張錢生

(中國科學(xué)院云南天文臺昆明650011)

博士學(xué)位論文摘要選登

恒星內(nèi)部對流超射

張錢生?

(中國科學(xué)院云南天文臺昆明650011)

恒星內(nèi)部存在著對流運(yùn)動,對流運(yùn)動起到輸運(yùn)物質(zhì)和能量的作用,會對恒星結(jié)構(gòu)和演化產(chǎn)生重要的影響.由于對流的輸運(yùn)作用,物質(zhì)和能量會從對流不穩(wěn)定區(qū)向?qū)α鞣€(wěn)定區(qū)擴(kuò)散,此現(xiàn)象被稱為對流超射.對流超射是當(dāng)前恒星物理最不確定和最困難因素之一.

描述恒星內(nèi)部對流超射的經(jīng)典方法是非局地混合長理論.但是,這種理論是唯象理論,建立在不牢固的基礎(chǔ)上,學(xué)者對此類唯象理論有多方面的批評和不滿.最近,日震學(xué)研究否定了非局地混合長理論框架下的對流超射圖景,同時(shí)表明,目前只有使用湍流模型描述對流超射才能產(chǎn)生符合日震學(xué)的結(jié)果,這為研究恒星內(nèi)部的對流超射指明了方向.

在本論文的綜述部分中,首先介紹了恒星內(nèi)部對流超射的經(jīng)典處理方法及其優(yōu)缺點(diǎn),然后詳細(xì)介紹了被日震學(xué)研究推薦的恒星湍流模型,包括模型的物理基礎(chǔ)、推導(dǎo)過程和優(yōu)缺點(diǎn).本論文的研究工作部分包含了湍流模型的理論分析和實(shí)際應(yīng)用方面,并建立了一個(gè)對流超射混合的新模型.

在恒星湍流模型的理論分析方面,通過合理的假設(shè)和簡化,得到了湍流模型的近似解和其在超射區(qū)中的漸近解,了解了超射區(qū)的結(jié)構(gòu).在很大的模型參數(shù)范圍內(nèi),得到的近似解和漸近解都與數(shù)值計(jì)算結(jié)果符合得很好.通過理論分析,還得到與模型參數(shù)無關(guān)的一個(gè)重要結(jié)果,即超射區(qū)的傳熱區(qū)大約為對流邊界之外的1 HK范圍內(nèi)(HK為湍流動能標(biāo)高).

在恒星湍流模型的應(yīng)用方面,有3個(gè)計(jì)算實(shí)例.在太陽模型的應(yīng)用中,發(fā)現(xiàn)湍流模型描述下的對流超射區(qū)的溫度梯度輪廓與日震學(xué)反演結(jié)果很好地符合,使用擴(kuò)散型對流超射混合和合適的參數(shù)可以同時(shí)大幅改善太陽模型的Li豐度、聲速輪廓和密度輪廓.在星團(tuán)小質(zhì)量恒星中使用與太陽模型相同的參數(shù)來描述對流殼層底部的超射混合,可以使星團(tuán)(研究了Hyades、Praesepe、NGC6633、NGC752、NGC3680和M67這6個(gè)星團(tuán))的Li豐度對有效溫度的關(guān)系與觀測符合,并估算出此類恒星的Li豐度損耗e-fold時(shí)標(biāo)為1 Gyr.在雙星HY Vir模型的應(yīng)用研究中,本文利用該雙星系統(tǒng)的觀測性質(zhì)研究了擴(kuò)散型對流超射混合的合適強(qiáng)度,然后研究了使用湍流模型和擴(kuò)散型對流超射混合的情況下的恒星內(nèi)部結(jié)構(gòu)特點(diǎn),發(fā)現(xiàn)前兩項(xiàng)應(yīng)用得到的參數(shù)同樣適用于HY Vir系統(tǒng)對流核超射,使HY Vir的恒星參數(shù)與觀測符合,并發(fā)現(xiàn)和解釋了擴(kuò)散型對流超射混合使超射區(qū)e-fold長度隨時(shí)間變大.

