Rotation Curves of Galaxies in Various Space Environments

A sample of giant Sb-Sc spiral galaxies for which there are highly accurate and extended rotation curves was considered. Having divided the galaxies into three groups as a function of the overall spatial density of luminosity (mass) within 0.5 Mpc ( _L ), we investigated the characteristics of the rotation curves as functions of _L . It turned out that for such massive galaxies, the shape of the rotation curve (the logarithmic gradient) and the Tully-Fisher relation do not depend on the overall space environment. The only difference is that the rotation curves of galaxies in regions with high _L can be traced out to smaller relative distances from the nucleus, on the average. This may be related to destruction of the outer regions of their gaseous disks in gravitational interaction with surrounding galaxies.     

The formation of a ring galaxy during a head-on collision between a disk and a spherical galaxy

The tidal force effects of a spherical galaxy passing head-on through a disk galaxy have been studied at various regions of the disk galaxy and for various orientations of the disk galaxy with respect to the direction of relative motion of the two galaxies. The density distribution of the disk galaxy is taken to be, (r)=_ce^–4r/R , where _c is the central density andR is the radius of the disk. The density distribution of the spherical galaxy is taken to be that of a oolytrope of indexn=4. It is found that as a result of the collision, through the central parts and the outer parts of the disk galaxy remain intact, the region in between these two regions disrupts. Thus a ring galaxy with a nucleus embedded in the ring-i.e., a ring galaxy of the RN-type, is formed.     

Flat rotation curves and mass distribution for spiral galaxies with a disk model

A method to fit flat rotation curves is presented, wherein the galactic density for a disk model is expressed in terms of a Dirichlet polynomial. This procedure allows us to obtain the total galactic mass and to predict the circular velocity at large galactocentric distances.Application of the method to the Galaxy, M31 and four Sc galaxies shows that a significant galactic mass is located beyond the optical radius although it is considerably smaller than the integral mass values obtained from current models with a massive corona included. Observed rotation curves and convergent total mass are obtained, thus the total mass for the Milky Way Galaxy is 5.69×10¹¹ M .     

A cosmic virial theorem

A new type of cosmic virial theorem is derived, representing a relation among the two-point and three-point galaxy correlation functions and the mean square relative peculiar velocity v ²(r) averaged over pairs of galaxies separated by distancer. The two correlation functions seem to be fairly well known, but v ²(r) at best is only very roughly estimated from available data. It might be possible to improve the estimate through a systematic program of redshift measurements in sample areas. If so, the cosmic virial theorem might yield an interesting measure of the mean mass density due to galaxies.Research supported in part by the National Science Foundation.     

On the formation of superdense gaseous cores in the nuclei of disk galaxies — I

A model for the formation of superdense gaseous cores by accretion in the nuclei of disk galaxies has been proposed. Equations for radial flow of gas into the nucleus in the presence of aweak galactic magnetic field have been solved, and time scales for the accretion of an exploding mass in the nucleus (10⁹ M ) have been obtained under several different situations in the absence of any rotation. The time scales are found to lie in the range between a few times 10⁷ yr and 10⁸ yr. Such time scales have been proposed by some authors for repeated explosions in the nuclei of galaxies; they have also proposed that spiral arms in disk galaxies are repeatedly formed and destroyed over such time scales. It is shown that the presence of rotational velocities in the infalling gas practically destroys the efficiency of the accretion process unless such velocities are dissipated by frictional forces within the system. Viscosity of gas is the most obvious dissipative agent. The problem of accretion of a rotating viscous gas will be discussed in a subsequent paper.     

Dark matter particles and the flat rotation curves of spiral galaxies

It is shown that a gas of massive bosonic particles (m 60 eV), e.g. Higgs particles, surrounding disk galaxies is able to generate the flat rotation curves of spiral galaxies without internal difficulties with physical principles. We have analyzed 36 galaxies and find good agreement with the empirical data.     

HI observations ofHII-galaxies

High-resolution observations of the star forming dwarf galaxies Haro 21 and Markarian 314 are presented and are compared with a set of narrow band (H) CCD images. TheHi system related to Haro 21 measures about 12 kpc in diameter and is much more extended than the optical emission. The optical light follows that of an exponential disk and has a scale length of only 600 pc. TheHi distribution shows a lack of neutral gas near its centre where most of the H emission is found. The velocity field is regular and shows the characteristics of a disk in differential rotation. The rotation curve is rising out to the last measured point and the total mass is estimated to be about 1.5×10¹⁰ M . This implies that Haro 21 is a galaxy which is dominated by Dark Matter.Partly based on observations collected at the European Southern Observatory, La Silla, Chile.     

