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

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1. Introduction

X-ray observations, beginning with the Einstein Observatory, have demonstrated that normal early-type galaxies are X-ray emitters, with 0.2-4 keV luminosities ranging from [FORMULA] to [FORMULA] (Fabbiano 1989; Fabbiano, Kim, & Trinchieri 1992). The X-ray luminosity [FORMULA] is found to correlate with the blue luminosity [FORMULA] ([FORMULA]), but there is a large scatter of roughly two orders of magnitude in [FORMULA] at any fixed [FORMULA] (Fig. 1). The observed X-ray spectra of galaxies with high [FORMULA] ratios are consistent with thermal emission from hot, optically thin gas, while those of low [FORMULA] objects can be mostly accounted for by emission from stellar sources (Kim, Fabbiano, & Trinchieri 1992).

[FIGURE] Fig. 1. The [FORMULA] diagram of early-type galaxies with X-ray emission detected by the Einstein satellite; X-ray fluxes are from the final catalog of Fabbiano et al. (1992). Apparent B magnitudes and distances are from Fabbiano et al. (1992) in Fig. 1a, and from Donnelly et al. (1990) in Fig. 1b (see Sect. 1). The dashed line gives an estimate for the stellar source contribution to [FORMULA] (from Kim et al. 1992). Also shown with triangles are the positions of the models calculated here (see Sect. 3.5), to which the stellar source contribution has been added.

The scatter in the [FORMULA] diagram has been recognized as the most striking feature of the X-ray properties of early-type galaxies. Using new apparent magnitudes and fundamental plane distances, it was shown that this scatter is reduced by 20%, but not eliminated (Donnelly, Faber & O'Connell 1990; see Fig. 1b). This result is based on the old estimate of the X-ray fluxes (that of Canizares, Fabbiano, & Trinchieri 1987), and on just half of the final sample of X-ray galaxies produced by Fabbiano et al. 1992 (see Eskridge, Fabbiano & Kim 1995 for a detailed comparison of the statistical results by Donnelly et al. with those obtained using the whole sample). One can argue that the large dispersion in [FORMULA] is definitively not the result of distance errors on the basis of the fact that a scatter of the same size as in Fig. 1a is present even in the distance-independent diagram of [FORMULA] versus the central stellar velocity dispersion (e.g., Eskridge et al. 1995).

Many theoretical models were developed to explain the findings above, including numerical simulations of the behavior of gas flows fed by stellar mass loss and heated by type Ia supernovae (SNIa). Steady state cooling flow models were investigated first (Nulsen et al. 1984, Sarazin & White 1987,1988), and it was found that these can only reproduce X-ray bright galaxies. Evolutionary models with a SNIa rate approximately constant with time have been carried out by Mathews & Loewenstein (1986), Loewenstein & Mathews (1987), and David, Forman, & Jones (1990, 1991). After a very brief initial wind phase, driven by the explosion of type II supernovae, the resulting flow evolution goes from a global inflow to a wind, which is experienced only by the smallest galaxies by the present time. David et al. (1991) conclude that all galaxies above [FORMULA] host a cooling flow. So, as in the steady state cooling flow scenario, the scatter in [FORMULA] at fixed [FORMULA] has to be explained by a combination of environmental differences (White & Sarazin 1991) and by large variations from galaxy to galaxy in the stellar mass loss rate per unit [FORMULA], the efficiency of thermalization of the stellar mass loss, and that of thermal instabilities in the hot gas. An alternative way of explaining the scatter in the [FORMULA] diagram is given by the evolutionary scenario of D'Ercole et al. (1989), and Ciotti et al. (1991, CDPR). Assuming that the SNIa explosion rate is declining with time slightly faster than the rate with which mass is lost by the stars, in the beginning the energy released by SNIa's can drive the gas out of the galaxies through a supersonic wind. As the collective SNIa energy input decreases, a subsonic outflow takes place, which gradually slows until a central cooling catastrophe leads to the onset of an inflow. At fixed [FORMULA], any of the three phases wind, outflow or inflow can be found at the present epoch, depending only on the various depths and shapes of the potential well of the galaxies. In this way both the large scatter in [FORMULA] and the trend in the spectral properties are accounted for at the same time: in the X-ray bright galaxies the soft X-ray emitting gas dominates the emission, being in the inflow phase, that resembles a cooling flow; in the X-ray faint galaxies the hard stellar emission dominates, these being in the wind phase.

