Changes in binding energy of interacting galaxies

It is shown that the fractional increase in binding energy of a galaxy in a fast collision with another galaxy of the same size can be well represented by the formula $$\xi _2 = 3({G \mathord{\left/ {\vphantom {G {M_2 \bar R}}} \right. \kern-\nulldelimiterspace} {M_2 \bar R}}) ({{M_1 } \mathord{\left/ {\vphantom {{M_1 } {V_p }}} \right. \kern-\nulldelimiterspace} {V_p }})^2 e^{ - p/\bar R} = \xi _1 ({{M_1 } \mathord{\left/ {\vphantom {{M_1 } {M_2 }}} \right. \kern-\nulldelimiterspace} {M_2 }})^3 ,$$ whereM ₁,M ₂ are the masses of the perturber and the perturbed galaxy, respectively,V _p is the relative velocity of the perturber at minimum separationp, and \(\bar R\) is the dynamical radius of either galaxy.     

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.     

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.     

Numerical simulations of interacting gas-rich barred galaxies: vertical impact of small companions

We investigate the dynamical effects of an interaction between an initially barred galaxy and a small spherical companion using an N -body/smoothed-particle-hydrodynamics algorithm. In the models described here the small companion passes through the disc of the larger galaxy nearly perpendicular to its plane. The impact positions and times are varied with respect to the phase of the bar and the dynamical evolution of the disc.
The interactions produce expanding ring structures, offset bars, spokes and other asymmetries in the stars and gas. These characteristic signatures of the interaction are present in the disc for about 1 Gyr. We find that in some cases it is possible to destroy the bar while keeping the disc structure. In general, the central impacts cause larger damage to the bar and the disc than the peripheral ones. The interaction tends to accelerate the transition from a strongly-barred galaxy to a weakly- or non-barred galaxy. The final disc morphology is determined more by the impact position relative to the bar rather than the impact time.     

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.     

Transfer of energy and angular momentum in the magnetic coupling between a rotating black hole and the surrounding accretion disc

The transfer of energy and angular momentum in the magnetic coupling (MC) of a rotating black hole (BH) with its surrounding accretion disc is discussed based on a mapping relation derived by considering the conservation of magnetic flux with two basic assumptions: (i) the magnetic field on the horizon is constant, (ii) the magnetic field on the disc surface varies as a power law with the radial coordinate of the disc. The following results are obtained: (i) the transfer direction of energy and angular momentum between the BH and the disc depends on the position of a co-rotation radius relative to the MC region on the disc, which is eventually determined by the BH spin; (ii) the evolution characteristics of a rotating BH in the MC process without disc accretion are depicted in a parameter space, and a series of values of the BH spin are given to indicate the evolution characteristics; (iii) the efficiency of converting accreted mass into radiation energy of a BH–disc system is discussed by considering the coexistence of disc accretion and the MC process; (iv) the MC effects on disc radiation and the emissivity index are discussed and it is concluded that they are consistent with the recent XMM–Newton observation of the nearby bright Seyfert 1 galaxy MCG–6-30-15 with reference to a variety of parameters of the BH–disc system.     

N-Body Simulation of a Deeply Penetrating Collision Between Unequal Galaxies

We study the tidal effects of a deeply penetrating collision between two spherical galaxies, one twice massive but less dense than the other, by numerical simulations. We consider the relative motion of the galaxies to be initially in a hyperbolic orbit. The collision parameters are so chosen that the primary (bigger) galaxy is just below the limit of disruption and the relative velocity of the pair is slightly in excess of the escape limit and the primary suffer greater tidal damage than the secondary. The primary develops a core halo structure and shows over all expansion while the secondary while the secondary shows contraction in the inner region and less significant expansion in the outer parts. The initially hyperbolic orbit is transformed into a parabolic orbit as a result of the collision. The result also indicate that the tidal interaction does not induce appreciable rotation in hyperbolic collision. We calculate the angle of deflection of the orbit and compare it with that computed using analytical work. The numerical work shows larger angle of deflection which is attributed to the large tidal effects of the bigger galaxy in the interpenetrating collision. This revised version was published online in July 2006 with corrections to the Cover Date.     

