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Astron. Astrophys. 333, 433-444 (1998)

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3. Evolution of the gas flows

We present here the results of the hydrodynamical simulations. The basic input parameters and output quantities are shown in Table 1. Two representative blue luminosities have been used to investigate the typical gas flow behavior, [FORMULA], and [FORMULA] ; the corresponding [FORMULA] are [FORMULA] and [FORMULA]. Various values of [FORMULA] are chosen. [FORMULA] is close to the most secure current estimate coming from optical surveys (which is [FORMULA], see Sect. 1.3); to consider the indications coming from the low iron abundances given by X-ray data (Sect. 1.2), we also explore the case [FORMULA] ; for comparison with the long-lived inflow case, we also use [FORMULA]. The distribution of the dark mass is broader than that of the luminous mass ([FORMULA] or [FORMULA]); the dark mass prevails outside one or two [FORMULA] if [FORMULA], or outside a few [FORMULA] if [FORMULA] (Fig. 2).


Table 1. Results of the JH model evolution. [FORMULA] is calculated for the (0.2-4) keV band; T is the emission weighted temperature of the flow. [FORMULA] is the gas mass flown to the center in 15 Gyrs; [FORMULA] and [FORMULA] are the gas masses that flow to the central sink and are lost from the galaxy, per unit time, at 15 Gyrs. At this time [FORMULA] [FORMULA] /yr, for the model with [FORMULA], and [FORMULA] /yr for the model with [FORMULA]. [FORMULA] is defined in Sect. 4.

[FIGURE] Fig. 2. The cumulative mass profiles normalized to the total stellar mass [FORMULA] of JH models with [FORMULA] and [FORMULA] ; the cases [FORMULA] and [FORMULA] are shown in each panel. Within [FORMULA], [FORMULA] and 0.3 respectively if [FORMULA] and [FORMULA] (upper panel); [FORMULA] and 1.1 if [FORMULA] and [FORMULA] (lower panel).

A general feature of all the evolutionary sequences, except for those with [FORMULA], is to develop a central inflow at early times, while the outer regions are still outgassing, i.e., a decoupled gas flow (see Fig. 3). The inflow region is bordered by a stagnation radius [FORMULA] that may range from a small fraction of [FORMULA] to many [FORMULA], at the end of the evolution (see Table 1). If [FORMULA] maintains its position within a few [FORMULA], we call the flow partial wind (hereafter PW; see the representative case in Fig. 3 and 4); if it increases considerably to more than [FORMULA], we call the resulting flow global inflow, even though this is strictly the case only when [FORMULA]. In the PW case, radiative losses suppress an outflow in the inner parts of the galaxy, causing a small inflow region, but a wind can be sustained in the external parts, where the gas density is much lower and the gas is also less tightly bound. The X-ray luminosity of PWs and inflows steadly decreases with time, following the decrease of [FORMULA] and of the heating. Note that the stagnation points resulting from the simulations are well outside the first grid point, so the flow is properly resolved.

[FIGURE] Fig. 3. The evolution of the number density n, the temperature T and the velocity v of the gas, in a typical PW case (the model with [FORMULA], [FORMULA], [FORMULA] and [FORMULA] in Table 1). The solid line refers to [FORMULA] Gyrs, the dotted line to [FORMULA] Gyrs, and the dashed line to [FORMULA] Gyrs. In this model the initially supersonic inflow slows until it becomes fully subsonic at [FORMULA] Gyrs; the outer sonic radius starts at [FORMULA] and moves outward, until it establishes at [FORMULA] from [FORMULA] Gyrs on.

[FIGURE] Fig. 4. Upper panel: the time evolution of the mass loss [FORMULA], of the mass inflowing into the central sink [FORMULA], and of the mass lost by the galaxy [FORMULA]. Lower panel: the time evolution of the stagnation radius [FORMULA]. All refers to the representative model chosen for Fig. 3.

Another general trend in the results is that, at fixed [FORMULA], as [FORMULA] and/or [FORMULA] decrease, the larger are the inflow region, [FORMULA], the mass accreted to the center [FORMULA], the mass flowing to the center per unit time [FORMULA], and the smaller is [FORMULA], the mass escaping the galaxy per unit time, because the heating is lower and/or the dark mass concentration is higher.

3.1. [FORMULA] models

For [FORMULA], and [FORMULA], these galaxies develop PWs with [FORMULA] varying from [FORMULA] to [FORMULA]. When [FORMULA] a global wind persists until the present time, and so [FORMULA] is very low. Even when [FORMULA] the hot gas, in PW, shows such a low [FORMULA] that the observed X-ray emission must be largely produced by the stellar sources, whose emission has been estimated to be of the order of [FORMULA] (see Fig. 1). When [FORMULA], the final [FORMULA], and the hot gas starts to dominate the X-ray emission of the galaxy. Significantly higher [FORMULA] values are obtained by increasing the gas temperature, not just by retaining more gas; in fact the model with [FORMULA] and [FORMULA], a global inflow that lasts for the whole galaxy lifetime, has just [FORMULA]. To increase the gas temperature and [FORMULA], the dark matter content must be increased first, because global winds are obtained by just increasing the SNIa heating. A deeper potential well by itself produces hotter gas, because of a higher gravitational compression during the inflow; moreover, it can be coupled to a larger inflow region, if [FORMULA] is kept constant, or to a higher heating without full degassing if [FORMULA] is increased.

