Alfvén-wave driven magnetic rotator winds from low-mass stars I: rotation dependences of magnetic braking and mass-loss rate
Munehito Shoda, Takeru K. Suzuki, Sean P. Matt, Steven R. Cranmer, Aline A. Vidotto, Antoine Strugarek, Victor See, Victor Réville, Adam J. Finley, Allan Sacha Brun
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 Alfvén-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 $τ_w \approx 2.59 \times 10^{30} {\rm \ erg} \ \left( Ω_\ast / Ω_\odot \right)^{2.82}$, yielding a spin-down law $Ω_\ast \propto t^{-0.55}$. 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 Alfvén 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 $P_w \propto Ω_\ast^{0.57}$, which is able to explain the lower-envelope of the observed stellar winds by Wood et al. 3. the location of the Alfvén radius is shown to scale in a way that is consistent with 1D analytic theory. Additionally, the precise scaling of the Alfvén radius matches previous works which used thermally-driven winds. Our results suggest that the Alfvén-wave driven magnetic rotator wind plays a dominant role in the stellar spin-down during the main-sequence.
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
Università di Catania（卡塔尼亚大学）；INAF-Osservatorio Astrofisico di Catania（意大利国家天体物理研究所卡塔尼亚天文台）
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…
Solar-like stars (M < 1.3 Msun) lose angular momentum through their magnetized winds. The resulting evolution of the surface rotation period, which can be directly measured photometrically, has the potential to provide an accurate indicator of stellar age, and is constrained by observations of rotation periods of coeval stars, such as members of Galactic open clusters. A prominent observational feature of the mass-rotation period diagrams of open clusters is a sequence of relatively slower rotators. The formation and persistence of this slow rotators sequence across several billion years imply…
The observed mass-age-rotation relationship in open clusters shows the progressive development of a slow-rotators sequence. The observed clustering on this sequence suggests that it corresponds to some equilibrium or asymptotic condition that still lacks a complete theoretical interpretation, crucial to our understanding of the stellar angular momentum evolution. We couple a rotational evolution model, which takes into account internal differential rotation, with classical and new proposals for the wind braking law, and fit models to the data using a MCMC method. The description of the evoluti…
We examine how tides, stellar evolution, and magnetic braking shape the rotation period (P$_{rot}$) evolution of low-mass stellar binaries up to orbital periods (P$_{orb}$) of 100 d across a wide range tidal dissipation parameters using two common equilibrium tidal models. We find that many binaries with P$_{orb} < 20$ d tidally lock, and most with $P_{orb} < 4$ d tidally lock into synchronous rotation on circularized orbits. At short P$_{orb}$, tidal torques produce a population of fast rotators that single-star only models of magnetic braking fail to produce. In many cases, we show that the …
We developed angular momentum evolution models for 0.5 and 0.8 $M_{\odot}$ stars. The parametric models include a new wind braking law based on recent numerical simulations of magnetised stellar winds, specific dynamo and mass-loss rate prescriptions, as well as core/envelope decoupling. We compare model predictions to the distributions of rotational periods measured for low mass stars belonging to star forming regions and young open clusters. Furthermore, we explore the mass dependence of model parameters by comparing these new models to the solar-mass models we developed earlier. Rotational …
We report rotational periods for 16 young brown dwarfs in the nearby Upper Scorpius association, based on 72 days of high-cadence, high-precision photometry from the Kepler space telescope's K2 mission. The periods range from a few hours to two days (plus one outlier at 5 days), with a median just above one day, confirming that brown dwarfs, except at the very youngest ages, are fast rotators. Interestingly, four of the slowest rotators in our sample exhibit mid-infrared excess emission from disks; at least two also show signs of disk eclipses and accretion in the lightcurves. Comparing these …
