SLAC Summer Institute, Lecture #2

The Cosmic Microwave Background Radiation

B. Winstein, U of Chicago

Main thrusts for the next decade.Lecture #3

How it is measured.Lecture #2

What is it? How its anisotropies are generated? What Physics does it reveal?

Lecture #1

SLAC Summer Institute, Lecture #2

Lecture #2: Measuring the Cosmic Microwave Background

• Radio telescopes• Receiver Types• Sources of Noise• Sensitivities• Observing trade-offs and strategies• From raw data to power spectra

SLAC Summer Institute, Lecture #2

Looking at a Point on the Sky

R.H. Dicke and colleagues, mid 1940s

SLAC Summer Institute, Lecture #2

Elements of a Radio Telescope

Antenna

Amplifier

Filter

Power Meter

Amplifier

SLAC Summer Institute, Lecture #2

Elements of a Radio Telescope

Antenna

Amplifier low-noise, high bandwidth

Filter selects ∆ν

Power Meter measures <E2>

Amplifier low frequency (DC)

SLAC Summer Institute, Lecture #2

Antenna Pattern

A: collecting areaΩ: beam solid angle

λ:wavelength

Mainbeam

Near side lobes

Far side lobes

AΩ = λ2Diffraction limit:

SLAC Summer Institute, Lecture #2

CMB Flux• Planck Spectrum:

• Example: • beam FWHM = 80; beam area = 8 cm2

• ν0 = 90 GHz; ∆ν = 10 GHz

• The CMB flux on the horn is then:• 2.5 x 10-13 Watts

Bν =2hν 3

c 21

ehν / kT −1W /m2 / str /Hz

SLAC Summer Institute, Lecture #2

Radiation Detection

Coherent Detectors(phase preserving)

[Bolometric Detectors tomorrow]

SLAC Summer Institute, Lecture #2

Signal Level from the CMB

Antenna

Amplifier low-noise, high bandwidth

Filter selects ∆ν

Power Meter measures <E2>

Amplifier low frequency (DC)

Gain

106

0.4

1mV/uW

100

10mV

30radiation

SLAC Summer Institute, Lecture #2

Heterodyne Receivers

• With coherent receivers one can “mix down” the radio frequency to an intermediate frequency (IF)

• Eg (84-100 GHz) x 82 GHz = 2-18 GHz– Signal can be manipulated on coax– Amplifiers are lower noise

SLAC Summer Institute, Lecture #2

Multistage RF amplification 1st stage most important (like photomultipliers)

CAPMAP: Chicago, Miami, Princeton

SLAC Summer Institute, Lecture #2

IF signals on coax(2-18 GHz)

Power detector

SLAC Summer Institute, Lecture #2

CAPMAP ReceiversCAPMAP Receivers

horn & lens

MMIC HEMTamplifier

LO chain &power amp

Warm section

IF section

Figures by M. Hedman

SLAC Summer Institute, Lecture #2

SLAC Summer Institute, Lecture #2

Crawford Hill, NJ

7 meter radio telescope

SLAC Summer Institute, Lecture #2

SLAC Summer Institute, Lecture #2

Dicke Paper

SLAC Summer Institute, Lecture #2

Atmospheric Noise

• The Atmosphere will both absorb incident radiation and emit its own radiation

• These are connected by Kirchoff’s Law

TSTC

TD = TSe−τ + TC (1− e−τ )

SLAC Summer Institute, Lecture #2

Atmospheric Noise continued

TD = TSe−τ + TC (1− e−τ )

45 K (TC = 250 K)0.2

TC∞

TS0

Detector Signal TD

Optical Depthτ

SLAC Summer Institute, Lecture #2

Atmospheric Absorption

90 GHZ

SLAC Summer Institute, Lecture #2

Amplifier Noise• Ideal amplifier: power generated (with

NO input) depends on its (physical) temperature T and ν

• State-of-the-art 90 GHz amplifiers:– T (physical) = 10 K– T (noise) = 45 K

p=hν

ehν / kT −1dν ⇒ kTdν

SLAC Summer Institute, Lecture #2

Components of the Signal

• 3 K from the CMB• 45 K from Amplifier Noise• 45 K from Atmospheric Noise

≈ 100 K system temperature

SLAC Summer Institute, Lecture #2

Sensitivity of the Radiometer

How well can we measure the temperature at a point on the sky?

∆T =Tsys

∆ν × tobs

=1mk

secin our case

Where does this come from?

SLAC Summer Institute, Lecture #2

Radiometer Sensitivity a la Dicke

Antenna Noise as a pulse train:

1/∆ν∆ν is receiver bandwidth

•Tsystem = 100 K•Tsignal = 1 µK = 10-8 of system Temp.

need 1016 pulses•Take ∆ν = 10 GHz

Count for 106 seconds for 1σ•Challenge to keep systematics (amplifier drifts, atmospheric noise, etc.) under control during this large integration time.

