ERC Synergy Grant in Astrophysics

**This project has just been funded for six years by a prestigious Synergy grant from the European Research Council (ERC). Four European experts on the Sun and stars, from the Astrophysics Department of CEA-Irfu / UMR AIM in France, the Max Planck Institute for Solar System Research (MPS) in Germany, the University of St Andrews in the United Kingdom and the University of Oslo in Norway, will pool their know-how and knowledge of the dynamics of our star and its twin stars. The objective is to determine over the next six years how the magnetic field is generated inside the Sun and how it creates solar spots on its surface and eruptions in its highly stratified atmosphere. To this end, the team will develop the most advanced complete Sun model using the most powerful supercomputers, known as Exa-scale, and will constrain it with observations from space missions, such as the European Space Agency's (ESA) Solar Orbiter, to be launched in 2020.**

© NASA/SDO

**VISION: Solar activity, with its many manifestations and eruptions of magnetized clouds and particles, has a direct impact on our technological society. Understanding it is therefore a major societal challenge. "The WHOLESUN project is an innovative multidisciplinary approach in solar physics that will lead to successful collaborations in Europe," predicts Professor Eric Priest of the University of St Andrews.
Indeed, in recent decades, research in solar physics has focused on studying the structure and dynamics of the interior of the Sun or the solar surface/atmosphere. The objective is to consolidate the studies of these two major solar regions, through strong synergies between the team members, in order to acquire an advanced understanding of their coupling and the Sun. "The detailed study of the (thermo)dynamic and magnetic coupling between the core of the Sun, the solar surface and the highly stratified atmosphere is absolutely essential if we want to address the key and open problems of solar physics" argues Dr. Antoine Strugarek (DAp-AIM) involved in the project. **

**The WHOLESUN project is made possible by advances in supercomputing. “The project will develop numerical models of the whole Sun that will run on exascale supercomputers that perform a billion billion arithmetic operations per second”, explains Principal Investigator Allan Sacha Brun from CEA Saclay France. The numerical models will be used in combination with observations to tackle many unsolved mysteries in solar physics. For example, it is not known how sunspots are formed, nor what triggers the most energetic solar flares.**

**Violent solar eruptions throw charged particles and radiation into space. "The origin of all the eruptive phenomena that we observe in the Sun’s atmosphere, however, lies much deeper within our star," explains Professor Laurent Gizon, one of the Principal Investigators of WHOLESUN.**

**Prof. Laurent Gizon (Principal Investigator)**- top left

** Dr. Vasilis Archontis (Principal Investigator)**- top right

** Prof. Mats Carlsson (Principal Investigator)**- bottom left

** Dr. Allan Sacha Brun (Corresponding Principal Investigator)**- bottom right

Preparation of the ERC Synergy oral at the end of August 2018.

**MPS**

Institutional staff

Prof. Laurent GizonDr. A. Birch

Dr. R. Cameron

D. Fournier, PhD

funded in part by Wholesun

(10/01/20 -)

Project staff

S. Cloutier, PhDfunded in part by Wholesun

(01/01/20 - )

Y. Bekki, PhD, Postdoc

funded by Wholesun

(03/01/20 - )

C. Gehan, PhD, Postdoc

funded by Wholesun

Former staff

......

...

**Fernando Moreno-Insertis (Co-Investigator)**

**University of Ioannina**

Institutional staff

Dr. Vasilis ArchontisProf. C. Allisandrakis

Prof. A. Nindos

Prof S. Patsourakos

Project staff

K. Moraitis, PostdocJ. Zhuleku, Postdoc

V. Agalianou, PhD

G. Agglou, PhD

Former staff

Prof. A. Hood*P. Syntelis*, Postdoc

(05/01/19 – )

A. Borissov*, Postdoc

(09/01/20 - )

G. Chouliaras*, PhD

(09/27/20 - )

* : University of St Andrew

** **

**Oslo University**

Institutional staff

Prof. Mats CarlssonProf. V. Hansteen

Prof. B. Gudiksen

Project staff

K. Krikova, PhD(01/09/2020 - 31/08/2024)

R. Robinson, PhD

(23/09/2019 - 24/09/2023)

A. Popovas, Research Software Engineer

(01/05/2018 - )

A. Prasad, Postdoc

(16/08/2021 - 15/08/2024)

S. Vik Furuseth, Postdoc

(09/08/2021 - 18/06/2025)

Q. Noraz, Postdoc, PhD defense 09/2022

(07/11/2022 - 06/11/2025)

Former staff

......

...

** **

**CEA**

Institutional staff

Dr. Allan Sacha BrunDr. P. Kestener

Associate Prof. M. Browning

Assistant Prof. L. Jouve

Dr A. Strugarek

Dr M. Delorme

(since 15/12/22)

Dr B. Perri

(since 01/09/22)

Project staff

A. Finley, Postdoc(12/01/20 - )

S. Hazra, Postdoc

(03/01/24 - )

G. Doebele, PhD(01/10/23 - )

C. Blume, PhD, visiting WS project (09/23 - 08/24)

Former staff

R. Pinto, Senior postdoc(01/06/20 - )

...

...

** **

**IAC**

Institutional staff

Prof. F. Moreno-InsertisProf. M. Collados

Prof. J. Trujillo-Bueno

Dr E. Khomenko

Project staff

B. Coronado, PhD, in kind contribution(11/01/20 - )

D. Nobrega, Postdoc

(03/01/21 - )

Manuel Luna, Senior postdoc, in kind contribution (05/19 - )

N. Vitas, Senior Postdoc

(03/01/21 - )

A. Perdomo, PhD student

(from start of the project)

E. Alsina Ballester, PhD student

(from 01/10/2023 onward)

S. Sen, PhD student

(agreed to start on 01/05/2023)

Former staff

......

...

Scientific Advisory Committee :

Prof. Paul Charbonneau, Prof. Louise, Harra, Prof. Moira Jardine, Prof. Takashi Sekii, Prof. Juri Toomre

Understanding the origin and diversity of the solar activity and turbulence requires to understand how the field is organized deep down inside its convection zone as toroidal fibril corrugated magnetic structures (ribbons) and how that “coherent” field emerges at the surface, evolves, sometimes erupts and contributes to the heating of the solar atmosphere. All fundamental aspects of this sequence are organized in WPs within the Whole Sun project, which we will describe in detail following the structure: Key Questions to be addressed, Rationale, Synergies, Methodology, Detailed Tasks Breakdown, Sub- Questions: After the description of the first 5 scientific WPs (WP1 to WP5), we describe in WP-X the key steps to develop the next generation global solar code GLOBUS2 to get ready for the Exa-scale supercomputer era. At the end, we outline the more administrative WPs (see Figure B1.3 of part B1 for a summary).

