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We assess whether gravity darkening, induced by a tidal interaction during a stellar fly-by, might be sufficient to explain the Great Dimming of Betelgeuse. Adopting several simple approximations, we calculate the tidal deformation and associated gravity darkening in a close tidal encounter, as well as the reduction in the radiation flux as seen by a distant observer. We show that, in principle, the duration and degree of the resulting stellar dimming can be used to estimate the minimum pericentre separation and mass of a fly-by object, which, even if it remains undetected otherwise, might be a black hole, neutron star, or white dwarf. Our estimates show that, while such fly-by events may occur in other astrophysical scenarios, where our analysis should be applicable, they likely are not large enough to explain the Great Dimming of Betelgeuse by themselves.

ABSTRACT We revisit Bondi accretion – steady-state, adiabatic, spherical gas flow on to a Schwarzschild black hole at rest in an asymptotically homogeneous medium – for stiff polytropic equations of state (EOSs) with adiabatic indices Γ > 5/3. A general relativistic treatment is required to determine their accretion rates, for which we provide exact expressions. We discuss several qualitative differences between results for soft and stiff EOSs – including the appearance of a minimum steady-state accretion rate for EOSs with Γ ≥ 5/3 – and explore limiting cases in order to examine these differences. As an example, we highlight results for Γ = 2, which is often used in numerical simulations to model the EOS of neutron stars. We also discuss a special case with this index, the ultrarelativistic ‘causal’ EOS, P = ρ. The latter serves as a useful limit for the still undetermined neutron star EOS above nuclear density. The results are useful, for example, to estimate the accretion rate on to a mini-black hole residing at the centre of a neutron star.