Recent ASCA observations seems to indicate that the SNIa's activity is suppressed in early-type galaxies, which implies that the CDPR scenario is essentially ruled out. Since this issue is far from closed (Sect. 1.3), it is still worthwile to explore the effects of SNIa's on the flows, using the updated rate given by recent optical surveys; this is lower than that adopted by CDPR, which was 0.67 the standard one estimated by Tammann (1982). This aspect, together with the need for changes in other galaxy properties crucial for the evolution of hot gas flows, are discussed below.

1.1. New stellar density profiles

Previous numerical simulations of hot gas flows used the King (1972) stellar density distribution mainly for computational ease. This distribution has an inner region of constant density (the so called "core") of the order of a few hundred parsecs, which keeps the time step of the numerical simulation reasonably small (a stellar density increase implies a reduction of the characteristic hydrodynamical time step). Another advantage of density profiles with a constant density core is that the central regions can be resolved using a larger grid size; this again allows a larger time step (see CDPR for a more quantitative discussion). It is well known though that a much better description of the surface brightness profiles of ellipticals is given by the de Vaucouleurs (1948) law. A very good fit to this law is given by the Jaffe (1983) and by the Hernquist (1990) distributions, that have the advantage that all their dynamical properties can be expressed analytically. These distributions belong to the family of the so called [FORMULA] -models, that has been widely explored recently (Dehnen 1993; Tremaine et al. 1994):

[EQUATION]

The density profile of the Hernquist law has [FORMULA], while that of the Jaffe law has [FORMULA]. Inside [FORMULA] the density of [FORMULA] -models increases as [FORMULA], a significant difference with respect to King models: over a few hundreds of parsecs at the center the [FORMULA] -models are power laws. The existence of cores of constant surface brightness has been definitively ruled out by ground based observations (Lauer 1985, Kormendy 1985), and recently by the Hubble Space Telescope (Jaffe et al. 1994; Lauer et al. 1995), that has shown how the central surface brightness profile is described by a power law as far in as can be observed, i.e., [FORMULA] pc in Virgo. From the point of view of a very accurate photometry, the surface brightness law implied by Eq. (1) cannot reproduce well both the envelope and the very center of all the ellipticals observed by HST. The Jaffe law, though, gives a general description of ellipticals accurate enough for the treatment of hot gas flows, on the scales that are relevant for the problem (from a few tens to several thousands of parsecs).

1.2. New dark matter estimates and distributions

Attempts to estimate the amount of nonluminous mass in elliptical galaxies have been made recently through extensive searches for dynamical evidence of dark matter, either with systematic observations of ionized gas probing the gravitational field (Pizzella et al. 1997) or with measurements of stellar velocity dispersions profiles out to large radii (e.g., Bertin et al. 1994; Carollo et al. 1995). These optical studies are confined to within one or two effective radii [FORMULA], and typically find that luminous matter dominates the mass distribution inside [FORMULA], while dark matter begins to be dynamically important at 2-3 [FORMULA]. In particular, for a sample of X-ray emitting galaxies, it has been found that dark matter halos are not much more massive than the luminous component, with the dark-to-luminous mass ratio [FORMULA] ; the value of [FORMULA] is most common (Saglia et al. 1993). X-ray emission from hot gas provides a great potential for mapping the mass of ellipticals to larger distances (e.g., Fabian et al. 1986). The standard method employed derives from the equation of hydrostatic equilibrium, and requires the knowledge of the gas temperature profile. Attempts to apply this technique to the Einstein data yielded a much larger component of dark matter than found from optical data, but these results are very uncertain because temperature profiles are poorly determined (Forman, Jones, & Tucker 1985; Fabbiano 1989). Using superior X-ray data provided by ROSAT and ASCA, Buote & Canizares (1997) proved that mass does not follow the optical light, out to many [FORMULA], in NGC720 and NGC1332. Adopting plausible gas and mass models, they find [FORMULA] for NGC1332, and [FORMULA] in NGC720 at 90% confidence; [FORMULA] prevails exterior to [FORMULA]. Similarly Mushotzky et al. (1994) derive [FORMULA] within [FORMULA] for NGC4636, and analogous results have been obtained from ROSAT data of NGC507 and NGC499 by Kim & Fabbiano (1995). AXAF will have the combined spatial and spectral resolution to measure accurately the presence of different spectral components, their relative flux and their spatial distribution, and to produce more accurate mass distribution from X-rays.

