Dwarf galaxy rotation curves and the core problem of dark matter haloes

The standard cold dark matter (CDM) model has recently been challenged by the claim that dwarf galaxies have dark matter haloes with constant-density cores, whereas CDM predicts haloes with steeply cusped density distributions. Consequently, numerous alternative dark matter candidates have recently been proposed. In this paper we scrutinize the observational evidence for the incongruity between dwarf galaxies and the CDM model. To this end, we analyse the rotation curves of 20 late-type dwarf galaxies studied by Swaters. Taking the effects of beam smearing and adiabatic contraction into account, we fit mass models to these rotation curves with dark matter haloes with different cusp slopes, ranging from constant-density cores to r ⁻² cusps. Even though the effects of beam smearing are small for these data, the uncertainties in the stellar mass-to-light ratio and the limited spatial sampling of the halo's density distribution hamper a unique mass decomposition. Consequently, the rotation curves in our sample cannot be used to discriminate between dark haloes with constant-density cores and r ⁻¹ cusps. We show that the dwarf galaxies analysed here are consistent with CDM haloes in a ΛCDM cosmology, and that there is thus no need to abandon the idea that dark matter is cold and collisionless. However, the data are also consistent with any alternative dark matter model that produces dark matter haloes with central cusps less steep than r ^−1.5. In fact, we argue that based on existing H  i rotation curves alone, at best weak limits can be obtained on cosmological parameters and/or the nature of the dark matter. In order to make progress, rotation curves with higher spatial resolution and independent measurements of the mass-to-light ratio of the disc are required.     

Simulations of stellar disks in galaxies with non-Newtonian interactions

We describe gravitationalN-body simulations to investigate whether various non-Newtonian interactions between the stars of a system could explain the flat rotational curves which are characteristic of actual isolated spiral galaxies. It is shown that replacing the standard Newtonian interaction by the models of Sanders (1984), Kuhn and Kruglyak (1987) and Milgrom (1983), no massive halo (or dark matter) is required to produce the flat rotational curves of the systems under consideration. All models also generate the exponential surface mass density distribution which is in agreement with that observed in disk-shaped galaxies. In relation to the spiral structure of galaxies, we present the evidence that the non-Newtonian interactions can reproduce the multiple armed patterns in stellar disks without dark matter.     

Dark matter and rotation curves of stars in galaxies

The dark matter accretion theory (around a central body) of the author on the basis of his 5‐dimensional Projective Unified Field Theory (PUFT) is applied to the orbital motion of stars around the center of the Galaxy. The departure of the motion from Newtonian mechanics leads to approximately flat rotation curves being in rough accordance with the empirical facts. The spirality of the motion is investigated.     

Scalar fields as dark matter in spiral galaxies: comparison with experiments

We present an exact solution for a static and axially symmetric spacetime, which is obtained from a scalar-tensor theory that comes from unification theories. As an attempt to model the dark matter (DM) in spiral galaxies we find that an exponential scalar potential is enough to explain the rotation curves in such galaxies. We also present the fitting to the rotation curve of six spiral galaxies and we find an excellent agreement between observational data and the results of our model.     

The rotation curves of flattened Sérsic bulges

I present a method to deproject the observed intensity profile of an axisymmetric bulge with arbitrary flattening to derive the three-dimensional luminosity density profile, and to calculate the contribution of the bulge to the rotation curve. I show the rotation curves for a family of fiducial bulges with Sérsic surface brightness profiles and with various concentrations and intrinsic axis ratios. Both parameters have a profound impact on the shape of the rotation curve. In particular, I show how the peak rotation velocity, as well as the radius where it is reached, depends on both parameters.
I also discuss the implications of the flattening of a bulge for the decomposition of a rotation curve and use the case of NGC 5533 to show the errors that result from neglecting it. For NGC 5533, neglecting the flattening of the bulge leads to an overestimate of its mass-to-light ratio by approximately 30 per cent and an underestimate of the contributions from the stellar disc and dark matter halo in the regions outside the bulge-dominated area.     

Towards a physical model for galactic rotation curves

Extensive and meticulous observations of the rotation curves of galaxies show that they are either flat or gently going up, but rarely decreasing, at large galactocentric distances. Here we show that the gravitational potential which would lead to such rotation curves arises naturally when the visible matter modelled as a collisionless Maxwellian gas is embedded in a dark halo of collisionless particles with a much higher dispersion in velocities.     

Lyman-break galaxies: high mass or low?

