Modelling the emergence and evolution of the rotation-activity relation

Main-sequence stars follow a well-defined rotation–activity relation. There are two primary regimes: saturated, where the fractional X-ray luminosity log(𝐿X/𝐿∗) is approximately constant, and unsaturated, where the fractional X-ray luminosity decreases with increasing Rossby number (or decreasing rotation rate). Pre-main sequence (PMS) stars have a larger scatter in log(𝐿X/𝐿∗) than main-sequence stars, are observed to have saturated levels of X-ray emission, and do not follow the rotation–activity relation. We investigate how PMS stars evolve in the rotation–activity plane and the timescale over which the X-ray rotation–activity relation emerges. Using observational data of ∼600 stars from four PMS clusters, stellar internal structure models, a rotational evolution model, and observed X-ray luminosity trends with age, we simulate the evolution of the PMS stars in the rotation–activity plane up to ages of 100 Myr. Our model reproduces the rotation–activity relation found for main-sequence stars, with higher-mass stars beginning to form the unsaturated regime from around 10 Myr. After ∼25 Myr, the gradient of the unsaturated regime matches that found for main-sequence stars. For stars of mass greater than 0.6M⊙, the maximum age by which a star has left the saturated regime correlates with when the star leaves the PMS. We find that an intra-cluster age spread is a key factor in contributing to the observed scatter in log(𝐿X/𝐿∗), particularly for ages < 10 Myr.