在电子計算机上計算中型质量恒星模型的数学方法

本文讨论在电子计算机上计算中型质量恒星模型的数学方法和程序实践。相应的模型是核外包层——产能薄壳——部分简并等温核模型。文中论述了核外包层解对初始值的连续依赖,提出用迭代法同时求解lnρ、lnP_e、y、z_1、z_2、ln_μ,并指明迭代的振动性质和加速迭代的方法。用理查逊外插估计核外包层解的积分精度。在计算核结构时采用牛顿三次插值程序进行费米-狄拉克函数的内插,估计了插值误差。     

用完全线性化方法计算非局部热动平衡大气模型

本文叙述了用完全线性化方法计算非局部热动平衡大气模型的计算过程程序设计,并对计算结果进行了讨论。     

非圆轨道GPS/LEO掩星反演地球大气参数的算法及讨论

在非圆轨道GPS和LEO卫星条件下，给出一种较为直接的GPS／LEO掩星反演地球大气参数技术中弯曲角序列的迭代算法，并在理论上对该迭代法的收敛性进行了严格的数学证明．利用GPS掩星反演模拟程序，定量估算了卫星圆轨道假设对GPS／LEO掩星反演地球大气参数的影响，并验证了在非圆轨道条件下各种迭代法的一致性．指出了文献中给出的级数展开迭代算法的不足之处．     

精密定轨用地球大气模型误差的补偿方法

本文提出了一种用于精密轨道确定的地球大气模型误差的补偿方法，这种方法采用改进 大气周日峰角的技术，有效地补偿了大气密度模型的误差，并具有较好的物理意义．与传统 的每圈改进一次加速度的方法比较，轨道确定达到了相当的径向精度，且避免了轨道改进参 数间的相关性，同时解算参数的数量也少了一半．     

用线性化分离法计算膨胀恒星大气的谱线形成

本研究了具有宏观运动的膨胀恒星大气中的转射转移过程，详细介绍如何利用线性化分离法计算运动大气谱线形成，并采用线性化分离法计算了Ｏｒｉ星的Ｈα线 Ｐ Ｃｙｇｎｉ轮廓。     

用改进的SPEA求解轨道转移的时间-能量极小化问题

提出了改进的SPEA，这是一种多目标进化算法，适于求解大尺度空间的多目标优化的Pareto最优解，并应用于求解轨道转移的时间—能量极小化问题，计算结果表明算法的有效性。     

基于Broyden方法的不对称与对称周期解延拓算法与应用

考虑周期解的数值延拓问题并提出基于Broyden拟牛顿法来延拓周期解的一种有效算法,先后以布鲁塞尔振子、平面圆型限制性三体问题(Planar Circular Restricted Three-Body Problem, PCRTBP)的周期解为例进行了验证.这里的Broyden方法包含线性搜索、正交三角分解求线性方程组的步骤.对一般的周期解,周期性条件方程组中含有周期作为待延拓参数,可用周期来决定积分时长,将解代入周期性条件得到积分型的非线性方程组,利用Broyden方法迭代延拓直至初值收敛.根据两次垂直通过一个超平面的轨道是对称周期轨道的性质,可采用插值的方法求得再次抵达超平面的解分量,得到周期性条件方程组,再用Broyden方法求解.结合哈密顿系统的对称性和PCRTBP周期轨道的一些分类,对2/1、3/1的内共振周期解族进行了数值研究.最后,对算法和计算结果做了总结和讨论.     

泊松分布下的非线性拟合

对一数据涨落服从泊松概率分布的实验数据组进行拟合,如果拟合函数是非线性的,常常只能采用某些近似方法。近似性之一,表现在将拟合函数线性化,或者采用某种参数寻优的方法。近似性之二,则是将泊松问题近似地看作高斯分布问题。本文从最大或然法出发,对两类不同概率分布情况下的曲线拟合进行了比较,给出了对泊松分布问题更严格的求解途径。对于特殊的非线性拟合函数y(x)=ae~(bx~N),直接给出了迭代解。本文对曲线拟合的“面积亏损”问题,也进行了讨论。     

卫星定位中的一种分步加权解算方法

卫星定位中,当可视卫星数目多于4颗时常采用加权最小二乘(Web Login Server,WLS)算法,对各卫星解算权重进行重新评估而获得最优解。然而由于受到多重因素的影响,权矩阵W的构造与确定一直是各类加权算法中的重点和难点。从线性测量方程组出发,通过研究迭代解算过程中用户等效伪距测量误差对坐标位置误差的传递与放大规律,提出了一种新的加权最小二乘解算方法,及其权矩阵的具体构造与实现方法,从而对各未知数进行分步加权与分离解算。通过全球定位系统(Global Positioning System,GPS)实测实验,对方法的可行性和精度水平进行了分析与验证。结果表明,使用该分步加权方法进行定位,解算结果准确度更高、稳定性更好。     

