Figure - available from: Royal Society Open Science
This content is subject to copyright.
![The observed field geometry on the main-sequence B0 star τ Sco, at two rotational phases, using Zeeman-Doppler imaging. The paths of arched magnetic field lines are clearly visible; it seems likely that they are associated with twisted flux tubes buried just below the surface—see §3.5. From Donati et al. [21]. Observations of this star taken several years apart show the same topology, confirming a lack of variability also in stars with complex magnetic topologies [7].](publication/282844248/figure/fig7/AS:1165379950915585@1654859640187/The-observed-field-geometry-on-the-main-sequence-B0-star-t-Sco-at-two-rotational-phases.jpeg)
The observed field geometry on the main-sequence B0 star τ Sco, at two rotational phases, using Zeeman-Doppler imaging. The paths of arched magnetic field lines are clearly visible; it seems likely that they are associated with twisted flux tubes buried just below the surface—see §3.5. From Donati et al. [21]. Observations of this star taken several years apart show the same topology, confirming a lack of variability also in stars with complex magnetic topologies [7].
Source publication
We review the current state of knowledge of magnetic fields inside stars,
concentrating on recent developments concerning magnetic fields in stably
stratified (zones of) stars, leaving out convective dynamo theories and
observations of convective envelopes. We include the observational properties
of A, B and O-type main-sequence stars, which have r...
Similar publications
Isolated magnetic white dwarfs have field strengths ranging from kilogauss to
gigagauss, and constitute an interesting class of objects. The origin of the
magnetic field is still the subject of a hot debate. Whether these fields are
fossil, hence the remnants of original weak magnetic fields amplified during
the course of the evolution of the proge...
Citations
... Major uncertainties in stellar rotation are tied to different aspects. For instance, stellar rotation is inextricably linked to magnetic field generation (e.g., Braithwaite & Spruit 2017;Brun & Browning 2017). The interaction between rotation and magnetic fields is not completely understood despite its influence on stellar activity, which affects processes such as starspots, flares, and the stellar wind. ...
We calculate new evolutionary models of rotating primordial very massive stars, with initial mass from 100 M ⊙ to 200 M ⊙ , for two values of the initial metallicity Z = 0 and Z = 0.0002. For the first time in this mass range, we consider stellar rotation and pulsation-driven mass loss, along with radiative winds. The models evolve from the zero-age main sequence until the onset of pair-instability. We discuss the main properties of the models during their evolution and then focus on the final fate and the possible progenitors of jet-driven events. All tracks that undergo pulsational-pair instability produce successful gamma-ray bursts (GRB) in the collapsar framework, while those that collapse directly to black holes (BH) produce jet-driven supernova events. In these latter cases, the expected black hole mass changes due to the jet propagation inside the progenitor, resulting in different models that should produce BH within the pair-instability black hole mass gap. Successful GRBs predicted here from zero metallicity, and very metal-poor progenitors, may be bright enough to be detected even up to redshift ∼20 using current telescopes such as the Swift-BAT X-ray detector and the JWST.
... These concern the kinds, stability, and effects of magnetic fields. There are several excellent textbooks and reviews on the topic-for example, [106][107][108][109][110][111][112]. ...
... The dipole mode may form a magnetosphere around the star; however, any toroidal field diffuses above the stellar surface such that the field can eventually become force free [111,140], meaning that the Lorentz force is zero, (∇ × B) × B = 0. While the magnetic field above the stellar surface can possess an azimuthal component (for example, due to stellar rotation shearing a pure dipole field), enclosed toroidal fields above the stellar surface are unstable and rapidly diffusive into the poloidal component. ...
... Similar to the above constraints, differential rotation could also lead to the local removal of an initial magnetic field if the difference in rotation frequency between adjacent layers is much larger than the Alfvén frequency [111,149]. In this case, the magnetic field may be wound-up such that a high magnetic diffusion effectively dissipates it, leaving no magnetic flux in differentially-rotating regions. ...
Magnetism is a ubiquitous property of astrophysical plasmas, yet stellar magnetism still remains far from being completely understood. In this review, we describe recent observational and modelling efforts and progress to expand our knowledge of the magnetic properties of high-mass stars. Several mechanisms (magneto-convection, mass-loss quenching, internal angular momentum transport, and magnetic braking) have significant implications for stellar evolution, populations, and end-products. Consequently, it remains an urgent issue to address and resolve open questions related to magnetism in high-mass stars.
... These concern the kinds, stability, and effects of magnetic fields. There are several excellent textbooks and reviews on the topic-for example, [106][107][108][109][110][111][112]. ...
... The dipole mode may form a magnetosphere around the star; however, any toroidal field diffuses above the stellar surface such that the field can eventually become force free [111,140], meaning that the Lorentz force is zero, (∇ × B) × B = 0. While the magnetic field above the stellar surface can possess an azimuthal component (for example, due to stellar rotation shearing a pure dipole field), enclosed toroidal fields above the stellar surface are unstable and rapidly diffusive into the poloidal component. ...
