Pith. sign in

REVIEW 3 major objections 4 minor 111 references

This paper argues that a self-sustained MRI dynamo in stellar radiative zones transports angular momentum and chemicals according to simple power-law scalings, with transport coefficients that become independent of viscosity at high Reynold

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-01 08:34 UTC pith:5KS3NIT3

load-bearing objection Useful, honest scalings for stratified MRI dynamo transport that stellar modelers will want to test; the main caveat the authors admit themselves—dynamo persistence only proven for one run—should be fixed in revision, not reject. the 3 major comments →

arxiv 2607.21059 v1 pith:5KS3NIT3 submitted 2026-07-23 astro-ph.SR

Transport of angular momentum and chemical elements by the MRI dynamo in stellar radiative zones

Laur\`ene Jouve , Fran\c{c}ois Ligni\`eres , J\'er\^ome Guilet , Alexis Vanbesien This is my paper
classification astro-ph.SR
keywords magneto-rotational instabilitydynamoangular momentum transportchemical mixingstellar radiative zonesstable stratificationshearing boxasteroseismology
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tries to establish that the magneto-rotational instability (MRI), acting as a self-sustained dynamo in a stably stratified stellar radiative zone, is an efficient transporter of both angular momentum and chemical elements. Using local shearing-box simulations with radial shear along gravity and rotation perpendicular to it, the authors derive power-law scalings for the turbulent Maxwell stress and the chemical flux in terms of stratification and rotation. They find that angular-momentum transport is dominated by the magnetic (Maxwell) stress, that chemical transport is more strongly suppressed by stable stratification than angular-momentum transport, and that both transport coefficients become independent of the microscopic viscosity in the high-Reynolds-number regime. If these scalings hold at stellar parameters, they would give 1D stellar evolution models a magnetic transport law that could explain the slowly rotating cores of red giants and separate the mixing of angular momentum from that of chemicals.

Core claim

At the paper's center is a zero-net-flux shearing-box dynamo: a random weak seed field is stretched into an axisymmetric azimuthal field, that field goes unstable to the MRI, and the resulting fluctuations generate a new radial field through a mean electromotive force, closing the loop. In the saturated state, the radial transport of angular momentum follows <b_x b_y>/(L^2 S^2) ~ (Pr N^2/Omega^2)^-0.58 (S/Omega)^-0.86, with the Maxwell stress roughly an order of magnitude larger than the Reynolds stress; the chemical flux follows <c v_x>/(S L^2 dC/dx) ~ (Pr N^2/Omega^2)^-1 (S/Omega)^0.92. Here N is the Brunt-Vaisala (buoyancy) frequency, Pr the ratio of viscosity to thermal diffusivity, S th

What carries the argument

The central object is the stratified, zero-net-flux MRI dynamo in a shearing box, a local Cartesian model of a differentially rotating patch of a star. It works through a loop: the imposed shear winds a weak radial seed field into an axisymmetric azimuthal field; that field is unstable to the magneto-rotational instability; non-axisymmetric fluctuations drive an electromotive force that regenerates the radial field. A linear stability analysis of this loop shows that stratification and rotation act through the combination Pr N^2/Omega^2, while thermal diffusion suppresses buoyancy in the low-Peclet-number regime, so that stratification is measured by kappa/N^2 rather than N alone. The correl

Load-bearing premise

The load-bearing premise is that every stratified run used in the fits is a genuine self-sustained dynamo; only one weakly stratified run was followed for long enough to exceed the magnetic field's own decay time, and the authors themselves note that some more stratified cases might lose turbulence if run longer.

What would settle it

Extend one of the stratified saturated cases at Pr N^2/Omega^2 near 0.5 and S/Omega = 1.5 beyond one magnetic diffusion time; if the magnetic energy decays rather than remaining saturated, the fitted exponents describe transient turbulence, not dynamo transport.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If the scalings survive stellar extrapolation, the stratified MRI dynamo would provide a candidate explanation for the near-rigid rotation inferred in subgiant and red-giant cores from asteroseismology.
  • Angular momentum and chemical elements are transported with different power laws, so 1D stellar models can legitimately use distinct turbulent coefficients for rotation and for abundance mixing.
  • Because the effective viscosity and diffusivity become independent of the microscopic viscosity at high Reynolds number, the prescription can be extrapolated to stellar Reynolds numbers without a free viscous parameter.
  • Rotation enhances the transport, particularly the Maxwell stress, so the mechanism is most efficient in fast rotators, the opposite of hydrodynamic shear instabilities.
  • Any weakly magnetized, differentially rotating radiative zone above a minimum seed field develops this turbulence; no special initial field geometry is required.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • A direct test of the scalings would be to run the same setup with a stabilizing compositional gradient; the paper's logic implies the transport would be suppressed wherever such a gradient is not erased by thermal diffusion, confining the mechanism to regions where a pre-existing magnetic field enforces rigid rotation.
  • The residual box-size dependence in the angular-momentum transport (through L in nu_t) suggests a geometric limit: at latitudes where rotation has a component along gravity, the effective vertical scale may differ, so the scalings are most naturally read as equatorial and could steepen or flatten elsewhere.
  • If the asymptotic regime is governed by magnetic Reynolds number rather than magnetic Prandtl number, as the paper speculates, stellar interiors with Pm < 1 but very high Rm would still be in the viscosity-independent regime; a targeted low-Pm high-Rm simulation would settle this.
  • The near-linear dependence of the chemical diffusivity on rotation and shear (D_t ~ beta S Omega kappa/N^2) predicts that fast rotators at fixed thermal stratification mix chemicals more vigorously, a trend that could be checked against surface lithium abundances in young stars.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The manuscript reports a large suite of zero-net-flux Boussinesq shearing-box simulations of the MRI in a stably stratified, rotating, radially sheared layer representing an equatorial stellar radiative zone. It argues that the turbulence is a self-sustained MRI dynamo and derives empirical scaling laws for radial angular-momentum and chemical transport as functions of PrN^2/Omega^2 and S/Omega (Eqs. 18-24), with additional Re and Pm dependencies fitted in Sec. 6. The authors conclude that, in the simulated regime, the Maxwell stress dominates, AM transport is less stratification-suppressed than the Tayler-Spruit prescription, chemical transport is even more suppressed and has a different rotation dependence, and that the effective transport coefficients become asymptotically independent of viscosity.