Host Institutions :

Saclay (lead), Gottingen (lead), St Andrews (contribution)

Members :

[Permanents]

MPS: Prof. Laurent Gizon, Dr. A. Birch, Dr. R. Cameron, St Andrews : Dr. Vasilis Archontis, Prof. A. Hood; Oslo Univ. : Prof. Mats Carlsson, Prof. V. Hansteen, Associate Prof. B. Gudiksen; CEA : Dr. Allan Sacha Brun, Dr. P. Kestener, Associate Prof. M. Browning, Assistant Prof. L. Jouve, Dr. A. Strugarek; IAS : Prof. F. Moreno-Insertis, Dr. M. Collados, Prof. J. Trujillo-Bueno, Dr. E. Khomenko.[Non-Permanents]

MPS: F. Kupka (Senior Postdoc, 05/01/19 – 06/30/20), K. Mandal (Postdoc, 11/01/19 - ), D. Fournier (PhD, 10/01/20 -), CEA : Q. Noraz (PhD, 10/08/19 - )Main question :

Why do we not see spots in solar dynamo simulations – the spot-dynamo paradox? Why are simulation of stellar convection off when it comes to describing their energy spectra? What controls the energy distribution among convective scales in stars – the solar convective conundrum? - WP1.1 Spot dynamo paradox? (most dynamo simulations don’t have spots!) - WP1.2 Convective conundrum? (what is the energy distribution among convection scales)

Rationale :

In WP1.1 we want to understand how dynamo self-consistently generated magnetic ribbons that can lead to the formation of Omega-loops. By developing dedicated high performance numerical simulations, we will study how highly concentrated magnetic bundles of field can be generated amidst large scale magnetic wreaths and we will track them all the way to the surface. The purpose of WP1.2 is to tackle the fundamental problem of the solar convection conundrum with state-ofthe- art numerical simulations, theory and observational constraints coming from helioseismology probing. We will resolve the discrepancy between ring diagram and time distance analysis by applying the two methods to synthetic data. In a next step, we will apply validated methods of helioseismology to SDO/HMI observations determine the true amplitude of, or obtain an upper limit for subsurface convective flows in the Sun. Given the key role of differential rotation in the dynamo mechanism and formation of toroidal magnetic structures (well known W-effect) and of convection in the overall surface dynamics of the Sun (and by extension its twins), better characterizing energy and angular momentum carrying scales and their relative importance is of the upmost importance to understand our star and its activity level.

Synergies :

Whether near surface or deep global convection, all groups need, study and model convective patterns and how these nonlinear turbulent motions tangle the magnetic field lines. Likewise, the origin of the field through dynamo action, of its cyclic behavior, of the presence of spots and how they all impact the atmosphere dynamics are essential ingredients to understand the solar activity. We will design and run the simulations and observational methods to explain the source of these inconsistencies between the models, and observations themselves and in comparing them.

Methodology :

Through dedicated numerical models, surface flows, magnetic field observations and helioseismology probing of inner flow motions we intend to constrain solar magnetohydrodynamics and propose solution to the spotdynamo paradox and convective conundrum. The numerical simulations will be based in the beginning on high resolution global rotating convection models like case F [3, 99] and on low diffusion cases such as case S3 published in [19, 20] using dynamic Smagorinsky sub grid treatment. ASH possess now the ability to have various profile and spatial dependency for its diffusivities [100]. We will also cast acoustic waves perturbations in 4-D data cubes to compute the propagation of waves through various models of subsurface and global convection. We will then apply time-distance helioseismology and ring-diagram analysis to these synthetic wavefields. As the true flows in the model are known; each intermediate step in the helioseismic data analysis can be validated. In this way, we will determine how the different helioseismic analysis methods “see” the subsurface flows. Once the methods are well understood, and potentially updated to be more robust, we will apply these methods to SDO/HMI observations to provide measurements (or an upper limit) of the strength of the subsurface flows associated with convection.

Detailed Tasks breakdown :

WP1.1: Task 1.1.1: Compute, analyse hpc simulation (resolution > 2000^3) of global rotating turbulent convection with ASH - study energy distribution vs degree l (cf Fig B2.1) and Prandlt number (Pr) Year 1-4 Task 1.1.2: Analyze large scale flow – adjust physical ingredients – Study role of sub grid scale treatment and influence of upper atmosphere boundary conditions Year 1-4 Task 1.1.3: As soon as Globus2 code of WP-X is ready, compute high resolution convection model with upper realistic atmosphere using multi resolution approach. Year 3-6 WP1.2; Task 1.2.1: Compute and analyse hpc simulation (> 2000^3) of global magnetized rotating turbulent convection dynamo with ASH going beyond Nelson et al. 2013, Year 1-4 Task 1.2.2: Study the sensitivity of the magnetic cyclic state to variations of model parameter (magnetic Pm), Evaluate magnetic energy budget and influence of upper atmosphere boundary conditions, Year 1,5 Task 1.2.3: Provide magnetic time-depend structures for flux emergence simulations in WP2, Year 1 - 5 Task 1.2.4: As soon as Globus2 code of WP-X is ready, compute high resolution convection model with upper realistic magnetized atmosphere using multi resolution approach. 4-6

Related questions :

- Supergranules rather granules are key for magnetic concentration, what is the relation between convection scales and magnetic structure formations - What set the 11 yr cycle? (alpha-omega vs B-L vs nonlinear dynamos)

References :

- Gizon, Cameron, Pourabdian, Liang, Fournier, Birch, and Hanson, 2020a, Science, 368 1469

- Auguston, Brun, Toomre, 2019, ApJ, 876 83.

- Birch, Schunker, Braun, and Gizon, 2019, A&A 628 A37

- Brun, Strugarek et al. 2021, ApJ submitted

- Cameron and Schüssler, 2020, A&A, 636 A7

- Goddard, Birch, Fournier, and Gizon, 2020, A&A 640 L10

- Hanson, Gizon and Liang, 2020, A&A 635 A109

- Hazra, Brun, Nandy, 2020a, A&A 642, A51

- Proxauf, Gizon, Löptien, Schou, Birch, and Bogart, 2020, A&A 634 A44

Host Institutions :

St Andrews (lead), MPS (lead), Saclay (lead), Oslo (contribution), IAC (contribution)

Members :

[Permanents]

MPS: Prof. Laurent Gizon, Dr. A. Birch, Dr. R. Cameron, St Andrews : Dr. Vasilis Archontis, Prof. A. Hood; Oslo Univ. : Prof. Mats Carlsson, Prof. V. Hansteen, Associate Prof. B. Gudiksen; CEA : Dr. Allan Sacha Brun, Dr. P. Kestener, Associate Prof. M. Browning, Assistant Prof. L. Jouve, Dr. A. Strugarek; IAS : Prof. F. Moreno-Insertis, Dr. M. Collados, Prof. J. Trujillo-Bueno, Dr. E. Khomenko.[Non-Permanents]

CEA: R. Pinto (Senior Postdoc: 01/06/20 -); StAndrews: P. Syntelis (Postdoc: 05/01/19 – 10/01/19), A. Borissov (Postdoc, 09/01/20 - )Main question :

How do magnetic fields emerge from the solar interior to the solar surface to form pore, sunspots, Ephemeral and Active Regions (ERs and ARs)?

