Changes in the gravitational energy of galaxies during collisions

The problem of the change in gravitational energy of a colliding galaxy due to tidal effects is considered. The change in the internal energy, the mass of escaping matter and the change in the mean radius of the test galaxy have been estimated for a relative velocity of 1000 km s^–1 for three distances of closest approach for the following four cases: (a) both galaxies centrally concentrated, (b) both galaxies homogeneous, (c) test galaxy centrally concentrated, field galaxy homogeneous, and (d) test galaxy homogeneous, field galaxy centrally concentrated. The masses and radii of the two galaxies are taken as 10¹¹ M and 10 kpc respectively. For simplicity, the galaxies are assumed to be spherically symmetric and the distribution of mass within a centrally concentrated galaxy is assumed to be that of a polytrope of indexn=4. The results also provide estimates for the minimum relative velocity a galaxy must have in order that it may not be captured by another to form a double system. It has been found that normally a relative velocity of less than about 500 km s^–1 will lead to the formation of a double galaxy by tidal capture. In the case of a head-on collision between two centrally concentrated galaxies even a relative velocity of about 1000 km s^–1 is small enough for tidal capture. The changes in the structure of the galaxies for relative velocities equal to velocity of escape are also indicated. These results show that there is no escape of matter from the test galaxy in cases (b) and (c). In the case (a) the escape of matter can be as high as 4% of the total mass. The head-on collision between galaxies are normally not accompanied by any escape of matter. All the gain in the internal energy of galaxies during such collisions results in increase in their dimensions. The fractional increase in the mean radius of the test galaxy in the head-on collision is 1.5 in the case (a), 3.2 in the case (b) and 0.01 in the case (c). In the case (d) the test galaxy will be disrupted by the tidal forces.     

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.     

A classification of galactic collisions for galaxies of unequal dimensions

The earlier work on classification of galactic collisions for identical galaxies is extended to the situations where the two colliding galaxies differ in mass and dimension. We consider collisions between galaxies of masses 10⁷, 10⁹, 10¹¹ and 10¹³ M and let their radii be 0.1, 1, 10 and 100 kpc, respectively. The density distribution in both galaxies is represented by that of a polytrope of indexn=4. The type of collision is determined for head-on collisions for initial relative velocities 500, 1000, 2000 and 3000 km s^–1. The corresponding final velocities are also indicated.     

Radio continuum and far-infrared emission from the galaxies in the Eridanus group

The Eridanus galaxies follow the well-known radio—FIR correlation. The majority (70%) of these galaxies have their star formation rates below that of the Milky Way. The galaxies that have a significant excess of radio emission are identified as low luminosity AGNs based on their radio morphologies obtained from the GMRT observations. There are no powerful AGNs (L _20cm > 10²³ W Hz⁻¹) in the group. The two most far-infrared and radio luminous galaxies in the group have optical and HI morphologies suggestive of recent tidal interactions. The Eridanus group also has two far-infrared luminous but radio-deficient galaxies. It is believed that these galaxies are observed within a few Myr of the onset of an intense star formation episode after being quiescent for at least a 100 Myr. The upper end of the radio luminosity distribution of the Eridanus galaxies (L _20cm ∼ 10²² W Hz⁻¹) is consistent with that of the field galaxies, other groups, and late-type galaxies in nearby clusters.     

Exchange of gravitational energy during a collision of galaxies

The problem of the change in internal energy of a colliding galaxy due to tidal effects is considered, assuming that the galaxies may be regarded as spherical stellar systems whose over-all structure remains unchanged during the collision and that the stars move in circular orbits. The numerical estimates thus made for the energy gained by the stars during the collision are compared with those derived on the basis of the assumption that the motions of the stars may be neglected during the encounter (the impulsive approximation) to test the adequacy of the latter approximation. If the two galaxies are of 10¹¹ M , of radii 10 kpc and of mass distribution that of a polytrope of indexn=4; and if the relative distance and velocity at their closest approach are taken as 2 kpc and 1000 km/sec respectively, the mass of escaping stars from a galaxy is estimated to be roughly 4% of the total mass of the galaxy and the total increase in the internal energy of a galaxy during the collision due to the tidal acceleration of all its stars is equal in magnitude to approximately 25% of its initial internal energy, about one-fifth of which is associated with the escaping stars.     

On the Andromeda to Milky Way mass ratio

We have explored the hypothesis that the total mass ratio of the two main galaxies of the Local Group, the Andromeda galaxy (M31) and the Milky Way (MW), can be constrained by measuring the tidal force induced by the surrounding mass distribution, M31 included, on the MW. We argue that the total mass ratio between the two groups can be approximated, at least qualitatively, by finding the tidal radius where the internal binding force of the MW balances the external tidal force acting on it. Since M31 is the massive tidal 'perturber' of the local environment, we have used a wide range of M31 to MW mass-ratio combinations to compute the corresponding tidal radii. Of these, only a few match the distance of the zero-tidal shell, i.e. the shell identified observationally by the outermost dwarf galaxies which do not show any sign of tidal effects. This is the key to constraining the best mass-ratio interval of the two galaxies. Our results favour a solution where the mass ratio ranges from 2 to 3, implying a massive predominance of M31.     

