有限厚度旋涡星系密度螺旋形扰动的Poisson方程渐近解

本文是在一个特殊模式下,对于有限厚度旋涡星系物质密度螺旋形扰动的三维引力势Poisson方程,用速变相法求出了一级渐近解。 为了解释旋涡星系的螺旋结构,林家翘等[1][2]曾求出引力势Poisson方程的渐近解。这一渐近解对于应用密度波的概念去解释旋涡形式星系的理论起着重要的作用。但是,这一渐近解是把星系中的物质近似地看成集中于星盘平面上,求解二维Poisson方程得到的。所以,不能用它讨论物质的垂直分布与垂直运动对螺旋结构的影响。后来,徐遐生[3]研究了星系盘有限厚度效应,但是他没有解出引力势的三维Poisson方程。我们根据旋涡星系中物质分布的实际情况,求出了三维Poisson方程在一个特殊模式下的解。     

面向类旋涡星系盘有效厚度的获取及图像处理方法

面向类(face-on)旋涡星系盘的有效厚度或标高不能通过表面亮度测光的方式测量.为了获得面向类旋涡星系盘的厚度参数,将基于三维星系盘引力势Poisson方程在等角对数螺旋型物质密度扰动情形下的解,运用一种解析法对面向类旋涡星系盘的标高进行测算.为了去除星系核球的光污染而获得旋臂最内点位置(r0)的重要参数,使用了在星系观测图像中扣除双成份(盘+核球)测光模型的图像处理方法.通过对旋涡星系相关结构参数的拟合测量,各得到了一个普通旋涡星系(S)与棒旋星系(SB)的有效厚度与相关参数,并给出了它们的球盘比(rb/rd)和星系盘的标长与厚度之比(rd/H).采用这种在观测图像中扣除双成份测光模型的方法,将更容易看清旋臂结构的最内端,因而这里获得的禁区半径r0的数值往往比从原星系图像上直接测量的数值要小,获得的星系盘有效厚度将更薄.     

三维旋涡星系的动力学研究

在三维对数螺线型密度扰动的引力Poisson方程严格解基础上,导出了对称平面(z=0)上三维混合盘密度波的色散关系,并以此讨论了对于不同类型扰动盘的局域稳定性,同时还计算了盘面上密度波的群速度．数值计算表明对数螺线型密度扰动,能比较好地满足扰动密度与扰动势反相位的关系;厚度和旋臂数目的增加有利于盘的稳定,而气体成分将导致盘不稳定;考虑厚度效应,银河系密度波传播的动力学时标与Toomre估计的数值相比将大大延长,至少需要4．17×109年,约占宇宙年龄的三分之一,从而可使以往密度波理论中得出的群速度太大的问题得到缓解．     

一个有限厚度旋涡星系模型

本文将三维引力势Poisson方程在一个特殊模式下的速变相一级渐近解用于三维定常模拟恒星盘。在考虑了垂直于星盘平面的运动和物理量的三维分布以后,得出了相应的色散关系。用Schmidt模型对银河系旋臂进行了实例计算,结果表明:在模拟太阳附近的两个主要旋臂——人马臂和英仙臂的情况下,在内林德布拉德共振圈和共转圈之间、在内林德布拉德共振圈以内以及在外林德布拉德共振圈以外等三个区域里,均可得到稳定模型。最后对在较厚旋涡星系中,螺旋波长随着离开星系盘中心平面的距离不同而变化的特征,作了一个简单的分析。我们认为,这种密度波波长随高度的变化或许可以解释以下观测现象:(1)在有些旋涡星系中旋臂有相当宽度。(2)在有些旋涡星系中,旋臂间界限不很分明。(3)在有些旋涡星系中,旋臂外侧亮度突然减弱,而内侧减弱很慢。     

一个有限厚度旋涡星系模型

本文将三维引力势Poisson方程在一个特殊模式下的速变相一级渐近解①用于三维定常模拟恒星盘。在考虑了垂直于星盘平面的运动和物理量的三维分布以后,得出了相应的色散关系。用Schmidt模型②③对银河系旋臂进行了实例计算,结果表明:在模拟太阳附近的两个主要旋臂——人马臂和英仙臂的情况下,在内林德布拉德共振圈和共转圈之间、在内林德布拉德共振圈以内以及在外林德布拉德共振圈以外等三个区域里,均可得到稳定模型。最后对在较厚旋涡星系中,螺旋波长随着离开星系盘中心平面的距离不同而变化的特征,作了一个简单的分析。我们认为,这种密度波波长随高度的变化或许可以解释以下观测现象:(1)在有些旋涡星系中旋臂有相当宽度。(2)在有些旋涡星系中,旋臂间界限不很分明。(3)在有些旋涡星系中,旋臂外侧亮度突然减弱,而内侧减弱很慢。     

