The stability of isothermal dark matter halos has been widely studied before. In this paper, we investigate the stability of non-isothermal fermionic dark matter halos. We show that in the presence of temperature gradient, the force due to the pressure has both inward and outward components. In some regions of halos, the inward force that provides stability is due to the pressure rather than gravity. Moreover, it is shown that higher temperature gradients lead to halos with lower mass and size. We prove that if the temperature is left as a free positive profile, one can place no phase-space lower bound on the mass of dark matter. For halos that are in the low degeneracy classic domain, we derive an analytic expression of their temperature in terms of their mass density and place an upper bound on the mass of dark matter by requiring that temperature is not negative. We then use the Burkert mass profile for the Milky Way to show that if the central temperature of the halo is a few Kelvins, the mass of dark matter cannot exceed a few keV.
Testing the isothermal Jeans model for self-interacting dark matter halos in the collapse phase
School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；School of Astronomy and Space Science, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）；Donostia International Physics Center (DIPC)（圣塞巴斯蒂安国际物理中心）；Department of Astronomy, Peking University（北京大学天文学系）；Kavli Institute for Astronomy and Astrophysics, Peking University（北京大学科维理天文与天体物理研究所）；Department of Physics and Astronomy, University of California, Riverside（加州大学河滨分校物理与天文学系）
N-body simulations predict that dark matter halos with different mass scales are described by a universal model, the Navarro-Frenk-White (NFW) density profiles. As a consequence of baryonic cooling effects, the halos will become more concentrated, and similar to an isothermal sphere over large range in radii ($\sim 300$ $h^{-1}$kpc). The singular isothermal sphere model however has to be truncated artificially at large radii since it extends to infinity. We model a massive galaxy halo as a combination of an isothermal sphere and an NFW density profile. We give an approximation for the mass con…
That the stellar halo of the Milky Way has a density profile which to first approximation satisfies $ρ\propto r^{-3}$ has been known for a long time. More recently, it has become clear that M31 also has such an extended stellar halo, which approximately follows the same radial scaling. Studies of distant galaxies have revealed the same phenomenology. Also, we now know that the density profiles of the globular cluster systems of our Galaxy and Andromeda to first approximation follow $ρ\propto r^{-3}$, $Σ\propto R^{-2}$ in projection. Recently, diffuse populations of stars have been detected sph…
Novel density profile for isothermal cores of dark matter halos
Massachusetts Institute of Technology（麻省理工学院）；University of Chicago（芝加哥大学）；University of Pennsylvania（宾夕法尼亚大学）；Princeton University（普林斯顿大学）；Center for Astrophysics, Harvard & Smithsonian（哈佛-史密松天体物理中心）；University of Rochester（罗切斯特大学）
We solve for the velocity fields of momentum-conserving supershells driven by feedback from supermassive black holes or nuclear star clusters (central massive objects: CMOs). We treat, for the first time, the case of CMOs embedded in gaseous protogalaxies with non-isothermal dark matter haloes having peaked circular-speed profiles. We find the CMO mass that is sufficient to drive any shell to escape any such halo. In the limit of large halo mass, relevant to real galaxies, this critical CMO mass depends only on the peak circular speed in the halo, scaling as M_crit \propto V_c,pk^4.
