黑洞Slim盘的整体解研究
摘要
物质通过吸积释放引力能是宇宙中各种天体活动能量的一个重要来源,特别是在对黑洞、中子星和白矮星等致密天体的研究中,吸积过程显得尤为重要。近些年随着天文观测的进步,吸积盘理论也发展到了当代径移主导吸积的范畴。Slim盘是一类光学厚,几何厚度可以和半径相当的径移主导吸积盘,目前已经被广泛的应用于解释各种超爱丁顿吸积的观测现象。
本文中主要介绍了笔者在攻读博士期间对于Slim模型的研究成果。通过改进高吸积率下Slim盘模型在垂向引力处理上的一些缺陷,计算了改进后模型的整体解并对其新的特性进行了讨论,证实了Slim盘模型在不考虑外流时其吸积率存在上限;此外还对放弃垂向流体静力学平衡假设后的Slim盘整体解进行了初步探讨;并且对含有外流的Slim盘结构做了计算和探讨。
第一章中首先讨论了黑洞的概念,对其基本性质、描述、研究和观测现状等做了一些简单的介绍;然后讲述了吸积理论的基本内容以及几种主流的吸积盘模型,对吸积盘的形成机制和物质供给做了讨论,并介绍了吸积盘模型在几种重要的天文观测现象上的应用。
第二章中首先介绍了爱丁顿光度的概念,解释为什么吸积盘有可能具有超爱丁顿的辐射光度,然后介绍了标准薄盘(SSD)的结构描述和计算方法,讨论了其模型、盘结构以及其在稳定性、适用的吸积率上限等方面的局限性。然后引入Slim盘的经典模型并介绍其详细的整体解计算方法和盘结构的基本性质。
第三章中首先通过一系列证据表明经典Slim盘模型在垂向引力上的处理具有一定缺陷,特别是在高吸积率下表现的尤为明显。然后从局域分析的角度出发,对改进垂向引力描述后的Slim盘结构和性质方面做了探讨。在此基础之上,我们又详细计算了改进后的Slim盘模型的结构,得到了跨声速点的整体解,提出Slim盘吸积率存在上限的重要结论,并对吸积率上限的形成原因和在不同参数下的变化情况做了讨论。接着我们初步探讨了当外边界物质供给超过此上限时盘的情况,提出了此时吸积盘很可能会产生外流。之后我们还在放弃垂向流体静力学平衡假设后,重新计算了Slim盘的整体解,并证实这种情况下Slim盘仍然存在着吸积率上限。
第四章中我们展示了国际上对于吸积盘数值模拟得到外流的一些结果,然后利用这些结果的结论,初步探讨了含有外流的Slim盘模型的整体解。
第五章是对下一步研究方向的介绍。
The gravitational energy released through accretion process is an important energy source for many astrophysical phenomena in the universe,especially for black holes,neutron stars and white dwarves.With the enormous advancement of astronomy observations during recently years,the accretion disk theory has developed into modern advection-dominated accretion paradigm.Slim disk is a kind of optically thick,advection dominated accretion flow,in which the disk height can be comparable with the disk radius.
This thesis introduces the research done by the author in the slim disk theory during my Ph.D course.By improving some inconsistency in the treatment of vertical gravitational force in the slim disk model,we find that there exists an upper limit of accretion rates for slim disks without outflows.More over,we have calculated the global solutions of slim disks after waiving the hydrostatic equilibrium in the vertical direction and made some discussions.Some calculations and discussions about slim disks with outflows are also presented.
In Chapter 1 we present introductory material on black holes and accretion disks.We discuss the basic concepts of black holes and make some brief introduction about its properties and features,classification,research history and observations.Then we introduce the basis of accretion theory and some popular accretion disk models.Some discussions have also been made about disk formation and matter supply,as well as the application of disk models to observations.
Chapter 2 is mainly about the calculations of accretion disks.First we introduce the concept of Eddington luminosity and explain why we could have super-Eddington radiation.Then we introduce the famous Shakura & Sunyaev Disk model,including its structure description and calculations,and discuss its limitation in disk stability and feasible accretion rates.Upon this we introduce the traditional slim disk model and describe how to calculate its global solutions.Some discussions about the basic properties of slim disks have also been presented.
In Chapter 3 we discuss the improvement to traditional slim disks in detail.First we present the proof that the traditional slim disk model has some hidden inconsistency in the treatment of vertical gravitational force,especially when dealing with high accretion rates.By correcting this inconsistency we have obtained some new results from regional analysis.To further test our results, we calculate the transonic global solutions in the improved slim disk model and show that the accretion rates of slim disks have an upper limit.Some discussions are done about this model, including the reason for the upper limit and its dependence on the disk parameters.We have also studied the situation when the matter supply surpasses this limit and propose that outflow seems unavoidable.Some further study show that the vertical hydrostatic equilibrium assumption may not hold for a thick disk,so we waive this assumption and calculate the global solutions again,and find that the main conclusion about the upper limit of accretion rates for slim disks still hold.
