Rotation Curves Of Dwarf Galaxies Research Articles

How the Redshift of Gravitons Explains Dark Matter and Dark Energy

The theory that gravitons lose energy by way of gravitational redshift while traveling in a gravitational field is applied to the expansion of the universe and to spiral and dwarf galaxy rotation curves using General Relativity. This is a graviton self interaction model which derives an expansion equation which is identical in form to the standard Lambda Cold Dark Matter model. In the domain of galaxies, spiral and dwarf galaxy rotation curves are matched using only baryonic mass. Thus, the requirement for dark matter and dark energy in the universe is replaced by this paradigm.

Measurement of the Dark Matter Velocity Dispersion with Dwarf Galaxy Rotation Curves

Warm dark matter has, by definition, a velocity dispersion. Let vhms(a)=vhms(1)/a be the root-mean-square velocity of non-relativistic warm dark matter particles in the early universe at expansion parameter a. vhms(1) is an adiabatic invariant. We obtain vhms(1) in the core of 11 dwarf galaxies dominated by dark matter, from their observed rotation curves, up to a rotation and relaxation correction. We obtain a mean 0.490 km/s and standard deviation 0.160 km/s, with a distribution peaked at the lower end. We apply a mild, data driven, rotation and relaxation correction that obtains the adiabatic invariant in the core of the galaxies: vhms(1)=0.406 ± 0.069 km/s. These two small relative standard deviations justify the prediction that the adiabatic invariant vhms(1) in the core of the galaxies is of cosmological origin if dark matter is warm. This result is in agreement with measurements of vhms(1) based on spiral galaxy rotation curves, galaxy ultra-violet luminosity distributions, galaxy stellar mass distributions, the formation of first galaxies, reionization, and the velocity dispersion cut-off mass.

Theory of Gravitons in Spiral and Dwarf Galaxy Rotation Curves

We hypothesize that gravitons contribute significantly to the process that flattens galaxy rotation curves. Gravitons travelling against a gravitational field experience an energy loss due to gravitational redshift identical to the effect on light. This energy loss requires an increased rotational velocity to stabilize a galaxy. We will show that this approach successfully explains the rotational properties of spiral and dwarf galaxies.

Core-envelope haloes in scalar field dark matter with repulsive self-interaction: fluid dynamics beyond the de Broglie wavelength

ABSTRACT Scalar field dark matter (SFDM) comprised of ultralight bosons has attracted great interest as an alternative to standard, collisionless cold dark matter (CDM) because of its novel structure-formation dynamics, described by the coupled Schrödinger–Poisson equations. In the free-field (‘fuzzy’) limit of SFDM (FDM), structure is inhibited below the de Broglie wavelength, but resembles CDM on larger scales. Virialized haloes have ‘solitonic’ cores of radius ∼λdeB, surrounded by CDM-like envelopes. When a strong enough repulsive self-interaction (SI) is also present, structure can be inhibited below a second length-scale, λSI, with λSI > λdeB – called the Thomas–Fermi (TF) regime. FDM dynamics differ from CDM because of quantum pressure, and SFDM-TF differs further by adding SI pressure. In the small-λdeB limit, however, we can model all three by fluid conservation equations for a compressible, γ = 5/3 ideal gas, with ideal gas pressure sourced by internal velocity dispersion and, for the TF regime, an added SI pressure, PSI ∝ ρ2. We use these fluid equations to simulate halo formation from gravitational collapse in 1D, spherical symmetry, demonstrating for the first time that SFDM-TF haloes form with cores the size of RTF, the radius of an SI-pressure-supported (n = 1)-polytrope, surrounded by CDM-like envelopes. In comparison with rotation curves of dwarf galaxies in the local Universe, SFDM-TF haloes pass the [‘too-big-to-fail’ + ‘cusp–core’]-test if RTF ≳ 1 kpc.

