Stellar magnetism: empirical trends with age and rotation

15 pages, 7 figures.International audienceWe investigate how the observed large-scale surface magnetic fields of low-mass stars (~0.1 -- 2 Msun), reconstructed through Zeeman-Doppler imaging (ZDI), vary with age t, rotation and X-ray emission. Our sample consists of 104 magnetic maps of 73 stars, from accreting pre-main sequence to main-sequence objects (1 Myr is related to age as $t^{-0.655 \pm 0.045}$. This relation has a similar dependence to that identified by Skumanich (1972), used as the basis for gyrochronology. Likewise, our relation could be used as an age-dating method ("magnetochronology"). The trends with rotation we find for the large-scale stellar magnetism are consistent with the trends found from Zeeman broadening measurements (sensitive to large- and small-scale fields). These similarities indicate that the fields recovered from both techniques are coupled to each other, suggesting that small- and large-scale fields could share the same dynamo field generation processes. For the accreting objects, fewer statistically significant relations are found, with one being a correlation between the unsigned magnetic flux and rotation period. We attribute this to a signature of star-disc interaction, rather than being driven by the dynamo