Approximate rotation curve solutions for the evolution of a viscous protogalactic disk

The problem of evolution of viscous protogalactic disks is examined. A modification of traditional turbulent viscosity theory is proposed which is based on the premise that the eddies are so small and numerous that each eddy can be considered to be large molecule. The radial flow term is omitted from the viscosity equation to make it tractable, and the radial flow is later reintroduced via the requirement of gravitational balance within the disk. The main result is a family of rotation curves that, as the system evolves, serially reproduces most types of observed rotation curves. With the use of Seiden's star formation theory, the present model produces an exponential-like luminosity profile whenever stars form and the viscous action ceases.Los Alamos National Laboratory is operated by the University of California for U.S. Dept. of Energy under contract W-7405-ENG-36.     

On the understanding of the observed flat or slowly rising rotation curves in large disk galaxies

Recent observations of the rotation curves of large disk galaxies of all Hubble-types have shown that they possess flat or slowly rising rotation curves up to large distances from the centre. It has been suggested here that such rotation curves are understood under normal fluid dynamical considerations provided that viscous (and/or magnetic) transfer of mass and angular momentum from inner to outer regions of these galaxies is efficient. Flow of gas from halo to the disk in regions close to the axis of rotation is also suggested. The existence of rising rotation curves in some galaxies with varying gradients and flat rotation curves in others suggest that probably these galaxies are not coeval. The formers are probably of more recent origin.     

原太阳吸积盘结构

计算了粘滞演化阶段原太阳吸积盘结构。采用稳态标准吸积盘模型来描述盘中湍动粘滞；忽略其径向能量传输，将垂直结构作为一维问题处理。假设盘作Keplerian较差旋转，处于流体力学平衡和局域热平衡，盘由粘滞耗散加热，能量通过对流和辐射向外传输。结果表明，对温度敏感的不透明度是决定盘结构的重要因素；原太阳吸积盘为冷的薄盘，盘中热对流不稳定性由外而内，由上而下地终结；行星的形成应首先开始于对流终结的区域。     

Protostellar angular momentum transport by spiral density waves

The gravitational collapse of molecular clouds or cloud cores is expected to lead to the formation of stars that begin their lives in a state of rapid rotation. It is known that, in at least some specific cases, rapidly rotating, slf-gravitating bodies are subject to instabilities that cause them to assume ellipsoidal shapes. In this paper we investigate the consequences of such instabilities on the angular momentum evolution of a star in the process of formation from a collapsing cloud, and surrounded by a protostellar disk, with a view toward applications to the formation of the Solar System. We use a specific model of star formation to demonstrate the possibility that such a star would become unstable, that the resulting distortion of the star would generate spiral density waves in the circumstellar disk, and that the torque associated with these waves would regulate the angular momentum of the star as it feeds angular momentum to the disk. We conclude that the angular momentum so transported to the disk would not spread the disk to, say, Solar System dimensions, by the action of the spiral density waves alone. However, a viscous disk could effectively extract stellar angular momentum and attain Solar System size. Our results also indicate that viscous disks could feed mass and angular momentum to a growing protostar in such a manner that distortions of the star would occur before gravitational torques could balance the influx of angular momentum. In other situations (in which the viscosity was small), a gap could be cleared between the disk and star.     

On the formation of protostellar disks

An analysis is presented of the hydrodynamic aspects of the growth of protostellar disks from the accretion (or collapse) of a rotating gas cloud. The size, mass, and radiative properties of protostellar disks are determined by the distribution of mass and angular momentum in the clouds from which they are formed, as well as from the dissipative processes within the disks themselves. The angular momentum of the infalling cloud is redistributed by the action of turbulent viscosity on a shear layer near the surface of the disk (downstream of the accretion shock) and on the radial shear across cylindrical surfaces parallel to the rotation axis. The fraction of gas that is fed into a central core (protostar) during accretion depends on the ratio of the rate of viscous diffusion of angular momentum to the accretion rate; rapid viscous diffusion (or a low accretion rate) promotes a large core-to-disk mass ratio. The continuum radiation spectrum of a highly viscous disk is similar to that of a steady-state accretion disk without mass addition. It is possible to construct models of the primitive solar nebula as an accretion disk, formed by the collapse of a slowly rotating protostellar cloud, and containing the minimum mass required to account for the planets. Other models with more massive disks are also possible.     

