Gravitational collapse of Bose-Einstein condensate dark matter halos

Abstract

We study the mechanisms of the gravitational collapse of the Bose-Einstein condensate dark matter halos, described by the zero temperature time-dependent nonlinear Schrödinger equation (the Gross-Pitaevskii equation), with repulsive inter-particle interactions. By using a variational approach, and by choosing an appropriate trial wave function, we reformulate the Gross-Pitaevskii equation with spherical symmetry as Newton's equation of motion for a particle in an effective potential, which is determined by the zero point kinetic energy, the gravitational energy, and the particles interaction energy, respectively. The velocity of the condensate is proportional to the radial distance, with a time dependent proportionality function. The equation of motion of the collapsing dark matter condensate is studied by using both analytical and numerical methods. The collapse of the condensate ends with the formation of a stable configuration, corresponding to the minimum of the effective potential. The radius and the mass of the resulting dark matter object are obtained, as well as the collapse time of the condensate. The numerical values of these global astrophysical quantities, characterizing condensed dark matter systems, strongly depend on the two parameters describing the condensate, the mass of the dark matter particle, and of the scattering length, respectively. The stability of the condensate under small perturbations is also studied, and the oscillations frequency of the halo is obtained. Hence these results show that the gravitational collapse of the condensed dark matter halos can lead to the formation of stable astrophysical systems with both galactic and stellar sizes.

Decay of ultralight axion condensates

“…Collapsing boson condensates have been investigated by a number of groups [67,68,69,70,64,71,72,73]. Recently, we found that supercritical QCD axion condensates, having masses larger than the maximal allowed stable mass, collapse towards the global minimum of the effective axion potential [64,73].…”

Approximation methods in the study of boson stars

“…Time-dependent solutions to the GP equation can be approximated using the variational method formulation of Pethick and Smith [59], which we have described above. A good example of such an application is the collapse of BECs [26][27][28][29]. In this case, the variational parameter σ is taken to be a function of time, σ(t), while the wavefunction is multiplied by some phase.…”

“…Axion stars were considered first around 30 years ago, originally suggested to form from collapse of overdense miniclusters in the early universe [10,11] (see also more recent simulations [12]). Since then, many properties of axion stars have been studied extensively; these include structural stability [13][14][15][16][17][18][19][20][21][22] (including nonzero angular momentum [23][24][25]), the process of gravitational collapse [26][27][28][29][30][31][32], and their decay through emission of relativistic particles [33][34][35][36][37][38]. There has recently been a significant amount of work regarding relativistic corrections more generally to the classical field description of axion stars [39][40][41][42].…”

“…This comparison of ansätze to the numerical solutions is imperative for the study of dynamical problems that are much more difficult to solve numerically. Some such dynamical problems that have been analyzed using the variational method are the collapse [26][27][28][29] and collisions [60,61] of BECs. In subsequent years, numerous authors have presented various ansätze for both static and dynamical problems, either to improve numerical agreement or computational efficiency [19,22,25,37].…”

Collapse of axion stars

“…The collapse of dark matter halos consisting of condensed scalar particles was examined by [37], using a time-dependent formalism that originated in [38], and utilized by [26,39]. The application of this method to an axion star, at leading-order in the self-interaction potential, was recently performed by [29].…”