Magnetic Angular Momentum Transport Research Articles

On the Maximum Black Hole Mass at Solar Metallicity

In high-metallicity environments the mass that black holes (BHs) can reach just after core collapse widely depends on how much mass their progenitor stars lose via winds. On one hand, new theoretical and observational insights suggest that early-stage winds should be weaker than what many canonical models prescribe. On the other hand, the proximity to the Eddington limit should affect the formation of optically thick envelopes already during the earliest stages of stars with initial masses M ZAMS ≳ 100 M ⊙, hence resulting in higher mass-loss rates during the main sequence. We use the evolutionary codes MESA and Genec to calculate a suite of tracks for massive stars at solar metallicity Z ⊙ = 0.014, which incorporate these changes in our wind-mass-loss prescription. In our calculations we employ moderate rotation, high overshooting, and magnetic angular momentum transport. We find a maximum BH mass MBH,max=28.3 M ⊙ at Z ⊙. The most massive BHs are predicted to form from stars with M ZAMS ≳ 250 M ⊙, with the BH mass directly proportional to its progenitor’s M ZAMS. We also find in our models that at Z ⊙ almost any BH progenitor naturally evolves into a Wolf–Rayet star due to the combined effect of internal mixing and wind mass loss. These results are considerably different from most recent studies regarding the final mass of stars before their collapse into BHs. While we acknowledge the inherent uncertainties in stellar evolution modeling, our study underscores the importance of employing the most up-to-date physics in BH mass predictions.

Scale-dependent analysis of angular momentum flux in high-resolution magnetohydrodynamic simulations for solar differential rotation

ABSTRACT In this work, we systematically investigate the scale-dependent angular momentum flux by analysing high-resolution three-dimensional magnetohydrodynamic simulations in which the solar-like differential rotation is reproduced without using any manipulations. More specifically, the magnetic angular momentum transport (AMT) plays a dominant role in the calculations. We examine the important spatial scales for the magnetic AMT. The main conclusions of our approach can be summarized as follows: 1. Turbulence transports the angular momentum radially inward. This effect is more pronounced in the highest resolution calculation. 2. The dominant scale for the magnetic AMT is the smallest spatial scale. 3. The dimensionless magnetic correlation is low in the high-resolution simulation. Thus, chaotic but strong small-scale magnetic fields achieve efficient magnetic AMT.

The spins of stripped B stars support magnetic internal angular momentum transport

In order to predict the spins of stellar remnants we need to understand the evolution of the internal rotation of stars, and to identify at which stage the rotation of the contracting cores of evolved stars decouples from their expanding envelopes. The donor stars of mass transferring binaries lose almost their entire envelope and may thus offer a direct view on their core rotation. After the mass transfer event they contract and fade rapidly, although they are well observable when caught in the short-lived B-star phase. The B-type primary of the galactic binary system LB-1, which was originally suggested to contain a massive black hole, is nicely explained as a stripped star accompanied by a fainter Be star. The narrow absorption lines in the primary’s spectrum signify extremely slow rotation, atypical of B-type main-sequence stars. Here we investigate the evolution of mass donors in generic grids of detailed binary evolution models, where both stars include differential rotation, internal angular momentum transport, and spin-orbit coupling. Whereas the mass gainers are typically spun-up during the mass transfer, we find that the spins of the stripped donor models depend sensitively on the employed mechanism for internal angular momentum transport. Purely hydrodynamic transport cannot explain the observed slow rotation, while models including magnetic angular momentum transport are able to reproduce the observed rotation of LB-1 and similar stars, independent of the initial rotation rate. In such models the spin of the white dwarfs that emerge at the end of the evolution is independent of the mass stripping. We find evidence that the mass transfer in LB-1 was moderately non-conservative.

