The Solar Twin Planet Search: IV. The Sun as a typical rotator and evidence for a new rotational braking law for Sun-like stars

It is still unclear how common the Sun is when compared to other similar stars in regards to some of its physical properties, such as rotation. Considering that gyrochronology relations are widely used today to estimate ages of stars in the main sequence, and that the Sun is used to calibrate it, it is crucial to assess if these procedures are acceptable. We analyze the rotational velocities -- limited by the unknown rotation axis inclination angle -- of an unprecedented large sample of solar twins in order to study the rotational evolution of Sun-like stars, and assess if the Sun is a typical rotator. We use high-resolution ($R = 115000$) spectra obtained with the HARPS spectrograph and ESO's 3.6 m telescope at La Silla Observatory. The projected rotational velocities for 82 solar twins are estimated by line profile fitting with synthetic spectra. Macroturbulence velocities are inferred from a prescription that accurately reflects their dependence with effective temperature and luminosity of the stars. Our sample of solar twins include some spectroscopic binaries with enhanced rotational velocities, and we do not find any non-spectroscopic binaries with unusually high rotation velocities. We verified that the Sun does not have a peculiar rotation, but the solar twins exhibit rotational velocities that depart from the Skumanich relation. The Sun is a regular rotator when compared to solar twins with a similar age. Additionally, we obtain a rotational braking law that better describes the stars in our sample ($v \propto t^{-0.6}$) in contrast to previous, often-used scalings.