Forecasts and Simulations for Relativistic Corrections to the Sunyaev-Zeldovich Effect

TL;DR

The paper develops a fast, halo-based painting approach to generate full-sky relativistic SZ (rSZ) maps within the Websky framework and uses these maps to forecast what a Simons Observatory–like survey can learn about cluster temperatures. By expanding the rSZ signal around a trial temperature and applying constrained component separation, the authors forecast high-significance measurements of mean cluster temperatures from stacked clusters and explore the temperature–mass–redshift relation, including degeneracies with normalization. They find that rSZ measurements are sensitive to the thermal history of intracluster gas and can complement X-ray data, but robust results require careful control of instrumental systematics (notably passband frequencies) and accurate mass/redshift information. The work provides a practical toolkit for pipeline validation, method development, and forecasting of rSZ science for upcoming CMB surveys, with implications for understanding AGN feedback and gas thermodynamics across cosmic time.

Abstract

The Sunyaev-Zeldovich (SZ) effect is a window into the astrophysical processes of galaxy clusters, and relativistic corrections (the "rSZ") promise to provide a global census of the gas feedback within clusters. Upcoming wide-field millimeter-wave surveys such as the Simons Observatory (SO), Fred Young Submillimeter Telescope, and CMB-S4 will make increasingly precise measurements of the SZ effect and its relativistic corrections. We present simulated full-sky maps of the rSZ effect and a fast code to generate it, for use in the development of analysis techniques and pipelines. As part of the websky simulation suite, our mock observations have semi-realistic cross-correlations with other large-scale structure tracers, offering insights into the formation and evolution of galaxy clusters and large-scale structure. As a demonstration of this, we examine what an SO-like experiment can learn from the rSZ effect. We find that high significance detections will be possible, provided that the instrumental systematics are under control, and that the evolution of cluster temperatures with mass and redshift can be probed in a manner complementary to X-ray measurements.

Figures (11)

• Figure 1: The spatially independent intensity change resulting from rSZ profiles with different temperatures, including the tSZ equivalent (k$_B$T$_e=0$). We see the largest differences in these profiles near the peak frequency ($\approx$ 350 GHz). Note, as electron temperature increases, the profile is dampened and its peak frequency is shifted to larger values. The coloured bands here represent the frequency bands of Simmons Observatory, and the grey bands represent the upcoming CCAT/FYST.
• Figure 2: Comparison of the rSZ signal from a single massive cluster as a function of distance from the cluster center, in arcminutes, using different mass-to-temperature scaling relationships. The mass-to-temperature scalings are obtained from fits to clusters from the BAHAMAS$+$MACSIS, IllustrisTNG, MAGNETICUM, and THE THREE HUNDRED PROJECT simulations. Inset provides a zoomed-in view for clarity. These profiles were generated for a frequency of $400$ GHz, a mass of $1.79\times10^{15} \mathrm{M}_\odot$, and $z = 0.4$. For comparison, the non relativistic tSZ effect, and the rSZ with a self-similar temperature are shown as dashed black and purple lines respectively.
• Figure 3: Visualization of a painted map covering a small cutout region of the sky, spanning $6^\circ \times 9^\circ$ in area. The maps are constructed using a Clenshaw-Curtis variant workspace. Lettered panels illustrate the following: a) The thermal SZ (tSZ) signal, b) The difference between the tSZ and relativistic SZ (rSZ) signals, c) The kinematic SZ (kSZ) signal, d) The difference between the combined tSZ $+$ kSZ signals and the rSZ signal. Since visual differences between the tSZ/kSZ and rSZ signals are not expected, plotting the difference enables inspection of regions with the greatest variance. As anticipated, notable differences are observed primarily within the largest galaxy clusters. These maps were calculated using a frequency of 280 GHz.
• Figure 4: Full sky simulated map of the rSZ traced as a temperature deviation from the CMB temperature. This figure was plotted using an HEALPix projection and was calculated at a frequency of 353 GHz.
• Figure 5: We apply the "spectroscopic" method to a sample of clusters in simulated SO-like data. This method uses the relativistic corrections to measure the the Compton-$y$ weighted difference between the true cluster signal and a trial temperature, $\bar{T}_e$. When the trial temperature is above (below) the true temperature, a negative (positive) residual is seen. A null is seen when the trial temperature matches the cluster temperature, as given by the rSZ spectral signature. The simulations in \ref{['fig:sims_SZ']} contain the non-relativistic thermal SZ effect and those in \ref{['fig:sims_rSZ']} use the relativistic tSZ simulations developed in this paper. The non-relativistic simulations favour zero temperature, as is expected as they lack the rSZ signal, whilst the measurements on the relativistic simulations show evidence for a non-zero temperature.