Significance. If the result holds, it provides a physically motivated magnetic transport prescription for 1D stellar evolution codes, with separate coefficients for angular momentum and chemical transport. The paper's strengths are its systematic parameter coverage, the collapse of the stratification dependence onto PrN^2/Omega^2, the supporting linear analysis in Appendix B, the box-size checks in Sec. 7 and Appendix F, and the authors' explicit statements about the limits of their regime. The main risk is that dynamo persistence is demonstrated for only one low-Re/Pm run, while many runs entering the scaling fits are integrated for less than a magnetic diffusion time. This directly affects the validity of the quoted exponents, which are the central quantitative deliverable. A second risk is the untested extrapolation from Pm=2-16 to stellar Pm<1. Both are fixable with additional diagnostics or by more carefully restricting the claims.

major comments (3)
  1. [Sec. 3.1, used in Secs. 4-5] The dynamo-persistence test is performed for a single run (Re=382, Pm=4, Rm~1.5e3), while the fits in Figs. 8, 9, 13 and Eqs. 18-22 use runs at Re=765-3058, Pm=8-16, typically for less than one magnetic diffusion time. The text states (Sec. 3.1) that 'dynamo action may be lost in some of these more stratified cases if computed on longer timescales.' If any of the runs used in the fits are decaying transients, the exponents -0.58, -0.62, -1.0 and 0.92 would describe transient turbulence, not equilibrium dynamo transport. The authors should either verify sustained magnetic energy over at least one magnetic diffusion time for stratified runs spanning the fitted range, especially near the stability boundary, or impose and report a well-defined persistence criterion and re-fit only runs satisfying it.
  2. [Sec. 6.2 and Sec. 7, Eqs. (25)-(33)] The conclusion that the transport coefficients become independent of viscosity rests on the Rm-asymptotic regime observed at Pm=2-16, Rm~2e4. Sec. 6.2 candidly states that the extrapolation to stellar Pm<1 is 'only speculate'. Since stellar Pm is typically below unity, the viscosity-independent forms in Eqs. (27) and (33) are not established for the target application. The abstract and Conclusions should either clearly mark these as extrapolations, or the authors should provide a concrete dynamical argument or accessible low-Pm test supporting the same asymptotic behavior. As written, the claim that transport coefficients are viscosity-independent is stronger than what the simulations establish.
  3. [Sec. 7, Fig. 16] The Maxwell stress depends on the box size in the z-direction, and the convergence when varying Lz is explicitly described as less clear than for Ly. Since Eq. (23) contains a prefactor alpha that enters the proposed stellar prescription, and Eq. (27) shows a residual L dependence, the absolute normalization of the turbulent viscosity is not reliably box-independent. The exponents may be robust, but the prefactor matters for 1D implementations. The authors should quantify the Lz dependence and its effect on the fitted prefactor, or explicitly state that only the scaling exponents are robust and that the absolute normalization is subject to this remaining uncertainty.
minor comments (4)
  1. [Sec. 3.1 and captions of Figs. 3-9] The manuscript would benefit from a table listing each run's Re, Pm, Rm, PrN^2/Omega^2, S/Omega, integration time, and magnetic diffusion time. This would make it easy to see which runs satisfy the persistence criterion and would strengthen the empirical basis of the fits.
  2. [Secs. 4-6, Appendix E] Fitted exponents are reported without uncertainties or scatter estimates. Given that the exponents vary with Re and the fits use a limited number of points, confidence intervals or at least a statement of run-to-run variability would improve the reliability of the claimed scalings.
  3. [Sec. 4.1, Fig. 7] The rescaling of the autocorrelation functions is used to infer the lengthscale scalings, but the quality of the collapse is judged only visually. A quantitative measure of the collapse (e.g., a reduced chi-square or rms deviation of the rescaled curves) would make the inferred scalings more objective.
  4. [Sec. 5.2, Fig. 12] In the bottom panel of Fig. 12, the x-axis is PrN^2/Omega^2, but several points appear to be at values outside the stated range 3e-2 to 1. Please clarify which points are used for the fits and which are excluded as the unstratified or decaying regime.

