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We test the truncated disc models using multiwavelength (optical/ultraviolet/X‐ray) data from the 2005 hard state outburst of the black hole  Swift  J1753.5−0127. This system is both fairly bright and has fairly low interstellar absorption, so gives one of the best data sets to study the weak, cool disc emission in this state. We fit these data using models of an X‐ray illuminated disc to constrain the inner disc radius throughout the outburst. Close to the peak, the observed soft X‐ray component is consistent with being produced by the inner disc, with its intrinsic emission enhanced in temperature and luminosity by reprocessing of hard X‐ray illumination in an overlap region between the disc and corona. This disc emission provides the seed photons for Compton scattering to produce the hard X‐ray spectrum, and these hard X‐rays also illuminate the outer disc, producing the optical emission by reprocessing.  However, the situation is very different as the outburst declines. The optical is probably cyclo‐synchrotron radiation, self‐generated by the flow, rather than tracing the outer disc. Similarly, limits from reprocessing make it unlikely that the soft X‐rays are directly tracing the inner disc radius. Instead they appear to be from a new component. This is seen more clearly in a similarly dim low/hard state spectrum from XTE J1118+480, where the 10 times lower interstellar absorption allows a correspondingly better view of the ultraviolet/extreme ultraviolet (EUV) emission. The very small emitting area implied by the relatively high temperature soft X‐ray component is completely inconsistent with the much larger, cooler, ultraviolet component which is well fit by a truncated disc. We speculate on the origin of this component, but its existence as a clearly separate spectral component from the truncated disc in XTE J1118+480 shows that it does not simply trace the inner disc radius, so cannot constrain the truncated disc models.

An additional soft X‐ray component in the dim low/hard state of black hole binaries