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.

We study the vertical structure of an edge-on low surface brightness galaxy UGC 7321 theoretically, which is one of the few wellobserved LSBs. We model it as a gravitationally coupled disk system of stars and atomic hydrogen gas in the potential of the dark matter halo and treat the realistic case where the rotation velocity varies with radius while solving for the vertical disk structure. We calculate the thickness of stellar and HI disks in terms of half-width at half-maximum of vertical density distribution in a region of R=0 to 12 kpc using input parameters as constrained by observations. We obtain a mildly increasing disk thickness up to R=6 kpc, in a fairly good agreement with observations, and predict a strong flaring beyond that. To obtain this trend in thickness of the stellar disk, the velocity dispersion of stars should fall exponentially at a rate of 3.2R D , whereas the typically assumed value of 2R D gives decreasing thickness with radius. We also show that a compact and dense halo as implied by the observed rotation curve is needed to explain this trend. Interestingly both the stellar and HI disks show flaring at outer disk region despite being dynamically dominated by the dark matter halo from the very inner radii. The resulting vertical stellar density distribution cannot be fitted by a single sech 2/n function in agreement with observations. Hence invoking a double disk model to explain the vertical structure of LSBs as done in the literature may not be necessary.

We study the vertical stellar distribution of the Milky Way thin disk treated as a gravitationally coupled system of stars, HI and H2 gas in the field of dark matter halo, from R = 4 to 22 kpc. We show that the gas and halo gravity mainly constrain this vertical distribution toward the mid-plane in the inner and the outer Galaxy, respectively. The halo gravity reduces the disk thickness by a factor of 3-4 in the outer Galaxy. Despite this constraining effect the disk thickness increases steadily with radius, flaring steeply beyond 17 kpc, making a flaring disk a generic result.

The self-consistent vertical density distribution in a thin, isothermal disc is typically given by a sech 2 law, as shown in the classic work by Spitzer (1942). This is obtained assuming that the radial and vertical motions are decoupled and only the vertical term is used in the Poisson equation. We argue that in the region of low density as in the outer disc this treatment is no longer valid. We develop a general, complete model that includes both radial and vertical terms in the Poisson equation and write these in terms of the full radial and vertical Jeans equations which take account of the non-flat observed rotation curve, the random motions, and the cross term that indicates the tilted stellar velocity ellipsoid. We apply it to the Milky Way and show that these additional effects change the resulting density distribution significantly, such that the mid-plane density is higher and the disc thickness (HWHM) is lower by 30-40% in the outer Galaxy. Further, the vertical distribution is no longer given as a sech 2 function even for an isothermal case. These predicted differences are now within the verification limit of new, high-resolution data for example from GAIA and hence could be confirmed.

The vertical density distribution of stars in a galactic disc is traditionally obtained by assuming an isothermal vertical velocity dispersion of stars. Recent observations from SDSS, LAMOST, RAVE, Gaia etc show that this dispersion increases with height from the mid-plane. Here we study the dynamical effect of such non-isothermal dispersion on the self-consistent vertical density distribution for the thin disc stars in the Galaxy, obtained by solving together the Poisson equation and the equation of hydrostatic equilibrium. We find that in the non-isothermal case the mid-plane density is lower, and the scale height is higher than the corresponding values for the isothermal distribution, due to higher vertical pressure, hence the distribution is vertically more extended. The change is $\sim 35 \%$ at the solar radius for a stars-alone disc for the typical observed linear gradient of +6.7 km s−1kpc−1 and becomes even higher with increasing radii and increasing gradients explored. The distribution shows a wing at high z, in agreement with observations, and is fitted well by a double $\operatorname{sech}^{2}$, which could be mis-interpreted as the existence of a second, thicker disc, specially in external galaxies. We also consider a more realistic disc consisting of gravitationally coupled stars and gas in the field of dark matter halo. The results show the same trend but the effect of non-isothermal dispersion is reduced due to the opposite, constraining effect of the gas and halo gravity. Further, the non-isothermal dispersion lowers the theoretical estimate of the total mid-plane density i.e, Oort limit value, by 16%.