Detailed models of interacting short-period massive binary stars

Context. The majority of massive stars are part of binary systems. In about a quarter of these, the companions are so close that mass transfer occurs while they undergo core hydrogen burning, first on the thermal and then on the nuclear timescale. The nuclear timescale mass transfer leads to observational counterparts: the semi-detached so-called massive Algol binaries. These systems may provide urgently needed tests of the physics of mass transfer. However, comprehensive model predictions for these systems are sparse. Aims. We use a large grid of detailed evolutionary models of short-period massive binaries and follow-up population synthesis calculations to derive probability distributions of the observable properties of massive Algols and their descendants. Methods. Our results are based on ∼10 000 binary model sequences calculated with the stellar evolution code MESA, using a metallicity suitable for the Large Magellanic Cloud (LMC), covering initial donor masses between 10 M⊙ and 40 M⊙ and initial orbital periods above 1.4 d. These models include internal differential rotation and magnetic angular momentum transport, non-conservative mass and angular momentum transfer between the binary components, and time-dependent tidal coupling. Results. Our models imply ∼30, or ∼3% of the ∼1000, core hydrogen burning O-star binaries in the LMC to be currently in the semi-detached phase. Our donor models are up to 25 times more luminous than single stars of an identical mass and effective temperature, which agrees with the observed Algols. A comparison of our models with the observed orbital periods and mass ratios implies rather conservative mass transfer in some systems, while a very inefficient one in others. This is generally well reproduced by our spin-dependent mass transfer algorithm, except for the lowest considered masses. The observations reflect the slow increase of the surface nitrogen enrichment of the donors during the semi-detached phase all the way to CNO equilibrium. We also investigate the properties of our models after core hydrogen depletion of the donor star, when these models correspond to Wolf-Rayet or helium+OB star binaries. Conclusions. A dedicated spectroscopic survey of massive Algol systems may allow to derive the dependence of the efficiency of thermal timescale mass transfer on the binary parameters, as well as the efficiency of semiconvective mixing in the stellar interior. This would be a crucial step towards reliable binary models up to the formation of supernovae and compact objects.

Magnetic fields and transport processes

In this presentation, we briefly discuss how magnetic angular momentum transport in stellar radiative zones can be constrained by asteroseismic measurements. We focus on the internal rotational properties deduced from rotational splittings of solar-like oscillations and how they can be used to characterize angular momentum transport in stellar interiors.

Asteroseismology of evolved stars to constrain the internal transport of angular momentum

Context. Asteroseismic observations enable the characterisation of the internal rotation of evolved stars. These measurements reveal that an unknown efficient angular momentum (AM) transport mechanism is needed for subgiant and red giant stars in addition to hydrodynamic transport processes. A revised prescription for AM transport by the magnetic Tayler instability has been recently proposed as a possible candidate for such a missing mechanism. Aims. We compare the rotational properties predicted by this magnetic AM transport to asteroseismic constraints obtained for evolved stars with a particular focus on the subgiant phase. Methods. We computed models accounting for the recent prescription for AM transport by the Tayler instability with the Geneva stellar evolution code for subgiant and red giant stars, for which an asteroseismic determination of both core and surface rotation rates is available. Results. The revised prescription for the transport by the Tayler instability leads to low core rotation rates after the main sequence that are in better global agreement with asteroseismic measurements than those predicted by models with purely hydrodynamic processes or with the original Tayler-Spruit dynamo. A detailed comparison with asteroseismic data shows that the rotational properties of at most two of the six subgiants can be correctly reproduced by models accounting for this revised magnetic transport process. This result is obtained independently of the value adopted for the calibration parameter in this prescription. We also find that this transport by the Tayler instability faces difficulties in simultaneously reproducing asteroseismic measurements available for subgiant and red giant stars. The low values of the calibration parameter needed to correctly reproduce the rotational properties of two of the six subgiants lead to core rotation rates during the red giant phase that are too high. Inversely, the higher values of this parameter needed to reproduce the core rotation rates of red giants lead to a very low degree of radial differential rotation before the red giant phase, which is in contradiction with the internal rotation of subgiant stars. Conclusions. In its present form, the revised prescription for the transport by the Tayler instability does not provide a complete solution to the missing AM transport revealed by asteroseismology of evolved stars.

