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1 Rayleigh scattering: blue sky thinking for future CMB observations arxiv: ; 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 )
3 Total cross section Photon scattering rate ν eff 8 9 c R A GHz, R He 0.1 (Lee 2005: Non-relativistic quantum calculation, for energies well below Lyman-alpha) Rayleigh only negligible compared to Thomson for n H 1+z ν obs GHz 4 ne
4 Visibility
5 Small-scale CMB Primary signal Primary + Rayleigh signal
6 Small-scale CMB cont. Hot spots are red, cold spots are blue Polarization is scattered and is red too Rayleigh difference signal: (photons scattered in to line of sight) (scattered out) τ R ΔT very correlated to primary ΔT
7 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 (possibly 5σ with Planck full mission) 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 Test of expansion and ionization history at recombination
8 Large-scale CMB 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 Rayleigh scattering probes Doppler terms independently of SW/ISW
9 Measure new primordial modes with Rayleigh Rayleigh spectrum? In principle could double number of modes compared to T+E! BUT: signal highly correlated to primary on small scales; need the uncorrelated part Solid: Rayleigh Rayleigh total; Dashed: uncorrelated part; Dots: error per Δl = 10 bin a from PRISM l
10 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
11 Three nearly-independent perturbation modes being probed ΔT T + Φ + ISW (anisotropic redshifting to constant temperature recombination surface) n v b : Doppler Polarization from quadrupole scattering Primary Rayleigh, Primary Rayleigh, Primary
12 Rayleigh polarization power spectra Solid: primary Dashed: primary + Rayleigh (857GHz) Large-scale polarization from scattering into the line of sight polarized CMB sky is blue but same quadrupole, so highly correlated to primary
13 Fractional total C l differences at realistic frequencies TT, EE, BB: ΔC l C l TE: TE ΔC l C l EE C l TT
14 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 Need sensitivity at 200GHz ν 800GHz (+probably higher for foreground separation efficiency; very hard above 350GHz from ground)
15 Conclusions Significant Rayleigh signal at ν 200 GHz; several percent on T, E at ν 500GHz Non-blackbody signal in the anisotropies (but no spectral distortion in monopole) Strongly correlated to primary signal on small scales (mostly damping) robust detection via cross-correlation? Powerful test of recombination physics/expansion Boosts large-scale polarization (except B modes from lensing) Multi-tracer probe of last-scattering - limited by noise/foregrounds, not cosmic variance May be able to provide additional primordial information (10,000+ modes) - mostly horizon-scale T modes at recombination from Doppler signal Questions: How well can foregrounds be removed/how large is uncorrelated foreground noise? (CIB, dust..) Could a relatively low-res FTS in space measure the extra modes? What about using information in line resonances? Backreaction effect of resonant couplings on baryon flow? Rayleigh-T-T bispectrum may be more sensitive to secondaries from sub-horizon dynamics?
16
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