3 An extremely strong correlation between radio and X-ray emissions during the low/hard state

In Figs. 1 to 4, we utilize the results from Table 1 and display the radio flux density at 8.6 GHz versus the X-ray flux in different energy bands. It is apparent from these plots that a strong correlation exists between these two emission regimes in GX 339-4. As all these measurements have been taken during the low/hard state or during the transition to the off state (which appears to be a weak luminosity version of the low/hard state), we can further deduce that this correlation is a property of the low/hard state. We note that this strong correlation extends over more than three orders of magnitude in X-ray flux (e.g. the 3-9 keV band for which we have the best coverage). The correlation appears to hold for the entire four year period covered by the observations. Specifically, the 1997 measurements lie on the same line as the measurements performed during the transition to the off state in 1999 (Figs. 1 to 4), even though there was a transition to the soft state between these sets of observations (Belloni et al. 1999; Nowak et al. 2002).

Figure 3: Same as Fig. 11, but for the X-ray flux in the 20-100 keV energy band.

Figure 4: Same as Fig. 1, but for the X-ray flux in the 100-200 keV energy band.

In order to quantify the level of the correlation, we have calculated for each of the X-ray bands the Spearman rank correlation coefficient (Barlow 1989) between the radio and X-ray fluxes (Table 2). For this calculation, all detections have been taken into account (i.e. including even the points which are not strictly simultaneous or affected by a small reflare in hard X-rays: 1999.08.17 and 1999.09.01). It is clear from this analysis that the relationship between the radio and the soft and hard X-ray fluxes is extremely strong (a Student's t-test (Barlow 1989) shows the significance of the correlation is greater than 99.9% for each of the energy bands). This points to a persistent coupling between the mechanism(s) of the origin of the radio and X-ray emissions while GX 339-4 is in the low/hard state. This is the strongest evidence to date for such a persistent relation.

 

 

Table 2: Spearman rank correlation coefficient, $r_{\rm s}$, and the two sided significance of its deviation from zero, p, between the radio flux density measured at 8.6 GHz and the X-ray flux measured in various energy bands. The number of data-points, N, used in the calculations is also indicated in the last column.

X-ray band	$r_{\rm s}$	p	N
3-9 keV	0.94	$7.0 \times\ 10^{-7}$	12
9-20 keV	0.96	$7.3 \times\ 10^{-6}$	10
20-100 keV	0.97	$2.2 \times\ 10^{-5}$	9
100-200 keV	0.95	$2.6 \times\ 10^{-4}$	8

It is possible to estimate a functional relationship between the flux densities in radio (e.g. 8.6 GHz) and in the various X-ray bands. A linear fit (on a log-log scale) is satisfactory for the four X-ray bands. If we denote $F_{{\rm Rad}}$ as the radio flux density (in mJy) at 8.64 GHz and $F_{\rm X}$ as the X-ray flux (in units of 10 $^{-10} \rm ~ erg ~s^{-1} ~cm^{-2}$) in a given energy band, the relation between these two fluxes can be expressed as $F_{\rm Rad} = a \times F_{\rm X}^{b}$, where a and b are the two constant coefficients given in Table 3. These relations are valid while GX 339-4 is in the standard low/hard state, as we recall that radio emission from GX 339-4 is quenched in the high/soft state (Fender et al. 1999; Corbel et al. 2000).

As the same correlation appears to be maintained over this four year period, it could be realistic to estimate the level of radio emission from GX 339-4 by only measuring its X-ray flux. We note that little scatter is observed around the fitting function for our measurements. This also indicates that there is probably little time delay between the radio and X-ray emission. We also note the index b apparently changes with X-ray energy band. This is consistent with previous X-ray observations that indicate that, with the hard state, the spectrum of GX 339-4 becomes spectrally harder as the source becomes fainter (e.g., Nowak et al. 2002).