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 flat
spectrum between 2 and 220 GHz, with a spectral index flatter than 0.15
(3sigma). There is no evidence for either a low- or high-frequency cut-off, but
in the mid-infrared (~30 microns) thermal emission from the OB-type companion
star becomes dominant. The integrated luminosity of this flat-spectrum emission
in quiescence is > 2 x 10^{31} erg/s (2 x 10^{24} W). Assuming the emission
originates in a jet for which non-radiative (e.g. adiabatic expansion) losses
dominate, this is a very conservative lower limit on the power required to
maintain the jet. A comparison with Cyg X-3 and GRS 1915+105, the other X-ray
binaries for which a flat spectrum at shorter than cm wavelengths has been
observed, shows that the jet in Cyg X-1 is significantly less luminous and less
variable, and is probably our best example to date of a continuous, steady,
outflow from an X-ray binary. The emissive mechanism reponsible for such a flat
spectral component remains uncertain. Specifically, we note that the radio-mm
spectra observed from these X-ray binaries are much flatter than those of the
`flat-spectrum' AGN, and that existing models of synchrotron emission from
partially self-absorbed radio cores, which predict a high-frequency cut-off in
the mm regime, are not directly applicable.Comment: Accepted for publication in MNRA