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 Str?mgren 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.

以下谷歌翻譯，不保證準(zhǔn)確性

目標(biāo)。 結(jié)果。 抽象的 模型數(shù)據(jù)（90 個(gè)表格）只能通過(guò)匿名 ftp 到 cdsarc.u?strasbg.fr (130.79.128.5) 或通過(guò) http://cdsweb.u?strasbg.fr/cgi?bin/qcat 在 CDS 上以電子形式提供?J/ A+A/467/1389 為了探索高金屬模型的適用性，我們計(jì)算了三個(gè)網(wǎng)格： (X, Z) = (0.64, 0.04)、(0.58, 0.06) 和 (0.46, 0.10)。對(duì)于所有這些網(wǎng)格，我們采用了富集定律ΔY/ ΔZ = 2.0，正如我們之前關(guān)于該主題的論文中所述。除了一些數(shù)值細(xì)節(jié)、最近對(duì)反應(yīng)14N(p, γ) 15O 速率的測(cè)量以及最近 Wolf?Rayet 階段的質(zhì)量損失率之外，輸入 物理幾乎與我們?cè)缙诠ぷ髦胁捎玫南嗤?關(guān)鍵詞。雙星：食 – 恒星：進(jìn)化 – 恒星：豐度 – 恒星：旋轉(zhuǎn) 可根據(jù)要求在 CD ROM 上提供其他數(shù)據(jù)。 食雙星、星團(tuán)、星系核球和具有高金屬含量的橢圓星系的天體物理特性。 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 電子郵 件：claret@iaa.es 目前的恒星模型網(wǎng)格的目的是完成我們之前的計(jì)算并提供一個(gè)工具來(lái)研究 兩個(gè)高金屬星團(tuán) NGC 6253 和 NGC 6791 被用來(lái)測(cè)試目前的計(jì)算結(jié)果非常令人滿意。另一方面，由于這一系列網(wǎng)格主要是為了研究近距雙星的潮汐演 化，我們分析了星團(tuán)和孤立雙星的環(huán)化時(shí)間的現(xiàn)狀?？梢酝ㄟ^(guò)匿名 ftp 從 CDS 檢索當(dāng)前模型（90 個(gè)表）。

一、簡(jiǎn)介

顯示出高金屬含量的食雙星并不常見(jiàn)。在少數(shù)檢測(cè)到的案例中，由于與基于舊不 透明度和核反應(yīng)速率的舊恒星模型進(jìn)行虛假比較，檢測(cè)到了金屬含量。盡管如 此，在星團(tuán)和至少兩個(gè)雙線食雙星中仍有高金屬星的觀測(cè)證據(jù)。富金屬星團(tuán)的兩 個(gè)顯著例子是 NGC 6791 (Carraro et al. 2006) 和 NGC 6253 (Twarog et al. 2003)。 NGC 6791 是一個(gè)古老的、鄰近的具有高金屬豐度的星團(tuán)。根據(jù)采 用的恒星模型，它們的年齡在 8 到 12 Gyr 之間。

這個(gè)星團(tuán)的金屬豐度仍然不精確，但最近，Gratton 等人。 (2006) 獲得了紅色 團(tuán)塊星的高分辨率光譜。使用光譜合成分析，他們能夠推導(dǎo)出 [Fe/H] = +0.47 ±0.04。另一方面，Twarog 等人。 (2003) 獲得了 NGC 6253 的 Str?mgren 系統(tǒng) + Ca Hβ 中的 CCD 測(cè)光。通過(guò)使用δm1和δhk指數(shù)，他們發(fā)現(xiàn) [Fe/H] 范 圍為 +0.7 到 +0.9。據(jù)我們所知，雙線食雙星金屬豐度最高的系統(tǒng)是 WW Aur， Southworth 等人對(duì)此進(jìn)行了詳細(xì)研究。 （2005 年）。半徑和質(zhì)量的平均精 度小于 1%。觀察結(jié)果只能適用于富含金屬的模型（Z = 0.06），盡管與系統(tǒng)中 存在的金屬線沒(méi)有明確的聯(lián)系。

預(yù)計(jì)富含金屬的恒星也會(huì)出現(xiàn)在星系核球和橢圓星系中， Z高達(dá)太陽(yáng)值 的 5 倍（例如 Moehler & Sweigart 2006；Sadler 1992）。較高的金屬豐度 （10?15 倍Z ）已被分配給類星體（Korista 等人 1996；Baldwin 等人 2003），盡管推斷的值有些不確定。目前富金屬恒星模型網(wǎng)格的目的是完成我 們之前的計(jì)算，并為研究食雙星、星團(tuán)、星系核球和高金屬豐度橢圓星系的天體 物理特性提供工具。

