The imitation game (r)evolutions: $Q$-star effective shadow from GRMHD analysis

Abstract

$Q$-stars are a class of boson stars arising in scalar-field theories with interacting potentials, minimally coupled to gravity. We show that, in certain regions of parameter space, the angular velocity of stable timelike circular geodesics around $Q$-stars can attain a maximum at a nonzero radius. Notably, this behaviour may occur for stable configurations. This feature has been argued to produce effective shadows, but so far it has only been investigated for unstable solutions. We test this possibility by performing general relativistic magnetohydrodynamic evolutions for a representative stable $Q$-star model. A low-density, low-luminosity central region is indeed observed to form and persist -- at least until the evolution becomes affected by numerical viscosity. As a proof of principle, this suggests that families of stable bosonic stars can act as black hole mimickers. Moreover, for the model at hand, a heuristic analysis shows that the effective shadow has a comparable size to that of a Schwarzschild black hole with the same mass. Importantly, this mechanism for generating an effective shadow does not rely on the object being ultracompact, or an ad hoc chosen accretion disk.

Figures (7)

• Figure 1: $Q$-star sequences for different values of the self-interacting parameters $g$ and $h$. We include for comparison the mini-boson star and show with arrows the effect of including a negative $g$ (for positive $g$ the behavior follows the opposite direction). Also with an arrow we indicate the effect of including a positive $h$ in the strong field region in the sequences of negative $g$. The thick blue curve denotes the second stable region: the relativistic stable branch.
• Figure 2: Selection of the reference $Q$-star. Panel (a) shows the radius and impact parameter corresponding to the location of the local maximum in the angular frequency profile for two sequences of $Q$-stars. Notably, two stable regions emerge, corresponding to the stable branches of the background metric identified in Fig. \ref{['fig:M-omega']}. A thin red line marks the reference $Q$-star used in the GRMHD simulations. Panel (b) presents the angular velocity, metric functions, and scalar field profile for this reference Q -star, alongside comparisons with a Schwarzschild black hole. In this figure, $r[M]$ is not the radial coordinate \ref{['eq:ansatz']}, but the areal radius in units of $M$, i.e., $r[M] := e^{F_1}r/M$.
• Figure 3: Map plot for values of $g$ and $h$ with a relativistic stable region around $(g=-10,h=12)$. Different colors are used to denote the largest values of the impact parameter $b(r_{\rm turn})$ for the corresponding values of $g$ and $h$. Crosses indicate that such values are not in the stable branch.
• Figure 4: Time series of the mass accretion rate $\dot{M}$ and radial magnetic flux $\Phi_{\rm B}$ through a spherical surface at $r=6\ M$.
• Figure 5: Snapshot of the simulation at $t=7220\ M$, showing density in code units ( top panels) and plasma beta magnetization $\beta \coloneqq p_{\rm gas}/p_{\rm mag}$( bottom panels) on the equatorial plane ( left panels) and the meridional plane ( right panels).