Space asteroseismology is revolutionizing our knowledge of the internal structure and dynamics of stars. A breakthrough is ongoing with the recent discoveries of signatures of strong magnetic fields ...in the core of red giant stars. The key signature for such a detection is the asymmetry these fields induce in the frequency splittings of observed dipolar mixed gravito-acoustic modes. We investigate the ability of the observed asymmetries of the frequency splittings of dipolar mixed modes to constrain the geometrical properties of deep magnetic fields. We use the powerful analytical Racah-Wigner algebra used in Quantum Mechanics to characterize the geometrical couplings of dipolar mixed oscillation modes with various possible realistic fossil magnetic fields' topologies and compute the induced perturbation of their frequencies. First, in the case of an oblique magnetic dipole, we provide the exact analytical expression of the asymmetry as a function of the angle between the rotation and magnetic axes. Its value provides a direct measure of this angle. Second, considering a combination of axisymmetric dipolar and quadrupolar fields, we show how the asymmetry is blind to unravel the relative strength and sign of each component. Finally, in the case of a given multipole, we show that a negative asymmetry is a signature of non-axisymmetric topologies. Therefore, asymmetries of dipolar mixed modes provide key but only partial information on the geometrical topology of deep fossil magnetic fields. Asteroseismic constraints should therefore be combined with spectropolarimetric observations and numerical simulations, which aim to predict the more probable stable large-scale geometries.
Recent measurements of magnetic field strength inside the radiative interior
of red giant stars open the way towards the characterization of the geometry of
stable large-scale magnetic fields. ...However, current measurements do not
properly constrain the topology of magnetic fields due to degeneracies on the
observed magnetic field signature on such $\ell=1$ mode frequencies. Efforts
focused towards unambiguous detections of magnetic field configurations are now
key to better understand angular momentum transport in stars. We investigate
the detectability of complex magnetic field topologies inside the radiative
interior of red giants. We focus on a field composed of a combination of a
dipole and a quadrupole (quadrudipole), and on an offset field. We explore the
potential of probing such magnetic field topologies from a combined measurement
of magnetic signatures on $\ell=1$ and quadrupolar ($\ell=2$) mixed mode
oscillation frequencies. We first derive the asymptotic theoretical formalism
for computing the asymmetric signature in frequency pattern for $\ell=2$ modes
due to a quadrudipole magnetic field. The degeneracy of the quadrudipole with a
dipole is lifted when considering both $\ell=1$ and $\ell=2$ mode frequencies.
In addition to the analytical derivation for the quadrudipole, we present the
prospect for complex magnetic field inversions using magnetic sensitivity
kernels from standard perturbation analysis for forward modeling. Using this
method, we demonstrate that offset fields may be mistaken for weak and centered
magnetic fields, resulting in underestimating magnetic field strength in
stellar cores. We emphasize the need to characterize $\ell=2$ mixed-mode
frequencies, (along with the currently characterized $\ell=1$ mixed modes), to
unveil the higher-order components of the geometry of buried magnetic fields,
and better constrain angular momentum transport inside stars.
Magnetic fields in the stellar interiors are key candidates to explain
observed core rotation rates inside solar-like stars along their evolution.
Recently, asteroseismic estimates of radial magnetic ...field amplitudes near the
hydrogen-burning shell (H-shell) inside about 24 red-giants (RGs) have been
obtained by measuring frequency splittings from their power spectra. Using
general Lorentz-stress (magnetic) kernels, we investigated the potential for
detectability of near-surface magnetism in a 1.3 $M_{\odot}$ star of
super-solar metallicity as it evolves from a mid sub-giant to a late sub-giant
into an RG. Based on these sensitivity kernels, we decompose an RG into three
zones - deep core, H-shell, and near-surface. The sub-giants instead required
decomposition into an inner core, an outer core, and a near-surface layer.