Circularity Check

0 steps flagged

No significant circularity: the scaling laws are empirical fits to new simulations, and the load-bearing inputs (equations, linear stability analysis, simulation outputs) are not constructed from the claimed conclusions.

full rationale

The paper's central claim is the construction of scaling laws from a large parameter survey of zero-net-flux shearing-box simulations, not a first-principles prediction. The scalings in Eqs. 18-24, 25-33 are explicitly presented as fits to measured stresses and fluxes (e.g., 'the fitted curve has a slope almost exactly equal to −1'; 'Fits shown by dotted lines...'), with the combined stratification parameter PrN^2/Ω^2 justified by an independently verified balance in the temperature equation (Appendix A) and by the small-Péclet-number linear analysis (Appendix B). The linear stability threshold and the claimed viscosity independence follow algebraically from the fitted forms plus the definitions of the Reynolds and Prandtl numbers; they are not assumed as inputs. The self-citations (Jouve et al. 2020; Gouhier et al. 2022; Meduri et al. 2024) are used for motivation and comparison, not to force the fitted exponents; no uniqueness theorem or ansatz is imported from the authors' prior work. The one honest limitation flagged in Sec. 3.1 — that dynamo action is verified beyond one magnetic diffusion time for only a single low-Re/Pm run and 'may be lost in some of these more stratified cases if computed on longer timescales' — concerns the physical interpretation of some fitted points, but it is a support/robustness caveat, not circularity: the measured stresses are still the simulations' outputs, and the paper does not redefine those outputs as the desired transport coefficients by construction. No step in the derivation chain reduces, by the paper's own equations or by self-citation, to its own inputs.

Axiom & Free-Parameter Ledger

10 free parameters · 8 axioms · 0 invented entities

The scaling laws rest on power-law exponents fitted to simulation data, a set of physical regime assumptions (small-Peclet balance, passive scalar, equatorial geometry, no mu-gradients), the unproven extension of high-Rm asymptotics to stellar Pm<1, and the assumption that the turbulence is a sustained dynamo in every fitted run. No new physical entities are introduced.

free parameters (10)
  • Maxwell stress exponent on PrN^2/Omega^2 = -0.58 (rounded to -0.5 in Eq. 29)
    Fitted to Fig. 8 and Appendix E; used in Eq. 18/23.
  • Reynolds stress exponent on PrN^2/Omega^2 = -0.62
    Fitted to Fig. 8; used in Eq. 20.
  • Chemical flux exponent on PrN^2/Omega^2 = -1.05 (rounded to -1)
    Fitted to Fig. 9 and Appendix E; used in Eq. 22.
  • Maxwell stress exponent on S/Omega = -0.86 (rounded to -1)
    Fitted in Fig. E.2; used in Eq. 18/23.
  • Reynolds stress exponent on S/Omega = +0.22
    Fitted in Fig. E.2; used in Eq. 20.
  • Chemical flux exponent on S/Omega = +0.92 (rounded to +1)
    Fitted in Fig. E.2; used in Eq. 22.
  • alpha exponent on Re = -0.58
    Fitted in Fig. 14; used to claim viscosity independence in Eq. 25.
  • beta exponent on Re = -0.81
    Fitted in Fig. 14; used in Eq. 31.
  • Prefactors alpha and beta = alpha ~ 1, beta ~ 0.4
    Order-unity coefficients set by fits, not derived; used in Eqs. 25 and 31.
  • Box aspect ratio L_y=L_z=6L_x = 6
    Chosen setup; Maxwell stress retains L_y/L_z sensitivity (Fig. 16, App. F), so the box scale enters Eq. 30.
axioms (8)
  • domain assumption Boussinesq MHD equations in the shearing-box approximation describe the equatorial stellar radiative zone.
    Sec. 2.1; local Cartesian model with rotation perpendicular to gravity; ignores curvature, spherical geometry, and latitudinal rotation component.
  • domain assumption Small-Peclet balance N^2 v_x ≈ kappa Delta f holds, so stratification is controlled by PrN^2/S^2 or PrN^2/Omega^2.
    Sec. 3.3 and Appendix A; verified in simulations, but if this balance breaks down at stellar parameters the scalings fail.
  • ad hoc to paper Dynamo action is sustained in all runs used to fit the scaling laws.
    Sec. 3.1: dynamo is demonstrated for only one run beyond one magnetic diffusion time; authors note it may be lost in strongly stratified cases on longer timescales.
  • domain assumption Linear MRI analysis in the low-Peclet limit, with k_y << k_x,k_z and inviscid growth rate compared to viscous damping, applies to the nonlinear simulations.
    Appendix B, Eqs. B.1-B.11; standard approximation but not a derivation of the nonlinear scalings.
  • domain assumption Chemical species is a passive scalar with constant background gradient and no back-reaction on stratification.
    Sec. 2.1 Eq. 5; ignores mu-gradients and chemical buoyancy, acknowledged as a limitation in Sec. 8.
  • ad hoc to paper High-Rm asymptotic regime inferred at Pm=2-16 and Rm~2e4 remains valid for stellar Pm<1.
    Sec. 6.2: the authors state this is speculation; the stellar extrapolation depends on it.
  • domain assumption Hydrodynamic instabilities are absent in all simulations; turbulence requires magnetic fields.
    Sec. 2.1/3.3; S/Omega<2 and fast rotation are stated to stabilize hydrodynamic modes, but no detailed evidence is shown.
  • ad hoc to paper The local box in the z (latitudinal) direction does not artificially set the transport scale.
    Sec. 7 and Fig. 16: convergence with L_z is less clear; box height enters the Maxwell stress expression and the stellar vertical scale is unknown.

pith-pipeline@v1.3.0-alltime-deepseek · 30238 in / 17355 out tokens · 179319 ms · 2026-08-01T08:34:32.195812+00:00 · methodology

0 comments
read the original abstract

The question of angular momentum transport by magnetic fields has recently been revived by the detection of magnetic fields in the deep interior of red giant stars. We aim at characterizing the efficiency of the transport of angular momentum and chemical elements in a stellar radiative zone subject to the magneto-rotational instability, in situations where hydrodynamical instabilities are not triggered. We use a large set of zero-net flux shearing-box simulations modelling a portion of a stellar radiative zone located close to the equatorial region. The shear is imposed in the direction of gravity, mimicking a radial differential rotation and rotation is perpendicular to gravity. We aim at establishing scaling laws between the transport efficiency and key parameters such as stratification and rotation. We obtain simulations where the MRI is triggered on the self-consistently built longitudinal field and then produces a state of self-sustained turbulence that we associate with dynamo action. We find that in the parameter range explored, both rotation and stable stratification strongly affect the vertical transport of angular momentum which is always dominated by the Maxwell stress component. In a similar way, we find that the transport of chemical composition is even more strongly affected by the stratification but less severely by rotation. Scaling laws are established and tentative extrapolations to stellar values are discussed. Transport by the stratified MRI dynamo is very promising to reconcile stellar evolution models and asteroseismic inversions of internal rotation rates of stars.

