arXiv subjects

Juri Toomre

Publications and source records attributed to Juri Toomre.

At least 19 recordsLinked to original sources

arXiv2025

Structure and Dynamics of the Sun's Interior Revealed by Helioseismic and Magnetic Imager

High-resolution helioseismology observations with the Helioseismic and Magnetic Imager (HMI) onboard Solar Dynamics Observatory (SDO) provide a unique three-dimensional view of the solar interior structure and dynamics, revealing a tremendous complexity of the physical processes inside the Sun. We present an overview of the results of the HMI helioseismology program and discuss their implications for modern theoretical models and simulations of the solar interior.

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arXiv2024

Confinement of the Solar Tachocline by a Non-Axisymmetric Dynamo

We recently presented the first 3D numerical simulation of the solar interior for which tachocline confinement was achieved by a dynamo-generated magnetic field. In this followup study, we analyze the degree of confinement as the magnetic field strength changes (controlled by varying the magnetic Prandtl number) in a coupled radiative zone (RZ) and convection zone (CZ) system. We broadly find three solution regimes, corresponding to weak, medium, and strong dynamo magnetic field strengths. In the weak-field regime, the large-scale magnetic field is mostly axisymmetric with regular, periodic polarity reversals (reminiscent of the observed solar cycle), but fails to create a confined tachocline. In the strong-field regime, the large-scale field is mostly non-axisymmetric with irregular, quasi-periodic polarity reversals, and creates a confined tachocline. In the medium-field regime, the large-scale field resembles a strong-field dynamo for extended intervals, but intermittently weakens to allow temporary epochs of strong differential rotation. In all regimes, the amplitude of poloidal field strength in the RZ is very well explained by skin-depth arguments, wherein the oscillating field that gives rise to the skin depth (in the medium- and strong-field cases) is a non-axisymmetric field structure rotating with respect to the RZ. These new simulations reaffirm that tachocline confinement by the solar dynamo (the so-called fast magnetic confinement scenario) is possible, but suggest a new picture in which non-axisymmetric field components rotating with respect to the RZ play the primary role, instead of the regularly reversing axisymmetic field associated with the 22-year cycle.

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arXiv2022

Confinement of the Solar Tachocline by Dynamo Action in the Radiative Interior

A major outstanding problem in solar physics is the confinement of the solar tachocline, the thin shear layer that separates nearly solid-body rotation in the radiative interior from strong differential rotation in the convection zone. Here, we present the first 3-D, global solar simulation in which a tachocline is confined by a self-excited dynamo. The non-axisymmetric magnetism is initially built in the convection zone and then diffusively imprints downward. Additionally, the field is locally amplified throughout the radiative interior by vigorous horizontal motions that arise from equatorial Rossby waves and possibly shear instabilities. Our work thus challenges the long-held notion that the Sun's dynamo magnetic field is amplified only as deep as the tachocline and stored in a quiescent radiative interior.

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arXiv2022

Longitudinally Modulated Dynamo Action in Simulated M-Dwarf Stars

M-dwarf stars are well known for the intense magnetic activity that many of them exhibit. In cool stars with near-surface convection zones, this magnetic activity is thought to be driven largely by the interplay of convection and the large scale differential rotation and circulations it establishes. The highly nonlinear nature of these flows yields a fascinatingly sensitive and diverse parameter space, with a wide range of possible dynamics. We report here on a set of three global MHD simulations of rapidly rotating M2 (0.4 $M_\odot$) stars. Each of these three models established nests of vigorous convection that were highly modulated in longitude at low latitudes. Slight differences in their magnetic parameters led each model to disparate dynamo states, but the effect of the convective nest was a unifying feature. In each case, the action of longitudinally modulated convection led to localized (and in one case, global) reversals of the toroidal magnetic field, as well as the formation of an active longitude, with enhanced poloidal field amplitudes and flux emergence.

