Stellar Convection: Modelling, Theory and Observations

26 Aug 2024, 09:00 → 20 Sept 2024, 18:00 Europe/Stockholm

Albano Building 3

Hideyuki Hotta (Chiba university), Isabelle Baraffe (University of Exeter), Markus Roth (Thüringer Landessternwarte Tautenberg), Petri Käpylä (Georg-August University of Göttingen)

CAUTION! Occasionally scammers contact participants claiming to assist you with accommodation and travel arrangements etc.

Please be vigilant and do not share information with them! Also, please notify the organizers if you are in any doubt about the legitimacy of an approach, and never hesitate to contact us with any further questions.  

Venue

Nordita, Stockholm, Sweden

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Focus Event

The first week of the program (26th-30th August) will be a traditional style conference covering the latest developments in the field.

Confirmed invited speakers

• Laurent Gizon (Max-Planck-Institute for Solar System Research, Göttingen)
• Dominic Bowman (Newcastle University)
• Friedrich Kupka (Univ. of Applied Sciences Technikum / Wolfgang Pauli Institute, Wien)
• Oleg Kochukhov (Uppsala University)
• Sacha Brun (CEA Paris-Saclay)
• Lisa Bugnet (IST Austria)
• Åke Nordlund (University of Copenhagen / ROCS Oslo)
• Geoffrey Vasil (University of Edinburgh)
• Bradley Hindman (University of Colorado Boulder)
• Ansgar Reiners (Göttingen University)
• Robert Andrassy (HITS, Heidelberg)
• Meridith Joyce (Konkoly Observatory / University of Wyoming)

 

Slots for contributed talks and posters are available, please remember to state this when sending your application!

Please note that the same application form is used for the focus event and the following program activity. Nordita can offer accommodation for a limited number of participants at BizAparments. Please note that these are preferentially allocated to long-term (2 weeks or more) participants.

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Schedule

After the focus event, the following three weeks will have specific thematic emphasis roughly according to:

• Week 2 Observations: How can numerical convection simulations be used to test and improve the methods of helio- and asteroseismology? What can we learn about convection zones and related phenomena of stars other than the Sun using asteroseismology? What are the possibilities to obtain information about magnetic fields within the solar convection zone?
• Week 3 Fundamentals: What is the cause of the convection conundrum? Are the numerical simulations lacking essential physics or is it enough to resolve the small-scale dynamo to land in the solar-like regime? Are more sophisticated treatments of the boundary layers near the surface and the base of the convection zone needed? Can subgrid-scale models be used to alleviate the resolution issue? Is is possible to construct a global stellar dynamo benchmark that can be used with iLES and more direct simulations?
• Week 4 Applications: How can the effects of rotation, magnetic fields, and non-locality be accounted for in 1D parameterizations of convection in stellar evolution codes? Do the more physically consistent models lead to significantly different results in the scope of stellar evolution? Which observational results are the most relevant to constrain parameterizations of  convection?

 

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Background

Understanding turbulent convection is of crucial importance in many fields of stellar astrophysics. For example, differential rotation and large-scale magnetic fields in stars owe their existence to turbulent convection. However, increasing evidence suggests that our understanding of stellar convection is much less complete than previously thought. The most dramatic manifestation of this is the wide discrepancy between the velocity amplitudes at large horizontal scales from helioseismic inferences and numerical simulations. This is the “convective conundrum” which is arguably the greatest open problem in stellar physics today. Furthermore, most stellar structure and evolution codes still use local mixing length models to describe convection whereas numerical simulations indicate that non-locality and interactions with rotation and magnetic fields are of crucial importance. We bring together experts in three-dimensional convection simulations, helio- and asteroseismology, theoreticians and observers present the latest developments and to address open problems in the field.

Application

All applications will be reviewed. The applicants are asked to give their General Data Protection Regulation (GDPR) consent. When clicking this, the applicant agrees to have their name on the Registrants List together with their dates of a potential visit. The dates can be changed any time. At a later point, for those who have made their bookings, it is mandatory to communicate changes to BizAppartments (or their respective accommodation) directly (and at least one week before their visit). Also, beware of emails from fraudsters.

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Sponsored by:

Monday 26 August

Reigstration & Coffee: Registration

1 Axel Brandenburg: Welcome address and practical info

2 Laurent Gizon: Probing the solar convection zone with inertial modes

The Sun supports a rich spectrum of global modes of oscillation in the inertial frequency range. Many of these modes can be identified by comparing their observed frequencies and horizontal velocity eigenfunctions at the surface to the linear eigenmodes of a set of adjustable rotating solar models. This provides sensitive diagnostics of the differential rotation and properties of the deep solar convection zone which are currently poorly constrained. These properties include the superadiabatic temperature gradient, the latitudinal entropy gradient, and the turbulent viscosity. In addition, nonlinear simulations indicate that the high-latitude inertial modes play a dynamical role and place a limit on the maximum allowed latitudinal differential rotation

3 Suprabha Mukhopadhyay: Numerical studies of inertial modes in the Sun using Dedalus

The Sun undergoes various oscillations through which we can probe deep into its convective interior. Inertial modes are low-frequency oscillations restored by the Coriolis force and have recently been observed on the Sun (Gizon et al., 2021). There have been several attempts to model the inertial modes employing several simplifying assumptions. In this work, we use Dedalus (Burns et al., 2020), a flexible spectral code, to compute the eigenmodes in the inertial frequency range. This framework helps us to examine the sensitivity of the modes to different model setups, including incompressible, anelastic, and fully compressible ones. Furthermore, we extend the linear model to include a free-surface boundary condition, the coupling with the radiative interior, and the effects of the magnetic field. In this talk, we shall present two main findings: the assumption of incompressibility is unjustified, and the inertial modes weakly couple with the radiative interior.

