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Register a new userDark matter halos and self similarity
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C. Alard
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This papers explores the self similar solutions of the Vlasov-Poisson system and their relation to the gravitational collapse of dynamically cold systems. Analytic solutions are derived for power law potential in one dimension, and extensions of these solutions in three dimensions are proposed. Next the self similarity of the collapse of cold dynamical systems is investigated numerically. The fold system in phase space is consistent with analytic self similar solutions, the solutions present all the proper self-similar scalings. An additional point is the appearance of an $x^{-(1/2)}$ law at the center of the system for initial conditions with power law index larger than $-(1/2)$. It is found that the first appearance of the $x^{-(1/2)}$ law corresponds to the formation of a singularity very close to the center. Finally the general properties of self similar multi dimensional solutions near equilibrium are investigated. Smooth and continuous self similar solutions have power law behavior at equilibrium. However cold initial conditions result in discontinuous phase space solutions, and the smoothed phase space density looses its auto similar properties. This problem is easily solved by observing that the probability distribution of the phase space density $P$ is identical except for scaling parameters to the probability distribution of the smoothed phase space density $P_S$. As a consequence $P_S$ inherit the self similar properties of $P$. This particular property is at the origin of the universal power law observed in numerical simulation for ${rho}/{sigma^3}$. The self similar properties of $P_S$ implies that other quantities should have also an universal power law behavior with predictable exponents. This hypothesis is tested using a numerical model of the phase space density of cold dark matter halos, an excellent agreement is obtained.
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The cosmological simulations indicates that the dark matter haloes have specific self similar properties. However the halo similarity is affected by the baryonic feedback, the momentum injected by the supernovae re-shape the dark matter core and transform it to a flat density core, with a scale length imposed by the baryonic feedback. Additionally the baryon feedback impose also an equilibrium condition, which when coupled with the imposed baryonic scale length induce a new type of similarity. The new self similar solution implies that the acceleration generated by dark matter is scale free, which in turns implies that the baryonic acceleration at a reference radius is also scale free. Constant dark matter and baryonic accelerations at a reference radius have effectively been observed for a large class of different galaxies, which is in support of this approach. The new self similar properties implies that the total acceleration at larger distances is scale free, the transition between the dark matter and baryons dominated regime occurs at a constant acceleration, and the maximum of the velocity curve which defines the amplitude of the velocity curve at larger distances is proportional to $M^{frac{1}{4}}$. These results demonstrates that in this self similar model, cold dark matter is consistent with the basics of MOND phenomenology for the galaxies. In agreement with the observation the coincidence between the self similar model and MOND is expected to break at the scale of clusters of galaxies. Some numerical experiments shows that the behavior of the density near the origin is closely approximated by a Einasto profile.
Wave dark matter ($psi$DM), which satisfies the Schrodinger-Poisson equation, has recently attracted substantial attention as a possible dark matter candidate. Numerical simulations have in the past provided a powerful tool to explore this new territory of possibility. Despite their successes to reveal several key features of $psi$DM, further progress in simulations is limited, in that cosmological simulations so far can only address formation of halos below $sim 2times 10^{11} M_odot$ and substantially more massive halos have become computationally very challenging to obtain. For this reason, the present work adopts a different approach in assessing massive halos by constructing wave-halo solutions directly from the wave distribution function. This approach bears certain similarity with the analytical construction of particle-halo (cold dark matter model). Instead of many collisionless particles, one deals with one single wave that has many non-interacting eigenstates. The key ingredient in the wave-halo construction is the distribution function of the wave power, and we use several halos produced by structure formation simulations as templates to determine the wave distribution function. Among different models, we find the fermionic King model presents the best fits and we use it for our wave-halo construction. We have devised an iteration method for constructing the nonlinear halo, and demonstrate its stability by three-dimensional simulations. A Milky-Way-sized halo has also been constructed, and the inner halo is found flatter than the NFW profile. These wave-halos have small-scale interferences both in space and time producing time-dependent granules. While the spatial scale of granules varies little, the correlation time is found to increase with radius by one order of magnitude across the halo.
We investigate self-gravitating equilibria of halos constituted by dark matter (DM) non-minimally coupled to gravity. In particular, we consider a theoretically motivated non-minimal coupling which may arise when the averaging/coherence length $L$ associated to the fluid description of the DM collective behavior is comparable to the local curvature scale. In the Newtonian limit, such a non-minimal coupling amounts to a modification of the Poisson equation by a term $L^2, abla^2rho$ proportional to the Laplacian of the DM density $rho$ itself. We further adopt a general power-law equation of state $ppropto rho^{Gamma}, r^alpha$ relating the DM dynamical pressure $p$ to density $rho$ and radius $r$, as expected by phase-space density stratification during the gravitational assembly of halos in a cosmological context. We confirm previous findings that, in absence of the non-minimal coupling, the resulting density $rho(r)$ features a steep central cusp and an overall shape mirroring the outcomes of $N-$body simulations in the standard $Lambda$CDM cosmology, as described by the classic NFW or Einasto profiles. Most importantly, we find that the non-minimal coupling causes the density distribution to develop an inner core and a shape closely following, out to several core scale radii, the Burkert profile. In fact, we highlight that the resulting mass distributions can fit, with an accuracy comparable to the Burkerts one, the co-added rotation curves of dwarf, DM-dominated galaxies. Finally, we show that non-minimally coupled DM halos are consistent with the observed scaling relation between the core radius $r_0$ and core density $rho_0$, in terms of an universal core surface density $rho_0times r_0$ among different galaxies.
We investigate unbound dark matter particles in halos by tracing particle trajectories in a simulation run to the far future (a = 100). We find that the traditional sum of kinetic and potential energies is a very poor predictor of which dark matter particles will eventually become unbound from halos. We also study the mass fraction of unbound particles, which increases strongly towards the edges of halos, and decreases significantly at higher redshifts. We discuss implications for dark matter detection experiments, precision calibrations of the halo mass function, the use of baryon fractions to constrain dark energy, and searches for intergalactic supernovae.
A new family of nonrelativistic, Newtonian, non-quantum equilibrium configurations describing galactic halos is introduced, by considering strange quark matter conglomerates with masses larger than about 8 GeV as new possible components of the dark matter. Originally introduced to explain the state of matter in neutron stars, such conglomerates may also form in the high-density and temperature conditions of the primordial Universe and then decouple from ordinary baryonic matter, providing the fundamental components of dark matter for the formation of pristine gravitational potential wells and the subsequent evolution of cosmic structures. The obtained results for halo mass and radius are consistent with the rotational velocity curve observed in the Galaxy. Additionally, the average density of such dark matter halos is similar to that derived for halos of dwarf spheroidal galaxies, which can therefore be interpreted as downscal
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