Simulating galactic outflows with kinetic supernova feedback

Feedback from star formation is thought to play a key role in the formation and evolution of galaxies, but its implementation in cosmological simulations is currently hampered by a lack of numerical resolution. We present and test a subgrid recipe to model feedback from massive stars in cosmological smoothed particle hydrodynamics simulations. The energy is distributed in kinetic form among the gas particles surrounding recently formed stars. The impact of the feedback is studied using a suite of high-resolution simulations of isolated disc galaxies embedded in dark haloes with total mass 10¹⁰ and  10¹²  h ⁻¹ M_⊙  . We focus, in particular, on the effect of pressure forces on wind particles within the disc, which we turn off temporarily in some of our runs to mimic a recipe that has been widely used in the literature. We find that this popular recipe gives dramatically different results because (ram) pressure forces on expanding superbubbles determine both the structure of the disc and the development of large-scale outflows. Pressure forces exerted by expanding superbubbles puff up the disc, giving the dwarf galaxy an irregular morphology and creating a galactic fountain in the massive galaxy. Hydrodynamic drag within the disc results in a strong increase in the effective mass loading of the wind for the dwarf galaxy, but quenches much of the outflow in the case of the high-mass galaxy.     

Density waves in the solar nebula: Diffential Lindblad torque

The differential torque between a two-dimensional fluid disc and an embedded perturber due to waves launched at its resonances is calculated. For a non-self-gravitating disc, the disturbance is in the form of pressure waves which propagate away from co-rotation and asymptotically become trailing spirals. The torque calculation includes lowest order contributions from gradients in various disc properties. The orbital drift rate of the perturber is determined and the results applied to the motion of preplanetary material in the solar nebula.     

The global structure of galactic discs

A statistical study of global galaxy parameters can help to improve our understanding of galaxy formation processes. In this paper we present the analysis of global galaxy parameters based on optical and near-infrared observations of a large sample of edge-on disc galaxies. We found a correlation between the ratio of the radial to vertical scale parameter and galaxy type: galaxies become systematically thinner when going from type S0 to type Sc, whereas the distribution seems to level off for later types. The observed scalelength ratios (and thus the radial colour gradients) largely represent the dust content of the galaxies. On average, the colour gradients indicated by the scalelength ratios increase from type Sa to at least type Sc. For galaxy types later than Sc, the average colour gradient seems to decrease again. The distribution of K -band (edge-on) disc central surface brightnesses is rather flat, although with a large scatter. However, the latest-type sample galaxies ( T  > 6) show an indication that their average disc central surface brightnesses may be fainter than those of the earlier types. This effect is probably not the result of dust extinction.     

0422−476: a shell galaxy with azimuthally distributed shells

A morphological and two-colour charge-coupled device photometry study of the shell galaxy 0422−476, one of the richest known azimuthally distributed shell galaxies, is presented. Taking this galaxy as a prototype, a general method for reducing observational data of these objects is defined and quantitative parameters for use in further theoretical studies are derived.
According to some recent models (e.g. that of Thomson and Wright in 1990), the shells in such a galaxy could be density waves induced in a thick disc population of dynamically cold stars by a weak interaction with another galaxy. In 0422−476 there is no evidence of either a conventional exponential disc or a thick disc. Although it is not possible to rule out the weak interaction model, the observations continue to favour the merger model (e.g. that of Quinn from 1984).     

A Model for the Cartwheel Ring Galaxy

A new model of the Cartwheel galaxy is presented, based on the nearly central inclined collision of a rigid companion galaxy with a self-gravitating disc containing both stars and gas. We assume that the intruder is the most distant companion (G3 in J. Higdon's notation). Two rings and a transient network of gaseous spokes develop after the passage of the companion. The expansion velocity of the outer ring is in agreement with the one observed for the atomic gas. At the end of the simulation, the position and velocity of the companion agree with those of G3. This revised version was published online in July 2006 with corrections to the Cover Date.     

