Potential energy of gravitationally interacting disk galaxies

Methods are developed for analysing the gravitational properties of disks having circularly symmetric distribution of matter. It is shown how this can be conveniently done by assuming that the surface density distribution may be approximated by a polynomial in ascending powers of the distance from the centre of the configuration. A theory has been developed to determine the gravitational potential of a single disk at any point in space in terms of the coefficients of the polynomial defining the surface distribution of matter, and the potential energy of two disks of arbitrary separation and orientation due to their mutual gravitational attraction. The basic functions, required for obtaining the potential in the plane of the disk and the mutual potential energy of two coplanar disks, have been tabulated. Two overlapping coplanar disks attract just like mass-points at a certain separation,r _c , of their centres. The force of attraction of disks is less than the force of attraction of mass-points having masses equal to the masses of the disks, if the separation of the centres is less thanr _c , and greater if the separation is greater thanr _c . For typical galaxies of equal radiiR,r _c ≈R.     

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.     

Tidal disruption of a disk galaxy

The tidal force effects of a spherical galaxy passing head-on through a disk galaxy have been studied for various orientations of the disk galaxy with respect to the direction of relative motion of the two galaxies. The density distribution of the spherical galaxy is taken to be that of a polytrope of indexn=4 and that of the disk galaxy is taken to be, (r)=_ce^–4r/R, where _c is the central density andR the radius of the disk. It is found that the disruptive effects due to the tidal force are minimum when the plane of the disk lies along the direction of relative motion, but are maximum when the plane of the disk is slightly inclined to this direction (about 15°). The tidal force effects at the median radius have also been computed. The tadal force effects are much higher in the interior region of the disk.     

CDM, Feedback and the Hubble Sequence

We have performed TreeSPH simulations of galaxy formation in a standard ΛCDM cosmology, including effects of star formation, energetic stellar feedback processes and a meta-galactic UV field, and obtain a mix of disk, lenticular and elliptical galaxies. The disk galaxies are deficient in angular momentum by only about a factor of two compared to observed disk galaxies. The stellar disks have approximately exponential surface density profiles, and those of the bulges range from exponential to r ^1/4, as observed. The bulge-to-disk ratios of the disk galaxies are consistent with observations and likewise are their integrated B-V colours, which have been calculated using stellar population synthesis techniques. Furthermore, we can match the observed I-band Tully-Fisher (TF) relation, provided that the mass-to-light ratio of disk galaxies is (M/L _I) ≃ 0.6–0.7. The ellipticals and lenticulars have approximately r ^1/4 stellar surface density profiles, are dominated by non-disklike kinematics and flattened due to non-isotropic stellar velocity distributions, again consistent with observations. This revised version was published online in September 2006 with corrections to the Cover Date.     

The formation of ring galaxies

The conditions under which a head-on collision between a disk galaxy and a spherical galaxy can lead to ring formation are investigated, using the impulsive approximation. The spherical galaxy is modeled as a polytrope of indexn=4 and radiusR _S and the disk galaxy as an exponential disk whose surface density is given by \(\sigma (r) = \sigma _c e^{ - 4r/R_D } \) , where σ _c is the central density andR _D is the radius of the disk. The formation and properties of the rings are closely related to the fractional change in binding energy of the disk galaxy, given by ΔU/?U?=γ _D β _D , where (GM _S ² R _D )/(V ² M _D R _S ² ),M _S andM _D being the masses of the spherical and disk galaxies, respectively, and β _D ≡β _D (n, σ, ?,i) is a function of the models of the two galaxies, the ratio of the radii of the two galaxies ?=R _S /R _D , and the angle of inclinationi, of the disk to the direction of relative motion of the two galaxies. Calculations are made for the caseR _S =R _D . Since practically the entire mass of the spherical galaxy, for the chosen model, lies within 1/3 of its radius, the radius of the spherical galaxy is effectively \(\tfrac{1}{3}\) that of the disk galaxy. It is found that as a result of the collision, the innermost and the outer parts of the disk galaxy are not much affected, but the intermediate region expands and gets evacuated, leading to the crowding of stars in a preferential region forming a ring structure. The rings are best formed for a normal, on-axis collision. For this case, rings form when ΔU/|U| lies between \(\tfrac{1}{2}\) and 2, while they are very sharp and bright when ΔU/|U| lies between \(\tfrac{1}{2}\) and 1. Within this range, as ΔU/|U| increases, the rings become sharper and their positions shift outwards with respect to the centre of the disk galaxy. The relationship $$\gamma _D = 0.0016 + 0.045s_{{\text{max}}}^2 ,$$ wheres _max is the radial distance of the density maximum of the ring from the centre of the disk galaxy (measured in terms of the radius of the disk galaxy as unit) enables us to finds _max from γ _D and vice versa, and interpret some prominent ring galaxies. The effect of introducing a bulge to the disk is to distribute the tidal disruptive effects more evenly and, hence, reduce the sharpness of the ring.     

