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 ~35% at the solar radius for a stars-alone disc for the typical observed linear gradient of +6.7 km $s^{-1}kpc^{-1}$ 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 $sech^{2}$ , 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%.

中文翻译：

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非等温星系盘中的垂直恒星密度分布

星系盘中恒星的垂直密度分布传统上是通过假设恒星的等温垂直速度色散来获得的。SDSS、LAMOST、RAVE、Gaia 等最近的观察表明，这种色散随着距中平面的高度而增加。在这里，我们通过求解泊松方程和流体静力平衡方程来研究这种非等温色散对银河系中薄盘星自洽垂直密度分布的动力学影响。我们发现在非等温情况下，由于垂直压力较高，中面密度较低，标高高于等温分布的相应值，因此分布在垂直方向上延伸得更多。对于 +6.7 公里的典型观测线性梯度 $s^{-1}kpc^{-1}$，对于单个恒星的圆盘而言，太阳半径处的变化约为 35%，并且随着半径的增加和梯度的增加而变得更高探索。该分布显示了高 z 处的机翼，与观测结果一致，并且由双 $sech^{2}$ 拟合得很好，这可能被误解为存在第二个更厚的圆盘，特别是在外部星系中。我们还考虑了一个更真实的圆盘，它由暗物质晕场中的引力耦合恒星和气体组成。结果显示出相同的趋势，但由于气体和晕重力的相反约束作用，非等温扩散的影响降低。此外，非等温色散将总中平面密度的理论估计值（即奥尔特极限值）降低了 16%。