We compute the effect of an orbiting gas disc in promoting the coalescence of a central supermassive black hole binary . Unlike earlier studies , we consider a finite mass of gas with explicit time dependence : we do not assume that the gas necessarily adopts a steady state or a spatially constant accretion rate , i.e . that the merging black hole was somehow inserted into a pre–existing accretion disc . We consider the tidal torque of the binary on the disc , and the binary ’ s gravitational radiation . We study the effects of star formation in the gas disc in a simple energy feedback framework . The disc spectrum differs in detail from that found before . In particular , tidal torques from the secondary black hole heat the edges of the gap , creating bright rims around the secondary . These rims do not in practice have uniform brightness either in azimuth or time , but can on average account for as much as 50 % of the integrated light from the disc . This may lead to detectable high–photon–energy variability on the relatively long orbital timescale of the secondary black hole , and thus offer a prospective signature of a coalescing black hole binary . We also find that the disc can drive the binary to merger on a reasonable timescale only if its mass is at least comparable with that of the secondary black hole , and if the initial binary separation is relatively small , i.e . a _ { 0 } \lesssim 0.05 pc . Star formation complicates the merger further by removing mass from the disc . In the feedback model we consider , this sets an effective limit to the disc mass . As a result , binary merging is unlikely unless the black hole mass ratio is \la 0.001 . Gas discs thus appear not to be an effective solution to the ‘ last parsec ’ problem for a significant class of mergers .