Figures

Figures reproduced from arXiv: 2607.21059 by Alexis Vanbesien, Fran\c{c}ois Ligni\`eres, J\'er\^ome Guilet, Laur\`ene Jouve.

Figure 1
Figure 1. Figure 1: Schematics of the geometry of the problem: a radial shear localized close to the equator, such that rotation and gravity are perpendicular. the momentum equation. In addition, instead of using the temperature variable, we use the buoyancy field f = αgδT (with δT the temperature fluctuation) which has the units of an acceleration. In such a setup, the equations for the solenoidal velocity field −→v , the so… view at source ↗
Figure 2
Figure 2. Figure 2: Focus on the initial phase of the instability: top panel: energy in the axisymmetric (denoted by a) and non￾axisymmetric (denoted by na) components of the magnetic field as a function of time for a case with a low level of stratification Pr = 10−4 , N/S = 11 and a shear to rotation ratio S/Ω = 1.5, initiated with a low-amplitude noise be￾low 10−3 . Units are indicated in parenthesis. Bottom panel: snapshot… view at source ↗
Figure 3
Figure 3. Figure 3: Temporal evolution of the magnetic and kinetic ener￾gies and volume-averaged chemical concentration (top) and absolute value of the Maxwell ⟨bxby⟩ and Reynolds stresses ⟨vxvy⟩ as a function of time (bottom) for a case with a low level of stratification Pr = 10−4 , N/S = 11 and a shear to rotation ratio S/Ω = 1.5. Units are indicated in paren￾thesis. On the bottom panel, the superimposed dashed lines indica… view at source ↗
Figure 4
Figure 4. Figure 4: Effect of stratification on the radial velocity vx, adimensioned with S L. From left to right, the values of PrN2 /S 2 are 1.2 × 10−2 , 1.2 × 10−1 , 4.9 × 10−1 and 2.5 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Same as Fig.4 but for the longitudinal magnetic field by. We note that the full turbulent velocity amplitude v rms was adopted here, instead of only the x-component v rms x (which may better represent the turnover timescale), as it was found to produce better results for the scaling. On the bottom panel of figure 7, we rescaled δz by a relevant lengthscale so that all curves would collapse. We find that in… view at source ↗
Figure 6
Figure 6. Figure 6: Mean values of the magnetic (top) and kinetic (bot￾tom) energies as a function of stratification measured by PrN2 /S 2 . Both the total and non-axisymmetric (denoted by na) components are shown in each panel. The magnetic energy is always strongly dominant. Note that this plot is made at Re = 1529 because more simulation points were available but trends are similar at Re = 765. 4.2. On the angular momentum… view at source ↗
Figure 8
Figure 8. Figure 8: Absolute value of the Maxwell and Reynolds stresses ⟨bxby⟩ and ⟨vxvy⟩ as a function of PrN2 /S 2 . Three sets of simulations varying Pr are performed, each set with different value of N 2 /S 2 . The impact of stratifica￾tion is clearly controlled by the product PrN2 /S 2 . The slope for the Maxwell stress is −0.58 and for the Reynolds stress −0.62, compatible with similar exponents. The left￾most vertical … view at source ↗
Figure 10
Figure 10. Figure 10: Snapshots of the radial velocity vx (upper row) and longitudinal magnetic field by (lower row) in units of S L, for different values of the Rossby number : Ro = 0.2, 0.5, 1 and 1.5 (from left to right). Other parameters are PrN2 /S 2 = 6 × 10−2 , Re = 765. we show snapshots of the radial component of the veloc￾ity field vx and of the longitudinal magnetic component by. We clearly see that rotation mainly … view at source ↗
Figure 11
Figure 11. Figure 11: Autocorrelation function of vy (defined by Eq. 16 but using vy instead of vx) as a function of δx, for different values of the Rossby number, in the weakly stratified case PrN2 /S 2 = 6×10−2 . Top: as a function of δx. Bottom: δx is rescaled by the square root of the product lo = v rms/2Ω and ls = (v rmsκ/N 2 ) 1/3 . As v rms does not vary much with Ro, we find that the scale lx is proportional to Ω−1/2 .… view at source ↗
Figure 13
Figure 13. Figure 13: Transport of chemical elements ⟨cvx⟩ as a function of the Rossby number (where S is fixed while Ω is varied), for two values of the stratification measured by PrN2 /S 2 . The dashed and dashed-dotted lines represent fitted pow￾erlaw scalings in both cases. Note that these scalings are obtained with fixed PrN2 /S 2 and are therefore different than that of equation 22 obtained with fixed PrN2 /Ω2 in the hig… view at source ↗
Figure 14
Figure 14. Figure 14: Transport of angular momentum denoted by α in equation 23 (top) and chemical element transport denoted by β in equation 24 (bottom) as a function of Re, for 4 val￾ues of Pr and at fixed N/S = 11 and S/Ω = 1.5 (i.e. in the range of PrN2 /Ω2 where the previous scalings were estab￾lished) and Pm = 16. Fits shown by dotted lines are based on the last three values of Re and for Pr ≥ 5 × 10−4 . The exponent is … view at source ↗
Figure 15
Figure 15. Figure 15: Re0.58 × α and Re0.81 × β as a function of Rm = RePm, for a stratification level PrN2 /Ω2 = 2.78 × 10−1 . An asymptotic regime seems to be reached for high values of Rm, for which there is no dependency on Rm anymore. νT I ∝ κ/N 2 . We see that the MRI transport is then less af￾fected by the stable stratification, as well as the minimum shear required for instability, which is proportional to N 2 /κ for t… view at source ↗
Figure 16
Figure 16. Figure 16: Maxwell stress as a function of the domain size in longitude Ly. The 3 points at Ly/Lx = 6 correspond to different values of Lz . Lx was kept fixed and equal to L in these calculations. of by in the dynamo loop, as all cases indeed showed a y￾component of the magnetic field strongly dominated by its m = 0 contribution. In a similar way as the studies performed by Simon et al. (2012), we tried to explore t… view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

