On the formation of degenerate heavy neutrino stars

Abstract

The dynamics of a self-gravitating cold Fermi gas is described using the analogy with an interacting self-gravitating Bose condensate having the same Thomas-Fermi limit. The dissipationless formation of a heavy neutrino star through gravitational collapse and ejection of matter is demonstrated numerically. Such neutrino stars offer an alternative to black holes for the supermassive compact dark objects at the centers of galaxies.Keywords: neutrino stars; boson stars; self-gravitating systems; galactic centers PACS: 02.60. Cb; 95.30.Lz; 95.35.+d; 98.35.Jk Supermassive neutrino stars, in which self-gravity is balanced by the degeneracy pressure of the cold fermions, have been a subject of speculation for more than three decades [1]. Originally, these objects were proposed as models for dark matter in galactic halos and clusters of galaxies, with neutrino masses in the ∼ eV range. More recently, however, degenerate superstars composed of weakly interacting fermions in the ∼ 10 keV range, have been suggested as an alternative to the supermassive black holes that are purported to exist at the centers of galaxies [2][3][4][5][6]. In fact, it has been shown [4] that such degenerate fermion stars could explain the whole range of supermassive compact dark objects which have been observed so far, with masses ranging from 10 6 to 3 × 10 9 M ⊙ , merely assuming that a weakly interacting quasi-stable fermion of mass m f ≃ 15 keV exists in nature.As an example, the most massive compact dark object ever observed, is located at the center of M87, with a mass M ≃ 3.2×10 9 M ⊙ [7]. Interpreting this object as a relativistic fermion star at the Oppenheimer-Volkoff [8] limit, yields a fermion mass of m f ≃ 15 keV and a fermion star radius of R = 4.45R S ≃ 1.5 light-days [3,4], where R S is the Schwarzschild radius. In this case there is little difference between the fermion star and black hole scenarios, because the radius of the last stable orbit around a Schwarzschild black hole is R = 3R S anyway.Extrapolating this down to the compact dark object at the center of our galaxy [9], which, having a mass M ≃ 2.6 × 10 6 M ⊙ , is at the lower limit of the mass range of the observed compact dark objects, we obtain, using the same fermion mass, a radius R ≃ 20 light-days ≃ 5 × 10 4 R S [2]. As the potential inside such a nonrelativistic fermion star is shallow, the spectrum of radiation emitted by accreting baryonic matter is cut off for frequencies larger than 10 13 Hz [3,5], as is actually observed in the spectrum of the enigmatic radio source Sgr A * at the galactic center [10]. A fermion star with radius R < ∼ 20 light-days and mass M ≃ 2.6 × 10 6 M ⊙ is also consistent [6] with the observed motion of stars within a projected distance of 6 to 30 light-days from Sgr A * [9].Of course, it is well-known that 15 keV lies squarely in the cosmologically forbidden mass range for stable active neutrinos ν [11]. The existence of such a massive active neutrino is also disfavoured by the Super-Kamiokande data [12]. However, as shown ...

Growth of perturbations in an expanding universe with Bose-Einstein condensate dark matter

“…In some cases, it can be relevant to go beyond the TF approximation and take the quantum pressure arising from the Heisenberg principle into account. This can regularize the dynamics on small scales, as shown by Bilic et al (2001) in their study of the formation of fermion stars by gravitational collapse. In our problem, this general situation is described by Eq.…”

“…We may also recall that classical and ultra relativistic fermion stars are equivalent to polytropes with index n = 3/2 and n = 3 respectively (Chandrasekhar 1939). The GPP system (11)-(2) with n = 3/2 has been studied by Bilic et al (2001) in relation to the formation of white dwarf stars by gravitational collapse. They show that the quantum pressure (Heisenberg) can regularize the dynamics on small scales.…”

Phase transitions in self-gravitating systems: Self-gravitating fermions and hard-sphere models

“…As suggested in Refs. [5,6,36], this dense degenerate nucleus could be an alternative to black holes at the center of galaxies. On the other hand, at large distances, the density of the (isothermal) self-gravitating Fermi gas decays like r −2 which is a condition that dark galactic halos must fulfill in order to reproduce the flat rotation curves of spiral galaxies [22].…”

Statistical Mechanics of Violent Relaxation in Stellar Systems

“…As shown by Chavanis & Sommeria [25], violent relaxation can lead to the formation of a dense degenerate nucleus with a small radius and a large mass. This massive degenerate nucleus could be an alternative to black holes at the center of galaxies [4,5,25] .…”