In this paper, we present the analysis of incoherent non-thermal radio emission from a sample of hot magnetic stars, ranging from early-B to early-A spectral type. Spanning a wide range of stellar parameters and wind properties, these stars display a commonality in their radio emission which presents new challenges to the wind scenario as originally conceived. It was thought that relativistic electrons, responsible for the radio emission, originate in current sheets formed, where the wind opens the magnetic field lines. However, the true mass-loss rates from the cooler stars are too small to explain the observed non-thermal broad-band radio spectra. Instead, we suggest the existence of a radiation belt located inside the inner magnetosphere, similar to that of Jupiter. Such a structure explains the overall indifference of the broad-band radio emissions on wind mass-loss rates. Further, correlating the radio luminosities from a larger sample of magnetic stars with their stellar parameters, the combined roles of rotation and magnetic properties have been empirically determined. Finally, our sample of early-type magnetic stars suggests a scaling relationship between the non-thermal radio luminosity and the electric voltage induced by the magnetosphere’s co-rotation, which appears to hold for a broader range of stellar types with dipole-dominated magnetospheres (like the cases of the planet Jupiter and the ultracool dwarf stars and brown dwarfs). We conclude that well-ordered and stable rotating magnetospheres share a common physical mechanism for supporting the generation of non-thermal electrons.

中文翻译：

---

有序磁层非热射电发射的比例关系：从主序带顶部到行星

在本文中，我们介绍了从早期 B 到早期 A 光谱类型的热磁星样本的非相干非热无线电发射的分析。这些恒星跨越广泛的恒星参数和风属性，在它们的无线电发射中表现出共性，这对最初设想的风情景提出了新的挑战。人们认为，负责无线电发射的相对论电子起源于形成的电流片，风打开了磁场线。然而，较冷恒星的真实质量损失率太小，无法解释观察到的非热宽带射电光谱。相反，我们建议存在位于内磁层内部的辐射带，类似于木星的辐射带。这种结构解释了宽带无线电发射对风质量损失率的总体差异。此外，将更大样本的磁星的射电光度与其恒星参数相关联，已根据经验确定了旋转和磁特性的组合作用。最后，我们的早期磁星样本表明，非热射电光度和磁层同向旋转引起的电压之间存在比例关系，这似乎适用于具有偶极子主导磁层的更广泛的恒星类型（比如木星和超冷矮星和褐矮星的例子）。我们得出结论，有序且稳定的旋转磁层具有共同的物理机制来支持非热电子的产生。