Abstract
Context. Observations show that the coronal X-ray emission of the Sun and other stars depends on the surface magnetic field. Aims. Using power-law scaling relations between different physical parameters, we aim to build an analytical model to connect the observed X-ray emission to the surface magnetic flux. Methods. The basis for our model are the scaling laws of Rosner, Tucker & Vaiana (RTV) that connect the temperature and pressure of a coronal loop to its length and energy input. To estimate the energy flux into the upper atmosphere, we used scalings derived for different heating mechanisms, such as field-line braiding or Alfvén wave heating. We supplemented this with observed relations between active region size and magnetic flux and derived scalings of how X-ray emissivity depends on temperature. Results. Based on our analytical model, we find a power-law dependence of the X-ray emission on the magnetic flux, LX ∝ Φm, with a power-law index m being in the range from about one to two. This finding is consistent with a wide range of observations, from individual features on the Sun, such as bright points or active regions, to stars of different types and varying levels of activity. The power-law index m depends on the choice of the heating mechanism, and our results slightly favor the braiding and nanoflare scenarios over Alfvén wave heating. In addition, the choice of instrument will have an impact on the power-law index m because of the sensitivity of the observed wavelength region to the temperature of the coronal plasma. Conclusions. Overall, our simple analytical model based on the RTV scaling laws gives a good representation of the observed X-ray emission. Therefore we might be able to understand stellar coronal activity though a collection of basic building blocks, like loops, which we can study in spatially resolved detail on the Sun.
Highlights
The Sun, other solar-like stars, and, in particular, other more active stars are sources of X-ray emission
Observations show that the coronal X-ray emission of the Sun and other stars depends on the surface magnetic field
We supplemented this with observed relations between active region size and magnetic flux and derived scalings of how X-ray emissivity depends on temperature
Summary
The Sun, other solar-like stars, and, in particular, other more active stars are sources of X-ray emission. These X-rays are mostly of a thermal nature and originate from stellar coronae due to the high temperatures, well above 1 MK, in their outer atmospheres. Observational studies show a clear dependence of the X-ray emission on the surface magnetic field for individual structures on the Sun as well as for stars as a whole. Studying the X-ray emission and the surface magnetic field of solar-like stars, Kochukhov et al (2020) found a relation of LX ∝ Φ2.68. Observations of different solar magnetic structures, such as active regions, bright points, or microflares, and of stars with various levels of activity, reveal power-law relations between X-ray emission and the magnetic field. There is quite a large scatter in the Xray observations of other stars, in part because the data usually used for a statistical analysis of the X-ray emission might capture different phases of stellar activity (e.g., Vidotto et al 2014)
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