For [FORMULA] and [FORMULA] the gas is always in a global inflow at the present time. The highest [FORMULA] is obtained when [FORMULA] and [FORMULA], i.e., when the heating by SNIa's and gravitational compression is the highest possible for the chosen ranges of these parameters. This [FORMULA] is still lower than the highest [FORMULA] observed at [FORMULA] (Fig. 1), a problem that was known also from previous works (see the references cited in the Introduction). However, [FORMULA] as high as [FORMULA] are comparable to those typical of poor clusters rather than single galaxies; at least some of them could be explained with accretion effects (see, e.g., Renzini et al. 1993; Bertin & Toniazzo 1995; Kim & Fabbiano 1995).

Note that for PWs ([FORMULA]) [FORMULA] is higher when [FORMULA] is lower, because the inflow region is larger. For global inflows ([FORMULA]) [FORMULA] is higher when [FORMULA] is also higher, because the gas is hotter. Altogether, the variation in [FORMULA] in Table 1 is a factor of [FORMULA] ; it is of a factor of [FORMULA] when [FORMULA], and just [FORMULA] when [FORMULA].

3.2. [FORMULA] models

Models with [FORMULA] again develop PWs, with quite larger central inflow regions than above for the same range of [FORMULA] and [FORMULA] values, due to a deeper potential well. The latter makes also the gas hotter. Larger inflow regions and higher gas temperatures, coupled to a larger mass return rate, make the X-ray emission in these galaxies always higher than that of the models described in Sect. 3.1, for the same [FORMULA]. [FORMULA] goes from [FORMULA] to [FORMULA], when the flow is a PW. So, it is always comparable to or higher than the estimate of the stellar X-ray emission at [FORMULA] (Fig. 1); this is in agreement with the fact that in Fig. 1 all galaxies lie above this estimate, for [FORMULA].

As expected, we always have global inflows if [FORMULA], and the highest [FORMULA] is reached when [FORMULA] and [FORMULA], i.e., again the most efficient way of increasing [FORMULA] when the flow is not decoupled is to increase [FORMULA], and then [FORMULA]. The spread in [FORMULA] is of a factor of [FORMULA] if [FORMULA], and very small for global inflows. The total spread is roughly of a factor of 30, lower than for [FORMULA].

3.3. Other models

In order to investigate how common is the PW phase, we have run two more series of evolutionary sequences corresponding to a low [FORMULA], and to [FORMULA] ; moreover, also the case [FORMULA] has been explored. The results are summarized in Table 2. PWs populate again most of the parameter space. The X-ray luminosity of [FORMULA] models remains at low values even at high [FORMULA], in agreement with the observations (Fig. 1); for many of these galaxies [FORMULA] is likely to be dominated by the stellar emission.


Table 2. Results of additional JH model evolutions. All quantities are defined as in Table 1. After 15 Gyrs [FORMULA] [FORMULA] /yr, for the model with [FORMULA], and [FORMULA] [FORMULA] /yr for the model with [FORMULA]. At fixed [FORMULA], the models with the larger [FORMULA] are less concentrated than required for them to lay exactly on the fundamental plane.

3.4. Emission temperatures and X-ray surface brightness profiles

Emission temperatures of the hot gas have been calculated recently by Matsumoto et al. (1997) and Buote & Fabian (1997), using ASCA data and two-temperature model fitting, for about 20 early-type galaxies. These temperatures cover the range [FORMULA] keV, and the bulk of values lies within 0.5-0.8 keV. The X-ray luminosity weighted emission temperatures of the models are given in Tables 1 and 2. They lie in the range [FORMULA] keV, and so are in good agreement with those observed. They increase with central velocity dispersion, dark matter mass, and SNIa rate. Note how a substantial SNIa's heating helps obtaining temperatures close to those observed; other possible sources of heating not studied here are the presence of an external pressure due to an intracluster or intragroup medium (e.g., Bertin & Toniazzo 1995), and that of a central black hole (Ciotti & Ostriker 1997).

The comparison with the observed X-ray surface brightness profiles [FORMULA] is more delicate, because there is not a typical profile, nor a range of typical profiles. In the next, first we examine what kind of [FORMULA] are shown by PWs (which are the resulting flow regimes of the bulk of the galaxies, in our scenario), and then we discuss how [FORMULA] of our models compare with the available observations.

In Fig. 5 we compare the shapes of the X-ray profiles of partial wind solutions with different stagnation radii with that of a global inflow with [FORMULA] (which closely resembles the cooling flow solution). When the stagnation radius is larger than the optical effective radius, the shape of [FORMULA] is indistinguishable from that of the inflow, over most of the galaxy. PWs with very small stagnation radii are instead less steep outside [FORMULA] ; this is because in the external regions the gas density is actually lower for the PW than for the inflow, but the prevailing effect is given by the higher gas temperature of the PW, produced by the higher [FORMULA]. So, judging from the shape of the [FORMULA] profile, inflows and PWs should be indistinguishable by X-ray observations, if [FORMULA] is a few [FORMULA]. Of course, when [FORMULA] is very small, [FORMULA] is very low too, and so these PWs are much less detectable by X-ray observations than global inflows.

