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.