The Cosmic Microwave Background Radiation...SLAC Summer Institute, Lecture #2 The Cosmic Microwave...
Transcript of The Cosmic Microwave Background Radiation...SLAC Summer Institute, Lecture #2 The Cosmic Microwave...
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