Inhomogeneous chemical evolution of dwarf spheroidal galaxies

Stellar abundance pattern of n-capture elements such as barium is used as a powerful tool to infer how the star formation proceeded in dwarf spheroidal (dSph) galaxies. It is found that the abundance correlation of barium with iron in stars belonging to dSph galaxies orbiting the Milky Way, i.e., Draco, Sextans, and Ursa Minor have a feature similar to that in Galactic metal-poor stars. The common feature of these two correlations can be realized by our in homogeneous chemical evolution model based on the supernova-driven star formation scenario if dSph stars formed from gas with a velocity dispersion of ∼ 26 km s^-1. This velocity dispersion together with the stellar luminosities strongly suggest that dark matter dominated dSph galaxies. The tidal force of the Milky Way links this velocity dispersion with the currently observed value ≲ 10 km s^-1 by stripping the dark matter in dSph galaxies. As a result, the total mass of each dSph galaxy is found to have been originally ∼ 25 times larger than at present. In this model, supernovae immediately after the end of the star formation can expel the remaining gas over the gravitational potential of the dSph galaxy. This revised version was published online in August 2006 with corrections to the Cover Date.     

Abell 851: Are we looking at the beginning of a merging process?

We present an XMM observation of the moderately distant (z=0.41)galaxy cluster CL 0939+4713 (Abell 851), an exceptionally rich cluster. The formation and evolution of clusters depends sensitively on cosmological parameters like the mean matter density in the universe Ο_m. Therefore it is important to determine the dynamical state of clusters at different redshifts, i.e. at different evolutionary states. The X-ray morphology alone is not the best indicator of the dynamical state, but it should be complemented with all other information available, e.g. the temperature map or the galaxy distribution. The combination of all findings gives a detailed picture of the state of a cluster. This analysis, of this relatively distant cluster, can be used as a basis for comparisons at lower and higher redshifts. The capability of XMM to perform spatially resolved spectroscopy can be used also to determine the distribution of the metal abundances. Not only the overall value of metallicity but also its spatial distribution gives important indications on the metal enrichment processes. The X-ray image shows pronounced substructure. There are two main subclusters which have also some internal structure. This is an indication that the cluster is a dynamically young system. This conclusion is supported by the temperature distribution: a hot region is found between the two main subclusters indicating that the cluster is in the process of a major merger, in which the two subclusters will probably collide in a few hundreds of Myr. The intra-cluster gas of CL 0939+4713 shows variations of the metal abundances. The optically richer subcluster has a somewhat higher metallicity. This finding together with the absence of post-starburst galaxies in this region gives interesting hints on the metal enrichment processes favouring recent enrichment processes like ram-pressure stripping or tidal stripping. Throughout this paper we use H ₀ =50 km s^-1Mpc^-1 and q ₀ =0.5; all errors are 90% confidence levels. This revised version was published online in July 2006 with corrections to the Cover Date.     

Tidal structures of z ∼ 1 galaxies in the Hubble Deep Field

An analysis of the images of objects in the Northern Hubble Space Telescope Deep Field has revealed twelve galaxies with tidal tails at redshifts from 0.5 to 1.5. The integrated characteristics of the newly discovered tidal structures are found to be similar to those of the tails of local interacting galaxies. The space density of galaxies with tidal tails is found to depend on z as (1+z)^4±1(q ₀=0.05), according to the data on objects with z=0.5–1.0. The exponent decreases to 3.6 if barred galaxies are included. The change in the rate of close encounters between galaxies of comparable masses (i.e., those that produce extended tidal structures) is estimated. If the rate of galactic mergers is governed by the same process, our data are indicative of the rapid evolution of galaxy merger rate toward z ～ 1.     

The fate of dwarf galaxies in clusters and the origin of intracluster stars

The main goal of this paper is to compare the relative importance of destruction by tides vs. destruction by mergers, in order to assess if tidal destruction of galaxies in clusters is a viable scenario for explaining the origin of intracluster stars. We have designed a simple algorithm for simulating the evolution of isolated clusters. The distribution of galaxies in the cluster is evolved using a direct gravitational N-body algorithm combined with a subgrid treatment of physical processes such as mergers, tidal disruption, and galaxy harassment. Using this algorithm, we have performed a total of 148 simulations. Our main results are:

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.     