Baryonic clues to the puzzling diversity of dwarf galaxy rotation curves

ABSTRACT We use a compilation of disc galaxy rotation curves to assess the role of the luminous component (‘baryons’) in the rotation curve diversity problem. As in earlier work, we find that rotation curve shape correlates with baryonic surface density: high surface density galaxies have rapidly rising rotation curves consistent with cuspy cold dark matter haloes; slowly rising rotation curves (characteristic of galaxies with inner mass deficits or ‘cores’) occur only in low surface density galaxies. The correlation, however, seems too weak to be the main driver of the diversity. In addition, dwarf galaxies exhibit a clear trend, from ‘cuspy’ systems where baryons are unimportant in the inner mass budget to ‘cored’ galaxies where baryons actually dominate. This trend constrains the various scenarios proposed to explain the diversity, such as (i) baryonic inflows and outflows during galaxy formation; (ii) dark matter self-interactions; (iii) variations in the baryonic mass structure coupled to rotation velocities through the ‘mass discrepancy–acceleration relation’ (MDAR); or (iv) non-circular motions in gaseous discs. Together with analytical modelling and cosmological hydrodynamical simulations, our analysis shows that each of these scenarios has promising features, but none seems to fully account for the observed diversity. The MDAR, in particular, is inconsistent with the observed trend between rotation curve shape and baryonic importance; either the trend is caused by systematic errors in the data or the MDAR does not apply. The origin of the dwarf galaxy rotation curve diversity and its relation to the structure of cold dark matter haloes remains an open issue.

Baryon-induced dark matter cores in the eagle simulations

ABSTRACT We examine the formation of dark matter (DM) cores in dwarf galaxies simulated with the eagle model of galaxy formation. As in earlier work, we find that the star formation (SF) gas density threshold (ρth) plays a critical role. At low thresholds (LT), gas is unable to reach densities high enough to dominate the gravitational potential before being dispersed by feedback from supernovae. LT runs show little effect on the inner DM profile, even in systems with extended and bursty SF, two ingredients often cited as critical for core formation. For higher thresholds, gas is able to dominate the gravitational potential before being ejected by feedback. This can lead to a substantial reduction in the inner DM content, but only if the gas is gravitationally important over an extended period of time, allowing the halo to contract before gas removal. Rapid assembly and removal of gas in short SF bursts is less effective at altering the inner DM content. Subsequent gas accretion may draw DM back in and reform a cusp, unless SF is bursty enough to prevent it, preserving the core. Thus, for the eagle SF + feedback model, there is no simple relation between core formation and SF history, contrary to recent claims. The dependence of the inner DM content of dwarfs on ρth hinders robust predictions and the interpretation of observations. A simulation of a $(12 \rm \ Mpc)^3$ volume with high ρth results in dwarfs with sizeable cores over a limited halo mass range, but with insufficient variety in mass profiles to explain the observed diversity of dwarf galaxy rotation curves.

No cores in dark matter-dominated dwarf galaxies with bursty star formation histories

ABSTRACT Measurements of the rotation curves of dwarf galaxies are often interpreted as requiring a constant density core at the centre, at odds with the ‘cuspy’ inner profiles predicted by N-body simulations of cold dark matter (CDM) haloes. It has been suggested that this conflict could be resolved by fluctuations in the inner gravitational potential caused by the periodic removal of gas following bursts of star formation. Earlier work has suggested that core formation requires a bursty and extended star formation history (SFH). Here we investigate the structure of CDM haloes of dwarf galaxies ($M_{{\rm DM}} \sim 10^9\!-\!5\times 10^{10}\, {\rm M}_\odot$) formed in the apostle (‘A Project of Simulating the Local Environment’) and auriga cosmological hydrodynamic simulations. Our simulations have comparable or better resolution than others that make cores ($M_{{\rm gas}} \sim 10^4\, {\rm M}_\odot$, gravitational softening ∼150 pc). Yet, we do not find evidence of core formation at any mass or any correlation between the inner slope of the DM density profile and temporal variations in the SFH. apostle and auriga dwarfs display a similar diversity in their cumulative SFHs to available data for Local Group dwarfs. Dwarfs in both simulations are DM-dominated on all resolved scales at all times, likely limiting the ability of gas outflows to alter significantly the central density profiles of their haloes. We conclude that recurrent bursts of star formation are not sufficient to cause the formation of cores, and that other conditions must also be met for baryons to be able to modify the central DM cusp.