Dynamical friction force exerted on spherical bodies

We present a rigorous calculation of the dynamical friction force exerted on a spherical massive perturber moving through an infinite homogenous system of field stars. By calculating the shape and mass of the polarization cloud induced by the perturber in the background system, which decelerates the motion of the perturber, we recover Chandrasekhar's drag force law with a modified Coulomb logarithm. As concrete examples, we calculate the drag force exerted on a Plummer sphere or a sphere with the density distribution of a Hernquist profile. It is shown that the shape of the perturber only affects the exact form of the Coulomb logarithm. The latter converges on small scales because encounters of the test and field stars with impact parameters less than the size of the massive perturber become inefficient. We confirm in this way the earlier results based on the impulse approximation of small angle scatterings.     

Near-infrared bulge–disc correlations of lenticular galaxies

We consider the luminosity and environmental dependence of structural parameters of lenticular galaxies in the near-infrared K band. Using a 2D galaxy image decomposition technique, we extract bulge and disc structural parameters for a sample of 36 lenticular galaxies observed by us in the K band. By combining data from the literature for field and cluster lenticulars with our data, we study correlations between parameters that characterize the bulge and the disc as a function of luminosity and environment. We find that scaling relations such as the Kormendy relation, photometric plane and other correlations involving bulge and disc parameters show a luminosity dependence. This dependence can be explained in terms of galaxy formation models in which faint lenticulars  ( M _T > −24.5)  formed via secular formation processes that likely formed the pseudo-bulges of late-type disc galaxies, while brighter lenticulars  ( M _T < −24.5)  formed through a different formation mechanism most likely involving major mergers. On probing variations in lenticular properties as a function of environment, we find that faint cluster lenticulars show systematic differences with respect to faint field lenticulars. These differences support the idea that the bulge and disc components fade after the galaxy falls into a cluster, while simultaneously undergoing a transformation from spiral to lenticular morphologies.     

Cosmic ray propagation and the star formation history of NGC 1961

We present new radio continuum data at four frequencies for the supermassive, peculiar galaxy NGC 1961. These observations allow us to separate the thermal and non-thermal radio emission and to determine the non-thermal spectral index distribution. This spectral index distribution in the galactic disc is unusual: at the maxima of the radio emission the synchrotron spectrum is very steep, indicating aged cosmic ray electrons. Away from the maxima the spectrum is much flatter. The steep spectrum of the synchrotron emission at the maxima indicates that a strong decline of the star formation rate has taken place at these sites. The extended radio emission is a sign of recent cosmic ray acceleration, probably by recent star formation. We suggest that a violent event in the past, most likely a merger or a collision with an intergalactic gas cloud, has caused the various unusual features of the galaxy.     

Intermediate-mass black holes and ultraluminous X-ray sources in the Cartwheel ring galaxy

Chandra and XMM–Newton observations of the Cartwheel galaxy show ∼17 bright X-ray sources  (≳5 × 10³⁸ erg s⁻¹)  , all within the gas-rich outer ring. We explore the hypothesis that these X-ray sources are powered by intermediate-mass black holes (IMBHs) accreting gas or undergoing mass transfer from a stellar companion. To this purpose, we run N -body/smoothed particle hydrodynamics simulations of the galaxy interaction which might have led to the formation of Cartwheel, tracking the dynamical evolution of two different IMBH populations: halo and disc IMBHs. Halo IMBHs cannot account for the observed X-ray sources, as only a few of them cross the outer ring. Instead, more than half of the disc IMBHs are pulled in the outer ring as a consequence of the galaxy collision. However, also in the case of disc IMBHs, accretion from surrounding gas clouds cannot account for the high luminosities of the observed sources. Finally, more than 500 disc IMBHs are required to produce ≲15 X-ray sources via mass transfer from very young stellar companions. Such number of IMBHs is very large and implies extreme assumptions. Thus, the hypothesis that all the observed X-ray sources in Cartwheel are associated with IMBHs is hardly consistent with our simulations, even if it is still possible that IMBHs account for the few (≲1–5) brightest ultraluminous X-ray sources.     

