Galaxy phase-space density data exclude Bose-Einstein condensate Axion Dark Matter

Light scalars (as the axion) with mass m ~ 10^{-22} eV forming a Bose-Einstein condensate (BEC) exhibit a Jeans length in the kpc scale and were therefore proposed as dark matter (DM) candidates. Our treatment here is generic, independent of the particle physics model and applies to all DM BEC, in or out of equilibrium. Two observed quantities crucially constrain DM in an inescapable way: the average DM density rho_{DM} and the phase-space density Q. The observed values of rho_{DM} and Q in galaxies today constrain both the possibility to form a BEC and the DM mass m. These two constraints robustly exclude axion DM that decouples just after the QCD phase transition. Moreover, the value m ~ 10^{-22} eV can only be obtained with a number of ultrarelativistic degrees of freedom at decoupling in the trillions which is impossible for decoupling in the radiation dominated era. In addition, we find for the axion vacuum misalignment scenario that axions are produced strongly out of thermal equilibrium and that the axion mass in such scenario turns to be 17 orders of magnitude too large to reproduce the observed galactic structures. Moreover, we also consider inhomogenous gravitationally bounded BEC's supported by the bosonic quantum pressure independently of any particular particle physics scenario. For a typical size R ~ kpc and compact object masses M ~ 10^7 Msun they remarkably lead to the same particle mass m ~ 10^{-22} eV as the BEC free-streaming length. However, the phase-space density for the gravitationally bounded BEC's turns to be more than sixty orders of magnitude smaller than the galaxy observed values. We conclude that the BEC's and the axion cannot be the DM particle. However, an axion in the mili-eV scale may be a relevant source of dark energy through the zero point cosmological quantum fluctuations.Comment: 8 pages, no figures. Expanded versio

Warm Dark Matter Galaxies with Central Supermassive Black-Holes

We generalize the Thomas-Fermi approach to galaxy structure to include self-consistently and non-linearly central supermassive black holes. This approach naturally incorporates the quantum pressure of the warm dark matter (WDM) particles and shows its full powerful and clearness in the presence of supermassive black holes (SPMHs). We find the main galaxy and central black hole magnitudes: halo radius r_h , halo mass M_h, black hole mass M_BH, velocity dispersion, phase space density, with their realistic astrophysical values, masses and sizes over a wide galaxy range. The SMBH masses arise naturally in this framework. Our extensive numerical calculations and detailed analytic resolution show that with SMBH's, both WDM regimes: classical (Boltzmann dilute) and quantum (compact) do necessarily co-exist in any galaxy: from the smaller and compact galaxies to the largest ones. The transition from the quantum to the classical region occurs precisely at the same point r_A where the chemical potential vanishes. A novel halo structure with three regions shows up: A small quantum compact core of radius r_A around the SMBH, followed by a less compact region till the BH influence radius r_i, and then for r> r_i the known halo galaxy shows up with its astrophysical size. Three representative families of galaxy plus central SMBH solutions are found and analyzed:small, medium and large galaxies having SMBH masses of 10^5, 10^7 and 10^9 M_sun respectively. A minimum galaxy size and mass ~ 10^7 M_sun larger than the one without SMBH is found. Small galaxies in the range 10^4 M_sun < M_h < 10^7 M_sun cannot harbor central SMBHs. We find novel scaling M_BH - r_h - M_h relations. The galaxy equation of state is derived: The pressure P(r) takes huge values in the SMBH vecinity and then sharply decreases entering the classical region following a local perfect gas behaviour.(Abridged)Comment: 31 pages, 14 figures, new materia

Equation of state, universal profiles, scaling and macroscopic quantum effects in Warm Dark Matter galaxies

The Thomas-Fermi approach to galaxy structure determines selfconsistently and nonlinearly the gravitational potential of the fermionic WDM particles given their quantum distribution function f(E). Galaxy magnitudes as the halo radius r_h, mass M_h, velocity dispersion and phase space density are obtained. We derive the general equation of state for galaxies (relation between the pressure and the density), and provide an analytic expression. This clearly exhibits two regimes: (i) Large diluted galaxies for M_h > 2.3 10^6 Msun corresponding to temperatures T_0 > 0.017 K, described by the classical self gravitating WDM Boltzman regime and (ii) Compact dwarf galaxies for 1.6 10^6 Msun > M_h>M_{h,min}=30000 (2keV/m)^{16/5} Msun, T_0<0.011 K described by the quantum fermionic WDM regime. The T_0=0 degenerate quantum limit predicts the most compact and smallest galaxy (minimal radius and mass M_{h,min}). All magnitudes in the diluted regime exhibit square root of M_h scaling laws and are universal functions of r/r_h when normalized to their values at the origin or at r_h. We find that universality in galaxies (for M_h > 10^6 Msun) reflects the WDM perfect gas behaviour. These theoretical results contrasted to robust and independent sets of galaxy data remarkably reproduce the observations. For the small galaxies, 10^6>M_h>M_{h,min} corresponding to effective temperatures T_0 < 0.017 K, the equation of state is galaxy dependent and the profiles are no more universal. These non-universal properties in small galaxies account to the quantum physics of the WDM fermions in the compact regime. Our results are independent of any WDM particle physics model, they only follow from the gravitational interaction of the WDM particles and their fermionic quantum nature.Comment: 21 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1309.229