Nordita_2024_Suprabha_Mukhopadhyay.pdf

12:10 Lunch

4 Geoff Vasil: Going in circles: rotation in the Sun for fun and profit

This talk will summarize the state of affairs on what's often called the "Convective conundrum." While ostensibly not having much to do with rotation, it's actually all about what we know regarding the degree of influence rotation has on interior flow amplitudes and the overall dynamical scales. The conundrum part comes from not seeing giant-scale motions at the surface. Is this null result because of poor signal-to-noise? Or are the long-default convective structure truly absent?

The talk will discuss some of the possible physics of rapidly rotating convection as well as how supergranulation might be conducting a coverup. I'll make the case that theory and simulations give good guesses about what's happening. But a definitive solution will likely have to wait for more and better data, hopefully coming from the polar regions where convection most feels that Coriolis effect.

5 Yuto Bekki: Effects of small-scale dynamo on rotating columnar convection in stellar convection zones

In the equatorial region of the stellar convection zone, rotating convection tends to form vortical columns that propagate in a prograde direction. These convective columns are often called “banana cells” or “thermal Rossby waves.” In numerical simulations, they are commonly observed and found to play a significant role in transporting angular momentum, driving solar-like differential rotation. However, they have never been successfully observed in solar surface observations. Bridging this gap between numerical simulations and solar observations remains an open challenge. A physical ingredient likely missing in most numerical models is small-scale dynamo, which is believed to operate vigorously in the Sun and stars but is very costly to resolve numerically. In this talk, we report a series of high-resolution numerical simulations of rotating magneto-convection using a local f-plane box at the equator with varying Rossby numbers. We find that with the presence of small-scale dynamo, thermal Rossby waves have smaller amplitudes and higher longitudinal wavenumbers. We also find that the generation of mean zonal flow is significantly suppressed by the small-scale dynamo, as the Maxwell stresses counteract the Reynolds stresses. Finally, we will briefly discuss possible implications for the convective conundrum.

14:40 Coffee

16:30 Reception (TBA)

Tuesday 27 August

6 Dominic Bowman: An asteroseismic view of convective boundary mixing in massive stars

During the main sequence the convective cores of massive stars act as engines that drive their evolution, but direct inference of core masses is challenging. Moreover, estimates are subject to unconstrained convective boundary mixing (CBM) processes owing to largely uncalibrated prescriptions in 1D stellar evolution models. The uncertain chemical and angular momentum transport mechanisms can lead to unwieldy interior mixing and rotation profiles, thus making it difficult to predict a massive star's evolutionary fate. However, thanks to ongoing space missions and our development of modern asteroseismic modelling techniques for massive stars, we are now able to deduce precise convective core masses and robustly measure (non-rigid) radial rotation profiles in main-sequence stars that span a wide range in mass and age within the HR diagram. In this talk, I will provide an introduction to asteroseismology of massive stars for the non-expert and highlight recent modern advances in forward asteroseismic modelling of such stars. The combination of space photometry, high-resolution spectroscopy, and Gaia astrometry for massive stars allows precise measurements of masses, core masses, and ages to better than 10-20% precision. Asteroseismic modelling of gravity-mode period spacing patterns and rotational multiplets also allow CBM, as well as the near-core and envelope rotation profiles to be inferred, thus providing important anchor points for calibrating angular momentum transport processes. Finally, the inclusion of magnetic fields in forward asteroseismic modelling also allows the strength and geometry of such fields and their impact on CBM to be probed through magneto-asteroseismology.

Bowman_Nordita_2024.pdf

7 Markus Roth: Probing Large-scale flows with eigenfunction perturbation analysis

Large-scale flows and magnetic field components inside the Sun or solar-like stars affect the resonant oscillations by perturbing the oscillation eigenfunctions. By eigenfunction perturbation analysis, conclusions can be drawn on these physical quantities.

10:40 Coffee

8 Catherine Blume: Inertial Oscillations in the Convection Zone

Recent observations of Rossby waves and other more exotic forms of inertial oscillations in the Sun’s convection zone have kindled the hope that such waves might be used as a seismic probe of the Sun’s interior. Here, we present a 3D numerical simulation in spherical geometry that models the Sun’s convection zone and upper radiative interior. This model features a wide variety of inertial oscillations, including both sectoral and tesseral Rossby waves, retrograde mixed inertial modes, prograde thermal Rossby waves, the recently observed high-frequency retrograde (HFR) vorticity modes, and what may be latitudinal overtones of these HFR modes. We suggest that many of the retrograde inertial waves that appear in the convection zone, including the HFR modes, are in fact all related, being latitudinal overtones that are mixed modes with the prograde thermal Rossby waves. This unifying picture greatly reduces the many different observed and modeled waves in the convection zone into two categories: equatorial Rossby waves and this new collection of mixed modes

Blume_Nordita.pdf

9 Whitney Powers: Searching for signatures of oscillation in turbulent, low Prandtl number convection

In a rotating system with low Prandtl numbers (Pr < 0.7) the onset of convection occurs as oscillations rather than the stationary onset observed in non-rotating Rayleigh-Bénard convection. As we raise the Rayleigh number above onset, standard stationary convection will occur, however the oscillatory branch persists, and at low wavenumbers the system is unstable to oscillations but not to stationary convection. Studies of solar super-granulation such as Beck and Duvall (2001) show that the auto-correlation function for super-granulation becomes anti-correlated after approximately 40 hours. This behavior is reminiscent of the oscillatory branch of low Prandtl number rotating convection. We present simulations of low-Prandtl number rotating convection to determine if oscillatory signatures persist above convective onset, and if this mechanism could explain the anti-correlation of solar super-granulation.

