Stellar Spin-down Research Articles

THE DEPENDENCE OF STELLAR MASS AND ANGULAR MOMENTUM LOSSES ON LATITUDE AND THE INTERACTION OF ACTIVE REGION AND DIPOLAR MAGNETIC FIELDS

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 Alfv\'en 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 large-scale field is important for spin-down rates and that angular momentum loss is not a simple function of large scale magnetic field strength. We find that changing the latitude of magnetic spots can modify mass and angular momentum loss rates by a factor of two. The general effect that causes these differences is the closing down of large-scale open field at mid- and high-latitudes by the addition of the small-scale field. These effects might give rise to modulation of mass and angular momentum loss through stellar cycles, and present a problem for ab initio attempts to predict stellar spin-down based on wind models. For all the magnetogram cases considered here, from dipoles to various spotted distributions, we find that angular momentum loss is dominated by the mass loss at mid-latitudes. The spin-down torque applied by magnetized winds therefore acts at specific latitudes and is not evenly distributed over the stellar surface, though this aspect is unlikely to be important for understanding spin-down and surface flows on stars.

The role of complex magnetic topologies on stellar spin-down

AbstractThe rotational braking of magnetic stars through the extraction of angular momentum by stellar winds has been studied for decades, leading to several formulations. We recently demonstrated that the dependency of the braking law on the coronal magnetic field topology can be taken into account through a simple scalar parameter: the open magnetic flux. The Zeeman-Doppler Imaging technique has brought the community a reliable and precise description of the surface magnetic field of distant stars. The coronal structure can then be reconstructed using a potential field extrapolation, a technique that relies on a source surface radius beyond which all field lines are open, thus avoiding a computationally expensive MHD simulations. We developed a methodology to choose the best source surface radius in order to estimate open flux and magnetic torques. We apply this methodology to five K-type stars from 25 to 584 Myr and the Sun, and compare the resulting torque to values expected from spin evolution models.

Magnetic Field - Stellar Winds Interaction

AbstractAs per the recent study by the MiMeS collaboration, only about 10% of massive stars possess organized global magnetic fields, typically dipolar in nature. The competition between such magnetic fields and highly non-linear radiative forces that drive the stellar winds leads to a highly complex interaction. Such an interplay can lead to a number of observable phenomena, e.g. X-ray, wind confinement, rapid stellar spindown. However, due to its complexity, such an interaction cannot usually be modeled analytically, instead numerical modeling becomes a necessary tool. In this talk, I will discuss how numerical magnetohydrodynamic (MHD) simulations are employed to understand the nature of such magnetized massive star winds.

Dynamical tides in eccentric binaries and tidally excited stellar pulsations in Kepler KOI-54

Recent observation of the tidally-excited stellar oscillations in the main-sequence binary KOI-54 by the KEPLER satellite provides a unique opportunity for studying dynamical tides in eccentric binary systems. We develop a general theory of tidal excitation of oscillation modes of rotating binary stars, and apply our theory to tidally excited gravity modes (g-modes) in KOI-54. The strongest observed oscillations, which occur at 90 and 91 times the orbital frequency, are likely due to prograde m=2 modes (relative to the stellar spin axis) locked in resonance with the orbit. The remaining flux oscillations with frequencies that are integer multiples of the orbital frequency are likely due to nearly resonant m=0 g-modes; such axisymmetric modes generate larger flux variations compared to the m=2 modes, assuming that the spin inclination angle of the star is comparable to the orbital inclination angle. We examine the process of resonance mode locking under the combined effects of dynamical tides on the stellar spin and orbit and the intrinsic stellar spindown. We show that KOI-54 can naturally evolve into a state in which at least one m=2 mode is locked in resonance with the orbital frequency. Our analysis provides an explanation for the fact that only oscillations with frequencies less than 90-100 times the orbital frequency are observed. We have also found evidence from the published KEPLER result that three-mode nonlinear coupling occurs in the KOI-54 system. We suggest that such nonlinear mode coupling may explain the observed oscillations that are not harmonics of the orbital frequency.

