Sean P. Matt

Accretion-powered stellar winds as a solution to the stellar angular momentum problem

We compare the angular momentum extracted by a wind from a pre-main-sequence star to the torques arising from the interaction between the star and its Keplerian accretion disk. We find that the wind alone can counteract the spin-up torque from mass accretion, solving the mystery of why accreting pre-main-sequence stars are observed to spin at less than 10% of breakup speed, provided that the mass outflow rate in the stellar winds is ~10% of the accretion rate. We suggest that such massive winds will be driven by some fraction of the accretion power. For observationally constrained typical parameters of classical T Tauri stars, needs to be between a few and a few tens of percent. In this scenario, efficient braking of the star will terminate simultaneously with accretion, as is usually assumed to explain the rotation velocities of stars in young clusters.

MAGNETIC BRAKING FORMULATION FOR SUN-LIKE STARS: DEPENDENCE ON DIPOLE FIELD STRENGTH AND ROTATION RATE

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 percent. 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, surface gravity, and spin rate, and which is valid for both slow and fast rotators.

Disk Formation by Asymptotic Giant Branch Winds in Dipole Magnetic Fields

We present a simple, robust mechanism by which an isolated star can produce an equatorial disk. The mechanism requires that the star have a simple dipole magnetic field on the surface and an isotropic wind acceleration mechanism. The wind couples to the field, stretching it until the field lines become mostly radial and oppositely directed above and below the magnetic equator, as occurs in the solar wind. The interaction between the wind plasma and magnetic field near the star produces a steady outflow in which magnetic forces direct plasma toward the equator, constructing a disk. In the context of a slow (10 km s-1) outflow (10-5 M☉ yr-1) from an asymptotic giant branch star, MHD simulations demonstrate that a dense equatorial disk will be produced for dipole field strengths of only a few Gauss on the surface of the star. A disk formed by this model can be dynamically important for the shaping of planetary nebulae.

ACCRETION-POWERED STELLAR WINDS. III. SPIN-EQUILIBRIUM SOLUTIONS

We compare the stellar wind torque calculated in a previous work (Paper II) to the spin-up and spin-down torques expected to arise from the magnetic interaction between a slowly rotating (~10% of breakup) pre-main-sequence star and its accretion disk. This analysis demonstrates that stellar winds can carry off orders of magnitude more angular momentum than can be transferred to the disk, provided that the mass outflow rates are substantially greater than the solar wind. Thus, the equilibrium spin state is simply characterized by a balance between the angular momentum deposited by accretion and that extracted by a stellar wind. We derive a semianalytic formula for predicting the equilibrium spin rate as a function only of the ratio of w/a and a dimensionless magnetization parameter, Ψ ≡ B2*R2*(avesc)−1, where w is the stellar wind mass outflow rate, a is the accretion rate, B* is the stellar surface magnetic field strength, R* is the stellar radius, and vesc is the surface escape speed. For parameters typical of accreting pre-main-sequence stars, this explains spin rates of ~10% of breakup speed for w/a ~ 0.1. Finally, the assumption that the stellar wind is driven by a fraction of the accretion power leads to an upper limit to the mass flow ratio of w/a 0.6.

The Effect of Magnetic Topology on Thermally Driven Wind: Toward a General Formulation of the Braking Law

Stellar wind is thought to be the main process responsible for the spin down of main-sequence stars. The extraction of angular momentum by a magnetized wind has been studied for decades, leading to several formulations for the resulting torque. However, previous studies generally consider simple dipole or split monopole stellar magnetic topologies. Here we consider, in addition to a dipolar stellar magnetic field, both quadrupolar and octupolar configurations, while also varying the rotation rate and the magnetic field strength. Sixty simulations made with a 2.5D cylindrical and axisymmetric set-up, and computed with the PLUTO code, were used to find torque formulations for each topology. We further succeed to give a unique law that fits the data for every topology by formulating the torque in terms of the amount of open magnetic flux in the wind. We also show that our formulation can be applied to even more realistic magnetic topologies, with examples of the Sun in its minimum and maximum phases as observed at the Wilcox Solar Observatory, and of a young K-star (TYC-0486-4943-1) whose topology has been obtained by Zeeman-Doppler Imaging.

Simulation‐based Investigation of a Model for the Interaction between Stellar Magnetospheres and Circumstellar Accretion Disks

We examine, parametrically, the interaction between the magnetosphere of a rotating young stellar object and a circumstellar accretion disk using 2.5-dimensional (cylindrically symmetric) numerical magnetohydrodynamic simulations. The interaction drives a collimated outflow, and we find that the jet formation mechanism is robust. For variations in initial disk density of a factor of 16, variations of stellar dipole strength of a factor of 4, and various initial conditions with respect to the disk truncation radius and the existence of a disk field, outflows with similar morphologies were consistently produced. Second, the system is self-regulating, where the outflow properties depend relatively weakly on the parameters above. The large-scale magnetic field structure rapidly evolves to a configuration that removes angular momentum from the disk at a rate that depends most strongly on the field and weakly on the rotation rate of the footpoints of the field in the disk and the mass outflow rate. Third, the simulated jets are episodic, with the timescale of jet outbursts identical to the timescale of magnetically induced oscillations of the inner edge of the disk. To better understand the physics controlling these disk oscillations, we present a semianalytical model and confirm that the oscillation period is set by the spin-down rate of the disk inner edge. Finally, our simulations offer strong evidence that it is indeed the interaction of the stellar magnetosphere with the disk, rather than some primordial field in the disk itself, that is responsible for the formation of jets from these systems.