A Research on the Evolution of Star Formation Activities of Early-type Galaxies

The observational investigation of the evolution of the star formation activities of early-type galaxies (ETGs) with redshifts helps us to understand the formation and evolution of this kind of galaxies. Combined with the highresolution images from HST/ACS (Hubble Space Telescope/Advanded Camera for Surveys) of the GEMS (Galaxy Evolution fromMorphology and SEDs) survey and the multi-band data from Spitzer, GALEX (Galaxy Evolution Explorer) and so on in the CDFS (Chandra Deep Field South) field, a complete sample including 456 ETGs with their redshifts in the range of 0.2 ≤ z ≤ 1.0 is selected on the basis of morphology, color and stellar mass. By using the stacking technique, the ultraviolet and infrared average luminosities of sample galaxies are measured, and the star formation rates of ETGs are estimated. The results indicate that the star formation rates of ETGs are relatively low (< 3 M yr⁻¹) and decrease with decreasing redshifts. The mass contributed by the star formation since z = 1 is less than 15%. The analyses of stellar populations also confirm that the bulk of the population of massive ETGs was formed in the early universe (z > 2).     

Clustering evolution between z=1 and today

We present results of an investigation of clustering evolution of field galaxies between a redshift of z ∼ 1 and the present epoch. The current analysis relies on a sample of ∼ 14000 galaxies in two fields of the COMBO 17 survey. The redshift distribution extends to z ∼ 1. The amplitude of the three-dimensional correlation function can be estimated by means of the projected correlation function w(r _p ). The validity of the deprojection was tested on the Las Campanas Redshift Survey (LCRS). In a flat cosmology with non-zero cosmological constant for bright galaxies (M _B ≤-18) the clustering growth is proportional to (1+z) ^-2. However, the measured clustering evolution clearly depends on Hubble type. While locally the clustering strength of early type galaxies is equal to that of the bright galaxies, at high redshifts they are much stronger clustered, and thus the clustering has to evolve much more slowly. This revised version was published online in August 2006 with corrections to the Cover Date.     

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)     

Gravitational potential energy of a disk-sphere pair of galaxies

Algebraic expressions are obtained for the interaction potential energy of a pair of galaxies in which one is disk shaped and the other spherical. The density distribution in the disk galaxy is represented by a polynomial in ascending powers of the distance from the centre of the disk while the density distribution in the spherical galaxy is represented by the superposition of spherical polytropes of integral indices. The basic functions required for obtaining the interaction potential energy of a coplanar disk-sphere pair of galaxies are tabulated. The forces of attraction between a coplanar disk-sphere pair of galaxies are shown graphically for two density models of disk and spherical galaxies. An overlapping coplanar disk-sphere pair of galaxies attract just like two mass-points at a certain separation,r _c, of their centres. The force of attraction is less than that of two mass-points having masses equal to the masses of the two galaxies, if the separation of the centres is less thanr _c, and greater if the separation is greater thanr _c.For a typical coplanar disk-sphere pair of galaxies (the density of the disk is represented by Model II and of the sphere by a polytropic indexn=4) of equal radii, we note the following. At a separation of 0.79R, R being the common radius of the two galaxies, the force of attraction between the pair is the same as if the entire mass of each galaxy is concentrated at its centre. The mass-point model for the two galaxies will overestimate the force of attraction by more than a factor of 10 if the separation is less than 0.36R. For separation greater than the radii of the galaxies the mass-point model will underestimate the force but the departure in this case is less than 33%.     

Chemistry in luminous AGN and starburst galaxies

Molecular line emission is a useful tool for probing the highly obscured inner kpc of starburst galaxies and buried AGNs. Molecular line ratios serve as diagnostic tools of the physical conditions of the gas—but also of its chemical properties. Both provide important clues to the type and evolutionary stage of the nuclear activity. While CO emission remains the main tracer for molecular distribution and dynamics, molecules such as HCN, HNC, HCO⁺, CN and HC₃N are useful for probing the properties of the denser (n≳10⁴ cm⁻³), star-forming gas. Here I discuss current views on how line emission from these species can be interpreted in luminous galaxies. HNC, HCO⁺ and CN are all species that can be associated both with photon dominated regions (PDRs) in starbursts—as well as X-ray dominated regions (XDRs) associated with AGN activity. HC₃N line emission may identify galaxies where the starburst is in the early stage of its evolution.     