Non-circular motions and the diversity of dwarf galaxy rotation curves

We use mock interferometric HI measurements and a conventional tilted-ring modelling procedure to estimate circular velocity curves of dwarf galaxy discs from the APOSTLE suite of {\Lambda}CDM cosmological hydrodynamical simulations. The modelling yields a large diversity of rotation curves for an individual galaxy at fixed inclination, depending on the line-of-sight orientation. The diversity is driven by non-circular motions in the gas; in particular, by strong bisymmetric fluctuations in the azimuthal velocities that the tilted-ring model is ill-suited to account for and that are difficult to detect in model residuals. Large misestimates of the circular velocity arise when the kinematic major axis coincides with the extrema of the fluctuation pattern, in some cases mimicking the presence of kiloparsec-scale density 'cores', when none are actually present. The thickness of APOSTLE discs compounds this effect: more slowly-rotating extra-planar gas systematically reduces the average line-of-sight speeds. The recovered rotation curves thus tend to underestimate the true circular velocity of APOSTLE galaxies in the inner regions. Non-circular motions provide an appealing explanation for the large apparent cores observed in galaxies such as DDO 47 and DDO 87, where the model residuals suggest that such motions might have affected estimates of the inner circular velocities. Although residuals from tilted ring models in the simulations appear larger than in observed galaxies, our results suggest that non-circular motions should be carefully taken into account when considering the evidence for dark matter cores in individual galaxies.

On the Dwarf Galaxy Rotation Curve Diversity Problem

In this paper, we show how baryonic physics can solve the problem of the striking diversity in dwarf galaxy rotation curves shapes. To this aim, we compare the distribution of galaxies of the SPARC sample, in the plane V2kpc-VRlast (V2kpc being the galaxy rotation velocity at 2 kpc, and VRlast being the outermost one), with that of galaxies that we simulated, taking account of baryonic effects. The scatter in the rotation curves in the V2kpc-VRlast plane, as well as the trend of the SPARC sample, and our simulated galaxy distribution is in good agreement. The solution of the “diversity” problem lies in the ability of the baryonic process to produce non-self-similar haloes, contrary to DM-only simulations. We show also that baryonic effects can reproduce the rotation curves of galaxies such as IC2574, which are characterized by a slow rise in radius. A solution to the diversity problem can be obtained taking the baryon physics effects appropriately into account.

Testing MOG, non-local gravity and MOND with rotation curves of dwarf galaxies

Modified Gravity (MOG) and Non-Local Gravity (NLG) are two alternative theories to General Relativity. They are able to explain the rotation curves of spiral galaxies and clusters of galaxies without including dark matter (Moffat & Rahvar 2013, 2014; Rahvar & Mashhoon 2014). In the weak-field approximation these two theories have similar forms, with an effective gravitational potential that has two components: (i) Newtonian gravity with the gravitational constant enhanced by a factor $(1+\alpha)$ and (ii) a Yukawa type potential that produces a repulsive force with length scale $1/\mu$. In this work we compare the rotation curves of dwarf galaxies in the LITTLE THINGS catalog with predictions of MOG, NLG and Modified Newtonian Dynamics (MOND). We find that the universal parameters of these theories, can fit the rotation curve of dwarf galaxies with a larger stellar mass to the light ratio compared to the nearby stars in the Milky Way galaxy. Future direct observations of mass function of stars in the dwarf galaxies can examine different modified gravity models.

