cmb polarization from rayleigh scattering - antony lewis
TRANSCRIPT
Polarization from Rayleigh scatteringBlue sky thinking for future CMB observations
Antony Lewis
http://cosmologist.info/
http://en.wikipedia.org/wiki/Rayleigh_scattering
Previous work: Takahara et al. 91, Yu, et al. astro-ph/0103149
Thomson Scattering
๐โ ๐โ
Rayleigh Scattering
๐+
Classical dipole scattering
Frequency independentGiven by fundamental constants:
๐๐ =8๐
3
๐2
4๐๐0๐๐๐2
2
Frequency dependentDepends on natural frequency ๐0 of target
๐๐ โ๐4
๐04 ๐๐
Both dipole scattering: same angular and polarization dependence (Boltzmann equations nearly the same)
Oscillating dipole ๐ = ๐0 sin(๐๐ก) ๐ โ radiated power โ ๐4๐02 sin2 ๐ dฮฉ
๐๐ ๐ง = โ๐๐ธ๐ง sin๐๐ก
โ ๐ =โ๐2๐ธ๐ง
๐๐๐2 sin ๐๐ก ๐
๐๐ ๐ง = โ๐๐ธ๐ง sin ๐๐ก โ ๐๐๐0z
โ ๐ =โ๐2๐ธ๐ง
๐๐(๐2โ๐0
2)sin ๐๐ก ๐
(๐nucleus โซ ๐๐)
(๐ โช ๐0)
http://farside.ph.utexas.edu/teaching/em/lectures/node95.html
Rayleigh scattering details
After recombination, mainly neutral hydrogen in ground state:
Early universe โ Neutral hydrogen (+small amount of Helium)
(Lee 2005: Non-relativistic quantum calculation, for energies well below Lyman-alpha)
๐eff โก8
9c RA โ 3.1 ร 106GHz
Only negligible compared to Thomson for ๐๐ป1+๐ง ๐obs
3ร106GHz
4โช ๐๐
Scattering rate
Total cross section โ
(๐ ๐ป๐ โ 0.1)
Visibility
In principle Rayleigh scattering could do tomography of last scattering and beyond
Expected signal as function of frequencyZero order: uniform blackbody not affected by Rayleigh scattering (elastic scattering, photons conserved)
1st order: anisotropies modified, no longer frequency independent
May be detectable signal at 200GHz โค ๐ โค 800GHz
Effects of Rayleigh scattering
โข Moves total visibility to lower redshift: larger sound horizon, so shift in peak scales
โข Total visibility function broader: additional scattering to lower redshifts โ more Silk damping
โข More total baryon-photon coupling:frequency independent longer tight coupling (< 0.04% - neglect)
Yu, Spergel, Ostriker, astro-ph/0103149
Rayleigh signal
Total (frequency ๐) = primary blackbody + Rayleigh signal
๐, ๐ โ {๐, ๐ธ, ๐ต}
Gaussian sky at multiple frequencies: sufficient statistics are
Sachs-Wolfe Doppler ISWTemperature perturbation atrecombination(Newtonian Gauge)
Large scales
Rayleigh signal only generated by sub-horizon scattering(no Rayleigh monopole background to distort by anisotropic photon redshifting)
Polarization
Generated by scattering of the blackbody quadrupole: similar to primary, but larger sound horizon
Temperature
Small scales
Primary signal Primary + Rayleigh signal
Rayleigh difference signal: photons scattered in to line of sight - scattered outโผ ๐๐ ฮ๐
Hot spots are red, cold spots are blue
Polarization is scattered and is red too
Not my pictureโฆ lost credit
Rayleigh temperature power spectrum
Solid: Rayleigh ร PrimaryDot-dashed: Rayleigh ร Rayleigh
Small-scale signal is highly correlatedto primary
Dots: naรฏve Planck sensitivity to the crossper ฮ๐/๐ = 10 bin
Can hope to isolate usingLow frequency ร High frequency
Note: not limited by cosmic variance of primary anisotropy โ multi-tracer probe of same underlying perturbation realization
Primary+Rayleigh 2 = Primary2 + 2 Primary ร Rayleigh + Rayleigh2
Rayleigh polarization power spectra
Solid: primary Dashed: primary + Rayleigh (857GHz)
Fractional differences at realistic frequencies
TE:TT, EE, BB: ฮ๐ถ๐๐ถ๐
ฮ๐ถ๐๐๐ธ
๐ถ๐๐ธ๐ธ๐ถ๐
๐๐
Detectability
Blue sky thinking โก ignore foregrounds
S/N per ๐ for primary ร 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 20๐ (several channels)
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
Solid: Rayleighร Rayleigh total; Dashed: uncorrelated part; Dots: error per ฮ๐
๐= 10 bin a from PRISM
TT EE
Rayleigh-Primary correlation coefficient
Scattering from same quadrupoleRayleigh only from sub-horizon (mainly Doppler)
Damping of the primary
Number of new modes with PRISM
New modes almost all in the ๐ โค 500 temperature signal: total โ 10 000 extra modes
More horizon-scale information (disentangle Doppler and Sachs-Wolfe terms?)
Would need much higher sensitivity to get more modes from polarization/high ๐
Define
Primary
Large scale ฮ๐
๐+ฮฆ+ ISW
(anisotropic redshifting to constant temperature recombination surface)
Doppler(Rayleigh, Primary)
Large scale n โ vb: Doppler
Polarization(Rayleigh, Primary)
Three different perturbation modes being probed
Large scale quadrupole scattering
โข Significant Rayleigh signal at ๐ โฅ 200 GHz; several percent on T, E at ๐ โฅ 500GHz
โข Strongly correlated to primary signal on small scales (mostly damping)โ robust detection via cross-correlation?
โข Multi-tracer probe of last-scattering - limited by noise/foregrounds, not cosmic variance
โข Boosts large-scale polarization (except B modes from lensing)
โข Must be modelled for consistency
โข Powerful consistency check on recombination physics/expansion
โข May be able to provide additional primordial information - mostly large-scale modes at recombination?
Conclusions
Question:
How well can foregrounds be removed/how large is uncorrelated foreground noise? (CIB, dust..)