Central Density Cusps Research Articles

From inflation to dark matter halo profiles: the impact of primordial non-Gaussianities on the central density cusp

It has recently been shown that local primordial non-Gaussianities (PNG) with significant amplitude (|f NL| ∼ 1000), at small (Mpc) scales, can help in forming simulated galaxies with more disky baryonic kinematics than in the Gaussian case, while generating matter power spectra that can differ by up to 20% from the Gaussian case at non-linear scales. Here, we explore in detail the consequences of such small-scale PNG on the dark matter halo profiles. We show in particular that, for negative f NL, dark matter halos formed in collisionless simulations are not always well described by the traditional Navarro-Frenk-White (NFW) profiles, as supported by their sparsity distribution. We conclude that NFW profiles are not as clear attractors for the density profiles of dark matter halos in the presence of PNG than in the case of a Gaussian contrast density field. We show how alternatives to the NFW profile can describe halos both in the Gaussian and non-Gaussian cases. From the combination of our sparsity analysis and the quality of the adjustments of the density profiles with a minimal extension to NFW, we conclude that z = 1 halos carry the most interesting information about PNG.

Building stellar bulges and halo cores from massive clumps observed in the DYNAMO-HST sample

ABSTRACT We present N-body simulations of the process of bulge formation in disc galaxies due to inward migration of massive stellar clumps. The process is accompanied by dark halo heating, with a quasi-isothermal core replacing the initial central density cusp, transforming an initially dark matter dominated central region into a baryon dominated one. The characteristics of the clumps are chosen to be compatible with low redshift observations of stellar clumps in DYNAMO-HST galaxies, which may be relatively long lived in terms of being robust against internal starburst-instigated disruption. We thus test for disruption due to tidal stripping using different clump internal radial profiles; Plummer, Hernquist, and Jaffe, in ascending order of see per central density profile. Our calculations predict that in order for clump migration to be effective in building galactic bulges and dark halo cores, steeply increasing central clump profiles, or a less massive or less concentrated haloes, are preferred. The dependence on such factors may contribute to the diversity in observed total mass distributions and resulting rotation curves in galaxies. When the process is most efficient, a ‘bulge-halo conspiracy’, with a singular isothermal total density akin to that observed bright galaxies, results.

Massive prompt cusps: a new signature of warm dark matter

ABSTRACT Every dark matter halo and subhalo is expected to have a prompt ρ ∝ r−1.5 central density cusp, which is a relic of its condensation out of the smooth mass distribution of the early Universe. The sizes of these prompt cusps are linked to the scales of the peaks in the initial density field from which they formed. In warm dark matter (WDM) models, the smoothing scale set by free streaming of the dark matter can result in prompt cusps with masses of order 107 M⊙. We show that WDM models with particle masses ranging from 2 to 6 keV predict prompt cusps that could detectably alter the observed kinematics of Local Group dwarf galaxies. Thus, prompt cusps present a viable new probe of WDM. A prompt cusp’s properties are highly sensitive to when it formed, so prospects can be improved with a better understanding of when the haloes of the Local Group dwarfs originally formed. Tidal stripping can also affect prompt cusps, so constraints on satellite galaxy orbits can further tighten WDM inferences.

The proper motion of stars in dwarf galaxies: distinguishing central density cusps from cores

ABSTRACT We show that measuring the proper motion of ∼2000 stars within a dwarf galaxy, with an uncertainty of 1 km s−1 at most, can establish whether the dark matter (DM) density profile of the dwarf has a central core or cusp. We derive these limits by building mock star catalogues similar to those expected from future astrometric Theia-like missions and including celestial coordinates, radial velocity and proper motion of the stars. The density field of the DM halo of the dwarf is sampled from an extended Navarro–Frank–White (eNFW ) spherical model, whereas the number density distribution of the stars is a Plummer sphere. The velocity field of the stars is set according to the Jeans equations. A Monte Carlo Markov chain algorithm applied to a sample of N ≳ 2000 stars returns unbiased estimates of the eNFW DM parameters within $10{{\ \rm per\, cent}}$ of the true values and with 1σ relative uncertainties ≲ 20 per cent. The proper motions of the stars lift the degeneracy among the eNFW parameters which appears when the line-of-sight velocities alone are available. Our analysis demonstrates that, by estimating the log-slope of the mass density profile estimated at the half-light radius, a sample of N = 2000 stars can distinguish between a core and a cusp at more than 8σ. Proper motions also return unbiased estimates of the dwarf mass profile with 1σ uncertainties that decrease, on average, from 2.65 dex to 0.15 dex when the size of the star sample increases from N = 100 to N = 6000 stars. The measure of the proper motions can thus strongly constrain the distribution of DM in nearby dwarfs and provides fundamental contribution to understanding the nature and the properties of DM.

