[Paper Review] The RASS-SDSS Galaxy Cluster Survey. III. Scaling relations of galaxy clusters

P. Popesso, A. Biviano+3 more|arXiv (Cornell University)|Nov 18, 2004

Galaxies: Formation, Evolution, PhenomenaPhysics and Astronomy67 references86 citations

TL;DR

This study analyzes the RASS-SDSS galaxy cluster sample to compare optical and X-ray luminosities as predictors of cluster mass, temperature, and velocity dispersion. Using SDSS spectroscopy and X-ray data, it finds that optical luminosity predicts cluster mass with 40% accuracy—superior to X-ray luminosity’s 55%—demonstrating that optical luminosity is a more reliable indicator of fundamental cluster properties than X-ray luminosity.

ABSTRACT

We use the RASS-SDSS galaxy cluster sample to compare the quality of optical and X-ray luminosities as predictors of other cluster properties such as their masses, temperatures, and velocity dispersions. We use the SDSS spectroscopic data to estimate the velocity dispersions and the virial masses of a subsample of 69 clusters within r_{500} and r_{200}. The ASCA temperature of the intra-cluster medium, T_X, is retrieved from the literature for a subsample of 49 clusters. For this subsample we estimate the cluster masses also by using the mass-temperature relation. We show that the optical luminosity, L_{op}, correlates with the cluster mass much better than the X-ray luminosity, L_X. L_{op} can be used to estimate the cluster mass with an accuracy of 40% while L_X can predict the mass only with a 55% accuracy. We show that correcting $L_X$ for the effect of a cool core at the center of a cluster, lowers the scatter of the $L_X-M$ relation only by 3%. We find that the scatter observed in the L_{op}-L_X relation is determined by the scatter of the L_X-M relation. The mass-to-light ratio in the SDSS i band clearly increases with the cluster mass with a slope 0.2\pm0.08. The optical and X-ray luminosities correlate in excellent way with both T_X and σ_V with an orthogonal scatter of 20% in both relations. Moreover, L_{op} and L_X can predict with the same accuracy both variables. We conclude that the cluster optical luminosity is a key cluster parameter since it can give important information about fundamental cluster properties such as the mass, the velocity dispersion, and the temperature of the intra-cluster medium.

Motivation & Objective

• To evaluate the effectiveness of optical and X-ray luminosities as predictors of cluster mass, temperature, and velocity dispersion.
• To assess the impact of cool-core effects on the scatter of scaling relations involving X-ray luminosity and mass.
• To determine whether optical luminosity provides a more accurate mass estimator than X-ray luminosity in a homogeneous, large-scale cluster sample.
• To investigate the mass-to-light ratio trend with cluster mass using SDSS i-band data.
• To examine the correlation between optical and X-ray luminosities and their predictive power for ICM temperature and velocity dispersion.

Proposed method

• The study uses the RASS-SDSS galaxy cluster sample, selecting 69 clusters with spectroscopic redshifts for velocity dispersion and virial mass estimation within r500 and r200.
• X-ray luminosities and ASCA temperatures (TX) are retrieved from the literature for a subsample of 49 clusters.
• Cluster masses are estimated using both the virial theorem and the mass–temperature relation to cross-validate results.
• The optical luminosity (Lop) is computed in the SDSS i-band using homogeneous photometry from DR2, with galaxy membership determined via spectroscopic redshifts.
• Orthogonal distance regression is used to analyze scatter in scaling relations, minimizing errors in both variables.
• Cool-core corrections are applied to X-ray temperatures where possible, and their impact on the Lx–M and Lop–TX relations is quantified.

Experimental results

Research questions

• RQ1 Does optical luminosity correlate more strongly with cluster mass than X-ray luminosity?
• RQ2 How does the presence of a cool core affect the scatter in the Lx–M and Lop–TX scaling relations?
• RQ3 Can optical luminosity predict cluster velocity dispersion and X-ray temperature with comparable accuracy to X-ray luminosity?
• RQ4 What is the trend of the mass-to-light ratio with increasing cluster mass?
• RQ5 How do the predictive accuracies of Lop and Lx compare for estimating cluster mass, temperature, and velocity dispersion?

Key findings

• Optical luminosity (Lop) predicts cluster mass with a 40% scatter, significantly better than X-ray luminosity (Lx), which predicts mass with a 55% scatter.
• Correcting X-ray luminosity for cool-core effects reduces the scatter in the Lx–M relation by only 3%, indicating that cool-core effects are not the dominant source of scatter.
• The scatter in the Lop–Lx relation is primarily driven by the scatter in the Lx–M relation, not by intrinsic Lop–Lx dispersion.
• The mass-to-light ratio in the SDSS i-band increases with cluster mass, with a slope of 0.2 ± 0.08, indicating a systematic increase in M/L with mass.
• Both Lop and Lx correlate with X-ray temperature (TX) and velocity dispersion (σV) with an orthogonal scatter of 20%, and both predict these variables with similar accuracy.
• The study concludes that optical luminosity is a superior and more reliable indicator of fundamental cluster properties than X-ray luminosity, especially in the context of large optical surveys like SDSS.