The dependence of the Rossby number and XUV-Lyα emission flux with age for solar-like G-type stars

Stellar parameters of 11 G-type stars with ages ranging from 0.1 to 8.5 Gyr, from the Sun in Time programme, were used to compute the Rossby number, K, for each star. The Rossby number for each star was calculated from the rotation period and the convective overturn time derived from spectral type (B - V). It was found to vary essentially as t(0.5), where t is the stellar age in Gyr. The Rossby number is used as an index of X-ray-ultraviolet (XUV) (1-1200 angstrom) and Ly alpha activity, defined as the ratio of the total emission flux in these spectral regions to the total bolometric emission. Expressions for the ratio of the stellar surface XUV and Ly alpha emission flux relative to present mean solar surface flux values are given in terms of K. It is shown that the observed activity in these stars varies as K-beta, where beta takes values of 2.5 and 1.5 for XUV and Ly alpha, respectively. Expressions for deriving the Rossby number from B - V and age are also given. Thus, one can use the stellar B - V and effective temperature variation with age to calculate the XUV and Ly alpha emission flux relative to present solar values. As an example, the evolution of the solar XUV and Ly alpha with age from 0.1 to 8.5 Gyr is given. The variation of the stellar ultraviolet flux with age can be used in photochemical models to study the evolution of planetary atmospheres orbiting such stars.