具有自适应并行回火的星点映射I：计算代码的实现
Starspot mapping with adaptive parallel tempering I: Implementation of computational code
摘要：
恒星黑子被认为是局部强磁场的区域，类似于太阳黑子，它们可以产生光度亮度调制。为了推断恒星和斑点的属性，如斑点的出现和衰减率，我们实现了星点建模的计算代码。它是实现自适应并行回火算法和重要性抽样算法的参数估计和模型选择的贝叶斯框架。为了评估代码的性能，我们将其应用于用3个点产生的合成光变曲线。光变曲线在光斑参数中指定，例如半径、强度、纬度、反射率和出射/衰减持续时间。这些光斑是相对于光球具有特定半径和强度的圆形，恒星的微分自转系数也包含在光变曲线中。结果，恒星和斑点的参数是唯一的推导。点的数量是正确的确定：3点模型是优选的，因为模型的证据是远远大于2点模型的数量级，并超过4点模型的一个更温和的因素，而光变曲线产生有2个或1个本地最小值在一个赤道旋转周期，通过调整经度的值。在考虑到斑点数目的差异的情况下，可以估计斑点的出现和衰减速率，误差小于一个数量级。
英文摘要：
Starspots are thought to be regions of locally strong magnetic fields, similar to sunspots, and they can generate photometric brightness modulations. To deduce stellar and spot properties, such as spot emergence and decay rates, we implement computational code for starspot modeling. It is implemented with an adaptive parallel tempering algorithm and an importance sampling algorithm for parameter estimation and model selection in the Bayesian framework. For evaluating the performance of the code, we apply it to synthetic light curves produced with 3 spots. The light curves are specified in the spot parameters, such as the radii, intensities, latitudes, longitudes, and emergence/decay durations. The spots are circular with specified radii and intensities relative to the photosphere, and the stellar differential rotation coefficient is also included in the light curves. As a result, stellar and spot parameters are uniquely deduced. The number of spots is correctly determined: the 3-spot model is preferable because the model evidence is much greater than that of 2-spot models by orders of magnitude and more than that of 4-spot model by a more modest factor, whereas the light curves are produced to have 2 or 1 local minimum during one equatorial rotation period by adjusting the values of longitude. The spot emergence and decay rates can be estimated with error less than an order of magnitude, considering the difference of the number of spots.
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