Discovery of the correlation between peak episodic jet power and X-ray peak luminosity of the soft state in black hole transients

Episodic jets are usually observed in the intermediate state of black hole transients during their X-ray outbursts. Here we report the discovery of a strong positive correlation between the peak radio power of the episodic jet $P_{\rm jet}$ and the corresponding peak X-ray luminosity $L_{\rm x}$ of the soft state (in Eddington units) in a complete sample of the outbursts of black hole transients observed during the RXTE era of which data are available, which follows the relation $\log P_{\rm jet}=(2.2\pm{0.3})+(1.6\pm0.2)\times \log {L_{\rm x}}$. The transient ultra-luminous X-ray source in M31 and HLX-1 in EXO 243-49 fall on the relation if they contain stellar mass black hole and either stellar mass black hole or intermediate mass black hole, respectively. Besides, a significant correlation between the peak power of the episodic jet and the rate-of-increase of the X-ray luminosity $\rm dL_{x}/dt$ during the rising phase of those outbursts is also found, following $\log P_{\rm jet}=(2.0\pm{0.4})+(0.7\pm0.2)\times \log {\rm d}L_{\rm x}/{\rm d}t$. In GX 339$-$4 and H 1743$-$322 in which data for two outbursts are available, measurements of the peak radio power of the episodic jet and the X-ray peak luminosity (and its rate-of-change) shows similar positive correlations between outbursts, which demonstrate the dominant role of accretion over black hole spin in generating episodic jet power. On the other hand, no significant difference is seen among the systems with different measured black hole spin in current sample. This implies that the power of the episodic jet is strongly affected by non-stationary accretion instead of black hole spin characterized primarily by the rate-of-change of the mass accretion rate.