Feedback and metal enrichment in cosmological SPH simulations – II. A multiphase model with supernova energy feedback

We have developed a new scheme to treat a multiphase interstellar medium in smoothed particle hydrodynamics simulations of galaxy formation. This scheme can represent a co-spatial mixture of cold and hot ISM components, and is formulated without scale-dependent parameters. It is thus particularly suited to studies of cosmological structure formation where galaxies with a wide range of masses form simultaneously. We also present new algorithms for energy and heavy element injection by supernovae, and show that together these schemes can reproduce several important observed effects in galaxy evolution. Both in collapsing systems and in quiescent galaxies our codes can reproduce the Kennicutt relation between the surface densities of gas and of star formation. Strongly metal-enhanced winds are generated in both cases with ratios of mass-loss to star formation which are similar to those observed. This leads to a self-regulated cycle for star formation activity. The overall impact of feedback depends on galaxy mass. Star formation is suppressed at most by a factor of a few in massive galaxies, but in low-mass systems the effects can be much larger, giving star formation an episodic, bursty character. The larger the energy fraction assumed available in feedback, the more massive the outflows and the lower the final stellar masses. Winds from forming discs are collimated perpendicular to the disc plane, reach velocities up to  ∼1000 km s⁻¹  , and efficiently transport metals out of the galaxies. The asymptotically unbound baryon fraction drops from >95 per cent to ∼30 per cent from the least to the most massive of our idealized galaxies, but the fraction of all metals ejected with this component exceeds 60 per cent regardless of mass. Such winds could plausibly enrich the intergalactic medium to observed levels.     

The Milky Way Galaxy as a strong gravitational lens

We study the gravitational lensing effects of spiral galaxies by taking a model of the Milky Way and computing its lensing properties. The model is composed of a spherical Hernquist bulge, a Miyamoto–Nagai disc and an isothermal halo. As a strong lens, a spiral galaxy like the Milky Way can give rise to four different imaging geometries. They are (i) three images on one side of the galaxy centre ('disc triplets'), (ii) three images with one close to the centre ('core triplets'), (iii) five images and (iv) seven images. Neglecting magnification bias, we show that the core triplets, disc triplets and fivefold imaging are roughly equally likely. Even though our models contain edge-on discs, their image multiplicities are not dominated by disc triplets. The halo is included for completeness, but it has a small effect on the caustic structure, the time delays and brightnesses of the images.
The Milky Way model has a maximum disc (i.e. the halo is not dynamically important in the inner parts). Strong lensing by nearly edge-on disc galaxies breaks the degeneracy between the relative contributions of the disc and halo to the overall rotation curve. If a spiral galaxy has a submaximum disc, then the astroid caustic shrinks dramatically in size, whilst the radial caustic shrinks more modestly. This causes changes in the relative likelihood of the image geometries, specifically (i) core triplets are now ∼9/2 times more likely than disc triplets, (ii) the cross-section for threefold imaging is reduced by a factor of ∼2/3, whilst (iii) the cross-section for fivefold imaging is reduced by ∼1/2. Although multiple imaging is less likely (the cross-sections are smaller), the average total magnification is greater. The time delays are smaller, as the total projected lensing mass is reduced.     

对旋涡星系M33的HII区复合体IC133中H_2O脉泽VLBI斑点图的分析

用多重分离的旋转膨胀环模型，分析了旋涡星系Ｍ３３的ＨＩＩ区复合体ＩＣ１３３中的１４个脉泽源斑的ＶＬＢＩ相对位置图，发现这１４个Ｈ２Ｏ脉泽源斑在ＨＩ区复合体盘上成环状，分布在二个不同的旋转膨胀盘环上．同时，也得到这１４个Ｈ２Ｏ脉泽源斑的运动学特性．