Rationale :

The emergence of magnetic fields (EMFs) on the Sun is a continual process whereby magnetic flux generated by dynamo in the solar interior rises to the solar surface and expands out into the solar atmosphere. Observations reveal that emergence occurs over a wide range of spatial and temporal scales, ranging from the small-scale internetwork field to the largest ARs and durations of hours to days [e.g. 1,2,3]. On theoretical grounds, it has long been suggested [1] that magnetic flux in the convection zone rises, due to magnetic buoyancy, to the solar surface where it can form bipolar pairs of sunspots. In addition, observations of the photospheric magnetic field distribution of emerging ARs have supported this scenario [e.g. 4]. Helioseismic observations can provide us with information about the evolution of the emerging fields below the photosphere by e.g. measuring the flow patterns associated with strong sub-surface magnetic flux concentrations of sunspot and emerging ARs. However, in-depth understanding of: i) how magnetic fields emerge from the deep solar interior to the solar surface and ii) the response of the solar surface to the key process of EMFs, requires advanced numerical studies of the coupling between GCD models and N-SFE experiments. Moreover, as the fields emerge, they transport energy and magnetic flux into the solar atmosphere, reconfigure the solar corona, and lead to the onset of solar phenomena, many of which are eruptive (such as jets, flares and CMEs). Thus, to understand key aspects of solar eruptive events (WP3) and the thermodynamic coupling of the solar atmosphere (WP4), it is crucial to understand the process of EMFs and then follow their long-term evolution using the most comprehensive theoretical, numerical and observational description to date.

Objectives :

Our main objective is, for the first time, to explore the nature of the interplay between dynamo, convection and EMF on various temporal/spatial scales towards the formation of ARs (and possibly ephemeral regions and the Quiet Sun). More precisely, our aim is to address the following questions: • What is the origin of solar ARs and why and how do they evolve and decay? • How does flux emergence link the subsurface global dynamo fields to the solar atmosphere, and how does it affect the dynamo? How is the 3-D magnetic field topology in different solar magnetic regions? The results of our study will produce predictive output for testing with observations from existing and upcoming solar missions (e.g. Solar Orbiter (EUI, PHI, STIX)).

Synergies :

To understand the effect that emerging and dispersing magnetic flux has on the solar surface, a combination of observations and advanced 3D modelling will be applied, since neither alone can determine unambiguously the physics of the proposed research. Therefore, the afore-mentioned objectives (WP2.1-WP2.3) can only be achieved through synergies between the team members in this application. On this basis, we will directly use: - magnetic field measurements in emerging flux regions at the solar surface, using various methods and techniques (SOHO/MDI magnetograms, spectro-polarimetry on high resolution ground facilities). We will use observational data from recent and future solar missions (Hinode, SDO, IRIS). - measurements of the upper-convection flow fields in emerging flux regions, inferred by helioseismology. - the available 3D MHD codes (ASH, Bifrost, Muram, Mancha) to perform realistic numerical experiments of the coupling between GCD and N-SFE. The results of the proposed research in WP2 will also be used towards achieving the goals described in WP3, WP4 and WP5. We should highlight that the experiments in this WP will follow the evolution of the system up to the photosphere, while the experiments in WP3 and WP4 will focus on the evolution of the system from the photosphere and above. On the other hand, we can verify the robustness of the results in WP2, by performing experiments using the new global code, which will be developed during WPX.

Methodology :

Observations: We will confront the numerical models of magnetic flux emergence developed in this WP with helioseismology applied to SDO/HMI observations of emerging (and pre-emergence) ARs. For each model for the origin of ARs we will predict the helioseismic signatures, for example wave travel times, that would be expected to result from the model. The prediction will be based on computational forward modeling using the finite-element frequency domain wave-equation solver described by [72]. We will then apply helioseismology to SDO/HMI observations for the appropriate subset of the 105 emerging ARs cataloged in [73]. A comparison of the observations and the forward model will determine if the model is consistent with the observations. Moreover, the numerical modeling effort will be complemented through use of observations (vector magnetograms, spectropolarimetric observations to study the Zeeman and Hanle effects in photospheric and chromospheric lines) carried out mainly from ground-based telescopes located on the IAC Observatories, which count among the most advanced in the world. Numerical simulations: To couple GCD with N-SFE simulations, we will use the existing GCD model by [20, 7] and the Radiative- MHD N-SFE model by [44], [74]. To couple the two models, we will not use kinematic emergence of a uniform, horizontal magnetic field through the bottom boundary as in the simulations by [44], [74]. Instead, we will use the outcome data of the GCD simulations (e.g. the magnetic and velocity fields in a horizontal layer near the top boundary, which is located 20 Mm below the photosphere) to drive the N-SFE simulations. In other words, we will use a time-dependent boundary condition at the bottom of the N-SFE model to drive flux emergence at the upper convection zone. This coupling is technically feasible and to achieve it we will use a similar method and techniques (e.g. rescaling the data from the GCD model to match the smaller scale of the N-SFE model, modify the output data from the spherical GCD model to make them compatible with the periodic horizontal boundary conditions of the N-SFE model in a Cartesian geometry, etc.) to the recent work by [18]. For the needs of this WP, we will also revise the existing N-SFE model. We will use a much deeper convection zone (20 Mm depth), in order to make it compatible with the height of the top boundary of the GCD model. Also, we will not use the highly stratified outer solar atmosphere and, thus, we can increase the horizontal size of the numerical domain to AR scales (e.g. up to 200 Mm) and keep sufficient resolution to resolve granular scales. From the GCD simulations, we will choose areas surrounding magnetic flux bundles with different physical properties (e.g. field strength, size, twist), which have emerged close to the top of the domain. We will choose structures at both hemispheres and at different (low/high) latitudes. Then, we will extract the data (mainly the magnetic and velocity field components) from these areas, with a high cadence and use them as a time-dependent boundary condition to the N-SFE model. We will follow the emergence of the magnetic structures after their advection through the bottom boundary of the N-SFE model. We will perform experiments with a pre-existing magnetic field in the N-SFE model (e.g. a vertical, uniform magnetic field with a strength of about 10 G) and without. We will study the photospheric response to the emergence of physically different magnetic flux structures (bundles) and explore whether they give rise to pores, sunspots, ERs or ARs. In each case, we will explore the onset mechanism and evolution of these phenomena (how / why) and the exact role of convection, near-surface emergence and dynamo on their driving and their manifestation at the solar surface. A full parametric study (e.g. changing the initial values of the critical parameters in the CGD and N-SFE models) will be performed to advance our understanding of the role of each one of these individual processes on the evolution of the coupled system. In addition, helioseismology (see methodology / observations) will help us to construct models, which are more consistent with the observations.