THE FACTORY AND THE BEEHIVE. I. ROTATION PERIODS FOR LOW-MASS STARS IN PRAESEPE

Stellar rotation periods measured from single-age populations are critical for investigating how stellar angular momentum content evolves over time, how that evolution depends on mass, and how rotation influences the stellar dynamo and the magnetically heated chromosphere and corona. We report rotation periods for 40 late-K to mid-M stars members of the nearby, rich, intermediate-age (~600 Myr) open cluster Praesepe. These rotation periods were derived from ~200 observations taken by the Palomar Transient Factory of four cluster fields from 2010 February to May. Our measurements indicate that Praesepe's mass-period relation transitions from a well-defined singular relation to a more scattered distribution of both fast and slow rotators at ~0.6 Msun. The location of this transition is broadly consistent with expectations based on observations of younger clusters and the assumption that stellar-spin down is the dominant mechanism influencing angular momentum evolution at 600 Myr. However, a comparison to data recently published for the Hyades, assumed to be coeval to Praesepe, indicates that the divergence from a singular mass-period relation occurs at different characteristic masses, strengthening the finding that Praesepe is the younger of the two clusters. We also use previously published relations describing the evolution of rotation periods as a function of color and mass to evolve the sample of Praesepe periods in time. Comparing the resulting predictions to periods measured in M35 and NGC 2516 (~150 Myr) and for kinematically selected young and old field star populations suggests that stellar spin-down may progress more slowly than described by these relations.

The independency of stellar mass-loss rates on stellar X-ray luminosity and activity level based on solar X-ray flux and solar wind observations

Stellar mass loss rates are an important input ingredient for stellar evolution models since they determine stellar evolution parameters such as stellar spin-down and increase in stellar luminosity through the lifetime of a star. Due to the lack of direct observations of stellar winds from Sun-like stars stellar X-ray luminosity and stellar level of activity are commonly used as a proxy for estimating stellar mass loss rates. However, such an intuitive activity --- mass loss rate relation is not well defined. In this paper, I study the mass loss rate of the Sun as a function of its activity level. I compare in-situ solar wind measurements with the solar activity level represented by the solar X-ray flux. I find no clear dependency of the solar mass flux on solar X-ray flux. Instead, the solar mass loss rate is scattered around an average value of $2\cdot10^{-14}\;M_\odot\;yr^{-1}$. This independency of the mass loss rate on level of activity can be explained by the fact that the activity level is governed by the large modulations in the solar close magnetic flux, while the mass loss rate is governed by the rather constant open magnetic flux. I derive a simple expression for stellar mass loss rates as a function of the stellar ambient weak magnetic field, the stellar radius, the stellar escape velocity, and the average height of the Alfv\'en surface. This expression predicts stellar mass loss rates of $10^{-15}-10^{-12}\;M_\odot\;yr^{-1}$ for Sun-like stars.

Meissner effect and vortex expulsion in color-superconducting quark stars, and its role for reheating of magnetars

Compact stars made of quark matter rather than confined hadronic matter, are expected to form a color superconductor. This superconductor ought to be threaded with rotational vortex lines, within which the star's interior magnetic field is at least partially confined. The vortices (and thus magnetic flux) would be expelled from the star during stellar spin-down, leading to magnetic reconnection at the surface of the star and the prolific production of thermal energy. In this paper, we show that this energy release can re-heat quark stars to exceptionally high temperatures, such as observed for Soft Gamma Repeaters (SGRs), Anomalous X-Ray pulsars (AXPs), and X-ray dim isolated neutron stars (XDINs). Moreover, our numerical investigations of the temperature evolution, spin-down rate, and magnetic field behavior of such superconducting quark stars suggest that SGRs, AXPs, and XDINs may be linked ancestrally. Finally, we discuss the possibility of a time delay before the star enters the color superconducting phase, which can be used to estimate the density at which quarks deconfine. From observations, we find this density to be of the order of five times that of nuclear saturation.

