A scaling relationship for nonthermal radio emission from ordered magnetospheres. II. Investigating the efficiency of relativistic electron production in the magnetospheres of BA-type stars

Magnetic BA-type stars typically host dipole-like magnetospheres. When detected as nonthermal radio sources, their luminosities are correlated with the stellar magnetic field and rotation speed. Rotation is crucial because the mechanism undergirding the relativistic electron production is powered by centrifugal breakouts (CBOs). Small-scale breakouts occur wherever magnetic tension does not balance out the centrifugal force, resulting in magnetic reconnection and particle acceleration. To investigate how physical conditions at the site of the CBOs affect the efficiency of the nonthermal electron acceleration mechanism, we broadly explore the parameter space governing radio emission by increasing the available sample of radio-loud magnetic stars. High-sensitivity VLA observations of 32 early-type magnetic stars were performed in the hope of identifying new centrifugally supported magnetospheres (CMs) and associated CBOs. We calculated the radio spectra produced by the gyrosynchrotron emission mechanism using a 3D modeling of a dipole-shaped corotating magnetosphere. We evaluated combinations of stellar parameters and equatorial thermal plasma densities. The number of relativistic electrons was constrained by the need to produce the emission level predicted by the well-known empirical scaling relationship for the radio emission from magnetic BA stars. About half of the observed early-type magnetic stars were detected, with radio luminosities that show an excellent agreement with the expected values, reinforcing the robust nature of the scaling relationship for CBO-powered radio emission. Comparing the competing centrifugal and magnetic effects on plasma locked in a rigidly rotating magnetosphere, we located the site of CBOs and inferred the local plasma density. We then estimated the efficiency of the CBO-powered acceleration mechanism needed to produce enough nonthermal electrons to support the expected radio emission level. Given a constant acceleration efficiency, relativistic electrons represent a fixed fraction of the local thermal plasma. Thus, we find that dense magnetospheres host many more energetic particles than less dense ones; consequently, with the other parameters remaining similar, they are shown to be intrinsically brighter radio sources.