On-Going Galaxy Formation

We investigate the process of galaxy formation as can be observed in the only currently forming galaxies - the so-called Tidal Dwarf Galaxies, hereafter TDGs - through observations of the molecular gas detected via its CO (Carbon Monoxide) emission. These objects are formed of material torn off of the outer parts of a spiral disk due to tidal forces in a collision between two massive galaxies. Molecular gas is a key element in the galaxy formation process, providing the link between a cloud of gas and a bona fide galaxy. We have detected CO in 8 TDGs (Braine, Lisenfeld, Duc and Leon, 2000: Nature 403, 867; Braine, Duc, Lisenfeld, Charmandaris, Vallejo, Leon and Brinks: 2001, A&A 378, 51), with an overall detection rate of 80%, showing that molecular gas is abundant in TDGs, up to a few 10⁸ M _⊙. The CO emission coincides both spatially and kinematically with the HI emission, indicating that the molecular gas forms from the atomic hydrogen where the HI column density is high. A possible trend of more evolved TDGs having greater molecular gas masses is observed, in accord with the transformation of HI into H₂. Although TDGs share many of the properties of small irregulars, their CO luminosity is much greater (factor ∼ 100) than that of standard dwarf galaxies of comparable luminosity. This is most likely a consequence of the higher metallicity (≳sim 1/3 solar) of TDGs which makes CO a good tracer of molecular gas. This allows us to study star formation in environments ordinarily inaccessible due to the extreme difficulty of measuring the molecular gas mass. The star formation efficiency, measured by the CO luminosity per Hα flux, is the same in TDGs and full-sized spirals. CO is likely the best tracer of the dynamics of these objects because some fraction of the HI near the TDGs may be part of the tidal tail and not bound to the TDG. Although uncertainties are large for individual objects, as the geometry is unknown, our sample is now of eight detected objects and we find that the ‘dynamical’ masses of TDGs, estimated from the CO line widths, seem not to be greater than the ‘visible’ masses (HI + H₂ + a stellar component). Although higher spatial resolution CO (and HI) observations would help reduce the uncertainties, we find that TDGs require no dark matter, which would make them the only galaxy-sized systems where this is the case. Dark matter in spirals should then be in a halo and not a rotating disk. Most dwarf galaxies are dark matter-rich, implying that they are not of tidal origin. We provide strong evidence that TDGs are self-gravitating entities, implying that we are witnessing the ensemble of processes in galaxy formation: concentration of large amounts of gas in a bound object, condensation of the gas, which is atomic at this point, to form molecular gas and the subsequent star formation from the dense molecular component. This revised version was published online in September 2006 with corrections to the Cover Date.     

A classification of galactic collisions

The effects of collisions between two galaxies on the test galaxy considered are classified as follows — Type A: the changes in the size and mass of the test galaxy are both negligible; Type B: There is significant increase in the size (at least 10%) or decrease in the mass (at least 1%) of the test galaxy or in both; Type C: The test galaxy becomes a component of a double galaxy by tidal capture; Type D: The test galaxy is disrupted by the tidal forces of the field galaxy.The type of collision is given as a function of the distance and speed at closest approach and also as a function of the initial impact parameter and speed at infinite separation of the two galaxies for two density models of the galaxies. Collisions in which the two galaxies do not penetrate each other are generally of type A while slow interpenetrating collisions are generally of type B. Types C and D occur in head-on or nearly head-on collisions if the relative speed of the two galaxies is sufficiently small; the former is favoured if the two galaxies do not differ appreciably in mass and density distribution. If one of the two galaxies is considerably less massive or less centrally concentrated than the other, it will be disrupted in slow close collisions.     

Shakbazian Compact Groups: Mass‐to‐light ratios and mass distribution models: I. ShCG 362 and ShCG 166

We present results of photometric observations under excellent seeing conditions of Shakbazian Compact Groups. We obtained the seeing‐unconvolved surface brightness profiles of individual galaxies in the I band. We also determined the B – I color index for each galaxy, and investigated the presence of cores in the early type galaxies. We constructed models for the mass distribution of the individual galaxies. The mass‐to‐light (𝔐/L) ratios have normal values, and the conclusion that these groups have little dark matter is confirmed. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Tidal dwarf galaxies at intermediate redshifts

We present the first attempt at measuring the production rate of tidal dwarf galaxies (TDGs) and estimating their contribution to the overall dwarf population. Using HST/ACS deep imaging data from GOODS and GEMS surveys in conjunction with photometric redshifts from COMBO-17 survey, we performed a morphological analysis for a sample of merging/interacting galaxies in the Extended Chandra Deep Field South and identified tidal dwarf candidates in the rest-frame optical bands. We estimated a production rate about 1.4×10⁻⁵ per Gyr per comoving volume for long-lived TDGs with stellar mass 3×10⁸⁻⁹ M_⊙ at 0.5<z<1.1. Together with galaxy merger rates and TDG survival rate from the literature, our results suggest that only a marginal fraction (less than 10%) of dwarf galaxies in the local universe could be tidally-originated. TDGs in our sample are on average bluer than their host galaxies in the optical. Stellar population modelling of optical to near-infrared spectral energy distributions (SEDs) for two TDGs favors a burst component with age 400/200 Myr and stellar mass 40%/26% of the total, indicating that a young stellar population newly formed in TDGs. This is consistent with the episodic star formation histories found for nearby TDGs.