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Astron. Astrophys. 345, 787-812 (1999)

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4. Initial conditions

The radial distribution of molecular gas in the Milky Way, as traced by CO, is essentially confined inside the solar circle, with a marked hole between 1 and 3 kpc and a strong central concentration associated to the nuclear ring/disc, whereas the HI presents a rather constant surface density extending far beyond [FORMULA] and an abrupt decline towards the centre below 3 kpc. The total gas mass within [FORMULA] is estimated to [FORMULA] [FORMULA], comprising [FORMULA] [FORMULA] of H2 (with a large uncertainty owing to the poorly known CO to H2 conversion factor) and [FORMULA] [FORMULA] of HI (Scoville 1992), plus 28% of helium and metals. For the gaseous disc, we have used the following initial mass distribution:

[EQUATION]

with [FORMULA] kpc, [FORMULA] and a total mass [FORMULA] [FORMULA], resulting in [FORMULA] [FORMULA] within the solar circle. Both radial and vertical profiles are Gaussian, and the disc is linearly flaring with radius, as observed in HI from a few kpc of the centre out to at least [FORMULA] (Merrifield 1992), achieving a thickness of 136 pc at [FORMULA]. The fast radial decline is aimed to spare SPH particles in the outer regions and hence increase the spatial resolution near the centre at fixed number of particles. The observed gas deficit between 1 and 3 kpc needs not to be reproduced since shocks will naturally deplete this region. The gas particles initially have pure circular velocities derived from the axisymmetric part of the total potential at [FORMULA].

The stellar and dark mass is divided into the same three components as in Paper I: a stellar nucleus-spheroid (NS), a stellar disc and a dark halo (DH), with their initial axisymmetric mass distribution described by the same analytical formulae, except for the disc. In Paper I we indeed noted that the adopted double exponential discs evolve into discs with too less mass outside the bar region according to the COBE/DIRBE near-IR and bulge microlensing data, and possibly an excess of mass in the central region when compared to the HI terminal velocity constraints. Instead of increasing the disc scale length, we choose here to soften the initial central mass density taking:

[EQUATION]

where [FORMULA] is the total disc mass, [FORMULA] the scale length, [FORMULA] the scale height and [FORMULA] the normalised vertical profile. The surface density remains exponential in the external disc, but continuously and differentiably joins an inner Gaussian distribution at [FORMULA], with a central value reduced by 40% relative to the purely exponential case. To compensate for the enhanced spatial density near the plane [FORMULA] caused by the additional gas component, we also replace the exponential vertical profile of Paper I by van der Kruit's (1988) profile:

[EQUATION]

with [FORMULA], between the exponential ([FORMULA]) and isothermal ([FORMULA]) cases.

The choice of the parameters are based on the simulations performed in Paper I, giving a strong weight to the [FORMULA] orbits versus HI terminal velocities test. The best models regarding this test are m06t4600 and m04t3000, whose initial axisymmetric models share the following interdependent properties: (i) a ratio of disc over NS mass of 0.8 within the spheroidal volume [FORMULA] kpc (where [FORMULA] and [FORMULA]), (ii) a total NS+disc mass of [FORMULA] [FORMULA] in the same volume and (iii) a circular velocity of 190 km s-1 just after the very steep central rise of the rotation curve, taking into account the velocity scales adjusted to the observed stellar velocity dispersion in Baade's window (see Table 3 of Paper I). The DH parameters, a and [FORMULA] are fixed as in the reference simulation m00, and the other parameters are adjusted to the former constraints and to a disc surface density on the solar circle of 60 [FORMULA] pc-2, yielding [FORMULA] [FORMULA], [FORMULA] [FORMULA] and [FORMULA] kpc. The mass density is softly truncated as in Paper I, at radius [FORMULA] kpc and over a width [FORMULA] kpc, and the initial kinematics rests on the same relations between the velocity moments as in simulations m00-m10, except that the asymptotic velocity anisotropy [FORMULA] and the transition radius [FORMULA] kpc for the NS component.

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© European Southern Observatory (ESO) 1999

Online publication: April 28, 1999
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