12:00 Lunch

10 Lisa Bugnet: Stellar Internal dynamics with Asteroseismology

11 Dhruba Mitra: Towards magnetoseismology : surface signature of sub-surface magentic fields

We solve for waves in a stratified medium with a spatially varying background magnetic field that points along a horizontal (x) direction, and with gravity that is directed along the vertical (z) direction. Static force balance determines the magnitude of the background magnetic field. We consider both an isothermal and a more realistic polytropic atmosphere. In both cases we calculate how the presence of the sub-surface magnetic field changes the the dispersion relations for the surface waves. Applications of our result are in magnetoseismology and nonlinear asteroseismology.

MagSeismo_Nordita.pdf

12 Kishore Gopalakrishnan: Magnetic effects on helioseismic modes in simulations of convection

Observationally, localized strengthening of the f mode is known to precede the emergence of solar active regions by up to 48 hours. Similar effects have been found in simplified numerical models. For the first time, we have been able to demonstrate such effects in a 3D simulation of convection. While a magnetic field near the top of the convection zone (CZ) strengthens the f mode, a magnetic field of equal strength near the bottom of the CZ produces a much weaker effect. I will also talk about how unresolved small-scale magnetic fields can be probed using local helioseismology. If time permits, I will also demonstrate the effect of internal reflection on the number of radial nodes of the p mode. This resolves a long-standing disagreement between simulations, where it has been reported that the lowest p mode has zero radial nodes, and observations, where the lowest p mode is thought to have one radial node.

kishore_2024-08-28.pdf

15:05 Coffee

13 Bradley Hindman: The Implications of the Sun's Differential Rotation on the Transport of Heat and Angular Momentum

We have known since the observations of Galileo that the Sun rotates differentially, with its equator rotating faster than its poles. More recently, helioseismology has demonstrated that this latitudinal variation in the rotation rate only occurs within the Sun's convection zone, while the underlying radiative interior rotates like a solid body. For obvious reasons, the sense of differential rotation with a rapidly rotating equator is called solar-like and the converse (rapidly rotating poles) is called antisolar. Through a variety of observational techniques we now know that the Sun is not alone; most if not all main sequence stars for which differential rotation can be measured possess solar-like differential rotation, whereas a handful of more evolved stars have been demonstrated to be antisolar. The Sun's observed rotation profile is a rich source of information about fluid transport properties within the solar interior, in particular, the transport of angular momentum and heat. In this review talk, I will present two fundamental puzzles that quickly arise when one considers the torque balance required to achieve the observed rotation profile: (1) why does the Sun's convection zone rotate with a fast equator? and (2) why does the radiative interior rotate like a solid body? The first of these puzzles emerges from the belief that turbulence should mix and homogenize angular momentum, which should therefore lead to antisolar differential rotation. The second emerges from the well-known tendency of latitudinal shear to "burrow" into neighboring stable layers on a short time-scale compared to the solar age. In other words, since the Sun's convection zone rotates differentially, why hasn't the radiative interior been dragged into a similar shearing state? I will present the current theoretical paradigm of angular momentum transport within a Sun-like star and discuss unresolved problems and weaknesses in this paradigm. Further, I will summarize recent work by several different authors that suggest that magnetism plays a crucial role in the Sun's torque balance and may provide an answer to the two puzzles

2024 Nordita - Stockholm Aug 23 (Hindman).pdf

14 Yoshiki Hatta: Inversion for inferring solar meridional circulation: the case with constraints on angular momentum transport inside the Sun

Meridional Circulation (MC) in the Sun is an essential component in the solar dynamo mechanism. There have thus been a number of attempts to infer the solar internal MC profile via, e.g., time-distance helioseismology. We have however not reached an agreement even about the large-scale morphology of the internal MC profile. For example, whether the MC profile is overall single-cell or double-cell is not evident. This is partly due to the difficulty in inverting measured travel times in which the signal of the solar MC is small. In this talk, we present inversion results obtained with an additional constraint that the angular momentum (AM) transport by MC should be equatorward. Putting this physical constraint is motivated by a recent numerical result (Hotta and Kusano 2021, Nature Astronomy) where the solar equator-fast rotation is successfully reproduced without any tweaking. Inversion of the travel times measured by Gizon et al. (2020, Science) with this constraint results in a double-cell MC profile. Our result is compatible with a theoretical argument that the AM transport by single-cell MC is always poleward when we assume the mass conservation in the convective zone. However, we have also confirmed that the averaging kernels targeting around the deep convective zone are not well localized enough for us to conclude that the solar MC profile is double-cell. Although we have thus not reached a definitive conclusion on the large-scale morphology of the solar MC profile yet, our attempts highlight the relevance of investigating the solar MC profile from both theoretical and observational perspectives.

Nordita_YH_20240827.pdf

Wednesday 28 August

15 Meridith Joyce: A Review of One-Dimensional Parameterizations of Convection and Their Applications

The treatment of convection in one dimension is a drastic simplification of an inherently three-dimensional process based on the bulk motion of fluids. However, one-dimensional parameterizations of convection remain necessary and useful in a number of applications, including the construction of stellar tracks, isochrones, and population synthesis models, and they perform reasonably well in these contexts. In this review, I will discuss the applications of one-dimensional treatments of convection, especially the Mixing Length Theory, in stellar interiors and stellar evolution. I will summarize the history of MLT and discuss its interactions with other modeling physics, including demonstrating the impact of variations in the convective mixing length on stellar models. I will review the successes and shortcomings of this formalism, as well as attempts to improve and extend it, including the Full Spectrum Turbulence model. I will discuss situations in which the use of time-dependent convection is worthwhile and the ways in which three-dimensional convective simulations might inform and improve one-dimensional treatments of convection in the future.

