Isothermal Halo Research Articles

A heuristic wave equation parameterizing BEC dark matter halos with a quantum core and an isothermal atmosphere

The Gross–Pitaevskii–Poisson equations that govern the evolution of self-gravitating Bose–Einstein condensates, possibly representing dark matter halos, experience a process of gravitational cooling and violent relaxation. We propose a heuristic parametrization of this complicated process in the spirit of Lynden-Bell’s theory of violent relaxation for collisionless stellar systems. We derive a generalized wave equation that was introduced phenomenologically in Chavanis (Eur Phys J Plus 132:248, 2017) involving a logarithmic nonlinearity associated with an effective temperature $$T_\mathrm{eff}$$ and a damping term associated with a friction $$\xi $$ . These terms can be obtained from a maximum entropy production principle and are linked by a form of Einstein relation expressing the fluctuation-dissipation theorem. The wave equation satisfies an H-theorem for the Lynden-Bell entropy and relaxes towards a stable equilibrium state which is a maximum of entropy at fixed mass and energy. This equilibrium state represents the most probable state of a Bose–Einstein condensate dark matter halo. It generically has a core-halo structure. The quantum core prevents gravitational collapse and may solve the core-cusp problem. The isothermal halo leads to flat rotation curves in agreement with the observations. These results are consistent with the phenomenology of dark matter halos. Furthermore, as shown in a previous paper (Chavanis in Phys Rev D 100:123506, 2019), the maximization of entropy with respect to the core mass at fixed total mass and total energy determines a core mass–halo mass relation which agrees with the relation obtained in direct numerical simulations. We stress the importance of using a microcanonical description instead of a canonical one. We also explain how our formalism can be applied to the case of fermionic dark matter halos.

Density spikes near black holes in self-interacting dark matter halos and indirect detection constraints

Self-interacting dark matter (SIDM) naturally gives rise to a cored isothermal density profile, which is favored in observations of many dwarf galaxies. The dark matter distribution in the presence of a central black hole in an isothermal halo develops a density spike with a power law of ${r}^{\ensuremath{-}7/4}$, which is shallower than ${r}^{\ensuremath{-}7/3}$ as expected for collisionless dark matter (CDM). Thus, indirect detection constraints on dark matter annihilations from the density spike could be relaxed in SIDM. Taking the most dense satellite galaxy of the Milky Way Draco as an example, we derive upper limits on the annihilation cross section and the black hole mass for both SIDM and CDM halos. For the former case, Draco could host an intermediate mass black hole even if dark matter is composed of thermal relics. We further explore the constraints from the Milky Way and M87, which host supermassive black holes, and show the upper limits on the annihilation cross section are significantly weakened in SIDM. Our results also indicate that the Event Horizon Telescope could provide a unique test of SIDM spikes.

Lens modelling of the strongly lensed Type Ia supernova iPTF16geu

ABSTRACT In 2016, the first strongly lensed Type Ia supernova (SN Ia), iPTF16geu, at redshift z = 0.409 with four resolved images arranged symmetrically around the lens galaxy at z = 0.2163, was discovered. Here, refined observations of iPTF16geu, including the time delay between images, are used to decrease uncertainties in the lens model, including the the slope of the projected surface density of the lens galaxy, Σ ∝ r1 − η, and to constrain the universal expansion rate H0. Imaging with Hubble Space Telescope provides an upper limit on the slope η, in slight tension with the steeper density profiles indicated by imaging with Keck after iPTF16geu had faded, potentially due to dust extinction not corrected for in host galaxy imaging. Since smaller η implies larger magnifications, we take advantage of the standard candle nature of SNe Ia constraining the image magnifications, to obtain an independent constraint of the slope. We find that a smooth lens density fails to explain the iPTF16geu fluxes, regardless of the slope, and additional substructure lensing is needed. The total probability for the smooth halo model combined with star microlensing to explain the iPTF16geu image fluxes is maximized at 12 per cent for η ∼ 1.8, in excellent agreement with Keck high-spatial-resolution data, and flatter than an isothermal halo. It also agrees perfectly with independent constraints on the slope from lens velocity dispersion measurements. Combining with the observed time delays between the images, we infer a lower bound on the Hubble constant, $H_0 \gtrsim 40\, {\rm km \ s^{-1} Mpc^{-1}}$, at 68.3 per cent confidence level.