利用正交变换方法计算协方差分析的统计量

证明用Givens—Gentleman正交变换给出的加仅最小二乘解与统计定轨理论求得的解一致．采用正交变换方法计算其它的一些重要的统计量,如考察协方差矩阵、摄动矩阵等,并计算这些量随时间的传播．这种算法的优点是通过降低法方程的条件数提高计算的稳定性,同时可以方便地对不同的参数组合情况求解而不需多次解算法方程．     

共生星双星的星风物质损失率的测定

共生星双星是一颗有强大星风物质损失的红巨星与一颗早型热星组成的特殊双星系统。由于早型热星在充满红巨星的星风物质的空间中环绕运行，可以产生Ｐ—Ｃｙｇｎｉ型谱线，通过对Ｐ—Ｃｙｇｎｉ型谱线的理论分析可以精确测定共生星双星的星风物质损失率。文章介绍了国际上比较有代表意义的一些共生星双星的工作，其中的方法几乎都是近十年中发展起来的。同时，文章还介绍了作者的一些工作。在谱线形成计算中考虑了较多的因素，如氢—氦混合气体的多能级跃迁问题、轨道运动引起的密度非径向分布问题等，并在轨道形状方面做了一些简化。反映了共生星双星谱线形成关键的周期性相位变化的特征，取得了比较满意的结果，对这个方法存在的问题和改进方向进行了一些简要讨论，此外，还介绍了作者在线性化分离法求解Ｎｏｎ－ＬＴＥ大气模型中所做的工作。     

Evolutionary stellar population synthesis at high spectral resolution: optical wavelengths

We present the single stellar population (SSP) synthesis results of our new synthetic stellar atmosphere models library with a spectral sampling of 0.3 Å, covering the wavelength range from 3000 to 7000 Å for a wide range of metallicities (twice solar, solar, half solar and 1/10 solar). The stellar library is composed of 1650 spectra computed with the latest improvements in stellar atmospheres. In particular, it incorporates non-local thermodynamic equilibrium (LTE) line-blanketed models for hot  ( T _eff≥ 27 500 K)  , and LTE line-blanketed models (Phoenix) for cool  (3000 ≤ T _eff≤ 4500 K)  stars. Because of the high spectral resolution of this library, evolutionary synthesis models can be used to predict the strength of numerous weak absorption lines and the evolution of the profiles of the strongest lines over a wide range of ages. The SSP results have been calculated for ages from 1 Myr to 17 Gyr using the stellar evolutionary tracks provided by the Geneva and Padova groups. For young stellar populations, our results have a very detailed coverage of high-temperature stars with similar results for the Padova and Geneva isochrones. For intermediate and old stellar populations, our results, once degraded to a lower resolution, are similar to the ones obtained by other groups (limitations imposed by the stellar evolutionary physics notwidthstanding). The limitations and advantages of our models for the analysis of integrated populations are described. The full set of the stellar library and the evolutionary models are available for retrieval at the websites http://www.iaa.csic.es/~rosa and http://www.iaa.csic.es/~mcs/sed@ , or on request from the first two authors.     

PopStar I: evolutionary synthesis model description

We present new evolutionary synthesis models for simple stellar populations for a wide range of ages and metallicities. The models are based on the Padova isochrones. The core of the spectral library is provided by the medium resolution Lejeune et al. atmosphere models. These spectra are complemented by Non Local Thermodynamic Equilibrium (NLTE) atmosphere models for hot stars that have an important impact on the stellar cluster's ionizing spectra: O, B and WR stellar spectra at the early ages, and spectra of post asymptotic giant branch stars and planetary nebulae, at intermediate and old ages. At young ages, our models compare well with other existing models, but we find that the inclusion of the nebular continuum, not considered in several other models, significantly reddens the integrated colours of very young stellar populations. This is consistent with the results of spectral synthesis codes particularly devised for the study of starburst galaxies. At intermediate and old ages, the agreement with the literature model is good and, in particular, we reproduce the observed colours of star clusters in Large Magellanic Cloud well. Given the ability to produce good integrated spectra from the far-ultraviolet to the infrared at any age, we consider that our models are particularly suited for the study of high-redshift galaxies. These models are available on the web site http://www.fractal-es.com/SEDmod.htm and also through the Virtual Observatory Tools on the PopStar server.     

