ABSTRACT

Aims. The aim of the present grid of stellar models is to complete our previous calculations and provide a tool for investigating the astrophysical properties of eclipsing binaries, stellar clusters, galactic bulges, and elliptical galaxies with a high metal content. Methods. To explore the applicability of high metallic models, we have computed three grids: (X, Z) = (0.64, 0.04), (0.58, 0.06), and (0.46, 0.10). For all these grids, we adopted an enrichment law ∆Y/∆Z = 2.0, as in our previous papers on this subject. The input physics is almost the same as adopted in our earlier work except for some numerical details, recent measurement of the rate for the reaction 14N(p, γ)15O, and the recent mass-loss rate for the Wolf-Rayet stages. Results. Two high-metallicity clusters, NGC 6253 and NGC 6791, were used to test the present calculations with very satisfactory results. On the other hand, as this series of grids was mainly designed to investigate the tidal evolution of close binaries, we analyse the present status of circularization times in both clusters and isolated binaries. The present models (90 tables) can be retrieved from the CDS via anonymous ftp.

Key words. binaries: eclipsing – stars: evolution – stars: abundances – stars: rotation

1. Introduction

Eclipsing binary stars that show high metal content are not all that common. In the few detected cases, the metal content was detected due to spurious comparison with old stellar models based on old opacities and nuclear reaction rates. In spite of this, there is observational evidence for high metallic stars in clusters and in at least two double-lined eclipsing binaries. The two conspicuous cases of metal-rich clusters are NGC 6791 (Carraro et al. 2006) and NGC 6253 (Twarog et al. 2003). NGC 6791 is an old, nearby cluster with high metallicity. Depending on the adopted stellar models, their ages are between 8 and 12 Gyr. The metallicity of this cluster is still imprecise, but recently, Gratton et al. (2006) obtained high-resolution spectrography of red clump stars. Using a spectrum synthesis analysis, they were able to derive [Fe/H] = +0.47 ± 0.04. On the other hand, Twarog et al. (2003) obtained CCD photometry in the Strömgren system + Ca Hβ for NGC 6253. By using the δm1 and δhk indices, they found [Fe/H] ranging from +0.7 up to +0.9. The system with highest metallicity of double-lined eclipsing binaries, as far as we known, is WW Aur, which has been studied in detail by Southworth et al. (2005). The average accuracies of the radii and masses are smaller than 1%. The observations can be itted only for metal-rich models (Z = 0.06), although there is no clear connection with the metallic lines present in the system.

Metal-rich stars are expected to also be present in galactic bulges and elliptical galaxies, with Z as high as 5 times the solar value (e.g. Moehler & Sweigart 2006; Sadler 1992). Higher metallicities (10–15 times Z) have been assignated to quasars (Korista et al. 1996; Baldwin et al. 2003) though the inferred values are somewhat uncertain. The aim of the present grid of metal-rich stellar models is to complete our previous calculations and provide a tool for investigating the astrophysical properties of eclipsing binaries, stellar clusters, galactic bulges, and elliptical galaxies with high metallicity. The present grids, together with those previously published (Claret 2004, 2005a, 2006), enable us to analyse their impact on the tidal evolution of close binaries whether located in clusters or isolated. We study the efects of changing the radius, mass, and depth of the convective layer on the circularization times in order to evaluate the impact of theoretical uncertainties. Even taking such uncertainties into account we show that the tidalbreaking and the radiative damping mechanisms are not eicient enough to match the observed levels of circularization.

