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.     

影响星系旋转曲线的几个因素

本文讨论了可能影响星系旋转曲线的若干因素,特别是星系整体运动和星系内局部运动对旋转曲线的影响。     

The structure and evolution of M 51-type galaxies

We discuss the integrated kinematic parameters of 20 M 51-type binary galaxies. A comparison of the orbital masses of the galaxies with the sum of the individual masses suggests that moderately massive dark halos surround bright spiral galaxies. The relative velocities of the galaxies in binary systems were found to decrease with increasing relative luminosity of the satellite. We obtained evidence that the Tully-Fisher relation for binary members could be flatter than that for local field galaxies. An enhanced star formation rate in the binary members may be responsible for this effect. In most binary systems, the direction of the orbital motion of the satellite coincides with the direction of the rotation of the main galaxy. Seven candidates for distant M 51-type objects were found in the Northern and Southern Hubble Deep Fields. A comparison of this number with the statistics of nearby galaxies provides evidence for the rapid evolution of the space density of M 51-type galaxies with redshift z. We assume that M 51-type binary systems could be formed through the capture of a satellite by a massive spiral galaxy. It is also possible that the main galaxy and its satellite in some of the systems have a common cosmological origin.     

Giant HVC’s and the Rotation Curves of the Milky Way and M31

We have modelled, for the cases of Milky Way and M31, the effects on the galactic discs, of the arrival at high velocity (≥150 km s⁻¹) of giant HI clouds, with masses of up to 10⁸M⊙. Predictions are compared with the detailed structure of the observed rotation curves for these two galaxies. The model explains the rises and falls observed at large distances from the centre of each galaxy, distributed with a degree of regularity in radius, in terms of a specific type of perturbations driven by the infall of the high velocity clouds (HVC's) arriving from the intracluster medium of the Local Group. The underlying rotation curve is explained conventionally via the distribution of the baryonic and dark matter components of the galaxy in question. This scenario, though tested here on the two major Local Group objects, is in principle applicable to galaxies undergoing minor mergers with subgalactic mass gas clouds.     

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.     

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.     

Mass discrepancies in galaxies: dark matter and alternatives

Neutral hydrogen line observations of the extended rotation curves of spiral galaxies imply that there exist significant discrepancies between the luminous and dynamical mass beyond the bright optical discs. This means either that galaxies contain significant quantities of non-luminous matter (matter with a mass-to-light ratio very much higher than that of ordinary stars), or that the law of gravity on the scale of galaxies is not the usual Newtonian inverse square law. Attempts to account for the observed discrepancy in the context of these two explanations are reviewed here with emphasis given to the second and less conventional alternative. It is argued that the standard picture of spiral galaxy halo and disc formation in the context of cold dark matter cannot account for the observed systematics of the discrepancy — notably rotation curves which are seen to be flat and featureless from the bright inner regions where the visible matter dominates the dynamics (in some cases overwhelmingly) to the outer regions where the dark halo dominates. It is demonstrated that in those galaxies with well-observed rotation curves, the discrepancy apparently appears below a critical acceleration. Any dark matter explanation of the discrepancy must account for this fact. Moreover, this would also eliminate empirically motivated modifications of Newton's law in which the deviation from 1/r occurs beyond a fundamental length scale. The suggestion by Milgrom in which the force law becomes essentially 1/r below a critical acceleration (MOND) can account for most of the observed systematics of galaxy rotation curves and, significantly, leads to the observed luminosity-velocity relationship in spiral galaxies (the Tully-Fisher law). Generally covariant theories of gravity which predict this phenomenology in the weak-field limit are described. Although there is not yet a theory which obviously meets all of the requirements for a physically viable alternative to dark matter, a generalized scalar-tensor theory of the form suggested by Bekenstein (phase coupling gravitation) is the currently leading candidate and has the advantage of being testable locally.     

Orientation of Galaxies in Clusters

A detailed analysis of the geometry of galaxies in clusters has been undertaken in both two and three dimensional space. The procedure was applied to the three Abell clusters A1644, A548 E and A548 W. No significant alignment trend of galaxies in clusters confirmed in three dimensional space was found. This result is consistent with the mixed dark matter model MDM of galaxy formation. The result is also consistent with Peebles suggestion that protogalaxies acquired angular momentum from tidal torques exerted by their neighbours in the early universe. The amount of angular momentum predicted by this mechanism could be described by a single dimensionless papameter λ≈ 0.8. N-body experiments have shown that λ has approximately normal distribution with mean value about 0.07 and with a standard deviation of about 0.03. From the analyic fit to flat rotation curves it is found that tidal torque can provide the observed angular momentum if the mean collapse factor is about 20 and the mean halo-to-disk mass ratio is of order 10. The MDM model does not predict any systematic relation between the tidal torques among the halos of galaxies and the large scale structures such as the clusters, superclusters of galaxies and giant voids in between. Further work in this area is still required. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

