The superclustering of hot gas: cosmological sensitivity in the Websky simulations

TL;DR

The paper investigates whether constrained oriented stacks of tSZ maps around supercluster regions encode additional cosmological information beyond isotropic cross-correlations. Using nine Websky-based simulations spanning variations in $oldsymbol{ m Omega_M}$ and $oldsymbol{ m Omega_\Lambda}$ (with fixed $oldsymbol{\sigma_8(z^*)}$) and multiple gas-pressure prescriptions pasted onto halos, it analyzes multipole moments $C_m(r)$ and $S_m(r)$ of the stacked Compton-$y$ maps. It finds that cosmology variations influence both one-halo and two-halo regimes, and higher-order moments carry cosmology sensitivity similar to the monopole in some cases, while gas physics mainly modulates the isotropic signal, allowing partial degeneracy breaking when using multiple moments. Environmental selection boosts the stacked signal by factors of several but reduces sample size, highlighting a trade-off between signal strength and statistics. The work advocates incorporating oriented, multipole analyses into future SZ–galaxy studies to sharpen cosmological constraints and to probe baryon physics with upcoming surveys such as LSST and the Simons Observatory.

Abstract

Combinations of galaxy surveys and cosmic microwave background secondaries, such as the thermal Sunyaev Zeldovich (tSZ) effect, are increasingly being used to jointly constrain cosmology and astrophysical properties of the gas within and beyond halos. Standard cross-correlations measure a directionless correlation between the microwave maps and galaxy catalogs. However, more information about the cosmic web structure can be captured by summary statistics which include environmental constraints and measure oriented correlations along axes of structure, such as filaments or superclusters. This work studies the sensitivity of multipole moments of constrained oriented stacks, a directional and environmentally-dependent statistic, to variations in cosmological and astrophysical parameters. We run nine different 2.4 Gpc-per-side simulations with the Websky algorithm, varying the dark matter energy density within flat $Λ$CDM, and create mock tSZ maps with each. We also apply six different gas prescriptions, imitating AGN feedback variations, to the fiducial cosmology. We analyze oriented stacks of the tSZ signal in supercluster regions in each simulation, focusing on signal out to $\sim20$ transverse Mpc from massive ($M>5\times10^{13}~M_\odot$) halos. The cosmology variations affect anisotropic and isotropic measurements similarly, while the halo-pasted gas variations mostly affect the isotropic signal. Our results suggest it is worthwhile to incorporate directional information into SZ-galaxy cross-correlations to increase cosmological sensitivity and help break degeneracies with gas physics.

Figures (11)

• Figure 1: $\sigma_\mathrm{8,var}(z)'$, as defined in Eq. \ref{['eq:sigma8_var']}, for the simulated cosmologies. Each cosmology has a different growth history, but the initial power spectrum normalization has been chosen such that $\sigma_\mathrm{8}$ converges at $z=0.5$ across all simulations. The narrower, darker band spans the range from which we select the stacking halo sample ($\sim100$ Mpc) and the wider band shows the range over which halos are projected into 2D number density maps, used for environmental selections and orientations ($\sim200$ Mpc).
• Figure 2: Above: halo mass functions for Cosmo1 (left) and Cosmo2 (right) at $z=0.5$, over the mass range used. Cosmo2 exhibits smaller differences due to the fixed matter density $\Omega_{\mathrm{M}}$. Below: halo surface mass density maps, smoothed with a Gaussian filter with FWHM=10 Mpc (half of the smoothing scale used for orientation), for all variations in Cosmo1 (upper) and Cosmo2 (lower). All simulations are run with the same initial seed. All plots cover a sky region of $\sim15^{\circ}\times15^{\circ}$ (which is 500 Mpc per side in the fiducial cosmology) projected along the $200$ Mpc line-of-sight axis, centered at $z=0.5$. The data is from a lightcone run, so within the $200$ Mpc extent, there is some evolution. The 80 Mpc scale bar corresponds to the side-length of the fiducial cosmology image in \ref{['fig:omegamh2fix_stack_img']}. The comoving distance to $z=0.5$ depends on cosmology, so within adjacent Cosmo1 plots, the halos are extracted from slabs that are $\sim$30--40 Mpc offset in comoving line-of-sight distance. Thus, the structure appearing in each map varies slightly from left to right. The differences in overall mass density are visually apparent, caused by varying $\Omega_\mathrm{M} h^2$. In Cosmo2, each successive plot shows halos from a slab $\sim$100--150 cMpc offset, hence the structure appears mostly distinct between neighboring maps. However, the maps are more statistically similar due to the fixed physical matter density.
• Figure 3: Oriented stacks of Compton-$y$, centered on a sample of $M>5\times10^{13}$$M_\odot$ halos constrained by large-scale $\nu$ and $e$ thresholds, for the 5 cosmologies in Cosmo1 (above) and Cosmo2 (below). Plots are shown with a logarithmic color scale to highlight differences in the far-field from the central stacked cluster. The angular size of each image is $2.3^{\circ}\times2.3^{\circ}$ (zoomed-in from the full $4^{\circ}\times4^{\circ}$ stack), but the comoving side-length varies as shown. The $\Omega_\mathrm{M}=0.32$ stack is identical in both rows. The clear horizontal asymmetry about the $y$-axis, and subtler asymmetry about the $x$-axis, is due to the gradient-based flip in the orientation procedure (\ref{['sec:methods']}). The images reveal the projected, averaged hot gas from 3D conglomerations of halos located up to comoving distances of 40 Mpc (transverse) and 100 Mpc (line-of-sight) away from the origin in the fiducial cosmology. The signal includes a combination of correlated supercluster structure as well as some uncorrelated foreground/background structure.
• Figure 4: Radial profiles of the first several cosine multipoles $C_m(r)$ (\ref{['eq:multipole_moments']}) of the oriented stacks shown in \ref{['fig:omegamh2fix_stack_img']} for the Cosmo1 (upper) and Cosmo2 (lower) suites. The $x$ axis is the distance from the stack center; the lower axis labels show the angular coordinates, while the upper axis translates this into comoving transverse distance for only the fiducial cosmology. The leftmost plots show the mean-$y$-subtracted $m=0$ curves, representative of the information available in an unoriented stack, while all other plots show higher-order moments, which contain signal due to orientation. The fiducial $\Omega_\mathrm{M}=0.32$ simulation result is shown in bold purple. Variations in $\Omega_\mathrm{M}$ impact the $y$ signal in both the one-halo regime, near $r=0$, and beyond. The effect on Cosmo1 is stronger due to the varying physical matter density; in the one-halo regime the amplitude scales with $\sim\Omega_\mathrm{M}^{1.8}$ and beyond $r\sim4'$ scale more strongly, as $\sim \Omega_\mathrm{M}^{4.5}$. The Cosmo2 variations have a weaker $\Omega_\mathrm{M}$ dependence.
• Figure 5: Integrated multipole power for both suites of simulations. The points connected by dashed lines (for visual purposes only) show the power in each moment according to \ref{['eq:integrated_power']}. The unconnected 'x'-shaped markers show the power for each moment from an unoriented stack for reference; only the $m=0$ moment has significant signal, which is identical to the oriented stack $m=0$ (blue), as expected. Any power in higher-order moments of the unoriented stacks can be thought of as noise power in the corresponding moment from the oriented stack. In both Cosmo1 and Cosmo2, the higher order moments of the oriented stack hold information that could be used to distinguish between the simulations, although the Cosmo2 case is more subtle.