... Similar to the above constraints, differential rotation could also lead to the local removal of an initial magnetic field if the difference in rotation frequency between adjacent layers is much larger than the Alfvén frequency [111,149]. In this case, the magnetic field may be wound-up such that a high magnetic diffusion effectively dissipates it, leaving no magnetic flux in differentially-rotating regions. ...
Magnetism is a ubiquitous property of astrophysical plasmas, yet stellar magnetism still remains far from being completely understood. In this review, we describe recent observational and modelling efforts and progress to expand our knowledge of the magnetic properties of high-mass stars. Several mechanisms (magneto-convection, mass-loss quenching, internal angular momentum transport, and magnetic braking) have significant implications for stellar evolution, populations, and end-products. Consequently, it remains an urgent issue to address and resolve open questions related to magnetism in high-mass stars.
... Much of the physics studied here could also apply to radiative stars such as white dwarfs and the radiative cores of red giants where internal fields can be detected through asteroseismology (Garc ía et al. 2014 ;Stello et al. 2016 ;Li et al. 2022 ) because of their impact on stellar oscillations (Fuller et al. 2015 ;Lecoanet et al. 2017 ;Loi 2021 ;Bugnet et al. 2021 ;Mathis et al. 2021 ). Magnetic upper main sequence stars have typical surface field strengths of ∼1 kG (see Braithwaite & Spruit 2017 for a re vie w) and surface magnetic pressures larger than surface gas pressures, such that magnetic forces could be strong. The surface magnetic morphologies are observed to be div erse: the y can be complex or simple, axisymmetric or non-axisymmetric, poloidal or toroidal (Landstreet & Mathys 2000 ;Kochukhov et al. 2011 ;Shultz et al. 2019 ). ...
Strong magnetic fields are observed in a substantial fraction of upper main sequence stars and white dwarfs. Many such stars are observed to exhibit photometric modulations as the magnetic poles rotate in and out of view, which could be a consequence of magnetic perturbations to the star’s thermal structure. The magnetic pressure is typically larger than the gas pressure at the star’s photosphere, but much smaller than the gas pressure in the star’s interior, so the expected surface flux perturbations are not clear. We compute magnetically perturbed stellar structures of young 3 M⊙ stars that are in both hydrostatic and thermal equilibrium, and which contain both poloidal and toroidal components of a dipolar magnetic field as expected for stable fossil fields. This provides semi-analytical models of such fields in baroclinic stably stratified regions. The star’s internal pressure, temperature, and flux perturbations can have a range of magnitudes, though we argue the most likely configurations exhibit flux perturbations much smaller than the ratio of surface magnetic pressure to surface gas pressure, but much larger than the ratio of surface magnetic pressure to central gas pressure. The magnetic pole is hotter than the equator in our models, but a cooler magnetic pole is possible depending on the magnetic field configuration. The expected flux variations for observed field strengths are δL/L ≲ 10−6, much smaller than those observed in magnetic stars, suggesting that observed perturbations stem from changes to the emergent spectrum rather than changes to the bolometric flux.
... From the structure of equation (17) it follows that its solution is completely determined by the function ( , ) and its derivatives. The solutions of equation (17) by the Galerkin method [36] give flows of two types [9]: 1) flows that are symmetric about the equator and 2) flows that are mirror-symmetric about the equator. In other words, flows whose streamlines do not cross the equator, and flows whose streamlines cross the equator. ...
... (1) ( , ) and (1) ( , ), are the radial and meridional components of the relict dipole magnetic field [36], respectively. The third component, (1) ( , , ), is the azimuthal magnetic field resulting from the interaction of differential rotation with the relict dipole field (Ω-effect). ...
... It follows from the first and second equations of system (23) that the components (1) and (1) of any form satisfy them, as long as they satisfy the equation div ⃗ 1 = 0. We have chosen the dipole form of these components [14], since the relict dipole magnetic field is well observed on the Sun [36]. Hence ...
The paper deals with the problem of explaining the origin and nature of the space-time variations in the magnetic activity of the Sun. It presents a new hydrodynamic model of the solar magnetic cycle, which uses helioseismological data on the differential rotation of the solar convective zone. The model is based on the hypothesis of the emergence of global flows as a result of the loss of stability of a differentially rotating plasma layer in the convective zone. First, the hydrodynamic global plasma flows are calculated without accounting for the effect of a magnetic field on them. Under this condition, it is shown that the solutions found describe all global flows observed on the surface of the Sun: permanent meridional circulation from the equator to the poles, torsional oscillations and space-time variations of the meridional flow. We conclude that the last two flows are azimuthal and meridional components of a single three-dimensional global hydrodynamic flow. Second, to simulate the dynamics of the magnetic field, the found velocities of global migrating flows and the spatial profile of the angular velocity of the internal differential rotation of the solar convective zone obtained from helioseismic measurements were used. Good coincidences have been obtained between the characteristics of the calculated dynamics of global migrating flows and the variable global magnetic fields generated by them with the observed values on the solar surface. An explanation is given for some phenomena on the surface of the Sun, which could not be explained within the framework of the available models.