111 extracted references · 10 canonical work pages · 1 internal anchor

  1. [1]

    , keywords =

    MRI turbulence in accretion discs at large magnetic Prandtl numbers. , keywords =. doi:10.1093/mnras/stac2656 , archivePrefix =. 2206.00497 , primaryClass =

    Pith/arXiv arXiv

  2. [2]

    The Theory of Homogeneous Turbulence

  3. [3]

    , keywords =

    Zones of Tayler Instability in Stars. , keywords =. doi:10.3847/1538-4357/ade547 , archivePrefix =. 2411.08492 , primaryClass =

    Pith/arXiv arXiv

  4. [4]

    , keywords =

    Small-scale Dynamo in Stably Stratified Turbulence. , keywords =. doi:10.3847/1538-4357/abc8ee , archivePrefix =. 2008.01025 , primaryClass =

    Pith/arXiv arXiv 2008

  5. [5]

    , keywords =

    MRI-driven dynamo at very high magnetic Prandtl numbers. , keywords =. doi:10.1093/mnras/stac2499 , archivePrefix =. 2205.08602 , primaryClass =

    Pith/arXiv arXiv

  6. [6]

    , keywords =

    The small-P \'e clet-number approximation in stellar radiative zones. , keywords =. doi:10.48550/arXiv.astro-ph/9908182 , archivePrefix =. astro-ph/9908182 , primaryClass =

    Pith/arXiv arXiv doi:10.48550/arxiv.astro-ph/9908182

  7. [7]

    Journal of Fluid Mechanics , year = 2006, month = mar, volume =

    The energy cascade in a strongly stratified fluid. Journal of Fluid Mechanics , year = 2006, month = mar, volume =. doi:10.1017/S0022112005008128 , adsurl =

    work page doi:10.1017/s0022112005008128 2006

  8. [8]

    Shear mixing in stellar radiative zones. II. Robustness of numerical simulations. , keywords =. doi:10.1051/0004-6361/201527946 , archivePrefix =. 1512.04223 , primaryClass =

    Pith/arXiv arXiv

  9. [9]

    Physical Review Fluids , keywords =

    Journey to the center of stars: The realm of low Prandtl number fluid dynamics. Physical Review Fluids , keywords =. doi:10.1103/PhysRevFluids.6.030501 , archivePrefix =. 2103.14214 , primaryClass =

    Pith/arXiv arXiv

  10. [10]

    , keywords =

    Localized magnetorotational instability and its role in the accretion disc dynamo. , keywords =. doi:10.1111/j.1365-2966.2008.13993.x , archivePrefix =. 0809.3871 , primaryClass =

    arXiv 2008

  11. [11]

    , keywords =

    Angular Momentum Transport in Stellar Interiors. , keywords =. doi:10.1146/annurev-astro-091918-104359 , archivePrefix =. 1809.07779 , primaryClass =

    Pith/arXiv arXiv

  12. [12]

    , keywords =

    Circulation and turbulence in rotating stars. , keywords =

  13. [13]

    Stellar Structure and Evolution

  14. [14]

    , keywords =

    Differential rotation decay in the radiative envelopes of CP stars. , keywords =. doi:10.1051/0004-6361:20030251 , archivePrefix =. astro-ph/0207129 , primaryClass =

    Pith/arXiv arXiv

  15. [15]

    A Powerful Local Shear Instability in Weakly Magnetized Disks. IV. Nonaxisymmetric Perturbations. , keywords =. doi:10.1086/172022 , adsurl =

    work page doi:10.1086/172022

  16. [16]

    , keywords =

    Assessing Quantitative Results in Accretion Simulations: From Local to Global. , keywords =. doi:10.1088/0004-637X/738/1/84 , archivePrefix =. 1103.5987 , primaryClass =

    Pith/arXiv arXiv

  17. [17]

    Science , keywords =

    Kepler Detected Gravity-Mode Period Spacings in a Red Giant Star. Science , keywords =. doi:10.1126/science.1201939 , adsurl =

    doi:10.1126/science.1201939

  18. [18]

    , keywords =

    Stability of the toroidal magnetic field in rotating stars. , keywords =. doi:10.1051/0004-6361/201220153 , archivePrefix =. 1302.2523 , primaryClass =

    Pith/arXiv arXiv

  19. [19]

    , keywords =

    Stability of the Toroidal Magnetic Field in Stellar Radiation Zones. , keywords =. doi:10.1088/0004-637X/747/2/137 , archivePrefix =. 1110.3340 , primaryClass =