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

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

Elliptical galaxies from mergers of discs

We analyse N -body galaxy merger experiments involving disc galaxies. Mergers of disc–bulge–halo models are compared to those of bulgeless, disc–halo models to quantify the effects of the central bulge on merger dynamics and the structure of the remnant. Our models explore galaxy mass ratios 1:1 through 3:1, and use higher bulge mass fractions than previous studies. A full comparison of the structural and dynamical properties with our observations is carried out. The presence of central bulges results in longer tidal tails, oblate final intrinsic shapes, surface brightness profiles with a higher Sérsic index, steeper rotation curves and oblate-rotator internal dynamics. Mergers of bulgeless galaxies do not generate long-lasting tidal tails, and their strong triaxiality seems inconsistent with observations; these remnants show shells, which we do not find in models including central bulges. Giant ellipticals with boxy isophotes and anisotropic dynamics cannot be produced by the mergers modelled here; they could be the result of mergers between lower luminosity ellipticals, themselves plausibly formed in disc-disc mergers.     

GHASP: an Hα kinematic survey of spiral and irregular galaxies – V. Dark matter distribution in 36 nearby spiral galaxies

The results obtained from a study of the mass distribution of 36 spiral galaxies are presented. The galaxies were observed using Fabry–Perot interferometry as part of the GHASP survey. The main aim of obtaining high-resolution Hα 2D velocity fields is to define more accurately the rising part of the rotation curves which should allow to better constrain the parameters of the mass distribution. The Hα velocities were combined with low resolution H  i data from the literature, when available. Combining the kinematical data with photometric data, mass models were derived from these rotation curves using two different functional forms for the halo: an isothermal sphere (ISO) and a Navarro–Frenk–White (NFW) profile. For the galaxies already modelled by other authors, the results tend to agree. Our results point at the existence of a constant density core in the centre of the dark matter haloes rather than a cuspy core, whatever the type of the galaxy from Sab to Im. This extends to all types the result already obtained by other authors studying dwarf and low surface brightness galaxies but would necessitate a larger sample of galaxies to conclude more strongly. Whatever model is used (ISO or NFW), small core radius haloes have higher central densities, again for all morphological types. We confirm different halo scaling laws, such as the correlations between the core radius and the central density of the halo with the absolute magnitude of a galaxy: low-luminosity galaxies have small core radius and high central density. We find that the product of the central density with the core radius of the dark matter halo is nearly constant, whatever the model and whatever the absolute magnitude of the galaxy. This suggests that the halo surface density is independent from the galaxy type.     

Formation of massive galaxies at the centre of a cluster

The formation of massive galaxies at the centre of a cluster is discussed here. The protogalaxies move with both rotation and random velocities through the gaseous medium pervading the cluster. Each galaxy is supposed to move through a resisting medium under the general gravitational field produced by the cluster as a whole. Also, the mass of the galaxy increases by accretion all the time as it moves through the medium. Using plausible laws for density of the medium and accretion of matter and solving equation of motion, we find that the galaxy loses angular momentum in the course of the time. The loss of angular momentum drives the galaxy towards the centre of the cluster. Thus over a sufficiently long time-scale several galaxies may merge in the central region of the cluster resulting in a single massive galaxy. The process can drive rise to several massive galaxies in the central region of the cluster.     

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.     

The onset of warps in Spitzer observations of edge-on spiral galaxies

We analyse warps in the nearby edge-on spiral galaxies observed in the Spitzer /Infrared Array Camera (IRAC) 4.5-μm band. In our sample of 24 galaxies, we find evidence of warp in 14 galaxies. We estimate the observed onset radii for the warps in a subsample of 10 galaxies. The dark matter distribution in each of these galaxies are calculated using the mass distribution derived from the observed light distribution and the observed rotation curves. The theoretical predictions of the onset radii for the warps are then derived by applying a self-consistent linear response theory to the obtained mass models for six galaxies with rotation curves in the literature. By comparing the observed onset radii to the theoretical ones, we find that discs with constant thickness can not explain the observations; moderately flaring discs are needed. The required flaring is consistent with the observations. Our analysis shows that the onset of warp is not symmetric in our sample of galaxies. We define a new quantity called the onset-asymmetry index and study its dependence on galaxy properties. The onset asymmetries in warps tend to be larger in galaxies with smaller disc scalelengths. We also define and quantify the global asymmetry in the stellar light distribution, that we call the edge-on asymmetry in edge-on galaxies. It is shown that in most cases the onset asymmetry in warp is actually anticorrelated with the measured edge-on asymmetry in our sample of edge-on galaxies and this could plausibly indicate that the surrounding dark matter distribution is asymmetric.     

