Polarized Foregrounds and the CMB Al Kogut/GSFC

Polarized Foregrounds and the CMB Al Kogut/GSFC

The Problem In A Nutshell Galactic foregrounds are 2 orders of magnitude brighter than primordial B-mode polarization from 30 to 200 GHz

Polarized vs Unpolarized Sky Cross-variance, diagonal elements only Unpolarized Emission Higher signal (better S/N ratio) Component confusion important CMB, synchrotron, free-free, thermal dust, spinning dust, Polarized Emission Fewer components, but lower S/N Synchrotron, thermal dust, CMB No evidence (yet) for more components "Best" component separation algorithm depends on what question you ask

Synchrotron: Status and Issues T Q s ( nˆ, υ) = T P s ( nˆ, υ γ ( ˆ 0 ) cos2 n) υ υ 0 βs nˆ) + C( nˆ) log( υ / υ ) ( 0 T P s ( nˆ, υ0) γ (nˆ) β s (nˆ) C(nˆ) Morphology at reference frequency Polarization angle (magnetic field) Spectral index Spectral curvature Parameters model superposition of emission along line of sight

Polarized Synchrotron: Status & Issues Morphology Large Angular Scales: WMAP 5-yr Data Reasonable S/N ratio at 22 GHz 4 pixels: S/N > 3 over 90% of sky Measure power spectrum to l ~ 100 Fractional Polarization Few percent in plane, larger at high lat Depolarization via line-of-sight effects Confusion from unpolarized stuff Kogut et al. 2007, ApJ, 665, 355

Polarized Synchrotron: Status & Issues Spectral Index Just beginning to measure β s (nˆ) Flatter in plane, steeper at high lat Limited by S/N in polarization Limited by confusion in intensity Gold et al. 2008, arxiv:0803:0715 Room for Improvement: S/N in polarization Confusion: Multiple components along same line of sight Cosmic ray connection (GALPROP project) Dobler & Finkbeiner 2007, arxiv:0712:1038

Polarized Synchrotron: Status & Issues Small-Scale Features Spectral curvature Interferometric maps at low frequencies No convincing detection yet Heavily contaminated by Faraday rotation Expected from cosmic ray data Waiting for sensitive mm-wave survey Curvature variation across sky? DRAO 1.4 GHz polarization Wolleben et al. 2006, A&A, 448, 411

Dust: Status and Issues T Q d ( nˆ, υ) = k w i= 1 i ε ( nˆ, υ) i cos2γ d ( nˆ) κ i υ υ 0 βi B υ ( T i ( nˆ)) T i (nˆ) ε ( nˆ, υ) i γ d (nˆ) β i κ i wi Dust temperature Fractional polarization Polarization angle (magnetic field) Spectral index Emissivity Weight (normalization) Admixture of species and emitting regions along line of sight

Polarized Dust: Status & Issues Large-Scale Morphology Q Large Angular Scales: WMAP 5-yr Data Low S/N at high latitude 4 pixels: S/N < 2 over 97% of sky Fractional Polarization Few percent in plane (depolarized) 2--4% at higher latitudes U Dunkley et al. 2008, arxiv:0803.0586

Q Polarized Dust: Status & Issues Small-Scale Morphology Small Angular Scales: ARCHEOPS Low S/N at high latitude Fractional polarization ~5% at 345 GHz New Dust Measurements Coming Soon U Planck HFI: 100, 143, 217, 353 GHz EBEX: 150, 250, 350, 450 GHz SPIDER: 100, 150, 220 GHz which brings up the question of spectra... -100 +100 μk Ponthieu et al. 2005, A&A, 444, 327

Polarized Dust: Status & Issues Frequency Dependence: Stokes I FDS Model Based on COBE Data Single Component Dust Emission / ν 2 B ν (T) <T> = 18.1 K, β=2.0 β=2.2 is better for ν < 300 GHz Two Components <T 1 > = 9.4 K, β 1 =1.7 <T 2 > = 16.2 K, β 2 =2.7 But χ 2 /DOF = 1.85 for best model Frequency (GHz) Finkbeiner, Davis, & Schlegel 1999, ApJ, 524, 867 Clearly an approximation!