    Pith/arXiv arXiv

  20. [20]

    , keywords =

    Angular Momentum Transport within Evolved Low-mass Stars. , keywords =. doi:10.1088/0004-637X/788/1/93 , archivePrefix =. 1405.1419 , primaryClass =

    Pith/arXiv arXiv

  21. [21]

    , keywords =

    Lithium in red giant stars: Constraining non-standard mixing with large surveys in the Gaia era. , keywords =. doi:10.1051/0004-6361/201936360 , archivePrefix =. 1910.12732 , primaryClass =

    Pith/arXiv arXiv 1910

  22. [22]

    , keywords =

    Understanding angular momentum transport in red giants: the case of KIC 7341231. , keywords =. doi:10.1051/0004-6361/201321473 , archivePrefix =. 1305.5630 , primaryClass =

    Pith/arXiv arXiv

  23. [23]

    , keywords =

    Seismic evidence for near solid-body rotation in two Kepler subgiants and implications for angular momentum transport. , keywords =. doi:10.1051/0004-6361/202038578 , archivePrefix =. 2007.02585 , primaryClass =

    Pith/arXiv arXiv 2007

  24. [24]

    , keywords =

    Seismic constraints on the radial dependence of the internal rotation profiles of six Kepler subgiants and young red giants. , keywords =. doi:10.1051/0004-6361/201322779 , archivePrefix =. 1401.3096 , primaryClass =

    Pith/arXiv arXiv

  25. [25]

    , keywords =

    Strong magnetic fields detected in the cores of 11 red giant stars using gravity-mode period spacings. , keywords =. doi:10.1051/0004-6361/202245282 , archivePrefix =. 2301.01308 , primaryClass =

    Pith/arXiv arXiv

  26. [26]

    , keywords =

    Lithium depletion and angular momentum transport in F-type and G-type stars in Galactic open clusters. , keywords =. doi:10.1051/0004-6361/202141094 , archivePrefix =. 2107.12060 , primaryClass =

    Pith/arXiv arXiv

  27. [27]

    , keywords =

    Angular momentum transport in stellar interiors constrained by rotational splittings of mixed modes in red giants. , keywords =. doi:10.1051/0004-6361/201219729 , archivePrefix =. 1207.1023 , primaryClass =

    Pith/arXiv arXiv

  28. [28]

    Asteroseismology of evolved stars to constrain the internal transport of angular momentum. II. Test of a revised prescription for transport by the Tayler instability. , keywords =. doi:10.1051/0004-6361/201936348 , archivePrefix =. 2001.11525 , primaryClass =

    Pith/arXiv arXiv 2001

  29. [29]

    Nature Astronomy , year = 2022, month = may, volume =

    The internal rotation of the Sun and its link to the solar Li and He surface abundances. Nature Astronomy , year = 2022, month = may, volume =. doi:10.1038/s41550-022-01677-0 , adsurl =

    doi:10.1038/s41550-022-01677-0 2022

  30. [30]

    Turbulence in stably stratified radiative zone

    Turbulence in stably stratified radiative zone. Multi-Dimensional Processes In Stellar Physics , year = 2020, editor =. doi:10.48550/arXiv.1911.07813 , archivePrefix =. 1911.07813 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1911.07813 2020

  31. [31]

    , keywords =

    The signature of the magnetorotational instability in the Reynolds and Maxwell stress tensors in accretion discs. , keywords =. doi:10.1111/j.1365-2966.2006.10824.x , archivePrefix =. astro-ph/0603178 , primaryClass =

    arXiv 2006

  32. [32]

    Influence of buoyancy

    Numerical simulations of the magnetorotational instability in protoneutron stars - I. Influence of buoyancy. , keywords =. doi:10.1093/mnras/stv727 , archivePrefix =. 1501.07636 , primaryClass =

    Pith/arXiv arXiv

  33. [33]

    Spiral arms as sheared gravitational instabilities

    II. Spiral arms as sheared gravitational instabilities. , year = 1965, month = jan, volume =. doi:10.1093/mnras/130.2.125 , adsurl =

    doi:10.1093/mnras/130.2.125 1965

  34. [34]

    MHD simulations of the magnetorotational instability in a shearing box with zero net flux. II. The effect of transport coefficients. , keywords =. doi:10.1051/0004-6361:20077943 , archivePrefix =. 0705.3622 , primaryClass =

    Pith/arXiv arXiv

  35. [35]

    a t station \

    Instabilit \"a t station \"a rer Rotation in Sternen. , year = 1968, month = jan, volume =

    1968

  36. [36]

    , year = 1967, month = nov, volume =

    Differential Rotation in Stars. , year = 1967, month = nov, volume =. doi:10.1086/149360 , adsurl =

    doi:10.1086/149360 1967

  37. [37]

    , keywords =

    Emergent mesoscale phenomena in magnetized accretion disc turbulence. , keywords =. doi:10.1111/j.1365-2966.2012.20835.x , archivePrefix =. 1203.0314 , primaryClass =

    arXiv 2012

  38. [38]

    , keywords =

    MHD simulations of the magnetorotational instability in a shearing box with zero net flux: the case Pm = 4. , keywords =. doi:10.1051/0004-6361/201014284 , archivePrefix =. 1004.2382 , primaryClass =

    Pith/arXiv arXiv

  39. [39]

    , keywords =

    Modelling coexisting GSF and shear instabilities in rotating stars. , keywords =. doi:10.1093/mnras/stab1927 , archivePrefix =. 2107.03978 , primaryClass =