A theory of galactic mass and rotation curves

The goal of this paper is to account for the complete observed rotation curves of disk galaxies without dark matter. To attain that goal, use is made of a conservation law from stability theory of linear waves, leading to a vector-based theory of gravitation. In the theory, galactic centers are sites of strong gravitational fields. The new theory predicts extra matter at the center of disk galaxies, which is well-known to be consistent with intergalactic dynamics. For given disk radiusr ₀ and edge tangential speedv, the greater the deviation of a rotation curve from linear (solid disk rotation), the greater the mass of the galaxy as a multiple of Newtonian massr ₀v²/G, up to a factor of about 1000. In an approximate calculation it turns out that disk density (r) (in kg m^–2) is proportional to 1/r for typical rotation curves. Rotation is characterized by two constants which in turn are determined by the edge speed and mass distribution. Not just any curve shape can be so obtained; in fact, the theoretically possible curves correspond to observed curves.     

Rotational dynamics of a deformable medium: Further generalization

Cauchy's fundamental first law of continuum mechanics is integrated over the whole mass of a self-gravitating deformable finite material continuum, viscolinear (i.e., Newtonian), not necessarily constrained to obey Stokes's condition, with viscosity coefficients given as arbitrary functions of the coordinates. The general Eulerian equation is derived, governing generalized rotation on which certain other cooperating deformations are superimposed. Finally, the explicit form of this equation is given for the case of a viscous gaseous polytrope.     

Peculiarities in the Formation of Molecular Clouds in the Central Regions of Spiral Galaxies

The limitations imposed by the shear instability on the formation of gigantic molecular clouds in the central regions of spiral galaxies are examined. The criteria obtained here are illustrated using the example of six galaxies for which the detailed rotation curves are known. The different mechanisms for formation of molecular clouds which apply in the central and edge regions of disk galaxies are evaluated.     

Predicting the maximum sunspot number and the associated geomagnetic activity indices a a $aa$ and A p $Ap$ for solar cycle 25

We are considering the spacetime described by the metric proposed by Mannheim and Kazanas. The effective potential and the circular orbits are discussed. The rotational velocity derived from the geodesics equation agrees with the observed flat galactic rotation curves. Finally, solutions to the Gordon equation for massless bosons evolving in this spacetime are obtained in terms of Heun general functions.

     

径向粘滞力对薄盘稳定性的影响

在吸积盘内由于吸积物质的径向运动，盘内物质间沿径向的粘滞力将会对盘的性质产生一定影响．本文计算了等温吸积盘中（考虑径向粘滞力）的不稳定性问题，对所求得的色散方程的分析表明，径向粘滞力将使吸积盘趋向稳定。本文还对径向粘滞力对盘的稳定性的影响作了物理解释，并发现径向粘滞力的引入不会引入新的稳定或不稳定模式。     

Rotation curves and mass distributions in flat self-gravitating disks

We have developed a new approach that allows the surface-density distribution in flat finite-radius galactic disk models to be reconstructed from an arbitrary smooth angular-velocity distribution. Upper limits for the disk mass and radius are shown to exist for a wide class of rotation curves analytically extended to the unseen part of the disk.     

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.”     

Does each spiral Galaxy house a slowly growing elliptical one?

N-body simulations performed by us suggest a mechanism for the generation of spiral waves in galaxies in which a mutual quasi-ellipsoidal rotating equilibrium configuration increasing slowly by accretion from the surrounding disk influences the density distribution of stars in the disk such as to give rise to a trailing spiral density wave. Interaction of the spiral wave with the viscous interstellar gas and mutual gravitation between the stars in the disk are believed to influence the form of the spiral. Nevertheless the basic assumption of conventional density wave theory according to which the mutual interaction of stars in the disk is essential for the formation of spirals may not be true.     

Model rotation curves of disk galaxies oriented at an arbitrary angle to the plane of the sky

We consider the effects of projection, absorption, and velocity dispersion on the shape of the rotation curve for a galaxy as a function of its disk inclination to the plane of the sky. We conclude that for galaxies with a fairly massive compact bulge these effects lead to a marked discrepancy between the rotation curve and the circular velocity curve even if their disks are viewed far from edge-on, especially for the rotation curves constructed from observations of the stellar component.     

