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Astron. Astrophys. 334, 829-839 (1998)

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2. Barred galaxy potential

For the sake of comparison, the barred galaxy potential used here is the one described in Pfenniger 1984 (P84). As often verified, the precise density shape far from the considered orbits is not important when describing the major orbits of a galactic potential: indeed their shapes depend mostly on the main symmetries of the problem.

The potential derives from two mass components, a Miyamoto-Nagai (1975) disc, whose potential reads,


and a triaxial [FORMULA] Ferrers (1877) bar of semi-axes a, b, c, whose density [FORMULA] is expressed by


where m is the scaled "ellipsoidal radius":


The corresponding potential [FORMULA] and forces are given in a closed form suited for numerical treatment in P84 2 3. Here we adopt the now widespread convention of aligning the bar major axis with the x -axis. The corotation radius [FORMULA] is put at the end of the major semi-axis a of the bar. The values of the fixed parameters are [FORMULA], [FORMULA], [FORMULA], [FORMULA], and [FORMULA], while [FORMULA] and [FORMULA] are variable satisfying [FORMULA].

The main change with the "main model" in P84 is the adoption of a much thicker, nearly prolate bar ([FORMULA] instead of 10), less eccentric ([FORMULA] instead of 4), but more massive ([FORMULA] instead of 0.1), so that the bar strength remains similar.

The first reason to adopt a nearly prolate bar is that the belief in the 80's that bars should be very flat in z ([FORMULA]) (e.g., Kormendy 1982; Wakamatsu & Hamabe 1984) which was based on a single case, NGC 4762, has not resisted the subsequent evidences coming from N -body simulations and from the shape of the Milky Way Bar (e.g., Zhao 1996; Fux 1997). While it is possible that flat growing bars start from a thin disk, the resulting fierce vertical resonances induced by the bar necessarily bend and inflate it, as shown clearly in the N -body simulations of Raha et al. (1991) and ours. As consequence a thick prolate bar demands a smaller ratio [FORMULA] and a larger bar mass in order to yield, when combined with the Miyamoto-Nagai disk, face-on projected isophotes compatible with the ones of barred galaxies (and N -body bars) with axis-ratios of the order of [FORMULA].

The second reason to choose a more massive but less eccentric bar is that the stability properties of the Lagrangian points [FORMULA] are then compatible to those found in N -body simulations, i.e. in self-consistent mass models (P90).

The prime goal to reach with this potential, i.e. to get a relatively realistic mass model computable with precision but without excessive compromise linked with easily tractable analytical formulae, is then achieved.

The length unit can be conveniently taken as the kpc, the time unit as [FORMULA], and the mass unit of the order of [FORMULA].

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© European Southern Observatory (ESO) 1998

Online publication: June 2, 1998