Superhumps in low-mass X-ray binaries

We propose a mechanism for the superhump modulations observed in optical ph otometry of at least two black-hole X-ray transients (SXTs). As in extreme mass-ratio cataclysmic variables (CVs), superhumps are assumed to result fr om the presence of the 3:1 orbital resonance in the accretion disc. This ca uses the disc to become non-axisymmetric and precess. However, the mechanis m for superhump luminosity variations in low-mass X-ray binaries (LMXBs) mu st differ from that in CVs, where it is attributed to a tidally-driven modu lation of the disc's viscous dissipation, varying on the beat between the o rbital and disc precession period. By contrast in LMXBs, tidal dissipation in the outer accretion disc is negligible: the optical emission is overwhel mingly dominated by reprocessing of intercepted central X-rays. Thus a diff erent origin for the superhump modulation is required. Recent observations and numerical simulations indicate that in an extreme mass-ratio system the disc area changes on the superhump period. We deduce that the superhumps o bserved in SXTs arise from a modulation of the reprocessed flux by the chan ging area. Therefore, unlike the situation in CVs, where the superhump ampl itude is inclination-independent, superhumps should be best seen in low-inc lination LMXBs, whereas an orbital modulation from the heated face of the s econdary star should be more prominent at high inclinations. Modulation at the disc precession period (10 s of days) may indicate disc asymmetries suc h as warping. We comment on the orbital period determinations of LMXBs, and the possibility and significance of possible permanent superhump LMXBs.