General-relativistic instability in rapidly accreting supermassive stars in the presence of dark matter

Abstract

Context. The collapse of supermassive stars (SMSs) via the general-relativistic (GR) instability would provide a natural explanation for the existence of the most extreme quasars. The presence of dark matter in SMSs is thought to potentially impact their properties, in particular their mass at collapse. Dark matter might be made of weakly interacting massive particles (WIMPs) that can be captured by the gravitational potential well of SMSs due to the interaction with the baryonic gas, favouring high dark matter densities in the star’s core. The annihilation of WIMPs can provide fuel to support the star before H-burning ignition, favouring low densities of baryonic gas, long stellar lifetimes, and high final masses. Aims. Here we estimate the impact of dark matter on the GR dynamical stability of rapidly accreting SMSs. Methods.We added a dark matter term to the relativistic equation of adiabatic pulsations and applied it to hylotropic structures in order to determine the onset point of the GR instability. We considered both a homogeneous dark matter background and density profiles of the form ∝exp(−r2/rχ2), typical for the case of WIMPs capture. The free choice of the central temperature in hylotropic models allowed us to consider SMSs fuelled by H-burning and by WIMP annihilation. Results. We find that, in principle, the dark matter gravitational field can completely remove the GR instability. However, for SMSs fuelled by H-burning the dark matter densities required to stabilise the star against GR are orders of magnitude above the values that are expected for the dark matter background. In the case of WIMPs capture, where the required densities can be reached in the centre of the star, the high centralisation of the dark matter component prevents any effect on the GR instability. On the other hand, for SMSs fuelled by WIMP annihilation, we find that the low densities of baryonic gas inhibit the destabilising GR corrections, which shifts the stability limit by typically an order of magnitude towards higher masses. As long as central temperatures ≲107 K are maintained by WIMP annihilation, the GR instability is reached only for stellar masses > 106 M⊙. Conclusions. Dark matter can impact the GR dynamical stability of SMSs only in the case of energetically significant WIMP annihilation. The detection of a SMS with mass > 106 M⊙ in an atomically cooled halo can be interpreted as evidence of WIMP annihilation in the star’s core.