16 Felix Ahlborn: Hydrodynamic simulations as a test bed for turbulent convection models

To date, the mixing length theory (MLT) is still the most common way to model convection in stars. However, MLT is neglecting important aspects of stellar turbulence. As an alternative, we implemented the turbulent convection theory by Kuhfuss (1987), in the stellar evolution code GARSTEC, which provides a more accurate description of the turbulent flow field in one spatial dimension. Using the GARSTEC models with Kuhfuss convection, we modelled a convectively burning main-sequence star. Subsequently, we set up three-dimensional hydrodynamic simulations based on the stellar models to compare with the results of the turbulent convection theory. These simulations were performed at the nominal luminosity of the star using the SLH (Seven-League-Hydro) code, which specialises in low Mach number flows. The hydrodynamic simulations confirm that the Kuhfuss theory accurately predicts the most relevant quantities for stellar structure and evolution, e.g. the turbulent kinetic energy profile or the morphology of the thermal stratification. We conclude that the Kuhfuss theory is an appropriate description of turbulent convection for stellar models.

Ahlborn_Nordita_upload.pdf

10:40 Coffee

17 Nobumitsu Yokoi: Non-equilibrium turbulence effects in stellar convection

Plumes are considered to play an important role in the transport in stellar convection. The non-equilibrium effect associated with plumes is linked to the variations of turbulence properties along the plume motions. With the response-function formulation of the renormalised perturbation theory, the non-equilibrium properties of turbulence can be incorporated into the analytical expressions of the turbulent fluxes such as the turbulent mass flux, the Reynolds and turbulent Maxwell stresses, and the turbulent heat/energy flux. A turbulence model with this non-equilibrium effect incorporated is proposed. This non-equilibrium turbulence model is applied to a two convection configurations: the locally or entropy-gradient driven convection and the non-locally or surface-cooling driven convection. The validation of the non-equilibrium turbulence model is sought in these two cases by comparing the results of turbulence model with those of direct numerical simulations (DNSs). The statistical and mean properties of turbulence in the two convection configurations are discussed, including the analysis of the probability distribution function and the turbulent energy flux.

18 Catherine Lovekin: Updates to SPHERLS: Radial stellar pulsation and convection

We present a newly updated version of SPHERLS, which can be used for modelling the interaction of convection and pulsation in radial pulsators. We present preliminary calculations to verify performance for RR Lyrae stars, as well as extensions to Cepheids. SPHERLS will be made publicly available, and is expected to have applications to a number of outstanding problems in understanding RR Lyrae and classical Cepheids.

Nordita_SPHERLS.pdf

12:00 Lunch

19 Friedrich Kupka: Fully turbulent RHD simulations and Reynolds stress models as tools for studying convective overshooting in stars

20 Manfred Küker: Simulations of convection in cool stars

We present numerical simulations of convection and magnetic field generation in stars with outer convection zones. We study the convection pattern, the generation of small-scale and large-scale magnetic fields, differential rotation, and meridional flows for different rotation rates and geometries

14:40 Coffee

21 Åke Nordlund: The Volleyball Sun Experiment

The Volleyball Sun experiment is based on the DISPATCH code framework, and is the first simulation of the Sun that covers the whole convection zone using no modifications of the physics (fully compressible MHD, realistic equation of state, with no modification of phase speeds). The convection zone is covered by a large number (up to more than 5 million) of small Cartesian "patches" (3D data cubes), with overlapping guard zones. The patches are arranged in a “volleyball geometry”, with 6 identical “faces”, in which patches are lined up in the (locally) longitudinal direction, with constant latitudinal offsets. The patches generated on the first face are duplicated, via permutation and reflection operations, to the remaining 5 faces. Each patch is exactly Cartesian (unigrid, with optional adaptive mesh refinement), with one axis exactly vertical, and the spherical geometry only enters via the guard zone interpolation mechanisms, which also handle the transformation of vector variable between the slightly tilted neighbors of each patch. The HD and MHD solvers can in principle be chosen freely, but to avoid problems in handling the very nearly adiabatic internal layers, we choose to use Riemann solvers with entropy per unit volume as the energy-related conserved variable. We use the FreeEOS equation of state, represented by a fast tabular lookup procedure. The calculations are carried out at the LUMI supercomputing center, under an Extreme Scale Access grant from EuropHPC. I will present first results, and additional details about the experiment, including methods to utilize GPU off-loading to handle radiative energy transfer and charged particle acceleration in the surface layers. On the basis of this first experiment, we plan to continue with a number of “zoom in” simulations, which use the larger scale results as initial and boundary conditions, while extending the computational domain locally into the chromosphere and corona, offering the opportunity to model, for the first time ab initio, the dynamics controlling solar “active regions”.

22 Tao Cai: Vortices in turbulent rotating convection: a new challenge in stellar convection theories

The influence of rotation on stellar convection remains a complex and not fully understood phenomenon. We use numerical simulations on f-planes to study the impact of rotation on stellar convection. Our findings indicate that large-scale vortices can be naturally generated as the rotational effect intensifies. Initially, with the increase in the rotational effect, the emergence of a large-scale cyclone is noted. As the rotational effect continues to amplify, we observe the appearance of both large-scale cyclones and anticyclones. This phenomenon is not limited to a specific latitude, as it has also been observed in the simulations of f-planes conducted at lower latitudes. When we incorporated the geometric effect into our study, we made an intriguing observation - the formation of vortex crystals in the polar regions. We notice that energy and vorticity transfers can be significantly different when large-scale vorticites appear, which brings a new challenge in stellar convective theories.

