The Cosmic Microwave Background Radiation B. Winstein, U of Chicago

Transcription

1 The Cosmic Microwave Background Radiation B. Winstein, U of Chicago Lecture #1 Lecture #2 What is it? How its anisotropies are generated? What Physics does it reveal? How it is measured. Lecture #3 Main thrusts for the next decade.

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

3 Looking at a Point on the Sky R.H. Dicke and colleagues, mid 1940s

4 Elements of a Radio Telescope Antenna Amplifier Filter Power Meter Amplifier

5 Elements of a Radio Telescope Antenna Amplifier low-noise, high bandwidth Filter selects ν Power Meter measures <E 2 > Amplifier low frequency (DC)

6 Antenna Pattern Near side lobes Main beam Diffraction limit: AΩ=λ 2 A: collecting area Ω: beam solid angle λ:wavelength Far side lobes

7 CMB Flux Planck Spectrum: B ν = 2hν 3 c 2 1 e hν / kt 1 W / m2 / str/ Hz Example: beam FWHM = 8 0 ; beam area = 8 cm 2 ν 0 = 90 GHz; ν = 10 GHz The CMB flux on the horn is then: 2.5 x Watts

8 Radiation Detection Coherent Detectors (phase preserving) [Bolometric Detectors tomorrow]

9 Signal Level from the CMB 3 0 radiation Gain Antenna Amplifier Filter low-noise, high bandwidth selects ν 1mV/uW Power Meter measures <E 2 > 100 Amplifier low frequency (DC) 10mV

10 Heterodyne Receivers With coherent receivers one can mix down the radio frequency to an intermediate frequency (IF) Eg ( GHz) x 82 GHz = 2-18 GHz Signal can be manipulated on coax Amplifiers are lower noise

11 CAPMAP: Chicago, Miami, Princeton Multistage RF amplification 1st stage most important (like photomultipliers)

12 IF signals on coax (2-18 GHz) Power detector

13 CAPMAP Receivers horn & lens MMIC HEMT amplifier Warm section LO chain & power amp IF section Figures by M. Hedman

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15 Crawford Hill, NJ 7 meter radio telescope

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17 Dicke Paper

18 Atmospheric Noise The Atmosphere will both absorb incident radiation and emit its own radiation These are connected by Kirchoff s Law T D = T S e τ + T C (1 e τ ) T S T C

19 Atmospheric Noise continued T D = T S e τ + T C (1 e τ ) Optical Depth τ 0 Detector Signal T D T S 0.2 T C 45 K (T C = 250 K)

20 Atmospheric Absorption 90 GHZ

21 Amplifier Noise Ideal amplifier: power generated (with NO input) depends on its (physical) temperature T and ν p = hν dν ktdν e hν / kt 1 State-of-the-art 90 GHz amplifiers: T (physical) = 10 K T (noise) = 45 K

22 Components of the Signal 3 K from the CMB 45 K from Amplifier Noise 45 K from Atmospheric Noise 100 K system temperature

23 Sensitivity of the Radiometer How well can we measure the temperature at a point on the sky? T = T sys ν t obs = 1mk sec in our case Where does this come from?

24 Radiometer Sensitivity a la Dicke Antenna Noise as a pulse train: 1/ ν ν is receiver bandwidth T system = 100 K T signal = 1 µk = 10-8 of system Temp. need pulses Take ν = 10 GHz Count for 10 6 seconds for 1σ Challenge to keep systematics (amplifier drifts, atmospheric noise, etc.) under control during this large integration time.

25 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, LN 2, the moon, and a few of the planets are useful for this purpose

26 Astronomical Effects Planets Galactic Emission Synchrotron Bremstrahlung Dust Extra-galactic sources Radio sources Use multiple frequencies Pick quiet regions Hot gas in Galaxy clusters (SZ effect) Gravitational Lensing (Lecture 3)

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28 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

29 Still looking at one spot Power Power with gain drift Change in power Signal change Change in power Sensitivity limit due To Gain drifts: W = k(t 1 + T sys )G ν W + W = k(t 1 + T sys )(G + G) ν W = G νk(t 1 + T sys ) W + W = k(t 1 + T + T sys )G ν W = G νk T T = G T sys G

30 Dicke Switching/Chopping Power at 1 Power at 2 difference Gain drift Signal change W 1 = k(t 1 + T sys )G ν W 2 = k(t 2 + T sys )G ν W W 1 W 2 = k(t 1 T 2 )G ν W + W = k(t 1 T 2 )(G + G) ν W + W = k(t 1 T 2 + T)(G) ν Sensitivity limit due To Gain drifts: T T sys = T 1 T 2 T sys G G

31 8 seconds of data (0.01 sec samples) unswitched switched

32 15 minutes of bad data

33 15 minutes of good data

34 1/f noise Noise Powers (amplifier+atmosphere) unswitched switched

35 Power Spectra Sensitivity: Cosmic variance C l C l = 2 2l +1

36 Cosmic Variance + noise C l C l = 2 4πw 1+ 2l +1 C l where w : total experimental weight [µk 2 ]

37 Cosmic Variance + noise + finite sky C l C l = 2 2l πw f sky f sky C l where f sky w : fraction of the sky observed : total experimental weight [µk 2 ]

38 Cosmic Variance + noise + finite sky + finite beam size C l C l = 2 2l +1 1 f sky + 4πw C l f sky e l 2 σ b 2 where f sky w : fraction of the sky observed : total experimental weight [µk 2 ] σ b : beam rms

39 Effect of Finite Beam Size MAP beam: 0.24 deg. CAPMAP beam: 0.05 deg.

40 Choosing the Observing Strategy Depends on l-coverage desired Depends on sensitivity desired Frequent switching desired Frequent redundancies Multiple time scales

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42 SENSITIVITY SIMULATIONS (using CfCP 32-node cluster) Sample variance Detector noise

43 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 (C l s) Capmap: inversion of 5760x5760 matrix Run likelihood for cosmological params.

44 !Radiometer Offsets! Residual Structure, µk vs. azimuth pixel

45 Modes with High S/N

46 Modes with High S/N Mean removed

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48 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

49 The Cosmic Microwave Background Radiation B. Winstein, U of Chicago Lecture #3 Main thrusts for the next decade.