Gauging the Contribution of X-ray Sources to Reionization Through the Kinetic Sunyaev-Zel'dovich Effect

Measurements of the kinetic Sunyaev-Zel'dovich (kSZ) effect from instruments such as the South Pole Telescope (SPT) and the Atacama Cosmology Telescope (ACT) will soon put improved constraints on reionization. Popular models assume that UV photons alone are responsible for reionization of the intergalactic medium. We explore the effects of a significant contribution of X-rays to reionization on the kSZ signal. Because X-rays have a large mean free path through the neutral intergalactic medium, they introduce partial ionization in between the sharp-edged bubbles created by UV photons. This smooth ionization component changes the power spectrum of the cosmic microwave background (CMB) temperature anisotropies. We quantify this effect by running semi-numerical simulations of reionization. We test a number of different models of reionization without X-rays that have varying physical parameters, but which are constrained to have similar total optical depths to electron scattering. These are then compared to models with varying levels of contribution to reionization from X-rays. We find that models with more than a 10% contribution from X-rays produce a significantly lower power spectrum of temperature anisotropies than all the UV-only models tested. The expected sensitivity of SPT and ACT may be insufficient to distinguish between our models, however, a non-detection of the kSZ signal from the epoch of reionization could result from the contribution of X-rays. It will be important for future missions with improved sensitivity to consider the impact of X-ray sources on reionization.Comment: 11 pages, 4 figures, modified to reflect updated SPT error bars, submitted to JCA

A coordinate-free approach to multivariate exponential families

We apply the invariant umbral calculus to obtain a coordinate-free approach to multivariate exponential families

DX-operator expansion

We characterize those linear operators that can be expressed as a sum over k of terms of the form f_k(D) x^k and give several examples

Sequences of binomial type with persistent roots

We find all sequences of polynomials (pn)n¿0with persistent roots (i.e.,pn(x)=cn(x-r1)(x-r2)···(x-rn)) that are of binomial type in Viskov's generalization of Rota's umbral calculus to generalized Appell polynomials. We show that such sequences only exist in the classical umbral calculus, the divided difference umbral calculus, and the new "hyperbolic" umbral calculus generated by[formula]. In each of these three umbral calculi, we also find all Sheffer sequences with persistent roots

Umbral calculus in Hilbert space

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