Searching for New Observational Signatures of the Dynamical Evolution of Star Clusters

Abstract We present a numerical study, based on Monte Carlo simulations, aimed at defining new empirical parameters measurable from observations and able to trace the different phases of the dynamical evolution of star clusters. As expected, a central density cusp, deviating from the King model profile, develops during the core collapse (CC) event. Although the slope varies during the post-CC oscillations, the cusp remains a stable feature characterizing the central portion of the density profile in all post-CC stages. We then investigate the normalized cumulative radial distribution (nCRD) drawn by all the cluster stars included within one half of the tridimensional half-mass radius (R ≤ 0.5r h ), finding that its morphology varies in time according to the cluster’s dynamical stage. To quantify these changes we defined three parameters: A 5, the area subtended by the nCRD within 5% of the half-mass radius, P 5, the value of the nCRD measured at the same distance, and S 2.5, the slope of the straight line tangent to the nCRD measured at R = 2.5%r h . The three parameters evolve similarly during the cluster’s dynamical evolution: after an early phase in which they are essentially constant, their values rapidly increase, reaching their maximum at the CC epoch and slightly decreasing in the post-CC phase, when their average value remains significantly larger than the initial one, in spite of some fluctuations. The results presented in this paper suggest that these three observable parameters are very promising empirical tools to identify the star cluster’s dynamical stage from observational data.

The abundance and structure of subhaloes near the free streaming scale and their impact on indirect dark matter searches

ABSTRACT The free streaming motion of dark matter particles imprints a cutoff in the matter power spectrum and set the scale of the smallest dark matter halo. Recent cosmological N-body simulations have shown that the central density cusp is much steeper in haloes near the free streaming scale than in more massive haloes. Here, we study the abundance and structure of subhaloes near the free streaming scale at very high redshift using a suite of unprecedentedly large cosmological N-body simulations, over a wide range of the host halo mass. The subhalo abundance is suppressed strongly below the free streaming scale, but the ratio between the subhalo mass function in the cutoff and no cutoff simulations is well fitted by a single correction function regardless of the host halo mass and the redshift. In subhaloes, the central slopes are considerably shallower than in field haloes, however, are still steeper than that of the NFW profile. Contrary, the concentrations are significantly larger in subhaloes than haloes and depend on the subhalo mass. We compare two methods to extrapolate the mass–concentration relation of haloes and subhaloes to z = 0 and provide a new simple fitting function for subhaloes, based on a suite of large cosmological N-body simulations. Finally, we estimate the annihilation boost factor of a Milky-Way-sized halo to be between 1.8 and 6.2.

Star clusters, self-interacting dark matter halos, and black hole cusps: The fluid conduction model and its extension to general relativity.

We adopt the fluid conduction approximation to study the evolution of spherical star clusters and self-interacting dark matter (SIDM) halos. We also explore the formation and dynamical impact of density cusps that arise in both systems due to the presence of a massive, central black hole. The large N-body, self-gravitating systems we treat are "weakly collisional": the mean free time between star or SIDM particle collisions is much longer than their characteristic crossing (dynamical) time scale, but shorter than the system lifetime. The fluid conduction model reliably tracks the "gravothermal catastrophe" in star clusters and SIDM halos without black holes. For a star cluster with a massive, central black hole, this approximation reproduces the familiar Bahcall-Wolf quasistatic density cusp for the stars bound to the black hole and shows how the cusp halts the "gravothermal catastrophe" and causes the cluster to re-expand. An SIDM halo with an initial black hole central density spike that matches onto to an exterior NFW profile relaxes to a core-halo structure with a central density cusp determined by the velocity dependence of the SIDM interaction cross section. The success and relative simplicity of the fluid conduction approach in evolving such "weakly collisional," quasiequilibrium Newtonian systems motivates its extension to relativistic systems. We present a general relativistic extension here.

