Central Density Cusps Research Articles

A Quantitative Study of Interacting Dark Matter in Halos

We study the evolution of Hernquist profile galaxies in the presence of self-interacting dark matter (SIDM), where the properties of the dark matter can be parameterized by one number, DM = σDMMT/a2, for a halo of mass MT and break radius a. While the halos form constant-density cores of size ~a/2 on the core-radius relaxation timescale (trc 1.7tdyn/DM), core collapse begins shortly thereafter, and a steeper 1/r2 central density cusp starts forming faster than predicted by two-body relaxation. The formation of the steeper central cusp is accelerated if the cooling baryons adiabatically compress the dark matter. The natural consequence of SIDM is to exacerbate rather than to mitigate astrophysical problems created by dark matter density cusps.

Formation of Cuspy Density Profiles: A Generic Feature of Collisionless Gravitational Collapse

Using the formalism of the spherical infall model, the structure of collapsed and virialized dark halos is calculated for a variety of scale-free initial conditions. In spite of the scale-free cosmological nature of the problem, the collapse of individual objects is not self-similar. Unlike most of previous calculations, the dynamics used here relies only on adiabatic invariants and not on self-similarity. This Letter focuses on the structure of the innermost part of the collapsed halos and addresses the problem of central density cusps. The slopes of density profiles at 1% of virial radius are calculated for a variety of cosmological models and are found to vary with the mass of the halos, power spectrum of density fluctuations, and Ω0. The inner slopes range between r-2.3 and r-2 with the limiting case of r-2 reached for the largest masses. The steep cusps found here correspond to the limiting case where all particles move on radial orbits. The introduction of angular momentum will make the density profile shallower. We expect this to resolve the discrepancy found between the calculated profiles and the ones found in high-resolution N-body simulations, where the exponent ranges from -0.5 to -1.5. The robust prediction here is that collisionless gravitational collapse in an expanding universe is expected to form density cusps and not halos with a core structure.

Annihilating cold dark matter

Structure formation with cold dark matter (CDM) predicts halos with a central density cusp, which are observationally disfavored. If CDM particles have an annihilation cross section sigmav approximately 10(-29)(m/GeV) cm(2), then annihilations will soften the cusps. We discuss plausible scenarios for avoiding the early Universe annihilation catastrophe that could result from such a large cross section. The predicted scaling of core density with halo mass depends upon the velocity dependence of sigmav, and s-wave annihilation leads to a core density nearly independent of halo mass, which seems consistent with observations.

New dark matter physics: Clues from halo structure

We examine the effect of primordial dark matter velocity dispersion and/or particle self-interactions on the structure and stability of galaxy halos, especially with respect to the formation of substructure and central density cusps. Primordial velocity dispersion is characterized by a ``phase density'' $Q\ensuremath{\equiv}\ensuremath{\rho}/〈{v}^{2}{〉}^{3/2},$ which for relativistically decoupled relics is determined by particle mass and spin and is insensitive to cosmological parameters. Finite Q leads to small-scale filtering of the primordial power spectrum, which reduces substructure, and limits the maximum central density of halos, which eliminates central cusps. The relationship between Q and halo observables is estimated. The primordial Q may be preserved in the cores of halos and if so leads to a predicted relation, closely analogous to that in degenerate dwarf stars, between the central density and velocity dispersion. Classical polytrope solutions are used to model the structure of halos of collisional dark matter, and to show that self-interactions in halos today are probably not significant because they destabilize halo cores via heat conduction. Constraints on masses and self-interactions of dark matter particles are estimated from halo stability and other considerations.

Collisional Dark Matter and the Structure of Dark Halos.