Angular momentum loss and stellar spin-down in magnetic massive stars

AbstractWe examine the angular momentum loss and associated rotational spin-down for magnetic hot stars with a line-driven stellar wind and a rotation-aligned dipole magnetic field. Our analysis here is based on our previous 2-D numerical MHD simulation study that examines the interplay among wind, field, and rotation as a function of two dimensionless parameters, W(=Vrot/Vorb) and ‘wind magnetic confinement’, η∗ defined below. We compare and contrast the 2-D, time variable angular momentum loss of this dipole model of a hot-star wind with the classical 1-D steady-state analysis by Weber and Davis (WD), who used an idealized monopole field to model the angular momentum loss in the solar wind. Despite the differences, we find that the total angular momentum loss averaged over both solid angle and time follows closely the general WD scaling ~ ṀΩR2A. The key distinction is that for a dipole field Alfvèn radius RA is significantly smaller than for the monopole field WD used in their analyses. This leads to a slower stellar spin-down for the dipole field with typical spin-down times of order 1 Myr for several known magnetic massive stars.

On Disk Braking of T Tauri Rotation

The rotation of T Tauri stars is thought to be slowed by coupling between the stellar magnetosphere and the circumstellar disk. Stassun and collaborators have recently questioned this picture, based on their observations of young stars in and near the Orion Nebula Cluster (ONC) that indicate little evidence for disk-mediated spin-down. However, stellar spin-down can occur no faster than the rate at which angular momentum is removed from the inner disk, either through viscous processes associated with accretion or by a wind. Observational estimates of these processes suggest that the timescales for angular momentum loss may be comparable to the ages of the ONC stars, so that disk braking may not be completely effective, at least among the lowest mass stars. Testing this hypothesis will require further measurements of mass accretion and mass-loss rates as well as determinations of rotational periods as a function of age.

The Angular Momentum Evolution of Very Low Mass Stars

We present theoretical models of the angular momentum evolution of very low mass stars (0.1-0.5 M☉). We also present models of solar analogs (0.6-1.1 M☉) for comparison with previous work. We investigate the effect of rotation on the effective temperature and luminosity of these stars. Rotation lowers the effective temperature and luminosity of the models relative to standard models of the same mass and composition. We find that the decrease in Teff and L can be significant at the higher end of our mass range but becomes small below 0.4 M☉. The effects of different assumptions about internal angular momentum transport are discussed. Formulae for relating Teff to mass and vrot are presented. We demonstrate that the kinetic energy of rotation is not a significant contribution to the luminosity of low-mass stars. Previous studies of the angular momentum evolution of low-mass stars concentrated on solar analogs and were complicated by uncertainties related to the internal transport of angular momentum. In this paper we extend our theoretical models for the angular momentum evolution of stars down to 0.1 M☉. We compare our models to rotational data from young open clusters of different ages to infer the rotational history of low-mass stars and the dependence of initial conditions and rotational evolution on mass. We find that the qualitative conclusions for stars below 0.6 M☉ do not depend on the assumptions about internal angular momentum transport with the exception of a zero-point shift in the angular momentum loss saturation threshold. We argue that this makes these low-mass stars ideal candidates for the study of the angular momentum loss law and distribution of initial conditions. For stars with masses between 0.6 and 1.1 M☉, scaling the saturation threshold by the Rossby number can reproduce the observed mass dependence of the stellar angular momentum evolution. We find that neither models with solid-body rotation nor differentially rotating models can simultaneously reproduce the observed stellar spin-down in the 0.6-1.1 M☉ range and for stars between 0.1 and 0.6 M☉. We argue that the most likely explanation is that the saturation threshold drops more steeply at low masses than would be predicted with a simple Rossby scaling. In young clusters there is a systematic increase in the mean rotation rate with decreased temperature below 3500 K (0.4 M☉). This suggests either inefficient angular momentum loss or mass-dependent initial conditions for stars near the fully convective boundary.