We reassess the hypothesis that Lyman-break galaxies (LBGs) at redshifts   z ∼ 3  mark the centres of the most massive dark matter haloes at that epoch. First we reanalyse the kinematic measurements of Pettini et al. and Erb et al. of the rest-frame optical emission lines of LBGs. We compare the distribution of the ratio of the rotation velocity to the central line width, against the expected distribution for galaxies with random inclination angles, modelled as singular isothermal spheres. The model fits the data well. On this basis we argue that the central line width provides a predictor of the circular velocity at a radius of several kpc. Assembling a larger sample of LBGs with measured line widths, we compare these results against the theoretical ΛCDM rotation curves of Mo, Mao & White, under the hypothesis that LBGs mark the centres of the most massive dark matter haloes. We find that the circular velocities are overpredicted by a substantial factor, which we estimate conservatively as  1.8 ± 0.4  . This indicates that the model is probably incorrect. The model of LBGs as relatively low-mass starburst systems, of Somerville, Primack & Faber, provides a good fit to the data.     

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.     

Does the Fornax dwarf spheroidal have a central cusp or core?

The dark matter dominated Fornax dwarf spheroidal has five globular clusters orbiting at ∼1 kpc from its centre. In a cuspy cold dark matter halo the globulars would sink to the centre from their current positions within a few Gyr, presenting a puzzle as to why they survive undigested at the present epoch. We show that a solution to this timing problem is to adopt a cored dark matter halo. We use numerical simulations and analytic calculations to show that, under these conditions, the sinking time becomes many Hubble times; the globulars effectively stall at the dark matter core radius. We conclude that the Fornax dwarf spheroidal has a shallow inner density profile with a core radius constrained by the observed positions of its globular clusters. If the phase space density of the core is primordial then it implies a warm dark matter particle and gives an upper limit to its mass of ∼0.5 keV, consistent with that required to significantly alleviate the substructure problem.     

The extended rotation curve and the dark matter halo of M33

We present the 21-cm rotation curve of the nearby galaxy M33 out to a galactocentric distance of 16 kpc (13 disc scalelengths). The rotation curve keeps rising out to the last measured point and implies a dark halo mass ≳5×10¹⁰ M_⊙. The stellar and gaseous discs provide virtually equal contributions to the galaxy gravitational potential at large galactocentric radii, but no obvious correlation is found between the radial distribution of dark matter and the distribution of stars or gas.
Results of the best fit to the mass distribution in M33 picture a dark halo which controls the gravitational potential from 3 kpc outward, with a matter density which decreases radially as R ^−1.3. The density profile is consistent with the theoretical predictions for structure formation in hierarchical clustering cold dark matter (CDM) models, and favours lower mass concentrations than those expected in the standard cosmogony.     

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.     

The peculiar rotation curve of NGC 157

We present the results of a new H i , optical, and Hα interferometric study of the nearby spiral galaxy NGC 157. Our combined C- and D-array observations with the VLA show a large-scale, ring-like structure in the neutral hydrogen underlying the optical disc, together with an extended, low surface density component going out to nearly twice the Holmberg radius. Beginning just inside the edge of the star-forming disc, the line of nodes in the gas disc commences a 60° warp, while at the same time, the rotation velocity drops by almost half its peak value of 200 km s⁻¹, before levelling off again in the outer parts. While a flat rotation curve in NGC 157 cannot be ruled out, supportive evidence for an abrupt decline comes from the ionized gas kinematics, the optical surface photometry, and the global H i profile. A standard 'maximum-disc' mass model predicts comparable amounts of dark and luminous matter within NGC 157. Alternatively, a model employing a disc truncated at 2 disc scalelengths could equally well account for the unusual form of the rotation curve in NGC 157.     

Dark matter halo structure in CDM hydrodynamical simulations

We have carried out a comparative analysis of the properties of dark matter haloes in N -body and hydrodynamical simulations. We analyse their density profiles, shapes and kinematical properties with the aim of assessing the effects that hydrodynamical processes might produce on the evolution of the dark matter component. The simulations performed allow us to reproduce dark matter haloes with high resolution, although the range of circular velocities is limited. We find that for haloes with circular velocities of [150–200] km s⁻¹ at the virial radius, the presence of baryons affects the evolution of the dark matter component in the central region, modifying the density profiles, shapes and velocity dispersions. We also analyse the rotation velocity curves of disc-like structures and compare them with observational results.     

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.     

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.     

