The Impact of Galaxy Cluster Mergers on Cosmological Parameter Estimation from Surveys of the Sunyaev‐Zel’dovich Effect

Abstract

Sensitive surveys of the Cosmic Microwave Background (CMB) will detect thousands of galaxy clusters via the Sunyaev-Zel'dovich (SZ) effect. Two SZ observables, the central or maximum and integrated Comptonization parameters y max and Y , relate in a simple way to the total cluster mass, which allow the construction of mass functions (MFs) that can be used to estimate cosmological parameters such as the ratio of the average matter density to the critical density Ω M , the normalization of the spectrum of initial density perturbations σ 8 , and the dark energy equation of state parameter w. However, clusters form from the mergers of smaller structures, events that can disrupt the equilibrium of intracluster gas upon which SZ-M relations rely. From a set of N-body/hydrodynamical simulations of binary cluster mergers, we calculate the evolution of Y and y max over the course of merger events and find that both parameters are transiently "boosted," primarily during the first core passage. We then use a semi-analytic technique developed by Randall et al. (2002) to estimate the effect of merger boosts on the distribution functions YF and yF of Y and y max , respectively, via cluster merger histories determined from extended Press-Schechter (PS) merger trees. The scatter in the Y -M and y max -M relations from merger boosts are found to be ∼ 2% and 25-30% respectively. To determine Ω M , σ 8 , and w, the boosted and nonboosted YFs and yFs are fit with analytic PS distributions as a function of redshift. We find that boosts do not induce an overall systematic effect on YFs, and the values of Ω M , σ 8 , and w (assumed constant) were returned to within 2% of values expected from the nonboosted YFs. The boosted yFs are significantly biased, however, causing Ω M to be underestimated by 15-45%, σ 8 to be overestimated by 10-25%, and w to be pushed to more negative values by 25-45%. We also fit YF as a function of redshift to cosmological models in which the dark energy parameter w varied with redshift to assess the effects of mergers on the inferred change in w with redshift. The values of Ω M , σ 8 , and the low-redshift value of w (w 0 ) were again reproduced to within 2%. For the largest change in w with z, which occurred between z = 0 and z = 1 for the models assumed, it was increased by about 0.04. Although this is twice as large as the merger effect on a constant value of w, it is still reasonably modest. We confirm that the integrated SZ effect, Y , is far more robust to mergers than y max , as previously reported by Motl et al. (2005) and similarly found for the X-ray equivalent Y X Poole et al. 2007), and we conclude that Y is the superior choice for a mass proxy when using SZ observations of galaxy clusters to constrain cosmological parameters.

The Influence of Mergers on Scatter and Evolution in Sunyaev–zel’dovich Effect Scaling Relations

“…The dashed line depicts Y fit using the best fit normalization for Y th + Y nt at z = 0 (see Equation (9)), which can be interpreted as a line of total energy. During the merger, 0 Gyr < t merger < 2 Gyr, we see large deviations from the line of total energy, a trend also observed by Wik et al (2008). At this epoch the clusters are actively undergoing major mergers, producing large merger shocks (see N12 for more details).…”

“…Specifically, while the normalization is sensitive to cluster astrophysics such as gas cooling, star formation, and energy feedback from stars and active galactic nuclei (AGNs), the scatter and evolution of the Y-M relation is fairly insensitive to the poorly understood cluster astrophysics (Nagai 2006;Fabjan et al 2011;Battaglia et al 2012). Cluster merger dynamics, on the other hand, has been shown to play an important role in determining the scatter and evolution of the Y-M relation (Wik et al 2008;Yang et al 2010;Krause et al 2012).…”

Planckearly results. XI. Calibration of the local galaxy cluster Sunyaev-Zeldovich scaling relations

“…As the total mass is not directly observable, such mass proxies are needed to leverage the statistical power of various large-scale surveys for cosmological applications. Since the gas pressure is directly related to the depth of the gravitational potential, the quantity D 2 A Y SZ is expected to scale particularly closely with the total mass, a claim supported by recent numerical simulations (e.g., White et al 2002;da Silva et al 2004;Motl et al 2005;Wik et al 2008;Aghanim et al 2009). SZ surveys for galaxy clusters thus have great potential to produce competitive cosmological constraints.…”

Planckintermediate results

“…Our observational and theoretical The SZ signal is of singular interest because it is not affected by cosmological dimming and because the total SZ flux or integrated Compton parameter, Y SZ , is expected to correlate particularly tightly with mass (e.g., Barbosa et al 1996;da Silva et al 2004;Motl et al 2005;Wik et al 2008;Aghanim et al 2009). SZ-detected cluster samples are thus expected to range to high redshift and be as near as possible to mass-selected, making them potentially very powerful cosmological probes.…”