The shape of the rotation curves of edge-on galaxies

We consider the effects of projection, internal absorption, and gas-or stellar-velocity dispersion on the measured rotation curves of galaxies with edge-on disks. Axisymmetric disk models clearly show that the rotational velocity in the inner galaxy is highly underestimated. As a result, an extended portion that imitates nearly rigid rotation appears. At galactocentric distances where the absorption is low (i.e., it does not exceed 0.3–0.5^m kpc^?1), the line profiles can have two peaks, and a rotation curve with minimum distortions can be obtained by estimating the position of the peak that corresponds to a higher rotational velocity. However, the high-velocity peak disappears in high-absorption regions and the actual shape of the rotation curve cannot be reproduced from line-of-sight velocity estimates. In general, the optical rotation curves for edge-on galaxies are of little use in reconstructing the mass distribution in the inner regions, particularly for galaxies with a steep velocity gradient in the central region. In this case, estimating the rotation velocities for outer (transparent) disk regions yields correct results.     

X射线脉冲星周期的变化与吸积盘边界的K-H不稳定性

本文在中子星磁层与吸积盘之间引入了一个速度、密度、压强和磁场都连续变化的有限厚度的剪切层,以代替Anzer理论中的切向间断面,用磁流体力学方法讨论了中子星磁层与吸积盘交界处等离子体可压缩情况下平面波扰动的K-H不稳定性。结果表明,K-H不稳定性依然存在,径向波矢扰动成为不稳定的主要模式。文中特别讨论了剪切层厚度取值对中子星自转的影响,表明适当调节剪切层厚度就可解释X射线脉冲星周期的变化。将此模型应用到脉冲X射线源Her X-1上,得到较好的结果。     

3‐D laser images of splash‐form tektites and their use in aerodynamic numerical simulations of tektite formation

Ten splash‐form tektites from the Australasian strewn field, with masses ranging from 21.20 to 175.00 g and exhibiting a variety of shapes (teardrop, ellipsoid, dumbbell, disk), have been imaged using a high‐resolution laser digitizer. Despite challenges due to the samples’ rounded shapes and pitted surfaces, the images were combined to create 3‐D tektite models, which captured surface features with a high fidelity (≈30 voxel mm^?2) and from which volume could be measured noninvasively. The laser‐derived density for the tektites averaged 2.41 ± 0.11 g cm^?3. Corresponding densities obtained via the Archimedean bead method averaged 2.36 ± 0.05 g cm^?3. In addition to their curational value, the 3‐D models can be used to calculate the tektites’ moments of inertia and rotation periods while in flight, as a probe of their formation environment. Typical tektite rotation periods are estimated to be on the order of 1 s. Numerical simulations of air flow around the models at Reynolds numbers ranging from 1 to 10⁶ suggest that the relative velocity of the tektites with respect to the air must have been <10 m s^?1 during viscous deformation. This low relative velocity is consistent with tektite material being carried along by expanding gases in the early time following the impact.     

The kinematic effects on the rotation curve of a galaxy

In this paper, it is pointed out that if the spiral galaxy revolves about some common centre as a whole, the rotation curve will be changed by the kinematic effects. The common centre could be the centre of supercluster or the centre of dark matter and luminous matter.The kinematic effects on rotation curve are calculated. The additional velocity caused by revolving about the common centre is obtained. In case the direction of revolution is opposite (or consistent) to the direction of rotation, then in the outer region of nucleus, a flat rotation curve could be changed to a constant negative (or postive) gradient. The 44 rotation curves of Sb and Sc galaxies are expressed by means of linear least-squares fit, from which the period of revolving and the ratio of tidal force to self-gravitating force are calculated for every galaxy in extreme cases. The periods for most galaxies are in the reasonable region about 10⁹ years. The tidal force is always less than gravitating force, so the system could be maintained in such a revolving cases. At last, rotation curves in all directions of disk are suggested to pick out the kinematic effects from pure rotation.Work supported by the National Science Foundation of China, under Grant No. 1860610.     

A method for constructing streamlines for the Sun's large scale flow from Doppler velocities

We show that, if the large scale departures from the mean differential rotation, measured by Howard and Harvey, represent nearly horizontal flow, we may under certain assumptions deduce a pattern of streamlines for these motions from the doppler line of sight velocities. This can be done with data from a single day, without having to construct the total flow from different projections of the (assumed) same velocity vectors seen on different days. Mathematically the method involves integrating a single first order inhomogeneous partial differential equation along a set of characteristic curves which are circles concentric with the center of the solar disk.The structure of the resulting streamline pattern could be compared to large scale magnetic patterns, and latitudinal transports of magnetic flux and momentum could be estimated.The National Center for Atmospheric Research is sponsored by the National Science Foundation.