We study how the internal structure of dark halos is affected if cold dark matter particles are assumed to have a large cross section for elastic collisions. We identify a cluster halo in a large cosmological N-body simulation and resimulate its formation with progressively increasing resolution. We compare the structure found in the two cases in which dark matter is treated as collisionless or as a fluid. For the collisionless case, the overall ellipticity of the cluster, the central density cusp, and the amount of surviving substructure are all similar to those found in earlier high-resolution simulations. Collisional dark matter results in a cluster that is more nearly spherical at all radii, has a steeper central density cusp, and has less-but still substantial-surviving substructure. As in the collisionless case, these results for a "fluid" cluster halo are expected to carry over approximately to smaller mass systems. The observed rotation curves of dwarf galaxies then argue that self-interacting dark matter can only be viable if intermediate cross sections produce structure that does not lie between the extremes we have simulated.

Rates of tidal disruption of stars by massive central black holes

There is strong evidence for some kind of massive dark object in the centres of many galaxy bulges. The detection of flares from tidally disrupted stars could confirm that these objects are black holes (BHs). Here we present calculations of the stellar disruption rates in detailed dynamical models of real galaxies, taking into account the refilling of the loss cone of stars on disruptable orbits by two-body relaxation and tidal forces in non-spherical galaxies. The highest disruption rates (one star per 104 yr) occur in faint (L≲1010 L⊙) galaxies, which have steep central density cusps. More luminous galaxies are less dense and have much longer relaxation times and more massive BHs. Dwarf stars in such galaxies are swallowed whole by the BH and hence do not emit flares; giant stars could produce flares as often as every 105 yr, although the rate depends sensitively on the shape of the stellar distribution function. We discuss the possibility of detecting disruption flares in current supernova searches. The total mass of stars consumed over the lifetime of the galaxy is of the order of 106 M⊙, independent of galaxy luminosity; thus, disrupted stars may contribute significantly to the present BH mass in galaxies fainter than ∼109 L⊙.

Regular and Chaotic Dynamics of Triaxial Stellar Systems

We use Laskar's frequency mapping technique to study the dynamics of triaxial galaxies with central density cusps and nuclear black holes. For ensembles of 10^4 orbits, we numerically compute the three fundamental frequencies of the motion, allowing us to map out the Arnold web. We also compute diffusion rates of stochastic orbits in frequency space. The objects of fundamental importance in structuring phase space are found to be the 3-dimensional resonant tori; even when stable, such tori are not necessarily associated with periodic orbits as in systems with only two degrees of freedom. Boxlike orbits are generically stochastic, but some tube orbits are stochastic as well. The spectrum of diffusion rates for box-like orbits at a given energy is well approximated as a power law over at least six decades. Models with high central concentrations -- steep central cusps or massive black holes -- exhibit the most stochasticity. A black hole with a mass of 0.3% the mass of the galaxy is as effective as the steepest central density cusp at inducing stochastic diffusion. There is a transition to global stochasticity in box-like phase space when the mass of a central black hole exceeds 2% the galaxy mass. We predict a greater average degree of dynamical evolution in faint ellipticals, due to their high central densities and short crossing times. The evolution time is estimated to be shorter than a galaxy lifetime for absolute magnitudes fainter than about -19 or -20, consistent with the observed change in many elliptical galaxy properties at this luminosity.

11.14. Massive black hole binaries in galactic nuclei

Many large ellipticals were believed to have large, flat core, of which the radius is typically a few percents of the effective radius (e.g., Lauer, 1985). However, HST observations (e.g., Lauer et al., 1995) have revealed that they are not flat cores at all. The “cores” observed by HST are actually very shallow central density cusps (ρ ~ r−0.5~–1). Such a shallow cusp poses a serious problem to almost any scenario of the formation of ellipticals. If these ellipticals do not have central black holes (MBHs), we are faced with very strange structure with the velocity dispersion decreasing inward. Neither dissipationless/dissipational collapse nor merging have been able to make such a density distribution.