Understanding the shape and diversity of dwarf galaxy rotation curves in ΛCDM

The shape and diversity of dwarf galaxy rotation curves is at apparent odds with dark matter halos in a $\Lambda$ Cold Dark Matter ($\Lambda$CDM) cosmology. We use mock data from isolated dwarf galaxy simulations to show that this owes to three main effects. Firstly, stellar feedback heats dark matter, leading to a 'coreNFW' dark matter density profile with a slowly rising rotation curve. Secondly, if close to a recent starburst, large HI bubbles push the rotation curve out of equilibrium, deforming the rotation curve shape. Thirdly, when galaxies are viewed near face-on, their best fit inclination is biased high. This can lead to a very shallow rotation curve that falsely implies a large dark matter core. All three problems can be avoided, however, by a combination of improved mass models and a careful selection of target galaxies. Fitting our coreNFW model to mock rotation curve data, we show that we can recover the rotation curve shape, dark matter halo mass $M_{200}$ and concentration parameter $c$ within our quoted uncertainties. We fit our coreNFW model to real data for four isolated dwarf irregulars, chosen to span a wide range of rotation curve shapes. We obtain an excellent fit for NGC 6822 and WLM, with tight constraints on $M_{200}$, and $c$ consistent with $\Lambda$CDM. However, IC 1613 and DDO 101 give a poor fit. For IC 1613, we show that this owes to disequilibria and its uncertain inclination $i$; for DDO 101, it owes to its uncertain distance $D$. If we assume $i_{\rm IC1613} \sim 15^\circ$ and $D_{\rm DDO101} \sim 12$ Mpc, consistent with current uncertainties, we are able to fit both galaxies very well. We conclude that $\Lambda$CDM appears to give an excellent match to dwarf galaxy rotation curves.

Dissipative dark matter and the rotation curves of dwarf galaxies

There is ample evidence from rotation curves that dark matter halos around disk galaxies have nontrivial dynamics. Of particular significance are: a) the cored dark matter profile of disk galaxies, b) correlations of the shape of rotation curves with baryonic properties, and c) Tully-Fisher relations. Dark matter halos around disk galaxies may have nontrivial dynamics if dark matter is strongly self interacting and dissipative. Multicomponent hidden sector dark matter featuring a massless `dark photon' (from an unbroken dark U(1) gauge interaction) which kinetically mixes with the ordinary photon provides a concrete example of such dark matter. The kinetic mixing interaction facilitates halo heating by enabling ordinary supernovae to be a source of these `dark photons'. Dark matter halos can expand and contract in response to the heating and cooling processes, but for a sufficiently isolated halo could have evolved to a steady state or `equilibrium' configuration where heating and cooling rates locally balance. This dynamics allows the dark matter density profile to be related to the distribution of ordinary supernovae in the disk of a given galaxy. In a previous paper a simple and predictive formula was derived encoding this relation. Here we improve on previous work by modelling the supernovae distribution via the measured UV and Hα fluxes, and compare the resulting dark matter halo profiles with the rotation curve data for each dwarf galaxy in the LITTLE THINGS sample. The dissipative dark matter concept is further developed and some conclusions drawn.

The unexpected diversity of dwarf galaxy rotation curves

We examine the circular velocity profiles of galaxies in {\Lambda}CDM cosmological hydrodynamical simulations from the EAGLE and LOCAL GROUPS projects and compare them with a compilation of observed rotation curves of galaxies spanning a wide range in mass. The shape of the circular velocity profiles of simulated galaxies varies systematically as a function of galaxy mass, but shows remarkably little variation at fixed maximum circular velocity. This is especially true for low-mass dark matter-dominated systems, reflecting the expected similarity of the underlying cold dark matter haloes. This is at odds with observed dwarf galaxies, which show a large diversity of rotation curve shapes, even at fixed maximum rotation speed. Some dwarfs have rotation curves that agree well with simulations, others do not. The latter are systems where the inferred mass enclosed in the inner regions is much lower than expected for cold dark matter haloes and include many galaxies where previous work claims the presence of a constant density "core". The "cusp vs core" issue is thus better characterized as an "inner mass deficit" problem than as a density slope mismatch. For several galaxies the magnitude of this inner mass deficit is well in excess of that reported in recent simulations where cores result from baryon-induced fluctuations in the gravitational potential. We conclude that one or more of the following statements must be true: (i) the dark matter is more complex than envisaged by any current model; (ii) current simulations fail to reproduce the effects of baryons on the inner regions of dwarf galaxies; and/or (iii) the mass profiles of "inner mass deficit" galaxies inferred from kinematic data are incorrect.

The dark matter haloes of dwarf galaxies: a challenge for the Λ cold dark matter paradigm?

