Stellar coronal X-ray emission and surface magnetic flux

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.

Stellar X-rays and magnetic activity in 3D MHD coronal models

“…In our analytical study, we found the power-law index m to be in the range from roughly one to almost two (Zhuleku et al 2020). This result agrees relatively well with most observations, but at least one more recent observation finds an even steeper power-law connection of L X ∝ Φ m with m of 2.68 (Kochukhov et al 2020).…”

“…We found that the temperature response function for temperatures below log 10 T [K] = 7 can be expressed as a power law (cf. Zhuleku et al 2020, their Fig. 1), R ∝ T α .…”

“…The dependence of the coronal X-ray emission on the surface magnetic field has been extensively studied for the Sun as well as for other stars (Fisher et al 1998;Pevtsov et al 2003;Vidotto et al 2014;Kochukhov et al 2020). In Zhuleku et al (2020), we developed an analytical model to describe the L X ∝ Φ m relation, where L X is the coronal X-ray emission and Φ the total surface unsigned magnetic flux.…”

“…Here Γ corresponds to 1/γ from the analytical model in Eq. ( 6) and Zhuleku et al (2020). The two scalings Eqs.…”

“…Our main objective is to relate the synthetic X-ray emission from the numerical models with the surface magnetic flux therein and compare this to the observed relationships. Furthermore, we compare our numerical results to our earlier analytical model (Zhuleku et al 2020), which is briefly summarized in Sect. 2.…”