The Evolution of X‐Ray Clusters and the Entropy of the Intracluster Medium

Abstract

The thermodynamics of the di †use, X-rayÈemitting gas in clusters of galaxies is determined by gravitational processes associated with infalling gas, shock heating and adiabatic compression, and nongravitational processes such as heating by supernovae, stellar winds, activity in central galactic nuclei, and radiative cooling. The e †ect of gravitational processes on the thermodynamics of the intracluster medium (ICM) can be expressed in terms of the ICM entropy. The entropy is a convenient variable as long as cooling is negligible, since it remains constant during the phase of adiabatic compression during accretion into the potential well, and it shows a single steplike increase during shock heating. Observations indicate that nongravitational processes also play a key role in determining the distribution of entropy in the ICM. In particular, an entropy excess with respect to that produced by purely gravitational processes has been recently detected in the centers of low-temperature systems. This type of entropy excess is believed to be responsible for many other properties of local X-ray clusters, including the L -T relation and the Ñat density cores in clusters and groups.In this paper we assume that the entropy excess is present in the intergalactic medium (IGM) baryons before the gas is accreted by the dark matter halos and reaches high densities. We use a generalized spherical model to compute the X-ray properties of groups and clusters for a range of initial entropy levels in the IGM and for a range of mass scales, cosmic epochs, and background cosmologies. In particular, we follow the formation of adiabatic cores during the Ðrst stages of the gravitational collapse and the subsequent evolution of the central entropy due to radiative energy loss. The model predicts the statistical properties of the cluster population at a given epoch and also allows study of the evolution of single X-ray halos as a function of their age.We Ðnd that the statistical properties of the X-ray clusters strongly depend on the value of the initial background entropy. Assuming a constant, uniform value for the background entropy, the present-day X-ray data are well Ðtted for the following range of values of the adiabatic constant : K * 4 ergs cm2 g~5@3 for clusters with average temperatures kT [ 2 keV and k B T /km p o2@3 \ (0.4^0.1) ] 1034 ergs cm2 g~5@3 for groups and clusters with average temperatures keV. K * \ (0.2^0.1) ] 1034 k B T \ 2 These values correspond to di †erent excess energy per particle of keV. The k B T º 0.1(K * /0.4 ] 1034) dependence of on the mass scale can be well reproduced by an epoch-dependent external entropy : K * the relation ergs cm2 g~5@3 Ðts the data over the whole temperature range.The model can be extended to include internal heating, but in this case the energy budget required to Ðt the X-ray properties would be much higher. Observations of both local and distant clusters can be used to trace the distribution and the evolution of the entropy in the cosmic baryons and to constrain the typi...

Formation of disc galaxies in preheated media: a preventative feedback model

“…(12), consistent with adiabatic hydrodynamical simulations and theoretical models for virial shock heating (e.g. Tozzi & Norman 2001;Voit, Kay & Bryan 2005;Lu & Mo 2007). In this model, we follow the commonly adopted energy-driven wind model, which assumes that the mass loading factor of star formation feedback is proportional to V −2 c , where Vc is the halo circular velocity at any given time.…”

“…Analytical models and hydrodynamic simulations of halo formation neglecting radiative cooling have shown that the radial profile of the specific entropy of the hot gas generated by accretion shocks roughly follows a powerlaw function of radius with a power index β ∼ 1.1 (e.g. Tozzi & Norman 2001;Voit, Kay & Bryan 2005;Lu & Mo 2007). When radiative cooling is included, the entropy profile can be modified.…”

Little evidence for entropy and energy excess beyond r500 - An end to ICM preheating?

“…The total amount of feedback energy available in the ICM is EICM = ∆E ICM µmp dmg . Since clusters lose energy due to X-ray cooling, we estimate total feedback energy deposited in the ICM by adding this lost energy to EICM; thus ∆E feedback = ∆EICM + ∆L bol tage, where ∆L bol is the bolometric luminosity in a given gas shell which is obtained by using the approximate cooling function ΛN given by Tozzi & Norman (2001) and tage is the average age of the cluster which we have approximated to be 5 Gyr based on the results of Smith & Taylor (2008). Finally, we estimate the mean non-gravitational energy per particle, <∆E>, from total energy divided by the total number of particles in the ICM (i.e M gas,obs µmp ).…”

“…In this scenario, the cluster forms from an already preheated and enriched gas due to feedback processes (such as galactic winds or AGN) heating up the surrounding gas at high redshifts. Preheating models require constant entropy level of 300 keV cm 2 in order to explain the break in c 2016 The Authors the self-similarity scaling relations (Tozzi & Norman 2001;Babul et al 2002;McCarthy et al 2002). In terms of ICM energetics, this typically translates into feedback energy of ∼ 1 keV per particle (Tozzi & Norman 2001;Pipino et al 2002;Finoguenov et al 2003).…”

“…Preheating models require constant entropy level of 300 keV cm 2 in order to explain the break in c 2016 The Authors the self-similarity scaling relations (Tozzi & Norman 2001;Babul et al 2002;McCarthy et al 2002). In terms of ICM energetics, this typically translates into feedback energy of ∼ 1 keV per particle (Tozzi & Norman 2001;Pipino et al 2002;Finoguenov et al 2003). However, there is an ambiguity in defining preheating energy/particle since it depends on the density at which gas is heated (less dense gas requires smaller energy to raise it to a particular entropic state).…”