Effects of hyperons on the dynamical deconfinement transition in cold neutron star matter

The influence of the presence of hyperons in dense hadronic matter on the quantum nucleation of quark matter is examined at low temperatures relevant to neutron star cores. We calculate the equation of state and the composition of matter before and after deconfinement by using a relativistic mean-field theory and an MIT bag model, respectively; the case in which hyperons are present in the hadronic system is considered, together with the case of the system without hyperons. We find that strangeness contained in hyperons acts to reduce a density jump at deconfinement as well as a lepton fraction in the hadronic phase. As a result of these reductions, a quark matter droplet being in a virtual or real state has its effective mass lightened and its electric charge diminished into nearly zero. The Coulomb screening of leptons on the droplet charge, which has significance to the droplet growth after nucleation in the absence of hyperons, is thus shown to be of little consequence. If the effective droplet mass is small enough to become comparable to the height of the potential barrier, the effect of relativity brings about an exponential increase in the rate of droplet formation via quantum tunneling, whereas the role played by energy dissipation in decelerating the droplet formation, dominant for matter without hyperons, becomes of less importance. For matter with and without hyperons, we estimate the overpressure needed to form the first droplet in the star during the compression due to stellar spin-down or mass accretion from a companion star. The temperature at which a crossover from the quantum nucleation to the Arrhenius-type thermal nucleation takes place is shown to be large compared with the temperature of matter in the core.

Spin-Down of Neutron Stars and Compositional Transitions in the Cold Crustal Matter

Transitions of nuclear compositions in the crust of a neutron star induced by stellar spin-down are evaluated at zero temperature. We construct a compressible liquid-drop model for the energy of nuclei immersed in a neutron gas, including pairing and shell correction terms, in reference to the known properties of the ground state of matter above neutron drip density, 4.3 × 1011 g cm−3. Recent experimental values and extrapolations of nuclear masses are used for a description of matter at densities below neutron drip. Changes in the pressure of matter in the crust due to the stellar spin-down are calculated by taking into account the structure of the crust of a slowly and uniformly rotating relativistic neutron star. If the initial rotation period is of the order of milliseconds, these changes cause nuclei, initially being in the ground-state matter above a mass density of about 3 × 1013 g cm−3, to absorb neutrons in the equatorial region where the matter undergoes compression, and to emit them in the vicinity of the rotation axis where the matter undergoes decompression. Heat generation by these processes is found to have significant effects on the thermal evolution of old neutron stars with low magnetic fields; the surface emission predicted from this heating is compared with the ROSAT observations of X-ray emission from millisecond pulsars and is shown to be insufficient to explain the observed X-ray luminosities (Iida and Sato, 1997).

Spin‐down of Neutron Stars and Compositional Transitions in the Cold Crustal Matter

Transitions of nuclear compositions in the crust of a neutron star induced by stellar spin-down are evaluated at zero temperature. We construct a compressible liquid-drop model for the energy of nuclei immersed in a neutron gas, including pairing and shell correction terms, in reference to the known properties of the ground state of matter above neutron drip density, $4.3 \times 10^{11} g cm^{-3}$. Recent experimental values and extrapolations of nuclear masses are used for a description of matter at densities below neutron drip. Changes in the pressure of matter in the crust due to the stellar spin-down are calculated by taking into account the structure of the crust of a slowly and uniformly rotating relativistic neutron star. If the initial rotation period is $\sim$ ms, these changes cause nuclei, initially being in the ground-state matter above a mass density of about $3 \times 10^{13} g cm^{-3}$, to absorb neutrons in the equatorial region where the matter undergoes compression, and to emit them in the vicinity of the rotation axis where the matter undergoes decompression. Heat generation by these processes is found to have significant effects on the thermal evolution of old neutron stars with low magnetic fields; the surface emission predicted from this heating is compared with the $ROSAT$ observations of X-ray emission from millisecond pulsars and is shown to be insufficient to explain the observed X-ray luminosities.