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arXiv2022

Powering Stellar Magnetism: Energy Transfers in Cyclic Dynamos of Sun-like Stars

We use the ASH code to model the convective dynamo of solar-type stars. Based on a series of 15 3-D MHD simulations spanning 4 bins in rotation and mass, we show what mechanisms are at work in these stellar dynamos with and without magnetic cycles and how global stellar parameters affect the outcome. We also derive scaling laws for the differential rotation and magnetic field based on these simulations. We find a weaker trend between differential rotation and stellar rotation rate, ($ΔΩ\sim (|Ω|/Ω_{\odot})^{0.46}$) in the MHD solutions than in their HD counterpart $(|Ω|/Ω_{\odot})^{0.66})$, yielding a better agreement with the observational trends based on power laws. We find that for a fluid Rossby number between $0.15 \lesssim Ro_f \lesssim 0.65$ the solutions possess long magnetic cycle, if $Ro_f \lesssim 0.42$ a short cycle and if $Ro_f \gtrsim 1$ (anti-solar-like differential rotation) a statistically steady state. We show that short-cycle dynamos follow the classical Parker-Yoshimura rule whereas the long-cycle period ones do not. We further demonstrate that the Rossby number dependency of the large-scale surface magnetic field in the simulation ($B_{L,surf} \sim Ro_{f}^{-1.26}$) agrees better with observations ($B_{V} \sim Ro_{s}^{-1.4 \pm 0.1}$) and differs from dynamo scaling based on the global magnetic energy ($B_{bulk} \sim Ro_{f}^{-0.5}$). We also show that up to few percents of the stellar luminosity can be channelled into the star's magnetism, hence providing a large energy reservoir for possible surface eruptive events.

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arXiv2021

Building and Maintaining a Solar Tachocline through Convective Dynamo Action

For more than thirty years, the dynamical maintenance of the thin solar tachocline has remained one of the central outstanding problems of stellar astrophysics. Three main theories have been developed to explain the tachocline's thinness, but so far none of them has been shown to work convincingly in the extreme parameter regime of the solar interior. Here, we present a rotating, 3D, spherical-shell simulation of a combined solar-like convection zone and radiative zone that achieves a tachocline built and maintained by convective dynamo action. Because of numerical constraints, the dynamo prevents the viscous spread of the tachocline instead of the Eddington-Sweet-time-scale radiative spread believed to occur in the Sun. Nonetheless, our simulation supports the scenario of tachocline confinement via the cyclic solar dynamo, and is the first time one of the main confinement scenarios has been realized in a global, 3D, spherical-shell geometry including nonlinear fluid motions and a self-consistently generated dynamo.

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arXiv2020

Revisiting the Sun's Strong Differential Rotation along Radial Lines

Current state-of-the-art models of the solar convection zone consist of solutions to the Navier-Stokes equations in rotating, 3D spherical shells. Such models are highly sensitive to the choice of boundary conditions. Here, we present two suites of simulations differing only in their outer thermal boundary condition, which is either one of fixed-entropy or fixed-entropy-gradient. We find that the resulting differential rotation is markedly different between the two sets. The fixed-entropy-gradient simulations have strong differential rotation contrast and isocontours tilted along radial lines (in good agreement with the Sun's interior rotation revealed by helioseismology), whereas the fixed-entropy simulations have weaker contrast and contours tilted in the opposite sense. We examine in detail the force balances in our models and find that the poleward transport of heat by Busse columns drives a thermal wind responsible for the different rotation profiles. We conclude that the Sun's strong differential rotation along radial lines may result from the solar emissivity being invariant with latitude (which is similar to the fixed-entropy-gradient condition in our models) and the poleward transport of heat by Busse columns. In future work on convection in the solar context, we strongly advise modelers to use a fixed-gradient outer boundary condition.

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arXiv2020

Probing the Influence of a Tachocline in Simulated M-Dwarf Dynamos

In recent years, observers have found that the fraction of M-stars demonstrating significant magnetic activity transitions sharply from roughly $10\%$ for main-sequence stars earlier (more massive) than spectral type M3.5 (0.35 M$_\odot$) to nearly $90\%$ for stars later than M3.5. The latter are typically rotating quite rapidly, suggesting differing spin-down histories. Tantalizingly, it is also later than M3.5 at which main-sequence stars become fully convective, and may no longer contain a tachocline, a layer of rotational shear revealed by helioseismology to separate the radiative zone (RZ) and convection zone (CZ). We turn here to the more massive M-stars to study the impact such a layer may have on their internal dynamics. Using the spherical 3D MHD simulation code Rayleigh, we compare the properties of convective dynamos generated within quickly rotating (1, 2, and 4 $Ω_\odot$) M2 (0.4 M$_\odot$) stars, with the computational domain either terminating at the base of the convection zone or permitting overshoot into the underlying stable region. We find that a tachocline is not necessary for the organization of strong toroidal wreaths of magnetism in these stars, though its presence can increase the coupling of mean field amplitudes to the stellar rotation rate. Additionally, in stars that undergo periodic cycles, we find that the presence of a tachocline tends to make the cycles both longer and more regular than they would have otherwise been. Finally, we find that the tachocline helps to enhance the surface poloidal fields and organize them into larger spatial scales, both of which provide favorable conditions for more rapid angular momentum loss through a magnetized stellar wind.