The cold dark matter halo mass function is much steeper than the galaxy stellar mass function on galactic and subgalactic scales. This difference is usually reconciled by assuming that the galaxy formation efficiency drops sharply with decreasing halo mass, so that virtually no dwarf galaxies form in halos less massive than ~ 10^10 M_sun. In turn, this implies that, at any given radius, the dark mass enclosed by a galaxy must exceed a certain minimum. We use rotation curves of dwarf galaxies compiled from the literature to explore whether their enclosed mass is consistent with these constraints. We find that almost one half of the dwarfs in our sample with stellar mass between 10^6-10^7 M_sun are at odds with this restriction: either they live in halos with masses substantially below 10^10 M_sun or there is a mechanism capable of reducing the dark mass enclosed by some of the faintest dwarfs. Neither possibility is easily accommodated within the standard LCDM scenario. Extending galaxy formation to halos well below 10^10 M_sun would lead to large numbers of dwarf galaxies in excess of current estimates; at the same time, the extremely low stellar mass of the systems involved makes it unlikely that baryonic effects can reduce their dark matter content. Resolving this challenge seems to require new insights into dwarf galaxy formation, or perhaps a radical revision of the prevailing paradigm.

HOW TO MAKE AN ULTRA-FAINT DWARF SPHEROIDAL GALAXY: TIDAL STIRRING OF DISKY DWARFS WITH SHALLOW DARK MATTER DENSITY PROFILES

In recent years the Sloan Digital Sky Survey has unraveled a new population of ultra-faint dwarf galaxies (UFDs) in the vicinity of the Milky Way (MW) whose origin remains a puzzle. Using a suite of collisionless N-body simulations, we investigate the formation of UFDs in the context of the tidal stirring model for the formation of dwarf spheroidal galaxies in the Local Group (LG). Our simulations are designed to reproduce the tidal interactions between MW-sized host galaxies and rotationally supported dwarfs embedded in 10^9 M_sun dark matter (DM) halos. We explore a variety of inner density slopes \rho \propto r^{-\alpha} for the dwarf DM halos, ranging from core-like (\alpha = 0.2) to cuspy (\alpha = 1), and different dwarf orbital configurations. Our experiments demonstrate that UFDs can be produced via tidal stirring of disky dwarfs on relatively tight orbits, consistent with a redshift of accretion by the host galaxy of z \sim 1, and with intermediate values for the halo inner density slopes (\rho \propto r^{-0.6}). The inferred slopes are in excellent agreement with those resulting from both the modeling of the rotation curves of dwarf galaxies and recent cosmological simulations of dwarf galaxy formation. Comparing the properties of observed UFDs with those of their simulated counterparts, we find remarkable similarities in terms of basic observational parameters. We conclude that tidal stirring of rotationally supported dwarfs represents a viable mechanism for the formation of UFDs in the LG environment.

Fitting dwarf galaxy rotation curves with conformal gravity

We continue our study of the application of the conformal gravity theory to galactic rotation curves. Previously we had studied a varied 111 spiral galaxy sample consisting of high surface brightness galaxies, low surface brightness galaxies and dwarf galaxies. With no free parameters other than galactic mass to light ratios, we had found that the theory is able to account for the systematics that is observed in the entire set of galactic rotation curves without the need for any dark matter whatsoever. In the present paper we extend our study to incorporate a further 27 galaxies of which 25 are dwarf galaxies and provide updated studies of 3 additional galaxies that had been in the original sample, and again without dark matter find fully acceptable fits, save only for just a few galaxies that we find to be somewhat troublesome. Our current study brings to 138 the number of rotation curves of galaxies that have been accounted for by the conformal gravity theory. Since one of the primary ingredients in the theory is a universal contribution to galactic motions coming from matter exterior to the galaxies, and thus independent of them, our study reinforces one of the central concepts of the conformal gravity studies, namely that invoking dark matter should be viewed as being nothing more than an attempt to describe global physics contributions in purely local galactic terms.