We study the predicted rotational evolution of solar-type stars from the pre-main sequence to the solar age with 1D rotating evolutionary models including physical ingredients. We computed rotating evolution models of solar-type stars including an external stellar wind torque and internal transport of angular momentum following the method of Maeder and Zahn with the code STAREVOL. We explored different formalisms and prescriptions available from the literature. We tested the predictions of the models against recent rotational period data from extensive photometric surveys, lithium abundances o…
The O8f?p star HD 108 is implied to have experienced the most extreme rotational braking of any magnetic, massive star, with a rotational period $P_{\rm rot}$ of at least 55 years, but the upper limit on its spindown timescale is over twice the age estimated from the Hertzsprung-Russell diagram. HD 108's observed X-ray luminosity is also much higher than predicted by the XADM model, a unique discrepancy amongst magnetic O-type stars. Previously reported magnetic data cover only a small fraction ($\sim$3.5\%) of $P_{\rm rot}$, and were furthermore acquired when the star was in a photometric and…
In this first work attempts to analytically explain the effects on the magnetic braking index, $q$, caused by the evolution of stellar velocity in main-sequence stars, and estimated by de Freitas \& De Medeiros (2013). We have found that the effect of $q$ is here a determining factor for understanding the delicate mechanisms that control the spin-down of stars as a function of the mass of stars. We note that our models predict that the calculated ages are distinct from gyrochronology ages. Indeed, the gyro-ages are measured considering only the canonical value of the Skumanich relation ($q$=3)…
Extended main-sequence turnoffs apparent in most young and intermediate-age clusters (younger than ~2 Gyr) are known features caused by fast rotating early-type (earlier than F-type) stars. Late-type stars are not fast rotators because their initial angular momenta have been quickly dispersed due to magnetic braking. However, the mass limit below which stars have been magnetically braked has not been well constrained by observation. In this paper, we present an analysis of the eMSTO of NGC 6819, an open cluster of an intermediate-age (~2.5 Gyr), believed to be comparable to the lifetime of sta…
Cool stars with outer convective envelopes are observed to have magnetic fields with a variety of geometries, which on large scales are dominated by a combination of the lowest order fields such as the dipole, quadrupole and octupole modes. Magnetised stellar wind outflows are primarily responsible for the loss of angular momentum from these objects during the main sequence. Previous works have shown the reduced effectiveness of the stellar wind braking mechanism with increasingly complex, but singular, magnetic field geometries. In this paper, we quantify the impact of mixed dipolar and quadr…
Towards a holistic magnetic braking model from the evolution of cataclysmic variables to stellar spin-down -- I: the spin-down of fully convective M-dwarfs
Magnetic confinement of stellar winds leads to the formation of magnetospheres, which can be sculpted into Centrifugal Magnetospheres (CMs) by rotational support of the corotating plasma. The conditions required for the CMs of magnetic early B-type stars to yield detectable emission in H$α$ -- the principal diagnostic of these structures -- are poorly constrained. A key reason is that no detailed study of the magnetic and rotational evolution of this population has yet been performed. Using newly determined rotational periods, modern magnetic measurements, and atmospheric parameters determined…
One of the characteristic features of low-mass stars is their propensity to shed large amounts of angular momentum throughout their evolution. This distinguishs them from brown dwarfs which remain fast rotators over timescales of gigayears. Brown dwarfs with rotation periods longer than a couple of days have only been found in star forming regions and young clusters. This is a useful constraint on the mass dependency of mechanisms for angular momentum regular in stars. Rotational braking by disks and winds become highly inefficient in the substellar regime. In this short review I discuss the o…
High-Resolution Modelling of Coronae and Winds in Solar-type Stars with Varying Rotation Rates II. Stellar Winds
Nanjing University（南京大学）；Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education（教育部现代天文与天体物理重点实验室（南京大学））；Leibniz Institute for Astrophysics Potsdam（波茨坦莱布尼茨天体物理研究所）；University of Birmingham（伯明翰大学）；Aalto University（阿尔托大学）；Max-Planck-Institut für Sonnensystemforschung（马克斯·普朗克太阳系研究所）；Nordita, KTH Royal Institute of Technology & Stockholm University（诺迪塔，皇家理工学院与斯德哥尔摩大学）
