Testing the thermal Sunyaev-Zel'dovich power spectrum of a halo model using hydrodynamical simulations

Statistical properties of LSS serve as powerful tools to constrain the cosmological properties of our Universe. Tracing the gas pressure, the tSZ effect is a biased probe of mass distribution and can be used to test the physics of feedback or cosmological models. Therefore, it is crucial to develop robust modeling of hot gas pressure for applications to tSZ surveys. Since gas collapses into bound structures, it is expected that most of the tSZ signal is within halos produced by cosmic accretion shocks. Hence, simple empirical halo models can be used to predict the tSZ power spectra. In this study, we employed the HMx halo model to compare the tSZ power spectra with those of several hydrodynamical simulations: the Horizon suite and the Magneticum simulation. We examined various contributions to the tSZ power spectrum across different redshifts, including the one- and two-halo term decomposition, the amount of bound gas, the importance of different masses and the electron pressure profiles. Our comparison of the tSZ power spectrum reveals discrepancies that increase with redshift. We find a 20% to 50% difference between the measured and predicted tSZ angular power spectrum over the multipole range $\ell=10^3-10^4$. Our analysis reveals that these differences are driven by the excess of power in the predicted two-halo term at low k and in the one-halo term at high k. At higher redshifts (z~3), simulations indicate that more power comes from outside the virial radius than from inside suggesting a limitation in the applicability of the halo model. We observe differences in the pressure profiles, despite the fair level of agreement on the tSZ power spectrum at low redshift with the default calibration of the halo model. In conclusion, our study suggests that the properties of the halo model need to be carefully controlled against real or mock data to be proven useful for cosmological purposes.