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.     

Possible interpretation of Rubin-Ford's observations on compact Hickson 88a object

In this paper the kinematic effects, caused by revolving to some common mass center, on the rotation curve and a possible mechanism leading to the asymmetry of rotation curve are considered. Recently, Rubin and Ford's observation on rotation curve of Hickson 88a has been explained by means of above mechanism. Finally, some discussions have also been given.     

Dynamical friction in dwarf galaxies

We present a simplified analytic approach to the problem of the spiralling of a massive body orbiting within the dark halo of a dwarf galaxy. This dark halo is treated as the core region of a King distribution of dark matter particles, in consistency with the observational result of dwarf galaxies having solid-body rotation curves. Thus we derive a simple formula which provides a reliable and general first-order solution to the problem, totally analogous to the one corresponding to the dynamical friction problem in an isothermal halo. This analytic approach allows a clear handling and a transparent understanding of the physics and the scaling of the problem. A comparison with the isothermal case shows that in the core regions of a King sphere, dynamical friction proceeds at a different rate, and is sensitive to the total core radius. Thus, in principle, observable consequences may result. In order to illustrate the possible effects, we apply this formula to the spiralling of globular cluster orbits in dwarf galaxies, and show how present-day globular cluster systems could, in principle, be used to derive better limits on the structure of dark haloes around dwarf galaxies, when the observational situation improves. As a second application, we study the way a massive black hole population forming a fraction of these dark haloes would gradually concentrate towards the centre, with a consequent deformation of an originally solid-body rotation curve. This effect allows us to set limits on the fraction/mass of any massive black hole minority component of the dark haloes of dwarf galaxies. In essence, we take advantage of the way the global matter distribution fixes the local distribution function for the dark matter particles, which in turn determines the dynamical friction problem.     

The high-mass end of the Tully–Fisher relation

We study the location of massive disc galaxies on the Tully–Fisher (TF) relation. Using a combination of K -band photometry and high-quality rotation curves, we show that in traditional formulations of the TF relation (using the width of the global H  i profile or the maximum rotation velocity), galaxies with rotation velocities larger than 200 km s⁻¹ lie systematically to the right of the relation defined by less massive systems, causing a characteristic 'kink' in the relations. Massive, early-type disc galaxies in particular have a large offset, up to 1.5 mag, from the main relation defined by less massive and later-type spirals.
The presence of a change in slope at the high-mass end of the TF relation has important consequences for the use of the TF relation as a tool for estimating distances to galaxies or for probing galaxy evolution. In particular, the luminosity evolution of massive galaxies since z ≈ 1 may have been significantly larger than estimated in several recent studies.
We also show that many of the galaxies with the largest offsets have declining rotation curves and that the change in slope largely disappears when we use the asymptotic rotation velocity as kinematic parameter. The remaining deviations from linearity can be removed when we simultaneously use the total baryonic mass (stars + gas) instead of the optical or near-infrared luminosity. Our results strengthen the view that the TF relation fundamentally links the mass of dark matter haloes with the total baryonic mass embedded in them.     

On the dynamics of the satellite galaxies in NGC 5044

The NGC 5044 galaxy group is dominated by a luminous elliptical galaxy that is surrounded by ∼160 dwarf satellites. The projected number density profile of this dwarf population deviates within ∼1/3 of the virial radius from a projected Navarro, Frenk and White (NFW) profile, which is assumed to approximate the underlying total matter distribution. By means of a semi-analytic model, we demonstrate that the interplay between gravitation, dynamical friction and tidal mass loss and destruction can explain the observed number density profile. We use only two parameters in our models: the total to stellar mass fraction of the satellite haloes and the disruption efficiency. The disruption efficiency is expressed by a minimum radius. If the tidal radius of a galaxy (halo) falls below this radius, it is assumed to become unobservable. The preferred parameters are an initial total to stellar mass fraction of ∼20 and a disruption radius of  4 kpc  . In that model, about 20 per cent of all the satellites are totally disrupted on their orbits within the group environment. Dynamical friction is less important in shaping the inner slope of the number density profile because the reduction in mass by tidal forces lowers the impact of the friction term. The main destruction mechanism is tide. In the preferred model, the total B -band luminosity of all disrupted galaxies is about twice the observed luminosity of the central elliptical galaxy, indicating that a significant fraction of stars are scattered into the intragroup medium. Dwarf galaxy satellites closer to the centre of the NGC 5044 group may exhibit optical evidence of partial tidal disruption. If dynamical friction forces the satellite to merge with the central elliptical, the angular momentum of the satellite tends to be removed at the apocentre passage. Afterwards, the satellite drops radially towards the centre.