Derivation of a generalized Schrödinger equation for dark matter halos from the theory of scale relativity

Abstract Using Nottale’s theory of scale relativity, we derive a generalized Schrodinger equation applying to dark matter halos. This equation involves a logarithmic nonlinearity associated with an effective temperature and a source of dissipation. Fundamentally, this wave equation arises from the nondifferentiability of the trajectories of the dark matter particles whose origin may be due to ordinary quantum mechanics, classical ergodic (or almost ergodic) chaos, or to the fractal nature of spacetime at the cosmic scale. The generalized Schrodinger equation involves a coefficient D , possibly different from ħ ∕ 2 m (where ħ is the Planck constant and m the mass of the particles), whose value for dark matter halos is D = 1 . 02 × 1 0 23 m2/s. This model is similar to the Bose–Einstein condensate dark matter model except that it does not require the dark matter particle to be ultralight. It can accommodate any type of particles provided that they have nondifferentiable trajectories. We suggest that the cold dark matter crisis may be solved by the fractal (nondifferentiable) structure of spacetime at the cosmic scale, or by the chaotic motion of the particles on a very long timescale, instead of ordinary quantum mechanics. The equilibrium states of the generalized Schrodinger equation correspond to configurations with a core-halo structure. The quantumlike potential generates a solitonic core that solves the cusp problem of the classical cold dark matter model. The logarithmic nonlinearity accounts for the presence of an isothermal halo that leads to flat rotation curves (it also accounts for the isothermal core of large dark matter halos). The damping term ensures that the system relaxes towards an equilibrium state. This property is guaranteed by an H -theorem satisfied by a Boltzmann-like free energy functional. In our approach, the temperature and the friction arise from a single formalism. They correspond to the real and imaginary parts of the complex friction coefficient present in the scale covariant equation of dynamics that is at the basis of Nottale’s theory of scale relativity. They may be the manifestation of a cosmic aether or the consequence of a process of violent relaxation and gravitational cooling on a coarse-grained scale.

How do stars affect ψDM haloes?

Wave dark matter ($\psi$DM) predicts a compact soliton core and a granular halo in every galaxy. This work presents the first simulation study of an elliptical galaxy by including both stars and $\psi$DM, focusing on the systematic changes of the central soliton and halo granules. With the addition of stars in the inner halo, we find the soliton core consistently becomes more prominent by absorbing mass from the host halo than that without stars, and the halo granules become "non-isothermal", "hotter" in the inner halo and "cooler" in the outer halo, as opposed to the isothermal halo in pure $\psi$DM cosmological simulations. Moreover, the composite (star+$\psi$DM) mass density is found to follow a $r^{-2}$ isothermal profile near the half-light radius in most cases. Most striking is the velocity dispersion of halo stars that increases rapidly toward the galactic center by a factor of at least 2 inside the half-light radius caused by the deepened soliton gravitational potential, a result that compares favorably with observations of elliptical galaxies and bulges in spiral galaxies. However in some rare situations we find a phase segregation turning a compact distribution of stars into two distinct populations with high and very low velocity dispersions; while the high-velocity component mostly resides in the halo, the very low-velocity component is bound to the interior of the soliton core, resembling stars in faint dwarf spheroidal galaxies.

Dissipative self-gravitating Bose-Einstein condensates with arbitrary nonlinearity as a model of dark matter halos

