrotron radiation is found to be linearly polarized

(power law (power law

distribution of distribution of

Cosmic Rays)Cosmic Rays)

22232

222

3

2BE

cm

BveP


SINGLE ELECTRON SYNCHROTRON EMISSION

For relativistic electrons, the emitted pulse is 1/ shorter due to relativistic beaming while the Doppler effect gives rise to a factor 1/2

B: Frequency of rotation

So for B = 10G, G, B is even lower when <1

B

B

G

1 7 6.

GB H z

1 7 6

Thus in frequency reach a critical value

So if B = 10 G, G, G = 176 Hz, to reach CC = 10 GHz, = 10 GHz, = 1.6 101044

In Synchrotron emission, we measure only the most relativistic In Synchrotron emission, we measure only the most relativistic particlesparticles

C G

3

42 sin


SYNCHROTRON ENERGY CONSIDERATIONS

Allow one to determine the minimum or equipartion energy

Inverse Compton effect

When the radiation density is equal to magnetic energy density there can be energy losses in addition to synchrotron energy losses. R & W don’t do much, but Kellermann & Owen give:

W S R VT O Tn

4

78

7

3

7

L

L

T TC om pton

Synch

M A X M A X

1

2 1 01

1

2 1 01 2

5

2

5

m ax

This is the basis of the statement: “1012 K is the highest source temperature possible”


Non-thermal sources

Cas A: at 100 MHz, SS= 3 10= 3 1044 Jy, Jy, s=4’ (source size), 4’ (source size), = 3 m = 300 cm

ST

cm

T

K T source

M B

2 6 5

3 1 0 2 6 51 6

9 1 0

7 5 1 0

0

2

2

44

8

.( ' )

( )

.

. ( )

Thermal sources have limit T = 2101044 K K

Assume that for Cas A, T=7.5 10Assume that for Cas A, T=7.5 1088 ( (mm3) 3) -2.8-2.8

What is the source temperature at 3 mm?What is the source temperature at 3 mm?

Source Source

Specral Specral

IndexIndex


SUNYAEV-ZELDOVICH EFFECT

Clusters of galaxies are filled with hot diffuse gas. Photons from the 3 K background are scattered in this cluster gas.

More photons are given energy than lose energy on the low frequency side of the Planck curve.

On the high frequency side, some photons are shifted to lower energies,

but still a reduction in the 3 K background. At 160 GHz, have a cross over from absorption at longer wavelengths to emission at shorter wavelengths, so have zero absorption. The

absorption is:T

TT N L

SZe e

2 2 4 1 0 3 4.

When combined with X ray luminosity, which is Bremsstrahlung (free-free), proportional to Ne

2 L, can solve for source distance. Given L, can solve for source distance. Given

velocity of source, get velocity of source, get HUBBLE CONSTANTHUBBLE CONSTANT. However there can be . However there can be systematic effects such as clumping. systematic effects such as clumping.

Lecture 3 page 30 Lecture 3 page 30

EXAMPLE OF S-Z EFFECT

The cluster CL0016 +16 shows on S-Z absorption of –700 K at 1 cm K at 1 cm wavelengthwavelength

Z = redshift of CL0016 +16 is 0.541Z = redshift of CL0016 +16 is 0.541

X ray data: TX ray data: Tee = 1.6 10 = 1.6 1088 K K

Cluster size = 30“ to 19”Cluster size = 30“ to 19”

RMS RMS NNee = 1.2 10 = 1.2 10-2-2 cm cm-3-3

So So Kcm

T

T

SZ

70010710310101024.2 4242834

Lecture 3 By Tom Wilson. Summary of Lecture 1 Noise in a Receiver time on source Receiver itself,...

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Transcript of Lecture 3 By Tom Wilson. Summary of Lecture 1 Noise in a Receiver time on source Receiver itself,...