Evolution of helium star plus carbon-oxygen white dwarf binary systems and implications for diverse stellar transients and hypervelocity stars

Context. Helium accretion induced explosions in CO white dwarfs (WDs) are considered promising candidates for a number of observed types of stellar transients, including supernovae (SNe) of Type Ia and Type Iax. However, a clear favorite outcome has not yet emerged. Aims. We explore the conditions of helium ignition in the WD and the final fates of helium star-WD binaries as functions of their initial orbital periods and component masses. Methods. We computed 274 model binary systems with the Binary Evolution Code, in which both components are fully resolved. Both stellar and orbital evolution were computed including mass and angular momentum transfer, tides, gravitational wave emission, differential rotation, and internal hydrodynamic and magnetic angular momentum transport. We worked out the parts of the parameter space leading to detonations of the accreted helium layer on the WD, likely resulting in the complete disruption of the WD to deflagrations, where the CO core of the WD may remain intact and where helium ignition in the WD is avoided. Results. We find that helium detonations are expected only in systems with the shortest initial orbital periods, and for initially massive WDs (MWD ≥ 1.0 M⊙) and lower mass donors (Mdonor ≤ 0.8 M⊙), which have accumulated helium layers mostly exceeding 0.1 M⊙. Upon detonation, these systems would release the donor as a hypervelocity pre-WD runaway star, for which we predict the expected range of kinematic and stellar properties. Systems with more massive donors or initial periods exceeding 1.5 h likely undergo helium deflagrations after accumulating 0.1 − 0.001 M⊙ of helium. Helium ignition in the WD is avoided in systems with helium donor stars below ∼0.6 M⊙, and leads to three distinctly different groups of double WD systems. Conclusions. The size of the parameter space open to helium detonation corresponds to only about 3% of the galactic SN Ia rate and to 10% of the SN Iax rate, while the predicted large amounts of helium (0.1 M⊙) in progenitors cannot easily be reconciled with observations of archetypical SN Ia. However, the transients emerging from these systems may contribute significantly to massive helium novae, calcium-rich SNe Ib, and, potentially, very close double degenerate systems that may eventually produce either ordinary or peculiar SNe Ia, or, for the smallest considered masses, R Coronae Borealis stars.

Rotation rate of the solar core as a key constraint to magnetic angular momentum transport in stellar interiors

Context. The internal rotation of the Sun constitutes a fundamental constraint when modelling angular momentum transport in stellar interiors. In addition to the more external regions of the solar radiative zone probed by pressure modes, measurements of rotational splittings of gravity modes would offer an invaluable constraint on the rotation of the solar core. Aims. We study the constraints that a measurement of the core rotation rate of the Sun could bring on magnetic angular momentum transport in stellar radiative zones. Methods. Solar models accounting for angular momentum transport by hydrodynamic and magnetic instabilities were computed for different initial velocities and disc lifetimes on the pre-main sequence to reproduce the surface rotation velocities observed for solar-type stars in open clusters. The internal rotation of these solar models was then compared to helioseismic measurements. Results. We first show that models computed with angular momentum transport by magnetic instabilities and a recent prescription for the braking of the stellar surface by magnetized winds can reproduce the observations of surface velocities of stars in open clusters. These solar models predict both a flat rotation profile in the external part of the solar radiative zone probed by pressure modes and an increase in the rotation rate in the solar core, where the stabilizing effect of chemical gradients plays a key role. A rapid rotation of the core of the Sun, as suggested by reported detections of gravity modes, is thus found to be compatible with angular momentum transport by magnetic instabilities. Moreover, we show that the efficiency of magnetic angular momentum transport in regions of strong chemical gradients can be calibrated by the solar core rotation rate independently from the unknown rotational history of the Sun. In particular, we find that a recent revised prescription for the transport of angular momentum by the Tayler instability can be easily distinguished from the original Tayler–Spruit dynamo, with a faster rotating solar core supporting the original prescription. Conclusions. By calibrating the efficiency of magnetic angular momentum transport in regions of strong chemical gradients, a determination of the solar core rotation rate through gravity modes is of prime relevance not only for the Sun, but for stars in general, since radial differential rotation precisely develops in these regions during the more advanced stages of evolution.