Tao Cai_Nordita2024.pdf

19:00 Conference dinner (TBA)

Thursday 29 August

23 Oleg Kochukhov: Convection and magnetic fields across the Hertzsprung-Russell diagram

Depending on the stellar mass, evolutionary phase, and interior structure, convection can be the source of stellar magnetism or be mutually exclusive with the presence of strong magnetic fields. In this talk, I will present an observational perspective on this highly nuanced relationship between stellar convection and magnetism. I will review observational evidence for the existence of magnetic fields on stellar surfaces and relate it to the convective behaviour of several interesting groups of main sequence stars.

24 Quentin Noraz: Magnetochronology of solar-type stars dynamos

The magnetism and rotation of cool stars evolve in an intertwined manner over secular times. However, recent observations have questioned this link, in particular as solar-type stars older than the Sun possibly exhibit stronger magnetic proxies and rotate faster than predicted. To assess how the combination of rotation and convection via the Rossby number influences the type of rotation and magnetism established, we analyse a set of 15 global MHD models of solar-type stars dynamo, and confront it to current observations. These models harbor different rotation and dynamo regimes as a function of the Rossby number Ro and show an overall agreement with observational trends, making us able to propose a physics-based ‘Sun in Time’ scenario : While aging and reaching intermediate Ro values, the dynamo nature changes and cycle periods increase to decadal ranges. In addition, we find that the magnetic field amplitude reaches a minimum around Ro~1, suggesting that a stalling of cool stars’ spin-down could originate from a minimum of their magnetism. Then, they may undergo a transition towards anti-solar DR and lose cycles, while building back a stronger large-scale field, and possibly revive their spin-down. We first discuss the numerical evidence of such a scenario, and further present an observational study of the Kepler field, seeking to identify high-Rossby stellar targets in order to constrain the Ro~1 limit. To this end, we developed an new observational formula for Ro, that could also be applied to future missions, such as PLATO.

Nordita24short.pdf

10:40 Coffee

25 Petri Käpylä: Effects of rotation on convective scale and subadibatic Deardorff layers

talk.pdf

26 Loren Matilsky: Dynamo Confinement of the Solar Tachocline

The solar tachocline is a narrow shear layer (no thicker than ~5% the solar radius), in which strong differential rotation in the convection zone (CZ) transitions to solid-body rotation in the adjacent radiative zone (RZ). How the tachocline can remain so thin at the current age of the Sun, despite the effect of 'radiative spread' (where latitudinal entropy gradients in the CZ spread inward via radiative diffusion and carry along a meridional circulation and differential rotation) remains a long-standing unresolved issue of stellar astrophysics. In the parameter regimes most accessible to global simulations, the simulated tachocline usually spreads viscously instead of radiatively (i.e. the CZ drags the RZ into differential rotation via a higher-than-realistic viscosity). In 2022, we explored a 3-D MHD simulation of a CZ-RZ system in which a dynamo was self-excited in the CZ, spread into the RZ, and confined a tachocline against viscous spread via magnetic torque. As a whole, this result was reminiscent of the 1-D 'fast magnetic confinement scenario', in which a poloidal dynamo-generated field (cycling with a period of 22 years) penetrates below the CZ to a magnetic skin depth, determined by the single cycle frequency. We have recently shown more carefully that the skin effect indeed well describes the amplitude of poloidal field strength in the RZ for several CZ-RZ dynamo simulations at different magnetic Prandtl numbers, even when the cycle is aperiodic (i.e. composed of many distinct frequencies). Overall, these results suggest a much wider range of operation for a general 'dynamo confinement scenario.' To assess if this scenario is realistic for the Sun, we also discuss our latest dynamo simulations for a tachocline in the radiative spreading regime.

2024-08-28_Nordita_Dynamo_Confinement_of_the_Solar_Tachocline.pdf

12:00 Lunch

27 Ansgar Reiners: Empirical constraints on convection: Stellar magnetic fields and solar convective blueshift

Two projects from solar and stellar spectroscopy relevant for stellar convection will be presented: 1) the CARMENES survey for exoplanets around M dwarfs observed 300 stars for more than five years. The entire data set was used to produce high-S/N spectra of the stars from which average surface magnetic fields were measured. The stars cover a large parameter range showing scaling relations relevant for convection and stellar dynamos. 2) In Göttingen, we are operating a 50cm solar telescope with a broadband high-resolution spectrometer that we use for developing spectral calibration techniques. The spectrometer provides unprecedented frequency accuracy with which we can determine line-by-line absolute Doppler shifts. We measured the depth-dependent convective blueshift across the solar surface (at different limb positions) providing useful constraints for solar convection and detailed empirical information about line profiles from the solar atmosphere seen under different projection angles.

