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 ($E_{\mathrm{c}\mathrm{u}\mathrm{t}}$) was distributed over 50–200 keV, and the photon index over 1.4–1.7. We found a clear anti-correlation ($E_{\mathrm{c}\mathrm{u}\mathrm{t}}\propto L^{-0.70\pm 0.06}$) between the X-ray luminosity ($L$) in 2–200 keV and $E_{\mathrm{c}\mathrm{u}\mathrm{t}}$, when $L$ is larger than $7\times {10}^{37}$ erg s${}^{-1}$ (assuming a distance of 8 kpc), while $E_{\mathrm{c}\mathrm{u}\mathrm{t}}$ 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.