The LX--T relation and intracluster gas fractions of X-ray clusters

Abstract

We re-examine the X-ray luminosity–temperature relation using a nearly homogeneous data set of 24 clusters selected for statistically accurate temperature measurements and absence of strong cooling flows. The data exhibit a remarkably tight power-law relation between bolometric luminosity and temperature with a slope 2.88 ± 0.15. With reasonable assumptions regarding cluster structure, we infer an upper limit on fractional variations in the intracluster gas fraction 〈(δ fgas fgas)2〉1/2≤ 15 per cent. A strictly homogeneous Ginga subset of 18 clusters places a more stringent limit of 9 per cent. Imaging data from the literature are employed to determine absolute values of fgas within spheres encompassing density contrasts δc=500 and 200 with respect to the critical density. Comparing binding mass estimates based on the virial theorem (VT) and the hydrostatic β-model (BM), we find a temperature-dependent discrepancy in fgas between the two methods caused by systematic variation of the outer slope parameter β with temperature. Mean values (for H0=50 km s−1 Mpc−1) range from f¯gas=0.10 for cool (T 4 keV) clusters using the BM at δc=200. There is evidence that cool clusters have a lower mean gas fraction than hot clusters, but it is not possible to assess the statistical significance of this effect in the present data set. The T dependence of the intracluster medium (ICM) density structure, coupled with the increase of the gas fraction with T in the VT approach, explains the steepening of the LX–T relation. The small variation about the mean gas fraction within this majority subpopulation of clusters presents an important constraint for theories of galaxy formation and supports arguments against an Einstein–de Sitter universe based on the population mean gas fraction and conventional, primordial nucleosynthesis. The apparent trend of lower gas fractions and more extended atmospheres in low-temperature systems is consistent with expectations of models incorporating the effects of galactic winds on the ICM.