Detailed task breakdown :

WP2.1: Task 2.1.1 Perform radiative MHD simulation with the Bifrost code, to model the upper convection zone (depth around 20 Mm) and solar surface domain (e.g up to 200 x 100 Mm). First run a purely hydrodynamic simulation to allow the convection to reach a static equilibrium stage. Years 1-2. Task 2.1.2 Extract the data from the GCD model and use them, as described in the methodology part of the WP, to advect the field inside the N-SFE model and to initiate the emergence of magnetic flux. Years 1-2. Task 2.1.3 Perform test-runs to identify and quantify possible inconsistencies in the coupling of the two models. Use the results to further improve the performance of the coupling. Years 1-2. WP2.2: Task 2.2.1 Perform simulations of flux emergence after the coupling between the CGD and the NSFE models. Run a series of experiments with low/high resolution and different horizontal sizes of the numerical domain. Check their effect on the evolution of the system. Years 1-6. Task 2.2.2 Analysis of the data produced by the simulations. Study of the formation of pores, sunspots, ephemeral regions and ARs. Years 1-6 Task 2.2.3 When Globus code of WX is ready, more experiments will be performed to study the emergence of magnetic flux from the deep solar interior to the solar surface. The results will be compared to the results obtained by the coupling code (GCD with N-SFE models) and explore the differences / similarities. This comparison will help us to verify the robustness of the results. Years 1-3. WP2.3: Task 2.3.1 Observations of ephemeral and emerging (and pre-emergence) ARs, as described in methodology. Collect the observational data and do the analysis. Years 1-3 Task 2.3.2 Use helio-seismology to confront the numerical models developed in this WP. Years 2-6 Task 2.3.3 Compare the results of the numerical experiments to observations. Use the comparison to: i) understand the strengths and limitations of the simulations and observations and ii) construct models more consistent with the observations. Years 1-6.

References :

- Patsourakos, S. et.al, SSR, V216, Issue 8, id 131 (2020).

Host Institutions :

St. Andrews (lead), Oslo (lead), IAC (contribution), Saclay (contribution)

Members :

[Permanents]

MPS: Prof. Laurent Gizon, Dr. A. Birch, Dr. R. Cameron, St Andrews : Dr. Vasilis Archontis, Prof. A. Hood; Oslo Univ. : Prof. Mats Carlsson, Prof. V. Hansteen, Associate Prof. B. Gudiksen; CEA : Dr. Allan Sacha Brun, Dr. P. Kestener, Associate Prof. M. Browning, Assistant Prof. L. Jouve, Dr. A. Strugarek; IAS : Prof. F. Moreno-Insertis, Dr. M. Collados, Prof. J. Trujillo-Bueno, Dr. E. Khomenko.[Non-Permanents]

Oslo: K. Krikova (PhD, 09/01/20 - ), StAndrews: G. Chouliaras (PhD,09/27/20 - ), IAC : B. Coronado (PhD, 11/01/20; in kind contribution), D. Nobrega (Post doc, 03/01/21 - ), M. Luna (senior postdoc, 05/19 - ; in kind contribution)Main question :

what is the interplay between the magnetic fields in the solar atmosphere and those in the interior that leads to the onset of eruptions, flares and jets? - WP3.1: Small-scale ejections in the chromosphere, transition region and low corona: onset and development following photospheric and subphotospheric evolution - WP3.2: Intermediate and large-scale jets and flares: destabilization and evolution resulting from photospheric and subphotospheric evolution. - WP3.3: The formation and destabilization of solar prominences. Coronal mass ejections.

Rationale :

a large number of ejective, often explosive, events are regularly recorded by solar telescopes in space and on the ground, ranging from the largest and most powerful of all (flares and coronal mass ejections) [75, 76, 77] through intermediate-scale events, like X-ray jets or microflares, [78, 79] down to a large variety of important small-scale ejections observed in various atmospheric layers like surges, spicules, Ellerman bombs, transition region jets or UV explosive events [80 - 84]. Flares and coronal mass ejections hurl magnetized plasma and subatomic particles out into the interplanetary medium, which can reach the Earth's surroundings, in particular its magnetosphere, with possibly damaging, potentially devastating, effects for our society. Flares have already been known for more than 100 years; X-ray jets were detected using the Yohkoh satellite in the 1990s and studied in depth only with the Hinode, SDO and Stereo space missions; some of the small-scale jets (e.g., the transition region jets), in turn, have been discovered only in the present decade thanks to the launching of the most recent generation of solar satellites (like, e.g., IRIS). In all those cases, the multidimensional physical understanding of the destabilization processes leading to the ejections and eruptions and of their time evolution is still in an initial phase. Two basic evolutionary patterns are assumed to be at the basis of those phenomena: (a) magnetized plasma emerges from the solar interior and profoundly perturbs the preexisting magnetic configuration in the atmosphere, leading to magnetic field line reconnection and plasma ejections; (b) an existing magnetic configuration in the atmosphere is forced to change through the motion of its footpoints at the surface: the perturbation can easily lead to destabilization, often causing the violent and explosive rearrangement of the magnetic connectivity patterns and the conversion of magnetic energy into kinetic and internal energy of the plasma and launching of jets and eruptions. The greatest challenges when trying to understand the physics of those ejections through either form of evolutionary pattern arise from the need to combine in one model the physics of the solar interior (in particular of the convective motions on granular, mesogranular and supergranular scales) and of the atmosphere, from the low layers (photosphere, chromosphere) to the corona, with all the attendant requirements of detailed (LTE and NLTE) radiative transfer calculations, inclusion of partial ionization / multi-fluid effects, heat conduction and optically thin radiative cooling.

