Future CMB Experiments

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Transcript of Future CMB Experiments

  • 1. Understanding CMB experimentsMartin Bucher, APC Paris April 2012AIMS Research Center

2. WMAP Internal Linear Combination (ILC) Map 3. Note on conventions d[T 2 ()] ( + 1)c=d[ln[ ] 2The natural units for a temperature/polarization map are K 2 .In the at sky approximation (after a CMB map has been subjected to atop-hat bandpass lter in harmonic space),d2 c1max d2c( ) T 2 ()= (4) = ( 2c ) = ln[ ] S2(2)2 42 min2Scale invariance implies that integral is logarithmically convergent.Curvature correction appear at higher order in an expansion in powers of 1/ , but nonatural way to extend curvature correction to scale invariance. 4. Reduction to a power spectrum +T () =a m Y m (), = (, ) S 2=2 m=In standard ination uctuations are very nearly Gaussian and theprobability of obtaining a sky map given a predicted theoretical powerspectrum (depending on a number of cosmological parameters ) is(th) 1|a m |2P({a m }|c ) = (constant) exp 12(th),m c (th)cor we may write 2 = 2 ln[P](obs) (obs)cc2 =(2 + 1) (th) 1 ln (th)+ (constant)cc(obs)where c= (2 + 1)1 m |a m |2 . The above is usually called likelihoodbecause we are interested in how it changes as we varying the parameters ofthe theoretical model, rather than predicting the outcome of the experiment. 5. Predicted temperature power spectrumCMB scalar anisotropies 1e+04 1e+02 l*(l+1)*CXX/2*pi [muK**2] 1e+00 1e02 2 5 10 20 50100200 500 1000 Multipole number (l)At low- the amplitude of the temperature uctuation is 33K (i.e.,T /T 1. 105 )As increases to 220, sees the rise to the rst acoustic peak, by a factor of 6 in temperature (and 6 in the power spectrum). Most of the power seen inthe CMB maps arises from the Doppler peak. The size of the spots is visible tothe eye and this is the salient feature (and not the scale invariance.)At larger one observes a sequence of secondary Doppler peaks (andcorresponding troughs) as well as Silk dampening, due to viscosity in the photonelectron-plasma as well as the nite width of the last scattering surface. 6. Including instrument noise (and incomplete skycoverage) 2 = Tsky (C + N)1 Tsky + log[det(Cth + N)] T In general, noise is assumed (to a rst approximation) uncorrelated between pixels but not necessarily uniform on the sky. Therefore, the N no longer takes the simple form N m; m =N mm N m; m = (constant)(1/ t) m (1/ t) m or even a less restricted form when non-whiteness (i.e., redness) of the noise is allowed. Warning : Although the above denes an exact representation of the likelihood, given the large number of pixels present, evaluating the above is not feasible, at least on all scales, and much work has gone into developing good approximations to the likelihood that are fast to compute. (If Npix = 106 for example, Npix = 1018 operations are required to invert a matrix.) 3 7. PolarizationPercentage linear polarization Correlation coefficient [cte/sqrt(ctt*cee)]250.60.420 Percent polarization [sqrt(cee/ctt)] TE correlation coefficient0.2150.0100.20.450.600 500100015002000250030000 500100015002000 2500 3000Multipole number Multipole number The CMB is also predicted to be mildly polarized. This polarization encodes complementary information. Polarization is represented by a double-headed vector or second-rank symmetric tensor on the celestial spehere.Pij (),in [K ] T (, n) = T () + Pij ()ni nj ,n (direction of linear polarizer) 8. Scalar and Tensor CMB Anisotropies with PLANCKRed=scalar (top to bottom) TT, TE, EE, BB (lensing)Blue=tensor (T/S=0.1) = TT, TE, EE, BB, dotted BB (T/S=0.01, 0.001)Green PLANCK capabilities = top single alm, bottom agressive binning 9. Illustrating Silk dampeningsqrt(l*(l+1)*cTT/2.pi) dotted,sqrt(l*(l+1)*cTT/2.pi)*exp(l/1000.) solid150100muK5000 500100015002000 2500 3000 Multipole 10. New effects take over at large 11. E and B Mode PolarizationE mode B mode(E)2 1Ym,ab =ab ab Y m ()( 1) ( + 1)( + 2)2(B)21Ym,ab = ac cb+ a bc c Y m ()( 1) ( + 1)( + 2) 2 12. Technologies for the detecting CMB uctuations 13. Microwave horns ACBAR hornsIdea is to admit only a single mode (in the transverse direction)so that the microwaves entering can be can be regarded as atwo-component scalar eld theorythat could either bedetected directly (as in Planck) or put onto a microstriptransmission line and modulated electronically.The horn is to produce as Gaussian a beam as possible withthe fastest falling side-loabs. The telescope in underiluminatedto prevent the sideloabs from seeing the instrument. 14. Schematic of single-mode detection h (6.6 1034 J s)= =kB TCMB (1.38 1023 J K 1 )(2.73 K )57 GHz Singlemode detectionFlux from microwave sky Matched impedance Transmission line resistor Microwave feed horn Return flux of resistor noise P = (power onto a single-mode transmission line) = 2 pW50 GHz 15. Review of photon counting statistics 1 Z = 1 + x + x2 + . . . = , x = exp[ /kB T ]1x x 1N = Z 1 x Z = = x1x exp[ /kB T ] 1 2 2x 2x N 2 = Z 1 xZ = + =2 N 2+ Nx(1 x)2 (1 x) Two limits and an intermediate regime (N = N ) :N 1 highly correlated arrival times, as if photons arrive in bunches ofN photons.N 1, nearly Poissonian (uncorrelated) arrival times.N 1, moderate bunching, postive correlation in arrival times. 