Dynamical friction on a satellite of a disk galaxy: The circular orbit

In a previous paper, we have studied dynamical friction during a parabolic passage of a companion galaxy past a disk galaxy. This paper continues with the study of satellites in circular orbits around the disk galaxy. Simulations of orbit decay in a self gravitating disk are compared with estimates based on two-body scattering theories; the theories are found to give a satisfactory explanation of the orbital changes. The disk friction is strongly dependent on the sense of rotation of the companion relative to the rotation of the disk galaxy as well as on the amount of mass in a spherical halo. The greatest amount of dynamical friction occurs in direct motion if no spherical halo is present. Then the infall time from the edge of the disk is about one half of the orbital period of the disk edge. A halo twice as massive as the disk increases the infall time four fold. The results of Quinn and Goodman, obtained with a non-self-gravitating method, agree well with our experiments with massive halos (Q ₀ 1.5), but are not usable in a more general case. We give analytic expressions for calculating the disk friction in galaxies of different disk/halo mass ratios.     

Rotation curve of galaxies by the force induced by mass of moving particles

Many attempts have been made to explain the flat rotation curve of spiral galaxies regardless of distance from the center, in disagreement with the Newtonian prediction that this speed should diminish as the inverse square of distance. One explanation for this discrepancy is that the galaxy is embedded in dark matter, which interacts with baryonic matter only gravitationally. Many studies have focused on finding the distribution of this dark matter that fits well with observed data, but it is by definition undetectable by current technology, and must therefore remain hypothetical. Instead of dark matter, we propose a novel force, named mirinae force, generated by the mass of relatively-moving particles, and demonstrate that this force explains the rotation curve and evolution of a galaxy in which some of the inner mass of the supermassive black hole at the galactic center is assumed to be revolving at a relativistic speed. The calculation yielded important results that support the existence of mirinae force and validate the proposed model: First, the mirinae force explains why most of the matter is in the galactic disk and in circular motion which is similar to that of particles in a cyclotron. Second, the mirinae force explains well both the flat rotation curve and the varied slope of the rotation curve observed in spiral galaxies. Third, at the flat velocity of 220 km/s, the inner mass of the Milky Way calculated by using the proposed model is 6.0×10¹¹ M _⊙, which is very close to 5.5×10¹¹ M _⊙ (r<50 kpc, including Leo I) estimated by using the latest kinematic information.     

The galactic centre

An attempt is made to present all the relevant observations of our galactic centre and to explain them by means of a working scheme that involves a minimum number ofad hoc assumptions.In this scheme, the central engine is Sgr A^*, a supermassive star of some 10³ M and surface temperature 3.6×10⁴ K in Keplerian rotation, fuelled by the strongly magnetized disk. It drives both a non-thermal (pair-plasma) wind and a thermal wind. Interactions with the central star cluster and with the circumnuclear disk give rise to the thermal vortex Sgr A West and to the non-thermal spill-over bubble Sgr A East. The relativistic pair plasma escapes supersonically through the galactic chimney into the galactic twin jets, as in Seyfert galaxies.     

Rotation curves for spiral galaxies in clusters and in the field

Rotation curves of spiral galaxies in clusters are compared with their counterparts in the field using three criteria: (1) inner and outer velocity gradients, (2)M/L gradients, and (3) Burstein's mass type methodology. Both H emission-line rotation curves and more extendedHi rotation curves are used. A good correlation is found between the outer gradient of the rotation curve and the galaxy's distance from the centre of the cluster, in the sense that the inner galaxies tend to have falling rotation curves while the outer galaxies, and field galaxies, tend to have flat or rising rotation curves. A correlation is also found between theM/L gradient across a galaxy and the galaxy's position in the cluster, with the outer galaxies having steeperM/L gradients. Mass types for field spirals are shown to be a function of both Hubble-type and luminosity, contrary to earlier results. The statistical difference between the distribution of mass types in clusters and in the field reported by Bursteinet al. is confirmed. These correlations indicate that the inner cluster environment can strip away some fraction of the mass in the outer halo of a spiral galaxy, or alternatively, may not allow the halo to form.     

On the relation between radius,luminosity, surface brightness,and surface density in elliptical galaxies

We have analyzed luminosity profiles of E galaxies studied by Strom and Strom in six clusters of galaxies. We have found a relationship between radius, luminosity, and surface brightness for galaxies in each of the clusters. A dependence of the zero point of the relation with the local projected density of galaxies is likewise found:r _{e proj} ^–0.14 L ^0.445 I _e ^–0.413 . This relationship implies (i) that there is not a universal luminosity profile for elliptical galaxies, (ii) the environmental variation of radius is larger than that produced by mergers of galaxies, (iii) distance to a galaxy can be estimated from apparent magnitude, surface brightness, angular size, and apparent local projected density of galaxies.     