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arXiv2020

Exploring Bistability in the Cycles of the Solar Dynamo through Global Simulations

The calling card of solar magnetism is the sunspot cycle, during which sunspots regularly reverse their polarity sense every 11 years. However, a number of more complicated time-dependent behaviors have also been identified. In particular, there are temporal modulations associated with active longitudes and hemispheric asymmetry, when sunspots appear at certain solar longitudes or else in one hemisphere preferentially. So far, a direct link between between this asymmetric temporal behavior and the underlying solar dynamo has remained elusive. In this work, we present results from global, 3D magnetohydrodynamic (MHD) simulations, which for the first time display both behavior reminiscent of the sunspot cycle (regular polarity reversals and equatorward migration of internal magnetic field) and asymmetric, irregular behavior that in the simulations we interpret as active longitudes and hemispheric asymmetry. The simulations are thus bistable, in that the turbulent convection can stably support two distinct flavors of magnetism at different times, in superposition, or with smooth transitions from one state to the other. We discuss this new family of dynamo models in the context of the extensive observations of the Sun's surface magnetic field with the Solar and Heliospheric Observatory (SOHO) and the Solar Dynamics Observatory (SDO), as well as earlier observations of sunspot number and synoptic maps. We suggest that the solar dynamo itself may be bistable in nature, exhibiting two types of temporal behavior in the magnetic field.

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arXiv2018

Exploring the Influence of Density Contrast on Solar Near-Surface Shear

The advent of helioseismology has determined in detail the average rotation rate of the Sun as a function of radius and latitude. These data immediately reveal two striking boundary layers of shear in the solar convection zone (CZ): a tachocline at the base, where the differential rotation of the CZ transitions to solid-body rotation in the radiative zone, and a 35-Mm-thick near-surface shear layer (NSSL) at the top, where the rotation rate slows by about 5% with increasing radius. Though asteroseismology cannot probe the differential rotation of distant stars to the same level of detail that helioseismology can achieve for the Sun, it is possible that many cool stars with outer convective envelopes possess similar differential rotation characteristics, including both a tachocline and a NSSL. Here we present the results of 3D global hydrodynamic simulations of spherical-shell convection for a Sun-like star at different levels of density contrast across the shell. The simulations with high stratification possess characteristics of near-surface shear, especially at low latitudes. We discuss in detail the dynamical balance of torques giving rise to the NSSL in our models and interpret what these balances imply for the real Sun. We further discuss the dynamical causes that may serve to wipe out near-surface shear at high latitudes, and conclude by offering some theories as to how this problem might be tackled in future work.

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arXiv2018

Exploring the Role of a Tachocline in M-Dwarf Magnetism

M-type stars are quickly stepping into the forefront as some of the best candidates in searches for habitable Earth-like exoplanets, and yet many M-dwarfs exhibit extraordinary flaring events which would bombard otherwise habitable planets with ionizing radiation. In recent years, observers have found that the fraction of M-stars demonstrating significant magnetic activity transitions sharply from roughly $10\%$ for main-sequence stars earlier (more massive) than spectral type M3.5 (0.35 M$_\odot$) to nearly $90\%$ for stars later than M3.5. Suggestively, it is also later than M3.5 at which main-sequence stars become fully convective, and may no longer contain a tachocline. Using the spherical 3D MHD simulation code Rayleigh, we compare the peak field strengths, topologies, and time dependencies of convective dynamos generated within a quickly rotating (2 $Ω_\odot$) M2 (0.4 M$_\odot$) star, with the computational domain either terminating at the base of the convection zone or including the tachocline. We find that while both models generate strong ($\sim$10kG), wreathlike toroidal fields exhibiting polarity reversals, the tachocline model provided a further reservoir for the toroidal field, which slowed the average reversal period from 100 rotations to more than 220 rotations and increased the spectral power of the low-order modes of the near-surface radial field by a factor of 4.