We develop a general formalism applying to Newtonian self-gravitating Bose-Einstein condensates. This formalism may find application in the context of dark matter halos. We introduce a generalized Gross-Pitaevskii equation including a source of dissipation (damping) and an arbitrary nonlinearity. Using the Madelung transformation, we derive the hydrodynamic representation of this generalized Gross-Pitaevskii equation and obtain a damped quantum Euler equation involving a friction force proportional and opposite to the velocity and a pressure force associated with an equation of state determined by the nonlinearity present in the generalized Gross-Pitaevskii equation. In the strong friction limit, we obtain a quantum Smoluchowski equation. These equations satisfy an H-theorem for a free energy functional constructed with a generalized entropy. We specifically consider the Boltzmann and Tsallis entropies associated with isothermal and polytropic equations of state. We also consider the entropy associated with the logotropic equation of state. We derive the virial theorem corresponding to the generalized Gross-Pitaevskii equation, damped quantum Euler equation, and quantum Smoluchowski equation. Using a Gaussian ansatz, we obtain a simple equation governing the dynamical evolution of the size of the condensate. We develop a mechanical analogy associated with this gross dynamics. We highlight a specific model of dark matter halos corresponding to a generalized Gross-Pitaevskii equation with a logarithmic nonlinearity and a cubic nonlinearity. It corresponds to a damped quantum Euler equation associated with a mixed entropy combining the Boltzmann and Tsallis entropies. It leads to dark matter halos with an equation of state $P=\rho k_{B} T_{\rm eff}/m+2\pi a_{s}\hbar^{2}\rho^{2}/m^{3}$ presenting a condensed core (BEC/soliton) and an isothermal halo with an effective temperature $T_{\rm eff}$ . We propose that this model provides an effective coarse-grained parametrization of dark matter halos experiencing gravitational cooling. Specific applications of our formalism to dark matter halos will be developed in future papers.

Two regimes of galaxy dynamics: mass models of NGC 5055 and DDO 154

We derive detailed dynamical models for two galaxies, the massive spiral galaxy NGC 5055 and the dwarf irregular DDO 154. We used Navarro, Frenk & White (NFW) and isothermal halo models for the dark matter (DM) distribution, along with the most recent and reliable radio observations of H i to determine the rotation curves of these galaxies. Contributions from the neutral gas and the luminous matter were accounted for. For NGC 5055, the latest stellar population synthesis (SPS) models, combining metallicity and age as indicators of the stellar mass-to-light ratio (M/L) were used to better constrain both the DM model and the contribution to the total mass from all components. The isothermal dark halo model successfully fitted both observed rotation curves with realistic values for stellar M/L, while the NFW model needed further constraints for M/L to fit the rotation curve of DDO 154. In the case of NGC 5055, we found the best-fitting M/L in the 3.6 μm band (M/L3.6) for stellar disc to be 0.57 ± 0.04 for isothermal, and 0.50 ± 0.05 for NFW DM model. The most probable value for M/L3.6 from SPS models is 0.46, which is in agreement within uncertainties with our best-fitting NFW model. In the case of DDO 154, we obtained the stellar disc M/L3.6 of 0.25 ± 0.20 for the isothermal DM model. The stellar disc M/L3.6 for the NFW model was fixed to 0.26, as best reasonable value. For NGC 5055, we derived radial profiles of stellar M/L for our best estimate for a particular DM model.

Dominant dark matter and a counter-rotating disc: MUSE view of the low-luminosity S0 galaxy NGC 5102

The kinematics and stellar populations of the low-mass nearby S0 galaxy NGC 5102 are studied from integral field spectra taken with the Multi-Unit Spectroscopic Explorer (MUSE). The kinematic maps reveal for the first time that NGC 5102 has the characteristic 2 sigma peaks indicative of galaxies with counter-rotating discs. This interpretation is quantitatively confirmed by fitting two kinematic components to the observed spectra. Through stellar population analysis we confirm the known young stellar population in the centre and find steep age and metallicity gradients. We construct axisymmetric Jeans anisotropic models of the stellar dynamics to investigate the initial mass function (IMF) and the dark matter halo of the galaxy. The models show that this galaxy is quite different from all galaxies previously studied with a similar approach: even within the half-light radius, it cannot be approximated with the self-consistent mass-follows-light assumption. Including an NFW dark matter halo, we need a heavy IMF and a dark matter fraction of 0.37+-0.04 within a sphere of one effective radius to describe the stellar kinematics. The more general model with a free slope of the dark matter halo shows that slope and IMF are degenerate, but indicates that a light weight IMF (Chabrier-like) and a higher dark matter fraction, with a steeper (contracted) halo, fit the data better. Regardless of the assumptions about the halo profile, we measure the slope of the total mass density to be -1.75+-0.04. This is shallower than the slope of -2 of an isothermal halo and shallower than published slopes for more massive early type galaxies.