Synergy :

the objectives of this working package can only be reached through a synergistic effort. Modelling of the onset and evolution of solar ejections and violent eruptions traditionally has been carried out using a highly idealized purely-magnetohydrodynamical approach. Three aspects are particularly relevant in this sense: (a) The important observational developments in the current decade concerning chromospheric and transition region jets, and the recent theroretical advances in their understanding using the radiation-MHD code Bifrost (as in figure B2.4, from Nobrega-Siverio et al 2016) make clear the need to tackle this problem through a synergistic approach. (b) The theoretical models so far make rough assumptions concerning the subphotospheric evolution leading to the ejections and violent eruptions. For progress, they must be combined with detailed understanding of the magnetic field evolution in the interior. This Working Package will therefore make use of the results of WP1 and WP2, including direct use of the magnetic distributions calculated within those WPs. Finally, (c) Solar ejections and eruptions involve all layers of the solar atmosphere from the photosphere to the corona, both concerning the preexisting structure leading to the fast evolution as well as their actual development. Understanding them requires the concomittant work of theory and observations, combining such different observational techniques as are needed to unravel the events detected in the low (photospheric, chromospheric), intermediate (transition region, low corona) and high atmospheric layers.

Methodology :

(a) Numerical models for the small- and intermediate spatial scales: the use of the radiation-MHD code on the upcoming exascale supercomputing installations will permit studying within the same model the evolution of the magnetic field in the subphotospheric and atmospheric layers including from at least several Megameters into the convection zone to the high corona, at the same time including refined ratiative transfer calculations in the low atmosphere, heat conduction and optically thin cooling in the corona. (b) Numerical models for the largest scales, combination of the results from the formation of rising magnetic ropes in the deep solar interior (WP 1 and 2) with the atmosphere models available within the present WP will permit important progress in understanding the formation and destabilization of prominences/filaments as well as the launching of large-scale flares. The numerical models will use the numerical codes and tools already available to the teams, but also, toward the final part of the project, it will use the advanced capabilities of the code developed under WPX, which will permit a new generation of calculations also within this package. (c) Observations and models: keeping the observational context at hand will be crucial in this working package. Our approach includes forward-modeling for direct comparison with the observations, as well as participation in observational campaigns to test the results of our models and prepare the way for new ones. Detailed Task breakdown: WP3.1: Task 3.1.1: Carry out three-dimensional radiative-MHD models of small-scale ejective phenomena in the low atmosphere (spicules, surges, Ellerman bombs, UV bombs) using the Bifrost code. This task must include realistic convection in the top several Megameters of the convection zone, profiting also, as the SyG project advances, from the experience gained within WP2. The box must necessarily reach intermediate levels in the corona (several tens of Mm). The simulations should use the most advanced modules available in the Bifrost code relevant for this WP at the time of execution. Timescale: years 1-4. Task 3.1.2: Carry out forward-modeling on the basis of the data obtained within 3.1.1 to compare the results with the observations at the photospheric, chromospheric and transition region levels. This should include NLTE radiation transfer techniques using the PORTA code, and advanced diagnostic methods, using the Hazel code. Timescale: years 2-5. WP3.2: Task 3.2.1: Carry out 3D idealized MHD models for the destabilization of coronal structures via photospheric motions leading to the ejection of mini-filaments and the production of hot (EUV and X-ray class) jets. The first models should be done using a standard idealized code like those recently used by the teams (stagger, Lare3D) and comparatively simple subsurface models. In the more advanced stages, surface distributions obtained through WP2 will be used to drive the coronal field. Timescale: years 1-5. Task 3.2.2: 3D modeling of hot (EUV / X-ray) jet production using a realistic radiation MHD code. This should include flux evolution within a self-consistent comparatively deep convection layer and reach from there to the corona. The experience gained with N-SFE models within WP2 can be important in guiding this task. In the final years of the project, the Globus code developed under WPX will be used. Timescale: years 2-6 Task 3.2.3: Forward-modeling of the results of 3.2.2, both concerning the low atmosphere and the EUV and X-ray emission in the corona. Timescale: years 3-6. WP3.3: Task 3.3.1: carry out numerical simulations to study the formation of prominences based on the shearing processes at the photosphere and the transport of mass along field lines to coronal heights. The focus will be twofold: (a) the shear is transported from subphotospheric levels to the corona but the mechanism is still unknown; (b) the origin of the prominence mass is the chromosphere but the mechanisms that transport it to the corona are not well understood. We will use the codes Mancha3D, Bifrost, Stagger. Timescl: years 1-5. Task 3.3.2: The same mechanism in the photosphere that forms the field structure can destabilize the prominence. We will carry out 3D numerical models to study the processes that cause the prominence destabilization and subsequent dynamics using our codes. We will be using the output of WP2 since it is the global evolution of the solar (sub)photospheric field that drives the eruptions. Timescale: years 1-6.

Related questions :

- what is the role of the large-scale surface magnetic field distribution (as caused by the subphotospheric motions) onto the creation and destabilization of structures in the atmosphere? - do the classical theoretical models of flare and CME launching resist the test of using detailed radiation transfer for photosphere, chromosphere and corona in the simulations? - what is the mutual relationship of small-scale and intermediate scale ejections and eruptions? - can one discriminate between flux emergence and photospheric footpoint motion as the major cause for the various types of ejections in the atmosphere? - what is the role of the partial ionization electrodynamics phenomena and of multi-fluid physics onto the eruptions in the atmosphere?

References :

- Nobrega-Siverio, D.; Moreno-Insertis, F.; Martínez-Sykora, J; Carlsson, M.; Szydlarski, M.; “Nonequilibrium ionization and ambipolar diffusion in solar magnetic flux emergence processes", Astron & Astrophys, 633, A66, 2020a

- Nobrega-Siverio, D.; Martínez-Sykora, J; Moreno-Insertis, F.; Carlsson, M.; “Ambipolar diffusion in the Bifrost Code", Astron & Astrophys, 638, A79, 2020b

- Joshi, R.; Chandra, R.; Schmieder, B.; Moreno-Insertis, F.; Aulanier, G.; Nóbrega-Siverio, D.; Devi, P.; “Case study of multi-temperature coronal jets for emerging flux MHD models”, Astron & Astrophys 639, A22, 2020.

- Madjarska, M.S.; Chae, J.; Moreno-Insertis, F.; Hou, Z.; Nóbrega-Siverio, D.; Kwak, H.; Galsgaard, K.; Cho, K.; “The chromospheric component of coronal bright points”, Astron & Astrophys, accepted, Dec 2020.

- Luna, M. & Moreno-Insertis, F. (2020): “Large-amplitude prominence oscillations following the impact by a coronal jet”. ApJ, submitted, Dec 2020.

