Coronal properties of black hole X-ray binaries in the hard state as seen by NuSTAR and Swift

TL;DR

This study measures coronal parameters in black hole X-ray binaries across a wide luminosity range using NuSTAR and Swift, revealing complex correlations that challenge existing accretion models.

Contribution

It provides the first comprehensive measurement of coronal photon index and electron temperature over six orders of magnitude in luminosity, uncovering unexpected correlations.

Findings

Confirmed a 'V'-shaped correlation between photon index and luminosity.

Discovered a 'Λ'-shaped correlation between electron temperature and luminosity.

Identified unexpected 'cooler when fainter' trend at low luminosities.

Abstract

In this work, we measure two important phenomenological parameters of corona (and hot accretion flow) in black hole X-ray binaries: the photon index $\Gamma$ and the electron temperature $\te$. Thanks to the capability of {\it NuSTAR} in hard X-rays, we measure these two parameters over six orders of magnitude in the 0.1-100 keV X-ray luminosity $\lx$, from $\sim 5\times10^{38} \ergs$ down to as low as $\sim 5\times10^{32} \ergs$. We confirm the existence of a "V"-shaped correlation between $\Gamma$ and $\lx$. Surprisingly, we observe a "$\Lambda$"-shaped correlation between $\te$ and $\lx$. The "cooler when brighter" branch in the high luminosity regime ($\lx \ga 3\times 10^{36} \ergs$) agrees with previous results and can be understood under the existing model of Compton scattering in the corona. On the other hand, the apparent "cooler when fainter" (positive $\te$-$\lx$ correlation) branch in the low-luminosity regime ($\lx \la 3\times 10^{36} \ergs$) is unexpected, thus it puts a new challenge to existing models of hot accretion flow/corona.