... We think it is safe to neglect magnetic diffusion, as the diffusion time across a star is long compared with its mainsequence lifetime (e.g. Braithwaite & Spruit 2017). We likewise suspect that differential rotation can be neglected, as M F 9 ...
Stars are born with magnetic fields, but the distribution of their initial field strengths remains uncertain. We combine observations with theoretical models of magnetic field evolution to infer the initial distribution of magnetic fields for AB stars in the mass range of 1.6 - 3.4 M$_{\odot}$. We tested a variety of distributions with different shapes and found that a distribution with a mean of $\sim$800 G and a full width of $\sim$600 G is most consistent with the observed fraction of strongly magnetized stars as a function of mass. Our most-favored distribution is a Gaussian with a mean of $\mu$ = 770 G and standard deviation of $\sigma$ = 146 G. Independent approaches to measure the typical field strength suggest values closer to 2 - 3 kG, a discrepancy that could suggest a mass-dependent and bimodal initial field distribution, or an alternative theoretical picture for the origin of these magnetic fields.
... We think it is safe to neglect magnetic diffusion, as the diffusion time across a star is long compared with its MS lifetime (e.g., Braithwaite & Spruit 2017). We likewise suspect that differential rotation can be neglected, as supercritical magnetic fields are likely strong enough to inhibit any significant shears from developing on the MS. ...
Stars are born with magnetic fields, but the distribution of their initial field strengths remains uncertain. We combine observations with theoretical models of magnetic field evolution to infer the initial distribution of magnetic fields for AB stars in the mass range of 1.6–3.4 M ⊙ . We tested a variety of distributions with different shapes and found that a distribution with a mean of ∼800 G and a full width of ∼600 G is most consistent with the observed fraction of strongly magnetized stars as a function of mass. Our most-favored distribution is a Gaussian with a mean of μ = 770 G and standard deviation of σ = 146 G. Independent approaches to measure the typical field strength suggest values closer to 2–3 kG, a discrepancy that could suggest a mass-dependent and bimodal initial field distribution, or an alternative theoretical picture for the origin of these magnetic fields.
... A systematic search for magnetic perturbations in red giants with detected oscillations will give the prevalence of red giants with magnetic fields below B c . The measurement of magnetic fields in the radiative cores of red giants will allow progress on the origin and evolution of the stellar magnetic field 22,23 . The origin of the detected fields could be a convective core dynamo occurring during the main sequence. ...
A red giant star is an evolved low- or intermediate-mass star that has exhausted its central hydrogen content, leaving a helium core and a hydrogen-burning shell. Oscillations of stars can be observed as periodic dimmings and brightenings in the optical light curves. In red giant stars, non-radial acoustic waves couple to gravity waves and give rise to mixed modes, which behave as pressure modes in the envelope and gravity modes in the core. These modes have previously been used to measure the internal rotation of red giants1,2, leading to the conclusion that purely hydrodynamical processes of angular momentum transport from the core are too inefficient³. Magnetic fields could produce the additional required transport4–6. However, owing to the lack of direct measurements of magnetic fields in stellar interiors, little is currently known about their properties. Asteroseismology can provide direct detection of magnetic fields because, like rotation, the fields induce shifts in the oscillation mode frequencies7–12. Here we report the measurement of magnetic fields in the cores of three red giant stars observed with the Kepler¹³ satellite. The fields induce shifts that break the symmetry of dipole mode multiplets. We thus measure field strengths ranging from about 30 kilogauss to about 100 kilogauss in the vicinity of the hydrogen-burning shell and place constraints on the field topology.
... The nature of fossil fields is fundamentally different from contemporaneously generated dynamo fields by a mechanical source (such as convection or differential rotation). Fossil field evolution is purely dissipative with no active field generation counteracting its slow dissipation (Braithwaite & Spruit 2017 ). In stellar layers where large-scale fossil fields spread through, it is expected that solid-body rotation will develop (e.g. ...
... Fossati et al. 2016 ;Shultz et al. 2019b ). Fossil magnetic fields are expected to evolve only by Ohmic dissipation (Wright 1969 ;Spruit 2004 ;Braithwaite & Spruit 2017 ), which has a longer timescale than the main sequence nuclear time-scale is (Cowling 1945 ;Spitzer 1958 ). Ho we ver, Ohmic dissipation remains riddled with uncertainties depending on the exact value of magnetic dif fusi vity (e.g. ...