Polarized Dust: Status & Issues Frequency Dependence: Fractional Polarization Molecular Clouds: Minimum near 350 GHz Different (local) environments Different dust species Vaillancourt 2002, ApJ, 142, 53 Fractional Polarization Warm Component Diffuse Cirrus: Monotonic change Same environment, different species Cold Component Hildebrand & Kirby 2004, ASP Conf Series 309, 515

Polarized Dust: Status & Issues Polarization Angle Polarization Angle γ (nˆ) Red: Heiles dust absorption Black: WMAP synchrotron Dust γ (nˆ) mostly traces synchrotron Differences are real & significant Heiles 2000, AJ, 119, 923 Page et al. 2007, ApJS, 170, 335, 327 Kogut et al. 2007, ApJ, 665, 355 Dust/Synchrotron Correlation

Foreground Cleaning Methods Template Cleaning Linear Combinations Pixel-By-Pixel Models

Template Methods T υ = T cmb k + i=1 υ α i X i + n Fit sky maps T υ at m frequency channels to set of k template maps X υ α i free or with fixed spectral index Advantages Handful of fitted parameters Good for low S/N maps Retains simple noise properties Full use of template spatial structure Can fit more templates than channels Disadvantages No unique component identification Non-negligible parameter covariance Assumes spatially invariant spectra Need template for each component

A Sampling of Template Maps Synchrotron Free-Free Haslam 408 MHz Finkbeiner Hα Map Thermal Dust WMAP K-Ka (I Map) FDS Model 8 Negligible Noise Penalty for Extra Templates WMAP K-band (Pol) "Spaghetti Fitting": Throw everything at the data and see what sticks

Cleaning Regimes Temperature Analysis: Signal-Dominated Light cleaning of weak foreground High signal-to-noise ratio per pixel E-Mode Polarization: Foreground-Dominated Modest cleaning of bright foregrounds Modest signal-to-noise ratio per pixel B-Mode Polarization: Foreground-Dominated Deep cleaning of bright foregrounds Low signal to noise ratio per pixel Require cleaning by factor of ~20

Deep Cleaning Example Cosmic Infrared Background Sky Channel Maps C+ (HI) 2 HI Dominant Galactic foreground 3 Spatial templates per channel Clean foregrounds by factor of 10 despite similar spectral shape Intensity (MJy/sr) Fixsen et al. 1998, ApJ, 508, 123 2000 500 250 167 125 100 Wavelength (μm)

Linear Combinations T = w i y i Choose w i to minimize sky variance subject to constraint ILC Map Sky Regions Monte Carlo Residuals -200 +200 μk Caveats w i Input maps smoothed to 1 FWHM, creating off-diagonal noise elements CMB/foreground covariance introduces (small) bias 2 2 2 2 σ ILC = σcmb σcf / σ fg Correct bias via Monte Carlo sims Residuals < 5 μk for θ > 10, but noise properties are complex =1-15 +15 μk Hinshaw et al. 2007, ApJS, 170, 288 Gold et al. 2008, arxiv:0803.0715

T Harmonic Filtering Replace pixel basis with spherical harmonics (or other basis set) = w y i i a lm i l = w Choose weights at each l to minimize sky variance, with wl i =1 1 C e w l = l ij i* j t e Cl 1 with Cl = alm alm computed from maps e a i lm i l B ILC Harmonic Advantages No smoothing (better resolution) Scale-dependent noise suppression Disadvantages Galactic plane contributes at all l Foreground leakage at smallest scales Iterative solution required Tegmark et al. 2003, PRD, 68, 123523

Principal Component Separation Define k (dimensionless) maps Diagonalize to get R = PΛP z = i y i t / σ with eigenmaps i with moment matrix a = P t z R ij = z i z t j Advantages Broadly applicable "blind" technique Number of "important" components Spatial maps of each component First few eigenmodes explain most of sky variance Disadvantages Eigenmaps Physical foregrounds Not great for low S/N components Valuable cross-check on other methods to determine number of foreground components De Oliveira-Costa et al. 2008, arxiv:0802.1525

Pixel-By-Pixel Techniques Explicitly model amplitude and frequency dependence T ( nˆ, Synchrotron: β -2.9 Thermal Dust: β +2.0 Advantages Explicit connection to astrophysics Allows constraints on spectral indices β i v υ i Ti n v ) = ( ˆ) 0 Disadvantages Non-linear fits parameter runaway Non-trivial component covariance Requires more channels than components Not an orthogonal frequency basis! Component CMB Synchrotron Total Worst-Case Parameter Count Thermal Dust Param 2 4 6 12 Notes Q, U (spectrum known) Q, U, β, Curvature Q, U, β for warm & cold components Excludes free-free or spinning dust "Some pixels are bigger than others"

