Polarization from Rayleigh scattering

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Brent McLaughlin
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91, Yu, et al. astro-ph/0103149 http://en.wikipedia.

1 Polarization from Rayleigh scattering Blue sky thinking for future CMB observations Previous work: Takahara et al. 91, Yu, et al. astro-ph/ Antony Lewis

2 Classical dipole scattering Oscillating dipole p = p 0 sin(ωt) z radiated power ω 4 p 0 2 sin 2 θ dω Thomson Scattering m e z = ee z sin ωt p = e2 E z m e ω2 sin ωt z Rayleigh Scattering m e z = ee z sin ωt m e ω 0 z e 2 E z p = m e (ω 2 ω 2 sin ωt z 0 ) (m nucleus m e ) p + e e Frequency independent Given by fundamental constants: Frequency dependent Depends on natural frequency ω 0 of target σ T = 8π 3 e 2 4πε 0 m e c 2 2 σ R ω4 ω 0 4 σ T (ω ω 0 ) Both dipole scattering: same angular and polarization dependence (Boltzmann equations nearly the same)

3 Rayleigh scattering details Early universe Neutral hydrogen (+small amount of Helium) After recombination, mainly neutral hydrogen in ground state: (Lee 2005: Non-relativistic quantum calculation, for energies well below Lyman-alpha) ν eff 8 9 c R A GHz Only negligible compared to Thomson for n H 1+z ν obs GHz 4 ne

4 Scattering rate Total cross section (R He 0.1)

5 Visibility In principle Rayleigh scattering could do tomography of last scattering and beyond

6 Expected signal as function of frequency Zero order: uniform blackbody not affected by Rayleigh scattering (elastic scattering, photons conserved) 1 st order: anisotropies modified, no longer frequency independent May be detectable signal at 200GHz ν 800GHz

7 Effects of Rayleigh scattering Moves total visibility to lower redshift: larger sound horizon, so shift in peak scales Total visibility function broader: additional scattering to lower redshifts more Silk damping More total baryon-photon coupling: frequency independent longer tight coupling (< 0.04% - neglect) Yu, Spergel, Ostriker, astro-ph/

8 Rayleigh signal Total (frequency i) = primary blackbody + Rayleigh signal X, Y {T, E, B} Gaussian sky at multiple frequencies: sufficient statistics are

9 Large scales Temperature Rayleigh signal only generated by sub-horizon scattering (no Rayleigh monopole background to distort by anisotropic photon redshifting) Temperature perturbation at recombination (Newtonian Gauge) Sachs-Wolfe Doppler ISW Polarization Generated by scattering of the blackbody quadrupole: similar to primary, but larger sound horizon

10 Small scales Primary signal Primary + Rayleigh signal Rayleigh difference signal: photons scattered in to line of sight - scattered out τ R ΔT

11 Not my picture lost credit Hot spots are red, cold spots are blue Polarization is scattered and is red too

12 Rayleigh temperature power spectrum Primary+Rayleigh 2 = Primary Primary Rayleigh + Rayleigh 2 Solid: Rayleigh Primary Dot-dashed: Rayleigh Rayleigh Dots: naïve Planck sensitivity to the cross per Δl/l = 10 bin Small-scale signal is highly correlated to primary Can hope to isolate using Low frequency High frequency Note: not limited by cosmic variance of primary anisotropy multi-tracer probe of same underlying perturbation realization

13 Rayleigh polarization power spectra Solid: primary Dashed: primary + Rayleigh (857GHz)

14 Fractional differences at realistic frequencies TT, EE, BB: ΔC l C l TE: TE ΔC l C l EE C l TT

15 Detectability Blue sky thinking ignore foregrounds S/N per l for primary Rayleigh cross-spectra (single channel) May be just detectable by Planck; strong signal in future CMB missions e.g. PRISM: Rayleigh amplitude measured to 0.4%, EE detected at 20σ (several channels)

16 Measure new primordial modes? In principle could double number of modes compared to T+E! BUT: signal highly correlated to primary on small scales; need the uncorrelated part TT EE Solid: Rayleigh Rayleigh total; Dashed: uncorrelated part; Dots: error per Δl l = 10 bin a from PRISM

17 Rayleigh-Primary correlation coefficient Rayleigh only from sub-horizon (mainly Doppler) Scattering from same quadrupole Damping of the primary

18 Number of new modes with PRISM Define New modes almost all in the l 500 temperature signal: total extra modes More horizon-scale information (disentangle Doppler and Sachs-Wolfe terms?) Would need much higher sensitivity to get more modes from polarization/high l

19 Large scale ΔT T + Φ + ISW (anisotropic redshifting to constant temperature recombination surface) Primary

20 Large scale n v b : Doppler Doppler (Rayleigh, Primary)

21 Large scale quadrupole scattering Polarization (Rayleigh, Primary) Three different perturbation modes being probed

22 Conclusions Significant Rayleigh signal at ν 200 GHz; several percent on T, E at ν 500GHz Strongly correlated to primary signal on small scales (mostly damping) robust detection via cross-correlation? Multi-tracer probe of last-scattering - limited by noise/foregrounds, not cosmic variance Boosts large-scale polarization (except B modes from lensing) Must be modelled for consistency Powerful consistency check on recombination physics/expansion May be able to provide additional primordial information - mostly large-scale modes at recombination? Question: How well can foregrounds be removed/how large is uncorrelated foreground noise? (CIB, dust..)

Rayleigh scattering:

Rayleigh scattering: blue sky thinking for future CMB observations arxiv:1307.8148; previous work: Takahara et al. 91, Yu, et al. astro-ph/0103149 http://en.wikipedia.org/wiki/rayleigh_scattering Antony