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arXiv2018

Driving Solar Giant Cells through the Self-Organization of Near-Surface Plumes

Global 3D simulations of solar giant-cell convection have provided significant insight into the processes which yield the Sun's observed differential rotation and cyclic dynamo action. However, as we move to higher resolution simulations a variety of codes have encountered what has been termed the convection conundrum. As these simulations increase in resolution and hence the level of turbulence achieved, they tend to produce weak or even anti-solar differential rotation patterns associated with a weak rotational influence (high Rossby number) due to large convective velocities. One potential culprit for this convection conundrum is the upper boundary condition applied in most simulations which is generally impenetrable. Here we present an alternative stochastic plume boundary condition which imposes small-scale convective plumes designed to mimic near-surface convective downflows, thus allowing convection to carry the majority of the outward solar energy flux up to and through our simulated upper boundary. The use of a plume boundary condition leads to significant changes in the convective driving realized in the simulated domain and thus to the convective energy transport, the dominant scale of the convective enthalpy flux, and the relative strength of the strongest downflows, the downflow network, and the convective upflows. These changes are present even far from the upper boundary layer. Additionally, we demonstrate that in spite of significant changes, giant cell morphology in the convective patterns is still achieved with self-organization of the imposed boundary plumes into downflow lanes, cellular patterns, and even rotationally-aligned banana cells in equatorial regions. This plume boundary presents an alternative pathway for 3D global convection simulations where driving is non-local and may provide a new approach towards addressing the convection conundrum.

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arXiv2017

On differential rotation and overshooting in solar-like stars

We seek to characterize how the change of global rotation rate influences the overall dynamics and large scale flows arising in the convective envelopes of stars covering stellar spectral types from early G to late K. We do so through numerical simulations with the ASH code, where we consider stellar convective envelopes coupled to a radiative interior with various global properties. As solar-like stars spin down over the course of their main sequence evolution, such change must have a direct impact on their dynamics and rotation state. We indeed find that three main states of rotation may exist for a given star: anti-solar-like (fast poles, slow equator), solar-like (fast equator, slow poles), or a cylindrical rotation profile. Under increasingly strict rotational constraints, the latter profile can further evolve into a Jupiter-like profile, with alternating prograde and retrograde zonal jets. We have further assessed how far the convection and meridional flows overshoot into the radiative zone and investigated the morphology of the established tachocline. Using simple mixing length arguments, we are able to construct a scaling of the fluid Rossby number $R_{of} = \tildeω/2Ω_* \sim \tilde{v}/2Ω_* R_*$, which we calibrate based on our 3-D ASH simulations. We can use this scaling to map the behavior of differential rotation versus the global parameters of stellar mass and rotation rate. Finally, we isolate a region on this map ($R_{of} \gtrsim 1.5-2$) where we posit that stars with an anti-solar differential rotation may exist in order to encourage observers to hunt for such targets.

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arXiv2017

Dynamo Scaling Relationships

This paper provides a brief look at dynamo scaling relationships for the degree of equipartition between magnetic and kinetic energies. Two simple models are examined, where one that assumes magnetostrophy and another that includes the effects of inertia. These models are then compared to a suite of convective dynamo simulations of the convective core of a main-sequence B-type star and applied to its later evolutionary stages.

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arXiv2016

The Magnetic Furnace: Intense Core Dynamos in B-stars

The dynamo action achieved in the convective cores of main-sequence massive stars is explored here through 3D global simulations of convective core dynamos operating within a young $\Msun{10}$ B-type star, using the anelastic spherical harmonic (ASH) code. These simulations capture the inner 65\% of this star by radius, encompassing the convective nuclear-burning core (about 23\% by radius) and a portion of the overlying radiative envelope. Eight rotation rates are considered, ranging from 0.05\% to 16\% of the surface breakup velocity, thereby capturing both convection that barely senses the effects of rotation and other situations in which the Coriolis forces are prominent. The vigorous dynamo action realized within all of these turbulent convective cores builds magnetic fields with peak strengths exceeding a megagauss, with the overall magnetic energy (ME) in the faster rotators reaching super-equipartition levels compared to the convective kinetic energy (KE). The core convection typically involves turbulent columnar velocity structures roughly aligned with the rotation axis, with magnetic fields threading through these rolls and possessing complex linkages throughout the core. The very strong fields are able to coexist with the flows without quenching them through Lorentz forces. The velocity and magnetic fields achieve such a state by being nearly co-aligned, and with peak magnetic islands being somewhat displaced from the fastest flows as the intricate evolution proceeds. As the rotation rate is increased, the primary force balance shifts from nonlinear advection balancing Lorentz forces to a magnetostrophic balance between Coriolis and Lorentz forces.