Evolution of star clusters on eccentric orbits

We study the evolution of star clusters on circular and eccentric orbits using direct $N$-body simulations. We model clusters with initially $N=8{\rm k}$ and $N=16{\rm k}$ single stars of the same mass, orbiting around a point-mass galaxy. For each orbital eccentricity that we consider, we find the apogalactic radius at which the cluster has the same lifetime as the cluster with the same $N$ on a circular orbit. We show that then, the evolution of bound particle number and half-mass radius is approximately independent of eccentricity. Secondly, when we scale our results to orbits with the same semi-major axis, we find that the lifetimes are, to first order, independent of eccentricity. When the results of Baumgardt and Makino for a singular isothermal halo are scaled in the same way, the lifetime is again independent of eccentricity to first order, suggesting that this result is independent of the Galactic mass profile. From both sets of simulations we empirically derive the higher order dependence of the lifetime on eccentricity. Our results serve as benchmark for theoretical studies of the escape rate from clusters on eccentric orbits. Finally, our results can be useful for generative models for cold streams and cluster evolution models that are confined to spherical symmetry and/or time-independent tides, such as Fokker-Planck models, Monte Carlo models, and (fast) semi-analytic models.

RADIO EMISSION FROM WEAK SPHERICAL SHOCKS IN THE OUTSKIRTS OF GALAXY CLUSTERS

In Kang (2015) we calculated the acceleration of cosmic-ray electrons and the ensuing radio synchrotron emission at weak spherical shocks that are expected to form in the outskirts of galaxy clusters.There we demonstrated that, at decelerating spherical shocks, the volume integrated spectra of both electrons and radiation deviate significantly from the test-particle power-laws predicted for constant planar shocks, because the shock compression ratio and the flux of injected electrons decrease in time. In this study, we consider spherical blast waves propagating into a constant density core surrounded by an isothermal halo with a decreasing density profile in order to explore how the deceleration rate of the shock speed affects the radio emission from accelerated electrons. The surface brightness profile and the volume-integrated radio spectrum of the model shocks are calculated by assuming a ribbon-like shock surface on a spherical shell and the associated downstream region of relativistic electrons. If the postshock magnetic field strength is about 7 microgauss, at the shock age of ~50 Myr, the volume-integrated radio spectrum steepens gradually with the spectral index from alpha_{inj} to alpha_{inj}+0.5 over 0.1-10 GHz, where alpha_{inj} is the injection index at the shock positionexpected from the diffusive shock acceleration theory. Such gradual steepening could explain the curved radio spectrum of the radio relic in cluster A2266, which was interpreted as a broken power-law by Trasatti et al. (2014), if the relic shock is young enough so that the break frequency falls in around 1 GHz.

The distribution of dark and luminous matter inferred from extended rotation curves

A better understanding of the formation of mass structures in the universe can be obtained by determining the amount and distribution of dark and luminous matter in spiral galaxies. To investigate such matters a sample of 12 galaxies, most with accurate distances, has been composed of which the luminosities are distributed regularly over a range spanning 2.5 orders of magnitude. Of the observed high quality and extended rotation curves of these galaxies decompositions have been made, for four different schemes, each with two free parameters. For a "maximum disc fit" the rotation curves can be well matched, yet a large range of mass-to-light ratios for the individual galaxies is required. For the alternative gravitational theory of MOND the rotation curves can be explained if the fundamental parameter associated with MOND is allowed as a free parameter. Fixing that parameter leads to a disagreement between the predicted and observed rotation curves for a few galaxies. When cosmologically motivated NFW dark matter halos are assumed, the rotation curves for the least massive galaxies can, by no means, be reproduced; cores are definitively preferred over cusps. Finally, decompositions have been made for a pseudo isothermal halo combined with a universal M/L ratio. For the latter, the light of each galactic disc and bulge has been corrected for extinction and has been scaled by the effect of stellar population. This scheme can successfully explain the observed rotations and leads to sub maximum disc mass contributions. Properties of the resulting dark matter halos are described and a ratio between dark and baryonic mass of approximately 9 for the least, and of approximately 5, for the most luminous galaxies has been determined, at the outermost measured rotation.