Gravitational potential energy of a pair of overlapping galaxies

The interaction of the gravitational potential energy of a pair of overlapping Plummer-model galaxies is determined exactly for various separationsr of their centres. It is shown that the results can be well represented by the simple relationW(r)=–GM ₁ M ₂/(r ²+ ²)^1/2, where 1/ is the average reciprocal distance between the stars of two galaxies of massesM ₁ andM ₂ when they have zero separation.     

A search for steep low-frequency radio spectra among quasars and clusters of galaxies

Using published flux densitiesS at low frequenciesv, radio spectra were constructed for 3C, 4C, and 4CT radio sources in Abell clusters of galaxies, radio galaxies outside Abell clusters, and quasars with known redshifts. About half the sources in rich Abell clusters (richness classesR>-2) have steep spectra between 38 and 178 MHz with spectral indices ₃₈ ¹⁷⁸ > whereSv ^–. However, radio galaxies outside clusters have values of ₃₈ ¹⁷⁸ 1.2, and no steep spectra were found among 170 quasars. The radio sources in rich clusters are probably confined by intergalactic gas, and the steep spectra develop over a period of 10⁹ yr as relativistic electrons lose energy. The absence of steep spectra among quasars does not necessarily mean that quasars never occur in rich clusters of galaxies, since quasars are probably being observed only in their early high-luminosity phases. The possibility that some quasar events occur in the nuclei of the dominant cD galaxies in clusters is discussed, but quasar events may occur in more than one type of galaxy.     

Kinematical properties of early-type galaxies

Summary In the last decade, our understanding of early-type galaxies has greatly changed: from rather uninteresting oblate spheroids flattened by rotation to multicomponent stellar systems whose structure, formation mechanisms, and evolution, are far from being understood. This new scenario is mainly the consequence of the huge growth, in quantity and in quality, of kinematical data obtained from high signal to noise spectral data. Rotation curves and velocity dispersion profiles extending out to almost 2 effective radii are now available, together with line asymmetry measurements, for the stellar components of a fairly large sample of galaxies. For a few galaxies, outer halo tracers such as globular clusters and/or planetary nebulae allow to explore the kinematics out at 4 6r _e. In this article we focus on these data giving particular emphasis on the most recent results. Reference is given to other review articles complementing the approach presented here.     

Spiral structure of galaxies two alternatives

At present the wave theory of the spiral structure of the galaxies includes two alternative viewpoints. Two types of spiral waves—short-wave and long-wave modes—can be excited. According to Lin and Shu (1964) the short-wave modeK is responsible for the spiral structure of the galaxies and, according to Marochniket al. (1972), the long-wave mode (K ₀). In our Galaxy theK -mode corresponds to the wave with an angular rotation velocity _p =11–13 kms^–1 kps^–1 and a radial group velocity directed from the periphery to the center. TheK ₀-mode corresponds to the wave having an angular rotation velocity _p =23 ± 3 kms^–1 kps^–1 and a radial group velocity directed from the center of the Galaxy to its periphery. The theoretical and observational evidences in favour of Marochniket al.'s (1972) model are given.     

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.     

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.     

Spin parameter and scale-free density perturbations in hierarchical clustering

The present attempt aims to predict the dependence of the spin parameter, , the angular momentum,J, and the typical radius,a _vir, on the mass,M, which have been found inN-body simulations of expanding density perturbations in hierarchical clustering, when virialization is attained. We show that M ⁰ for systems with same adimensional density distribution and velocity distribution, and in particular for scale-free density perturbations in hierarchical clustering. In the special case of ellipsoidal perturbations, it is also found:J M ^7/4,a _vir M ^1/2. All these results turn out to be in close agreement withN-body simulations, despite the simple model adopted. Expanding and virialized perturbations are modelled, respectively, by homogeneous and heterogeneous, similar ellipsoids which allow flat rotation curves far from the centre. Both energy and angular momentum maintain from a given time on, lying between the beginning of strong decoupling from the Hubble flow and the occurrence of maximum volume. Then the whole set of virialized ellipsoidal configurations with same energy and angular momentum are derived, and the dependence of the spin parameter on the anisotropy parameter, _pec is investigated. Turning our attention to the formation of galaxies, we derive the total mass as a function of the collapse factor, using the empirical anticorrelation between dark to visible mass ratio within the optical radius of disk galaxies and their luminous masses. Observational data related to a sample of elliptical galaxies provide evidence that the contraction in these bodies occurred in proportion to the square root of the ratio of total to luminous mass. On the contrary, it is deduced that dissipation of angular momentum in elliptical galaxies occurred more or less at the same rate. If both shape and anisotropy parameter are preserved during the collapse, typical axis rations ₂₁ = 0.98, ₃₁ = 0.69, are found to correspond to a moderate anisotropy, _pec 0.27, with a small dependence on the spin parameter in the range allowed.