Inclination effects on the X-ray emission of Galactic black-hole binaries

Context. Galactic black-hole X-ray binaries (BHBs) emit a compact, optically thick, mildly relativistic radio jet when they are in hard and hard-intermediate states. In these states, BHBs exhibit a correlation between the time lag of hard with respect to softer photons and the photon index of the power law component that characterizes the X-ray spectral continuum above ∼10 keV. The correlation, however, shows large scatter. In recent years, several works have brought to light the importance of taking into account the inclination of the systems to understand the X-ray and radio phenomenology of BHBs. Aims. Our objective is to investigate the role that the inclination plays on the correlation between the time lag and photon index. Methods. We obtained RXTE energy spectra and light curves of a sample of BHBs with different inclination angles. We computed the photon index and the time lag between hard and soft photons and performed a correlation and linear regression analysis of the two variables. We also computed energy spectra and light curves of BHBs using the Monte Carlo technique that reproduces the process of Comptonization in the jet. We account for the inclination effects by recording the photons that escape from the jet at different angles. From the simulated light curves and spectra we obtained model-dependent photon index and time lags, which we compared with those obtained from the real data. Results. We find that the correlation between the time lag and photon index is tight in low-inclination systems and becomes weaker in high-inclination systems. The amplitude of the lags is also larger at low- and intermediate-inclination angles than at high inclination. We also find that the photon index and time lag, obtained from the simulated spectra and light curves, also follow different relationships for different inclination angle ranges. Our jet model reproduces the observations remarkably well. The same set of models that reproduces the correlation for the low-inclination systems, also accounts for the correlation for intermediate- and high-inclination systems fairly well. Conclusions. The large dispersion observed in the time lag – photon index correlation in BHBs can naturally be explained as an inclination effect. Comptonization in the jet explains the steeper dependence of the lags on the photon index in low- and intermediate-inclination systems than in high-inclination systems