The radial density distribution of the dark haloes of ellipticals is not well constrained by observations; theoretical arguments favor a peaked profile (Ciotti & Pellegrini 1992; Evans & Collett 1997), and high resolution numerical simulations of dissipationless collapse produce a density distribution with [FORMULA] near the center (Dubinski & Carlberg 1991; Navarro, Frenk, & White 1996; White 1996; Fukushige & Makino 1997, and references therein). Previous works studying the hot gas flow evolution always used quasi isothermal haloes at least nine times more massive than the luminous component. We are motivated now to explore even the effects produced by dark haloes not as massive as supposed before, and not quasi-isothermal.

1.3. New Type Ia supernova rates

Nearby SNIa rates in early-type galaxies have been carefully reanalyzed recently, and this important ingredient of the simulations of hot gas flows has been revised. From optical surveys it was estimated to be 0.88 [FORMULA] SNu (Tammann 1982), and then 0.98 [FORMULA] SNu (van den Bergh & Tammann 1991). Most recent estimates agree on lower values: 0.25 [FORMULA] SNu (van den Bergh & McClure 1994) and 0.24 [FORMULA] SNu (Turatto, Cappellaro, & Benetti 1994), where [FORMULA] and 1 SNu = 1 SNIa per century per [FORMULA].

In principle, constraints on the SNIa rate can be given also by estimates of the iron abundance in galactic flows (see, e.g., Renzini et al. 1993, and references therein). These were first attempted using data from the Ginga satellite for NGC4472, NGC4636, NGC1399 (Ohashi et al. 1990; Awaki et al. 1991; Ikebe et al. 1992), and then from the BBXRT satellite for NGC1399, NGC4472 (Serlemitsos et al. 1993), and more recently from ASCA with a superior spectral energy resolution (Loewenstein et al. 1994; Awaki et al. 1994; Arimoto et al. 1997; Matsumoto et al. 1997). Under the assumption of solar abundance ratio, the analysis of all these data suggests a very low iron abundance, consistent with no SNIa's enrichment and even lower than that of the stellar component. However, some authors have found that more complex multi-temperature models with higher abundance give a better fit of the data (Kim et al. 1996, Buote & Fabian 1997). Moreover, the above results are based on iron line diagnostic tools whose reliability has been questioned (e.g., Arimoto et al. 1997), especially because of uncertainties affecting the Fe L-shell atomic physics for temperatures less than 2 keV, that are typical of hot gas flows in ellipticals (Liedahl, Osterheld, & Goldstein 1995). Line emission even in simple (e.g., isothermal) astrophysical plasmas needs to be understood, and reliable fits to the data made, before secure consequences concerning the SNIa rate can be drawn from X-ray determined abundances.

In summary, recent optical studies agree on a present epoch SNIa rate much lower than previously used, and indicate that also the dark matter content could be lower. Moreover, cuspier density profiles, especially for the stellar distribution, should be used. All this raises the question of whether the CDPR scenario is altered by these changes in the main ingredients of the problem, and more in general what are the effects on the properties of hot gas flows. In this paper we address these points, with a new set of hydrodynamical simulations. In Sect. 2 we present the galaxy models, the source terms, and the integration techniques. In Sect. 3 we discuss the main properties of the evolution of gas flows in our new models, and we compare them with the observations and the CDPR results. In Sect. 4 we discuss the results using energetic arguments, and in Sect. 5 the main conclusions are summarized.

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© European Southern Observatory (ESO) 1998

Online publication: April 20, 1998
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