Deadly Dark Matter Cusps versus Faint and Extended Star Clusters: Eridanus II and Andromeda XXV

Abstract The recent detection of two faint and extended star clusters in the central regions of two Local Group dwarf galaxies, Eridanus II and Andromeda XXV, raises the question of whether clusters with such low densities can survive the tidal field of cold dark matter halos with central density cusps. Using both analytic arguments and a suite of collisionless N-body simulations, I show that these clusters are extremely fragile and quickly disrupted in the presence of central cusps with . Furthermore, the scenario in which the clusters were originally more massive and sank to the center of the halo requires extreme fine tuning and does not naturally reproduce the observed systems. In turn, these clusters are long lived in cored halos, whose central regions are safe shelters for . The only viable scenario for hosts that have preserved their primordial cusp to the present time is that the clusters formed at rest at the bottom of the potential, which is easily tested by measurement of the clusters proper velocity within the host. This offers means to readily probe the central density profile of two dwarf galaxies as faint as and , in which stellar feedback is unlikely to be effective.

Bose-Einstein Condensate Dark Matter Halos Confronted with Galactic Rotation Curves

We present a comparative confrontation of both the Bose-Einstein Condensate (BEC) and the Navarro-Frenk-White (NFW) dark halo models with galactic rotation curves. We employ 6 High Surface Brightness (HSB), 6 Low Surface Brightness (LSB), and 7 dwarf galaxies with rotation curves falling into two classes. In the first class rotational velocities increase with radius over the observed range. The BEC and NFW models give comparable fits for HSB and LSB galaxies of this type, while for dwarf galaxies the fit is significantly better with the BEC model. In the second class the rotational velocity of HSB and LSB galaxies exhibits long flat plateaus, resulting in better fit with the NFW model for HSB galaxies and comparable fits for LSB galaxies. We conclude that due to its central density cusp avoidance the BEC model fits better dwarf galaxy dark matter distribution. Nevertheless it suffers from sharp cutoff in larger galaxies, where the NFW model performs better. The investigated galaxy sample obeys the Tully-Fisher relation, including the particular characteristics exhibited by dwarf galaxies. In both models the fitting enforces a relation between dark matter parameters: the characteristic density and the corresponding characteristic distance scale with an inverse power.

NON-UNIVERSALITY OF DARK-MATTER HALOS: CUSPS, CORES, AND THE CENTRAL POTENTIAL

Dark-matter halos grown in cosmological simulations appear to have central NFW-like density cusps with mean values of $d\log\rho/d\log r \approx -1$, and some dispersion, which is generally parametrized by the varying index $\alpha$ in the Einasto density profile fitting function. Non-universality in profile shapes is also seen in observed galaxy clusters and possibly dwarf galaxies. Here we show that non-universality, at any given mass scale, is an intrinsic property of DARKexp, a theoretically derived model for collisionless self-gravitating systems. We demonstrate that DARKexp - which has only one shape parameter, $\phi_0$ - fits the dispersion in profile shapes of massive simulated halos as well as observed clusters very well. DARKexp also allows for cored dark-matter profiles, such as those found for dwarf spheroidal galaxies. We provide approximate analytical relations between DARKexp $\phi_0$, Einasto $\alpha$, or the central logarithmic slope in the Dehnen-Tremaine analytical $\gamma$-models. The range in halo parameters reflects a substantial variation in the binding energies per unit mass of dark-matter halos.

Hierarchical Formation of Dark Matter Halos near the Cutoff Scale and Their Impact on Indirect Detections

AbstractThe smallest dark matter halos are formed first in the early universe (e.g., Hofmann et al. 2001; Berezinsky et al. 2003; Ishiyama et al. 2010). We present results of very large cosmological N-body simulations of the hierarchical formation and evolution of halos over a wide mass range, beginning from the formation of the smallest halos. In the largest simulation, the motions of 40963 particles in comoving boxes of side lengths 400 pc and 200 pc were followed. The particle masses were 3.4 × 10−11M⊙ and 4.3 × 10−12M⊙, ensuring that halos at the cutoff scale were represented by 30,000 and 230,000 particles, respectively. We found that the central density cusp is much steeper in these halos than in larger halos (dwarf-galaxy-sized to cluster-sized halos), and scales as ρ ∝ r-(1.5–1.3). The cusp slope gradually becomes shallower as the halo mass increases.The slope of halos 50 times more massive than the smallest halo is approximately −1.3. No strong correlation exists between inner slope and the collapse epoch. The cusp slope of halos above the cutoff scale seems to be reduced primarily due to major merger processes. The concentration, estimated at the present universe, is predicted to be 60–70, consistent with theoretical models and earlier simulations, and ruling out simple power law mass-concentration relations. Such halos could still exist in the present universe with the same steep density profiles. Strongly depending on the subhalo mass function and the adopted concentration model, the steeper inner cusps of halos near the cutoff scale enhance the annihilation luminosity of a Milky Way sized halo between 12 to 67 (Ishiyama 2014).