Host Institutions :

Oslo (lead), Saclay (lead), St Andrews (contribution), IAC (contribution)

Members :

[Permanents]

MPS: Prof. Laurent Gizon, Dr. A. Birch, Dr. R. Cameron, St Andrews : Dr. Vasilis Archontis, Prof. A. Hood; Oslo Univ. : Prof. Mats Carlsson, Prof. V. Hansteen, Associate Prof. B. Gudiksen; CEA : Dr. Allan Sacha Brun, Dr. P. Kestener, Associate Prof. M. Browning, Assistant Prof. L. Jouve, Dr. A. Strugarek; IAS : Prof. F. Moreno-Insertis, Dr. M. Collados, Prof. J. Trujillo-Bueno, Dr. E. Khomenko.[Non-Permanents]

Oslo: R. Robinson (PhD, 09/23/19 - ), CEA: A. Finley (Postdoc, 12/1/20 - )Main question :

The atmosphere of the Sun is characterized by an interplay of competing physical processes. These include convection, radiation, conduction, magnetic field interactions, ion-neutral effects. How do these processes couple in the multi-scale atmosphere of the Sun and in determining the energy flows?

Rationale :

At the top of the convection zone lies the solar surface, the photosphere, comprised of convection cells and threaded with magnetic fields. Above the photosphere, we find the outer solar atmosphere where, astonishingly, the temperature starts to rise; the chromosphere with temperatures around 10,000 K, the transition region, the hot (> 1 MK) corona, the solar wind, and the outer heliosphere, extending out to more than twice the distance of Pluto. Understanding the non-intuitive rise in temperature and the processes driving the supersonic solar wind outflow that inflates the solar heliosphere has been a central goal of solar physics since the discovery that the corona is hot in the late 1930’s. The solar magnetic field, generated in the convection zone and photosphere, is at the heart of these thorny problems. In the solar photosphere, the plasma dominates the magnetic field, forcing the field to continual motion. The emergence and displacement of magnetic flux at photospheric heights as the plasma does work on the field imply an upwardly propagating energy flux. The magnetic field is also the primary agent for transporting this “mechanical” energy from the convection zone into the outer solar atmosphere where it is dissipated. A wide variety of physical mechanisms have been proposed, but the complexity of the atmosphere has precluded consensus on which of these mechanisms dominate the heating of the solar atmosphere and drive violent eruptions.

Synergy :

The modelling of the outer atmosphere of the Sun (and stars) has so far employed computational domains that extend up into the corona but only down to the upper layers of the convection zone. The initial magnetic field and the magnetic field advected through the bottom boundary of the computational domain are free parameters in such models. The whole Sun project will combine the expertise on the generation of the magnetic field with the expertise on the physics of the outer atmosphere, thereby replacing these free parameters. This will enable an understanding of how energy is distributed, flows among various scales and heats the upper solar layers.

Methodology :

We will use the experiments and studies in WP2 and WP3 to assess in detail how magnetic structures are formed, emerge and interact, how energy is transported and dissipated. First, results from WP2 and WP3 will be fed into local simulations of the outer atmosphere and later we will also develop global, coupled simulations. The latter entails developing new methods that enable different physical descriptions in different regimes. This will be addressed in WPX. Detailed Task breakdown: 4.1 Run local models from the convection zone to the corona with initial magnetic field and flux emergence through lower boundary given by global simulations – Years 1-3 4.1.1 Small computational box capable of simulating areas without large spatial scales: quiet Sun, network patches, pores 4.1.2 Larger computational box to simulate pores, jets, effects of flux emergence on outer atmosphere 4.2 Drive local models of the outer atmosphere with time-dependent lower boundary taken from global simulations – Years 2-4 4.2.1 Small computational box to examine effects of magnetic flux properties such as orientation with respect to ambient field, twist, and amplitude on outer atmosphere dynamics and energetics 4.2.2 Large computational box with strong field/flux tube from global simulation to form (ephemeral) active region and related phenomena (e.g. flares). 4.3 Couple internal simulation with outer atmosphere with interactions going in both directions – Years 3-5 4.4 Fully integrated simulations – Years 4-6 Complementary questions: 1. Study how the various atmospheric layers are heated (reconnection, waves, shocks,..) and/or respond (e.g. magnetic coupling) during the events described in WP3? 2. Perform the same study for the Quiet Sun? (e.g. using experiments from WP2 which do not lead to the formation of an AR but to a Quiet Sun region).

References :

- Shoda M.,…, Brun, A.S., et al., 2020, "Alfvén-wave-driven Magnetic Rotator Winds from Low-mass Stars. I. Rotation Dependences of Magnetic Braking and Mass-loss Rate", ApJ, 896, 123

- Ahuir J., Brun A. S., Strugarek A., 2020, "From stellar coronae to gyrochronology: A theoretical and observational exploration", A&A, 635, A170

- Perri B., Brun A. S., Strugarek A., Réville V., 2020, "Impact of solar magnetic field amplitude and geometry on cosmic rays diffusion coefficients in the inner heliosphere", JSWSC, 10, 55

- Brun A. S., Strugarek A., 2020, "Stellar magnetism: bridging dynamos and winds", mdps.conf, 171

- Hazra et al. 2020b, ”Modelling solar wind variations over an 11-yr cycle with Alfvèn wave heating”, ApJ, submitted

Host Institutions :

Saclay (lead), Gottingen (lead), Oslo (contribution), St Andrews (contribution)

Members :

[Permanents]

MPS: Prof. Laurent Gizon, Dr. A. Birch, Dr. R. Cameron, St Andrews : Dr. Vasilis Archontis, Prof. A. Hood; Oslo Univ. : Prof. Mats Carlsson, Prof. V. Hansteen, Associate Prof. B. Gudiksen; CEA : Dr. Allan Sacha Brun, Dr. P. Kestener, Associate Prof. M. Browning, Assistant Prof. L. Jouve, Dr. A. Strugarek; IAS : Prof. F. Moreno-Insertis, Dr. M. Collados, Prof. J. Trujillo-Bueno, Dr. E. Khomenko.[Non-Permanents]

CEA: Q. Noraz (PhD, 10/01/19 -), MPS : C. Goddard (Postdoc, 05/01/19 – 06/01/20), S. Cloutier (PhD, 01/01/20 - ), StAndrews : A. Borrisov (Postdoc, 09/01/20 - )Main question :

The future and the past of the Sun? Is the Sun a “normal” solar-like star? How do dynamo, convection, flux emergence and heating processes change with different global stellar parameters (rotation, mass, Teff) and metallicity? - WP5.1: Effect of metallicity on convection, dynamo action, flux emergence and heating - WP5.2: Effect of mass (e.g. aspect ratio and energy input) on dynamo, convection, flux emergence, heating processes and superflares - WP5.3: Effect of Rotation rate on dynamo and flux emergence complexity and latitude of emergence - WP5.4: Effects of evolution, tracking the Sun over time (as in [85])

Rationale :

By comparing the Sun to other stars and by exploring the regime diagram in mass, aspect ratio, luminosity, rotation rate and metallicity we are able to understand the fundamental mechanisms at work in solar-like stars. This further informed us on the past and future of the Sun, as we know that young stars are fast magnetically active rotators and old stars are quieter and slowly rotating. We propose in WP5.2 to tackle this challenging question and to characterize how much magnetic free energy given the star’s mass (or equivalently luminosity) can be store into magnetic flux ribbons that could then emerge and supply the required energetic content and complex magnetic topology for such super flare to occur. Such problematic clearly demonstrate how important it is to link all layers ans evolutionary stage of magnetic field generation, emergence and destabilization throughout our designed 5 WPs. We will be able to assess what are the effective factor of conversion from dynamo to eruptive events and heating of the upper atmosphere, comparing with observations such as [86] and extending it to solar-like stars via our calibrated models.