1726145161209_Reiners.pdf

28 Nishant Singh: On active latitudes and magnetic flux concentrations in convection simulations

Traces of cyclic large-scale magnetic fields are seen at some preferred latitudes in some recent simulations. These seem intimately related to the appearance of large-scale vortices that are in turn affected by the growing magnetic field. Analysis of these simulations reveals that there is no large-scale dynamo, and unlike most previous studies, a small-scale dynamo operates and coexists with the large-scale flows. Spontaneous formation of localized magnetic structures, resembling active regions (ARs) or sunspots, has proved to be more challenging in simulations of turbulent magneto-convection. We will discuss some developments on these topics based on numerical and observational studies.

nishant-talk.pdf

14:40 Coffee

29 Sacha Brun: Powering solar-type stars magnetism: How are magnetic cycles established and driven?

We present an extensive study on the dynamo origin of solar-type star's magnetism, based on a series of 32 3D MHD global numerical simulations of rotating magnetised convection. We quantify how the combination of rotation and convection via the Rossby number influences the type of magnetism established (short or long cycles, statistically steady activity) and their expected differential rotation (solar-like, anti-solar, cylindrical or almost solid). This large survey allows us to propose a possible solution to why the Sun possesses a long decadal cycle and a conical differential rotation. The solar conical differential rotation and decadal cycle are recovered in a specific range of Rossby numbers, which opens up the possibility to use this dimensional parameter to define a path in parameter space towards more and more turbulent models while retaining key force balances thought to operate in the Sun. We further assess the amount of energy needed to maintain such angular velocity profiles and magnetic activity. We find that between 0.1 and 3% of the stellar luminosity can be converted into magnetic energy, giving plenty of energy for surface eruptive events to occur. We also compute the magnetic energy spectra and show how the dipole and quadrupole magnetic fields evolve as the Sun ages and compare the trend found with observations finding a good overall agreement. In particular interesting regimes at low and high Rossby number are identified.

30 Andrius Popovas: Towards realistic simulations of solar dynamics

Due largely to computational resource limitations, solar research evolved as distinct “internal-” and “surface-” related research fields, preventing an integrated global view of the Sun's complex plasma dynamics. However, the Sun encompasses large-scale hierarchical structures, extending from its deep core to its outer atmosphere. Magnetic flux, pivotal for many phenomena, such as sunspots and solar flares, may be generated through both local and large-scale dynamo actions within the solar interior, interacting with motions in the convection zone that are ultimately driven by cooling at the very surface. The current advancements in high performance computing (HPC) infrastructure finally allows us to address the burgeoning need for an integrated understanding of the solar dynamics from the core to the photosphere and beyond. In this talk I will present the current state of our ongoing work – the global compressible MHD simulations covering the entire convection zone of the Sun.

Popovas - Realistic simulations of solar dynamics.pdf

Friday 30 August

31 Robert Andrassy: Convective boundary mixing: Theory and numerical simulations

Convection has traditionally been described by the mixing-length theory (MLT) in one-dimensional numerical models of stellar evolution. The MLT, due to its local nature, does not provide any information about mass exchange between a convective layer and a neighbouring stably-stratified layer. Theoretical arguments, laboratory experiments, as well as decades of astronomical observations suggest that convective boundary mixing (CBM) is a real phenomenon playing a vital role in our understanding of stellar physics and evolution. However, the physical processes involved in CBM depend on the type of convection zone in question and the mixing rate is difficult to quantify in most cases relevant to stars. I will provide an overview of our current understanding of CBM along with some historical developments leading to it. I will argue that the growth of convective layers can already be simulated with confidence in late stages of massive star evolution and that simplified hydrodynamic simulations combined with analytical theory are beginning to provide predictive models of CBM even for stars on the main sequence.

talk_Andrassy.pdf

32 Axel Brandenburg: Entropy rain

The flux from a radiating surface depends significantly on the opacity and its functional dependence on temperature. This is why the correct depth of the convection zone was only known since the discovery of the H-minus opacity by Wildt (1938). This leads to the concept of convection driven by cooling from above rather than heating from below, which is sometimes also called entropy rain. An important feature is that the enthalpy flux cannot be modeled solely by the superadiabatic gradient, but there is also the Deardorff term that carries enthalpy outward. This contribution can also lead to weakly subadiabatic convection and may be responsible for convection on length scales smaller than the local scale height

Stockholm24conv.pdf

10:40 Coffee

33 Igor Rogachevskii: Convection and magnetic fields of low-mass main sequences stars: Non-linear dynamo theory and mean-field numerical simulations

Our theoretical and numerical analysis of convection and magnetic fields for low-mass main sequences stars (of the spectral classes from M5 to G0) rotating much faster than the Sun, have suggested that the generated large-scale magnetic field is caused by the mean-field $\alpha^2\Omega$ dynamo, whereby the $\alpha^2$ dynamo is modified by a weak differential rotation. Even for a weak differential rotation, the behaviour of the magnetic activity is changed drastically from aperiodic regime to non-linear oscillations and appearance of a chaotic behaviour with increase of the differential rotation. Periods of the magnetic cycles decrease with increase of the differential rotation, and they vary from tens to thousand years. This long-term behaviour of the magnetic cycles may be related to the characteristic time of the evolution of the magnetic helicity density of the small-scale field. The performed analysis is based on the mean-field simulations (MFS) of the $\alpha^2\Omega$ and $\alpha^2$ dynamos and a developed non-linear theory of convection and dynamos.

Rogachevskii.pdf

34 Markus Roth: Closing remarks

Monday 2 September

35 Meet and greet for newcomers and brainstorming

Tuesday 3 September

36 Virtual Nordic Dynamo Seminar; "The solar dynamo begins near the surface" (Geoff Vasil)

https://indico.fysik.su.se/event/8871/

Online participants, please note the zoom-link:
https://stockholmuniversity.zoom.us/j/940229961

Recording of the talk

Wednesday 4 September

37 Brad: Helioseismic determination of convective velocities / Geoff, Petri: Effect of rotation on convection

2024 Nordita - Stockholm Sep 4 (Hindman).pdf

talk_petri.pdf

Thursday 5 September

38 Igor, Nishant: Formation of sunspots

Sunspots-Rogachevskii.pdf

Friday 6 September

39 Petri: Effects of small-scale dynamo on convection

talk_petri.pdf

Monday 9 September

40 Loren Matilsky: Could there be a connection between observations of tilted solar isorotation contours and latitudinally invariant emissive flux?

