With this study, we showed that the previously observed correlation between X-ray and radio fluxes during the low-hard state of GX 339-4 (Hannikainen et al. 1998; Corbel et al. 2000) extends over more than three decades in X-ray luminosity. The observations, spread over almost four years, indicated that the same fitting functions probably hold during these years, despite an intervening state transition. The radio emission in GX 339-4 is likely associated with the optically thick synchrotron emission from the compact jet (Corbel et al. 2000). The very strong correlation of radio emission with X-ray flux indicates that synchrotron processes may also play a role at high energies.

It has already been pointed out for GX 339-4 that the near infrared/optical bands show a spectral break that may indicate that the X-ray spectrum is an extension of the optically thin synchrotron emission from the compact jet (Corbel & Fender 2002). Specifically, the infrared points are consistent with an extrapolation of the slope from the radio, while the infrared/optical break extrapolates to the observed X-rays. The jet model, originally developed for AGN and previously applied to XTE J1118+480 (Markoff et al. 2001), has been further improved and also applied to these datasets (with additional optical data), and is discussed in a companion paper (Markoff et al. 2003). Markoff et al. (2003) showed that the jet model can account for the broadband spectra of GX 339-4 radio through optical through X-ray, primarily by only changing two parameters: the jet power and the location of the acceleration zone. The fact that the correlation holds at very low X-ray luminosity indicates that a compact jet is also produced when the source is close to quiescence. Therefore, the broadband emission of the jets has to be taken into account when studying the bolometric luminosity of black hole in quiescence, e.g. Campana & Stella (2000) and Garcia et al. (2001).

Table 3: Parameters of the function used to fit the radio flux density (in mJy) at 8.6 GHz, $F_{{\rm Rad}}$ , versus the flux, $F_{\rm X}$ , measured in a given energy band ((in unit of 10 $^{-10} \rm ~ erg ~s^{-1} ~cm^{-2}$ ). The relation is expressed as $F_{\rm rad}= a~\times~F_{\rm X}^{b}$ .
X-ray band a b

3-9 keV 1.721 $\pm$ 0.035 0.706 $\pm$ 0.011

9-20 keV 1.739 $\pm$ 0.035 0.715 $\pm$ 0.011

20-100 keV 0.667 $\pm$ 0.041 0.774 $\pm$ 0.021

100-200 keV 1.024 $\pm$ 0.287 0.891 $\pm$ 0.104

**Table 3:** Parameters of the function used to fit the radio flux density (in mJy) at 8.6 GHz, $F_{{\rm Rad}}$ , versus the flux, $F_{\rm X}$ , measured in a given energy band ((in unit of 10 $^{-10} \rm ~ erg ~s^{-1} ~cm^{-2}$ ). The relation is expressed as $F_{\rm rad}= a~\times~F_{\rm X}^{b}$ .
X-ray band	a	b
3-9 keV	1.721 $\pm$ 0.035	0.706 $\pm$ 0.011
9-20 keV	1.739 $\pm$ 0.035	0.715 $\pm$ 0.011
20-100 keV	0.667 $\pm$ 0.041	0.774 $\pm$ 0.021
100-200 keV	1.024 $\pm$ 0.287	0.891 $\pm$ 0.104

It is interesting to note that the radio flux at 8.6 GHz is proportional to the X-ray flux as $F_{\rm rad} \propto~F_{\rm X}^{+0.71}$ (in the 3-9 and 9-20 keV bands) and that the same behaviour with the same index b has recently been found to hold for the black hole transient V404 Cyg (Gallo et al. 2002). The jet model of Markoff et al. (2003) successfully explains this dependency analytically using the formalism developed in Falcke & Biermann (1996). Indeed, if the only varying parameter of the model is the power in the jet, then the X-ray flux is expected to vary as $F_{\rm X} \propto~F_{\rm rad}^{+1.41}$ , i.e. $F_{\rm rad} \propto~F_{\rm X}^{+0.71}$ , completely consistent with the behaviour of GX 339-4 and V404 Cyg. The current versions of the jet model, however, do not account for the evolution of the exponent, b, in $F_{\rm rad} \propto~F_{\rm X}^{b}$ , for the higher energy X-ray bands, as is found for GX 339-4 (Table 3). If a jet is the underlying cause of the overall radio/X-ray correlation, the model may need to be further developed in order to explain this detailed behavior. However, it is important to point out that these higher energies include the canonical "100 keV cutoff'' region in the data, where one expects the X-rays to decrease in comparison to the radio emission. However, the simplified accretion disk model used by Markoff et al. (2003) currently does not include all spectral components, e.g., the contribution from reflection which are often observed in the hard state X-ray spectra of BHC (e.g., Done 2002). Studies like these clearly show, however, that including jet emission processes in any models of BHC spectra in their low/hard state is crucially important to fully understand the physical processes in these sources.

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