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

By P. Tozzi, C. Norman. 2000

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The thermodynamics of the diffuse, X-ray-emitting 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 effect 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 flat 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 first 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 find 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 fitted for the following range of values of the adiabatic constant: K* ≡ kBT/μmpρ2/3 = (0.4 ± 0.1) × 1034 ergs cm2 g-5/3 for clusters with average temperatures kT > 2 keV and K* = (0.2 ± 0.1) × 1034 ergs cm2 g-5/3 for groups and clusters with average temperatures kBT < 2 keV. These values correspond to different excess energy per particle of kBT ≥ 0.1(K*/0.4 × 1034) keV. The dependence of K* on the mass scale can be well reproduced by an epoch-dependent external entropy: the relation K* = 0.8(1 + z)-1 × 1034 ergs cm2 g-5/3 fits 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 fit 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 typical epoch and the source of the heating processes. The X-ray satellites Chandra and XMM can add to our knowledge of the history of the cosmic baryons, already derived from the high-redshift, low-density gas observed in the QSO absorption-line clouds, by imaging the hot, higher density plasma observed in groups and clusters of galaxies.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/3ecb937a83c4871e438506303b3995065eb4eca9

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Citations in the corpus

INTRACLUSTER MEDIUM ENTROPY PROFILES FOR A CHANDRA ARCHIVAL SAMPLE OF GALAXY CLUSTERS (2009, result): “Our mean slope of α ≈ 1.2 is not statistically different from the theoretical value of α = 1.1 found by Tozzi & Norman (2001) using semianalytic models and α = 1.2 found by Voit et al. (2005) using models with gravitational effects only.”
Jet-regulated cooling catastrophe (2010, neutral): “Indeed, at T = 3.5 keV, the relative difference in the net cooling rate between a zero and a one-third of solar metallicity plasma is 0.2 according to Tozzi & Norman (2001).”
CONSTRAINING THE MILKY WAY'S HOT GAS HALO WITH O vii AND O viii EMISSION LINES (2014, background): “This slope is the characteristic entropy profile for gas accreting onto virialized objects in the absence of radiative cooling or additional heat- ing due to feedback (Tozzi & Norman 2001; Voit et al. 2005).”
X-ray spectroscopy of galaxy clusters: studying astrophysical processes in the largest celestial laboratories (2009, background): “Purely gravitational models of smooth and cold accretion of gas into the cluster (e.g. Tozzi & Norman 2001) predict entropy profiles in clusters of the formS (r) ∝ r1.”
Fossil H ii regions: self-limiting star formation at high redshift (2003, methodology): “The models we construct are in the spirit of Voit et al (2002); Tozzi & Norman (2001); Oh & Benson (2003); Babul et al (2002), which match observations of low-redshift cluster X-ray profiles well.”
The Detectability of the First Stars and Their Cluster Enrichment Signatures (2003, background): “The properties of ICM may also provide information as to the energetics of SNe , whose high-energy output is suggestive of the well-known entropy floor problem (Loewenstein 2000; Lloyd-Davies, Ponman, & Cannon 2000; Tozzi & Norman 2001; Borgani et al. 2001).”
Gas entropy in a representative sample of nearby X-ray galaxy clusters (REXCESS): relationship to gas mass fraction (2009, neutral): “1 (Tozzi & Norman 2001; Borgani et al. 2005; Voit et al. 2002, 2005; Mitchell et al. 2009).”
Galaxy Clusters in Hubble Volume Simulations: Cosmological Constraints from Sky Survey Populations (2001, background): “…dominated by gravitational shock heating after an initial, early epoch of preheating (Evrard & Henry 1991; Kaiser 1991; Bower 1997; Cavaliere, Menzi & Tozzi 1999; Balogh, Babul & Patton 1999; Llyod-Davies, Ponman & Cannon 2000; Bower et al. 2001; Bialek, Evrard & Mohr 2001; Tozzi & Norman 2001).”
Physical Implications of the X-ray Properties of Galaxy Groups and Clusters (2001, result): “1997, 1998; 1999; Balogh, Babul & Patton 1999; Wu, Fabian & Nulsen 2000; Lowenstein 2000; Tozzi & Norman 2001; Voit & Bryan 2001).”
X-ray spectroscopy of the Virgo Cluster out to the virial radius (2011, background): “1 (Tozzi & Norman 2001; Voit 2005).”
LoCuSS: comparison of observed X-ray and lensing galaxy cluster scaling relations with simulations (2008, neutral): “1 (e.g. Tozzi & Norman 2001; Kay 2004).”
Feedback heating by cosmic rays in clusters of galaxies (2007, neutral): “We manually truncate the cooling below a minimum temperature of 0.03 keV, since equation (35) is only valid for kBT > 0.03 keV (Tozzi & Norman 2001).”
Deep inside the core of Abell 1795: the Chandra view (2001, background): “…behaviour traces the shock heating (more significant at larger radius) at which the intracluster gas has been subjected during its history of accretion inthe gravitational potential well, whereas the efficiency of thecooling has removed the central gas at lower entropy (cf. Tozzi & Norman 2001).”
On the Origin of Intracluster Entropy (2003, methodology): “Including simple corrections for preheating and radiative cooling yields analytical smooth accretion models whose entropy distributions agree well with the numerical models of Tozzi & Norman (2001).”
Measuring Ωm with the ROSAT Deep Cluster Survey (2001, background): “For instance, in their model for non–gravitational gas heating, Tozzi & Norman (2001) predict masses which can differ by about 20–30% with respect to those obtained from the above M–”
The Birmingham-CfA cluster scaling project - III. Entropy and similarity in galaxy systems (2003, methodology): “…hence result in an isentropic core, but in high mass systems (and at large radii in low mass ones) it has essentially no effect, since the post-shock temperature is just T = 1 3 µmpv 2 i (Tozzi & Norman 2001), where vi is the velocity at which gas, with mean particle mass µmp, flows into the shock.”
Hot Gas In and Around Elliptical Galaxies (2003, background): “…have adopted a stronger assumption: that all baryonic gas, including gas currently in both groups and clusters, experienced some “non-gravitational” heating (star formation, Pop III stars, AGN, etc.) prior to its entry into the dark halos (e.g. Tozzi & Norman 2001; Borgani et al 2001, 2002).”
Planck intermediate results: V. Pressure profiles of galaxy clusters from the Sunyaev-Zeldovich effect (2012, positive): “In the cluster surroundings, accretion along ﬁlaments is three-dimensional and non-spherical (Tozzi & Norman 2001) and the initial conditions of the accretion shock are driven by the thermodynamical state of the (pre-shocked) in-falling material (Voit et al. 2002, 2003).”