Synergy :

Putting the Sun in a stellar context is essential to understand its specificity, to use it as a Rosetta stone to understand other solar like stars and in return to constraint its dynamics. The Saclay and Gottingen’s group have a long experience in looking at the Sun as a star and in modelling and observing them, experience that will greatly benefit the other groups to broaden the range of applications of the various tools fine-tuned to the solar case but that can be used efficiently for other stars.

Methodology :

From models and simulations jointly developed by all groups on the Sun in WP1 to WP4 expand their applications to different global parameters such as: rotation rate (low, solar, fast), mass/luminosity/aspect ratio and metallicity (low, solar, high).

Detailed Tasks breakdown :

WP5.1: Task 5.1.1: Compute low-Z simulations of solar dynamo and of flux emergence in link with WP1, 2 Task 5.1.2: Compute high-Z simulations of solar dynamo and flux emergence in link with WP1, 2: Years 2-5 Task 5.1.3: Compare low-Z, high-Z and solar metallicity models computed in WP1, Years 2-5 Task 5.1.4: Assess magnetic energy, Poynting flux in link with WP3 and WP4, Years 3-6 WP5.2: Task 5.2.1: Compute lower mass model of solar-like dynamo (around 0.95/0.9/0.85 Msol), Years 2-5 Task 5.2.2: Compute higher mass model of solar-like dynamo (around 1.05/1.1/1.15 Msol), Years 2-5 Task 5.2.3: Compare solar-like star dynamo models with solar case computed in WP1, Years 2-5 Task 5.2.4: Assess magnetic energy, Poynting flux in link with WP3 and WP4, Years 3-6 WP5.3: Task 5.3.1: Compute slowly rotating (Ro>1) model of solar-like star (improve upon [4]), Years 3-6 Task 5.3.2: Compute fast rotating model (Ro < 0.2) of solar-like star (improve upon [4]), Years 3-6 Task 5.3.3: Compare mean flows of solar-like star models with solar case computed in WP1, Years 3-6 Task 5.3.4:Provide rotation profile and scaling laws for mean flows vs Z, M*, Omega*, Years 4-6 WP5.4: Task 5.4.1: 1-D solar-like star evolution model at (low, solar and high metallicity) with Starevol code (as in Gallet et al. 2017), Years 2-3 Task 5.4.2: Select key instants along the track to run specific simulations to assess influence of evolution on the Sun’s dynamics – do so by optimizing simulations with previous WP5.x run set – Years 4-6 Complementary questions: - Rotation history and internal profile vs age? - Dynamo type, cycle period vs spectral type, Main mechanism? Occurrence of Grand minima in stars? - Flux emergence vs global parameters (rotation, aspect ratio, luminosity, etc ...) - Impact of metallicity on convection, flux emergence, wind and coronal temperature? - Impact of global parameters on convection, wind and coronal temperature?

References :

- Takehiro S.-i ., Brun A. S., Yamada M., 2020, "Assessment of Critical Convection and Associated Rotation States in Models of Sun-like Stars Including a Stable Layer", ApJ, 893, 83

- Brun A. S., Strugarek A., 2019, "Turbulence, magnetism, and transport inside stars", EAS, 82, 311

- Brun, Strugarek et al. 2021, ApJ submitted

Stellar atmospheres are very complex, and very different physical regimes are present in the convection zone, photosphere, chromosphere, transition region and corona. To understand the details of the atmosphere it is necessary to simulate the whole atmosphere since the different layers interact strongly. These physical regimes are very diverse and numerically stiff and it takes a highly efficient massively parallel numerical code to solve the associated equations in a timely manner by using the unique resources that Exascale supercomputers are going to provide. All groups have developed and still maintained broadly used state-of-the-art solar physics codes (ASH [87, 2], Bifrost [88], Muram [89], Mancha [90]) that have unique specificities but would benefit from input and coupling from the other’s group code. The outcome of one code could be use instead to improve what is considered as a boundary condition in the other code. These codes and their soft coupling will provide the back bone to develop the new generation solar code for the exa-scale era and beyond, that is being global with realistic physics and atmosphere on a versatile mesh/parallelism framework..

Understanding the origin and diversity of the solar activity and turbulence requires to understand how the field is organized deep down inside its convection zone as toroidal fibril corrugated magnetic structures (ribbons) and how that “coherent” field emerges at the surface, evolves, sometimes erupts and contributes to the heating of the solar atmosphere. All fundamental aspects of this sequence are organized in WPs within the Whole Sun project, which we will describe in detail following the structure: Key Questions to be addressed, Rationale, Synergies, Methodology, Detailed Tasks Breakdown, Sub- Questions: After the description of the first 5 scientific WPs (WP1 to WP5), we describe in WP-X the key steps to develop the next generation global solar code GLOBUS2 to get ready for the Exa-scale supercomputer era. At the end, we outline the more administrative WPs (see Figure B1.3 of part B1 for a summary).

Host Institutions :

Saclay (lead), Oslo (lead), Gottingen (contribution), IAC (contribution)

Members :

[Permanents]

MPS: Prof. Laurent Gizon, Dr. A. Birch, Dr. R. Cameron, St Andrews : Dr. Vasilis Archontis, Prof. A. Hood; Oslo Univ. : Prof. Mats Carlsson, Prof. V. Hansteen, Associate Prof. B. Gudiksen; CEA : Dr. Allan Sacha Brun, Dr. P. Kestener, Associate Prof. M. Browning, Assistant Prof. L. Jouve, Dr. A. Strugarek; IAS : Prof. F. Moreno-Insertis, Dr. M. Collados, Prof. J. Trujillo-Bueno, Dr. E. Khomenko.[Non-Permanents]

CEA: M. Delorme (Senior postdoc/HPC researcher, 12/06/19), Oslo: Andrius Popovas (Research Software Engineer) 01.03.2020, MPS : F. Kupka (Senior Postdoc, 05/01/19 – 06/30/20), Y. Bekki (PhD -> postdoc ; 03/01/20 - )Main question :

What could be the best numerical techniques to study Solar dynamics and magnetic activity in the Exa-scale supercomputer era and beyond?