The formation of faint ring structures

In a previous paper (Chatterjee, 1984), we studied the formation of ring galaxies due to head-on collisions between disk and spherical galaxies. The rings so formed are quite prominent and well defined. However, in the domain of rings, there are many faint rings which are ill defined and are so faint that they lie on the borderline of detectability. In this paper the formation of such rings is investigated.Using the impulsive approximation technique, in this paper we study an off-center collision between an exponential model disk galaxy and a polytropic (n=4) model spherical galaxy, in which the spherical galaxy moves normal to the plane of the disk galaxy and grazes its periphery. The radii of the two galaxies are taken to be equal, but due to the high central concentration of the spherical galaxy its radius is effectively one-third that of the disk galaxy. It is found that, as a result of the collision, the disk galaxy expands and attains an oblate shape. If the fractional change in binding energy of the disk galaxy, U/|U|, lies between 0.001 to 0.01, then a faint ring structure is formed which does not close on itself. If U/|U|0.01, then in addition to the faint ring a bridge and tail are formed. The ability of such low-energy collisions to affect even minor structural changes in the disk is due to the preferentially higher energy changes occurring in the side nearer to the perturbing galaxy than in the opposite side. Consequently, the structural changes produced are asymmetric.Such a faint ring may elude detection on photographs, but it will be revealed by sensitive photometric observations. There are several examples of such faint ring structures embedded in disks, which have been detected by observation.     

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.     

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.     

Head-on Collision of Disk–Sphere Galaxies

Numerical simulations are performed to study the tidal effects of non-merging rapid head-on collision between a disk galaxy and a spherical galaxy. The disk consists of three components – a disk, a bulge and a halo – and the spherical galaxy is a Plummer model. The galaxies have the same dimensions with different mass ratios viz., 2, 1 and 0.5. They move in a rectilinear orbit with a relative velocity of 1000 km s⁻¹. None of the simulations leads to the merger of the galaxies by tidal capture. The results of our simulations indicate that although tidal effects are sensitive to both the mass ratio and the inclination of the disk to the orbital plane, it is the mass ratio which is more important in producing tidal damage to the less massive galaxy. The spherical galaxy undergoes considerable tidal effects if the mass of the disk is same or larger. On the other hand the collisions in which the mass of the spherical galaxy is more, result in the formation of a ring structure after the closest approach and the structure disappears by the end of the simulations.     

Correlation between the densities of X-ray sources and interstellar gas

The distribution of X-ray sources in our galaxy is obtained, assuming that the absolute X-ray luminosities of these sources are the same. The distribution is found to be in good correlation with the distribution of interstellar gas. The density of X-ray sources is nearly proportional to the square density of gas. This indicates that X-ray sources are comparatively young. The relation between the densities of X-ray sources and gas allows us to estimate the X-ray intensities of various objects such as Magellanic Clouds and Andromeda nebula, and also to obtain the average X-ray luminosity of spiral galaxies. The latter should increase as the age of a galaxy decreases, since the amount of gas decreases as the galaxy evolves. Under the assumptions that the gas density is inversely proportional to the age and that galaxies older thant ₀/30 are visible in X-rays, wheret ₀ is the present age of the universe, the contribution of X-ray sources in distant galaxies to the background component is calculated. The intensity and the spectrum of the background component of X-rays thus obtained are in fair agreement with observed ones in the energy range between 1 and 4 keV but significantly deviate from the latter at high energies.     

A Catalog of Isolated Galaxy Pairs Limited to Absolute Magnitude -18.5 Drawn from HyperLEDA Database

The present paper is devoted to the construction of a catalog of isolated galaxy pairs extracted from the HyperLEDA extragalactic database. The radial velocities of the galaxies in the pairs are in the range [3000, 16000] km s^?1. In order to get an unbiased pair catalog as complete as possible, we have limited the absolute magnitude of the galaxies to M ≤ ?18.5. The criteria used to define the isolated galaxy pairs are the following: 1) velocity criterion: radial velocity difference between the pair members ΔV < 500 kms^?1; 2) interdistance criterion: projected distance between the members r_p < 1 Mpc; 3) reciprocity criterion: each member is the closest galaxy to the other one, which excludes multiplets; 4) isolation criterion: we define a pair as isolated if the ratio ρ = r₃/r_p of the projected distance of the pair to its closest galaxy (this one having a velocity difference lower than 500 km s^?1 with respect to the pair) and the members projected interdistance r_p is larger than 2.5.We have searched for these closest galaxies first in HyperLEDA M-limited source catalog, then in the full one.We have managed not to suppress the small number of pairs having close-by but faint dwarf galaxy companions. The galaxy pair catalog lists the value of ρ for each isolated pair. This method allows the user of the catalog to select any isolation level (beyond the chosen limit ρ > 2.5). Our final catalog contains 13 114 galaxy pairs, of which 57% are fairly isolated withρ > 5, and 30% are highly isolated with ρ ≥ 10.     

