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

TL;DR

This work tests and extends the CBO-powered framework for non-thermal radio emission from BA-type stars with rigidly rotating, ordered magnetospheres. By adding 32 radio observations with the VLA and performing 3D gyro-synchrotron modeling, it strengthens the empirical relation $L_{ u, ext{rad}} \propto L_{ ext{CBO}}$ and links the emission to the magnetospheric plasma density and CBO location. A simplified energy-density balance locates the CBO site $R_{ ext{CBO}}$, while detailed spectra show how the required relativistic-electron column density $n_r \times l$ scales with $L_{ ext{CBO}}$, offering insight into the acceleration efficiency. The results explain why some stars are radio loud while others are not, emphasizing plasma density and geometry as key dispersive factors, and point to future ultra-sensitive, wide-band facilities to further test and calibrate the model.

Abstract

Magnetic BA stars host dipole-like magnetospheres. When detected as radio sources, their luminosities correlate with the magnetic field and rotation. Rotation is crucial because the mechanism undergirding the relativistic electron production is powered by centrifugal breakouts. CBOs occur wherever magnetic tension does not balance centrifugal force; the resulting magnetic reconnection provides particle acceleration. To investigate how physical conditions at the site of the CBOs affect the efficiency of the acceleration mechanism, we broadly explore the parameter space governing radio emission by increasing the sample of radio-loud magnetic stars. High-sensitivity VLA observations of 32 stars were performed in the hope of identifying new centrifugal magnetospheres and associated CBOs. We calculated gyro-synchrotron spectra using 3D modeling of a dipole-shaped magnetosphere. We evaluated combinations of parameters. The number of relativistic electrons was constrained by the need to produce the emission level predicted by the scaling relationship for the radio emission from magnetic BA stars. About half of the observed stars were detected, with luminosities in 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 acceleration mechanism needed to produce enough non-thermal electrons to support the radio emission level. Given a constant acceleration efficiency, relativistic electrons represent a fixed fraction of the local thermal plasma. Thus, dense magnetospheres host more energetic particles than less dense ones; consequently, with other parameters similar, they are intrinsically brighter radio sources.

Figures (13)

• Figure 1: Cartoon summarizing the overall scenario explaining the radio emission originating from the axisymmetric dipole-shaped centrifugal magnetosphere (CM) surrounding a typical fast-rotating BA-type magnetic star (meridian cross-section). The radio emission is a consequence of the centrifugal breakout (CBO) events suffered by the magnetically confined co-rotating plasma. In stars with CM, the CBO site is located at distances larger than the Keplerian co-rotation radius (represented by the dipole line crossing the magnetic equator at distance $R_{\text{K}}$). At the distance where the centrifugal force acting on the equatorial plasma disk (pictured by the equatorial shaded red area beyond $R_{\text{K}}$) wins over the magnetic tension, the thermal plasma escapes outward, and the CBOs occur, with consequent generation of an extended current sheet, where oppositely oriented magnetic field vectors exist in small-scale spatial regions. The reconnection of magnetic fields with opposite polarity is likely the acceleration mechanism responsible for isotropically distributed non-thermal electrons. The fraction of relativistic electrons (represented by the thick blue arrows) confined within the magnetic shell, defined by the last closed magnetic field line (marked by the thick black solid line) and the open field line (marked by the dashed solid line) related to the length ($l$) of the reconnection region, propagates inward along the magnetic field lines toward the poles, radiating in the radio regime via the gyro-synchrotron emission mechanism. This incoherent non-thermal emission mechanism produces a continuum radio spectrum covering a wide spectral range. The green-shaded area represents the corresponding brightness spatial distribution of the radio emission.
• Figure 2: Maps of the 9 early-type magnetic stars detected at 9 GHz (see Fig. \ref{['fig:maps_tentativ_undetected']} for the tentative detected and undetected sources). The maps are centered at the source's position corrected for the proper motion. Pixels above the $2\sigma$ threshold are displayed in grey levels (from the light grey corresponding to the $2\sigma$ level up to the black for the brightest pixel of the map). The light-blue contours of each map show the brighter pixels starting from 99% of the source peak going down to the $3\sigma$ level. For the brightest sources, all levels spaced in steps of 99%, 90%, 75%, 50%, 35%, 30%, 25%, 20% from the peak are displayed (all levels are $\geq 3\sigma$). The red ellipses located at the positions where the stars are expected represent the sky regions covered by the First Null Beam Width (FNBW); this is about twice the Half Power Beam Width (HPBW), displayed in the bottom left corner.
• Figure 3: Histograms of the stellar parameters of all the BA-type magnetic stars discovered radio loud, blue shaded area. The stellar sample analyzed in this paper (parameters listed in Table \ref{['tab:star_param']}) has been added to the large samples of stars already analyzed in other papers Leto2021Shultz2022Das_Driessen2025. The red dotted line in each panel marks the value where the distributions peak, note that the medians of the distributions ($\langle d \rangle=148$ pc; $\langle T_{\text{eff}}\rangle=13.4$ kK; $\langle \log g \rangle=4.05$; $\langle R_{\ast}\rangle=2.8$ R$_{\odot}$; $\langle M_{\ast}\rangle=3.8$ M$_{\odot}$; $\langle B_{\text{p}} \rangle=3.9$ kG; $\langle P_{\text{rot}}\rangle=1.5$ d) fall in the same bin. The parameter distributions of the non-detected stars reported in this paper are also shown (shaded area by the oblique black lines).
• Figure 4: $L_{\nu, {\mathrm {rad}}}$--$L_{\mathrm{CBO}}$ diagram. Different symbols are used to distinguish the stars analyzed in this paper from the stars already analyzed in other papers Leto2021Shultz2022Das_Driessen2025. The shaded diagonal bands represent the region at $1\sigma$ (gray) and $3\sigma$ (light-gray) statistical confidence levels obtained by the linear fit of the data. Open downward triangles locate the BA-type magnetic stars not detected by the VLA observations reported in this paper (below the $3\sigma$ detection threshold); the downward arrowhead corresponds to the luminosity estimated using the RMS measured on the radio maps ($1\sigma$ level).
• Figure 5: Diagram $\log g$--$T_{\mathrm{eff}}$. Dashed and dot-dashed black lines are taken from Babel1996, the dotted line is taken from Hunger_Groote1999. These lines locate the zone where stellar winds are theoretically expected. Dark grey zone: homogeneous wind; grey zone: multicomponent wind; light grey zone: multicomponent wind with a lower fraction of hydrogen coupled to metals. These zones are obtained by extrapolating the original curves to encompass a range of parameters large enough to include all the BA-type magnetic stars reported in this paper, as well as other stars already discovered to be radio-loud. The pink zone, delimited by the black solid line (and its extrapolations), identifies a region on the $\log g$--$T_{\mathrm{eff}}$ parameter's space that is outside the wind zones but where several radio-loud stars still fall. The fact that there are detected stars outside the wind zone perhaps means that the wind zones do not have robust boundaries. On the other hand, the presence of undetected stars in the wind regions requires additional highly sensitive radio observations to see whether these stars are indeed radio quiet or have only very faint radio emissions.