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arXiv2015

Large-Eddy Simulations of Magnetohydrodynamic Turbulence in Heliophysics and Astrophysics

We live in an age in which high-performance computing is transforming the way we do science. Previously intractable problems are now becoming accessible by means of increasingly realistic numerical simulations. One of the most enduring and most challenging of these problems is turbulence. Yet, despite these advances, the extreme parameter regimes encountered in space physics and astrophysics (as in atmospheric and oceanic physics) still preclude direct numerical simulation. Numerical models must take a Large Eddy Simulation (LES) approach, explicitly computing only a fraction of the active dynamical scales. The success of such an approach hinges on how well the model can represent the subgrid-scales (SGS) that are not explicitly resolved. In addition to the parameter regime, heliophysical and astrophysical applications must also face an equally daunting challenge: magnetism. The presence of magnetic fields in a turbulent, electrically conducting fluid flow can dramatically alter the coupling between large and small scales, with potentially profound implications for LES/SGS modeling. In this review article, we summarize the state of the art in LES modeling of turbulent magnetohydrodynamic (MHD) flows. After discussing the nature of MHD turbulence and the small-scale processes that give rise to energy dissipation, plasma heating, and magnetic reconnection, we consider how these processes may best be captured within an LES/SGS framework. We then consider several specific applications in heliophysics and astrophysics, assessing triumphs, challenges, and future directions.

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arXiv2015

Grand Minima and Equatorward Propagation in a Cycling Stellar Convective Dynamo

The 3-D magnetohydrodynamic (MHD) Anelastic Spherical Harmonic (ASH) code, using slope-limited diffusion, is employed to capture convective and dynamo processes achieved in a global-scale stellar convection simulation for a model solar-mass star rotating at three times the solar rate. The dynamo generated magnetic fields possesses many time scales, with a prominent polarity cycle occurring roughly every 6.2 years. The magnetic field forms large-scale toroidal wreaths, whose formation is tied to the low Rossby number of the convection in this simulation. The polarity reversals are linked to the weakened differential rotation and a resistive collapse of the large-scale magnetic field. An equatorial migration of the magnetic field is seen, which is due to the strong modulation of the differential rotation rather than a dynamo wave. A poleward migration of magnetic flux from the equator eventually leads to the reversal of the polarity of the high-latitude magnetic field. This simulation also enters an interval with reduced magnetic energy at low latitudes lasting roughly 16 years (about 2.5 polarity cycles), during which the polarity cycles are disrupted and after which the dynamo recovers its regular polarity cycles. An analysis of this grand minimum reveals that it likely arises through the interplay of symmetric and antisymmetric dynamo families. This intermittent dynamo state potentially results from the simulations relatively low magnetic Prandtl number. A mean-field-based analysis of this dynamo simulation demonstrates that it is of the $α$-$Ω$ type. The time scales that appear to be relevant to the magnetic polarity reversal are also identified.

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arXiv2015

Helioseismic Imaging of Fast Convective Flows Throughout the Near-Surface Shear Layer

Using a new implementation of ring-diagram helioseismology, we ascertain the strength and spatial scale of convective flows throughout the near-surface shear layer. Our ring-diagram technique employs highly overlapped analysis regions and an efficient method of 3D inversion to measure convective motions with a resolution that ranges from $3 \ \mathrm{Mm}$ at the surface to $80 \ \mathrm{Mm}$ at the base of the layer. We find the rms horizontal flow speed to peak at $427 \ \mathrm{m \ s^{-1}}$ at the photosphere and fall to a minimum of $124 \ \mathrm{m \ s^{-1}}$ between $20 \ \mathrm{Mm}$ and $30 \ \mathrm{Mm}$. From the velocity amplitude and the dominant horizontal scales seen at each depth, we infer the level of rotational influence on convection to be low near the surface, but transition to a significant level at the base of the near-surface shear layer with a Rossby number varying between 2.2 to as low as 0.1.

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