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

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2. The models

2.1. Galaxy models

Following the discussion in Sections 1.1 and 1.2, our model galaxies are a superposition of a Jaffe density distribution for the luminous matter [FORMULA] [Eq. (1) with [FORMULA], [FORMULA], [FORMULA] ], and of a Hernquist distribution for the dark matter [Eq. (1) with [FORMULA], [FORMULA], [FORMULA] ]. We call these two-component mass models JH models. Both density distributions have finite mass, and so no truncation radius is applied. The relation between the scale length [FORMULA] and the effective radius for the Jaffe model is [FORMULA]. We constrain the luminous body to lie on the fundamental plane of elliptical galaxies (Djorgovski & Davis 1987; Bender, Burstein, & Faber 1992). The input observables are [FORMULA], and the central value of the projected velocity dispersion [FORMULA]. The stellar mass is related to [FORMULA] through the projected virial theorem, as described in Ciotti, Lanzoni, & Renzini (1996); the luminous matter distribution is then completely defined, because it is assumed that the stellar mass-to-light ratio is constant with radius, and the orbital distribution is isotropic. The dark matter distribution is determined by choosing the ratios of the dark to luminous mass ([FORMULA]), and of the dark to luminous core radius ([FORMULA]). The basic dynamical properties of the JH models (radial trend of the velocity dispersion, kinetic and potential energy, etc.) are given in the Appendix.

2.2. Source terms

The time evolving input ingredients of the numerical simulations are the rates of stellar mass loss, of SNIa heating, and of thermalization of the stellar velocity dispersion; these are calculated as in CDPR, where a detailed description is given. Here we summarize only the main properties of the input quantities. The stellar mass loss rate is accurately described by [FORMULA], where [FORMULA] is in [FORMULA], and [FORMULA] is time in units of 15 Gyr; in the numerical code the exact mass return prescribed by the stellar evolution theory is used. The SNIa heating rate is parameterized as [FORMULA], where [FORMULA] erg is the kinetic energy injected in the ISM by one SNIa, [FORMULA] SNu, and [FORMULA]. When [FORMULA] and [FORMULA] [FORMULA] is the rate estimated by Tammann (1982). [FORMULA] is assumed to be decreasing with time just faster than the stellar mass loss rate. Unfortunately, given our enduring ignorance of the nature of the SNIa's progenitors (e.g., Branch et al. 1995) the evolution of the SNIa rate is not known; some arguments though, as an observed pronounced correlation of the rate with the star formation rate along the Hubble sequence, favour a declining rate (see also Renzini et al. 1993; Ruiz-Lapuente, Burkert, & Canal 1995; Renzini 1996). With the assumptions above the specific heating for the gas is decreasing with time, and so we have the wind/outflow/inflow secular evolution in the CDPR models (Sect. 1). This direction of the evolution of the flow is maintained as long as [FORMULA] decreases faster than [FORMULA], and the results do not qualitatively depend on the particular slope adopted for [FORMULA] ; when this slope is much higher than that of [FORMULA], though, too much iron is produced at early times (see Renzini et al. 1993 for a more extensive discussion).

The heating given by the thermalization of the stellar velocity dispersion at each radius is determined using the velocity dispersion profile obtained by solving the Jeans equation in the global isotropic case (see the Appendix).

2.3. Numerical simulations

The time-dependent equations of hydrodynamics with source terms, and the numerical code used to solve them, are fully described in CDPR, together with the initial conditions. We adopt here a higher spatial resolution in the central regions of the galaxies: the central grid spacing is 30 pc instead of 100 pc. This allows a better sampling of the inner regions now described by a power law, and is adequate to highlight the differences in the flow properties between JH models and King models plus a quasi isothermal dark halo. The model galaxies are initially devoid of gas, a situation produced by the galactic winds established by type II supernovae, early in the evolution of elliptical galaxies. The gas flow evolution is followed for 15 Gyrs.

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© European Southern Observatory (ESO) 1998

Online publication: April 20, 1998
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