Stellar population models for young stellar clusters

Stellar population models are a very useful tool to derive the stellar cluster age and luminosity mass from its integrated light. Evolutionary synthesis models depend on the stellar evolutionary tracks and the stellar libraries used to predict the spectral energy distribution of the stellar populations. In this review, I briefly comment on the new models that have incorporated the new evolutionary tracks with rotation and new computations for the evolutionary tracks of the TP-AGB. A more extended summary is also given of the current status of the most recent high-resolution stellar libraries at optical wavelengths and their implementation in evolutionary synthesis models. A comparison of the results obtained fitting the optical spectra of LMC and SMC stellar clusters with different high spectral resolution evolutionary synthesis models is also presented.     

Measurement of the limb darkening coefficient of stars

This paper introduces a new method of describing the limb darkening phenomenon of stellar atmospheres in the 1st and 2nd order approximations. The limb darkening coefficients are given by direct measurements of relevant physical quantities or measurements of flux and a supplementary quantity, namely, the star's surface temperature. The comparison either with solar observations or with the method of numerical simulation of the atmosphere shows that the new method can very accurately describe the star's limb darkening and determine its relevant coefficients. The accuracy of the new direct method is assessed using 176 observational data points of the Sun, and the mean fractional differences is found to be 0.38% for the 1st-, and 0.26% for the 2nd-order approximations. The mean differences of the indirect method are close to, and slightly larger than these values. When compared with numerical models of the atmosphere, the differences are in the range from under 1% to under 3%.     

Abundances and absolute stellar magnitudes for F and G supergiants of Magellanic Clouds

Using high-resolution spectra, we study 31 yellow supergiants of the Large and Small Magellanic Clouds by the method of atmosphere models. Abundance values of 20 chemical elements are determined. It is shown that ??-elements are in a slight excess and neutron-capture elements have an excess up to 0.60 dex. Approbation of a new technique for the determination of absolute stellar magnitudes of late-type supergiants is performed. The technique is based on the use of the spectroscopic criterion, namely, depth-line ratios for iron. Absolute stellar magnitudes of nine supergiants of the Large Magellanic Cloud are calculated using this technique. A value of the distance modulus of the Large Magellanic Cloud is estimated: m ? M = 18.4 ± 0.3 ^m .     

A new method of calculating multi-level non-LTE line formation

This paper introduces a new method of solving the equation of multi-level non-LTE radiative transfer subject to constraints. This method is based on the combination of the advantages of the complete linearization method by Auer and Mihalas (1969) and the simple separated-iteration technique (Mihalas, 1978). First, linearize the equation of radiative transfer and constraints, respectively, then solve the linearized equation of the radiative transfer and linearized constraints, separately. It overcomes the disadvantages of requiring the simultaneous solution of the corresponding equations by the complete linearization method and the poor convergence of the simple separated-iteration technique. Therefore, it not only can deal with complex models, but also has a high speed of convergence in the calculation of multi-level NLTE line formation.     

Orbital separation amplification in fragile binaries with evolved components

The secular stellar mass loss causes an amplification of the orbital separation in fragile, common proper motion, binary systems with separations of the order of 1000 A.U. In these systems, companions evolve as two independent coeval stars as they experience negligible mutual tidal interactions or mass transfer. We present models for how post-main sequence mass-loss statistically distorts the frequency distribution of separations in fragile binaries. These models demonstrate the expected increase in orbital separation resulting from stellar mass-loss, as well as a perturbation of associated orbital parameters. Comparisons between our models and observations resulting from the Luyten survey of wide visual binaries, specifically those containing MS and white-dwarf pairs, demonstrate a good agreement between the calculated and the observed angular separation distribution functions.     

The rotation of 53 Be stars

Through spectral observations we obtained the rotational velocity Vsini for 53 Be stars, and estimated the values of V and i on the basis of Hutching's method. We analysed the effect of rotation on the width of emission lines and used the emission peak separation to determine the relative size of the shell and the photosphere and the dilution factor. We discuss in depth fast rotating models where stellar winds are present and their relation to the Be phenomenon.     

恒星大气物理参量的非参数估计方法

恒星大气物理参量（有效温度、表面重力、化学丰度）是导致恒星光谱差异的主要因素．恒星大气物理参量的自动测量是LAMOST等大规模巡天望远镜所产生的海量天体光谱数据自动处理中一个重要研究内容．针对测量大样本的恒星光谱数据估计每个恒星的大气物理参量，提出了一种基于变窗宽核函数的估计算法：变窗宽算法是对固定窗宽算法的改进，分为3个步骤：（1）将历史恒星光谱数据进行PCA处理，得到光谱的低维特征数据；（2）利用特征数据与其物理参数的对应关系，建立一种变窗宽的非参数估计模型；（3）利用该估计模型，直接计算待测恒星光谱的3个物理参量（有效温度、表面重力、金属丰度）．实验结果表明：该方法与固定窗宽估计模型以及在其他文献中报道的方法相比，具有较高的估计精度和鲁棒性．