2. Characteristics of the models

In order to explore the applicability of high metallic models, we have computed three grids: (X, Z) = (0.64, 0.04), (0.58, 0.06), and (0.46, 0.10). For all these grids, we adopted an enrichment law ∆Y/∆Z = 2.0, as in our previous papers on this subject. The input physics is almost the same as adopted in Claret (2004). However, some updates were implemented concerning nuclear reaction rates (Runkle 2003; Formicola et al. 2004), numerical accuracy (e.g. the size of the triangle used to deine an envelope in the HR diagram that is important for avoiding numericaloscillations in xbf – see Fig. 9) and, mass loss rates for the WolfRayet stages, in massive stars. For the latter we have adopted the recent formalism by Nugis & Lamers (2000), which takes the dependence on metallicity and luminosity into account. We do not describe the adopted input physics here, but for a quick reference we give a summary in Table 1 of the main characteristics of the present grids. For completeness, we briely discuss the mass loss of massive stars. As pointed out by Mowlavi et al. (1998), the criterion for deining a Wolf-Rayet star may be diferent for the one adopted for lower metallicities. Due to the large uncertainties involved, we adopt the same criterion here as was considered in our previous papers. In contrast to Mowlavi et al. (1998), who stop the calculations at 60 M, we computed models up to 125 M, always keeping in mind the large inaccuracy of the mass-loss rates in this mass range. The corresponding HR diagrams for the three grids can be seen in Figs. 1–3 for (X, Z) = (0.64, 0.04), (0.58, 0.06), and (0.46, 0.10), respectively. One of the showiest characteristic of the massive stars in these igures is that, due to their lower initial hydrogen content, they reach the Wolf-Rayet stage earlier, still during the mainsequence. Mowlavi et al. (1998) ind that the models that are more massive than 60 M lose almost their initial mass during the main-sequence at Z = 0.10. Our results do not completly agree with this. For example, a model with an initial mass of 125 M (Z = 0.10) achieves the end of the main-sequence with about 30 M. Such a discrepancy is probably due to the diferent adopted mass-loss rates. Another interesting feature of the high metallic models is that they are hotter and more luminous than their metal-poor counterparts, as already pointed out by Mowlavi et al. (1998), who analyse the case of a 3 M model. A simple homology approximation can be used to illustrate this feature: the luminosity depends on the mean molecular weight as µa, where a is greater than zero. Considering, for example, µ for (X, Z) = (0.64, 0.04) and (0.46, 0.10) for a ixed mass, a decrease in the hydrogen content and an increase in Z implies a heavier mean molecular weight, hence an increase in luminosity. This efect can be inspected in Fig. 4 for the case of a 10 M model where the high luminosities and efective temperatures of (X, Z) = (0.46, 0.10) models can be easily noted if compared with the less metallic ones. On the other hand, lifetimes of hydrogen-burning phase are expected to be shorter in more metallic models due to their lower hydrogen content. Their higher luminosities and efective temperatures also contribute to a decrease in the lifetimes. For example, we have found that the lifetime ratio (almost independent on mass) of the (0.64, 0.04) set and the (0.46, 0.10) one is around 2.3 (Fig. 5). In the case of core helium-burning, the situation is similar but the ratio of lifetimes between both sets is reduced to about 1.8. For models with masses higher than ≈40 M, the lifetime of core helium burning is almost independent of the mass.

以下谷歌翻译，不保证准确性

目标。 结果。 抽象的 模型数据（90 个表格）只能通过匿名 ftp 到 cdsarc.u‑strasbg.fr (130.79.128.5) 或通过 http://cdsweb.u‑strasbg.fr/cgi‑bin/qcat 在 CDS 上以电子形式提供?J/ A+A/467/1389 为了探索高金属模型的适用性，我们计算了三个网格： (X, Z) = (0.64, 0.04)、(0.58, 0.06) 和 (0.46, 0.10)。对于所有这些网格，我们采用了富集定律ΔY/ ΔZ = 2.0，正如我们之前关于该主题的论文中所述。除了一些数值细节、最近对反应14N(p, γ) 15O 速率的测量以及最近 Wolf‑Rayet 阶段的质量损失率之外，输入 物理几乎与我们早期工作中采用的相同。 关键词。双星：食 – 恒星：进化 – 恒星：丰度 – 恒星：旋转 可根据要求在 CD ROM 上提供其他数据。 食双星、星团、星系核球和具有高金属含量的椭圆星系的天体物理特性。 2006 年 10 月 26 日收到 / 2007 年 1 月 28 日接受 Instituto de Astrofísica de Andalucía, CSIC, Apartado 3004, 18080 Granada, Spain 电子邮 件：claret@iaa.es 目前的恒星模型网格的目的是完成我们之前的计算并提供一个工具来研究 两个高金属星团 NGC 6253 和 NGC 6791 被用来测试目前的计算结果非常令人满意。另一方面，由于这一系列网格主要是为了研究近距双星的潮汐演 化，我们分析了星团和孤立双星的环化时间的现状。可以通过匿名 ftp 从 CDS 检索当前模型（90 个表）。

一、简介

显示出高金属含量的食双星并不常见。在少数检测到的案例中，由于与基于旧不 透明度和核反应速率的旧恒星模型进行虚假比较，检测到了金属含量。尽管如 此，在星团和至少两个双线食双星中仍有高金属星的观测证据。富金属星团的两 个显着例子是 NGC 6791 (Carraro et al. 2006) 和 NGC 6253 (Twarog et al. 2003)。 NGC 6791 是一个古老的、邻近的具有高金属丰度的星团。根据采 用的恒星模型，它们的年龄在 8 到 12 Gyr 之间。

