Coronal Properties of Black Hole X-Ray Binaries in the Hard State as Seen by NuSTAR and Swift

In this work we measure two important phenomenological parameters of corona (and hot accretion flow) in black hole X-ray binaries: the photon index Γ and the electron temperature ${{kT}}_{{\rm{e}}}$ . Thanks to the capability of the Nuclear Spectroscopic Telescope Array in hard X-rays, we measure these two parameters over six orders of magnitude in the 0.1-100 keV X-ray luminosity ${L}_{{\rm{X}}}$ , from ∼5 × 10³⁸ $\mathrm{erg}\,{{\rm{s}}}^{-1}$ down to as low as ∼5 × 10³² $\mathrm{erg}\,{{\rm{s}}}^{-1}$ . We confirm the existence of a "V"-shaped correlation between Γ and ${L}_{{\rm{X}}}$ . Surprisingly, we observe a "Λ"-shaped correlation between ${{kT}}_{{\rm{e}}}$ and ${L}_{{\rm{X}}}$ . The "cooler when brighter" branch in the high-luminosity regime ( ${L}_{{\rm{X}}}$ ≳ 3 × 10³⁶ $\mathrm{erg}\,{{\rm{s}}}^{-1}$ ) 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 ${{kT}}_{{\rm{e}}}$ - ${L}_{{\rm{X}}}$ correlation) branch in the low-luminosity regime ( ${L}_{{\rm{X}}}$ ≲ 3 × 10³⁶ $\mathrm{erg}\,{{\rm{s}}}^{-1}$ ) is unexpected, thus it puts a new challenge to existing models of hot accretion flow/corona.