The very flat radio-millimetre spectrum of Cygnus X-1

We present almost-simultaneous detections of Cygnus X-1 in the radio and mm regimes, obtained during the low/hard X-ray state. The source displays a f lat spectrum between 2 and 220 GHz, with a spectral index \alpha\ less than or equal to 0.15 (3 sigma). There is no evidence for either a low- or high -frequency cut-off, but in the mid-infrared (similar to 30 mu m) thermal em ission from the OB-type companion star becomes dominant. The integrated lum inosity of this flat-spectrum emission in quiescence is greater than or equ al to 2 x 10(31) erg s(-1) (2 x 10(24) W). Assuming the emission originates in a jet for which non-radiative (e.g. adiabatic expansion) losses dominat e, this is a very conservative lower limit on the power required to maintai n the jet. A comparison with Cyg X-3 and GRS 1915 + 105, the other X-ray bi naries for which a flat spectrum at shorter than cm wavelengths has been ob served, shows that the jet in Cyg X-1 is significantly less luminous and le ss variable, and is probably our best example to date of a continuous, stea dy, outflow from an X-ray binary. The emissive mechanism responsible for su ch a flat spectral component remains uncertain. Specifically, we note that the radio-mm spectra observed from these X-ray binaries are much flatter th an those of the 'flat-spectrum' AGN, and that existing models of synchrotro n emission from partially self-absorbed radio cores, which predict a high-f requency cut-off in the mm regime, are not directly applicable.