Title: Constructing semi-empirical sunspot models for helioseismology Show Chinese title

Title: 构建用于日震学的半经验太阳黑子模型

Abstract: One goal of helioseismology is to determine the subsurface structure of sunspots. In order to do so, it is important to understand first the near-surface effects of sunspots on solar waves, which are dominant. Here we construct simplified, cylindrically-symmetric sunspot models, which are designed to capture the magnetic and thermodynamics effects coming from about 500 km below the quiet-Sun $\tau_{5000}=1$ level to the lower chromosphere. We use a combination of existing semi-empirical models of sunspot thermodynamic structure (density, temperature, pressure): the umbral model of Maltby et al. (1986) and the penumbral model of Ding and Fang (1989). The OPAL equation of state tables are used to derive the sound speed profile. We smoothly merge the near-surface properties to the quiet-Sun values about 1mm below the surface. The umbral and penumbral radii are free parameters. The magnetic field is added to the thermodynamic structure, without requiring magnetostatic equilibrium. The vertical component of the magnetic field is assumed to have a Gaussian horizontal profile, with a maximum surface field strength fixed by surface observations. The full magnetic field vector is solenoidal and determined by the on-axis vertical field, which, at the surface, is chosen such that the field inclination is 45$^\circ$ at the umbral-penumbral boundary. We construct a particular sunspot model based on SOHO/MDI observations of the sunspot in active region NOAA 9787. The helioseismic signature of the model sunspot is studied using numerical simulations of the propagation of f, p$_1$, and p$_2$ wave packets. These simulations are compared against cross-covariances of the observed wave field. We find that the sunspot model gives a helioseismic signature that is similar to the observations. Show Chinese abstract

Abstract: 日震学的一个目标是确定太阳黑子的地下结构。 为了做到这一点，首先了解太阳黑子对太阳波的近表面影响是很重要的，这些影响是主要的。 在这里，我们构建了简化的、轴对称的太阳黑子模型，这些模型旨在捕捉从安静太阳$\tau_{5000}=1$层以下约500公里到低色球层的磁场和热力学效应。 我们使用现有的半经验太阳黑子热力学结构（密度、温度、压力）模型的组合：Maltby等（1986）的本影模型和Ding和Fang（1989）的半影模型。 使用OPAL状态方程表来推导声速剖面。 我们将近表面特性平滑地合并到表面以下约1毫米处的安静太阳值。 本影和半影半径是自由参数。 磁场被添加到热力学结构中，不需要磁静力平衡。 磁场的垂直分量假定具有高斯水平分布，最大表面磁场强度由表面观测确定。 整个磁场矢量是无散的，并由轴向垂直磁场确定，该磁场在表面被选择为使本影-半影边界处的磁场倾角为45$^\circ$。 我们基于SOHO/MDI对活动区NOAA 9787中的太阳黑子的观测构建了一个特定的太阳黑子模型。 使用f、p$_1$和p$_2$波包传播的数值模拟来研究模型太阳黑子的日震特征。 这些模拟与观测到的波场的交叉协方差进行比较。 我们发现，太阳黑子模型给出的日震特征与观测结果相似。