Rotational evolution of slow-rotator sequence stars. II. Modeling the wind braking and the rotational coupling in the entire mass range of solar-like stars

TL;DR

The study addresses how magnetized wind braking and interior angular-momentum transport shape the rotational evolution of solar-like stars along the slow-rotator sequence across $0.4\,M_\odot$ to $1.25\,M_\odot$. It employs a two-zone rotational model with disk-locking and a mass-dependent coupling timescale $\\tau_{cpl}$, fitted to open-cluster rotation data (ages $\sim0.1$--$4$ Gyr), and tests multiple wind-braking mass scalings $f_{M_*}$. The key finding is a robust broken-power-law for $\\tau_{cpl}(M_*)$ with a break near $0.60\,M_\odot$, and a wind-braking term best described by $f_{M_*}=I_e/I_{e,\odot}$, leading to a near mass-independent surface torque via a semi-empirical product $K_w f_{M_*}$. This yields a physically motivated, mass-aware gyrochronology framework and clarifies the coupling between interior angular-momentum transport and surface braking, with prospects for extending the model to weakened braking and fully convective regimes.

Abstract

In recent years, ground- and space-based photometric surveys have characterized the rotational evolution of solar-like stars to an unprecedented level of detail. In this work we focus on the slow-rotator sequence, an emergent feature recognizable in the color-period diagram of Galactic open clusters. Understanding the evolution of this sequence is a promising avenue to formulate a robust rotation period-mass-age relation, which can be used to estimate stellar ages. Our model of the rotational evolution of stars on the slow-rotator sequence takes into account magnetized wind braking and the rotational decoupling between the radiative interior and the convective envelope. This decoupling naturally develops as the internal redistribution of angular momentum lags behind the loss of angular momentum at the stellar surface, and is parameterized in the model by a rotational coupling timescale. Using literature data on rotation and membership of stars in a selection of open clusters of age between 100 Myr and 4 Gyr, we constrain the mass dependence of the two competing processes of wind braking at the surface and angular momentum transport in the interior. Consistently with our previous findings, our best-fitting model requires a mass-dependent coupling timescale; this result is insensitive to the details of the wind braking model used. We show that the mass dependence of the coupling timescale follows a broken power-law in the entire solar-like mass range (0.4-1.25 Msun), with the exponent change occurring at ~ 0.6 Msun. At the same time, our approach can be used to infer semi-empirically the mass dependence of the wind braking model that best fits the observational constraints. Based on our findings, we propose a novel wind braking law with a particularly simple mass term, directly proportional to the moment of inertia of the convective envelope of the star.

Figures (12)

• Figure 1: Non--parametric fitting of the slow--rotator sequence of the Pleiades. Top panel: color--period diagram; the empirical constraints on the slow--rotator sequence extracted from the non-parametric fit are shown as empty red squares with error bars. Bottom left: normalized fit residuals; the grey dashed lines represent deviations of $\pm 2.5 \times \sigma$ from the mean. Bottom right: cumulative distribution of the normalized fit residuals compared with that of a normal distribution.
• Figure 2: Same as Figure \ref{['fig:ple_npf']}, but for M67.
• Figure 3: Prescriptions for the mass dependence of the wind braking law, $f_{M_*}$, considered in our models. The range of variability due to stellar evolution in the age range spanned by our models ($\approx 0.1$--$4$ Gyr) is also shown. The increase in the variability width at the two ends of the mass range is due to the prolonged pre-main sequence phase, and to the earlier onset of the post-main sequence phase, respectively, in comparison with the stars in the middle of the mass range.
• Figure 4: Rotational isochrones from our model "ienv" (blue lines with triangles) compared with the non-parametric fit of the slow--rotator sequence (black circles with error bars) in the mass--period diagram of the clusters in our compilation. Individual stars are also shown as orange circles.
• Figure 5: Rotational evolution according to model "ienv" for stars of mass $0.4$--$1.25\, M_\odot$. In each panel, the angular velocity of the convective envelope is plotted as a blue solid line, the angular velocity of the radiative interior is plotted as a dashed orange line, and the constraints from the non-parametric fits of the slow--rotator sequence are shown as black circles with error bars (the surface period of the Sun is also shown in the appropriate panel).