Slow pressure modes in thin accretion discs-猫眼课题宝

薄吸积盘中的慢压力模式

DOI：

发表时间：

2009

期刊：

影响因子：

通讯作者：

中科院分区：

文献类型：

作者：

T. D. Saini;Mamta Gulati;S. Sridhar

大质量致密天体周围的薄吸积盘可以支持方位波数m = 1的线性区域中的慢压力振荡模式。我们认为，有限的，由正压流体组成的，具有不同表面密度的圆盘，并通过WKB分析和本征值问题的数值解证明，这些模式是稳定的，并具有与圆盘大小相当的空间尺度。我们证明了本征值方程可以映射成Schr¨ odinger型方程。对该方程的分析表明，所有本征模都具有离散谱。我们发现，所有的模型，我们已经考虑支持负频率本征模，然而，正的本征频率模式只存在于幂律光盘，apriitfor物理上无趣的值的幂律指数β和正压指数γ.关键词：吸积盘;流体力学;波;方法：分析1引言低质量光盘轨道大规模紧凑的机构是一个feature许多天文系统。当圆盘的动力学由中心体的牛顿引力支配时，圆盘可被认为是近似凯普勒的。在纯开普勒势中，偏心轨道不进动，因为轨道频率等于周转频率。在近似开普勒圆盘中，轨道频率和周转频率之间有微小的差别。这可能是由于圆盘的自重、气体圆盘中的热压力以及无碰撞圆盘中的随机运动。这种频率的差异表现为偏心轨道的岁差，其岁差率与轨道频率和周转频率相比很小。然后，光盘可能能够支持大规模的，缓慢的，不平衡的模式（Kato 1983; Sridhar，Syer & Touma 1999; Lee & Goodman 1999; Sridhar & Touma 1999）。在线性区域，这些模具有方位角频率m = 1，其第一个系统研究是由特里梅因（2001）完成的。他研究了各种类型的圆盘中的慢模式（流体、无碰撞和软化重力），重点主要放在圆盘的自重力的影响上。特别是，WKB分析表明，当马赫数M远大于Toomre Q参数（这两个参数都在§ 2中定义）时，流体盘可以支持大尺度慢模态。这种分析背后的假设是圆盘的自重支配着圆盘的流体压力。然而，白矮星和中子星周围的薄吸积盘并非如此。事实上，对于白矮星周围的圆盘（Frank，King & Raine 2002），我们可以估计M = 50，Q = 10

@ABSTRACT Thin accretion discs around massive compact objects can support slow pressure modesof oscillations in the linear regime that have azimuthal wavenumber m = 1. We con-sider ﬁnite, ﬂat discs composed of barotropic ﬂuid for various surface density proﬁlesand demonstrate–through WKB analysis and numerical solution of the eigenvalueproblem–that these modes are stable and have spatial scales comparable to the size ofthe disc. We show that the eigenvalue equation can be mapped to a Schr¨odinger-likeequation. Analysisofthis equationshows that all eigenmodes havediscretespectra. Weﬁnd that all the models we have considered support negative frequency eigenmodes;however, the positive eigenfrequency modes are only present in power law discs, albeitfor physically uninteresting values of the power law index β and barotropic index γ.Key words: accretion discs; hydrodynamics; waves; methods: analytical 1 INTRODUCTIONLow-mass discs orbiting massive compact bodies are a fea-ture of many astronomical systems. When the dynamics ofa disc is dominated by the Newtonian gravitational force ofthe central body, the disc may be considered nearly Kep-lerian. In a purely Keplerian potential eccentric orbits donot precess because the orbital frequency is equal to theepicyclic frequency. In a nearly Keplerian disc there is asmall diﬀerence between the orbital and epicyclic frequen-cies. This could be due to the self-gravity of the disc, ther-mal pressure in a gas disc, and random motions in a col-lisionless disc. This diﬀerence in frequencies manifests as aprecession of eccentric orbits at rates that are small com-pared to the orbital and epicyclic frequencies. Then the discmay be able to support large-scale, slow, lopsided modes(Kato 1983; Sridhar, Syer & Touma 1999; Lee & Goodman1999; Sridhar & Touma 1999). In the linear regime, thesemodes have azimuthal frequency, m = 1, whose ﬁrst sys-tematic investigation is due to Tremaine (2001). He stud-ied slow modes in various types of discs (ﬂuid, collision-less and softened gravity), with the focus largely on the ef-fect of the self-gravity of the disc. In particular, a WKBanalysis was used to show that the ﬂuid disc can supportlarge-scale slow modes when the Mach number, M, is muchlarger than the Toomre Q parameter (both parameters aredeﬁned in § 2). The assumption behind this analysis is thatthe self-gravity of the disc dominates ﬂuid pressure. How-ever, such is not the case for thin accretion discs aroundwhite dwarfs and neutron stars. Indeed, for a disc around awhite dwarf (Frank, King & Raine 2002), we can estimateM ∼ 50 and Q ∼ 10

Slow pressure modes in thin accretion discs

薄吸积盘中的慢压力模式

文献摘要

被引文献

相似文献