Rotation Curves Of Spiral Galaxies Research Articles

The radial Tully-Fisher relation for spiral galaxies - I

We find a new Tully-Fisher-like relation for spiral galaxies holding at different galactocentric radii. This Radial Tully-Fisher (RTF) relation allows us to investigate the distribution of matter in the optical regions of spiral galaxies. This relation, applied to three different samples of rotation curves of spiral galaxies, directly proves that: 1) the rotation velocity of spirals is a good measure of their gravitational potential and both the RC’s amplitudes and profiles are well predicted by galaxy luminosity 2) the existence of a dark component, less concentrated than the luminous one, and 3) a scaling law, according to which, inside the disk optical size: Mdark/Mlum = 0.5(LB/10 11 LB⊙) −0.7 .

Low surface brightness galaxy rotation curves in the low energy limit of Rn gravity: no need for dark matter?

We investigate the possibility that the observed flatness of the rotation curves of spiral galaxies is not evidence for the existence of dark matter haloes, but rather a signal of the breakdown of General Relativity. To this aim, we consider power-law fourth-order theories of gravity obtained by replacing the scalar curvature R with f(R) =f 0 R n in the gravity Lagrangian. We show that, in the low energy limit, the gravitational potential generated by a point-like source may be written as Φ(r) ∝ r -1 [1 + (r/r c ) β ] with β a function of the slope n of the gravity Lagrangian and r c a scalelength depending on the gravitating system properties. In order to apply the model to realistic systems, we compute the modified potential and the rotation curve for spherically symmetric and for thin disc mass distributions. It turns out that the potential is still asymptotically decreasing, but the corrected rotation curve, although not flat, is higher than the Newtonian one, thus offering the possibility to fit rotation curves without dark matter. To test the viability of the model, we consider a sample of 15 low surface brightness galaxies with combined H [I and Ha measurements of the rotation curve extending in the putative dark matter dominated region. We find a very good agreement between the theoretical rotation curve and the data using only stellar disc and interstellar gas when the slope n of the gravity Lagrangian is set to the value n = 3.5 (giving β = 0.817) obtained by fitting the Type Ia supernova Hubble diagram with the assumed power-law f(R) model and no dark matter. The excellent agreement between theoretical and observed rotation curves and the values of the stellar mass-to-light ratios in agreement with the predictions of population synthesis models make us confident that R n gravity may represent a good candidate to solve both the dark energy problem on cosmological scales and the dark matter one on galactic scales with the same value of the slope n of the higher-order gravity Lagrangian.

X-ray gas in the galaxy cluster Abell 2029: conformal gravity versus dark matter

Conformal gravity has a weak-field limit that augments the Newtonian potential -GM/R by a linear potential γc 2 R/2. Mannheim has shown that an appropriate choice of y enables a satisfying fit to the flat rotation curves of large spiral galaxies and simultaneously to the rising rotation curves of low surface brightness galaxies, without invoking dark matter. Here, we extend to larger scales the comparison of Newtonian and conformal gravity by analysis of X-ray gas in the Abell 2029 galaxy cluster. The Newtonian analysis yields a mass profile rising roughly as M α R 2 from 10 10 M ⊙ at 2kpc to 10 14 M ⊙ at 200kpc, and this can be interpreted as the profile of an extensive dark matter halo that dominates the cluster potential. In conformal gravity, the potential is non-uniform inside a spherical shell, so that both interior and exterior mass distributions must be taken into account. We derive the conformal gravity potential both inside and outside a spherical shell, enabling the evaluation of potentials for spherically symmetric mass distributions. A conformal gravity analysis of X-ray gas in Abell 2029 then yields a total mass profile that rises from 10 10 M ⊙ at 2kpc to 1.4 x 10 12 M ⊙ at 30 kpc, and then remains roughly constant out to 300 kpc. With this mass profile, conformal gravity is able to bind the X-ray gas with no need for dark matter. However, integrating the X-ray gas density profile gives a baryon mass of 10 13 M ⊙ inside 200 kpc, nearly 10 times more than what is required to hold the hot gas in hydrostatic equilibrium. This discrepancy may rule out conformal gravity unless there is a significant breakdown of hydrostatic equilibrium in the outskirts of the potential well. The required velocities, V ∼ 2000 km s -1 , may be observable via Doppler profiles in high-resolution X-ray spectroscopy. It is also possible that the mass distribution outside the cluster significantly reduces conformal gravity in the cluster outskirts. Our approximate treatment of this effect suggests that it is negligible, but a more sophisticated analysis might yield a different conclusion.