MOSFIRE AND LDSS3 SPECTROSCOPY FOR AN [O II] BLOB ATz= 1.18: GAS OUTFLOW AND ENERGY SOURCE

We report our Keck/MOSFIRE and Magellan/LDSS3 spectroscopy for an [OII] Blob, OIIB10, that is a high-$z$ galaxy with spatially extended [OII]$\lambda\lambda3726,3729$ emission over 30 kpc recently identified by a Subaru large-area narrowband survey. The systemic redshift of OIIB10 is $z=1.18$ securely determined with [OIII]$\lambda\lambda4959,5007$ and H$\beta$ emission lines. We identify FeII$\lambda$2587 and MgII$\lambda\lambda$2796,2804 absorption lines blueshifted from the systemic redshift by $80\pm50$ and $260\pm40$ km s$^{-1}$, respectively, which indicate gas outflow from OIIB10 with the velocity of $\sim 80-260$ km s$^{-1}$. This outflow velocity is comparable with the escape velocity, $250\pm140$ km s$^{-1}$, estimated under the assumption of a singular isothermal halo potential profile. Some fraction of the outflowing gas could escape from the halo of OIIB10, suppressing OIIB10's star-formation activity. We estimate a mass loading factor, $\eta$, that is a ratio of mass outflow rate to star-formation rate, and obtain $\eta>0.8\pm 0.1$ which is relatively high compared with low-$z$ starbursts including U/LIRGs and AGNs. The major energy source of the outflow is unclear with the available data. Although no signature of AGN is found in the X-ray data, OIIB10 falls in the AGN/star-forming composite region in the line diagnostic diagrams. It is possible that the outflow is powered by star formation and a type-2 AGN with narrow FWHM emission line widths of $70-130$ km s$^{-1}$. This is the first detailed spectroscopic study of oxygen-line blobs, which includes the analyses of the escape velocity, the mass loading factor, and the presence of an AGN, and a significant step to understanding the nature of oxygen-line blobs and the relation with gas outflow and star-formation quenching at high redshift.

To be or not to be oblate: the shape of the dark matter halo in polar ring galaxies

With the aim to determine the spatial distribution of the dark matter halo, we investigate two polar ring galaxies NGC 4262 and SPRC-7. For both galaxies the stellar kinematics data for the central galaxy were obtained from optical spectroscopy at the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences. The information about polar gaseous components was taken from the optical 3D-spectroscopic observations of ionized gas (for SPRC-7) and H {\sc i} radio observations (for NGC 4262). SPRC-7 is the system with a relative angle $\delta=73^{\circ}$ towards the central galaxy and a quite massive stellar-gaseous polar component. Meanwhile NGC 4262 is the classic polar case with $\delta=88^{\circ}$ where the polar ring mainly consists of neutral gas with a negligible stellar contribution to the mass. We are hence dealing with two different systems and the results are quite diverse too. The observed properties of both galaxies were compared with the results of self consistent simulations of velocity fields of the polar component along with the rotation curve of the central lenticular galaxy. For SPRC-7 we have found a slightly flattened halo towards the polar plane with the axis ratio $c/a \simeq 1.7 \pm 0.2$ for the isothermal halo model and $c/a \simeq 1.5 \pm 0.2$ for the NFW model. The case of NGC 4262 is more unusual, the shape of the dark matter distribution varies strongly with radius. Namely, the dark matter halo is fattened in the vicinity of the galactic disc ($c/a \approx 0.4 \pm 0.1$), however it is prolate far beyond the central galaxy ($c/a \approx 1.7$ for the isothermal halo and $c/a \approx 2.3$ for NFW).

IS THE MILKY WAY'S HOT HALO CONVECTIVELY UNSTABLE?