HD 142990 (V 913 Sco; B5 V) is a He-weak star with a strong surface magnetic field and a short rotation period ($P_{\rm rot} \sim 1$ d). While it is clearly a rapid rotator, recent determinations of $P_{\rm rot}$ are in formal disagreement. In this paper we collect magnetic and photometric data with a combined 40-year baseline in order to re-evaluate $P_{\rm rot}$ and examine its stability. Both period analysis of individual datasets and $O-C$ analysis of the photometric data demonstrate that $P_{\rm rot}$ has decreased over the past 30 years, violating expectations from magnetospheric braking…
As the closest open cluster to the Sun, the Hyades is an important benchmark for many stellar properties, but its members are also scattered widely over the sky. Previous studies of stellar rotation in the Hyades relied on targeted observations of single stars or data from shallower all-sky variability surveys. The re-purposed Kepler mission, K2, is the first opportunity to measure rotation periods ($P_{rot}$) for many Hyads simultaneously while also being sensitive to fully convective M dwarf members. We analyze K2 data for 65 Hyads and present $P_{rot}$ values for 48. Thirty-seven of these a…
A rotating fluid star, endowed with a magnetic field, can undergo a form of precessional motion: a sum of rigid-body free precession and a non-rigid response. On secular timescales this motion is dissipated by bulk and shear viscous processes in the stellar interior and magnetospheric braking in the exterior, changing the inclination angle between the rotation and magnetic axes. Using our recent solutions for the non-rigid precessional dynamics, and viscous dissipation integrals derived in this paper, we make the only self-consistent calculation to date of these dissipation rates. We present t…
As an open cluster orbits the Milky Way, gravitational fields distort it, stripping stars from the core and forming tidal tails. Recent work has identified tidal tails of the Praesepe cluster; we explore rotation periods as a way to confirm these candidate members. In open clusters, the rotation period distribution evolves over time due to magnetic braking. Since tidally stripped stars originally formed within the cluster, they should follow the same period distribution as in the cluster core. We analyze 96 candidate members observed by NASA's Transiting Exoplanet Survey Satellite (TESS) missi…
While stellar rotation periods $P_\mathrm{rot}$ may be measured from broadband photometry, the photometric modulation becomes harder to detect for slower rotators, which could bias measurements of the long-period tail of the $P_\mathrm{rot}$ distribution. Alternatively, the $P_\mathrm{rot}$ distribution of stars can be inferred from their projected rotation velocities $v\sin i$ and radii $R$, without being biased against photometrically quiet stars. We solve this inference problem using a hierarchical Bayesian framework, which (i) is applicable to heteroscedastic measurements of $v\sin i$ and …
We analyze {\it K2} light curves for 794 low-mass ($1 > M_* > 0.1$ $M_{\odot}$) members of the $\approx$650-Myr-old open cluster Praesepe, and measure rotation periods ($P_{rot}$) for 677 of these stars. We find that half of the rapidly rotating $>$0.3 $M_{\odot}$ stars are confirmed or candidate binary systems. The remaining $>0.3$ $M_{\odot}$ fast rotators have not been searched for companions, and are therefore not confirmed single stars. We found previously that nearly all rapidly rotating $>$0.3 $M_{\odot}$ stars in the Hyades are binaries, but we require deeper binary searches in Praesep…
The magnetic chemically peculiar (mCP) stars of the upper main sequence exhibit strong, globally-organised magnetic fields which are inclined to the rotational axis and facilitate the development of surface abundance inhomogeneities resulting in photometric and spectroscopic variability. Therefore, mCP stars are perfectly suited for a direct measurement of the rotational period without the need for any additional calibrations. We have investigated the rotational properties of mCP stars based on an unprecedentedly large sample consisting of more than 500 objects with known rotational periods. U…
