The time-lag -- photon-index correlation in GX 339--4

Abstract

Black-hole transients exhibit a correlation between the time lag of hard photons with respect to softer ones and the photon index of the hard X-ray power law. The correlation is not very tight and therefore it is necessary to examine it source by source. The objective of the present work is to investigate in detail the time-lag -- photon-index correlation in GX 339-4. We have obtained RXTE energy spectra and light curves and have computed the photon index and the time lag of the $9-15$ keV photons with respect to the $2-6$ keV ones. The observations cover the first stages of the hard state, the pure hard state, and the hard-intermediate state. At low $\Gamma$, the correlation is positive and it becomes negative at large $\Gamma$. By assuming that the hard X-ray power law index $\Gamma$ is produced by inverse Compton scattering of soft disk photons in the jet, we have reproduced the entire correlation by varying two parameters in the jet: the radius of the jet at its base $R_0$ and the Thomson optical depth along the jet ${\tau }_{\parallel }$. We have found that, as the luminosity of the source increases, $R_0$ initially increases and then decreases. This behavior is expected in the context of the Cosmic Battery. As a further test of our model, we predict the break frequency in the radio spectrum as a function of the photon index during the rising part of an outburst.

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• Quasi-periodic oscillations in GX 339-4 during the 2021 Outburst observed with Insight-HXMT
• Evolution of the truncated disc and inner hot-flow of GX 339-4
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• The inner flow geometry in MAXI J1820+070 during hard and hard-intermediate states
• A quantitative explanation of the radio--X-ray correlation in black-hole X-ray binaries
• Probing black-hole accretion through time variability
• The role of outflows in black-hole X-ray binaries
• Inclination Dependence of The Time-Lag -- Photon-Index Correlation in BHXRBs and its Explanation with a Simple Jet Model