The peculiar motion of the galaxies

The result of SANDAGE and TAMMANN (1975) that the peculiar motion of the galaxies superimposed on the HUBBLE flow is probably smaller than 50 km/s shows that the kinetic energy density of the “galaxy gas” was always smaller than the energy density of radiation or matter if the galaxies were formed later than z ≈︂ 10⁴. The galaxies possessed initial velocities 0.2 c if they orginated in the recombination area.     

Potential and force due to thin disk and spherical galaxies

The determination of the potential and force due to a thin exponential model disk galaxy and a polytropicn=4 model spherical galaxy are conducted in the light of the study of collision dynamics.Results indicate that the potential due to the sphere and the disk along its plane are equal at a distance of about 1/3R, whereR is the radius of either configuration. Interior to this distance, the potential due to the sphere is greater than that due to the disk and beyond this distancevice versa.These results are expected to lead to the construction of simple models for galaxies, useful in the study of collision dynamics.     

Spread of matter over a neutron-star surface during disk accretion: Deceleration of rapid rotation

The accretion of hot slowly rotating gas onto a supermassive black hole is considered. The important case where the velocities of turbulent pulsations at the Bondi radius r _B are low, compared to the speed of sound c _s, is studied. Turbulence is probably responsible for the appearance of random average rotation. Although the angular momentum at r _B is low, it gives rise to the centrifugal barrier at a depth r _c = l ² /GM _BH ≪ r _B, that hinders supersonic accretion. The numerical solution of the problem of hot gas accretion with finite angular momentum is found taking into account electron thermal conductivity and bremsstrahlung energy losses of two temperature plasma for density and temperature near Bondi radius similar to observed in M87 galaxy. The saturation of the Spitzer thermal conductivity was also taken into account. The parameters of the saturated electron thermal conductivity were chosen similar to the parameters used in the numerical simulations of interaction of the strong laser beam radiation with plasma targets. These parameters are confirmed in the experiments. It is shown that joint action of electron thermal conductivity and free-free radiation leads to the effective cooling of accreting plasma and formation of the subsonic settling of accreting gas above the zone of a centrifugal barrier. A toroidal condensation and a hollow funnel that separates the torus from the black hole emerge near the barrier. The barrier divides the flow into two regions: (1) the settling zone with slow subKeplerian rotation and (2) the zone with rapid supersonic nearly Keplerian rotation. Existence of the centrifugal barrier leads to significant decrease of the accretion rate Ṁ in comparison with the critical Bondi solution for γ = 5/3 for the same values of density and temperature of the hot gas near Bondi radius. Shear instabilities in the torus and related friction cause the gas to spread slowly along spirals in the equatorial plane in two directions.As a result, outer (r > r _c) and inner (r < r _c) disks are formed. The gas enters the immediate neighborhood of the black hole or the zone of the internal ADAF flow along the accretion disk (r < r _c). Since the angular momentum is conserved, the outer disk removes outward an excess of angular momentum along with part of the matter falling into the torus. It is possible, that such outer Keplerian disk was observed by Hubble Space Telescope around the nucleus of the M87 galaxy in the optical emission lines. We discuss shortly the characteristic times during which the accretion of the gas with developed turbulence should lead to the changes in the orientation of the torus, accretion disk and, possibly, of the jet.     

The environmental dependence of u-, g-, r-, i-, and z-band luminosities for galaxies above and below the value of Mr*

Using two volume-limited Main galaxy samples of the Sloan Digital Sky Survey Data Release 6 (SDSS DR6), we have explored the difference of the environmental dependence of u-, g-, r-, i-, and z-band luminosities between galaxies above and below the value of M _r^*. It turns out that in the luminous volume-limited sample, all the five band luminosities strongly correlate with local environments. Because the u-band luminosity of galaxies still strongly depends on local environments in the faint volumelimited sample, we conclude that M _r^* is not an important characteristic parameter for the environmental dependence of the u-band luminosity. It is worth noting that for the u-band, the subsample at low density has a higher proportion of luminous galaxies and a lower proportion of faint galaxies than the one at high density, which is opposite to widely accepted conclusion: luminous galaxies exist preferentially in the densest regions of the universe, but faint galaxies are located preferentially in low density regions. Our results show that the environmental dependence of luminosity is not a single trend in different luminosity regions and for different bands.     