Statistical Mechanics of the Self-Gravitating Gas: Thermodynamic Limit, Unstabilities and Phase Diagrams

We show that the self-gravitating gas at thermal equilibrium has an infinite volume limit in the three ensembles (GCE, CE, MCE) when (N, V) -> infty, keeping N/V^{1/3} fixed, that is, with eta = G m^2 N/[ V^{1/3} T] fixed. We develop MonteCarlo simulations, analytic mean field methods (MF) and low density expansions. We compute the equation of state and find it to be locally p(r) = T rho_V(r), that is a local ideal gas equation of state. The system is in a gaseous phase for eta < eta_T = 1.51024...and collapses into a very dense object for eta > eta_T in the CE with the pressure becoming large and negative. The isothermal compressibility diverges at eta = eta_T. We compute the fluctuations around mean field for the three ensembles. We show that the particle distribution can be described by a Haussdorf dimension 1 < D < 3.Comment: 12 pages, Invited lecture at `Statistical Mechanics of Non-Extensive Systems', Observatoire de Paris, October 2005, to be published in a Special issue of `Les Comptes rendus de l'Acade'mie des sciences', Elsevie

Warm dark matter primordial spectra and the onset of structure formation at redshift z

Analytic formulas reproducing the warm dark matter (WDM) primordial spectra are obtained for WDM particles decoupling in and out of thermal equilibrium which provide the initial data for WDM non-linear structure formation. We compute and analyze the corresponding WDM overdensities and compare them to the CDM case. We consider the ratio of the WDM to CDM primordial spectrum and the WDM to CDM overdensities: they turn to be self-similar functions of k/k_{1/2} and R/R_{1/2} respectively, k_{1/2} and R_{1/2} being the wavenumber and length where the WDM spectrum and overdensity are 1/2 of the respective CDM magnitudes. Both k_{1/2} and R_{1/2} show scaling as powers of the WDM particle mass m while the self-similar functions are independent of m. The WDM primordial spectrum sharply decreases around k_{1/2} with respect to the CDM spectrum, while the WDM overdensity slowly decreases around R_{1/2}. The nonlinear regions where WDM structure formation takes place are shown and compared to those in CDM: the WDM non-linear structures start to form later than in CDM, and as a general trend, decreasing the DM particle mass delays the onset of the non-linear regime. The non-linear regime starts earlier for smaller objects than for larger ones; smaller objects can form earlier both in WDM and CDM. We compute and analyze the differential mass function dN/dM for WDM at redshift z in the Press-Schechter approach. The WDM suppression effect of small scale structure increases with the redshift z. Our results for dN/dM are useful to be contrasted with observations, in particular for 4 < z < 12. We perfom all these studies for the most popular WDM particle physics models. Contrasting them to observations should point out the precise value of the WDM particle mass in the keV scale, and help to single out the best WDM particle physics model (Abridged).Comment: 18 pages, 8 figures. To appear in Phys Rev

Quantum WDM fermions and gravitation determine the observed galaxy structures

Quantum mechanics is necessary to compute galaxy structures at kpc scales and below. This is so because near the galaxy center, at scales below 10 - 100 pc, warm dark matter (WDM) quantum effects are important: observations show that the interparticle distance is of the order of, or smaller than the de Broglie wavelength for WDM. This explains why all classical (non-quantum) WDM N-body simulations fail to explain galactic cores and their sizes. We describe fermionic WDM galaxies in an analytic semiclassical framework based on the Thomas-Fermi approach, we resolve it numerically and find the main physical galaxy magnitudes: mass, halo radius, phase-space density, velocity dispersion, fully consistent with observations, including compact dwarf galaxies. Namely, fermionic WDM treated quantum mechanically, as it must be, reproduces the observed galaxy DM cores and their sizes. [In addition, as is known, WDM simulations produce the right DM structures in agreement with observations for scales > kpc]. We show that compact dwarf galaxies are natural quantum macroscopic objects supported against gravity by the fermionic WDM quantum pressure (quantum degenerate fermions) with a minimal galaxy mass and minimal velocity dispersion. Interestingly enough, the minimal galaxy mass implies a minimal mass m_{min} for the WDM particle. The lightest known dwarf galaxy (Willman I) implies m > m_{min} = 1.91 keV. These results and the observed halo radius and mass of the compact galaxies provide further indication that the WDM particle mass m is approximately around 2 keV.Comment: 15 pages, 2 figures, expanded version to appear in Astroparticle Physics. admin note: substantial text overlap with arXiv:1204.309