Bose-Einstein condensation of dark matter solves the core/cusp problem

We analyze the observed properties of dwarf galaxies, which are dark matter dominated astrophysical objects, by assuming that dark matter is in the form of a strongly-coupled, dilute Bose-Einstein condensate. The basic astrophysical properties of the condensate (density profile, rotational velocity, and mass profile, respectively), are derived from a variational principle. To test the validity of the model we compare first the tangential velocity equation of the model with a sample of eight rotation curves of dwarf galaxies. We find a good agreement between the theoretically predicted rotation curves (without any baryonic component) and the observational data. The mean value of the logarithmic inner slope of the mass density profile of dwarf galaxies is also obtained, and it is shown that the observed value of this parameter is in agreement with the theoretical results. The predictions of the Bose-Einstein condensate model are also systematically compared with the predictions of the standard Cold Dark Matter model. The non-singular density profiles of the Bose-Einstein condensed dark matter generally show the presence of an extended core, whose presence is due to the strong interaction between dark matter particles.

The Rotation Curves of Dwarf Galaxies: A Problem for Cold Dark Matter?

We address the issue of accuracy in recovering density profiles from observations of rotation curves of galaxies. We observe and analyze our models in much the same way as observers do the real galaxies. Our models include stellar disks, disks with bars, and small bulges. We find that the tilted-ring model analysis produces an underestimate of the central rotational velocity. In some cases the galaxy halo density profile seems to have a flat core, while in reality it does not. We identify three effects that explain the systematic biases: inclination, small bulge, and bar. Inclination effects are due to the finite thickness of the disk, bar, or bulge. Admixture of a nonrotating bulge component reduces the rotational velocity. A small (200-500 pc) bulge may be overlooked, leading to systematic bias even on relatively large (~1 kpc) distances. In the case of a disk with a bar, the underestimate of the circular velocity is larger because of a combination of noncircular motions and random velocities. The effect of the bar depends on the angle that the bar makes with the line of sight. Signatures of bars can be difficult to detect in the surface brightness profiles of the model galaxies. The variations of inclination angle and isophote position angle with radius are more reliable indicators of bar presence than the surface brightness profiles. The systematic biases in the central ~1 kpc of galaxies are not large. Each effect separately gives typically a few km s-1 error, but the effects add up. In some cases the error in circular velocity was a factor of 2, but typically we get about a 20% effect. The result is the false inference that the density profile of the halo flattens in the central parts. Our observations of real galaxies show that for a large fraction of galaxies the velocity of gas rotation (as measured by emission lines) is very close to the rotation of the stellar component (as measured by absorption lines). This implies that the systematic effects discussed in this paper are also applicable both for the stars and emission-line gas.

The impact of cooling and feedback on disc galaxies

In the standard picture of galaxy formation, mass and angular momentum are the two main parameters that determine the properties of disc galaxies. The details of how the gas inside dark matter haloes is transformed into a luminous disc, however, depend strongly on the physics of star formation, feedback and cooling, which are poorly understood. The efficiencies of these astrophysical processes are ultimately responsible for setting the galaxy mass fractions fgal defined as the ratio of galaxy mass (disc plus bulge) to total virial mass. Therefore, if we could somehow determine fgal(Mvir) from observations of the luminous component of disc galaxies, this would allow us to put stringent constraints on the efficiencies of cooling and feedback. This, however, requires estimating the total virial mass, which is a delicate problem. In this paper we use detailed, analytical models for the formation of disc galaxies to investigate the impact that cooling and feedback have on their structural properties. In particular, we investigate which observables extracted directly from the models are best suited as virial mass estimators, and to what extent they allow the recovery of the model input parameters regarding the feedback and cooling efficiencies. Contrary to naive expectations, the luminosities and circular velocities of disc galaxies are extremely poor indicators of total virial mass. Instead, we show that the product of disc scalelength and rotation velocity squared yields a much more robust virial mass estimate, which allows a fairly accurate recovery of the galaxy mass fractions as a function of the virial mass. We also show that feedback can cause a narrow correlation between fgal and the halo spin parameter, as found recently by van den Bosch, Burkert & Swaters from an analysis of dwarf galaxy rotation curves. Finally, we investigate the impact that cooling and feedback have on the colours, metallicities, star formation histories and Tully–Fisher relation of disc galaxies.

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

ABSTRA C T 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 constantdensity cores to r 22 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 21 cusps. We show that the dwarf galaxies analysed here are consistent with CDM haloes in a LCDM 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 21.5 . 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.