Tuesday 10 September

41 Daniel Lecoanet: Measuring Magnetic Fields in Stellar Interiors (Virtual Nordic Dynamo Seminar)

Stars are key components of galaxies and exoplanetary systems, and are progenitors for supernova explosions and compact object binaries. Magnetic fields in stellar interiors can affect nucleosynthetic yields and chemical transport, magnetic activity (and hence habitability of exoplanets), and rotation rate of compact remnants. Despite their importance, not much is known about magnetic fields inside stars. In this talk, I will describe a new method to infer magnetic field strengths in stellar interiors. This combines asteroseismic observations of stellar pulsation modes by space missions like CoRoT and TESS with theoretical and numerical calculations of magnetic wave properties in stars. I will also show how similar mechanisms may explain observations of efficient tidal dissipation in same exoplanetary systems. The nascent field of magneto-asteroseismology is providing better and better measurements of stellar magnetic fields, and will play an important role in our understanding of stellar structure and evolution.

https://stockholmuniversity.zoom.us/j/940229961

Wednesday 11 September

42 Frank Robinson: Modeling the outer layers of rapidly rotating stars

Radiative hydrodynamic simulations in the near-surface regions of a rapidly rotating star show that a combination of rotation and radiative cooling creates a zonal velocity profile in which the motion of fluid parcels near the surface is independent of rotation. Their motion is controlled by the strong up and down flows generated by radiative cooling. The fluid parcels in the deeper layers, on the other hand, are controlled by rotation. authors: Frank Robinson, Sarbani Basu and Joel Tanner

rotating_convection_robinsonfrank.pdf

Thursday 12 September

43 Daniel Lecoanet: Mixing near Convective Boundaries

Convective motions in stars extend beyond the boundary of a convection zone, leading to additional mixing in the radiative zone. This occurs in both solar-type stars, and more massive stars with convective cores. This mixing is especially important for massive stars, leading to larger core masses and main sequence lifetimes of massive stars. In this talk, I will review some previous ideas around radiative-convective interfaces. In particular, I will describe convective overshoot which causes chemical mixing, and convective penetration which causes thermodynamic mixing. I will present a series of simulations exhibiting significant convective penetration, and present mechanistic and parametric descriptions of the phenomenon. When implemented in stellar evolution models, these effects compare favorably to asteroseismic observations.

Friday 13 September

44 Radostin Simitev: Differential rotation in convecting spherical shells with non-uniform viscosity and entropy diffusivity

Contemporary three-dimensional physics-based simulations of the solar convection zone disagree with observations. They feature differential rotation substantially different from the true rotation inferred by solar helioseismology and exhibit a conveyor belt of convective “Busse” columns not found in observations. To help understand this so-called “convection conundrum”, we use a three dimensional pseudospectral simulation code to investigate how radially non-uniform viscosity and entropy diffusivity affect differential rotation and convective flow patterns in density-stratified rotating spherical fluid shells. We find that radial non-uniformity in fluid properties enhances polar convection, which, in turn, induces non-negligible lateral entropy gradients that lead to large deviations from differential rotation geostrophy due to thermal wind balance. We report simulations wherein this mechanism maintains differential rotation patterns very similar to the true solar profile outside the tangent cylinder, although discrepancies remain at high latitudes. This is significant because differential rotation plays a key role in sustaining solar-like cyclic dipolar dynamos.

Simitev20240912Nordita.pdf

45 Geert Brethouwer: Effect of rotation on Couette flows: heat and momentum transfer, flow structure and stability

Simulations show that rotation has a large influence on heat and momentum transfer
in plane Couette and Taylor-Couette flows. We also observe that in certain cases the
Reynolds analogy breaks down and the heat transfer can become much faster than
momentum transfer. We also discuss the effect of rotation on the
structure and stability of plane Couette flow.

Monday 16 September

46 Teresa Braun: Applying the Kuhfuss Turbulent Convection Theory to Convective Envelopes

In 1D stellar evolution models, the process of convection is often described using the mixing length theory (MLT). However, MLT does not account for all relevant aspects of turbulence. For example, it does not account for non-locality, what makes ad hoc extensions necessary. The Kuhfuss theory is one of the theories that attempts to derive a more complete picture of turbulent convection. In this theory, non-locality is not implemented artificially, but is inherent in the theory. Both versions of the Kuhfuss theory, the 1-equation model and the 3-equation model, are implemented in the stellar evolution code GARSTEC. Ahlborn et al. (2022) tested both versions on convective cores on the main sequence and found promising results. Building on these results, we tested the Kuhfuss theory for convective envelopes. We applied the 1-equation model of the Kuhfuss convection theory to a stellar model calibrated to the Sun. Using helioseismic measurements of quantities of the convective envelope and interior structure, we tested the Kuhfuss theory and quantified the differences between the Kuhfuss theory compared to MLT. We found that the 1-equation model does not model the temperature stratification in the convective boundary mixing region well. We therefore conclude that the more complex 3-equation model is needed to appropriately model the temperature stratification in the convective boundary mixing region.