Sometimes, adding a few choices Dust Emission Synch Free-Free

Can make a simple situation complicated! Synchrotron HARD SOFT Thermal Dust Haze QU I Anomalous Emission Free-Free

Fitting The Spectral Index Log(T) Noise easily leads to unphysical values for β Low S/N Small channel separation Multiple foreground components Sim: 7 Channels 25--38 GHz, Input = Synch + FF Model = Synch + FF Log(ν) Possible Solutions To Problem: Add More/Better Channels Use bigger pixels Impose Priors Fit "Effective" Index Residual Error (μk) Model = One "Radio" Component Instrument Noise (μk) Brandt et al. 1994, ApJ, 424, 1

Pixel-By-Pixel Fit to Polarization Maps + f d ( n) T d ( nˆ) cos(2 β ( ˆ) log( / ) ( / ) s n + C υ υ υ υk β γ d ( nˆ)) ( υ / υ ) d W β ( ˆ) log( / ) ( / ) s n + C υ υ υ υk β γ ( nˆ)) ( υ / υ ) d Q( nˆ, υ) = P ( nˆ) cos(2γ ( nˆ)) K + s f d ( n) T d s U ( nˆ, υ) = P ( nˆ) sin(2γ ( nˆ)) K With free parameters s s ( nˆ) sin(2 d W P s (nˆ) γ s (nˆ ) β s (nˆ) C f d (n) β d γ d (nˆ) T d (nˆ) Polarized synchrotron amplitude, P = (Q 2 + U 2 ) 1/2 Synchrotron polarization angle Synchrotron spectral index (flat prior -4 < β < -2) Synchrotron spectral curvature Dust fractional polarization Dust spectral index (fixed at +2.0) Dust polarization angle (fixed by starlight model) Dust intensity (fixed by FDS model 8) Fit β s (nˆ) and f d (n) in bigger pixels!

Pixel-by-Pixel Polarized Model Synchrotron Spectral Index f d (n) = 0.010 ± 0.004 in plane 0.036 ± 0.011 outside P06 mask Kogut et al. 2007, ApJ, 665, 355

Fitting Intensity + Polarization Problem: Polarization adds ~6 more parameters T cmb, T s, T ff, T d β s, β ff, β d, Q cmb, U cmb, Q s, U s, Q d, U d "Brute-Force" techniques become inefficient Look to parameter-fitting algorithms to insert into pixel-by-pixel machinery Markov Chain Monte Carlo Gibbs Sampling

Markov Chain Monte Carlo Techniques WMAP 5-year IQU data Nside=64 (0.9 pixels) 10 parameters per pixel T cmb, T s, T ff, T d, β s, β d, Mean Best-Fit Point Q s, Q d, Q cmb, U cmb Fix β ff = -2.14 Fix synch and dust polarization angle using K-band data Get parameter values, errors, and covariance for each pixel Gold et al. 2008, arxiv:0803.0715

Foreground Status Cleaning "machinery" under control Algorithms exist and work as advertised Multiple methods yield consistent results No sign yet of any ultimate limit Astrophysics not quite there yet Just starting to map polarized foregrounds Considerable uncertainty in fitted parameters Biggest need is more data!

Implications for Technology

Foregrounds and Frequency Bands Channel placement vs foreground component Synchrotron Low frequency (ν < 40 GHz) Dust High frequency (ν > 250 GHz) Limiting factor likely to be real estate in focal plane Low frequency channels are expensive! External synchrotron data (WMAP, Planck) Foreground spectra smooth and (probably) monotonic Only need high S/N for internal templates Many bands with fewer detectors/band? With seven free parameters, you can fit a charging rhino

Decision Tree Science Goal CMB Astrophysics Detection Characterization Maximize S/N in few bands Limited number of bands Heavy use of external data Template cleaning Clear CMB/FG separation Broad frequency coverage Large number of bands Multiple cleaning techniques Good S/N in FG bands Broad frequency coverage Modest number of bands Pixel-by-pixel cleaning

Counting Coup Bands Optimist: My glass is half full B-mode detection needs just 3 bands Pessimist: My glass is half empty B-mode detection needs >9 bands NASA: My glass has 50% contingency! Fly more bands than you think you need