We develop a model of Bose-Einstein condensate dark matter halos with a solitonic core and an isothermal atmosphere based on a generalized Gross-Pitaevskii-Poisson equation [P.H. Chavanis, Eur. Phys. J. Plus 132, 248 (2017)]. This equation provides a heuristic coarse-grained parametrization of the ordinary Gross-Pitaevskii-Poisson equation accounting for violent relaxation and gravitational cooling. It involves a cubic nonlinearity taking into account the self-interaction of the bosons, a logarithmic nonlinearity associated with an effective temperature, and a source of dissipation. It leads t…
In this paper, we formulate a new model of density distribution for halos made of warm dark matter (WDM) particles. The model is described by a single microphysics parameter - the mass (or, equivalently, the maximal value of the initial phase-space density distribution) of dark matter particles. Given the WDM particle mass and the parameters of a dark matter density profile at the halo periphery, this model predicts the inner density profile. In case of initial Fermi-Dirac distribution, we successfully reproduce cored dark matter profiles from N-body simulations. Also, we calculate the core ra…
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_Ω and h, respectively characterizing the rise of the rotation curve and the lumi…
We solve for the velocity fields of momentum-conserving supershells driven from galaxy centres by steady winds from supermassive black holes or nuclear star clusters (central massive objects: CMOs). We look for the critical CMO mass that allows such a shell to escape from its host galaxy. In the case that the host galaxy dark matter halo is a singular isothermal sphere, we find that the critical CMO mass derived by King, which scales with the halo velocity dispersion as M_crit \propto σ^4, is necessary, but not by itself sufficient, to drive shells to large radii in the halo. Furthermore, a CM…
We study fundamental properties of steady, spherically symmetric, isothermal galactic outflow in appropriate gravitational potential models. We aim at constructing a universal scale free theory not only for galactic winds, but also for winds from clusters/groups of galaxies. In particular, we consider effects of mass-density distribution on the formation of transonic galactic outflows under several models of the density distribution profile predicted by cosmological simulations of structure formation based on the cold dark matter (CDM) scenario. In this study, we have clarified that there exis…
Recent claims of observational evidence for self-interacting dark matter (SIDM) have relied on a semi-analytic method for predicting the density profiles of galaxies and galaxy clusters containing SIDM. We present a thorough description of this method, known as isothermal Jeans modelling, and then test it with a large ensemble of haloes taken from cosmological simulations. Our simulations were run with cold and collisionless dark matter (CDM) as well as two different SIDM models, all with dark matter only variants as well as versions including baryons and relevant galaxy formation physics. Usi…
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 [P.H. Chavanis, Eur. Phys. J. Plus {\bf 132}, 248 (2017)]) involving a logarithmic nonlinearity associated with an effective temperatu…
In this paper, the recently proposed mass dimension one fermionic field is supposed to be responsible for the dark matter halo around galactic nuclei, through the quantum degeneracy pressure effect of the field. It will be showed that the mass-ratio relation for dwarf galaxies can be well explained for a particle dark matter mass of about $100 - 200$eV. For a large galaxy, as Milky Way, the observational data for rotation curve can be well reproduced for a particle mass of about 23eV, with the addition of other substructures.
Direct detection of Weakly Interacting Massive Particle (WIMP) candidates of Dark Matter (DM) is studied within the context of a self-consistent truncated isothermal model of the finite-size dark halo of the Galaxy based on the "King model" of the phase space distribution function of collisionless DM particles. Our halo model takes into account the modifications of the phase-space structure of the halo due to the gravitational influence of the observed visible matter in a self-consistent manner. The parameters of the halo model are determined by a fit to a recently determined circular rotation…
We have performed a series of numerical experiments to investigate how the primordial thermal velocities of fermionic dark matter particles affect the physical and phase space density profiles of the dark matter haloes into which they collect. The initial particle velocities induce central cores in both profiles, which can be understood in the framework of phase space density theory. We find that the maximum coarse-grained phase space density of the simulated haloes (computed in 6 dimensional phase space using the EnBid code) is very close to the theoretical fine-grained upper bound, while the…
