The radiative efficiency of a radiatively inefficient accretion flow

A recent joint XMM-Newton/Nuclear Spectroscopic Telescope Array (NuSTAR) observation of the accreting neutron star Cen X-4 (L_X ∼ 10³³ erg s^-1) revealed a hard power-law component (Γ ∼ 1-1.5) with a relatively low cut-off energy (∼10 keV), suggesting bremsstrahlung emission. The physical requirements for bremsstrahlung combined with other observed properties of Cen X-4 suggest the emission comes from a boundary layer rather than the accretion flow. The accretion flow itself is thus undetected (with an upper limit of L_flow ≲ 0.3L_X). A deep search for coherent pulsations (which would indicate a strong magnetic field) places a 6 per cent upper limit on the fractional amplitude of pulsations, suggesting the flow is not magnetically regulated. Considering the expected energy balance between the accretion flow and the boundary layer for different values of the neutron star parameters (size, magnetic field, and spin) we use the upper limit on L_flow to set an upper limit of ɛ ≲ 0.3 for the intrinsic radiative efficiency of the accretion flow for the most likely model of a fast-spinning, non-magnetic neutron star. The non-detection of the accretion flow provides the first direct evidence that this flow is indeed `radiatively inefficient', i.e. most of the gravitational potential energy lost by the flow before it hits the star is not emitted as radiation.