Magnetocentrifugally driven flows from young stars and disks. 1: A generalized model

We propose a generalized model for stellar spin-down, disk accretion, and truncation, and the origin of winds, jets, and bipolar outflows from young stellar objects. We consider the steady state dynamics of accretion of matter from a viscous and imperfectly conducting disk onto a young star with a strong magnetic field. For an aligned stellar magnetosphere, shielding currents in the surface layers of the disk prevent stellar field lines from penetrating the disk everywhere except for a range of radii about pi = R(sub x), where the Keplerian angular speed of rotation Omega(sub x) equals the angular speed of the star Omega(sub *). For the low disk accretion rates and high magnetic fields associated with typical T Tauri stars, R(sub x) exceeds the radius of the star R(sub *) by a factor of a few, and the inner disk is effectively truncated at a radius R(sub t) somewhat smaller than R(sub x). Where the closed field lines between R(sub t) and R(sub x) bow sufficiently inward, the accreting gas attaches itself to the field and is funneled dynamically down the effective potential (gravitational plus centrifugal) onto the star. Contrary to common belief, the accompanying magnetic torques associated with this accreting gas may transfer angular momentum mostly to the disk rather than to the star. Thus, the star can spin slowly as long as R(sub x) remains significantly greater than R(sub *). Exterior to R(sub x) field lines threading the disk bow outward, which makes the gas off the mid-plane rotate at super-Keplerian velocities. This combination drives a magnetocentrifugal wind with a mass-loss rate M(sub w) equal to a definite fraction f of the disk accretion rate M(sub D). For high disk accretion rates, R(sub x) is forced down to the stellar surface, the star is spun to breakup, and the wind is generated in a manner identical to that proposed by Shu, Lizano, Ruden, & Najita in a previous communication to this journal. In two companion papers (II and III), we develop a detailed but idealized theory of the magnetocentrifugal acceleration process.

Spin-down of rapidly rotating, convective stars

We construct a model for the spin-down of rapidly rotating, convective stars. We assume that rotation and convection cause a star to rotate differentially, that differential rotation and convection generate a magnetic dynamo, that a magnetic dynamo gives rise to mass loss and a magnetically controlled stellar wind, and that such a wind results in angular momentum loss and hence stellar spin-down. Using the model, we show that a protostar accreting from a circumstellar disc reaches an equilibrium rotation period significantly below break-up. We also show that the spin-down rates we derive are consistent with those required to drive the orbital evolution of cataclysmic variables.

Stellar Winds and Spindown in Red Giants

Recent observations of rotation rates in G and K giants show a sudden drop in the rotation rate at spectral type G5. The observed behavior requires a strong external brake, such as applied by a magnetized stellar wind. Since spectral type G5 coincides with the onset of deep envelope convection in giants, a dynamo mechanism is suggested as the controlling factor. Stellar evolution models have been used to estimate the time scale for the rotational braking, the angular momentum loss rate, and the required magnetic field strengths.

Stellar Winds and Spindown in Solar Type Stars

The angular momentum loss produced by stellar winds is reviewed and a simple model of angular momentum loss with multipole fields is presented in which the field is potential when the flow speed is less than the Alfvén speed, and radial when greater than the Alfvén speed. The simpler the magnetic geometry, the larger is the angular momentum loss rate. This result is used to explain the rotational discontinuity across the Vaughan-Preston gap as being due to a sudden increase in angular momentum loss when the dynamo field switches from a quadropole to a dipole geometry.The evolution of the internal rotation of stars as a result of surface angular momentum loss is considered. In the absence of a magnetic field, differential rotation can drive instabilities which then transport angular momentum out from the interior down the angular velocity gradient. Other instabilities such as that caused by the build up of 3He can also transport angular momentum outwards. If angular momentum is transported by such weak turbulence, it also makes the star more homogeneous than standard evolutionary models and lowers the predicted value of the solar neutrino flux.The recent results on rotational splitting of solar oscillations are considered: these suggest that the inside of the sun is spinning faster than the surface and are compatible with models in which angular momentum is transported by mild turbulence. But data is scarce — and in such circumstances the speculations of the theorist must be viewed with caution!