611 {gamma} Doradus stars Kepler data

These three observables guide the mode identifications and can be used to estimate the near-core rotation rate. We find many stars are hotter and show longer period-spacing patterns than theory. Using the traditional approximation of rotation (TAR), we inferred the asymptotic spacings, the near-core rotation rates, and the radial orders of the g and r modes.

Most stars have a near-core rotation rate around 1d^-1^ and an asymptotic spacing around 4000s. We also find that many stars rotate more slowly than predicted by theory for unclear reasons. 11 stars show rotational splittings with fast rotation rates. We compared the observed slope-rotation relation with the theory and find a large spread.

We detected rotational modulations in 58 stars and used them to derive the core-to-surface rotation ratios. The interiors rotate faster than the cores in most stars, but by no more than 5 per cent.