The black hole X-ray binary XTE J1550–564 was monitored extensively at X-ray , optical and infrared wavelengths throughout its outburst in 2000 .
We show that it is possible to separate the optical/near-infrared ( OIR ) jet emission from the OIR disc emission .
Focussing on the jet component , we find that as the source fades in the X-ray hard state , the OIR jet emission has a spectral index consistent with optically thin synchrotron emission ( \alpha \approx - 0.6 to -0.7 , where F _ { \nu } \propto \nu ^ { \alpha } ) .
This jet emission is tightly and linearly correlated with the X-ray flux ; L _ { OIR,jet } \propto L _ { X } ^ { 0.98 \pm 0.08 } suggesting a common origin .
This is supported by the OIR , X-ray and OIR to X-ray spectral indices being consistent with a single power law ( \alpha = -0.73 ) .
Ostensibly the compact , synchrotron jet could therefore account for \sim 100 per cent of the X-ray flux at low luminosities in the hard state .
At the same time , ( i ) an excess is seen over the power law decay of the X-ray flux at the point in which the jet would start to dominate , ( ii ) the X-ray spectrum slightly softens , which seems to be due to a high energy cut-off or break shifting to a lower energy , and ( iii ) the X-ray rms variability increases .
This may be the strongest evidence to date of synchrotron emission from the compact , steady jet dominating the X-ray flux of an X-ray binary .
For XTE J1550–564 , this is likely to occur within the luminosity range \sim ( 2 \times 10 ^ { -4 } – 2 \times 10 ^ { -3 } ) L _ { Edd } on the hard state decline of this outburst .
However , on the hard state rise of the outburst and initially on the hard state decline , the synchrotron jet can only provide a small fraction ( \sim a few per cent ) of the X-ray flux .
Both thermal Comptonization and the synchrotron jet can therefore produce the hard X-ray power law in accreting black holes .
In addition , we report a phenomenonological change in the OIR spectral index of the compact jet from possibly a thermal distribution of particles to one typical of optically thin synchrotron emission , as the jet increases in energy over these \sim 20 days .
Once the steady jet is fully formed and the infrared and X-ray fluxes are linearly correlated , the spectral index does not vary ( maintaining \alpha = -0.7 ) while the luminosity decreases by a factor of ten .
These quantitative results provide unique insights into the physics of the relativistic jet acceleration process .