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Register a new userEvolution of Dark Matter Phase-Space Density Distributions in Equal-Mass Halo Mergers
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Added by
Stelios Kazantzidis
Publication date
2009
fields
Physics
and research's language is
English
Authors
Ileana M. Vass
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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.
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We study the evolution of phase-space density during the hierarchical structure formation of LCDM halos. We compute both a spherically-averaged surrogate for phase-space density (Q) and the coarse-grained distribution function f(x,v) for dark matter particles that lie within~2 virial radii of four Milky-Way-sized dark matter halos. The estimated f(x,v) spans over four decades at any radius. Dark matter particles that end up within two virial radii of a Milky-Way-sized DM halo at $z=0$ have an approximately Gaussian distribution in log(f) at early redshifts, but the distribution becomes increasingly skewed at lower redshifts. The value corresponding to the peak of the Gaussian decreases as the evolution progresses and is well described by a power-law in (1+z). The highest values of f are found at the centers of dark matter halos and subhalos, where f can be an order of magnitude higher than in the center of the main halo. The power-law Q(r) profile likely reflects the distribution of entropy (K = sigma^2/rho^{2/3} propto r^{1.2}), which dark matter acquires as it is accreted onto a growing halo. The estimated f(x, v), on the other hand, exhibits a more complicated behavior. Although the median coarse-grained phase-space density profile F(r) can be approximated by a power-law in the inner regions of halos and at larger radii the profile flattens significantly. This is because phase-space density averaged on small scales is sensitive to the high-f material associated with surviving subhalos, as well as relatively unmixed material (probably in streams) resulting from disrupted subhalos, which contribute a sizable fraction of matter at large radii. (ABRIDGED)
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 pseudo phase space density, Q ~ {rho}/{sigma}^3, overestimates the maximum phase space density by up to an order of magnitude. The density in the inner regions of the simulated haloes is well described by a pseudo-isothermal profile with a core. We have developed a simple model based on this profile which, given the observed surface brightness profile of a galaxy and its central velocity dispersion, accurately predicts its central phase space density. Applying this model to the dwarf spheroidal satellites of the Milky Way yields values close to 0.5 keV for the mass of a hypothetical thermal warm dark matter particle, assuming the satellite haloes have cores produced by warm dark matter free streaming. Such a small value is in conflict with the lower limit of 1.2 keV set by observations of the Lyman-{alpha} forest. Thus, if the Milky Way dwarf spheroidal satellites have cores, these are likely due to baryonic processes associated with the forming galaxy, perhaps of the kind proposed by Navarro, Eke and Frenk and seen in recent simulations of galaxy formation in the cold dark matter model.
High resolution N-body simulations have all but converged on a common empirical form for the shape of the density profiles of halos, but the full understanding of the underlying physics of halo formation has eluded them so far. We investigate the formation and structure of dark matter halos using analytical and semi-analytical techniques. Our halos are formed via an extended secondary infall model (ESIM); they contain secondary perturbations and hence random tangential and radial motions which affect the halos evolution at it undergoes shell-crossing and virialization. Even though the density profiles of NFW and ESIM halos are different their phase-space density distributions are the same: rho/sigma^3 ~ r^{-alpha}, with alpha=1.875 over ~3 decades in radius. We use two approaches to try to explain this ``universal slope: (1) The Jeans equation analysis yields many insights, however, does not answer why alpha=1.875. (2) The secondary infall model of the 1960s and 1970s, augmented by ``thermal motions of particles does predict that halos should have alpha=1.875. However, this relies on assumptions of spherical symmetry and slow accretion. While for ESIM halos these assumptions are justified, they most certainly break down for simulated halos which forms hierarchically. We speculate that our argument may apply to an ``on-average formation scenario of halos within merger-driven numerical simulations, and thereby explain why alpha=1.875 for NFW halos. Thus, rho/sigma^3 ~ r^{-1.875} may be a generic feature of violent relaxation.
For the first time, we obtain the analytical form of black hole space-time metric in dark matter halo for the stationary situation. Using the relation between the rotation velocity (in the equatorial plane) and the spherical symmetric space-time metric coefficient, we obtain the space-time metric for pure dark matter. By considering the dark matter halo in spherical symmetric space-time as part of the energy-momentum tensors in the Einstein field equation, we then obtain the spherical symmetric black hole solutions in dark matter halo. Utilizing Newman-Jains method, we further generalize spherical symmetric black holes to rotational black holes. As examples, we obtain the space-time metric of black holes surrounded by Cold Dark Matter and Scalar Field Dark Matter halos, respectively. Our main results regarding the interaction between black hole and dark matter halo are as follows: (i) For both dark matter models, the density profile always produces cusp phenomenon in small scale in the relativity situation; (ii) Dark matter halo makes the black hole horizon to increase but the ergosphere to decrease, while the magnitude is small; (iii) Dark matter does not change the singularity of black holes. These results are useful to study the interaction of black hole and dark matter halo in stationary situation. Particularly, the cusp produced in the $0sim 1$ kpc scale would be observable in the Milky Way. Perspectives on future work regarding the applications of our results in astrophysics are also briefly discussed.
Dark matter-only simulations predict that dark matter halos have steep, cuspy inner density profiles, while observations of dwarf galaxies find a range of inner slopes that are often much shallower. There is debate whether this discrepancy can be explained by baryonic feedback or if it may require modified dark matter models. In Paper 1 of this series, we obtained high-resolution integral field H$alpha$ observations for 26 dwarf galaxies with $M_*=10^{8.1}-10^{9.7}textrm{M}_odot$. We derived rotation curves from our observations, which we use here to construct mass models. We model the total mass distribution as the sum of a generalized Navarro-Frenk-White (NFW) dark matter halo and the stellar and gaseous components. Our analysis of the slope of the dark matter density profile focuses on the inner 300-800 pc, chosen based on the resolution of our data and the region resolved by modern hydrodynamical simulations. The inner slope measured using ionized and molecular gas tracers is consistent, and it is additionally robust to the choice of stellar mass-to-light ratio. We find a range of dark matter profiles, including both cored and cuspy slopes, with an average of $rho_{rm DM}sim r^{-0.74pm 0.07}$, shallower than the NFW profile, but steeper than those typically observed for lower-mass galaxies with $M_*sim 10^{7.5}textrm{M}_odot$. Simulations that reproduce the observed slopes in those lower-mass galaxies also produce slopes that are too shallow for galaxies in our mass range. We therefore conclude that supernova feedback models do not yet provide a fully satisfactory explanation for the observed trend in dark matter slopes.
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