We investigate the convective stability of two popular types of model of the gas distribution in the hot Galactic halo. We first consider models in which the halo density and temperature decrease exponentially with height above the disk. These halo models were created to account for the fact that, on some sight lines, the halo's X-ray emission lines and absorption lines yield different temperatures, implying that the halo is non-isothermal. We show that the hot gas in these exponential models is convectively unstable if $\gamma<3/2$, where $\gamma$ is the ratio of the temperature and density scale heights. Using published measurements of $\gamma$ and its uncertainty, we use Bayes' Theorem to infer posterior probability distributions for $\gamma$, and hence the probability that the halo is convectively unstable for different sight lines. We find that, if these exponential models are good descriptions of the hot halo gas, at least in the first few kiloparsecs from the plane, the hot halo is reasonably likely to be convectively unstable on two of the three sight lines for which scale height information is available. We also consider more extended models of the halo. While isothermal halo models are convectively stable if the density decreases with distance from the Galaxy, a model of an extended adiabatic halo in hydrostatic equilibrium with the Galaxy's dark matter is on the boundary between stability and instability. However, we find that radiative cooling may perturb this model in the direction of convective instability. If the Galactic halo is indeed convectively unstable, this would argue in favor of supernova activity in the Galactic disk contributing to the heating the hot halo gas.

THE INITIAL CONDITIONS AND EVOLUTION OF ISOLATED GALAXY MODELS: EFFECTS OF THE HOT GAS HALO

We construct several Milky Way-like galaxy models containing a gas halo (as well as gaseous and stellar disks, a dark matter halo, and a stellar bulge) following either an isothermal or an NFW density profile with varying mass and initial spin. In addition, galactic winds associated with star formation are tested in some of the simulations. We evolve these isolated galaxy models using the GADGET-3 N-body/hydrodynamic simulation code, paying particular attention to the effects of the gaseous halo on the evolution. We find that the evolution of the models is strongly affected by the adopted gas halo component, particularly in the gas dissipation and the star formation activity in the disk. The model without a gas halo shows an increasing star formation rate (SFR) at the beginning of the simulation for some hundreds of millions of years and then a continuously decreasing rate to the end of the run at 3 Gyr. Whereas the SFRs in the models with a gas halo, depending on the density profile and the total mass of the gas halo, emerge to be either relatively flat throughout the simulations or increasing until the middle of the run (over a gigayear) and then decreasing to the end. The models with the more centrally concentrated NFW gas halo show overall higher SFRs than those with the isothermal gas halo of the equal mass. The gas accretion from the halo onto the disk also occurs more in the models with the NFW gas halo, however, this is shown to take place mostly in the inner part of the disk and not to contribute significantly to the star formation unless the gas halo has very high density at the central part. The rotation of a gas halo is found to make SFR lower in the model. The SFRs in the runs including galactic winds are found to be lower than those in the same runs but without winds. We conclude that the effects of a hot gaseous halo on the evolution of galaxies are generally too significant to be simply ignored. We also expect that more hydrodynamical processes in galaxies could be understood through numerical simulations employing both gas disk and gas halo components.

Dark atoms: asymmetry and direct detection

We present a simple UV completion of Atomic Dark Matter (aDM) in which heavy right-handed neutrinos decay to induce both dark and lepton number densities. This model addresses several outstanding cosmological problems: the matter/anti-matter asymmetry, the dark matter abundance, the number of light degrees of freedom in the early universe, and the smoothing of small-scale structure. Additionally, this realization of aDM may reconcile the CoGeNT excess with recently published null results and predicts a signal in the CRESST Oxygen band. We also find that, due to unscreened long-range interactions, the residual unrecombined dark ions settle into a diffuse isothermal halo.

Constraining the orbital history of the Magellanic Clouds: a new bound scenario suggested by the tidal origin of the Magellanic Stream

Bound orbits have traditionally been assigned to the Large and Small Magellanic Clouds (LMC and SMC, respectively) in order to provide a formation scenario for the Magellanic Stream (MS) and its Leading Arm (LA), two prominent neutral hydrogen (HI) features connected to the LMC and SMC. However, Hubble Space Telescope (HST) measurements of the proper motions of the LMC and SMC have challenged the plausibility of bound orbits, causing the origin of the MS to re-emerge as a contested issue. We present a new tidal model in which structures resembling the bifurcated MS and elongated LA are able to form in a bound orbit consistent with the HST proper motions. The LMC and SMC have remained bound to each other only recently in our model despite being separately bound to the Milky Way for more than 5 Gyr. We find that the MS and LA are able to form as a consequence of LMC-dominated tidal stripping during the recent dynamical coupling of the LMC and SMC. Our orbital model depends on our assumption that the Milky Way has a constant circular velocity of V_cir=250 km/s up to 160 kpc, which implies a massive isothermal halo that is not completely rejected by observations.