SLAC Summer Institute, Lecture #2

Calibration of Radiometers

• Shine various BBs on the system and measure the response, check linearity, etc.– Allows expressing signal levels in terms of

equivalent temperatures– In the field, LN2, the moon, and a few of the

planets are useful for this purpose

SLAC Summer Institute, Lecture #2

Astronomical Effects

• Planets• Galactic Emission

– Synchrotron– Bremstrahlung– Dust

• Extra-galactic sources– Radio sources– Hot gas in Galaxy clusters (SZ effect)– Gravitational Lensing (Lecture 3)

Use multiple frequenciesPick quiet regions

SLAC Summer Institute, Lecture #2

SLAC Summer Institute, Lecture #2

Instrumental Effects• Amplifier Drifts

– Use “Dicke switching”• Electrical Grounding

– Critical with such high gains• Mechanical pickup

– telescope motion; mechanical refrigerator• Optics/ground pickup

– shield radiometer from the 300K ground• Thermal regulation

– Gains vary with temperature

SLAC Summer Institute, Lecture #2

Still looking at one spot …

W = k(T1 + Tsys)G∆νW + ∆W = k(T1 + Tsys)(G + ∆G)∆ν∆W = ∆G∆νk(T1 + Tsys)

W + ∆W = k(T1 + ∆T + Tsys)G∆ν∆W =G∆νk∆T∆TTsys

=∆GG

Power

Power with gain drift

Change in power

Signal change

Change in power

Sensitivity limit dueTo Gain drifts:

SLAC Summer Institute, Lecture #2

Dicke Switching/ChoppingW1 = k(T1 + Tsys)G∆νW2 = k(T2 + Tsys)G∆νW ≡W1 −W2 = k(T1 − T2)G∆νW + ∆W = k(T1 −T2 )(G + ∆G)∆νW + ∆W = k(T1 −T2 + ∆T )(G)∆ν∆TTsys

= T1 −T2

Tsys

∆GG

Power at 1

Power at 2

difference

Gain drift

Signal change

Sensitivity limit dueTo Gain drifts:

SLAC Summer Institute, Lecture #2

8 seconds of data(0.01 sec samples)

unswitched

switched

SLAC Summer Institute, Lecture #2

15 minutes of “bad” data

SLAC Summer Institute, Lecture #2

15 minutes of good data

SLAC Summer Institute, Lecture #2

Noise Powers(amplifier+atmosphere)

“unswitched”

“switched”

“1/f” noise

SLAC Summer Institute, Lecture #2

Power Spectra Sensitivity: Cosmic variance

∂ClCl

= 22l +1

SLAC Summer Institute, Lecture #2

Cosmic Variance + noise

∂ClCl

= 22l+1

⟨1+ 4πwCl

⟩

w : total experimental “weight” [µK2]where

SLAC Summer Institute, Lecture #2

Cosmic Variance + noise + finite sky

∂ClCl

= 22l +1

⟨ 1fsky

+ 4πwCl

fsky ⟩

fskyw

: fraction of the sky observed

: total experimental “weight” [µK2]where

SLAC Summer Institute, Lecture #2

Cosmic Variance + noise + finite sky + finite beam size∂ClCl

=2

2l+1⟨ 1fsky

+4πwCl

fsky el 2σ b

2 ⟩

fskywσb

: fraction of the sky observed

: total experimental “weight” [µK2]

: beam rms

where

SLAC Summer Institute, Lecture #2

“MAP” beam: 0.24 deg.

“CAPMAP” beam: 0.05 deg.

Effect of Finite Beam Size

SLAC Summer Institute, Lecture #2

Choosing the Observing Strategy

• Depends on l-coverage desired• Depends on sensitivity desired• Frequent switching desired• Frequent redundancies• Multiple time scales

SLAC Summer Institute, Lecture #2

SLAC Summer Institute, Lecture #2

SENSITIVITY SIMULATIONS (using CfCP 32-node cluster)

Sample varianceDetector noise

SLAC Summer Institute, Lecture #2

Data Processing

• Calibrate; de-glitch time series• Bin in sky coordinates• Offset removal

– Mean, slope, quadratic?• Make a map

– Pixels will be correlated• Run likelihood for power in l-bands (Cls)

– Capmap: inversion of 5760x5760 matrix• Run likelihood for cosmological params.

SLAC Summer Institute, Lecture #2

Residual Structure, µK vs. azimuth pixel

!Radiometer Offsets!

SLAC Summer Institute, Lecture #2

Modes withHigh S/N

SLAC Summer Institute, Lecture #2

Modes withHigh S/NMean removed

SLAC Summer Institute, Lecture #2

SLAC Summer Institute, Lecture #2

Final Check: Null Tests

• Create maps that should have no signal– First 1/2 of data minus second 1/2– Alternate signs on samples in each pixel– Day minus night––

SLAC Summer Institute, Lecture #2

The Cosmic Microwave Background Radiation

B. Winstein, U of Chicago

Main thrusts for the next decade.Lecture #3