Luminosity dependence of the electron temperature in the bright hard state of the black hole candidate GX 339--4

We have analyzed 200 Rossi X-ray Timing Explorer observations of the black hole candidate GX 339--4, all from the bright hard state periods between 1996 and 2005. Purpose of our study is to investigate the radiation mechanisms in the hard state of GX 339--4. The broadband 3--200 keV spectra were successfully modeled by a simple analytic model, power--law with an exponential cut-off modified with a smeared edge. The obtained energy cut-off ($E_{\rm{cut}}$) was distributed over 50--200 keV, and the photon index over 1.4--1.7. We found a clear anti-correlation ($E_{\rm{cut}} \propto L^{-0.70\pm0.06}$) between the X-ray luminosity ($L$) in 2--200 keV and $E_{\rm{cut}}$, when $L$ is larger than $7 \times 10^{37}$ erg s$^{-1}$ (assuming a distance of 8 kpc), while $E_{\rm{cut}}$ is roughly constant at around 200 keV when $L$ is smaller than $7 \times 10^{37}$ erg s$^{-1}$. This anti-correlation remained unchanged by adopting a more physical thermal Comptonization model, which resulted in the anti-correlation that can be expressed as $kT_{\rm{e}} \propto L^{-0.24\pm0.06}$. These anti-correlations can be quantitatively explained by a picture in which the energy-flow rate from protons to electrons balances with the inverse Compton cooling.