braun-nordita-conference-pdf.pdf

Tuesday 17 September

47 Igor Rogachevskii: New Aspects in Mean-Field Dynamo Theory (Virtual Nordic Dynamo Seminar)

Nonlinear mean-field dynamo theories take into account algebraic and dynamic quenching of alpha effect and algebraic quenching of turbulent magnetic diffusivity.
However, the theories of the algebraic quenching do not take into account the effect of modification of the source of turbulence by the growing large-scale magnetic field. This phenomenon is due to the dissipation of the strong large-scale magnetic field resulting in an increase of the total turbulent energy. This effect has been studied using the budget equation for the total turbulent energy (which takes into account the feedback of the generated large-scale magnetic field on the background turbulence). As the result of this effect, a nonlinear dynamo number decreases with increase of the large-scale magnetic field, so that that the mean-field dynamo instabilities are always saturated by the strong large-scale magnetic field. Effects of fast rotation on a density stratified turbulent convection is discussed as well. In particular, we consider a mean-field theory of differential rotation and generation of large-scale vorticity in a density stratified rotating turbulent convection. The theory takes into account a combined effect of the turbulent heat flux and anisotropy of turbulent convection on the Reynolds stress. The used model of the background turbulent convection takes into account an increase of the turbulence anisotropy and a decrease of the turbulent correlation time with increase of the rotation rate. Applications to the solar and stellar dynamos as well as formation of large spots observed as immense storms in great planets (e.g., the Great Red Spot in Jupiter and large spots in Saturn) are discussed.

Nonlinear-Dynamos-Rogachevskii.pdf

Wednesday 18 September

48 Kirill Kuzanyan: Experimental and numerical modeling of turbulent convection with open boundary conditions in liquid medium

We have run a series of model experiments to study the properties of turbulent convection in a rectangular cell at Rayleigh numbers or order 10^8 to 10^9 and Prandtl number Pr=6.1 for water, with uniformly heated bottom solid boundary and free upper surface (quasi-stationary heat flux). Two cases of the horizontally extended cell aspect ratio were considered: 2:1:1, characterized by the presence of a pronounced stable cell large-scale circulation, and 4:4:1, characterized by an ensemble of quasi-stationary convective cells. Laboratory measurements using stereoPIV method enable us to run long time series to accumulate sufficiently reliable statistical data. Furthermore, numerical simulations provide three-dimensional vector velocity fields with high resolution. We compare experimental and numerical results in the overlapping range of parameters. The spatial and temporal correlation scales in the bulk of the turbulent flow are obtained by correlation and wavelet analysis.
Qualitative Results of analysis of experiments are as follows:
1. We have established that persistent large scale structures (circulation cells) exist for several hundreds of turnover times without significant changes of their shape.
2. Numerical experiments gave a solution which agrees with laboratory modeling for the mean flow and rms turbulent pulsations in the bulk of the medium.
3. Due to surface phenomena of water, the boundary conditions occur to be close to a stiff boundary layer (no-slip and no-penetration conditions). It was confronted with a comparative experiment with silicon oil on convection with open boundary conditions (free-slip flow).
4. We have achieved qualitative scale separation between large scale structures and turbulent eddies, both in numerical and laboratory experiments. The correlation lengths in vertical direction are several times smaller than the vertical size of the entire setup. Thus, we have shown that the properties which have earlier been found for air convection by Elperin et al. (2006) and Bukai et al. (2009) can qualitatively be extended for convection of liquids. The data enable one to compute some components of statistical correlators that enter the meanfield MHD dynamo equations. These results are of interest to understanding geophysical and astrophysical flows. The work is supported by RSF grant 21-72-20067.
1. Elperin, Tov ; Golubev, Ilia ; Kleeorin, Nathan ; Rogachevskii, Igor // Physics of Fluids, Volume 18, Issue 12, pp. 126601-126601-11 (2006)
2. Bukai, M. ; Eidelman, A. ; Elperin, T. ; Kleeorin, N. ; Rogachevskii, I. ; Sapir-Katiraie, I.// Physical Review E, vol. 79, Issue 6, id. 066302 (2009)

Thursday 19 September

49 Youhei Masada: Topological structure of the Sun’s thermal convection and its implications for modeling the turbulent transport inside the Sun

The theoretical model for describing the Sun’s thermal convection remains incomplete. While the theory of stellar evolution is grounded in turbulent energy transport described by the gradient diffusion model and mixing length (ML) theory, recent research has increasingly called its validity into question. A notable example of this skepticism is the “convection conundrum”, a significant issue in solar physics (e.g., Hanasoge et al. 2013; Rast 2020; Hotta et al. 2023). According to ML theory, solar convection should display a hierarchical, multi-scale structure, yet there is a marked discrepancy between theoretical predictions and observations, particularly in the low-wavenumber modes where the observed convection power is notably weaker. The ultimate goal of our research is to achieve a comprehensive understanding of thermal convection and turbulent energy transport within the solar interior. There are at least two potential driving mechanisms for solar convection. One mechanism is driven by local entropy gradients (e.g., Kippenhahn & Weigert 1990), while the other is a non-local, non-equilibrium convection driven by surface radiative cooling (e.g., Spruit 1997; Yokoi et al. 2022). The former mechanism forms the basis of stellar evolution theory; however, due to the inconsistencies between ML theory and observations, such as the convection conundrum, the latter model is receiving renewed attention. To accurately model turbulent energy transport within the solar interior, we are currently investigating the driving mode of solar convection using various machine learning techniques. In our recent study (Masada et al. 2024, in prep.), we have examined the topological structure of the Sun’s granular convection using topological data analysis (TDA). Our analysis, utilizing persistence diagrams (PDs), has revealed that the solar granule is characterized by long-lived "topological defects”, suggesting greater compatibility with a cooling-driven convective structure. In my talk, I will present our recent efforts in studying solar convection, with a particular focus on our TDA analysis and its implications for modeling the convective transport inside the Sun.

Friday 20 September

50 Carolina Ortiz Rodríguez: Star-in-a-box setup for late-type stars

stellarconvectionprogram_ortiz.pdf