Evolution of solar-type activity: acoustic and magnetic energy generation and propagation in $\beta $ Hydri (G2 IV)

We examine the acoustic and magnetic energy generation and propagation in $\beta $  Hydri (G2 IV). The underlying motivation for this work is based on the solar, stellar, and galactic relevance of $\beta $  Hyi (a star in the Southern hemisphere), which is readily understood as a prime example and proxy of the future Sun – thus allowing assessments and analyses of the secular decay of solar activity. Regarding the magnetic energy generation, we consider longitudinal flux tube waves. We also assess acoustic waves. For the acoustic wave energy flux, the difference between the results obtained for $\beta $  Hyi and the Sun is significantly smaller than typically attained for main-sequence stars, which is largely due to the gravity-dependence of the acoustic energy generation. Furthermore, we study the height-dependent behavior of the magnetic energy flux for different magnetic filling factors corresponding to different flux tube spreadings. Finally, we comment on possible directions of future research.