通過上述研究提供的線索,本論文在流體力學(xué)方程組的基礎(chǔ)上建立了湍流化學(xué)組分通量的湍動對流模型,解出了其局地模型的對流/超射混合的擴(kuò)散系數(shù).擴(kuò)散系數(shù)表達(dá)式在對流不穩(wěn)定區(qū)與超射區(qū)有著不同的近似行為,揭示了湍動對流運(yùn)動在超射區(qū)中的性質(zhì)與對流不穩(wěn)定區(qū)不同:在超射區(qū)中,浮力阻做負(fù)功,流體在其平衡位置附近運(yùn)動,混合特征尺度比對流不穩(wěn)定區(qū)里的情況小得多.該結(jié)果揭示了超射區(qū)中的擴(kuò)散系數(shù)很小,混合效率很低,在多方面與經(jīng)典模型不同,而與日震學(xué)和數(shù)值模擬相符合.最后,將這個(gè)新的超射混合模型應(yīng)用于恒星模型中,利用一些觀測特性定標(biāo)了模型參數(shù)的大小,并解釋其物理含義.

In stellar interiors,the turbulent thermal convection transports matters and energy, and dominates the structure and evolution of stars.The convective overshoot,which results from the non-local convective transport from the convection zone to the radiative zone,is one of the most uncertain and difficult factors in stellar physics at present.

The classical method for studying the convective overshoot is the non-local mixinglength theory(NMLT).However,the NMLT bases on phenomenological assumptions,and leads to contradictions,thus the NMLT was criticized in literature.At present,the helioseismic studies have shown that the NMLT cannot satisfy the helioseismic requirements, and have pointed out that only the turbulent convection models(TCMs)can be accepted.

In the fi rst part of this thesis,models and derivations of both the NMLT and the TCM were introduced.In the second part,i.e.,the work part,the studies on the TCM(theoretical analysis and applications),and the development of a new model of the convective overshoot mixing were described in detail.

In the work of theoretical analysis on the TCM,the approximate solution and the asymptotic solution were obtained based on some assumptions.The structure of the overshoot region was discussed.In a large space of the free parameters,the approximate/ asymptotic solutions are in good agreement with the numerical results.We found an important result that the scale of the overshoot region in which the thermal energy transport is e ff ective is 1 HK(HK is the scale height of turbulence kinetic energy),which does not depend on the free parameters of the TCM.

We applied the TCM and a simple overshoot mixing model in three cases.In the solar case,it was found that the temperature gradient in the overshoot region is in agreement with the helioseismic requirements,and the pro fi les of the solar lithium abundance,sound speed, and density of the solar models are also improved.In the low-mass stars of open clusters Hyades,Praesepe,NGC6633,NGC752,NGC3680,and M67,using the model and parameter same to the solar case to deal with the convective envelope overshoot mixing,the lithium abundances on the surface of the stellar models were consistent with the observations.In the case of the binary HY Vir,the same model and parameter also make the radii and e ff ective temperatures of HY Vir stars with convective cores be consistent with the observations.

Based on the implications of the above results,we found that the simple overshoot mixing model may need to be improved signi fi cantly.Motivated by those implications,we established a new model of the overshoot mixing based on the fl uid dynamic equations,and worked out the di ff usion coefficient of convective mixing.The di ff usion coefficient shows di ff erent behaviors in convection zone and overshoot region.In the overshoot region,the buoyancy does negative works on fl ows,thus the fl uid fl ows around the equilibrium location, which leads to a small scale and low efficiency of overshoot mixing.The physical properties are signi fi cantly di ff erent from the classical NMLT,and consistent with the helioseismic studies and numerical simulations.The new model was tested in stellar evolution,and its parameter was calibrated.

Convective Overshoot in Stellar Interior

ZHANG Qian-sheng
(Yunnan Observatories,Chinese Academy of Sciences,Kunming 650011)

?2013-07-01獲得博士學(xué)位,導(dǎo)師:云南天文臺李焱研究員;zqs@ynao.ac.cn

10.15940/j.cnki.0001-5245.2015.04.011