Mass Segregation and Equipartition of Energy in Two Globular Clusters with Central Density Cusps.

view Abstract Citations (25) References (42) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Mass Segregation and Equipartition of Energy in Two Globular Clusters with Central Density Cusps. Sosin, Craig Abstract We begin by presenting the analysis of a set of deep B- and V-band images of the central density cusp of the globular cluster M30 (NGC 7099), taken with the Faint Object Camera aboard the Hubble Space Telescope. These images are the first to resolve lower-mass main-sequence stars in the cluster's central 10". From the positions of individual stars, we measure an improved position for the cluster center; this new position is 2".6 from the previously known position. We find no evidence of a "flat," constant-surface-density core; however, the data do not rule out the presence of a core of radius up to 1".9 (95% confidence level). We measure a logarithmic cusp slope (d log σ/d log r) of - 0.76±0.07 (1-sigma) for stars with masses between 0.69 and 0.76 Msun, and - 0.82±0.11 for stars with masses between 0.57 and 0.69 Msun. We also compare the overall mass function (MF) of the cluster cusp with the MF of a field at r =4'.6 (near the cluster half-mass radius). The observed degree of mass segregation is well matched by the predictions of an isotropic, multimass King model. We then use the Jeans equation to compare the structure of M30 with that of M15, another cusped cluster, using data from this and a previous paper. We find that M30 is very close to achieving equipartition of energy between stellar species, at least over the observed range in mass and radius, while M15 is not. This difference may be a result of the longer relaxation time in the observed field in M15. The data also suggest that the degree of mass segregation within the two cluster cusps is smaller than one would expect from the measurements at larger radius. If so, this phenomenon might be the result of gravothermal oscillations, of centrally-concentrated populations of binaries, or of a ∼103 Msun black hole in one or more clusters. Publication: The Astronomical Journal Pub Date: October 1997 DOI: 10.1086/118581 arXiv: arXiv:astro-ph/9707251 Bibcode: 1997AJ....114.1517S Keywords: GLOBULAR CLUSTERS: INDIVIDUAL: M30; GLOBULAR CLUSTERS: INDIVIDUAL: M15; GALAXY: STELLAR CONTENT; Astrophysics E-Print: doi:10.1086/118581 full text sources arXiv | ADS | data products SIMBAD (3) MAST (1) ESA (1)

Periodic Orbits in Triaxial Galaxies with Weak Cusps.

The orbital structure of triaxial models with weak central density cusps, $\rho\propto r^{-\gamma}, gamma < 1$, is investigated. The stability of the $x$- (long-) axis orbit -- and hence the existence of box orbits -- depends sensitively on $\gamma$; the range of model shapes for which the $x$-axis orbit is stable becomes progressively smaller as $\gamma$ approaches one. The banana and fish boxlets in the $x-z$ (long axis-short axis) plane are stable over a wide range of model parameters. The boxlets in the $x-y$ and $y-z$ planes are generally vertically unstable.

Dynamical Stability ofN‐Body Models for M32 with a Central Black Hole

We study the stability of stellar dynamical equilibrium models for M32. Kinematic observations show that M32 has a central dark mass of ~3 × 106 M☉, most likely a black hole, and a phase-space distribution function that is close to the form f = f(E, Lz). M32 is also rapidly rotating; 85%-90% of the stars have the same sense of rotation around the symmetry axis. Previous work has shown that flattened, rapidly rotating two-integral models can be bar-unstable. We have performed N-body simulations to test whether this is the case for M32. This is the first stability analysis of two-integral models that have both a central density cusp and a nuclear black hole. Particle realizations with N = 512,000 were generated from distribution functions that fit the photometric and kinematic data of M32. We constructed equal-mass particle realizations and also realizations with a mass spectrum to improve the central resolution. Models were studied for two representative inclinations, i = 90° (edge-on) and i = 55°, corresponding to intrinsic axial ratios of q = 0.73 and q = 0.55, respectively. The time evolution of the models was calculated with a self-consistent field code on a Cray T3D parallel supercomputer. We find both models to be dynamically stable. This implies that they provide a physically meaningful description of M32 and that the inclination of M32 (and hence its intrinsic flattening) cannot be strongly constrained through stability arguments. Previous work on the stability of f(E, Lz) models has shown that the bar mode is the most common unstable mode for systems rounder than q ≈ 0.3 (i.e., E7) and that the likelihood for this mode to be unstable increases with flattening and rotation rate. The f(E, Lz) models studied for M32 are not bar-unstable, and M32 has a higher rotation rate than nearly all other elliptical galaxies. This suggests that f(E, Lz) models constructed to fit data for real elliptical galaxies will generally be stable, at least for systems rounder than q 0.55, and possibly for flatter systems as well.

