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Episodic jets are usually observed in the intermediate state of black holetransients during their X-ray outbursts. Here we report the discovery of astrong 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 thesoft state (in Eddington units) in a complete sample of the outbursts of blackhole transients observed during the RXTE era of which data are available, whichfollows 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 EXO243-49 fall on the relation if they contain stellar mass black hole and eitherstellar mass black hole or intermediate mass black hole, respectively. Besides,a significant correlation between the peak power of the episodic jet and therate-of-increase of the X-ray luminosity $\rm dL_{x}/dt$ during the risingphase of those outbursts is also found, following $\log P_{\rmjet}=(2.0\pm{0.4})+(0.7\pm0.2)\times \log {\rm d}L_{\rm x}/{\rm d}t$. In GX339$-$4 and H 1743$-$322 in which data for two outbursts are available,measurements of the peak radio power of the episodic jet and the X-ray peakluminosity (and its rate-of-change) shows similar positive correlations betweenoutbursts, which demonstrate the dominant role of accretion over black holespin in generating episodic jet power. On the other hand, no significantdifference is seen among the systems with different measured black hole spin incurrent sample. This implies that the power of the episodic jet is stronglyaffected by non-stationary accretion instead of black hole spin characterizedprimarily by the rate-of-change of the mass accretion rate.

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