We present the results of a systematic study of the magnetic fields and other properties of the Ap stars with resolved magnetically split lines. This study is based on new measurements of the mean magnetic field modulus, the mean longitudinal magnetic field, the crossover, the mean quadratic magnetic field, and the radial velocity of 43 stars, complemented by magnetic data from the literature for 41 additional stars. Stars with resolved magnetically split lines represent a significant fraction, of the order of several percent, of the whole population of Ap stars. Most of them are genuine slow …
Over the course of their lifetimes, the rotation of solar-type stars goes through different phases. Once they reach the zero-age main sequence, their global rotation rate decreases during the main sequence until at least the solar age, approximately following the empirical Skumanich's law and enabling gyrochronology. Older solar-type stars might then reach a point of transition when they stop braking, according to recent results of asteroseismology. Additionally, recent 3D numerical simulations of solar-type stars show that different regimes of differential rotation can be characterized with t…
In this paper we report 23 magnetic field measurements of the B3IV star HD 23478: 12 obtained from high resolution Stokes $V$ spectra using the ESPaDOnS (CFHT) and Narval (TBL) spectropolarimeters, and 11 from medium resolution Stokes $V$ spectra obtained with the DimaPol spectropolarimeter (DAO). HD 23478 was one of two rapidly rotating stars identified as potential "centrifugal magnetosphere" hosts based on IR observations from the Apache Point Observatory Galactic Evolution Experiment survey. We derive basic physical properties of this star including its mass ($M=6.1^{+0.8}_{-0.7}\,M_\odot$…
Rotation evolution of late-type stars is dominated by magnetic braking and the underlying factors that control this angular momentum loss are important for the study of stellar spin-down. In this work, we study angular momentum loss as a function of two different aspects of magnetic activity using a calibrated Alfvén wave-driven magnetohydrodynamic wind model: the strengths of magnetic spots and their distribution in latitude. By driving the model using solar and modified solar surface magnetograms, we show that the topology of the field arising from the net interaction of both small-scale and…
Stellar rotation was proposed as a potential age diagnostic that is precise, simple, and applicable to a broad range of low-mass stars ($\leq$1 $M_\odot$). Unfortunately, rotation period $(P_{\rm rot})$ measurements of low-mass members of open clusters have undermined the idea that stars spin down with a common age dependence (i.e., $P_{\rm rot} \propto \sqrt{\rm age}$): K dwarfs appear to spin down more slowly than F and G dwarfs. Agüeros et al. (2018) interpreted data for the $\approx$1.4-Gyr-old cluster NGC 752 differently, proposing that after having converged onto a slow-rotating sequence…
We present our analysis of HD~35502 based on high- and medium-resolution spectropolarimetric observations. Our results indicate that the magnetic B5IVsnp star is the primary component of a spectroscopic triple system and that it has an effective temperature of $18.4\pm0.6\,{\rm kK}$, a mass of $5.7\pm0.6\,M_\odot$, and a polar radius of $3.0^{+1.1}_{-0.5}\,R_\odot$. The two secondary components are found to be essentially identical A-type stars for which we derive effective temperatures ($8.9\pm0.3\,{\rm kK}$), masses ($2.1\pm0.2\,M_\odot$), and radii ($2.1\pm0.4\,R_\odot$). We infer a hierarc…
About 10% of stars more massive than ${\approx}\,1.5\,\mathrm{M}_\odot$ have strong, large-scale surface magnetic fields and are being discussed as progenitors of highly-magnetic white dwarfs and magnetars. The origin of these fields remains uncertain. Recent 3D magnetohydrodynamical simulations have shown that strong magnetic fields can be generated in the merger of two massive stars. Here, we follow the long-term evolution of such a 3D merger product in a 1D stellar evolution code. During a thermal relaxation phase after the coalescence, the merger product reaches critical surface rotation, …
It is debated whether close-in giant planets can form in-situ and if not, which mechanisms are responsible for their migration. One of the observable tests for migration theories is the current value of the angle between the stellar equatorial plane and the orbital plane, called the obliquity. After the main migration mechanism has ended, the obliquity and the semi-major axis keep on evolving due to the combined effects of tides and magnetic braking. The observed correlation between effective temperature and measured projected obliquity in known short-period systems has been taken as evidence …