Helium ignition in rotating magnetized CO white dwarfs leading to fast and faint rather than classical Type Ia supernovae

Based mostly on stellar models which do not include rotation, CO white dwarfs which accrete helium at rates of about $\sim 10^{-8}~\mathrm{M}_\odot/\mathrm{yr}$ have been put forward as candidate progenitors for a number of transient astrophysical phenomena, including supernovae of Type Ia, and the peculiar and fainter Type Iax supernovae. Here we study the impact of accretion-induced spin-up including the subsequent magnetic field generation, angular momentum transport, and viscous heating on the white dwarf evolution up to the point of helium ignition. We resolve the structure of the helium accreting white dwarf models with a one dimensional Langrangian hydrodynamic code, modified to include rotational and magnetic effects. We find magnetic angular momentum transport, which leads to quasi solid-body rotation, profoundly impacts the evolution of the white dwarf models. Our rotating lower mass ($0.54$ and $0.82~\mathrm{M}_\odot$) models accrete up to 50\% more mass up to ignition compared to the non-rotating case and the opposite for our more massive models. Furthermore, we find that rotation leads to up to 10-times smaller helium ignition densities, except for the lowest adopted initial white dwarf mass. Ignition densities of order $10^6\,\mathrm{g/cm}^3$ are only found for the lowest accretion rates and for large amounts of accreted helium $\gtrsim 0.4\,\mathrm{M}_\odot$. However, correspondingly massive donor stars would transfer mass at much higher rates. We expect explosive He-shell burning to mostly occur as deflagrations and at $\dot{M}>2\cdot10^{-8}~\mathrm{M}_\odot/\mathrm{yr}$, regardless of white dwarf mass. Our results imply that helium accretion onto CO white dwarfs at the considered rates is unlikely to lead to explosions of the CO core or to classical Type,Ia supernovae, but may instead produce events like faint and fast hydrogen-free supernovae.

ANGULAR MOMENTUM TRANSPORT IN SOLAR-TYPE STARS: TESTING THE TIMESCALE FOR CORE-ENVELOPE COUPLING

We critically examine the constraints on internal angular momentum transport which can be inferred from the spin down of open cluster stars. The rotation distribution inferred from rotation velocities and periods are consistent for larger and more recent samples, but smaller samples of rotation periods appear biased relative to vsini studies. We therefore focus on whether the rotation period distributions observed in star forming regions can be evolved into the observed ones in the Pleiades, NGC2516, M34, M35, M37, and M50 with plausible assumptions about star-disk coupling and angular momentum loss from magnetized solar-like winds. Solid body models are consistent with the data for low mass fully convective stars but highly inconsistent for higher mass stars where the surface convection zone can decouple for angular momentum purposes from the radiative interior. The Tayler-Spruit magnetic angular momentum transport mechanism, commonly employed in models of high mass stars, predicts solid-body rotation on extremely short timescales and is therefore unlikely to operate in solar-type pre-MS and MS stars at the predicted rate. Models with core-envelope decoupling can explain the spin down of 1.0 and 0.8 solar mass slow rotators with characteristic coupling timescales of 55+-25 Myr and 175+-25 Myr respectively. The upper envelope of the rotation distribution is more strongly coupled than the lower envelope of the rotation distribution, in accord with theoretical predictions that the angular momentum transport timescale should be shorter for more rapidly rotating stars. Constraints imposed by the solar rotation curve are also discussed (Abridged)

Rotation Profiles of Solar-like Stars with Magnetic Fields

We investigate the rotation profile of solar-like stars with magnetic fields. A diffusion coefficient of magnetic angular momentum transport is deduced. Rotating stellar models with different mass incorporating the coefficient are computed to give the rotation profiles. The total angular momentum of a solar model with only hydrodynamic instabilities is about 13 times larger than that of the Sun at the age of the Sun, and this model can not reproduce quasi-solid rotation in the radiative region. However, the solar model with magnetic fields not only can reproduce an almost uniform rotation in the radiative region, but also a total angular momentum that is consistent with the helioseismic result at the 3 sigma level at the age of the Sun. The rotation of solar-like stars with magnetic fields is almost uniform in the radiative region, but for models of 1.2-1.5 M(circle dot), there is an obvious transition region between the convective core and the radiative region, where angular velocity has a sharp radial gradient, which is different from the rotation profile of the Sun and of massive stars with magnetic fields. The change of angular velocity in the transition region increases with increasing age and mass.