旋涡星系中对任意旋臂倾角一致有效的密度-引力势渐近关系

本文给出对于臂数m≥2的旋涡星系(正常旋涡星系或棒旋星系),对任意旋臂倾角(0≤|β|≤π/2)一致有效的扰动密度-扰动引力势渐近关系。在|β|≤1的特殊情形,它回到紧卷波的各种已知渐近关系;在|β|不小的情形,这一新结果适用于讨论构成棒旋星系的“开展模式”(open mode)。     

旋涡星系随uUbble序列的一些统计性质

对发表在A＆Ap Supplement Series上的365个旋涡星系的一些参数(如表示旋臂缠卷松紧程度的参数A、切向角μ、盘的扁度H／D25以及厚度等)随Hubble序列变化的关系进行了统计研究．首次得到这些参量的平均值;并且从统计结果可以明显地看到Hubble对旋涡星系的分类只是一种定性的、只有统计意义上的分类;另外,从我们的统计结果看,密度波理论的色散关系对大多数旋涡星系是成立的,即大多数旋涡星系的旋臂满足紧卷螺旋波的要求．     

旋涡星系随Hubble序列的一些统计性质

对发表在Ａ＆ＡｐＳｕｐｐｌｅｍｅｎｔ Ｓｅｒｉｅｓ上３６５个旋涡星系的一些参数（如表示旋臂缠卷松紧程度的参数Λ、切向角ｕ、盘的扁度Ｈ／Ｄ２５以及厚度等）随Ｈｕｂｂｌｅ序列变化的关系进行了统计研究。首次得到这些参量的平均值;并且从统计结果可以明显地看到Ｈｕｂｂｌｅ对旋涡星系的分类只是一种定性的、只有统计意义上的分类;另外,从我们的统计结果看,密度波理论的色散关系对大多数旋涡星系是成立的,即大多数旋涡     

旋涡星系密度波理论中Poisson积分的简化及应用

本文给出了旋涡星系密度波理论中Poisson积分的一种简化方法。这一简化的最重要应用在于利用它计算旋涡模式时可节省大量计算机时。此外本文还利用这种简化方法对一系列密度——引力势渐近关系进行了系统的数值检验。 用这一简化方法计算核函数比用未简化的核函数形式直接计算节省机时八十四倍。当在数值模式理论研究中大量计算Poisson积分时,应用本文提出的简化将有效地提高计算效率并保证足够高的精度。     

旋涡星系的厚度的估算

本文利用文[1]中所求得的扰动引力势的严格解,当此解由无旋臂区向有旋臂区连续过渡时,在解中出现一非波动项,对此项作出估计,可得出厚度(H=2/α)与开始形成旋臂处的半径的r_0关系:αr_0=7(α为星系半厚度的倒数).我们由[2]选出了50颗旋涡星系,并测定了它们的r_0,由此定出了星系盘的平均厚度.     

Density wave formation in differentially rotating disk galaxies: Hydrodynamic simulation of the linear regime

Most rapidly and differentially rotating disk galaxies, in which the sound speed (thermal velocity dispersion) is smaller than the orbital velocity, display graceful spiral patterns. Yet, over almost 240 yr after their discovery in M51 by Charles Messier, we still do not fully understand how they originate. In this first paper of a series, the dynamical behavior of a rotating galactic disk is examined numerically by a high-order Godunov hydrodynamic code. The code is implemented to simulate a two-dimensional flow driven by an internal Jeans gravitational instability in a nonresonant wave–“fluid” interaction in an infinitesimally thin disk composed of stars or gas clouds. A goal of this work is to explore the local and linear regimes of density wave formation, employed by Lin, Shu, Yuan and many others in connection with the problem of spiral pattern of rotationally supported galaxies, by means of computer-generated models and to compare those numerical results with the generalized fluid-dynamical wave theory. The focus is on a statistical analysis of time-evolution of density wave structures seen in the simulations. The leading role of collective processes in the formation of both the circular and spiral density waves (“heavy sound”) is emphasized. The main new result is that the disk evolution in the initial, quasilinear stage of the instability in our global simulations is fairly well described using the local approximation of the generalized wave theory. Certain applications of the simulation to actual gas-rich spiral galaxies are also explored.     

