The X-Ray Background as a Probe of Density Fluctuations at High Redshift

TL;DR

This paper predicts large-scale angular fluctuations in the X-ray background to probe high-redshift density fluctuations, analyzing effects like structure and observer motion, and compares predictions with observations.

Contribution

It introduces a formalism to predict XRB fluctuations from density fluctuations, considering effects like the dipole and harmonic spectrum, and compares with observational data.

Findings

The predicted dipole amplitude matches HEAO1 XRB measurements.

The harmonic spectrum declines with multipole l as l^{-0.4}.

Sachs-Wolfe and Doppler effects are negligible in the XRB.

Abstract

The X-Ray Background (XRB) probes structure on scales intermediate between those explored by local galaxy redshift surveys and by the COBE Microwave Background measurements. We predict the large scale angular fluctuations in the XRB, expressed in terms of spherical harmonics for a range of assumed power-spectra and evolution scenarios. The dipole is due to large scale structure as well as to the observer's motion (the Compton-Getting effect). For a typical observer the two effects turn out to be comparable in amplitude. The coupling of the two effects makes it difficult to use the XRB for independent confirmation of the CMB dipole being due to the observer's motion. The large scale structure dipole (rms per component) relative to the monopole is in the range $a_{1m}/a_{00} \sim (0.5-9.0) \times 10^{-3} $. The spread is mainly due to the assumed redshift evolution scenarios of the X-ray volume emissivity $\rho_x(z)$. The dipole's prediction is consistent with a measured dipole in the HEAO1 XRB map. Typically, the harmonic spectrum drops with $l$ like $a_{lm} \sim l^{-0.4}$. This behaviour allows us to discriminate a true clustering signal against the flux shot noise, which is constant with $l$, and may dominate the signal unless bright resolved sources are removed from the XRB map. We also show that Sachs-Wolfe and Doppler (due to the motion of the sources) effects in the XRB are negligible. Although our analysis focuses on the XRB, the formalism is general and can be easily applied to other cosmological backgrounds.