In Chapter 4 we first present the results of disk structure simulations.Then by applying these results we make some calculations about slim disks with outflows.
Chapter 5 is about the research plan in the future.
本文中主要介绍了笔者在攻读博士期间对于Slim模型的研究成果。通过改进高吸积率下Slim盘模型在垂向引力处理上的一些缺陷,计算了改进后模型的整体解并对其新的特性进行了讨论,证实了Slim盘模型在不考虑外流时其吸积率存在上限;此外还对放弃垂向流体静力学平衡假设后的Slim盘整体解进行了初步探讨;并且对含有外流的Slim盘结构做了计算和探讨。
第一章中首先讨论了黑洞的概念,对其基本性质、描述、研究和观测现状等做了一些简单的介绍;然后讲述了吸积理论的基本内容以及几种主流的吸积盘模型,对吸积盘的形成机制和物质供给做了讨论,并介绍了吸积盘模型在几种重要的天文观测现象上的应用。
第二章中首先介绍了爱丁顿光度的概念,解释为什么吸积盘有可能具有超爱丁顿的辐射光度,然后介绍了标准薄盘(SSD)的结构描述和计算方法,讨论了其模型、盘结构以及其在稳定性、适用的吸积率上限等方面的局限性。然后引入Slim盘的经典模型并介绍其详细的整体解计算方法和盘结构的基本性质。
第三章中首先通过一系列证据表明经典Slim盘模型在垂向引力上的处理具有一定缺陷,特别是在高吸积率下表现的尤为明显。然后从局域分析的角度出发,对改进垂向引力描述后的Slim盘结构和性质方面做了探讨。在此基础之上,我们又详细计算了改进后的Slim盘模型的结构,得到了跨声速点的整体解,提出Slim盘吸积率存在上限的重要结论,并对吸积率上限的形成原因和在不同参数下的变化情况做了讨论。接着我们初步探讨了当外边界物质供给超过此上限时盘的情况,提出了此时吸积盘很可能会产生外流。之后我们还在放弃垂向流体静力学平衡假设后,重新计算了Slim盘的整体解,并证实这种情况下Slim盘仍然存在着吸积率上限。
第四章中我们展示了国际上对于吸积盘数值模拟得到外流的一些结果,然后利用这些结果的结论,初步探讨了含有外流的Slim盘模型的整体解。
第五章是对下一步研究方向的介绍。
The gravitational energy released through accretion process is an important energy source for many astrophysical phenomena in the universe,especially for black holes,neutron stars and white dwarves.With the enormous advancement of astronomy observations during recently years,the accretion disk theory has developed into modern advection-dominated accretion paradigm.Slim disk is a kind of optically thick,advection dominated accretion flow,in which the disk height can be comparable with the disk radius.
This thesis introduces the research done by the author in the slim disk theory during my Ph.D course.By improving some inconsistency in the treatment of vertical gravitational force in the slim disk model,we find that there exists an upper limit of accretion rates for slim disks without outflows.More over,we have calculated the global solutions of slim disks after waiving the hydrostatic equilibrium in the vertical direction and made some discussions.Some calculations and discussions about slim disks with outflows are also presented.
In Chapter 1 we present introductory material on black holes and accretion disks.We discuss the basic concepts of black holes and make some brief introduction about its properties and features,classification,research history and observations.Then we introduce the basis of accretion theory and some popular accretion disk models.Some discussions have also been made about disk formation and matter supply,as well as the application of disk models to observations.
Chapter 2 is mainly about the calculations of accretion disks.First we introduce the concept of Eddington luminosity and explain why we could have super-Eddington radiation.Then we introduce the famous Shakura & Sunyaev Disk model,including its structure description and calculations,and discuss its limitation in disk stability and feasible accretion rates.Upon this we introduce the traditional slim disk model and describe how to calculate its global solutions.Some discussions about the basic properties of slim disks have also been presented.
In Chapter 3 we discuss the improvement to traditional slim disks in detail.First we present the proof that the traditional slim disk model has some hidden inconsistency in the treatment of vertical gravitational force,especially when dealing with high accretion rates.By correcting this inconsistency we have obtained some new results from regional analysis.To further test our results, we calculate the transonic global solutions in the improved slim disk model and show that the accretion rates of slim disks have an upper limit.Some discussions are done about this model, including the reason for the upper limit and its dependence on the disk parameters.We have also studied the situation when the matter supply surpasses this limit and propose that outflow seems unavoidable.Some further study show that the vertical hydrostatic equilibrium assumption may not hold for a thick disk,so we waive this assumption and calculate the global solutions again,and find that the main conclusion about the upper limit of accretion rates for slim disks still hold.
In Chapter 4 we first present the results of disk structure simulations.Then by applying these results we make some calculations about slim disks with outflows.
Chapter 5 is about the research plan in the future.
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