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

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4. An energetic explanation for the occurrence of the PW in different galaxy models

The origin of PWs, and of the flows of a different nature obtained by CDPR, can be explained qualitatively in terms of the local [FORMULA] function. The global [FORMULA] is defined as the ratio between the energy required to steadily extract the gas lost by the stars per unit time from the galactic potential well ([FORMULA]), and the heating supplied by the SNIa explosions plus the thermalization of the stellar velocity dispersion ([FORMULA]). [FORMULA] was introduced by CDPR to predict the expected flow phases in King galaxies, and was shown to work remarkably well by the numerical simulations: when [FORMULA] the flow turned out to be an inflow, when [FORMULA] a wind. In Tables 1 and 2 most of the resulting flow phases are not global, but PWs, and so we are moved to investigate in more detail the distribution of the energetics inside the galaxy models. This distribution in fact can be much different for two galaxies with the same global [FORMULA]. The local [FORMULA] is defined as

[EQUATION]

where

[EQUATION]

[EQUATION]

and

[EQUATION]

where [FORMULA] is the total potential, [FORMULA] is the one-dimensional isotropic velocity dispersion obtained by solving the Jeans equations for the adopted mass model (e.g., Binney & Tremaine 1987), and [FORMULA] is the specific mass return rate. The global [FORMULA] is obtained by replacing the differentials in Eq. (2) with their integrals over the whole galaxy.

The differences in the flow behavior of JH models and models with a central constant density region can be understood with the aid of Fig. 6, where [FORMULA] is shown for four representative one-component models. These have the same global [FORMULA], and so from an energetical point of view are globally equivalent. Three of them are [FORMULA] -models, with [FORMULA], i.e., they are the Jaffe model, the Hernquist model, and a model with a core. The fourth density distribution is described in the Appendix, and is flatter at the center than the [FORMULA] model, but for large r it decreases [FORMULA], as all the [FORMULA] -models. This distribution is studied for its similarity with the King (1972) model, that needs the annoying introduction of a truncation radius, and has more complicated dynamical properties.

[FIGURE] Fig. 6. The radial trend of [FORMULA] as a function of [FORMULA] for the models considered in Sect. 4. The ratio [FORMULA] is given by 0.76, 1.82, 2.87, 1.73 respectively for the Jaffe (solid line), Hernquist (dotted), [FORMULA] (short-dashed) and the model described in the Appendix (long-dashed).

It is apparent from Fig. 6 that the steeper the density profile, the stronger is the variation of [FORMULA] across the galaxy, and the higher are the values that it reaches at the center. This explains why a strong decoupling can be present in the flow of highly concentrated systems: a [FORMULA] significantly higher than unity in the central regions produces a central inflow, while in the external parts a degassing is energetically possible because [FORMULA]. This can happen when the global [FORMULA] is either [FORMULA] or [FORMULA] (see Fig. 6 and Table 1), so this parameter is not a good indicator of the flow phase for highly concentrated systems. If [FORMULA] decreases, the radius where [FORMULA] moves inward for all the models, and so a larger part of the galaxy is degassing. Note a fundamental difference in the trend of [FORMULA] as a function of [FORMULA] for models with a core and cuspier models: while in cuspy models there is always a region with [FORMULA], even though small, this is not the case for core models, in which such a region suddenly appears by increasing [FORMULA], with a size larger than the core.

A second effect on [FORMULA] is produced by the dark halo. If this halo is more diffuse than the stellar mass, increasing [FORMULA] makes more bound the external regions, when [FORMULA] is kept constant, and so the radius at which [FORMULA] moves outward (see Fig. 7 for the case of JH models).

[FIGURE] Fig. 7. The radial trend of [FORMULA] as a function of [FORMULA] for the JH model. The different curves are labelled with the value of [FORMULA], while the global [FORMULA] and [FORMULA] are constant at the values indicated.

The trend of [FORMULA] for models with a core explains the results of the numerical simulations for King models plus diffuse quasi-isothermal dark halos obtained by CDPR and Pellegrini & Fabbiano (1994). The flow phases found by CDPR with [FORMULA] were all global; with low [FORMULA], instead, the flow can be decoupled again, as found by Pellegrini & Fabbiano (1994) in their detailed modeling of the X-ray properties of two ellipticals. This because with high [FORMULA] the region with [FORMULA] constant is very large (of the order of the core radius of the dark halo), while with low [FORMULA] this region is of the order of the stellar core radius.

In summary, the combined effect of SNIa's and dark matter is more varied for models with a core than for JH models: for a large range of [FORMULA] values, the latter keep in PWs with a varying [FORMULA], while the former can be in wind, PWs, outflows or inflows.

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© European Southern Observatory (ESO) 1998

Online publication: April 20, 1998
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