High-Resolution Modelling of Coronae and Winds in Solar-type Stars with Varying Rotation Rates I. X-ray Coronae

TL;DR

This study models the coronae of four solar-type stars across a wide range of rotation rates using the SWMF-AWSoM framework fed by dynamo-generated surface magnetic maps. By incorporating small-scale magnetic flux and Alfvén-wave–driven heating, the simulations produce dense, ultra-hot coronal plasmas dominated by closed-field regions, with synthetic X-ray spectra and luminosities that broadly reproduce observed $L_X/L_{bol}$ trends and a scaling $L_X \propto \langle|\mathbf{B}|\rangle^{1.75}$. Emission measure analyses indicate good agreement for hot and ultra-hot components, though cooler plasma is overestimated due to transition-region density modeling, affecting EUV predictions. The results support Alfvén-wave heating as a viable mechanism for solar-type star coronae and lay groundwork for future time-dependent studies of eruptive events, with implications for stellar activity and planetary environments.

Abstract

Stellar coronae are believed to be the main birthplace of various stellar magnetic activities. However, the structures and properties of stellar coronae remain poorly understood. Using the Space Weather Modelling Framework with the Alfvén Wave Solar Model (SWMF-AWSoM) and dynamo-generated surface magnetic maps, here we model the coronae of four solar-type stars. By incorporating the Sun, our work covers a range of stars with the rotation varying from 1.0 to 23.3 $Ω_\odot$ (periods of 25 to 1 days). Guided by observations, we scale the magnetic field strength with increasing rotation, covering a range between 6.0 G to 1200 G approximately. In our models, energy release associated with small-scale magnetic flux is a key source of coronal heating and is essential for reproducing realistic coronal structures. Our models capture dense (1$-$2 orders of magnitude higher than solar values) and ultra-hot ($\sim 10\,\mathrm{MK}$) coronae dominated by closed field structures. Using the CHIANTI atomic database, we also compute synthetic X-ray spectra and derive the corresponding X-ray luminosities $(L_X)$, which follow a scaling law to magnetic field $L_X \propto \langle|\mathbf{B}|\rangle^{1.75}$. Furthermore, the coronal X-ray emission is found to be rotationally modulated by the alternating presence of bright active regions and dark coronal holes. These results provide new insights into the extremely high-energy coronae of rapidly rotating solar-type stars, which differ markedly from the Sun.

Figures (6)

• Figure 1: Magnetic boundary conditions in terms of topology (panel a) and field strength (panel b) in our models. (a) Surface radial magnetic field ($B_r$) in our models. The first column shows solar radial magnetograms from SDO/HMI, while the remaining columns display dynamo-generated radial maps from Viviani2018, scaled by a factor of 1/3 to match the magnetic field strengths observed in solar-type stars. The top and bottom rows represent the stellar activity minimum and maximum phases, respectively. Negative $B_r$ is shown in blue, while positive $B_r$ is shown in red. (b) Colored squares and triangles indicate mean magnetic field strengths of our stars at their minimum and maximum activity levels, respectively. The gray dots represent observed values by employing Zeeman Broadening with masses between $0.7$--$1.3~M_\odot$ and radii between $0.7$--$1.3~R_\odot$Kochukhov2020. The gray dashed line shows our power-law fit for their non-saturated stars. An animation with a duration of 23 s is available online, which shows the surface distribution of the radial magnetic field for stars at different rotation rates.
• Figure 2: Simulated stellar coronal structures at the yz-plane. The first and second columns correspond to the activity minimum phase, while the third and fourth columns represent the activity maximum phase. In each case, the first and third columns show the distribution of electron temperature ($T_{\mathrm{e}}$) as contour maps and electron number density ($n$) as color maps, both plotted on the yz-plane for each star. The second and fourth columns display the corresponding magnetic field lines, which are traced from seed points located only in the yz-plane. The magnetograms used are the same as those presented in Figure \ref{['fig1']}.
• Figure 3: Comparison of observed and simulated Emission Measure Distributions (EMDs). Colored lines represent our model results. For each color, the dark solid lines and light dash-dotted lines indicate cases at maximum and minimum activity levels, respectively. The dashed gray lines show the reconstructed EMDs based on observations of HIP 67522 Maggio2024, AU Mic Sanz-Forcada2025, AD Leo Sanz-Forcada2025, and $\it{\iota}$ Horologii Sanz-Forcada2019, plotted from top to bottom according to their overall emission measure values. The gray shaded regions indicate predicted EMDs for stars with $\log F_\mathrm{X} =$$4.0$ to $7.0$ based on Wood2018. The shading from dark to light gray corresponds to increasing $F_\mathrm{X}.$
• Figure 4: Synthetic X-ray spectra for our modelled stars and the Sun. The energy bin size is $\Delta E = 0.1$ keV. Several significant emission lines are also pointed out.
• Figure 5: Stellar X-ray luminosity normalised by bolometric luminosity ($L_\mathrm{X}/L_\mathrm{bol}$) as a function of Rossby number (Panel (a)) and mean surface magnetic field strength (Panel (b)). Colored square and triangle markers represent model results, with colors consistent with Figure \ref{['fig4']}. Squares indicate the minimum cases, while triangles correspond to the maximum cases. A constant bolometric luminosity of $L_\mathrm{bol} = 3.828 \times 10^{33}~\mathrm{erg\,s^{-1}}$ is assumed for all simulated cases. Gray circles in Panel (a) and (b) are observations taken from Wright2011 and Kochukhov2020, respectively, with the black and gray lines representing their empirical relations. The red dashed line shows a log-log linear fit to our solar-type data.