Reionization Revisited: Secondary CMB Anisotropies and Polarization

TL;DR

The paper revisits secondary CMB anisotropies and polarization during reionization, showing that mildly nonlinear density fluctuations yield a kinetic SZ signal that naturally extends the Vishniac effect, with potentially comparable power at arcminute scales under gas-tracing assumptions. It introduces an all-sky Limber formalism for scalar and tensor sources and derives explicit expressions for temperature and polarization spectra arising from density and ionization modulations, including patchy reionization scenarios. While secondary polarization in adiabatic CDM is predicted to be exceedingly small, the work highlights how observations of B-mode polarization can constrain the amplitude and coherence of the velocity field, and discusses the limitations and model dependencies of these signals. Overall, the study provides a comprehensive framework to quantify nonlinear secondary anisotropies and polarization, offering a pathway to glean information about reionization physics and structure formation from high-precision CMB data.

Abstract

Secondary CMB anisotropies and polarization provide a laboratory to study structure formation in the reionized epoch. We consider the kinetic Sunyaev-Zel'dovich effect from mildly nonlinear large-scale structure and show that it is a natural extension of the perturbative Vishniac effect. If the gas traces the dark matter to overdensities of order 10, as expected from simulations, this effect is at least comparable to the Vishniac effect at arcminute scales. On smaller scales, it may be used to study the thermal history-dependent clustering of the gas. Polarization is generated through Thomson scattering of primordial quadrupole anisotropies, kinetic (second order Doppler) quadrupole anisotropies and intrinsic scattering quadrupole anisotropies. Small scale polarization results from the density and ionization modulation of these sources. These effects generically produce comparable E and B-parity polarization, but of negligible amplitude (0.001-0.01 uK) in adiabatic CDM models. However, the primordial and kinetic quadrupoles are observationally comparable today so that a null detection of B-polarization would set constraints on the evolution and coherence of the velocity field. Conversely, a detection of a cosmological B-polarization even at large angles does not necessarily imply the presence of gravity waves or vorticity. For these calculations, we develop an all-sky generalization of the Limber equation that allows for an arbitrary local angular dependence of the source for both scalar and symmetric trace-free tensor fields on the sky.

Figures (12)

• Figure 1: Temperature anisotropies for the fiducial $\Lambda$CDM model with $\tau=0.1$ ($z_i=13$). The secondary density ($\delta_b$) modulated signal has been calculated under the assumption that the gas traces the dark matter. The ionization-modulated signal assumes patches of $5$ Mpc comoving size and duration of patchiness $\delta z_i/(1+z_i)=0.25$.
• Figure 2: Polarization for the fiducial $\Lambda$CDM model with $\tau=0.1$ separated into $E$ (solid lines) and $B$ (dashed lines) contributions. Secondary anisotropies from the primordial quadrupole are labeled (Prim. $Q$): (upper) homogeneous scattering; (lower) density ($\delta_b$) and ionization ($X$) modulated scattering following Fig. \ref{['fig:temp']}. For the kinematic quadrupole, the homogeneous and density modulated signals are shown; the ionization modulated and intrinsic quadrupole signals falls below this range. Note that the $B$-parity polarization induced by gravitational lensing is much larger than any of these secondary $B$ signals.
• Figure 3: Velocity-density decoupling and density nonlinearities. For the fiducial $\Lambda$CDM model the velocity and density fields decorrelate in the Vishniac calculation ($I_V^{\rm dec}/I_V \approx 1$) before the onset of nonlinearity in the density field, especially at high redshift where most of the scattering occurs.
• Figure 4:
• Figure 5: Maximal nonlinear enhancement of the Vishniac effect. Under the assumption that the gas density traces the dark matter density into the deeply nonlinear regime the Vishniac effect is significantly enhanced by nonlinearities at $\ell \ga 1000$ especially in the late reionization scenarios.