Deep HST/FOC Imaging of the Central Density Cusp of the Globular Cluster M15

Using the Faint Object Camera on the repaired Hubble Space Telescope, we have observed two fields in the globular cluster M15: the central density cusp, and a field at r = 20''. These are the highest-resolution images ever taken of this cluster's dense core, and are the first to probe the distribution of stars well below the main-sequence turnoff. After correction for incompleteness, we measure a logarithmic cusp slope (d log \sigma / d log r) of -0.70 +- 0.05 (1-sigma) for turnoff (~ 0.8 \Msun) stars over the radial range from 0.3'' to 10''; this slope is consistent with previous measurements. We also set an approximate upper limit of ~1.5'' (90% confidence limit) on the size of any possible constant-surface-density core, but discuss uncertainties in this limit that arise from crowding corrections. We find that fainter stars in the cusp also have power-law density profiles: a mass group near 0.7 \Msun has a logarithmic slope of -0.56 +- 0.05 (1-sigma) over the radial range from 2'' to 10''. Taken together, the two slopes are not well matched by the simplest core-collapse or black-hole models. We also measure a mass function at r = 20'', outside of the central cusp. Both of the FOC fields show substantial mass segregation, when compared with a mass function measured with the WFPC2 at r = 5'. In comparing the overall mass functions of the two FOC fields and the r = 5' field, we find that the radial variation of the mass function is somewhat less than that predicted by a King-Michie model of the cluster, but greater than that predicted by a Fokker-Planck model taken from the literature.

Triaxial Galaxies with Cusps

We have constructed fully self-consistent models of triaxial galaxies with central density cusps. The triaxial generalizations of Dehnen's spherical models are presented, which have densities that vary as 1/r^gamma near the center and 1/r^4 at large radii. We computed libraries of about 7000 orbits in each of two triaxial models with gamma=1 (weak cusp) and gamma=2 (strong cusp); these two models have density profiles similar to those of the core and power-law galaxies observed by HST. Both mass models have short-to-long axis ratios of 1:2 and are maximally triaxial. A large fraction of the orbits in both model potentials are stochastic, as evidenced by their non-zero Liapunov exponents. We show that most of the stochastic orbits in the strong- cusp potential diffuse relatively quickly through their allowed phase-space volumes, on time scales of 100 - 1000 dynamical times. Stochastic orbits in the weak-cusp potential diffuse more slowly, often retaining their box-like shapes for 1000 dynamical times or longer. Attempts to construct self- consistent solutions using just the regular orbits failed for both mass models. Quasi-equilibrium solutions that include the stochastic orbits exist for both models; however, real galaxies constructed in this way would evolve near the center due to the continued mixing of the stochastic orbits. We attempted to construct more nearly stationary models in which stochastic phase space was uniformly populated at low energies. These ``fully mixed'' solutions were found to exist only for the weak-cusp potential. No significant fraction of the mass could be placed on fully-mixed stochastic orbits in the strong-cusp model, demonstrating that strong triaxiality can be inconsistent with a high central density.

Bars in Cusps

In order to investigate the stability properties of galaxy models with central density cusps, TV-body simulations of oblate models with density ρ ∝ m–1 (m+a)–3 where m2=R2+[z/q]2 and distribution functions f(E, Lz) (computed as in Dehnen, 1995) have been performed with the following results. 1.An E7 model with identical amounts of stars of either sense of rotation was stable over 30 tdyn(r=a). This is interesting for the bending instability has been argued to set in at about this flattening and be responsible for the absence of flatter elliptical galaxies (Merritt &amp; Sellwood, 1994).2.Rapidly rotating E≳E5 models quickly form weak bars inside the cusp, which are stronger for the more flattened, faster rotating initial configurations. The bars grow in a self similar fashion from inside out: the pattern speed decreases with increasing bar length and time. This process is initiated at the origin, where, because of finite AT, the actual density no longer follows the power law, and stops when the edge of the cusp is reached. A typical example is given in the figure showing the z-y-coordinates of particles with |z|&lt;0.1a after ≃20tdyn(r=a) for an initially rapidly rotating E7-model. The bar has axis ratios of about 5:3:1, and extends almost to corotation. However, it has no sharp edge, but an inhomogenous density with a cusp steeper than the initial model. No sign of a buckling insta-bility has been observerd.

