In asteroseismology an important diagnostic of the evolutionary status of a
star is the small frequency separation which is sensitive to the gradient of
the mean molecular weight in the stellar interior. It is thus interesting to
discuss the classical age-activity relations in terms of this quantity.
Moreover, as the photospheric magnetic field tends to suppress the amplitudes
of acoustic oscillations, it is important to quantify the importance of this
effect by considering various activity indicators. We propose a new class of
age-activity relations that connects the Mt. Wilson S index and the average
scatter in the light curve with the small frequency separation and the
amplitude of the p-mode oscillations. We used a Bayesian inference to compute
the posterior probability of various empirical laws for a sample of 19
solar-like active stars observed by the Kepler telescope. We demonstrate the
presence of a clear correlation between the Mt. Wilson S index and the
relative age of the stars as indicated by the small frequency separation, as
well as an anti-correlation between the S index and the oscillation
amplitudes. We argue that the average activity level of the stars shows a
stronger correlation with the small frequency separation than with the absolute
age that is often considered in the literature. The phenomenological laws
discovered in this paper have the potential to become new important diagnostics
to link stellar evolution theory with the dynamics of global magnetic fields.
In particular we argue that the relation between the Mt. Wilson S index and
the oscillation amplitudes is in good agreement with the findings of direct
numerical simulations of magneto-convection.Comment: 5 pages, 4 figures, 2 tables. Accepted for publication in A&