... Magnetic fields are much more efficient at transporting angular momentum than purely hydrodynamic processes such as meridional currents and shear instabilities (e.g. Mestel 1999 ;Spruit 1999Spruit , 2002Kulsrud 2005 ;Braithwaite & Spruit 2017 ). The rotation of the star leads to Maxwell stresses, which result in losing angular momentum from the star. ...
Magnetic fields can drastically change predictions of evolutionary models of massive stars via mass-loss quenching, magnetic braking, and efficient angular momentum transport, which we aim to quantify in this work. We use the mesa software instrument to compute an extensive main-sequence grid of stellar structure and evolution models, as well as isochrones, accounting for the effects attributed to a surface fossil magnetic field. The grid is densely populated in initial mass (3–60 M⊙), surface equatorial magnetic field strength (0–50 kG), and metallicity (representative of the Solar neighbourhood and the Magellanic Clouds). We use two magnetic braking and two chemical mixing schemes and compare the model predictions for slowly rotating, nitrogen-enriched (‘Group 2’) stars with observations in the Large Magellanic Cloud. We quantify a range of initial field strengths that allow for producing Group 2 stars and find that typical values (up to a few kG) lead to solutions. Between the subgrids, we find notable departures in surface abundances and evolutionary paths. In our magnetic models, chemical mixing is always less efficient compared to non-magnetic models due to the rapid spin-down. We identify that quasi-chemically homogeneous main sequence evolution by efficient mixing could be prevented by fossil magnetic fields. We recommend comparing this grid of evolutionary models with spectropolarimetric and spectroscopic observations with the goals of (i) revisiting the derived stellar parameters of known magnetic stars, and (ii) observationally constraining the uncertain magnetic braking and chemical mixing schemes.
... The nature of fossil fields is fundamentally different from contemporaneously generated dynamo fields by a mechanical source (such as convection or differential rotation). Fossil field evolution is purely dissipative with no active field generation counteracting its slow dissipation (Braithwaite & Spruit 2017). In stellar layers where large-scale fossil fields spread through, it is expected that solid-body rotation will develop (e.g. ...
... Observed samples of magnetic A-type stars and compact remnants are consistent with the magnetic flux being conserved over time (e.g., Landstreet et al. 2007Landstreet et al. , 2008Wickramasinghe & Ferrario 2005;Neiner et al. 2017;Martin et al. 2018;Sikora et al. 2019a), whereas other observational evidence (including that for OB stars) suggests magnetic flux decay (e.g., Fossati et al. 2016;Shultz et al. 2019b). Fossil magnetic fields are expected to evolve only by Ohmic dissipation (Wright 1969;Spruit 2004;Braithwaite & Spruit 2017), which has a longer timescale than the main sequence nuclear timescale (Cowling 1945;Spitzer 1958). However, Ohmic dissipation remains riddled with uncertainties depending on the exact value of magnetic diffusivity (e.g., Charbonneau & MacGregor 2001) and the geometry of the magnetic field since more complex fields dissipate faster. ...
... Magnetic fields are much more efficient at transporting angular momentum than purely hydrodynamic processes such as meridional currents and shear instabilities (e.g., Mestel 1999;Spruit 1999Spruit , 2002Kulsrud 2005;Braithwaite & Spruit 2017). The rotation of the star leads to Maxwell stresses, which result in losing angular momentum from the star. ...
Magnetic fields can drastically change predictions of evolutionary models of massive stars via mass-loss quenching, magnetic braking, and efficient angular momentum transport, which we aim to quantify in this work. We use the MESA software instrument to compute an extensive main-sequence grid of stellar structure and evolution models, as well as isochrones, accounting for the effects attributed to a surface fossil magnetic field. The grid is densely populated in initial mass (3-60 M$_\odot$), surface equatorial magnetic field strength (0-50 kG), and metallicity (representative of the Solar neighbourhood and the Magellanic Clouds). We use two magnetic braking and two chemical mixing schemes and compare the model predictions for slowly-rotating, nitrogen-enriched ("Group 2") stars with observations in the Large Magellanic Cloud. We quantify a range of initial field strengths that allow for producing Group 2 stars and find that typical values (up to a few kG) lead to solutions. Between the subgrids, we find notable departures in surface abundances and evolutionary paths. In our magnetic models, chemical mixing is always less efficient compared to non-magnetic models due to the rapid spin-down. We identify that quasi-chemically homogeneous main sequence evolution by efficient mixing could be prevented by fossil magnetic fields. We recommend comparing this grid of evolutionary models with spectropolarimetric and spectroscopic observations with the goals of i) revisiting the derived stellar parameters of known magnetic stars, and ii) observationally constraining the uncertain magnetic braking and chemical mixing schemes.
