Internal rotation of post-main sequence stars: theoretical advances and their relation to internal magnetism

Post-main sequence stars, in particular subgiants and red giants, are useful probes of internal and envelope rotation rates through asteroseismology, which in turn enables testing theories of angular momentum redistribution in stellar interiors. In the past years, thousands of measurements of internal and envelope rotation rates of red giants were done, enabling testing and refinement of various theories of internal rotation in stellar models. Moreover, recent measurements of internal magnetic fields in red giant branch stars put additional constraints on theories of rotation dominated by magnetic angular momentum transport. Currently, stellar models cannot simultaneously explain the existence of strong internal magnetic fields (as measured by asteroseismology) and their internal rotation. However, internal magnetism is one of the most promising candidates to explain the internal rotation of post-main sequence stars, hence addressing these topics simultaneously is fundamental to make advances in the theory of stellar interiors. In this talk I will discuss recent theoretical advances and results from direct numerical simulations on the theory of internal rotation in subgiants and red giants, and their relation to internal magnetism, with an emphasis on their comparison to current asteroseismic constraints and results from stellar evolution models.

On the importance of dynamo action in stellar radiative zones

The large observational dataset currently available has revealed our ignorance regarding angular momentum redistribution during the stars’ life. Angular momentum (AM) transport in stars results from a variety of physical mechanisms in which internal gravity waves (IGW) and magnetic fields are expected to play a role. While magnetic fields have been well constrained at the surface of several massive and intermediate-mass stars, their origin and properties in deep stellar radiative interiors are still debated, despite recent promising detections in the core of some red giant stars. Therefore, the modelling of AM transport in stellar radiative layers only relies on theoretical and numerical estimates of magnetic fields. Our recent 3D numerical simulations show that a dynamo could occur in such deep radiative regions. However, they do not take into account the mutual interactions of IGW and dynamo-generated magnetic field.

To do so, we adapt our numerical strategy and model the dynamics induced by IGW and dynamo-generated magnetic fields using a simple 1D description applicable to various stellar evolutionary stages. As dynamo action and the propagation of IGW are 3D processes that have characteristic timescales very short compared to typical periods associated with structural evolution of stars, we propose a mean-field 1D model by taking advantage of the dynamo coefficients computed from 3D spherical simulations. In this model, the necessary mean shear flow to trigger the dynamo results from the dissipation of monochromatic IGW generated in existing adjacent convective layers, which are expected to drive the formation of an oscillating rotational shear layer, the so-called Shear Layer Oscillation (SLO). In turn, magnetic effects can act on the mean flow through the Lorentz force. We show that the inclusion of magnetic fields adds up to the already very complex nonlinear problem and gives rise to the emergence of new dynamical regimes. Particularly, the fast SLO generated very close to the place where IGW are generated is perturbed by magnetic fields. This dynamical change can filter the wave energy spectrum transmitted towards further layers, with potential influence on the long-term evolution of the inner rotation.

Our new results on magnetic fields modelling enable us to consider more realistic prescriptions for magnetic effects in stellar evolution codes. Nevertheless, magnetic effects can redistribute AM on very short timescales (much shorter than the stellar evolutionary timescale). We thus show in addition that a new numerical strategy is required to make reliable predictions, in which the time step is correctly adapted to the relevant physical processes.

Magnetic webs and the missing angular momentum transport problem

This talk will present an overview of some recent theoretical developments in our understanding of magnetized, rotating radiative zones. A key realization has been that stable magnetic field configurations and differential rotation are incompatible. Stable fields either enforce corotation and efficiently transport angular momentum or are destroyed by differential rotation. Configurations that can survive are dubbed “magnetic webs.” I will provide theoretical bounds on the minimum magnetic field strength needed to enforce corotation, and emphasize that these bounds are below the current detection threshold of asteroseismology. I will then show that magnetic webs can explain observations of slow core rotation rates on the early RGB.

Understanding Post-main-sequence Stellar Magnetism: On the Origin of Pollux’s Weak Surface Magnetic Field

The magnetic field of red giants is still poorly understood today. Close to the core, asteroseismology has revealed magnetic fields of several hundred thousand gauss, but close to the surface, spectropolarimetric observations of the red giant Pollux only showed an average field of the order of 1 G. Using the ASH code, we conducted a series of 3D nonlinear magnetohydrodynamical simulations aiming at modeling the dynamo process operating within the extended convective envelope of a star similar to the red giant Pollux. We find that the dynamo is efficient even for the slow rotation considered and that large-scale fields are generated and maintained. We further test the correlation between the scale of the convective motions and the surface magnetic field geometry by varying the Prandtl number in our simulations. We show in particular that the value and the geometry of the modeled surface field depend directly on the coupling scales between the magnetic and the velocity fields, with larger convective cells leading to a stronger large-scale magnetic field. We also verify that the dynamo and the geometry of the resulting field are robust against a change of the initial conditions. We then compare our simulations to the observed field and find average \(|B_\ell|\) of about 7 G for the simulation with large convective cells, and down to 2 G for the smaller-scale simulation, very close to the observed value. Finally, we suggest the possibility of the reversal of the red giant’s magnetic field.

Asteroseismic imprints of strong non-axisymmetric fields in the cores of red giants

To date, magnetic fields have been asteroseismically measured in nearly one hundred red giant cores. However, most analyses assume weak magnetic fields and slow rotation so that perturbation theory can be applied. The “traditional approximation of rotation and magnetism” (TARM) method can predict gravity-mode frequencies under strong magnetic fields and rapid rotation rates. So far, this formalism requires the magnetic field to be symmetric about the rotation axis.