16. Noise for a noiseless (perfect) detector operating thein Rayleigh-Jeans (classical) regime I= ()tI t [Integration time (in sec) () [Bandwidth (in Hz) Basically, ()1 is the rate of independent realizations of an independent Gaussian stochastic process. In the presence of detector noise, which may be characterized as a system temperature Tsys one has Tdetector = Tsignal + Tsystem and ITsys= 1+()tITsig Robert Dicke, 1947 Mirrors and other optical elements can be very hot and if they are also very reective do not add much noise. Tout = (1 )Tin + Toptics where is a small absorption probability. 17. Quantum correction to radio astronomers formula Correction factor to linear dependence of occupation number (intensity) on temperatured(ln[N])x exp[x]=d(ln[T ]) (exp(x) 1) Correction to intensity uctuation2 IN2 + N1= ()t =1+ ()tIN2N 2Tx 2 exp[3x] = ()tT(exp[x] 1)2 where x = h/kB T = (/57 GHz). 18. Characterization of the detector noise (I)Resistor10(nV/Hz^0.5) 10.00100.00 1000.00Frequency (Hz) Yogi bolometer at 110 mK 10-15 (W/Hz^0.5) 10-16 10-17 10-18 0.01 0.101.00 10.00100.00 1000.00Frequency (Hz) From Giard et al. (astro-ph/9907208 ) To a rst approximation, the detector noise is (white-noise) + (1/f - noise ). One uses modulation (repeated scanning of the same circle in the sky) to remove 1/f noise. 19. Characterization of the detector noise (II) As a rst approximation, one assumes that detector noise in a sky map is uncorrelated between pixels with variance inversely proportional to the pixel integration time. For equal integration time for each pixelN = N0 (i.e., a white-noise spectrum, rather than the very red approximately scale-invariant CMB spectrum c 2 .) Non-uniform sky coverage, let t() be the integration time in the direction and expand t 1/2 () = t 1/2 m Y m (summation implied). Then 1/2 (N 1 ) ,m; ,m = t 1/2mt m (Note that if sky coverage is incomplete N 1 is well-dened, but its inverse N is not.) 20. Problem of far side-lobesAiry diffraction pattern (from a unapodized circular aperature)Airy diffraction pattern (logarithmic scale) Airy diffraction pattern (linear scale)1.0 1e010.8 1e030.6Intensity Intensity 1e050.4 1e070.2 1e090.020 10010 202010010 20theta/sigma_theta theta/sigma_theta While a Gaussian may be a good approximation near the beam center, diffraction theory tells us that without an innite aperature exponential fall-off of the point spread function is not possible. 2 2J1 (x)I(x) = I0 , x = (/beam ) x 21. Escaping the Earth, Sun and Moon at L2L2-Earth distance = 1.5e6 km Earth-Moon distance = 4.0e5 kmFor Planck standards one needs about 109 rejection towardsun ! And a very high rejection toward the Earth as well. 22. Observations from the ground (I) Atmospheric interference. Calculated optical depth through the atmosphere for a good ground-based site like the South Pole or Dome-C in Winter (black) and at balloon altitude (red). Frequency bands for sub-orbital experiments must be carefully chosen to avoid the emission by molecular lines. Moreover, emission from oxygen lines is circularly polarized and care must be taken to avoid a signicant polarized signal from the tails of these lines. 23. Observations from the ground (II) Numerous CMB polarization experiments from the ground and balloons at various stages : QUaD, BICEP ; BRAIN, CLOVER, EBEx, PAPPA, PolarBear, QUIET and SpiderFar side lobes Scanning strategy (must scan at constant zenith angle) Polarization from interaction of Zeeman splitting by earths magnetic eld of oxygen lines. Atmospheric backscattering (very polarized) could be a serious problem. [See L. Pietranera et al., Observing the CMB polarization through ice, MNRAS 346, 645 (2007)]. Lack of stability and partial sky coverage 24. Modulation strategies (I) It is not a good idea to measure the polarization as a very small difference between two very large quantities. For example, Q = Ex () Ex () Ey () Ey () . Signal typePower d(T 2 )/d(log[ ]) CMB Monopole T01012.5 K 2 T anisotropy103 K 2 E anisotropy101.5 K 2 B anisotropy106 K 2 The deadly sins of B polarization measurement can be ranked (from most serious to less serious) as follows :T0 B leakage. (E.g. polarization from reections, far side lobes,standing waves in instrument)T B leakage. (E.g., subtracting two polarized beams havingdifferent uncharacterized ellipticity)E B leakage. (E.g., poorly calibrated polarization angle, crosspolarization) 25. Toward Measuring the Polarization Directly : PhaseSwitch ModulationPhase switchMixerBolometersEy(Ex Ey )(1) I1 Horn OMTI2Ex(Ex Ey )I1 = (Ex Ey )2 = Ex 2 + Ey 2 Ex EyI2 = (Ex Ey )2 = Ex 2 + Ey 2 Ex Ey 26. Rotating Half-Wave PlateBolometers EyMixer (Ex + Ey ) I1Ex , EyHorn OMT Ex(Ex E