We discuss the nature of phase transitions in the fermionic King model which describes tidally truncated quantum self-gravitating systems. This distribution function takes into account the escape of high energy particles and has a finite mass. On the other hand, the Pauli exclusion principle puts an upper bound on the phase space density of the system and stabilizes it against gravitational collapse. As a result, there exists a statistical equilibrium state for any accessible values of energy and temperature. We plot the caloric curves and investigate the nature of phase transitions as a funct…
Galaxies show different halo scaling relations such as the Radial Acceleration Relation, the Mass Discrepancy Acceleration Relation (MDAR) or the dark matter Surface Density Relation (SDR). At difference with traditional studies using phenomenological $Λ$CDM halos, we analyze the above relations assuming that dark matter (DM) halos are formed through a Maximum Entropy Principle (MEP) in which the fermionic (quantum) nature of the DM particles is dully accounted for. For the first time a competitive DM model based on first physical principles, such as (quantum) statistical-mechanics and thermod…
We study the core mass -- halo mass relation of bosonic dark matter halos, in the form of self-gravitating Bose-Einstein condensates, harbouring a supermassive black hole. We use the ``velocity dispersion tracing'' relation according to which the velocity dispersion in the core $v_c^2\sim GM_c/R_c$ is of the same order as the velocity dispersion in the halo $v_h^2\sim GM_h/r_h$ (this relation can be justified from thermodynamical arguments) and the approximate analytical mass-radius relation of the quantum core in the presence of a central black hole obtained in our previous paper [P.H. Chavan…
The atomic hydrogen gas (HI) disk in the outer region (beyond ~10 kpc from the centre) of Milky Way can provide valuable information about the structure of the dark matter halo. The recent 3-D thickness map of the outer HI disk from the all sky 21-cm line LAB survey, gives us a unique opportunity to investigate the structure of the dark matter halo of Milky Way in great detail. A striking feature of this new survey is the North-South asymmetry in the thickness map of the atomic hydrogen gas. Assuming vertical hydrostatic equilibrium under the total potential of the Galaxy, we derive the model …
We derive the main physical galaxy properties: mass, halo radius, phase space density and velocity dispersion from a semiclassical gravitational approach in which fermionic WDM is treated quantum mechanically. They turn out to be compatible with observations. Pauli Principle implies for the fermionic DM phase-space density Q(r) = rho(r)/sigma^3(r) the quantum bound Q(r) < K m^4/hbar^3, where m is the DM particle mass, sigma(r) is the DM velocity dispersion and K is a pure number of order one which we estimate. N-body galaxy simulations produce a divergent Q(r) at r = 0 violating this quantum b…
We consider the possibility that dark matter halos are made of quantum particles such as fermions or bosons in the form of Bose-Einstein condensates. In that case, they generically have a "core-halo" structure with a quantum core that depends on the type of particle considered and a halo that is relatively independent of the dark matter particle and that is similar to the NFW profile of cold dark matter. We model the halo by an isothermal gas with an effective temperature $T$. We then derive the core mass -- halo mass relation $M_c(M_v)$ of dark matter halos from an effective thermodynamical m…
The back-reaction of baryons on the dark matter halo density profile is of great interest, not least because it is an important systematic uncertainty when attempting to detect the dark matter. Here, we draw on a large suite of high resolution cosmological hydrodynamical simulations, to systematically investigate this process and its dependence on the baryonic physics associated with galaxy formation. The inclusion of baryons results in significantly more concentrated density profiles if radiative cooling is efficient and feedback is weak. The dark matter halo concentration can in that case in…
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 $δ=73^{\circ}$ towards the centra…
We present rotation curve fits to 175 late-type galaxies from the Spitzer Photometry & Accurate Rotation Curves (SPARC) database using seven dark matter (DM) halo profiles: pseudo-isothermal (pISO), Burkert, Navarro-Frenk-White (NFW), Einasto, Di Cintio (2014, DC14), coreNFW, and a new semi-empirical profile named Lucky13. We marginalize over stellar mass-to-light ratio, galaxy distance, disk inclination, halo concentration and halo mass (and an additional shape parameter for Einasto) using a Markov Chain Monte Carlo method. We find that cored halo models such as the DC14 and Burkert profiles …
We study a sample of 39 massive early-type lens galaxies at redshift z < 0.3 to determine the slope of the average dark-matter density profile in the innermost regions. We keep the strong lensing and stellar population synthesis modeling as simple as possible to measure the galaxy total and luminous masses. By rescaling the values of the Einstein radius and dark-matter projected mass with the values of the luminous effective radius and mass, we combine all the data of the galaxies in the sample. We find that between 0.3 and 0.9 times the value of the effective radius the average logarithmic sl…
An Enhanced Isothermal Jeans Approach to Constraining Dark Matter Self-Interactions from Galactic Kinematics