Central density cusps in the Lemaître-Tolman solutions

The character of the central density profile in the Lema\^{\i}tre-Tolman (LT) solutions plays a fundamental role in their application as cosmological models. This same character is studied here for these solutions used to model complete gravitational collapse. A necessary condition for the development of a black hole (not even locally naked singularities) is developed. This condition allows a finite (invariantly) defined range in central density cusps. If one demands no density cusps in the initial conditions, then this work shows that the LT solutions never produce even locally naked singularities.

Early flattening of dark matter cusps in dwarf spheroidal galaxies

Simulations of the clustering of cold dark matter yield dark-matter halos that have central density cusps, but observations of totally dark-matter dominated dwarf spheroidal galaxies imply that they do not have cuspy central density profiles. We use analytic calculations and numerical modelling to argue that whenever stars form, central density cusps are likely to be erased. Gas that accumulates in the potential well of an initially cuspy dark-matter halo settles into a disc. Eventually the surface density of the gas exceeds the threshold for fragmentation into self-gravitating clouds. The clouds are massive enough to transfer energy to the dark-matter particles via dynamical friction on a short time-scale. The halo's central cusp is heated to form a core with central logarithmic density slope gamma=0 before stellar feedback makes its impact. Since star formation is an inefficient process, the clouds are disrupted by feedback when only a small fraction of their mass has been converted to stars, and the dark matter dominates the final mass distribution.

Hierarchical formation of Dark Matter Halos near the Free Streaming Scale, and Their Implications on Indirect Dark Matter Search

AbstractThe smallest dark matter halos are formed first in the early universe. According to recent studies, the central density cusp is much steeper in these halos than in larger halos and scales as ρ ∝ r−(1.5−1.3). We present results of very large cosmological N-body simulations of the hierarchical formation and evolution of halos over a wide mass range, beginning from the formation of the smallest halos. We confirmed early studies that the inner density cusps are steeper in halos at the free streaming scale. The cusp slope gradually becomes shallower as the halo mass increases. The slope of halos 50 times more massive than the smallest halo is approximately -1.3. The concentration parameter is nearly independent of halo mass, and ruling out simple power law mass-concentration relations. The steeper inner cusps of halos near the free streaming scale enhance the annihilation luminosity of a Milky Way sized halo between 12 to 67%.

HIERARCHICAL FORMATION OF DARK MATTER HALOS AND THE FREE STREAMING SCALE

The smallest dark matter halos are formed first in the early universe. According to recent studies, the central density cusp is much steeper in these halos than in larger halos and scales as $\rho \propto r^{-(1.5-1.3)}$. We present results of very large cosmological $N$-body simulations of the hierarchical formation and evolution of halos over a wide mass range, beginning from the formation of the smallest halos. We confirmed early studies that the inner density cusps are steeper in halos at the free streaming scale. The cusp slope gradually becomes shallower as the halo mass increases. The slope of halos 50 times more massive than the smallest halo is approximately $-1.3$. No strong correlation exists between inner slope and the collapse epoch. The cusp slope of halos above the free streaming scale seems to be reduced primarily due to major merger processes. The concentration, estimated at the present universe, is predicted to be $60-70$, consistent with theoretical models and earlier simulations, and ruling out simple power law mass-concentration relations. Microhalos could still exist in the present universe with the same steep density profiles.

GAMMA-RAY SIGNAL FROM EARTH-MASS DARK MATTER MICROHALOS

Earth-mass dark matter microhalos with size of ~100 AUs are the first structures formed in the universe, if the dark matter of the Universe are made of neutralino. Here, we report the results of ultra-high-resolution simulations of the formation and evolution of these microhalos. We found that microhalos have the central density cusps of the form $\rho \propto r^{-1.5}$, much steeper than the cusps of larger dark halos. The central regions of these microhalos survive the encounters with stars except in very inner region of the galaxy down to the radius of a few hundreds pcs from the galactic center. The annihilation signals from nearest microhalos are observed as gamma-ray point-sources (radius less than 1'), with unusually large proper motions of ~0.2 degree per year. Their surface brightnesses are ~10% of that of the galactic center. Their S/N ratios might be better if they are far from the galactic plane. Luminosities of subhalos are determined only by their mass, and they are more than one order of magnitude luminous than the estimation by Springel et al. (2008): A boost factor can be larger than 1000. Perturbations to the millisecond pulsars by gravitational attractions of nearby earth-mass microhalos can be detected by the observations of Parkes Pulsar Timing Array (PPTA).

