The Solar Wind in Time II: 3D stellar wind structure and radio emission

In this work, we simulate the evolution of the solar wind along its main sequence lifetime and compute its thermal radio emission. To study the evolution of the solar wind, we use a sample of solar mass stars at different ages. All these stars have observationally-reconstructed magnetic maps, which are incorporated in our 3D magnetohydrodynamic simulations of their winds. We show that angular-momentum loss and mass-loss rates decrease steadily on evolutionary timescales, although they can vary in a magnetic cycle timescale. Stellar winds are known to emit radiation in the form of thermal bremsstrahlung in the radio spectrum. To calculate the expected radio fluxes from these winds, we solve the radiative transfer equation numerically from first principles. We compute continuum spectra across the frequency range 100 MHz - 100 GHz and find maximum radio flux densities ranging from 0.05 - 8.3 $\mu$Jy. At a frequency of 1 GHz and a normalised distance of d = 10 pc, the radio flux density follows 0.24 $(\Omega/\Omega_{\odot})^{0.9}$ (d/[10pc])$^2$ $\mu$Jy, where $\Omega$ is the rotation rate. This means that the best candidates for stellar wind observations in the radio regime are faster rotators within distances of 10 pc, such as $\kappa^1$ Ceti (2.83 $\mu$Jy) and $\chi^1$ Ori (8.3 $\mu$Jy). These flux predictions provide a guide to observing solar-type stars across the frequency range 0.1 - 100 GHz in the future using the next generation of radio telescopes, such as ngVLA and SKA.