    Pith/arXiv arXiv

  40. [40]

    Turbulent Transport by Diffusive Stratified Shear Flows: From Local to Global Models. I. Numerical Simulations of a Stratified Plane Couette Flow. , keywords =. doi:10.3847/1538-4357/837/2/133 , archivePrefix =. 1610.04320 , primaryClass =

    Pith/arXiv arXiv

  41. [41]

    , keywords =

    Internal rotation of 13 low-mass low-luminosity red giants in the Kepler field. , keywords =. doi:10.1051/0004-6361/201629186 , archivePrefix =. 1702.07910 , primaryClass =

    Pith/arXiv arXiv

  42. [42]

    , keywords =

    Tayler-Spruit dynamo in stably stratified rotating fluids: Application to proto-magnetars. , keywords =. doi:10.1051/0004-6361/202451337 , archivePrefix =. 2407.01775 , primaryClass =

    Pith/arXiv arXiv

  43. [43]

    , keywords =

    Numerically Determined Transport Laws for Fingering (``Thermohaline'') Convection in Astrophysics. , keywords =. doi:10.1088/2041-8205/728/2/L29 , archivePrefix =. 1011.3461 , primaryClass =

    Pith/arXiv arXiv 2041

  44. [44]

    , keywords =

    Slowing the spins of stellar cores. , keywords =. doi:10.1093/mnras/stz514 , archivePrefix =. 1902.08227 , primaryClass =

    Pith/arXiv arXiv 1902

  45. [45]

    , keywords =

    Excitation of Gravity Waves by Fingering Convection, and the Formation of Compositional Staircases in Stellar Interiors. , keywords =. doi:10.1088/0004-637X/808/1/89 , archivePrefix =. 1505.07759 , primaryClass =

    Pith/arXiv arXiv

  46. [46]

    , keywords =

    Core rotation braking on the red giant branch for various mass ranges. , keywords =. doi:10.1051/0004-6361/201832822 , archivePrefix =. 1802.04558 , primaryClass =

    Pith/arXiv arXiv

  47. [47]

    , keywords =

    On unstably stratified toroidal magnetic fields in stars. , keywords =. doi:10.1093/mnras/193.4.833 , adsurl =

    work page doi:10.1093/mnras/193.4.833

  48. [48]

    , keywords =

    Additional Results for Unstable Stratified Toroidal Magnetic Fields in Stars. , keywords =. doi:10.1007/BF00648660 , adsurl =

    work page doi:10.1007/bf00648660

  49. [49]

    , keywords =

    Axisymmetric investigation of differential rotation in contracting stellar radiative zones. , keywords =. doi:10.1051/0004-6361/202039248 , archivePrefix =. 2011.08884 , primaryClass =

    Pith/arXiv arXiv 2011

  50. [50]

    , keywords =

    Angular momentum transport in a contracting stellar radiative zone embedded in a large-scale magnetic field. , keywords =. doi:10.1051/0004-6361/202141613 , archivePrefix =. 2201.02645 , primaryClass =

    Pith/arXiv arXiv

  51. [51]

    , keywords =

    Transport Properties of the Azimuthal Magnetorotational Instability. , keywords =. doi:10.3847/1538-4357/aa917d , archivePrefix =. 1705.03785 , primaryClass =

    Pith/arXiv arXiv

  52. [52]

    , keywords =

    Dynamo Action in a Quasi-Keplerian Taylor-Couette Flow. , keywords =. doi:10.1103/PhysRevLett.119.164501 , archivePrefix =. 1708.07695 , primaryClass =

    Pith/arXiv arXiv

  53. [53]

    , keywords =

    Testing Convergence for Global Accretion Disks. , keywords =. doi:10.1088/0004-637X/772/2/102 , archivePrefix =. 1306.0243 , primaryClass =

    Pith/arXiv arXiv

  54. [54]

    , keywords =

    Nonaxisymmetric Magnetorotational Instabilities in Cylindrical Taylor-Couette Flow. , keywords =. doi:10.1103/PhysRevLett.104.044502 , archivePrefix =. 0910.0206 , primaryClass =

    Pith/arXiv arXiv

  55. [55]

    , keywords =

    Three-dimensional evolution of magnetic fields in a differentially rotating stellar radiative zone. , keywords =. doi:10.1051/0004-6361/201425240 , archivePrefix =. 1412.2900 , primaryClass =

    Pith/arXiv arXiv

  56. [56]

    , keywords =

    Interplay between magnetic fields and differential rotation in a stably stratified stellar radiative zone. , keywords =. doi:10.1051/0004-6361/202037828 , archivePrefix =. 2006.08230 , primaryClass =

    Pith/arXiv arXiv 2006

  57. [57]

    , keywords =

    Impact of dimensionless numbers on the efficiency of magnetorotational instability induced turbulent transport. , keywords =. doi:10.1111/j.1365-2966.2007.11888.x , archivePrefix =. 0704.2943 , primaryClass =

    arXiv 2007

  58. [58]

    , keywords =

    Magnetic fields of 30 to 100 kG in the cores of red giant stars. , keywords =. doi:10.1038/s41586-022-05176-0 , archivePrefix =. 2208.09487 , primaryClass =

    Pith/arXiv arXiv

  59. [59]

    , keywords =

    Internal magnetic fields in 13 red giants detected by asteroseismology. , keywords =. doi:10.1051/0004-6361/202347260 , archivePrefix =. 2309.13756 , primaryClass =

    Pith/arXiv arXiv

  60. [60]