这个星团的金属丰度仍然不精确，但最近，Gratton 等人。 (2006) 获得了红色 团块星的高分辨率光谱。使用光谱合成分析，他们能够推导出 [Fe/H] = +0.47 ±0.04。另一方面，Twarog 等人。 (2003) 获得了 NGC 6253 的 Strömgren 系统 + Ca Hβ 中的 CCD 测光。通过使用δm1和δhk指数，他们发现 [Fe/H] 范 围为 +0.7 到 +0.9。据我们所知，双线食双星金属丰度最高的系统是 WW Aur， Southworth 等人对此进行了详细研究。 （2005 年）。半径和质量的平均精 度小于 1%。观察结果只能适用于富含金属的模型（Z = 0.06），尽管与系统中 存在的金属线没有明确的联系。

预计富含金属的恒星也会出现在星系核球和椭圆星系中， Z高达太阳值 的 5 倍（例如 Moehler & Sweigart 2006；Sadler 1992）。较高的金属丰度 （10‑15 倍Z ）已被分配给类星体（Korista 等人 1996；Baldwin 等人 2003），尽管推断的值有些不确定。目前富金属恒星模型网格的目的是完成我 们之前的计算，并为研究食双星、星团、星系核球和高金属丰度椭圆星系的天体 物理特性提供工具。

目前的网格以及之前发表的网格（Claret 2004, 2005a, 2006）使我们能 够分析它们对靠近双星的潮汐演化的影响，无论它们是位于集群中还是孤立 的。我们研究了改变对流层的半径、质量和深度对圆化时间的影响，以评估理论 不确定性的影响。即使考虑到这些不确定性，我们也表明潮汐破坏和辐射阻尼 机制的效率不足以匹配观察到的循环水平。

二、机型特点

为了探索高金属模型的适用性，我们计算了三个网格： （X， Z）=（0.64， 0.04），（0.58，0.06）和（0.46，0.10）。对于所有这些网格，我们采用了富集定 律ΔY/ΔZ = 2.0，正如我们之前关于该主题的论文中所述。输入物理与 Claret (2004) 中采用的几乎相同。

然而，对核反应速率（Runkle 2003；Formicola 等 2004）、数值精度（例如， 用于定义 HR 图中的包络线的三角形的大小，这对于避免数值xbf中的振荡（见图 9）以及大质量恒星中 Wolf Rayet 阶段的质量损失率。 对于后者，我们采用了

Nugis & Lamers (2000) 最近的形式，它采用考虑到金属丰度和光度的依赖性。我们的确是此处不描述采用的输入物理场，但为了快速参考，我们在表 1 中总结了主要特征

目前的网格

为了完整起见，我们简要讨论大质量恒星的质量损失。正如 Mowlavi 等 人指出的那样。 (1998)，定义 Wolf‑Rayet 星的标准可能与 125 M (Z = 0.10) 达到主序列的结尾 和 (0.46, 0.10) 对于固定质量，氢的减少 那些。另一方面，氢燃烧相的寿命 预计在更多金属模型中会更短，因为它们 还计算了接近双星系统的潮汐演化。在 等，这是为每个模型提供的。 含量和Z的增加意味着较重的平均分子 这样，谐波k2、 k3和k4可用于测试 约 30 M 。这种差异可能是由于不同 一种用于较低金属丰度。由于涉及到很大的不确定性关系，我们在这里采用与 我们之前的论文中所考虑的相同的标准。与 Mowlavi 等人相反。 Nugis & Lamers (2000) 最近的形式主义，它采用 氢含量较低。它们具有更高的亮度和有效 例如，我们发现 (0.64, 0.04) 组和 (0.46, 0.10) 组的寿命比（几乎与质量无 关）为 高金属模型的另一个有趣特征是 对于(X, Z) = (0.64, 0.04), (0.58, 0.06) 和 (0.46, 0.10)，分别。大质量恒星最 显着的特征之一这些数字是，由于它们的初始氢含量较低， (X, Z) = (0.46, 0.10)的光度和有效温度 也可以通过以下方式计算（并与导出的年龄进行比较） 谁分析了一个3M模型的案例。一个简单的同调近似可以用来说明这个特征： 光度 考虑到金属丰度和光度的依赖性。我们的确是 质量超过 60 M的物体几乎失去了它们的初始质量 , 大量的。 比零。例如，考虑 μ for (X, Z) = (0.64, 0.04) 与本系列的前几篇论文一样，一些参数与 目前的网格。 同意这一点。例如，一个初始质量为 重量，因此增加了亮度。对于 10 M模型的情况，这种效果可以在图 4 中看到， 其中高 (1998)，在 60 M时停止计算，我们计算了高达 125 M的模型，Z = 0.10处的主序列。我们的结果并不完全始终牢记在此质 量范围内的质量损失率图存在1 和很图大的2 中不看准到。 确性。1‑3 三个网格对应的 HR 图可以在