目前的網(wǎng)格以及之前發(fā)表的網(wǎng)格（Claret 2004, 2005a, 2006）使我們能 夠分析它們對(duì)靠近雙星的潮汐演化的影響，無(wú)論它們是位于集群中還是孤立 的。我們研究了改變對(duì)流層的半徑、質(zhì)量和深度對(duì)圓化時(shí)間的影響，以評(píng)估理論 不確定性的影響。即使考慮到這些不確定性，我們也表明潮汐破壞和輻射阻尼 機(jī)制的效率不足以匹配觀察到的循環(huán)水平。

二、機(jī)型特點(diǎn)

為了探索高金屬模型的適用性，我們計(jì)算了三個(gè)網(wǎng)格： （X， Z）=（0.64， 0.04），（0.58，0.06）和（0.46，0.10）。對(duì)于所有這些網(wǎng)格，我們采用了富集定 律ΔY/ΔZ = 2.0，正如我們之前關(guān)于該主題的論文中所述。輸入物理與 Claret (2004) 中采用的幾乎相同。

然而，對(duì)核反應(yīng)速率（Runkle 2003；Formicola 等 2004）、數(shù)值精度（例如， 用于定義 HR 圖中的包絡(luò)線的三角形的大小，這對(duì)于避免數(shù)值xbf中的振蕩（見(jiàn)圖 9）以及大質(zhì)量恒星中 Wolf Rayet 階段的質(zhì)量損失率。 對(duì)于后者，我們采用了

Nugis & Lamers (2000) 最近的形式，它采用考慮到金屬豐度和光度的依賴性。我們的確是此處不描述采用的輸入物理場(chǎng)，但為了快速參考，我們?cè)诒?1 中總結(jié)了主要特征

目前的網(wǎng)格

為了完整起見(jiàn)，我們簡(jiǎn)要討論大質(zhì)量恒星的質(zhì)量損失。正如 Mowlavi 等 人指出的那樣。 (1998)，定義 Wolf?Rayet 星的標(biāo)準(zhǔn)可能與 125 M (Z = 0.10) 達(dá)到主序列的結(jié)尾 和 (0.46, 0.10) 對(duì)于固定質(zhì)量，氫的減少 那些。另一方面，氫燃燒相的壽命 預(yù)計(jì)在更多金屬模型中會(huì)更短，因?yàn)樗鼈?還計(jì)算了接近雙星系統(tǒng)的潮汐演化。在 等，這是為每個(gè)模型提供的。 含量和Z的增加意味著較重的平均分子 這樣，諧波k2、 k3和k4可用于測(cè)試 約 30 M 。這種差異可能是由于不同 一種用于較低金屬豐度。由于涉及到很大的不確定性關(guān)系，我們?cè)谶@里采用與 我們之前的論文中所考慮的相同的標(biāo)準(zhǔn)。與 Mowlavi 等人相反。 Nugis & Lamers (2000) 最近的形式主義，它采用 氫含量較低。它們具有更高的亮度和有效 例如，我們發(fā)現(xiàn) (0.64, 0.04) 組和 (0.46, 0.10) 組的壽命比（幾乎與質(zhì)量無(wú) 關(guān)）為 高金屬模型的另一個(gè)有趣特征是 對(duì)于(X, Z) = (0.64, 0.04), (0.58, 0.06) 和 (0.46, 0.10)，分別。大質(zhì)量恒星最 顯著的特征之一這些數(shù)字是，由于它們的初始?xì)浜枯^低， (X, Z) = (0.46, 0.10)的光度和有效溫度 也可以通過(guò)以下方式計(jì)算（并與導(dǎo)出的年齡進(jìn)行比較） 誰(shuí)分析了一個(gè)3M模型的案例。一個(gè)簡(jiǎn)單的同調(diào)近似可以用來(lái)說(shuō)明這個(gè)特征： 光度 考慮到金屬豐度和光度的依賴性。我們的確是 質(zhì)量超過(guò) 60 M的物體幾乎失去了它們的初始質(zhì)量 , 大量的。 比零。例如，考慮 μ for (X, Z) = (0.64, 0.04) 與本系列的前幾篇論文一樣，一些參數(shù)與 目前的網(wǎng)格。 同意這一點(diǎn)。例如，一個(gè)初始質(zhì)量為 重量，因此增加了亮度。對(duì)于 10 M模型的情況，這種效果可以在圖 4 中看到， 其中高 (1998)，在 60 M時(shí)停止計(jì)算，我們計(jì)算了高達(dá) 125 M的模型，Z = 0.10處的主序列。我們的結(jié)果并不完全始終牢記在此質(zhì) 量范圍內(nèi)的質(zhì)量損失率圖存在1 和很圖大的2 中不看準(zhǔn)到。 確性。1?3 三個(gè)網(wǎng)格對(duì)應(yīng)的 HR 圖可以在