[FIGURE] Fig. 5. The X-ray surface brightness profile of three models with [FORMULA], [FORMULA] and [FORMULA]: the solid line corresponds to a global inflow ([FORMULA]), the dotted line to a PW with [FORMULA] (the model with [FORMULA] in Table 1), and the dashed line to a PW with [FORMULA] (the model with [FORMULA] in Table 1). The heavy dot-dashed line is the optical surface brightness profile in arbitrary units.

Now let's turn to the comparison with the observations. When [FORMULA] of the gas flow is very low, and the X-ray emission is dominated by the contribution of the stellar sources, our models exhibit the X-ray profile of the underlying stellar population. No detailed [FORMULA] for low [FORMULA] galaxies is available yet from the observations. When [FORMULA] of the flow is high, the observations - especially those produced by ROSAT - show a large variety of shapes for [FORMULA], often modified also by the interaction with the environment (e.g., Trinchieri, Fabbiano & Kim 1997). Using Einstein data, Trinchieri, Fabbiano, & Canizares (1986) found that the observed [FORMULA] tend to follow the optical ones, for few best studied X-ray bright galaxies. In our scenario such galaxies host PWs with large stagnation radii, or inflows; these flow phases have the same problems as cooling flows to reproduce X-ray profiles following the optical ones: they are too peaked (see Fig. 5). They can be brought in agreement with the observed [FORMULA] by the introduction of distributed mass deposition due to thermal instabilities in the hot gas, as shown and discussed in detail by Sarazin & Ashe 1989, and Bertin & Toniazzo 1995; another possibility is stationary convective accretion onto a central massive black hole (Tabor & Binney 1993), or unstable accretion (Ciotti & Ostriker 1997).

A detailed comparison with [FORMULA] observed for a specific galaxy requires a large number of simulations to find whether there is a combination of input parameters (with the possible addition of the effect of the environment, and/or of a central black hole) that gives a model reproducing the observations. This goes beyond the scope of this paper; it has been done successfully for NGC4365, in the framework of the CDPR scenario, by Pellegrini & Fabbiano (1994).

3.5. Effects of the new ingredients

We summarize here the main properties of the flows, and the main differences with the results obtained by CDPR, produced by the new mass distributions and by the reduction of [FORMULA] and [FORMULA]. The global wind phase disappears for all galaxies except the smallest ones (see the case [FORMULA] in Table 2): a central inflow, even though very small, is always present from the beginning of the evolution. As a consequence the outflow phase - the transition from a global wind to a global inflow in CDPR - also disappears. Large [FORMULA] variations are produced in the JH models by the different size of the central inflow region. Most of the observed spread in [FORMULA] at fixed [FORMULA] can be reproduced again, as it was in CDPR (Fig. 1): besides the observed variation from galaxy to galaxy in [FORMULA] and in the concentration [FORMULA], a spread in the dark matter content, and/or a variation in the SNIa rate can produce large variations in [FORMULA] and in the gas temperature, and then in [FORMULA] (of even a factor of [FORMULA], Table 1 and Fig. 1). If [FORMULA] remains at low values ([FORMULA]), though, it is difficult to reproduce [FORMULA] higher than a few times [FORMULA] (Table 2), and so to cover all the observed [FORMULA] variation. Moreover, for a given range of variation of [FORMULA] and [FORMULA], more luminous galaxies show less scatter in [FORMULA].

Another property of the flows in JH models is to accumulate cold gas at their centers, during the evolution ([FORMULA] in Tables 1 and 2). This mass when [FORMULA] ranges from [FORMULA] to [FORMULA]. Evidence of cold gas at the center of bright X-ray galaxies has come recently from the high column densities ([FORMULA]) required to obtain good fits of their X-ray spectra. The BBXRT data require [FORMULA] of cold gas in NGC1399 (Serlemitsos et al. 1993); to fit the ASCA data of NGC4472, [FORMULA] of cold material are needed (Awaki et al. 1994); ASCA data require central column densities larger than the Galactic value also for NGC4636, NGC4406, NGC720, NGC1399, NGC1404, NGC4374 (Arimoto et al. 1997). It has been suggested to explain this finding as the accumulation of cold material by a steady state cooling flow. This accumulation could have been produced by a PW as well; moreover, even different amounts of cold material can be naturally explained in this scenario (see the large variations of [FORMULA] in Table 1). So, the finding of cold matter at the center of early-type galaxies cannot be considered as evidence for a long lived cooling flow. Note however that the accuracy of these [FORMULA] absorption measurements could be affected by the uncertainties plaguing plasma spectra, and producing the iron-L problem (Sect. 1.3).

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© European Southern Observatory (ESO) 1998

Online publication: April 20, 1998