Comment on “Scalar-tensor gravity coupled to a global monopole and flat rotation curves”

The recent paper by Lee and Lee [Phys. Rev. D 69, 127502 (2004)] may strongly leave the impression that astronomers have established that the rotation curves of spiral galaxies are flat. We show that the old paradigm of flat rotation curves lacks, today, any observational support and following it at face value leads to intrinsically flawed alternatives to the standard dark matter scenario. On the other hand, we claim that the rich systematics of spiral galaxy rotation curves, which reveals, in the standard Newtonian gravity framework, the phenomenon of dark matter, in alternative scenarios, works as a unique benchmark.

Spiral Galaxy Rotation Curves Determined from Carmelian General Relativity

Equations of motion, in cylindrical co-ordinates, for the observed rotation of gases within the gravitational potential of spiral galaxies have been derived from Carmeli's Cosmological General Relativity theory. A Tully-Fisher type relation results and rotation curves are reproduced without the need for non-baryonic halo dark matter. Two acceleration regimes are discovered that are separated by a critical accleration $\approx 4.75 \times 10^{-10}$ $m.s^{-2}$. For accelerations larger than the critical value the Newtonian force law applies, but for accelerations less than the critical value the Carmelian regime applies. In the Newtonian regime the accelerations fall off as $r^{-2}$, but in the Carmelian regime the accelerations fall off as $r^{-1}$. This is new physics but is exactly what is suggested by Migrom's phenomenological MOND theory.

Comment on “General relativity resolves galactic rotation without exotic dark matter” by F.I. Cooperstock and S. Tieu

The general relativistic model of Cooperstock and Tieu, which attempts to fit rotation curves of spiral galaxies without invoking dark matter, is tested empirically using observations of the Milky Way. In particular, predictions for the mass density in the solar neighbourhood and the vertical density distribution at the position of the Sun are compared with observations. It is shown that the model of Cooperstock and Tieu, which was so constructed that it gives an excellent fit of the observed rotation curve, singularly fails to reproduce the observed local mass density and the vertical density profile of the Milky Way.

Testing Bekenstein's relativistic Modified Newtonian Dynamics with lensing data

We propose to use multiple-imaged gravitational lenses to set limits on gravity theories without dark matter, specifically tensor-vector-scalar (TeVeS) theory, a theory which is consistent with fundamental relativistic principles and the phenomenology of Modified Newtonian Dynamics (MOND) theory. After setting the framework for lensing and cosmology, we analytically derive the deflection angle for the point lens and the Hernquist galaxy profile, and study their patterns in convergence, shear and amplification. Applying our analytical lensing models, we fit galaxy-quasar lenses in the CfA-Arizona Space Telescope Lens Survey (CASTLES) sample. We do this with three methods, fitting the observed Einstein ring sizes, the image positions, or the flux ratios. In all the cases, we consistently find that stars in galaxies in MOND/TeVeS provide adequate lensing. Bekenstein's toy μ function provides more efficient lensing than the standard MOND μ function. But for a handful of lenses, a good fit would require a lens mass orders of magnitude larger/smaller than the stellar mass derived from luminosity unless the modification function μ and modification scale a 0 for the universal gravity were allowed to be very different from what spiral galaxy rotation curves normally imply. We discuss the limitation of present data and summarize constraints on the MOND μ function. We also show that the simplest TeVeS 'minimal-matter' cosmology, a baryonic universe with a cosmological constant, can fit the distance-redshift relation from the supernova data, but underpredicts the sound horizon size at the last scattering. We conclude that lensing is a promising approach to differentiate laws of gravity.

A Large Dark Matter Core in the Fornax Dwarf Spheroidal Galaxy?

We use measurements of the stellar velocity dispersion profile of the Fornax dwarf spheroidal galaxy to derive constraints on its dark matter distribution. Though the data are unable to distinguish between models with small cores and those with cusps, we show that a large > 1 kpc dark matter core in Fornax is highly implausible. Irrespective of the origin of the core, reasonable dynamical limits on the mass of the Fornax halo constrain its core radius to be no larger than 700 pc. We derive an upper limit core radius of 300 pc by demanding that the central phase space density of Fornax not exceed that directly inferred from the rotation curves of low-mass spiral galaxies. Further, if the halo is composed of warm dark matter then phase-space constraints force the core to be quite small in order to avoid conservative limits from the Ly alpha forest power spectrum, implying a core radius < 85 pc. We discuss our results in the context of the idea that the extended globular cluster distribution in Fornax can be explained by the presence of a large 1.5 kpc core. A self-consistent core of this size would be drastically inconsistent with the expectations of standard warm or cold dark matter models, and would also require an unreasonably massive dark matter halo, with a maximum circular velocity of 200 km/s.

