Forecasting Angular Cross Correlations Between Diffuse X-ray Emission
  and the Thermal Sunyaev-Zel'dovich Effect
  X-ray emission and the thermal Sunyaev-Zel'dovich distortion to the Cosmic
Microwave Background are two important handles on the gas content of the
Universe. The cross-correlation between these effects eliminates noise bias and
reduces observational systematic effects. Using analytic models for the cluster
profile, we develop a halo model formalism to study this cross-correlation and
apply it to forecast the signal-to-noise of upcoming measurements from eROSITA
and the Simons Observatory. In the soft X-ray band (0.5--2 keV), we forecast a
signal-to-noise of 174 for the cross-power spectrum. Over a wide range of the
scales, the X-rays will be signal-dominated, and so sample variance is
important. In particular, non-Gaussian (4-point) contributions to the errors
highlight the utility of masking massive clusters. Masking clusters down to
$10^{14}\ M_\odot$ increases the signal-to-noise of the cross-spectrum to 201.
We perform a Fisher Analysis on the fitting coefficients of the Battaglia et
al. gas profiles and on cosmological parameters. We find that the cross
spectrum is most sensitive to the overall scale of the profiles of pressure and
electron density, as well as cosmological parameters $\sigma_8$ and $H_0$, but
that the large number of parameters form a degenerate set, which makes
extracting the information more challenging. Our modeling framework is
flexible, and in the future, we can easily extend it to forecast the spatial
cross-correlations of surveys of X-ray lines available to
high-energy-resolution microcalorimetry, to studies of the Warm-Hot
Intergalactic Medium, and other effects.