Constraints on dark matter physics from dwarf galaxies through galaxy cluster haloes

One of the predictions of the standard cold dark matter model is that dark haloes have centrally divergent density profiles. An extensive body of rotation curve observations of dwarf and low surface brightness galaxies shows the dark haloes of those systems to be characterized by soft constant-density central cores. Several physical processes have been proposed to produce soft cores in dark haloes, each one with different scaling properties. With the aim of discriminating among them we have examined the rotation curves of dark-matter-dominated dwarf and low surface brightness galaxies and the inner mass profiles of two clusters of galaxies lacking a central cD galaxy and with evidence of soft cores in the centre. The core radii and central densities of these haloes scale in a well-defined manner with the depth of their potential wells, as measured through the maximum circular velocity. As a result of our analysis we identify self-interacting cold dark matter as a viable solution to the core problem, where a non-singular isothermal core is formed in the halo centre surrounded by a Navarro, Frenk & White profile in the outer parts. We show that this particular physical situation predicts core radii in agreement with observations. Furthermore, using the observed scalings, we derive an expression for the minimum cross-section ( σ ) which has an explicit dependence with the halo dispersion velocity ( v ). If m _x is the mass of the dark matter particle: σ m _x ≈4×10⁻²⁵ (100 km s⁻¹  v ⁻¹) cm² GeV⁻¹.     

Inferring dark halo structure from observed scaling laws of late-type galaxies and LSBs

We re-examine the Fall & Efstathiou scenario for galaxy formation, including the dark halo gravitational reaction to the formation of the baryon disc, as well as continuous variations in the intrinsic halo density profile. The recently published rotation curves of low surface brightness (LSB) and dwarf galaxies together with previously known scaling relations provide sufficient information on the present-day structure of late-type disc galaxies to invert the problem. By requiring that the models reproduce all the observational restrictions we can fully constrain the initial conditions of galaxy formation, with a minimum of assumptions, in particular without the need to specify a cold dark matter (CDM) halo profile. This allows one to solve for all the initial conditions, in terms of the halo density profile, the baryon fraction and the total angular momentum. We find that a unique initial halo shape is sufficient to accurately reproduce the rotation curves of both LSB and normal late-type spiral galaxies. This unique halo profile differs substantially from that found in standard CDM models. A galactic baryon fraction of 0.065 is found. The initial value of the dimensionless angular momentum is seen to be the principal discriminator between the galaxy classes we examine. The present-day scalings between structural parameters are seen to originate in the initial conditions.     

Galaxy cluster masses without non-baryonic dark matter

We apply the modified acceleration law obtained from Einstein gravity coupled to a massive skew symmetric field,   F _μνλ  , to the problem of explaining X-ray galaxy cluster masses without exotic dark matter. Utilizing X-ray observations to fit the gas mass profile and temperature profile of the hot intracluster medium (ICM) with King 'β-models', we show that the dynamical masses of the galaxy clusters resulting from our modified acceleration law fit the cluster gas masses for our sample of 106 clusters without the need of introducing a non-baryonic dark matter component. We are further able to show for our sample of 106 clusters that the distribution of gas in the ICM as a function of radial distance is well fitted by the dynamical mass distribution arising from our modified acceleration law without any additional dark matter component. In a previous work, we applied this theory to galaxy rotation curves and demonstrated good fits to our sample of 101 low surface brightness, high surface brightness and dwarf galaxies including 58 galaxies that were fitted photometrically with the single-parameter mass-to-light ratio ( M / L )_stars. The results obtained there were qualitatively similar to those obtained using Milgrom's phenomenological Modified Newtonian Dynamics (MOND) model, although the determined galaxy masses were quantitatively different, and MOND does not show a return to Keplerian behaviour at extragalactic distances. The results obtained here are compared to those obtained using Milgrom's phenomenological MOND model which does not fit the X-ray galaxy cluster masses unless an auxiliary dark matter component is included.     

The dark matter distribution in disc galaxies

We use high-quality optical rotation curves of nine low-luminosity disc galaxies to obtain the velocity profiles of the surrounding dark matter haloes. We find that they increase linearly with radius at least out to the edge of the stellar disc, implying that, over the entire stellar region, the density of the dark halo is about constant.
The properties of the mass structure of these haloes are similar to those found for a number of dwarf and low surface brightness galaxies, but provide a more substantial evidence of the discrepancy between the halo mass distribution predicted in the cold dark matter scenario and those actually detected around galaxies. We find that the density law proposed by Burkert reproduces the halo rotation curves, with halo central densities ( ρ ₀∼1–4×10⁻²⁴ g cm⁻³) and core radii ( r ₀∼5–15 kpc) scaling as ρ ₀∝ r ₀^−2/3.     

On the apparent coupling of neutral hydrogen and dark matter in spiral galaxies

We have studied a mass model for spiral galaxies in which the dark matter surface density is a scaled version of the observed H  i surface density. Applying this mass model to a sample of 24 spiral galaxies with reliable rotation curves, one obtains good fits for most galaxies. The scaling factors cluster around 7, after correction for the presence of primordial helium. For several cases, however, different, often larger, values are found. For galaxies that cannot be fitted well, the discrepancy occurs at large radii and results from a fairly rapid decline of the H  i surface density in the outermost regions. Because of such imperfections and in view of possible selection effects, it is not possible to conclude here that there is a real coupling between H  i and dark matter in spiral galaxies.