We generalize the TARM formalism to apply to arbitrary magnetic field geometries, including cases where the magnetic and rotation axes are misaligned, as well as fields with no symmetry axis at all. The resulting gravity modes exhibit a rich diversity of wave behavior, including oblique pulsation and avoided crossings. We also clarify the domains of validity of perturbation theory and the TARM formalism.

Internal rotation of post-main-sequence stars: the current observational landscape

The advent of ultra-high photometry space missions such as CoRoT, Kepler, TESS and soon PLATO, has revolutionized our understanding of the physical processes governing stellar evolution by enabling to directly probe stellar interiors through asteroseismology. Internal rotation measurements have revealed that significant amounts of angular momentum are transported inside stars, the mechanisms of which are not yet well understood, even though magnetic fields are thought to play a major role. However, rotation impacts the lifetime of stars, therefore understanding angular momentum transport is of crucial importance not only for stellar physics, but also for fields relying on the precise and accurate determination of stellar ages, such as exoplanetology and Galactic archaeology. In this context, post-main-sequence stars represent an ideal laboratory since they offer the opportunity to study the physical conditions in the stellar core through the mixed modes in their oscillation spectrum, a region that is otherwise largely inaccessible to measurements.

This talk will focus on the current observational landscape brought by asteroseismology on the internal rotation of post-main-sequence stars, including subgiants, red giant branch stars that have an inert helium core, and horizontal branch giants that burn helium in their core. The link between unusual internal rotation and planet engulfment will also be addressed, as well as the opportunities that future missions will bring.

Recent observational developments in post-main-sequence stellar magnetism

Magnetic fields are believed to play a key role in the evolution and mass loss of cool evolved stars, yet their direct detection at stellar surfaces remains challenging. High-resolution spectropolarimetry is now providing new insights into the magnetism of these objects across multiple evolutionary stages. Surface magnetic fields have been detected in post-AGB stars, red supergiants, and most recently in the Mira-type AGB star chi Cygni, where a mean longitudinal field of ~3 G was measured with a pulsation-phase dependence suggestive of a link with shock dynamics. Meanwhile, maser polarimetry probes magnetic fields in the circumstellar envelopes of Mira stars at several stellar radii. An apparent disconnect between photospheric and circumstellar magnetic field properties opens intriguing questions about the origin, structure, and role of magnetism throughout the extended atmospheres of these pulsating evolved stars.

Life After Death: Remnant Magnetic Fields in Cool White Dwarfs

The detection of core magnetic fields in red giants allows us to track the evolution of magnetism throughout the post-main-sequence. Inevitably, these giants will end their lives as white dwarfs which frequently host magnetic fields as well. Magnetic white dwarfs thus serve as an important anchor: any model that evolves a field throughout the post-main-sequence should successfully predict what we observe in the white dwarf phase. To determine trends in the magnetic white dwarf population and test evolutionary models of the magnetic field, spectroscopic surveys are critical for studying a statistically robust sample of targets. In this talk, I will discuss our results from the SDSS 100 pc sample, which is the largest volume-limited sample of magnetic white dwarfs to date. I will discuss how we identify and measure the fields, and show that the distribution of these objects forms a unique group of cool objects which likely form via single-star evolution. While crystallization has been invoked to explain the origin of these fields, I will show that instead the fields likely originate from a core-convective dynamo that forms on the main-sequence and persists through the giant phase. Finally, I will highlight some of the recent developments on modeling the field evolution, which importantly attempt to match the observed field strengths both in red giants and white dwarfs.

Large ensemble study of variations in oscillation frequencies of 15,000 Kepler red giants.

Solar and stellar oscillation frequencies and their amplitudes have been observed to shift systematically with surface magnetic activity cycles, providing an important diagnostic for inferring magnetic-cycle-like behaviour in other stars without high-resolution spectroscopic measurements. In our study, we provide a first-of-its-kind large ensemble of measurements of these frequency shifts using a cross-correlation method on 15,000 Kepler red giant stars. We observe over 250 stars displaying significant frequency shift amplitudes: peak-to-peak amplitude greater than 3 times their uncertainties. Additionally, we compare these measurements with various stellar parameters to determine which parameters may affect stellar variability. Such variability measurements play a vital role in our ability to infer accurate physical stellar parameters from oscillation frequencies.

Anti-Solar Differential Rotation May Have Revived Magnetic Braking in the Subgiant 31 Aquilae

A decade of data and models have established that sun-like stars undergo a phase of weakened magnetic braking (WMB) during the latter half of the main sequence. The weakened braking appears to be the result of a collapse of the global dynamo, leading to a dramatic decrease in the large scale dipole field strength and inferred mass loss rates. The declining impact of the Coriolis force in the envelopes of slowly rotating stars may trigger a cascade of changes that ultimately disrupts the large-scale organized magnetic fields.

Here we present observations of the subgiant 31 Aql, which appears to reside firmly within the WMB regime, and yet has a robust inferred torque that is consistent with more “standard” magnetic braking scenarios. We argue that this apparent “revived braking” may be due to the completion of a transition from solar-like to anti-solar differential rotation that occurs as Rossby numbers increase during the physical expansion onto the subgiant branch.

We present the observational and theoretical argument for 31 Aql’s unexpected behavior, and also evaluate the consistency of this revived braking scenario with the broader body of observational evidence that already exists in support of WMB.