Title: Modeling the vertical distribution of the Milky Way's flat subsystem objects Show Chinese title

Title: 模拟银河系扁平子系统天体的垂直分布

Abstract: This paper is an initial stage of consideration of the general problem of joint modeling of the vertical structure of a Galactic flat subsystem and the average surface of the disk of the Galaxy, taking into account the natural and measurement dispersions. We approximate the average surface of the Galactic disk with a polynomial model and determine its parameters by minimizing the squared deviations of objects along the normal to the model surface. The developed method allows us to simultaneously identify significant details of the Galactic warping and estimate the offset $z_\odot$ of the Sun relative to the average (non-flat) surface of the Galactic disk and the vertical scale of the object system for an arbitrary area of the disk covered by data. The method is applied to data on classical Cepheids. Significant local extremes of the average disk surface model were found: the minimum in the first Galactic quadrant and the maximum in the second. A well-known warp in the third quadrant has been confirmed. The optimal order of the model was found to be $n_\text{o}=4$. The local (near the Sun, $n_\text{o}=0$) estimate of $z_\odot = 28.1 \pm \left.6.1\right|_{\text{stat.}}\left.{}\pm1.3\right|_{\text{cal.}}$ pc is close to the non-local ($n_\text{o}=4$) $z_\odot = 27.1 \pm \left.8.8\right|_{\text{stat.}}\left.{}^{+1.3}_{-1.2}\right|_{\text{cal.}}$ pc, which suggests that the proposed method eliminates the influence of warping on the $z_\odot$ estimate. However, the non-local estimate of the vertical standard deviation of Cepheids $\sigma_{\rho} = 132.0 \pm \left.3.7\right|_{\text{stat.}}\left.{}^{+6.3}_{-5.9}\right|_{\text{cal.}}$ pc differs significantly from the local $\sigma_{\rho} = \left.76.5 \pm 4.4\right|_{\text{stat.}}\left.{}^{+3.6}_{-3.4}\right|_{\text{cal.}}$ pc, which means the need to introduce more complex models outside the Sun's vicinity. Show Chinese abstract

Abstract: 本文是对银河系扁平子系统垂直结构和银河系盘面平均表面联合建模这一一般问题的初步考虑。我们用多项式模型近似银河系盘面的平均表面，并通过最小化沿模型表面法线方向的物体平方偏差来确定其参数。该方法使我们能够同时识别银河系翘曲的重要细节，并估计太阳相对于银河系盘面平均（非平面）表面的偏移量$z_\odot$以及任意数据覆盖的盘面区域的物体系统的垂直尺度。该方法应用于经典造父变星的数据。发现了平均盘面模型的显著局部极值：第一银河象限的最小值和第二象限的最大值。第三象限已知的翘曲得到了证实。发现模型的最佳阶数为$n_\text{o}=4$。太阳附近的局部（$n_\text{o}=0$）估计的$z_\odot = 28.1 \pm \left.6.1\right|_{\text{stat.}}\left.{}\pm1.3\right|_{\text{cal.}}$光年接近非局部（$n_\text{o}=4$）的$z_\odot = 27.1 \pm \left.8.8\right|_{\text{stat.}}\left.{}^{+1.3}_{-1.2}\right|_{\text{cal.}}$光年，这表明所提出的方法消除了翘曲对$z_\odot$估计的影响。 然而，造父变星垂直标准差的非局部估计$\sigma_{\rho} = 132.0 \pm \left.3.7\right|_{\text{stat.}}\left.{}^{+6.3}_{-5.9}\right|_{\text{cal.}}$pc 与局部估计$\sigma_{\rho} = \left.76.5 \pm 4.4\right|_{\text{stat.}}\left.{}^{+3.6}_{-3.4}\right|_{\text{cal.}}$pc 存在显著差异，这意味着需要在太阳附近以外引入更复杂的模型。