Nonlinear Kinetic Sunyaev-Zeldovich Effect

Abstract

We derive fully nonlinear expressions for temperature fluctuations from the kinetic SunyaevZeldovich effect, the scattering of cosmic microwave background (CMB) photons off hot electrons in bulk motion. Our result reproduces the Ostriker-Vishniac effect to second order in perturbation theory but contains important nonlinear contributions from the electron velocities and densities that were neglected previously. We use the recently developed halo model for nonlinear gravitational clustering to compute the nonlinear CMB power spectrum, which dominates the primary anisotropy on small angular scales.PACS numbers: 98.80. Es, 98.65.Dx, 98.70.Vc Introduction.-Scattering of cosmic microwave background (CMB) photons from hot electrons in galaxies and clusters changes the apparent brightness of the CMB, inducing anisotropies in the observed temperature, the SunyaevZeldovich (SZ) effect [1]. The kinetic SZ effect due to scattering off ionized matter in bulk peculiar motion can be separated from the thermal SZ effect due to electron pressure by its different dependence on photon frequency; in particular, the kinetic effect dominates at frequencies around 218 GHz where the thermal effect vanishes. These foreground contributions are overwhelmed by primary anisotropies for spherical harmonic index smaller than a few thousand but can dominate at higher .The kinetic SZ effect vanishes at leading order in perturbation theory for small inhomogeneities [2,3] (see below). At second order, however, it generates temperature fluctuations on arcminute angular scales, as first pointed out by Ostriker and Vishniac (OV) [4,5]. The OV power spectrum has since been studied in some detail [6][7][8][9][10][11]. In this letter we investigate analytically the fully nonlinear effect, which has not been much studied previously but is potentially important because reionized material in the low-redshift universe mostly resides in collapsed, high density objects. Our analytical approach complements recent kinetic SZ studies with hydrodynamical simulations [12] and helps to provide physical insight into why simulation results differ greatly on small scales.The fractional temperature distortion due to the kinetic SZ effect along the line-of-sight unit vectorγ is

Beyond the Damping Tail: Cross‐Correlating the Kinetic Sunyaev‐Zel’dovich Effect with Cosmic Shear

“…Thus, in the high-k limit the integrand is significant only for qTk, and we can drop terms of order O(q/k). A similar approximation has been used previously to calculate the mode coupling integrals for the kSZ power spectrum (Hu 2000a;Ma & Fry 2002;Cooray 2001a). In this approximation T 3 ¼ T 1 , and we get, introducing the dimensionless power spectra Á 2 T and Á 2 nl ,…”

“…At second order in perturbation theory, this is known as the Ostriker-Vishniac effect (Ostriker & Vishniac 1986;Vishniac 1987;Dodelson & Jubas 1995;Hu & White 1996), whereas the full nonlinear signal is referred to as the kSZ effect. This full nonlinear contribution has been studied in detail both analytically (Hu 2000a;Ma & Fry 2002;Zhang, Pen, & Trac 2004) and numerically (Gnedin & Jaffe 2001;Springel, White, & Hernquist 2001;da Silva et al 2001;Zhang et al 2004).…”

“…Here we proceed by analogy with previous analytical studies of the kSZ power spectrum. The power spectrum of the radial momentum component is Hu (2000a) and then the joint numerical and analytical work of Ma & Fry (2000) suggested that the dominant contribution comes from nonlinear densities coupling to linear bulk velocity flows. Furthermore, because of the cancellations that occur in the projection (Kaiser 1984), only the curl component of the projected momentum p, i.e., the component perpendicular ton in the Fourier domain that we thus denote p ?…”

“…Then we can write for the power spectrum of the radial momentum component pn (Hu 2000a;Ma & Fry 2000) where P p ? p ?…”

“…. This assumes that the dominant contribution to the power spectrum of the radial momentum comes from nonlinear densities coupling to linear bulk velocity flows (Hu 2000a;Ma & Fry 2002; although see also Zhang et al 2004). The right panel of Figure 2 shows the three-dimensional autopower spectrum P pnpn at z ¼ 0:5.…”