Disk Thicknesses and Some Parameters of 108 Non-Edge-On Spiral Galaxies

We present disk thicknesses, some other parameters and their statistics of 108 non-edge-on spiral galaxies. The method for determining the disk thickness is based on solving Poisson's equation for a disturbance of matter density in three-dimensional spiral galaxies. From the spiral arms found we could obtain the pitch angles, the inclination of the galactic disk, and the position of the innermost point (the forbidden region with radius r 0 to the galactic center) of the spiral arm, and finally the thickness.     

Spiral-Vortex Structure in the Gaseous Disks of Galaxies

General ideas, as well as experimental and theoretical efforts concerning the prediction and discovery of new structures in the disks of spiral galaxies – giant anticyclones - are reviewed. A crucial point is the development of a new method to restore the full vector velocity field of the galactic gas from the line-of-sight velocity field. This method can be used to get self-consistent solutions for the following problems: 1) determination of non-circular velocities associated with spiral-vortex structure; 2) determination of fundamental parameters of this structure: pattern speed, corotation radius, location of giant anticyclones; 3) refinement of galactic rotation curves taking into account regular non-circular motion in the spiral density wave, which makes it possible to build more accurate models of the mass distribution in the galaxy; 4) refinement of parameters of the rotating gaseous disk: inclination angle, center of rotation and position angle of the major dynamical axis, systematic velocity. The method is demonstrated using the restoration of the velocity field of the galaxy NGC 157 as an example. Results for this and some other spiral galaxies suggest that giant anticyclones are a universal property of galaxies with grand design structure.     

Estimating the dark halo mass from the relative thickness of stellar disks

We analyze the relationship between the mass of a spherical component and the minimum possible thickness of stable stellar disks. This relationship for real galaxies allows the lower limit on the dark halo mass to be estimated (the thinner the stable stellar disk is, the more massive the dark halo must be). In our analysis, we use both theoretical relations and numerical N-body simulations of the dynamical evolution of thin disks in the presence of spherical components with different density profiles and different masses. We conclude that the theoretical relationship between the thickness of disk galaxies and the mass of their spherical components is a lower envelope for the model data points. We recommend using this theoretical relationship to estimate the lower limit for the dark halo mass in galaxies. The estimate obtained turns out to be weak. Even for the thinnest galaxies, the dark halo mass within four exponential disk scale lengths must be more than one stellar disk mass.     

Comparison of theoretical models of the dark matter distribution in low-surface-brightness galaxies with observations

The observed rotation curves of four low-surface-brightness galaxies are compared with the predictions of three models of the dark matter distribution with various degrees of singularity at the center or without it. Contrary to the assertions in the literature, the results of fitting the rotation curves by the least-squares method using a chi-square distribution with optimal parameters (dark matter halo, bulge, and disk) do not yet allow any one of the models to be uniquely preferred. The NFW and Burkert models have the highest significance levels for two of the four galaxies and for the other two, respectively. At the same time, using the NFW model in the latter two cases leads to an estimate of the disk surface density close to the photometric one, which may suggest that these models are more realistic. The surface density estimates for the galactic disks based the criterion of their marginal gravitational stability have also been used. The disks of the galaxies under consideration may be overheated, because the modeling using these estimates gives larger deviations of the model rotation curves from the observed ones than in the case where the surface density is assumed to be a free parameter. Using the disk surface density estimates based on the criterion of marginal gravitational stability does not change the preference in choosing the shape of the dark matter density profile in the galaxies under consideration compared to the case with a “free disk.”     