Some Systematic Properties of Rotation Curves

The rotation curves of spiral galaxies obey strong scaling relations. These include the Tully-Fisher and baryonic Tully-Fisher relations, and the mass discrepancy–acceleration relation. These relations can be used to place constraints on the mass-to-light ratios of stars. Once the stellar mass is constrained, the distribution of dark matter follows. The shape of the dark matter distribution is consistent with the expectations of NFW halos exterior to 1 kpc, but the amplitude is wrong. This is presumably related to the long-standing problem of the normalization of the Tully-Fisher relation and may imply a downturn in the amplitude of the power spectrum at small scales. More fundamentally, the persistent success of MOND remains a troubling fact.

The Carmeli Metric Correctly Describes Spiral Galaxy Rotation Curves

The metric by Carmeli accurately produces the Tully-Fisher type relation in spiral galaxies, a relation showing the fourth power of the rotation speed proportional to the mass of the galaxy. And therefore it is claimed that it is also no longer necessary to invoke dark matter to explain the anomalous dynamics in the arms of spiral galaxies. An analysis is presented here showing Carmeli’s 5 dimensional space-time-velocity metric can also indeed describe the rotation curves of spiral galaxies based on the properties of the metric alone.

MIRROR MATTER-TYPE DARK MATTER

There are six main things which any non-baryonic dark matter theory should endeavour to explain: (1) The basic dark matter particle properties [mass, stability, darkness]; (2) The similarity in cosmic abundance between ordinary and non-baryonic dark matter, ΩB~Ω dark ; (3) Large scale structure formation; (4) Microlensing (MACHO) events; (5) Asymptotically flat rotation curves in spiral galaxies; (6) The impressive DAMA/NaI annual modulation signal. Only mirror matter-type dark matter appears capable of explaining all six of these desirable features. The purpose of this article is to provide an up-to-date and pedagogical review of this dark matter candidate.

Modelling the rotational curves of spiral galaxies with a scalar field

In a previous work (Mbelek 1998), we modelled the rotation curves (RC) of spiral galaxies by including in the equation of motion of the stars the dynamical terms from an external real self-interacting scalar field, ψ, minimally coupled to gravity and which respects the equivalence principle in the weak fields and low velocity approximation. This model appeared to have three free parameters: the turnover radius, r0, the maximum tangential velocity, , plus a strictly positive integer, n. Here, we propose a new improved version where the coupling of the ψ-field to dark matter is emphasized at the expense of its self-interaction. This reformulation presents the very advantageous possibility that the same potential is used for all galaxies. Using at the same time a quasi-isothermal dark matter density and the scalar field helps to better fit the RC of spiral galaxies. In addition, new correlations are established.

Structure and kinematics of edge-on galaxy discs – III. The rotation curves in the gas

A technique is introduced for deriving the gaseous rotation curves of edge-on spiral galaxies. The entire major axis position-velocity (XV) diagram is modelled with a set of rings in a least-squares sense, allowing for the effects of beam-smearing and line-of-sight projection. The feasibility of the technique is demonstrated by applying it to good quality H I XV diagrams of eight edge-on spirals. For seven additional spirals the XV diagrams are of insufficient quality, and the H I rotational velocities derived earlier using the envelope-tracing method are retained. The H I results are augmented with the optical emission line (H II) kinematics to arrive at estimates of the full rotation curves. A detailed comparison of the H I and H II kinematics shows that the discs in our sample are sufficiently transparent at the heights above the plane where we have taken our optical spectra to derive the stellar kinematics. In several of these spirals the H II is mainly confined to the spiral arms and does not extend out to the edge of the H I layer, which may have caused the H II velocity profiles to be significantly narrower than those of H I.

Constraining the Magnetic Effects on HiRotation Curves and the Need for Dark Halos

The density profiles of dark halos are usually inferred from the rotation curves of disk galaxies based on the assumption that the gas is a good tracer of the gravitational potential of the galaxies. Some authors have suggested that magnetic pinching forces could alter significantly the rotation curves of spiral galaxies. In contrast to other studies that have concentrated on the vertical structure of the disk, here we focus on the problem of magnetic confinement in the radial direction to determine the magnetic effects on the H I rotation curves. It is shown that azimuthal magnetic fields hardly speed up H I disks of galaxies as a whole. In fact, based on virial constraints we show that the contribution of galactic magnetic fields to the rotation curves cannot be larger than ~10 km s-1 at the outermost point of H I detection, if the galaxies did not contain dark matter at all, and is up to 20 km s-1 in the conventional dark halo scenario. The procedure to estimate the maximum effect of magnetic fields is general and applicable to any particular galaxy disk. The inclusion of the surface terms, namely, the intergalactic (thermal, magnetic, or ram) pressure, does not change our conclusions. Other problems related to the magnetic alternative to dark halos are highlighted. The relevance of magnetic fields in the cuspy problem of dark halos is also discussed.