What Prevents Internal Gravity Waves from Disturbing the Solar Uniform Rotation?

Internal gravity waves (IGWs) are naturally produced by convection in stellar envelopes, and they could be an important mechanism for transporting angular momentum in the radiative interiors of stars. Prior work has established that they could operate over a short enough timescale to explain the internal solar rotation as a function of depth. We demonstrate that the natural action of IGWs is to produce large-scale oscillations in the solar rotation as a function of depth, which is in marked contrast to the nearly uniform rotation in the outer radiative envelope of the Sun. An additional angular momentum transport mechanism is therefore required, and neither molecular nor shear-induced turbulent viscosity is sufficient to smooth out the profile. Magnetic processes, such as the Tayler-Spruit dynamo, could flatten the rotation profile. We therefore conclude that IGWs must operate in conjunction with magnetic angular momentum transport processes if they operate at all. Furthermore, both classes of mechanisms must be inhibited to some degree by mean molecular weight gradients in order to explain the recent evidence for a rapidly rotating embedded core in the Sun, should it be confirmed by a further analysis of solar g-mode oscillations.

A Revised Prescription for the Tayler‐Spruit Dynamo: Magnetic Angular Momentum Transport in Stars

Angular momentum transport by internal magnetic fields is an important ingredient for stellar interior models. In this paper we critically examine the basic heuristic assumptions in the model of the Tayler-Spruit dynamo, which describes how a pinch-type instability of a toroidal magnetic field in differentially rotating stellar radiative zones may result in large-scale fluid motion. We agree with prior published work both on the existence of the instability and its nearly horizontal geometry for perturbations. However, the approximations in the original Acheson dispersion relation are valid only for small length scales, and we disagree that the dispersion relation can be extrapolated to horizontal length scales of order the radius of the star. We contend that dynamical effects, in particular, angular momentum conservation, limit the maximum horizontal length scale. We therefore present transport coefficients for chemical mixing and angular momentum redistribution by magnetic torques that are significantly different from previous published values. The new magnetic viscosity is reduced by 2-3 orders of magnitude compared to the old one, and we find that magnetic angular momentum transport by this mechanism is very sensitive to gradients in the mean molecular weight. The revised coefficients are more compatible with empirical constraints on the timescale of core-envelope coupling in young stars than the previous ones. However, solar models including only this mechanism possess a rapidly rotating core, in contradiction with helioseismic data. Previous studies had found strong core-envelope coupling, both for solar models and for the cores of massive evolved stars. We conclude that the Tayler-Spruit mechanism may be important for envelope angular momentum transport but that some other process must be responsible for efficient spin-down of stellar cores.

Angular momentum transport and element mixing in the stellar interior

The purpose of this work was to obtain diffusion coefficient for the magnetic angular momentum transport and material transport in a rotating solar model. We assumed that the transport of both angular momentum and chemical elements caused by magnetic fields could be treated as a diffusion process. The diffusion coefficient depends on the stellar radius, angular velocity, and the configuration of magnetic fields. By using of this coefficient, it is found that our model becomes more consistent with the helioseismic results of total angular momentum, angular momentum density, and the rotation rate in a radiative region than the one without magnetic fields. Not only can the magnetic fields redistribute angular momentum efficiently, but they can also strengthen the coupling between the radiative and convective zones. As a result, the sharp gradient of the rotation rate is reduced at the bottom of the convective zone. The thickness of the layer of sharp radial change in the rotation rate is about 0.036 $R_{\odot}$ in our model. Furthermore, the difference of the sound-speed square between the seismic Sun and the model is improved by mixing the material that is associated with angular momentum transport.