Temperature profiles

Spatially resolved spectroscopic observations from X-ray satellites have opened the possibility of determining in detail the temperature structure of the ICM. ASCA observations [3] have established that temperature profiles are characterized by negative gradients. Beppo-SAX observations [4] have shown that such negative gradients do not extend down to the innermost cluster central regions, where instead an isothermal regime is observed, possibly followed by a decline of the temperature towards the center, at least for relaxed clusters. The much improved sensitivity of the Chandra satellite provides now a much more detailed picture of the central temperature profiles [5, 6]). Relaxed clusters are generally shown to have a smoothly declining profile toward the centre, reaching values which are about half of the overall virial cluster temperature in the innermost sampled regions, with non relaxed clusters having, instead, a greater diversity of temperature profiles. At the same time, observations with the XMM-Newton satellite demonstrated that the central regions of relaxed clusters are characterized by a spectrum with no significant or, at most, weak emission lines associated with soft atomic energy transitions [7, 8]). The consequence of this result is that a small amount of cooled gas should be present in the cluster cooling regions, thus implying a small value for the mass deposition rate. While this is in contradiction with the standard model of cooling flows [9], it is in much better agreement with optical observations on the brightest cluster galaxies, which imply a fairly low rate of star formation [10]. Therefore, the emerging picture suggests that gas cooling is responsible for the decline of the temperature in the central regions of clusters, while some mechanism of energy feedback should be responsible for preventing gas overcooling, thereby suppressing the mass deposition and the resulting star formation.

As for hydrodynamical simulations, they have shown to be generally rather successful in reproducing the negative temperature gradients outside the "cool core" regions [3, 12, 13], where gas cooling is unimportant. On the other hand, including gas cooling in hydrodynamical simulations has been shown to produce temperature profiles which, in the core regions, are generally steeper than those in non-radiative simulations. This is illustrated in the left panel of Figure 1 where we show the effect of introducing radiative cooling and different forms of feedback in simulations of a galaxy cluster [11]. While the temperature profiles are left essentially unchanged for R> 0.2Rvir, the effect of cooling is that of steepening the profiles in the innermost regions. The

Fig. 1. Left panel: temperature profiles from hydrodynamical simulations of galaxy clusters. In all panels the dotted and the solid curves correspond to a non radiative run and to a run including cooling and star formation, respectively. The other curves represent results for different recipes of gas heating. Right panel: the relationship between gas density and pressure for a subset of the simulations shown in the right panel. The two straight lines are for polytropic models with 7 = 1 and 7 = 5/3 (from [11]).

Fig. 1. Left panel: temperature profiles from hydrodynamical simulations of galaxy clusters. In all panels the dotted and the solid curves correspond to a non radiative run and to a run including cooling and star formation, respectively. The other curves represent results for different recipes of gas heating. Right panel: the relationship between gas density and pressure for a subset of the simulations shown in the right panel. The two straight lines are for polytropic models with 7 = 1 and 7 = 5/3 (from [11]).

counter-intuitive conclusion that cooling gives rise to a temperature increase in cluster cores has actually a fairly simple explanation. If not counteracted by some sort of feedback, cooling is so efficient at removing gas from the hot phase, it leads to a suppression of pressure support at the cluster centre. As a consequence, more external gas falls toward the centre, thus undergoing heating by adiabatic compression. This effect is illustrated in the right panel of Fig.1, where we show the relation between gas density and pressure for a subset of the simulations whose temperature profiles are reported in the left panel. The two solid lines in this plot show the relation for an adiabatic effective equation of state, p x pgi^, and for an isothermal one, p x pgas. Quite apparently, the ICM in the non-radiative run behaves in a nearly isothermal way in the central regions, with a slope approaching 7 ~ 1. On the other hand, the effect of cooling is clearly that of steepening this relation at the centre, such that it approaches the adiabatic slope. This is exactly what is expected for gas undergoing adiabatic compression.

In Figure 2 I show a comparison between the observed temperature profiles and those predicted by simulations, which include gas cooling, star formation and energy feedback from galactic winds powered by SN [13]. Although this sort of feedback has been shown to produce a realistic cosmic star formation history [14], it is not efficient enough to regulate gas cooling and, therefore, to produce realistic temperature profiles. They are always

R/R1B0 R/R2500

Fig. 2. Left panel: comparison between temperature profiles from Beppo-SAX observations [4] and from a cosmological simulation including radiative cooling, star formation and SN feedback. Right panel: comparison between the same set of simulations and the best-fit curve to the observed inner Chandra temperature profiles [5]. Figure taken from [13].

R/R1B0 R/R2500

Fig. 2. Left panel: comparison between temperature profiles from Beppo-SAX observations [4] and from a cosmological simulation including radiative cooling, star formation and SN feedback. Right panel: comparison between the same set of simulations and the best-fit curve to the observed inner Chandra temperature profiles [5]. Figure taken from [13].

steeper, and have an inversion from negative to positive gradients at too small cluster-centric distances, with respect to observations.

The fact that overcooling and incorrect temperature profiles are two aspects of the same problem is also shown by the right panel of Figure 3. Here we compare the fraction of baryons converted into stars for the same set of simulated clusters and for observed clusters. Quite apparently, simulations still show an excess of cooling inside clusters, despite the fact that the cosmic values of the stellar fraction is consistent with observational estimates [14]. Since cooling is a runaway process, its efficiency increases with resolution. Therefore, one may wonder whether this estimate of the star fraction from simulations is reliable or represents a lower limit, due to the finite force and mass resolutions. In fact, the left panel of Figure 3 suggests that this not the case. This plot shows the dependence of the star fraction on the mass resolution for simulations of four clusters, which include feedback from galactic winds. Only for one of them, results are also shown in the case that galactic winds are turned off. Remarkably, the presence of efficient feedback makes cooling efficiency independent of resolution, while excluding it makes the runaway cooling reappear. These results demonstrate that, even if feedback is successful in terms of preventing the cooling runaway, it is not guaranteed to provide the correct thermal structure in the central regions of galaxy clusters.

Vice versa, the fact that a feedback mechanism is able to produce the correct temperature profiles does not guarantee that it also prevents overcooling. For instance, the simulations presented in [15] used a selective heating model, in which the energy release from SN is used to target ad hoc those gas particles which are just about to undergo cooling, increasing their entropy to a critical value. With this approach, they were able to produce temperature profiles which are in better agreement with observations. However, the resulting stellar fraction was still found to be too high, > 25 per cent.

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Fig. 3. Left panel: a comparison between observed (points with errorbars; from [16]) and the simulated fraction of cluster baryons contained in stars (from [13]). Right panel: the dependence of the stellar fraction on resolution for simulations of four clusters, both including galactic winds (filled symbols) and without galactic winds (open circles; from [17]).

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