The disk luminosity deficit as a tracer of receding disk during Soft-to-Hard transitions in Black Hole X-ray Binaries

Tracing the evolution of the thin accretion disk during the soft-to-hard state transition in black hole X-ray binaries (BHXRBs) remains difficult because conventional spectral estimates of the disk inner radius become highly model-dependent once the thermal component weakens. We present evidence that the thin disk recedes during this transition, obtained from a systematic study of RXTE/PCA observations of 26 BHXRBs. In 24 outbursts, the disk luminosity decays exponentially in the soft state, then drops significantly below the extrapolated baseline. This thermal luminosity deficit is considered a signature of reduced accretion efficiency, caused by the outward receding of the optically thick disk. Under this framework, we found that the estimated characteristic truncation radius increases rapidly as the systems evolve through the soft-to-hard transition. This interpretation is supported by timing analysis: in observations with well-constrained power density spectra, the characteristic frequencies of broadband noise and low-frequency QPOs generally decrease as the inferred truncation radius increases, consistent with the expansion of a hot inner flow. The onset and rapidity of recession vary substantially across different sources and outbursts. Our results demonstrate that luminosity deficits provide a practical empirical tracer of thin disk receding during soft-to-hard transitions, when direct spectral radius measurements become unreliable.