STATISTICAL MECHANICS OF COLLISIONLESS ORBITS. I. ORIGIN OF CENTRAL CUSPS IN DARK-MATTER HALOS

We present an equilibrium statistical mechanical theory of collisionless self-gravitational systems with isotropic velocity distributions. Compared to existing standard theories, we introduce two changes: (1) the number of possible microstates is computed in energy (orbit) space rather than phase space and (2) low occupation numbers are treated more appropriately than using Stirling's approximation. Combined, the two modifications predict that the relaxed parts of collisionless self-gravitating systems, such as dark-matter halos, have a differential energy distribution N(E) ~ [exp(phi_0 - E) - 1], dubbed "DARKexp". Such systems have central power-law density cusps rho(r) ~ r^-1, which suggests a statistical mechanical origin of cusps in simulated dark-matter halos.

EVOLUTION OF DARK MATTER PHASE-SPACE DENSITY DISTRIBUTIONS IN EQUAL-MASS HALO MERGERS

We use dissipationless N-body simulations to investigate the evolution of the true coarse-grained phase-space density distribution f(x,v) in equal-mass mergers between dark matter (DM) halos. The halo models are constructed with various asymptotic power-law indices ranging from steep cusps to core-like profiles and we employ the phase-space density estimator ``Enbid'' developed by Sharma & Steinmetz to compute f(x,v). The adopted force resolution allows robust phase-space density profile estimates in the inner ~1% of the virial radii of the simulated systems. We confirm that mergers result in a decrease of the coarse-grained phase-space density in accordance with expectations from Mixing Theorems for collisionless systems. We demonstrate that binary mergers between identical DM halos produce remnants that retain excellent memories of the inner slopes and overall shapes of the phase-space density distribution of their progenitors. The robustness of the phase-space density profiles holds for a range of orbital energies, and a variety of encounter configurations including sequences of several consecutive merger events, designed to mimic hierarchical merging, and collisions occurring at different cosmological epochs. If the progenitor halos are constructed with appreciably different asymptotic power-law indices, we find that the inner slope and overall shape of the phase-space density distribution of the remnant are substantially closer to that of the initial system with the steepest central density cusp. These results explicitly demonstrate that mixing is incomplete in equal-mass mergers between DM halos, as it does not erase memory of the progenitor properties. Our results also confirm the recent analytical predictions of Dehnen (2005) regarding the preservation of merging self-gravitating central density cusps.

Self-consistent triaxial de Zeeuw-Carollo models

We use the standard method of Schwarzschild to construct self-consistent solutions for the triaxial de Zeeuw & Carollo (1996) models with central density cusps. ZC96 models are triaxial generalizations of spherical γ-models ofDehnen whose densities vary as r -γ near the center and r -4 at large radii and hence, possess a central density core for γ = 0 and cusps for γ > 0. We consider four triaxial models from ZC96, two prolate triaxials: (p, q) = (0.65,0.60) with y = 1.0 and 1.5, and two oblate triaxials: (p, q) = (0.95, 0.60) with γ = 1.0 and 1.5. We compute 4500 orbits in each model for time periods of 10 5 T D . We find that a large fraction of the orbits in each model are stochastic by means of their nonzero Liapunov exponents. The stochastic orbits in each model can sustain regular shapes for ∼10 3 T D or longer, which suggests that they diffuse slowly through their allowed phase-space. With the exception of the oblate triaxial models with y = 1.0, our attempts to construct self-consistent solutions employing only the regular orbits fail for the remaining three models. However, the self-consistent solutions are found to exist for all models when the stochastic and regular orbits are treated in the same way because the mixing-time, ∼10 4 T D , is shorter than the integration time, 10 5 T D . Moreover, the fully-mixed solutions can also be constructed for all models when the stochastic orbits are fully mixed at 15 lowest energy shells. Thus, we conclude that the self-consistent solutions exist for our selected prolate and oblate triaxial models withy = 1.0 and 1.5.

Completely analytical families of anisotropic -models

We present new analytical distribution functions for anisotropic spherical galaxies. They have the density profiles of the γ-models, which allow a wide range of central density slopes, and are widely used to fit elliptical galaxies and the bulges of spiral galaxies. Most of our models belong to two two-parameter families. One of these parameters is the slope y of the central density cusp. The other allows a wide range of varying radial and tangential anisotropies, at either small or large radii. We give analytical formulas for their distribution functions, velocity dispersions, and the manner in which energy and transverse velocity are distributed between orbits. We also give some of their observable properties, including line-of-sight velocity profiles which have been computed numerically. Our models can be used to provide a useful tool for creating initial conditions for N-body and Monte Carlo simulations.