    Asteroseismology of evolved stars to constrain the internal transport of angular momentum. V. Efficiency of the transport on the red giant branch and in the red clump. , keywords =. doi:10.1051/0004-6361/202243389 , archivePrefix =. 2205.03490 , primaryClass =

    Pith/arXiv arXiv

  61. [61]

    Asteroseismology of evolved stars to constrain the internal transport of angular momentum. VI. Testing a parametric formulation for the azimuthal magneto-rotational instability. , keywords =. doi:10.1051/0004-6361/202245519 , archivePrefix =. 2302.07811 , primaryClass =

    Pith/arXiv arXiv

  62. [62]

    , keywords =

    The non-axisymmetric instability of a cylindrical shear flow containing an azimuthal magnetic field. , keywords =. doi:10.1093/mnras/279.1.152 , adsurl =

    work page doi:10.1093/mnras/279.1.152

  63. [63]

    Science , keywords =

    Spin-down by dynamo action in simulated radiative stellar layers. Science , keywords =. doi:10.1126/science.abk2169 , archivePrefix =. 2206.13819 , primaryClass =

    Pith/arXiv arXiv

  64. [64]

    , keywords =

    On self-sustained dynamo cycles in accretion discs. , keywords =. doi:10.1051/0004-6361:200810152 , archivePrefix =. 0807.1703 , primaryClass =

    Pith/arXiv arXiv

  65. [65]

    , keywords =

    Angular momentum and chemical transport by azimuthal magnetorotational instability in radiative stellar interiors. , keywords =. doi:10.1051/0004-6361/202347672 , adsurl =

    doi:10.1051/0004-6361/202347672

  66. [66]

    A Powerful Local Shear Instability in Weakly Magnetized Disks. I. Linear Analysis. , keywords =. doi:10.1086/170270 , adsurl =

    doi:10.1086/170270

  67. [67]

    Philosophical Transactions of the Royal Society of London Series A , keywords =

    On the Instability of Toroidal Magnetic Fields and Differential Rotation in Stars. Philosophical Transactions of the Royal Society of London Series A , keywords =. doi:10.1098/rsta.1978.0066 , adsurl =

    arXiv 1978

  68. [68]

    , keywords =

    Seismic detection of core magnetic fields in red giants using the gravity offset. , keywords =. doi:10.1051/0004-6361/202558608 , archivePrefix =. 2602.14570 , primaryClass =

    arXiv

  69. [69]

    Soviet Journal of Experimental and Theoretical Physics , year = 1959, month = nov, volume =

    Stability of an Ideally Conducting Liquid Flowing between Cylinders Rotating in a Magnetic Field. Soviet Journal of Experimental and Theoretical Physics , year = 1959, month = nov, volume =

    1959

  70. [70]

    , keywords =

    On magnetic instabilities and dynamo action in stellar radiation zones. , keywords =. doi:10.1051/0004-6361:20077653 , archivePrefix =. 0707.3287 , primaryClass =

    Pith/arXiv arXiv

  71. [71]

    Shear mixing in stellar radiative zones. I. Effect of thermal diffusion and chemical stratification. , keywords =. doi:10.1051/0004-6361/201423655 , archivePrefix =. 1404.6199 , primaryClass =

    Pith/arXiv arXiv

  72. [72]

    , keywords =

    Turbulent transport in radiative zones of stars. , keywords =. doi:10.1051/0004-6361/201220577 , archivePrefix =. 1301.4151 , primaryClass =

    Pith/arXiv arXiv

  73. [73]

    Journal of Plasma Physics , keywords =

    Dynamo theories. Journal of Plasma Physics , keywords =. doi:10.1017/S0022377819000539 , archivePrefix =. 1903.07829 , primaryClass =

    Pith/arXiv arXiv 1903

  74. [74]

    , keywords =

    Angular momentum transport by the GSF instability: non-linear simulations at the equator. , keywords =. doi:10.1093/mnras/stz1386 , archivePrefix =. 1905.06962 , primaryClass =

    Pith/arXiv arXiv 1905

  75. [75]

    , keywords =

    Local stability of differential rotation in magnetized radiation zones and the solar tachocline. , keywords =. doi:10.1093/mnras/stae2342 , archivePrefix =. 2410.06989 , primaryClass =

    Pith/arXiv arXiv

  76. [76]

    , keywords =

    Sustained Magnetorotational Turbulence in Local Simulations of Stratified Disks with Zero Net Magnetic Flux. , keywords =. doi:10.1088/0004-637X/713/1/52 , archivePrefix =. 0909.1570 , primaryClass =

    Pith/arXiv arXiv

  77. [77]

    , keywords =

    Locality of MHD Turbulence in Isothermal Disks. , keywords =. doi:10.1088/0004-637X/694/2/1010 , archivePrefix =. 0901.0273 , primaryClass =

    Pith/arXiv arXiv

  78. [78]

    , keywords =

    On the nature of magnetic turbulence in rotating, shearing flows. , keywords =. doi:10.1093/mnrasl/slv200 , archivePrefix =. 1512.03739 , primaryClass =

    Pith/arXiv arXiv

  79. [79]

    , keywords =

    Saturation of the magnetorotational instability in the unstratified shearing box with zero net flux: convergence in taller boxes. , keywords =. doi:10.1093/mnras/stv2815 , archivePrefix =. 1512.01106 , primaryClass =

    Pith/arXiv arXiv

  80. [80]

    , keywords =

    Local Simulations of the Magnetorotational Instability in Core-collapse Supernovae. , keywords =. doi:10.1088/0004-637X/759/2/110 , archivePrefix =. 1209.2360 , primaryClass =

    Pith/arXiv arXiv

Showing first 80 references.