Rationale :

Stellar atmospheres are very complex, and very different physical regimes are present in the convection zone, photosphere, chromosphere, transition region and corona. To understand the details of the atmosphere it is necessary to simulate the whole atmosphere since the different layers interact strongly. These physical regimes are very diverse and numerically stiff and it takes a highly efficient massively parallel numerical code to solve the associated equations in a timely manner by using the unique resources that Exascale supercomputers are going to provide.

Synergy :

All groups have developed and still maintained broadly used state-of-the-art solar physics codes (ASH [87, 2], Bifrost [88], Muram [89], Mancha [90]) that have unique specificities but would benefit from input and coupling from the other’s group code. The outcome of one code could be use instead to improve what is considered as a boundary condition in the other code. These codes and their soft coupling will provide the back bone to develop the new generation solar code for the exa-scale era and beyond, that is being global with realistic physics and atmosphere on a versatile mesh/parallelism framework.

Methodology :

To develop a modern code we must use a different approach than in late 90’s/early 2000’s. Multi-platform parallelism, mesh structuring, numerical algorithm and physical modules must be made independent. Today, in most solar codes all these aspects are too interdependent. Key bottlenecks have been identified and recent developments in applied mathematics and numerical analysis have made it possible to lift them. We intend to implement these new techniques in a new global realistic solar MHD code. A dedicated computing task force will be created for the development of the GLOBUS2 code. Around the coPI and Dr. A.S. Brun (ASH code) and high performance scientific software expert Dr. P. Kestener (both part of CEA poles), the 4 computing Engineers that will be hired by each PI HI and the tenured computing experts in each research groups e.g. B. Gudiksen (Bifrost code), R. Cameron (Muram code), V. Archontis (Lare3D code) and E. Khomenko (Mancha code). Regular in-person or remote meetings will be organized to ensure the fast development and validation of the code by implementing the following tasks:

Detailed Tasks breakdown - Key Technical points to lift:

Task X.0: regular follow up and hands on computer meetings of the task force (see above) to have clear objectives and milestones for the successful development of the GLOBUS2 code. Task X.1: Design tools to shape the refined mesh (cubed-sphere); the locally refined grid will be built in an iterative / recursive way (as done in p4est library; see Fig B2.8). The refinement constraint can be purely geometric or based on local physics variable (density, ...). We will allow for mesh refinement right after a check-point restart. Grid technique resolved both poles and r=0 singularity. Task X.2: Design high-performance IO routines: physics variable and mesh-metadata (cell size, cell location, refinement level, cubed-sphere sub-domain) will be clearly separated. We will design IO routines for both output and input (check-point restart) using current state of the art parallel IO libraries (HDF5 or the like). Task X.3: Design the core solver object for multi-architecture execution: generic data containers for both mesh metadata and heavy data (physics variables). When the application starts, the distributed memory mesh decomposition as well as the ghost cell MPI communications pattern is setup for the entire simulation run. Task X.4: Validate non-cartesian geometry. This basically consists in re-introducing in the cartesian solver numerical terms containing the Jacobian associated to the isoparametric transformations between the local cubed-sphere cell and the reference orthogonal unit cell. We will first use the uniformly refined cubed-sphere, and in a second step used a radially refined cubed-cubed to test the ability of our algorithm to handle properly the borders between neighbouring cells at different refinement level. Task X.5: Design the high-order numerical solver based on the spectral difference method (SDM, a Discontinuous Galerkin like numerical scheme) which have already been demonstrated to be very efficient when implemented for streaming architectures (GPU, KNL, ...). We will build upon current expertise to adapt the cartesian implementation to the cubed-sphere geometry. Task X.6: Modify the compressible Euler SDM numerical scheme to handle magnetic field (MHD). We will add some dissipative terms as well: viscous flux, magnetic resistivity and finally physics terms for thermal conduction and static gravity. The static gravity might require a careful implementation, i.e. a numerical method which is able to preserve a hydrostatic equilibrium. Fig B2.8: Three examples of multi-resolution grids developed with the p4est library: spherical shell with (left panel; r=[0.7,1.8] Rsol) or without (middle; r=[0.5,1] Rsol) a stretched grid to solve for the lower atmosphere and full sphere (right; r=[0,1] Rsol) cases [91]. Comparing the left and middle cases, having a stretched grid above the highly-resolved surface leads to a workload gain of more than 50% overall. Task X.7: Low-Mach / High-Mach regime: Implement numerical solvers that could be efficient at all Mach regime [97,98]. Evaluation of modifications for our spectral difference solver. Validate High/low plasma beta regimes (ratio of gas pressure to magnetic pressure) Task X.8: Validate GLOBUS2 code with benchmark on convective dynamo [92] and emergence [88, 89] Task X.10: Implement realistic microscopic physics such as: OPAL equation of state (EoS) [93], OPAL opacity [94] or Opacity project [95; 96 – web service] opacity look up tables with various metallicity Z input, Partial ionization of species. Improve top boundary conditions by allowing non-impenetrable wall for dynamo simulations and realistic atmosphere (WP1-WP2-WP4). Task X.11: evaluate performance of parallel in time techniques. Task X.12 Depending on progress, the implementation of non-grey atmosphere will be investigated in Globus2. With the experience gained with Bifrost and Muram codes and the expertise in radiative transfer at IAC and Maison de la Simulation, we clearly have all the required know-how to implement radiative transfer methods. The code infrastructure will be design such as to allow easy expansion of the equations set to include a better treatment of the radiative hydrodynamics effects. In a first stage, we will rely on statistics of the flow coming from local simulations to improve the realism of the atmosphere considered in the global dynamo simulations.

----------------------

See also :

Strugarek A., Beaudoin P., Charbonneau P., Brun A.S., Do Nascimento Jr J.D. solar and stellar magnetic cycles with nonlinear dynamo simulations", Science (14/07/2017)

Augustson, K., Bruin, A.S., Toomre, J., ApJ 809, 149, (2015)

Gudiksen B., Carlsson, M. et al. A&A, 531,154, (2011)

Brun, A.~S., Miesch, M.~S., Toomre, J., ApJ, 614, 1073-1098 (2004)

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Press release CEA-CNRS (Published on 25 October 2018 )

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MPG Newsroom (Published on 23 October 2018 )

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