Massive Halos in Millennium Gas Simulations: Multivariate Scaling Relations

Abstract

The joint likelihood of observable cluster signals reflects the astrophysical evolution of the coupled baryonic and dark matter components in massive halos, and its knowledge will enhance cosmological parameter constraints in the coming era of large, multi-wavelength cluster surveys. We present a computational study of intrinsic covariance in cluster properties using halo populations derived from Millennium Gas Simulations (MGS). The MGS are re-simulations of the original 500 h −1 Mpc Millennium Simulation performed with gas dynamics under two different physical treatments: shock heating driven by gravity only (GO) and a second treatment with cooling and preheating (PH). We examine relationships among structural properties and observable X-ray and Sunyaev-Zel'dovich (SZ) signals for samples of thousands of halos with M 200 ≥ 5 × 10 13 h −1 M ⊙ and z < 2. While the X-ray scaling behavior of PH model halos at low-redshift offers a good match to local clusters, the model exhibits non-standard features testable with larger surveys, including weakly running slopes in hot gas observable-mass relations and ∼ 10% departures from self-similar redshift evolution for 10 14 h −1 M ⊙ halos at redshift z ∼ 1. We find that the form of the joint likelihood of signal pairs is generally well-described by a multivariate, log-normal distribution, especially in the PH case which exhibits less halo substructure than the GO model. At fixed mass and epoch, joint deviations of signal pairs display mainly positive correlations, especially the thermal SZ effect paired with either hot gas fraction (r = 0.88/0.69 for PH/GO at z = 0) or X-ray temperature (r = 0.62/0.83). The levels of variance in X-ray luminosity, temperature and gas mass fraction are sensitive to the physical treatment, but offsetting shifts in the latter two measures maintain a fixed 12% scatter in the integrated SZ signal under both gas treatments. We discuss halo mass selection by signal pairs, and find a minimum mass scatter of 4% in the PH model by combining thermal SZ and gas fraction measurements.

Observational probes of cosmic acceleration

“…The main difficulty that simulation methods face is our incomplete understanding of baryonic physics, particularly galaxy formation feedback processes. These difficulties can be minimized by defining new X-ray observables that are expected to be robust to these details, and through careful exploration of the sensitivity of the observable-mass relation to the physics that goes into the simulations (e.g., Nagai et al, 2007;Rudd and Nagai, 2009;Stanek et al, 2010;Fabjan et al, 2011;Battaglia et al, 2012). The simulations themselves are steadily improving thanks to increased computer power, more sophisticated algorithms, and the availability of better data to test the input physics.…”

“…While an overall shift in the normalization of the multi-variate observable-mass relation P (X 1 , X 2 |M ) is still degenerate with cosmology, the addition of the clustering signalwhich depends on cluster masses directly -allows one to jointly calibrate P (X 1 , X 2 |M ) while still improving the cosmological constraints relative to those derived from a single observable (Cunha, 2009). The improvement is driven by the fact that using two cluster observables simultaneously allows one to better constrain the scatter of the observable-mass relation (see also Stanek et al, 2010). Given the large overlap between many of the currently ongoing or near future cluster surveys (e.g., DES fully overlaps with SPT), we expect this type of analysis to become increasingly important in the coming decade.…”

CoMaLit – IV. Evolution and self-similarity of scaling relations with the galaxy cluster mass

“…Stanek et al (2010) presented a computational study of the intrinsic covariance of cluster observables using the Millennium Gas Simulations. Two different physical treatments were proposed: shock heating driven by gravity only, or a second treatment with cooling and preheating.…”

“…Stanek et al (2010) found that the evolution with redshift might be negative (γz ∼ −0.34) in presence of cooling and preheating. In agreement with simulations, we did not detect any departure from the self-similar scaling, with βY -Z = 1.50 ± 0.21.…”

“…The second paper presented the formalism to calibrate an observable cluster property against the cluster mass and applied the methodology to the Sunyaev-Zel'dovich If gravity is the dominant process, the resulting self-similar model predicts scaling relations in form of scale-free power laws (Kaiser 1986;Giodini et al 2013). Numerical simulations (Stanek et al 2010;Fabjan et al 2011) confirmed these scalings and showed that intrinsic scatters around the median relations approximately follow a log-normal distribution. This basic theoretical scheme is very successful in describing observed scaling relations in Xray and SZ (Ettori 2013(Ettori , 2015.…”