Additionally, we find that for a low-frequency g-dominated dipolar mode in the
presence of a typical stable magnetic field, ~25% of the frequency shift comes
from the H-shell and the remaining from deeper layers. The ratio of the
subsurface tangential field to the radial field in H-burning shell decides if
subsurface fields may be potentially detectable. For p-dominated dipole modes
close to $\nu_\rm{max}$, this ratio is around two orders of magnitude smaller
in subgiant phases than the corresponding RG. Further, with the availability of
magnetic kernels, we propose lower limits of field strengths in crucial layers
in our stellar model during its evolutionary phases. The theoretical
prescription outlined here provides the first formal way to devise inverse
problems for stellar magnetism and can be seamlessly employed for slow
rotators.
Rotation is typically assumed to induce strictly symmetric rotational splitting into the rotational multiplets of pure p- and g-modes. However, for evolved stars exhibiting mixed modes, avoided ...crossings between different multiplet components are known to yield asymmetric rotational splitting, particularly for near-degenerate mixed-mode pairs, where notional pure p-modes are fortuitiously in resonance with pure g-modes. These near-degeneracy effects have been described in subgiants, but their consequences for the characterisation of internal rotation in red giants has not previously been investigated in detail, in part owing to theoretical intractability. We employ new developments in the analytic theory of mixed-mode coupling to study these near-resonance phenomena. In the vicinity of the most p-dominated mixed modes, the near-degenerate intrinsic asymmetry from pure rotational splitting increases dramatically over the course of stellar evolution, and depends strongly on the mode mixing fraction \(\zeta\). We also find that a linear treatment of rotation remains viable for describing the underlying p- and g-modes, even when it does not for the resulting mixed modes undergoing these avoided crossings. We explore observational consequences for potential measurements of asymmetric mixed-mode splitting, which has been proposed as a magnetic-field diagnostic. Finally, we propose improved measurement techniques for rotational characterisation, exploiting the linearity of rotational effects on the underlying p/g modes, while still accounting for these mixed-mode coupling effects.
One of the major discoveries of asteroseismology is the signature of a strong extraction of angular momentum (AM) in the radiative zones of stars across the entire Hertzsprung-Russell diagram, ...resulting in weak core-to-surface rotation contrasts. Despite all efforts, a consistent AM transport theory, which reproduces both the internal rotation and mixing probed thanks to the seismology of stars, remains one of the major open problems in modern stellar astrophysics. A possible key ingredient to figure out this puzzle is magnetic field with its various possible topologies. Among them, strong axisymmetric toroidal fields, which are subject to the so-called Tayler MHD instability, could play a major role. They could trigger a dynamo action in radiative layers while the resulting magnetic torque allows an efficient transport of AM. But is it possible to detect signatures of these deep toroidal magnetic fields? The only way to answer this question is asteroseismology and the best laboratories of study are intermediate-mass and massive stars because of their external radiative envelope. Since most of these are rapid rotators during their main-sequence, we have to study stellar pulsations propagating in stably stratified, rotating, and potentially strongly magnetised radiative zones. For that, we generalise the traditional approximation of rotation, which provides in its classic version a flexible treatment of the adiabatic propagation of gravito-inertial modes, by taking simultaneously general axisymmetric differential rotation and toroidal magnetic fields into account. Using this new non-perturbative formalism, we derive the asymptotic properties of magneto-gravito-inertial modes and we explore the different possible field configurations. We found that the magnetic effects should be detectable for equatorial fields using high-precision asteroseismic data.
