银河系的非等温垂直分布函数
Non-isothermal vertical distribution functions for the Milky Way
AI总结：
本研究针对银河系垂直结构的伪等温分布假设，通过统计论证与两体散射力学分析，推导了非等温垂直分布函数族，指出GMC的近银道面分布及库仑对数的速度相关性是偏离伪等温的主因。
AI中文摘要：
我们的银河系的垂直结构通常被认为遵循伪等温分布。然而，并没有先验理由表明这种形式会由巨分子云（GMCs）的散射产生，因为GMCs被限制在银道面附近的一个薄层内，因此不会使恒星在垂直相空间中均匀随机化。我们首先提出一个简单的统计论证，在GMCs为薄盘分布的极限情况下推导了一种新的垂直分布函数（DF），该函数引入了一个额外的${J_z}^{-α}$因子，其中$α>0$且随不同的势场而变化。有鉴于此，我们在更符合实际的延展GMCs分布中，从两体散射的力学机制出发重新推导了垂直加热的扩散系数。由此得到的漂移系数和扩散系数在$v_z$上呈现强非线性，尤其是在相对速度较低时，弱局域相遇的有效作用范围可能会消失。我们确定了定态解，还通过数值方法求解了含时系数的轨道平均Fokker-Planck方程。我们发现，在这两种情况下，垂直作用量分布都与伪等温情况的分布存在偏差，并提出了一类新的垂直分布函数族，它是对伪等温形式的推广。我们发现导致非等温性的两个主要因素是：（i）被限制在银道面附近的GMC分布；（ii）库仑对数$Λ$在小速度下具有强速度相关性，不能像通常采用的假设那样被视为常数。
英文摘要：
The vertical structure of our Galaxy has commonly been assumed to follow a pseudo-isothermal distribution. However, there is no \textit{a priori} reason to expect this form to arise from scattering by giant molecular clouds (GMCs), since GMCs are confined to a narrow layer around the Galactic midplane and therefore do not randomise stars uniformly in vertical phase space. We first present a simple statistical argument to derive a new vertical distribution function (DF), in the limiting case of a razor-thin distribution of GMCs, which admits an extra factor of ${J_z}^{-α}$, where $α>0$ and varies for different potentials. In light of this, we revisit the diffusion coefficients for vertical heating from the mechanics of two-body scattering, in a more realistic, extended distribution of GMCs. The resulting drift and diffusion coefficients are strongly non-linear in $v_z$, particularly at low relative velocities, where the effective range of weak, local encounters can vanish. We determine stationary solutions, and also numerically solve the orbit-averaged Fokker--Planck equation with time-dependent coefficients. We find, in both cases, a vertical action distribution that deviates from that of the pseudo-isothermal case, and propose a new, family of vertical DFs that generalise the pseudo-isothermal form. We find the two primary agents of non-isothermality are: (i) a GMC distribution confined near the midplane, and (ii) the fact that the Coulomb logarithm, $Λ$ is strongly velocity-dependent at small velocities, and cannot be treated as a constant, contrary to the commonly adopted assumption.