Peking University（北京大学）；Kavli Institute for Astronomy and Astrophysics, Peking University（北京大学 Kavli 天体物理与天文研究所）；School of Physics and Astronomy, Beijing Normal University（北京师范大学物理学院）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；School of Astronomy and Space Science, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）；Shanghai Astronomical observatory, Chinese Academy of Sciences（中国科学院上海天文台）
A cylindrical model for the dark matter halo of disk galaxies is developed. At the center of the cylinder, in the plane perpendicular to the long axis, the rotation curve is constant for distances much less than the cylinder length and Keplerian at much greater distances. The rotation curve is equivalent to the spherical truncated flat (TF) profile, a model derived empirically from the radial velocity dispersion of the Milky Way dark halo. It is shown that an isothermal, self-gravitating cylinder of length 89 kpc can account for the observed radial velocity dispersion of the Milky Way dark hal…
Hot ionized gas is important in the baryon cycle of galaxies and contributes the majority of their ``missing baryons''. Until now, most semi-analytic models of galaxy formation have paid little attention to hot gaseous haloes and their X-ray emission. In this paper, we adopt the one-dimensional model from Sharma et al. instead of the isothermal sphere to describe the radial distribution of hot gas in the L-Galaxies semi-analytic model. The hot gas halo can be divided into two parts according to the ratio of the local thermal instability time-scale and the free-fall time-scale: a cool core with…
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 pha…
We combine the isothermal Jeans model and the model of adiabatic halo contraction into a simple semi-analytic procedure for computing the density profile of self-interacting dark-matter (SIDM) haloes with the gravitational influence from the inhabitant galaxies. We show that the model agrees well with cosmological SIDM simulations over the entire core-forming stage and up to the onset of gravothermal core-collapse. Using this model, we show that the halo response to baryons is more diverse in SIDM than in CDM and depends sensitively on galaxy size, a desirable link in the context of the struct…
Dwarf spheroidal galaxies (dSphs) are the most compact dark matter-dominated objects observed so far. The Pauli exclusion principle limits the number of fermionic dark matter particles that can compose a dSph halo. This results in a well-known lower bound on their particle mass. So far, such bounds were obtained from the analysis of individual dSphs. In this paper, we model dark matter halo density profiles via the semi-analytical approach and analyse the data from eight `classical' dSphs assuming the same mass of dark matter fermion in each object. First, we find out that modelling of Carina …
N-body simulations predict that dark matter haloes are described by specific density profiles on both galactic- and cluster-sized scales. Weak gravitational lensing through the measurements of their first and second order properties, shear and flexion, is a powerful observational tool for investigating the true shape of these profiles. One of the three-parameter density profiles recently favoured in the description of dark matter haloes is the Einasto profile. We present exact expressions for the shear and the first and second flexions of Einasto dark matter haloes derived using a Mellin-trans…
The 21-cm signal from the epoch of cosmic dawn prior to reionization consists of a promising observable to gain new insights into the dark matter (DM) sector. In this paper, we investigate its potential to constrain mixed (cold + non-cold) dark matter scenarios that are characterised by the non-cold DM fraction ($f_{\rm nCDM}$) and particle mass ($m_{\rm nCDM}$). As non-cold DM species, we investigate both a fermionic (sterile neutrino) and a bosonic (ultra-light axion) particle. We show how these scenarios affect the global signal and the power spectrum using a halo-model implementation of th…
Current theories of structure formation predict specific density profiles of galaxy dark matter haloes, and with weak gravitational lensing we can probe these profiles on several scales. On small scales, higher-order shape distortions known as flexion add significant detail to the weak lensing measurements. We present here the first detection of a galaxy-galaxy flexion signal in space-based data, obtained using a new Shapelets pipeline introduced here. We combine this higher-order lensing signal with shear to constrain the average density profile of the galaxy lenses in the Hubble Space Telesc…
We used high resolution dark matter only cosmological simulations to investigate the structural properties of Lambda Cold Dark Matter ($Λ$CDM) haloes over cosmic time. The haloes in our study range in mass from $\sim 10^{10}$ to $\sim 10^{12} \mathrm{M}_\odot$, and are resolved with $10^5$ to $10^7$ particles. We fit the spherically averaged density profiles of DM haloes with the three parameter Einasto function. For our sample of haloes, the Einasto shape parameter, $α$, is uncorrelated with the concentration, $c$, at fixed halo mass, and at all redshifts. Previous reports of an anti-correlat…
