The post-disk (or primordial) spin distribution of M dwarf stars

¹ Department of Astrophysics, University of Vienna, Türkenschanzstrasse 17, 1180 Vienna, Austria
e-mail: lukasg90@unet.univie.ac.at
² Department of Earth Sciences, University of Hawai’i at Mānoa, Honolulu, HI 96822, USA
³ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany

Received: 10 March 2022
Accepted: 4 June 2023

Abstract

Context. The rotation periods of young low-mass stars after disks have dissipated (≲-pagination10 Myr) but before magnetized winds have removed significant angular momentum is an important launch point for gyrochronology and models of stellar rotational evolution; the rotation of these stars also regulates the magnetic activity and the intensity of high-energy emission that affects any close-in planets. A recent analysis of young M dwarf stars suggests a distribution of specific angular momentum (SAM) that is mass-independent, but the physical basis of this observation is unclear.

Aims. We investigate the influence of an accretion disk on the angular momentum (AM) evolution of young M dwarfs, whose parameters govern the AM distribution after the disk phase, and whether this leads to a mass-independent distribution of SAM.

Methods. We used a combination of protostellar spin and implicit hydrodynamic disk evolution models to model the innermost disk (∼0.01 AU), including a self-consistent calculation of the accretion rate onto the star, non-Keplerian disk rotation, and the influence of stellar magnetic torques over the entire disk lifetime. We executed and analyzed over 500 long-term simulations of the combined stellar and disk evolution.

Results. We find that above an initial rate of Ṁ_crit ∼ 10⁻⁸ M_⊙ yr⁻¹, accretion “erases” the initial SAM of M dwarfs during the disk lifetime, and stellar rotation converges to values of SAM that are largely independent of initial conditions. For stellar masses > 0.3 M_⊙, we find that observed initial accretion rates Ṁ_init are comparable to or exceed Ṁ_crit. Furthermore, stellar SAM after the disk phase scales with the stellar magnetic field strength as a power law with an exponent of −1.1. For lower stellar masses, Ṁ_init is predicted to be smaller than Ṁ_crit and the initial conditions are imprinted in the stellar SAM after the disk phase.

Conclusions. To explain the observed mass-independent distribution of SAM, the stellar magnetic field strength has to range between 20 G and 500 G (700 G and 1500 G) for a 0.1 M_⊙ (0.6 M_⊙) star. These values match observed large-scale magnetic field measurements of young M dwarfs and the positive relation between stellar mass and magnetic field strength agrees with a theoretically motivated scaling relation. The scaling law between stellar SAM, mass, and the magnetic field strength is consistent for young stars, where these parameters are constrained by observations. Due to the very limited number of available data, we advocate for efforts to obtain more such measurements. Our results provide new constraints on the relation between stellar mass and magnetic field strength and they can be used as initial conditions for future stellar spin models, starting after the disk phase.