The delayed radio emission in the black hole X-ray binary MAXI J1348$-$630

We explore the coupling between the accretion flow and the jet in black hole X-ray binary (BHXRB) MAXI J1348-630 by analyzing the X-ray and radio observations during its 2019 outburst. We measure the time delay between the radio and Comptonization fluxes with the interpolated cross-correlation function. For the first time, we find that the radio emission lags behind the X-ray Comptonization emission by about 3 days during the rising phase covering the rising hard state and the following soft state. Such a long radio delay indicates that the Comptonization emission most likely originates from the advection-dominated accretion flow rather than the jet in this source. The Comptonization luminosity $L_{\rm C}$ in 0.1-100 keV and the radio luminosity $L_{\rm R}$ at 5.5 GHz, after considering the radio delay of $\sim 3$ days, follow the correlation with a slope $\beta = 3.04 \pm 0.93$, which is much steeper than the previously reported $\beta = 0.6$ or 1.40 using the total luminosity in the limited band (e.g., 1-10 keV) in the literature. This highlights the necessity of considering (1) the time delay, (2) the spectral decomposition, and (3) the broad energy band, in the radio-X-ray correlation analysis. As the jet reappears during the decaying phase (covering the soft state and the following decaying hard state) and the mini-outburst, the Componization and the radio emission appear to be almost simultaneous. And, the radio-Compton correlation during the mini-outburst becomes shallow with the correlation slope $\beta = 1.11 \pm 0.15$. These indicate an intrinsic difference in the accretion-jet coupling physics between the main outburst and the mini-outburst.