DAMA and the self-similar infall halo model

The annual modulation in the rate of WIMP recoils observed by the DAMA collaboration at high significance is often analyzed in the context of an isothermal Maxwell-Boltzmann velocity distribution. While this is the simplest model, there is a need to consider other well motivated theories of halo formation. In this paper, we study a different halo model, that of self similar infall which is characterized by the presence of a number of cold streams and caustics, not seen in simulations. It is shown that the self similar infall model is consistent with the DAMA result both in amplitude and in phase, for WIMP masses exceeding $\approx$ 250 GeV at the 99.7% confidence level. Adding a small thermal component makes the parameter space near $m_\chi$ = 12 GeV consistent with the self similar model. The minimum $\chi^2$ per degree of freedom is found to be 0.92(1.03) with(without) channeling taken into account, indicating an acceptable fit. For WIMP masses much greater than the mass of the target nucleus, the recoil rate depends only on the ratio $\sigma_{\rm p}/m_\chi$ which is found to be $\approx$ 0.06 femtobarn/TeV. However as in the case of the isothermal halo, the allowed parameter space is inconsistent with the null result obtained by the CDMS and Xenon experiments for spin-independent elastic scattering. Future experiments with directional sensitivity and mass bounds from accelerator experiments will help to distinguish between different halo models and/or constrain the contribution from cold flows.

Self-consistent nonspherical isothermal halos embedding zero-thickness disks

Disk-halo decompositions of galaxy rotation curves are generally performed in a parametric way. We construct self-consistent models of nonspherical isothermal halos embedding a zero-thickness disk, by assuming that the halo distribution function is a Maxwellian. The method developed here can be used to study other physically-based choices for the halo distribution function and the case of a disk accompanied by a bulge. In a preliminary investigation we note the existence of a fine tuning between the scalelengths R_{\Omega} and h, respectively characterizing the rise of the rotation curve and the luminosity profile of the disk, which surprisingly applies to both high surface brightness and low surface brightness galaxies. This empirical correlation identifies a much stronger conspiracy than the one required by the smoothness and flatness of the rotation curve (disk-halo conspiracy). The self-consistent models are characterized by smooth and flat rotation curves for very different disk-to-halo mass ratios, hence suggesting that conspiracy is not as dramatic as often imagined. For a typical rotation curve, with asymptotically flat rotation curve at V_{\infty} (the precise value of which can also be treated as a free parameter), and a typical density profile of the disk, self-consistent models are characterized by two dimensionless parameters, which correspond to the dimensional scales (the disk mass-to-light ratio M/L and the halo central density) of standard disk-halo decompositions. We show that if the rotation curve is decomposed by means of our self-consistent models, the disk-halo degeneracy is removed and typical rotation curves are fitted by models that are below the maximum-disk prescription. Similar results are obtained from a study of NGC 3198. Finally, we quantify the flattening of the spheroidal halo, which is significant, especially on the scale of the visible disk.

Dark matter dominance at all radii in the superthin galaxy UGC 7321

We model the shape and density profile of the dark matter halo of the low surface brightness, superthin galaxy UGC 7321, using the observed rotation curve and the Hi scale height data as simultaneous constraints. We treat the galaxy as a gravitationally coupled system of stars and gas, responding to the gravitational potential of the dark matter halo. An isothermal halo of spherical shape with a core density in the range of 0.039–0.057M⊙pc-3 and a core radius between 2.5 and 2.9kpc, gives the best fit to the observations for a range of realistic gas parameters assumed. We find that the best-fit core radius is only slightly higher than the stellar disc scale length (2.1kpc), unlike the case of the high surface brightness galaxies where the halo core radius is typically 3–4 times the disc scale length of the stars. Thus our model shows that the dark matter halo dominates the dynamics of the low surface brightness, superthin galaxy UGC 7321 at all radii, including the inner parts of the galaxy.