GALACTIC AND ASTROPHYSICAL SIZES FROM SCALAR-TENSOR THEORY OF GRAVITY

We investigate the weak-field limit of scalar-tensor theory of gravity and show that results are directly depending on the coupling and self-interaction potential of the scalar field. In particular, corrections are derived for the Newtonian potential. We discuss astrophysical applications of the results, in particular the flat rotation curves of spiral galaxies.

Radial Distributions of Dark and Luminous Matter in Bright Spiral Galaxies

We present a work in progress investigating the radial distributions of dark and luminous matter in local bright spiral galaxies spanning a range of Hubble types. the distributions are derived from multiband imaging (BVRJHK) predominately from the Ohio State University Bright Spiral Galaxy Survey (OSUBSGS) and rotation curves from the literature. We use stellar colour-MIL relationships from Bell &amp; de Jong (2001, ApJ, 550, 212) to create radial stellar mass surface density profiles for each of our galaxies. These profiles are used to create rotation curves for the stellar component; gas masses are derived from HI when available. the resulting stellar and gas mass rotation curves are compared to observed (total mass) rotation curves, and the rotation due to dark matter is determined for each galaxy. Fits to Navarro, Frenk, &amp; White (1996, ApJ, 462, 563; NFW) halo profiles are shown. We present this analysis for 2 example galaxies from our sample of nearly 50. We will use this data to investigate correlations between these mass components and physical properties of galaxies.

Molar mass estimate of dark matter from the dark mass distribution measurements

We study the distribution of dark matter versus visible matter using a set of data obtained from strong gravitational lensing in the galaxy cluster $\mathrm{CL}0024+1654$ and another set of data inferred from the universal rotation curves in spiral galaxies. The important feature of these two dramatically different observations is that the mass density profile of both visible and dark components can be estimated. From these measurements we deduce the mass of the dark matter particle and our estimate of the mass for the dark matter particle is ${\ensuremath{\mu}}_{d}\ensuremath{\approx}200--700\mathrm{MeV}.$ We contrast our estimates from $\mathrm{CL}0024+1654$ data and the universal rotation curves of the spiral galaxies and discuss their consistency.

Missing Mass as Evidence for Modified Newtonian Dynamics at Low Accelerations

Milgrom has proposed that the appearance of discrepancies between the Newtonian dynamical mass and the directly observable mass in astronomical systems could be due to a breakdown of Newtonian dynamics in the limit of low accelerations rather than the presence of unseen matter. Milgrom's hypothesis, modified Newtonian dynamics or MOND, has been remarkably successful in explaining systematic properties of spiral and elliptical galaxies and predicting in detail the observed rotation curves of spiral galaxies with only one additional parameter — a critical acceleration which is on the order of the cosmologically interesting value of cH0. Here we review the empirical successes of this idea and discuss its possible extension to cosmology and structure formation.

NEWTONIAN LIMIT OF STRING-DILATON GRAVITY

We study the weak-field limit of string-dilaton gravity and derive corrections to the Newtonian potential having strength directly depends on the self interaction potential and the nonminimal coupling of the dilaton scalar field. We discuss also possible astrophysical applications of the results, in particular the flat rotation curves of spiral galaxies.

Gravitational Lensing by Burkert Halos

We investigate the gravitational lensing properties of dark matter halos with Burkert profiles. We derive an analytic expression for the lens equation and use it to compute the magnification, impact parameter, and image separations for strong lensing. For the scaling relation that provides the best fits to spiral galaxy rotation curve data, Burkert halos will not produce strong lensing, even if this scaling relation extends up to masses of galaxy clusters. Tests of a simple model of an exponential stellar disk superposed on a Burkert profile halo demonstrate that strong lensing is unlikely without an additional concentration of mass in the galaxy center (e.g., a bulge). The fact that most strong lenses on galactic scales are elliptical galaxies suggests that a strong central concentration of baryons is required to produce image splitting. This solution is less attractive for clusters of galaxies, which are generally considered to be dark matter dominated even at small radii. There are three possible implications of these results: (1) dark halos may have a variety of inner profiles, (2) dark matter halos may not follow a single scaling relation from galaxy scale up to cluster scale, and/or (3) the splitting of images (even by clusters of galaxies) may in general be due to the central concentration of baryonic material in halos rather than dark matter.