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Inclination Dependence of The Time-Lag -- Photon-Index Correlation in BHXRBs and its Explanation with a Simple Jet Model

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 نشر من قبل Pablo Reig
 تاريخ النشر 2019
  مجال البحث فيزياء
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Recently, we reported an observational correlation between a) the time-lag of the hard (9 - 15 keV) with respect to the soft (2 - 5 keV) X-ray photons in black-hole X-ray binaries (BHXRBs) and b) the power-law photon index $Gamma$ of the X-ray spectrum. This was physically explained with a simple jet model, i.e., a model where the Comptonization (the Compton upscattering of soft photons) happens in the jet. Here, we report the inclination dependence of this correlation, which we also explain with our jet model. Photons that emerge at different polar angles from the jet axis have different spectra and different time-lags. Because of this, we can explain quantitatively the type-B QPOs of GX 339-4 as resulting from a precessing jet.



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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 sou rce. 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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We have performed a timing and spectral analysis of a set of black-hole binaries to study the correlation between the photon index and the time lag of the hard photons with respect to the soft ones. We provide further evidence that the timing and spe ctral properties in black-hole X-ray binaries are coupled. In particular, we find that the average time lag increases as the X-ray emission becomes softer. Although a correlation between the hardness of the X-ray spectrum and the time (or phase) lag has been reported in the past for a handful of systems, our study confirms that this correlated behaviour is a global property of black-hole X-ray binaries. We also demonstrate that the photon-index - time-lag correlation can be explained as a result of inverse Comptonization in a jet.
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