The constraining effect of gas and the dark matter halo on the vertical stellar distribution of the Milky Way

We study the vertical stellar distribution of the Milky Way thin disk in detail with particular focus on the outer disk. We treat the galactic disk as a gravitationally coupled, three-component system consisting of stars, atomic hydrogen gas, and molecular hydrogen gas in the gravitational field of the dark matter halo. The self-consistent vertical distribution for stars and gas in such a realistic system is obtained for radii between 4-22 kpc. The inclusion of an additional gravitating component constrains the vertical stellar distribution toward the mid-plane, so that the mid-plane density is higher, the disk thickness is reduced, and the vertical density profile is steeper than in the one-component, isothermal, stars-alone case. We show that the stellar distribution is constrained mainly by the gravitational field of gas and dark matter halo in the inner and the outer Galaxy, respectively. We find that the thickness of the stellar disk (measured as the HWHM of the vertical density distribution) increases with radius, flaring steeply beyond R=17 kpc. The disk thickness is reduced by a factor of 3-4 in the outer Galaxy as a result of the gravitational field of the halo, which may help the disk resist distortion at large radii. The disk would flare even more if the effect of dark matter halo were not taken into account. Thus it is crucially important to include the effect of the dark matter halo when determining the vertical structure and dynamics of a galactic disk in the outer region.Comment: 8 pages,7 figures, Accepted for publication in A &

Flaring stellar disk in the low surface brightness galaxy UGC 7321

We theoretically study the vertical structure of the edge-on low surface brightness (LSB) galaxy UGC 7321. This is one of the few well-observed LSBs. We modeled it as a gravitationally coupled disk system of stars and atomic hydrogen gas in the potential of the dark matter halo and treated the realistic case where the rotation velocity varies with radius. We used a dense and compact halo as implied by the observed rotation curve in this model. We calculated the thickness of stellar and HI disks in terms of the half-width at half-maximum of the vertical density distribution in a region of R=0 to 12 kpc using input parameters constrained by observations. We obtain a mildly increasing disk thickness up to R=6 kpc, in a good agreement with the observed trend, and predict a strong flaring beyond this. To obtain this trend, the stellar velocity dispersion has to fall exponentially at a rate of 3.2R_D , while the standard value of 2R_D gives a decreasing thickness with radius. Interestingly, both stellar and HI disks show flaring in the outer disk region although they are dynamically dominated by the dark matter halo from the very inner radii. The resulting vertical stellar density distribution cannot be fit by a single sech^2/n function, in agreement with observations, which show wings at larger distances above the mid-plane. Invoking a double-disk model to explain the vertical structure of LSBs as done in the literature may therefore not be necessary.Comment: 10 pages, 11 figures, published in A&

Gravitational potential energy of a multi-component galactic disk

We calculate ab initio the gravitational potential energy per unit area for a gravitationally coupled multi-component galactic disk of stars and gas, which is given as the integration over vertical density distribution, vertical gravitational force, and vertical distance. This is based on the method proposed by Camm for a single-component disk, which we extend here for a multi-component disk by deriving the expression of the energy explicitly at any galactocentric radius R. For a self-consistent distribution, the density and force are obtained by jointly solving the equation of vertical hydrostatic equilibrium and the Poisson equation. Substituting the numerical values for the density distribution and force obtained for the coupled system, in the derived expression of the energy, we find that the energy of each component remains unchanged compared to the energy for the corresponding single-component case. We explain this surprising result by simplifying the above expression for the energy of a component analytically, which turns out to be equal to the surface density times the squared vertical velocity dispersion of the component. However, the energy required to raise a unit test mass to a certain height z from the mid-plane is higher in the coupled case. The system is therefore more tightly bound closer to the mid-plane, and hence it is harder to disturb it due to an external tidal encounter.Comment: 11 pages, 5 figures, Accepted for publication in Astronomy & Astrophysic