Galactic dynamos and galactic winds

Spiral galaxies host dynamically important magnetic fields which can affect gas flows in the disks and halos. Total magnetic fields in spiral galaxies are strongest (up to 30 μG) in the spiral arms where they are mostly turbulent or tangled. Polarized synchrotron emission shows that the resolved regular fields are generally strongest in the interarm regions (up to 15 μG). Faraday rotation measures of radio polarization vectors in the disks of several spiral galaxies reveal large-scale patterns which are signatures of coherent fields generated by a mean-field dynamo. Magnetic fields are also observed in radio halos around edge-on galaxies at heights of a few kpc above the disk. Cosmic-ray driven galactic winds transport gas and magnetic fields from the disk into the halo. The halo scale height and the electron lifetime allow to estimate the wind speed. The magnetic energy density is larger than the thermal energy density, but smaller than the kinetic energy density of the outflow. There is no observation yet of a halo with a large-scale coherent dynamo pattern. A global wind outflow may prevent the operation of a dynamo in the halo. Halo regions with high degrees of radio polarization at very large distances from the disk are excellent tracers of interaction between galaxies or ram pressure of the intergalactic medium. The observed extent of radio halos is limited by energy losses of the cosmic-ray electrons. Future low-frequency radio telescopes like LOFAR and the SKA will allow to trace halo outflows and their interaction with the intergalactic medium to much larger distances.     

Relationship between the thickness of stellar disks and the relative mass of a dark galactic halo

We analyze the R-and K _s-band photometric profiles for two independent samples of edge-on galaxies. The thickness of old stellar disks is shown to be related to the relative masses of the spherical and disk components of galaxies. The radial-to-vertical scale length ratio for galactic disks increases (the disks become thinner) with increasing total mass-to-light ratio of the galaxies, which reflects the relative contribution of the dark halo to the total mass, and with decreasing central deprojected disk brightness (density). Our results are in good agreement with numerical models of collisionless disks that evolved to a marginally stable equilibrium state. This suggests that, in most galaxies, the vertical stellar-velocity dispersion, on which the equilibrium-disk thickness depends, is close to a minimum value that ensures disk stability. The thinnest edge-on disks appear to be low-brightness galaxies in which the dark-halo mass far exceeds the stellar-disk mass.     

Determination of the Thickness of Non-Edge-on Disk Galaxies

We propose a method to determine the thickness of non-edge-on disk galaxies from their observed structure of spiral arms, based on the solution of the truly three-dimensional Poisson‘s equation for a logarithmic disturbance of density and under the condition where the self-consistency of the density wave theory is no longer valid. From their measured number of arms, pitch angle and location of the innermost point of the spiral arms, we derive and present the thicknesses of 34 spiral galaxies.     

The test for suppressed dynamical friction in a constant density core of dwarf galaxies

The dynamical friction problem is a long-standing dilemma about globular clusters (hereafter GCs) belonging to dwarf galaxies. GCs are strongly affected by dynamical friction in dwarf galaxies, and are presumed to fall into the galactic centre. But, GCs do exist in dwarf galaxies generally. A solution of the problem has been proposed. If dwarf galaxies have a core dark matter halo which has constant density distribution in its centre, the effect of dynamical friction will be weakened considerably, and GCs should be able to survive beyond the age of the Universe. Then, the solution argued that, in a cored dark halo, interaction between the halo and the GC constructs a new equilibrium state, in which a part of the halo rotates along with the GC (corotating state). The equilibrium state can suppress the dynamical friction in the core region. In this study, I tested whether the solution is reasonable and reconsidered why a constant density, core halo suppresses dynamical friction, by means of N -body simulations. As a result, I conclude that the true mechanism of suppressed dynamical friction is not the corotating state, although a core halo can actually suppress dynamical friction on GCs significantly.     

Application of the global modal approach to the spiral galaxies

We have tested the applicability of the global modal approach in the density wave theory of spiral structure for a sample of spiral galaxies with measured axisymmetric background properties. We report here the results of the simulations for four galaxies: NGC 488, NGC 628, NGC 1566, and NGC 3938. Using the observed radial distributions for the stellar velocity dispersions and the rotation velocities we have constructed the equilibrium models for the galactic disks in each galaxy and implemented two kinds of stability analyses - the linear global analysis and 2D-nonlinear simulations. In general, the global modal approach is able to reproduce the observed properties of the spiral arms in the galactic disks. The growth of spirals in the galactic disks can be physically understood in terms of amplification by over-reflection at the corotation resonance. Our results support the global modal approach as a theoretical explanation of spiral structure in galaxies. This revised version was published online in August 2006 with corrections to the Cover Date.