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Register a new userMagnetic Braking Formulation for Sun-Like Stars: Dependence on Dipole Field Strength and Rotation Rate
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Sean P. Matt
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We use two-dimensional axisymmetric magnetohydrodynamic simulations to compute steady-state solutions for solar-like stellar winds from rotating stars with dipolar magnetic fields. Our parameter study includes 50 simulations covering a wide range of relative magnetic field strengths and rotation rates, extending from the slow- and approaching the fast-magnetic-rotator regimes. Using the simulations to compute the angular momentum loss, we derive a semi-analytic formulation for the external torque on the star that fits all of the simulations to a precision of a few percents. This formula provides a simple method for computing the magnetic braking of sun-like stars due to magnetized stellar winds, which properly includes the dependence on the strength of the magnetic field, mass loss rate, stellar radius, suface gravity, and spin rate and which is valid for both slow and fast rotators.
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Magnetic fields play an important role at all stages of stellar evolution. In Sun-like stars, they are generated in the outer convective layers. Studying the large-scale magnetic fields of these stars enlightens our understanding of the field properties and gives us observational constraints for the field generation models. In this review, I summarise the current observational picture of the large-scale magnetic fields of Sun-like stars, in particular solar-twins and planet-host stars. I discuss the observations of large-scale magnetic cycles, and compare these cycles to the solar cycle.
We study the distribution of the photometric rotation period (Prot), which is a direct measurement of the surface rotation at active latitudes, for three subsamples of Sun-like stars: one from CoRoT data and two from Kepler data. We identify the main populations of these samples and interpret their main biases specifically for a comparison with the solar Prot. Prot and variability amplitude (A) measurements were obtained from public CoRoT and Kepler catalogs combined with physical parameters. Because these samples are subject to selection effects, we computed synthetic samples with simulated biases to compare with observations, particularly around the location of the Sun in the HR diagram. Theoretical grids and empirical relations were used to combine physical parameters with Prot and A. Biases were simulated by performing cutoffs on the physical and rotational parameters in the same way as in each observed sample. A crucial cutoff is related with the detectability of the rotational modulation, which strongly depends on A. The synthetic samples explain the observed Prot distributions of Sun-like stars as having two main populations: one of young objects (group I, with ages younger than ~1 Gyr) and another of MS and evolved stars (group II, with ages older than ~1 Gyr). The proportions of groups I and II in relation to the total number of stars range within 64-84% and 16-36%, respectively. Hence, young objects abound in the distributions, producing the effect of observing a high number of short periods around the location of the Sun in the HR diagram. Differences in the Prot distributions between the CoRoT and Kepler Sun-like samples may be associated with different Galactic populations. Overall, the synthetic distribution around the solar period agrees with observations, which suggests that the solar rotation is normal with respect to Sun-like stars within the accuracy of current data.
In previous work we identified six Sun-like stars observed by Kepler with exceptionally clear asteroseismic signatures of rotation. Here, we show that five of these stars exhibit surface variability suitable for measuring rotation. In order to further constrain differential rotation, we compare the rotation periods obtained from light-curve variability with those from asteroseismology. The two rotation measurement methods are found to agree within uncertainties, suggesting that radial differential rotation is weak, as is the case for the Sun. Furthermore, we find significant discrepancies between ages from asteroseismology and from three different gyrochronology relations, implying that stellar age estimation is problematic even for Sun-like stars.
Observations of stellar rotation show that low-mass stars lose angular momentum during the main sequence. We simulate the winds of Sun-like stars with a range of rotation rates, covering the fast and slow magneto-rotator regimes, including the transition between the two. We generalize an Alfven-wave driven solar wind model that builds on previous works by including the magneto-centrifugal force explicitly. In this model, the surface-averaged open magnetic flux is assumed to scale as $B_ast f^{rm open}_ast propto {rm Ro}^{-1.2}$, where $f^{rm open}_ast$ and ${rm Ro}$ are the surface open-flux filling factor and Rossby number, respectively. We find that, 1. the angular momentum loss rate (torque) of the wind is described as $tau_w approx 2.59 times 10^{30} {rm erg} left( Omega_ast / Omega_odot right)^{2.82}$, yielding a spin-down law $Omega_ast propto t^{-0.55}$. 2. the mass-loss rate saturates at $dot{M}_w sim 3.4 times 10^{-14} M_odot {rm yr^{-1}}$, due to the strong reflection and dissipation of Alfven waves in the chromosphere. This indicates that the chromosphere has a strong impact in connecting the stellar surface and stellar wind. Meanwhile, the wind ram pressure scales as $P_w propto Omega_ast^{0.57}$, which is able to explain the lower-envelope of the observed stellar winds by Wood et al. 3. the location of the Alfven radius is shown to scale in a way that is consistent with 1D analytic theory. Additionally, the precise scaling of the Alfven radius matches previous works which used thermally-driven winds. Our results suggest that the Alfven-wave driven magnetic rotator wind plays a dominant role in the stellar spin-down during the main-sequence.
We present a detailed study of the two Sun-like stars KIC 7985370 and KIC 7765135, aimed at determining their activity level, spot distribution, and differential rotation. Both stars were discovered by us to be young stars and were observed by the NASA Kepler mission. The stellar parameters (vsini, spectral type, Teff, log g, and [Fe/H]) were derived from optical spectroscopy which allowed us also to study the chromospheric activity from the emission in the core of Halpha and CaII IRT lines. The high-precision Kepler photometric data spanning over 229 days were then fitted with a robust spot model. Model selection and parameter estimation are performed in a Bayesian manner, using a Markov chain Monte Carlo method. Both stars came out to be Sun-like with an age of about 100-200 Myr, based on their lithium content and kinematics. Their youth is confirmed by the high level of chromospheric activity, comparable to that displayed by the early G-type stars in the Pleiades cluster. The flux ratio of the CaII-IRT lines suggests that the cores of these lines are mainly formed in optically-thick regions analogous to solar plages. The model of the light curves requires at least seven enduring spots for KIC 7985370 and nine spots for KIC 7765135 for a satisfactory fit. The assumption of longevity of the star spots, whose area is allowed to evolve in time, is at the heart of our approach. We found, for both stars, a rather high value of the equator-to-pole differential rotation (dOmega~0.18 rad/day) which is in contrast with the predictions of some mean-field models of differential rotation for fast-rotating stars. Our results are instead in agreement with previous works on solar-type stars and with other models which predict a higher latitudinal shear, increasing with equatorial angular velocity.
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