We define and study statistical ensembles of matter density profiles describing spherically symmetric, virialized dark matter haloes of finite extent with a given mass and total gravitational potential energy. Our ensembles include spatial degrees of freedom only, a microstate being a spherically symmetric matter density function. We provide an exact solution for the grand canonical partition functional, and show its equivalence to that of the microcanonical ensemble. We obtain analytically the mean profiles that correspond to an overwhelming majority of microstates. All such profiles have an …
Spherical systems with polytropic equations of state are of great interest in astrophysics. They are widely used to describe neutron stars, red giants, white dwarfs, brown dwarfs, main sequence stars, galactic halos, and globular clusters of diverse sizes. In this paper we construct analytically a family of self-gravitating spherical models in the post-Newtonian approximation of general relativity. These models present interesting cusps in their density profiles which are appropriate for the modeling of galaxies and dark matter halos. The systems described here are anisotropic in the sense tha…
After deducing the density profiles and gravitational potential functions of eight galaxies from the rotation velocity data from THINGS, we find that the density decreases exponentially with the potential in substantial regions of the haloes. Such behavior is in agreement with that of a single-component isothermal Boltzmann gas, and suggests that an effective description in terms of a Boltzmann gas is possible for dark matter in these regions. This could be an indication that dark matter self-interactions are sufficient in strength and number to lead to thermal equilibrium in these regions. We…
A new model of the Milky Way (MW) halo component of the dispersion measure (DM) for extragalactic sources, such as fast radio bursts (FRBs), is presented in light of recent diffuse X-ray observations. In addition to the spherical component of isothermal gas ($kT\sim0.3$ keV) in hydrostatic equilibrium with the Galactic gravitational potential, our model includes a disk-like non-spherical hot gas component to reproduce the directional dependence of the observed X-ray emission measure (EM). The total gas mass ($1.2\times10^{11}\,M_{\odot}$) is dominated by the spherical component, and is consist…
Inverse mass cascade is a key feature of the intermediate statistically steady state for self-gravitating collisionless dark matter flow (SG-CFD). This paper focus on effects of mass cascade on halo energy, momentum, dispersion, size, and density. Halo with fast mass accretion has an expanding core. Mass cascade forms a new layer of mass that deforms the original halo and induces nonzero radial flow (outwards in core and inwards in outer regions). The inward/outward flow leads to an extra length scale (scale radius) that is not present in isothermal profile. Halo concentration c=3.5 can be der…
We present results for a galaxy-galaxy lensing study based on imaging data from the Canada-France-Hawaii Telescope Legacy Survey Wide. From a 12 million object multi-colour catalogue for 124 deg^2 of photometric data in the u*g'r'i'z' filters we compute photometric redshifts (with a scatter of σ_{Δz/(1+z)} = 0.033 and an outlier rate of η=2.0 per cent for i'<=22.5) and extract galaxy shapes down to i'=24.0. We select a sample of lenses and sources with 0.05 < z_d <= 1 and 0.05 < z_s <= 2. We fit three different galaxy halo profiles to the lensing signal, a singular isothermal sphere (SIS), a t…
Australia Telescope Compact Array HI-line observations of the nearby dwarf galaxy NGC 1705 are presented. The data are used to trace the gravitational potential of the galaxy out to several stellar disc scale lengths. A rotation curve is derived for the system and used to generate mass models. Dark matter dominates the gravitational potential at nearly all galactocentric radii. NFW and pseudo-isothermal sphere halo parameterisations allowing for good reproductions of the observations. The models suggest NGC 1705 to have a dark matter halo that it much denser and more compact than previously th…
(Abridged) The analysis of the rotation curves (RCs) of spiral galaxies provides an efficient diagnostic for studying the properties of dark matter halos and their relations with the baryonic material. We have modeled the RCs of galaxies from The HI Nearby Galaxy Survey (THINGS) with the Einasto halo model, which has emerged as the best-fitting model of the halos arising in dissipationless cosmological N-body simulations. We find that the RCs are significantly better fit with the Einasto halo than with either a pseudo-isothermal sphere (Iso) or Navarro-Frenk-White (NFW) halo models. In our bes…
We study the directional effect of the expected axion dark matter signal in a resonant cavity of an axion haloscope detector, for cavity geometries not satisfying the condition that the axion de Broglie wavelength $λ_a$ is sufficiently larger than the cavity dimensions $L$ for a fully coherent conversion, i.e. $λ_a \gtrsim 2πL$. We focus on long thin cavities immersed in dipole magnets and find, for appropriately chosen cavity lengths, an O(1) modulation of the signal with the cavity orientation with respect the momentum distribution of the relic axion background predicted by the isothermal sp…
