Abstract
We present a general recipe for constructing N-body realizations of galaxies comprising near spherical and disc components. First, an exact spherical distribution function for the spheroids (halo and bulge) is determined, such that it is in equilibrium with the gravitational monopole of the disc components. Second, an N-body realization of this model is adapted to the full disc potential by growing the latter adiabatically from its monopole. Finally, the disc is sampled with particles drawn from an appropriate distribution function, avoiding local-Maxwellian approximations. We performed test simulations and find that the halo and bulge radial density profile very closely match their target model, while they become slightly oblate due to the added disc gravity. Our findings suggest that vertical thickening of the initially thin disc is caused predominantly by spiral and bar instabilities, which also result in a radial re-distribution of matter, rather than scattering off interloping massive halo particles.
Highlights
Generating an equilibrium N-body representation of a multicomponent galaxy is of importance for a number of applications, for example the study of bars (e.g. Debattista & Sellwood 2000; Athanassoula 2002), warps (e.g. Ideta et al 2000) and galaxy mergers, both minor (e.g. Mihos et al 1995; Walker, Mihos & Hernquist 1996) and major (e.g. Heyl, Hernquist & Spergel 1996; Naab, Burkert & Hernquist 1999)
In the case where ra → ∞, the anisotropy of the halo is the same at all radii, β = −α. This approach has the advantage that the distribution function is exact for a spherically symmetric system, and remains in equilibrium, maintaining its original density profile
It should be noted that up until this point the velocity distribution of the disc has not been a factor in the calculations, so the halo and bulge created by this process can be re-used in simulations with identical disc density profiles, but different disc kinematics
Summary
Generating an equilibrium N-body representation of a multicomponent galaxy is of importance for a number of applications, for example the study of bars (e.g. Debattista & Sellwood 2000; Athanassoula 2002), warps (e.g. Ideta et al 2000) and galaxy mergers, both minor (e.g. Mihos et al 1995; Walker, Mihos & Hernquist 1996) and major (e.g. Heyl, Hernquist & Spergel 1996; Naab, Burkert & Hernquist 1999). Kroupa & Penarrubia-Garrido (2001) extended this approach to include a non-spherical halo, but maintained the approximation to a Maxwellian distribution for the particle velocities This method is not rigorous and Hernquist (1993) himself suggested that ‘in the future, it will likely be necessary to refine the basic approach as computer hardware and software permit simulations with particle numbers significantly in excess of those discussed here’. The major problem with this approach is summed up by Widrow & Dubinski (2005) when they state that the combined model constructed in this way ‘may bare [sic] little resemblance to the corresponding isolated components, a situation which is cumbersome for model building’.
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