The opacity of spiral galaxy disks: IX. Dust and gas surface densities

Our aim is to explore the relation between gas, atomic and molecular, and dust in spiral galaxies. Gas surface densities are from atomic hydrogen and CO line emission maps. To estimate the dust content, we use the disk opacity as inferred from the number of distant galaxies identified in twelve HST/WFPC2 fields of ten nearby spiral galaxies. The observed number of distant galaxies is calibrated for source confusion and crowding with artificial galaxy counts and here we verify our results with sub‐mm surface brightnesses from archival Herschel ‐SPIRE data. We find that the opacity of the spiral disk does not correlate well with the surface density of atomic (H I) or molecular hydrogen (H₂) alone implying that dust is not only associated with the molecular clouds but also the diffuse atomic disk in these galaxies. Our result is a typical dust‐to‐gas ratio of 0.04, with some evidence that this ratio declines with galactocentric radius, consistent with recent Herschel results. We discuss the possible causes of this high dust‐to‐gas ratio; an over‐estimate of the dust surface‐density, an under‐estimate of the molecular hydrogen density from CO maps or a combination of both. We note that while our value of the mean dust‐to‐gas ratio is high, it is consistent with the metallicity at the measured radii if one assumes the Pilyugin & Thuan (2005) calibration of gas metallicity. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The gas content in galactic disks: Correlation with kinematics

We consider the relationship between the total HI mass in late-type galaxies and the kinematic properties of their disks. The mass M_HI for galaxies with a wide variety of properties, from dwarf dIrr galaxies with active star formation to giant low-brightness galaxies, is shown to correlate with the product V_cR₀ (V_c is the rotational velocity, and R₀ is the radial photometric disks cale length), which characterizes the specific angular momentum of the disk. This correlation, along with the decrease in the relative mass of the gas in a galaxy with increasing V_c, can be explained in terms of the previous assumption that the gas density in the disks of most galaxies is maintained at a level close to the threshold (marginal) stability of a gaseous layer to local gravitational perturbations. In this case, the regulation mechanism of the star formation rate associated with the growth of local gravitational instability in the gaseous layer must play a crucial role in the evolution of the gas content in the galactic disk.     

Recent investigations on disk galaxies in massive halos

Numerical experiments undertaken to investigate the longevity and behavior of dark-lane elliptical galaxies are described. This is dynamically the same problem as a disk galaxy in a massive halo. Spiral galaxies are disks from a dynamical point of view. A disk of particles embedded in a self-consistent galaxy provides the basic model used for the experiments. This model is applicable to ordinary disk galaxies if the disk is interpreted as the visible galaxy and the galaxy is interpreted as the massive halo thought to be present around disk galaxies. Fully three-dimensional fully self-consistentn-body computer programs that can handle 100,000 particles are used for the experiments. The background galaxy is oblate, and the disk is inclined to the axis of the oblate galaxy, so the disk precesses differentially to produce a warp. A surprising result is that the galaxy center shifted, leaving the disk center orbiting around the galaxy center. This produces interesting phenomena reminiscent of observations in the region of the Galactic center.     

Determining the character of motion in quiet and active galaxies with a satellite companion

A galaxy model with a satellite companion is used to study the character of motion for stars moving in the x ‐y plane. It is observed that a large part of the phase plane is covered by chaotic orbits. The percentage of chaotic orbits increases when the galaxy has a dense nucleus of massM_n. The presence of the dense nucleus also increases the stellar velocities near the center of the galaxy. For small values of the distance R between the two bodies, low energy stars display a chaotic region near the centre of the galaxy, when the dense nucleus is present, while for larger values of R the motion in active galaxies is regular for low energy stars. Our results suggest that in galaxies with a satellite companion, the chaotic character of motion is not only a result of galactic interaction but also a result caused by the dense nucleus. Theoretical arguments are used to support the numerical outcomes. We follow the evolution of the galaxy, as mass is transported adiabatically from the disk to the nucleus. Our numerical results are in satisfactory agreement with observational data from M51‐type binary galaxies (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

核盘晕星系相互作用的模拟研究

用一个星系相互作用数值模拟的综合三体模型，研究椭圆星系是否由盘星系合并而成。结果表明，主要取决于星系的盘面和星系运行轨道面的夹角。如果夹角不等于零，盘星系的相互作用是可能形成椭圆星系的，否则还是盘星系。