Astrophysical Bose-Einstein condensates and superradiance

We investigate gravitational analogue models to describe slowly rotating objects (e.g., dark-matter halos, or boson stars) in terms of Bose-Einstein condensates, trapped in their own gravitational potentials. We begin with a modified Gross-Pitaevskii equation, and show that the resulting background equations of motion are stable, as long as the rotational component is treated as a small perturbation. The dynamics of the fluctuations of the velocity potential are effectively governed by the Klein-Gordon equation of an “Eulerian metric,” where we derive the latter by the use of a relativistic Lagrangian extrapolation. Superradiant scattering on such objects is studied. We derive conditions for its occurrence and estimate its strength. Our investigations might give an observational handle to phenomenologically constrain Bose-Einstein condensates.

Figure 1

Particle-number density $n_0(r)$ (left) and velocity $|{\mathit{v}}_0(r)|$ (right) for $d=3$ in units where $m=1$, and for $r_{\max }=500$ as well as $|{\mathit{v}}_0(r_{\max })|=10$.

Figure 2

$|\mathcal{R}{|}^2-1$ as a function of frequency for $d=3$ and for various values of $\mathrm{\Omega }≔v_{\mathrm{T}}/|{\mathit{v}}_0(r_{\max }^{*})|$. The other parameters are $m=1$, $r_{\max }^{*}=500$ and $|{\mathit{v}}_0(r_{\max }^{*})|=10$.