The non-dipolar magnetic fields of accreting T Tauri stars

Models of magnetospheric accretion on to classical T Tauri stars often assume that stellar magnetic fields are simple dipoles. Recently published surface magnetograms of BP Tau and V2129 Oph have shown, however, that their fields are more complex. The magnetic field of V2129 Oph was found to be predominantly octupolar. For BP Tau, the magnetic energy was shared mainly between the dipole and octupole field components, with the dipole component being almost four times as strong as that of V2129 Oph. From the published surface maps of the photospheric magnetic fields, we extrapolate the coronal fields of both stars, and compare the resulting field structures with that of a dipole. We consider different models where the disc is truncated at, or well within, the Keplerian corotation radius. We find that although the structure of the surface magnetic field is particularly complex for both stars, the geometry of the larger scale field, along which accretion is occurring, is somewhat simpler. However, the larger scale field is distorted close to the star by the stronger field regions, with the net effect being that the fractional open flux through the stellar surface is less than would be expected with a dipole magnetic field model. Finally, we estimate the disc truncation radius, assuming that this occurs where the magnetic torque from the stellar magnetosphere is comparable to the viscous torque in the disc.

SPIN EVOLUTION OF ACCRETING YOUNG STARS. II. EFFECT OF ACCRETION-POWERED STELLAR WINDS

We present a model for the rotational evolution of a young, solar-mass star interacting magnetically with an accretion disk. As in a previous paper (Paper I), the model includes changes in the stars mass and radius as it descends the Hayashi track, a decreasing accretion rate, and a prescription for the angular momentum transfer between the star and disk. Paper I concluded that, for the relatively strong magnetic coupling expected in real systems, additional processes are necessary to explain the existence of slowly rotating pre-main-sequence stars. In the present paper, we extend the stellar spin model to include the effect of a spin-down torque that arises from an accretion-powered stellar wind (APSW). For a range of magnetic field strengths, accretion rates, initial spin rates, and mass outflow rates, the modeled stars exhibit rotation periods within the range of 1-10 days in the age range of 1-3 Myr. This range coincides with the bulk of the observed rotation periods, with the slow rotators corresponding to stars with the lowest accretion rates, strongest magnetic fields, and/or highest stellar wind mass outflow rates. We also make a direct, quantitative comparison between the APSW scenario and the two types of disk-locking models (namely, the X-wind and Ghosh & Lamb type models) and identify some remaining theoretical issues for understanding young star spins.

SPIN EVOLUTION OF ACCRETING YOUNG STARS. I. EFFECT OF MAGNETIC STAR-DISK COUPLING

We present a model for the rotational evolution of a young, solar mass star interacting with an accretion disk. The model incorporates a description of the angular momentum transfer between the star and the disk due to a magnetic connection, and includes changes in the stars mass and radius and a decreasing accretion rate. The model also includes, for the first time in a spin evolution model, the opening of the stellar magnetic field lines, as expected to arise from twisting via star-disk differential rotation. In order to isolate the effect that this has on the star-disk interaction torques, we neglect the influence of torques that may arise from open field regions connected to the star or disk. For a range of magnetic field strengths, accretion rates, and initial spin rates, we compute the stellar spin rates of pre-main-sequence stars as they evolve on the Hayashi track to an age of 3 Myr. How much the field opening affects the spin depends on the strength of the coupling of the magnetic field to the disk. For the relatively strong coupling (i.e., high magnetic Reynolds number) expected in real systems, all models predict spin periods of less than ~3 days, in the age range of 1-3 Myr. Furthermore, these systems typically do not reach an equilibrium spin rate within 3 Myr, so that the spin at any given time depends upon the choice of initial spin rate. This corroborates earlier suggestions that, in order to explain the full range of observed rotation periods of approximately 1-10 days, additional processes, such as the angular momentum loss from powerful stellar winds, are necessary.

Effect of the stellar spin history on the tidal evolution of close-in planets

We investigate how the evolution of the stellar spin rate affects, and is affected by, planets in close orbits, via star-planet tidal interactions. To do this, we used a standard equilibrium tidal model to compute the orbital evolution of single planets orbiting both Sun-like stars and 0.1 M\odot M-dwarfs. We tested two stellar spin evolution profiles, one with fast initial rotation (P=1.2 day) and one with slow initial rotation (P=8 day). We tested the effect of varying the stellar and planetary dissipation and the planets mass and initial orbital radius. Conclusions: Tidal evolution allows to differentiate the early behaviors of extremely close-in planets orbiting either a rapidly rotating star or a slowly rotating star. The early spin-up of the star allows the close-in planets around fast rotators to survive the early evolution. For planets around M-dwarfs, surviving the early evolution means surviving on Gyr timescales whereas for Sun-like stars the spin-down brings about late mergers of Jupiter planets. In light of this study, we can say that differentiating between one spin evolution from another given the present position of planets can be very tricky. Unless we can observe some markers of former evolution it is nearly impossible to distinguish the two very different spin profiles, let alone intermediate spin profiles. Though some conclusions can still be drawn from statistical distributions of planets around fully convective M-dwarfs. However, if the tidal evolution brings about a merger late in its history it can also entail a noticeable acceleration of the star in late ages, so that it is possible to have old stars that spin rapidly. This raises the question of better constraining the age of stars.