The Structure of Dark Matter Halos in Dwarf Galaxies

Recent observations indicate that dark matter haloes have flat central density profiles. Cosmological simulations with non-baryonic dark matter predict however self similar haloes with central density cusps. This contradiction has lead to the conclusion that dark matter must be baryonic. Here it is shown that the dark matter haloes of dwarf spiral galaxies represent a one parameter family with self similar density profiles. The observed global halo parameters are coupled with each other through simple scaling relations which can be explained by the standard cold dark matter model if one assumes that all the haloes formed from density fluctuations with the same primordial amplitude. We find that the finite central halo densities correlate with the other global parameters. This result rules out scenarios where the flat halo cores formed subsequently through violent dynamical processes in the baryonic component. These cores instead provide important information on the origin and nature of dark matter in dwarf galaxies.

Globular cluster photometry with the Hubble Space Telescope. 2: U, V, and I measurements of M15

The projected density distribution of resolved stars near the center of M15 is shown to be consistent with either a power-law cusp N(r) approximately r(exp alpha), with alpha approximately -0.85 +/- 0.2, or with a King model with a core of radius approximately less than 2 sec. The inferred slope is in agreement with the theoretical value, alpha = -0.75, calculated by Bahcall and Wolf for the distribution of equal-mass stars surrounding a massive black hole and is also consistent with the radial profile expected from core collapse without a central black hole. The object AC 214 is a candidate for the central density cusp. Analysis of Monte Carlo simulations of the diffuse light indicates that, using current analysis techniques and available data, the residual light is not a reliable indicator of the true density distribution. This is contrary to earlier work. Photometric measurements in V and I of more than 5 x 10(exp 3) stars (and in U, V, and I of approximately greater than 1500 stars) are used to construct color-magnitude diagrams in the central 1 min of M15. Fourteen blue straggler candidates are identified in the inner 20 sec. The central color gradient noticed by previous researchers is caused by a central depletion of bright red giant stars rather than an excess of blue stragglers or blue horizontal branch stars.

A family of models for spherical stellar systems

We describe a one-parameter family of models of stable sperical stellar systems in which the phase-space distribution function depends only on energy. The models have similar density profiles in their outer parts (rho propotional to r(exp -4)) and central power-law density cusps, rho proportional to r(exp 3-eta), 0 less than eta less than or = 3. The family contains the Jaffe (1983) and Hernquist (1990) models as special cases. We evaluate the surface brightness profile, the line-of-sight velocity dispersion profile, and the distribution function, and discuss analogs of King's core-fitting formula for determining mass-to-light ratio. We also generalize the models to a two-parameter family, in which the galaxy contains a central black hole; the second parameter is the mass of the black hole. Our models can be used to estimate the detectability of central black holes and the velocity-dispersion profiles of galaxies that contain central cusps, with or without a central black hole.

HUBBLE SPACE TELESCOPE OBSERVATIONS OF THE CENTER OF GLOBULAR CLUSTER M15

ABSTRACT Images of the dense center of globular cluster M15 (NGC 7078) have been obtained with the Hubble Space Telescope in the V and I filters. Accurate photometry is possible in the very densest part of the cluster center with rms errors of <0.3 magnitudes for stars down to the main sequence turnoff. Evidence for radial segregation between horizontal branch, red giant branch, and blue straggler stars is presented. We discuss the possibility of the existence of a central stellar density cusp which does not flatten into a small central core at radii less than 2 arcseconds.