Stellar interiors are the seat of efficient transport of angular momentum all along their evolution. Understanding the dependence of the turbulent transport triggered by the shear instabilities due ...to the differential rotation in stellar radiation zones is mandatory. Indeed, it constitutes one of the cornerstones of the rotational transport and mixing theory which is implemented in stellar evolution codes to predict the rotational and chemical evolutions of stars. We investigate horizontal shear instabilities in stellar radiation zones by considering the full Coriolis acceleration with both the dimensionless horizontal component \(\tilde{f}\) and the vertical component \(f\). We performed a linear stability analysis for a horizontal shear flow with a hyperbolic tangent profile, both numerically and asymptotically using the WKBJ approximation. As in the traditional approximation, we identified the inflectional and inertial instabilities. The inflectional instability is destabilized as \(\tilde{f}\) increases and its maximum growth rate increases significantly, while the thermal diffusivity stabilizes the inflectional instability similarly to the traditional case. The inertial instability is also strongly affected; for instance, the inertially unstable regime is extended in the non-diffusive limit as \(0<f<1+\tilde{f}^{2}/N^{2}\), where \(N\) is the dimensionless Brunt-V\"ais\"al\"a frequency. More strikingly, in the high-thermal-diffusivity limit, it is always inertially unstable at any colatitude \(\theta\) except at the poles (i.e., \(0^{\circ}<\theta<180^{\circ}\)). Using the asymptotic and numerical results, we propose a prescription for the effective turbulent viscosities induced by the instabilities to be possibly used in stellar evolution models. The characteristic time of this turbulence is short enough to redistribute efficiently angular momentum and mix chemicals in the radiation zones.
Asteroseismology has revealed small core-to-surface rotation contrasts in stars in the whole HR diagram. This is the signature of strong transport of angular momentum (AM) in stellar interiors. One ...of the plausible candidates to efficiently carry AM is magnetic fields with various topologies that could be present in stellar radiative zones. Among them, strong axisymmetric azimuthal magnetic fields have received a lot of interest. Indeed, if they are subject to the so-called Tayler instability, the accompanying triggered Maxwell stresses can transport AM efficiently. In addition, the electromotive force induced by the fluctuations of magnetic and velocity fields could potentially sustain a dynamo action that leads to the regeneration of the initial strong axisymmetric azimuthal magnetic field. The key question we aim to answer is: can we detect signatures of these deep strong azimuthal magnetic fields? The only way to answer this question is asteroseismology and the best laboratories of study are intermediate-mass and massive stars. Most of these are rapid rotators during their main-sequence. Therefore, we have to study stellar pulsations propagating in stably stratified, rotating, and potentially strongly magnetised radiative zones. We generalise the traditional approximation of rotation by simultaneously taking general axisymmetric differential rotation and azimuthal magnetic fields into account in a non-perturbative way. Using this new formalism, we derive the asymptotic properties of magneto-gravito-inertial (MGI) waves and their period spacings. We find that toroidal magnetic fields induce a shift in the period spacings of MGI modes. An equatorial azimuthal magnetic field with an amplitude of the order of \(10^5\,\rm G\) leads to signatures that can be detectable thanks to modern space photometry. More complex hemispheric configurations are more difficult to observe.
Due to be launched late 2026, the PLATO mission will bring the study of main-sequence solar-type and low-mass stars into a new era. In particular, PLATO will provide the community with a stellar ...sample with solar-type oscillations and activity-induced brightness modulation of unequalled size. We present here the main features of the analysis module that will be dedicated to measure stellar surface rotation and activity in the PLATO Stellar Analysis System.
Our knowledge of the dynamics of stars has undergone a revolution thanks to the simultaneous large amount of high-quality photometric observations collected by space-based asteroseismology and ...ground-based high-precision spectropolarimetry. They allowed us to probe the internal rotation of stars and their surface magnetism in the whole Hertzsprung-Russell diagram. However, new methods should still be developed to probe the deep magnetic fields in those stars. Our goal is to provide seismic diagnoses that allow us to sound the internal magnetism of stars. Here, we focus on asymptotic low-frequency gravity modes and high-frequency acoustic modes. Using a first-order perturbative theory, we derive magnetic splittings of their frequencies as explicit functions of stellar parameters. As in the case of rotation, we show how asymptotic gravity and acoustic modes can allow us to probe the different components of the magnetic field in the cavities where they propagate. This demonstrates again the high potential of using mixed-modes when this is possible.
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