Radio emission from colliding outflows in high-mass X-ray binaries with strongly magnetized neutron stars

We present a toy model for radio emission in HMXBs with strongly magnetized neutron stars (NS) where wind-collision region is formed by the NS outflow and stellar wind of massive companion. Radio expected from synchrotron radiation shock-accelerated electrons free-free wind. found that predicted relation between GHz luminosity ($L_R$) accretion X-ray ($L_X$) can be written as $L_R \propto L_X^b$ most parameters. No correlation X-rays ($b=0$) when thermal dominates radio. typically find steep ($b=12/7$) sub-Eddington luminosities more shallow one ($b=2(p-1)/7$) super-Eddington luminosities, $p$ power-law index accelerated electrons. The maximum independent properties, while it depends on momentum, binary separation distance, minimum electron Lorentz factor. Using Bayesian approach we modelled observations \sj cover wide range mass rates. Our results support shock origin detections at luminosities. However, no physically meaningful parameters could phase outburst, suggesting different origin. Future sensitive instruments might reveal large number NSs radio, allowing determination slope $L_R-L_X$ relation, putting scenario into test.