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 kT _ { e } .
Thanks to the capability of NuSTAR in hard X-rays , we measure these two parameters over six orders of magnitude in the 0.1-100 keV X-ray luminosity L _ { { x } } , from \sim 5 \times 10 ^ { 38 } { erg s ^ { -1 } } down to as low as \sim 5 \times 10 ^ { 32 } { erg s ^ { -1 } } .
We confirm the existence of a “ V ” -shaped correlation between \Gamma and L _ { { x } } .
Surprisingly , we observe a “ \Lambda ” -shaped correlation between kT _ { e } and L _ { { x } } .
The “ cooler when brighter ” branch in the high luminosity regime ( L _ { { x } } \ga 3 \times 10 ^ { 36 } { erg 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 _ { e } - L _ { { x } } correlation ) branch in the low-luminosity regime ( L _ { { x } } \la 3 \times 10 ^ { 36 } { erg s ^ { -1 } } ) is unexpected , thus it puts a new challenge to existing models of hot accretion flow/corona .