Research projects

  • Comprehensive magneto-convection simulations including the solar photosphere
  • Subphotospheric structures
  • Dynamics of the Sun's large-scale magnetic field
  • Stellar magnetism
  • Past projects

  • Comprehensive magneto-convection simulations including the solar photosphere

    Quiet-Sun magnetic fields

    Dynamics of vortex flows and accompanying MHD wave modes in the lower solar atmosphere.

    N. Yadav, R. Cameron

    Magnetic fields are generated in the turbulent solar interior, cross the photosphere and extending into the solar atmosphere where they become space filling. Observations indicate that the vortices couple the solar interior with the atmosphere, carrying energy from the solar interior to the outer atmosphere. We use MURaM simuations of radiative magnetoconvection extending across the photosphere and identify vortices using an eigenanalysis of the velocity gradient tensor. We find rapidly swirling features which are sites of local heating. These swirling structures extend upwards from the photosphere into the outer atmosphere. We also find that although the velocity streamlines are showing swirling structures, the associated test particle pathlines are more consistent with wave-like motion.

    Snapshot of velocity streamlines for a vortex displaying relatively low pressure on vortex site.

    Quiet-Sun magnetic fields

    Observations and modelling of Poynting flux through the solar photosphere

    P. Chitta, R. Cameron

    The transport of magnetic energy generated by convective motions through the photosphere into the solar atmosphere is believed to heat the solar and stellar coronae to several million degrees. We combine state-of-the-art numerical simulations and the available highest spatial resolution observations (~ 75 km) to understand the magneto-convective processes and their observable signatures. For numerical simulations we use MURaM, a 3D MHD code that provides realistic simulations of the solar magneto-convection in the photosphere. For observations we use data obtained from the two flights of Sunrise, and GREGOR telescope among other space and ground based telescopes.

    The figure shows simulated magnetic field at photospheric height. The solid lines are magnetic field lines that expand into the solar atmosphere. Studying how these field lines are advected due to turbulent convection will give us a handle on the Poynting flux through the solar atmosphere.

    Quiet-Sun magnetic fields

    Small-scale dynamo action

    A. Vögler, M. Schüssler, R. Moll, J. Pietarila Graham, R.Cameron, S. Danilovic

    Various observations indicate the existence of significant amounts of magnetic flux ubiquitous in the `quiet Sun', i.e., outside active regions, with mixed polarity on small scales. Since idealized Boussinesq closed-box simulations of Cattaneo (ApJ, 1999) showed dynamo action of non-helical instationary convection, the existence of a similar process based upon granular convection of the Sun has been discussed. Removing the idealizations in a realistic simulation with the MURaM code, we have found that solar surface convection seems indeed capable of supporting a dynamo process: for sufficiently large magnetic Reynolds number, the magnetic energy of an initial weak seed field grows exponentially and saturates at levels consistent with the observational inferences.

    The generated surface field has a small/scale structure with mixed polarity (right panel: vertical field image near optical unity; the size of the magnified inset is about 1200 km x 1200 km on the Sun) and shows an association with the intergranular downflow lanes.

    Spectral transfer analysis of the MURaM dynamo rules out the tangling of magnetic field lines (turbulent cascade) and Alfvénization of turbulent velocity fluctuations ("turbulent induction") as sources of small-scale magnetic field (see figure below). Rather, small-scale fluid motions stretch small-scale magnetic field to produce more small-scale magnetic field and the scales involved become smaller with increasing Reynolds number. This is a small-scale turbulent dynamo.

    Rate of magnetic energy production by stretching (blue solid) and compression (blue dotted), magnetic energy lost (red) and gained (black) from the turbulent cascade versus horizontal spatial frequency. Magnetic field is produced predominantly at scales near 65 km from stretching motions.

    Vertical cuts of the vertical component of the magnetic field (top), and vertical velocity (bottom) from a dynamo simulation. The magnetic field is concentrated in the turbulent down flow lanes.

    The basic dynamo mechanism was found to be a universal property of magnetic fields and turbulent morions, with the same process operating in homogeneous turbulence, convectively driven turbulence and in our comprehensive photospheric simulations.


  • A solar surface dynamo, Vögler, A.; Schüssler, M., Astron. Astrophys., 465, L43-L46 (2007).
  • Turbulent small-scale dynamo action in solar surface simulations, J. Pietarila Graham, R. Cameron, M. Schüssler, ApJ, Vol. 714, pp. 1606-1616, 2010
  • Universality of the Small-Scall Dynamo Mechanics , R. Moll, J. Pietarila Graham, J. Pratt, R. H. Cameron, W.-C. Müller, M. Schüssler, ApJ, Vol. 736, article id. A36, 2011

    Turbulent solar magnetic fields

    J. Pietarila Graham, S. Danilovic, M. Schüssler

    Observations of small-scale magnetic fields fields from Hinode and numerical simulations of dynamo action in the photospheric layers of the Sun are compared. Using turbulence theory to motivate self-similar scaling laws, a lower bound of 50G is derived for the unsigned quiet-Sun vertical flux. This agrees with our MURaM simulation-based estimate and (considering vector magnitudes) resolves the discrepancy between Hanle and Zeeman observations.

    Top: Portion of magnetic flux remaining after averaging over boxes of increasing size (from Hinode observation). A self-similar power-law is abundantly clear for 2 decades of length scales down to the resolution limit. Bottom: Flux remaining after averaging over 200 km X 200 km boxes for MURaM as a function of magnetic Reynolds number, ReM. Extrapolation to solar ReM indicates at least 80% cancellation at 200 km resolution.

    Probability distribution functions of magnetic field strengths from the simulations (solid line), from the Hinode observations (dashed lines), the inversions of synthetic stokes-diagnostics created from the simulations (dash dot) and when an observational noise level of 0.0011 is added (dotted line). The observational peak that was previously considered solar is seen to be solely due to noise.


  • Turbulent Magnetic Fields in the Quiet Sun: Implications of Hinode Observations and Small-Scale Dynamo Simulations, Pietarila Graham, J., Danilovic, S., Schüssler, M., ApJ, Volume 693, 1728-1735 (2009).

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    Understanding the observed brightness of magnetic elements

    D. Röhrbein, S. Danilovic, R. H. Cameron, M. Schüssler

    One use of comprehensive photospheric simulations is to better understand observations. In this work we have focussed on trying to understand the observed intensity flux relationship which shows that beyond a certain level the intensity of points associated with high magnetic field strengths begins to fall even when pores and sunspots are excluded. We found that the observed relationship could be explained by the limited resolving power of available telescopes. The prediction is that as higher resolution telescopes become available a monotonic increase in intensity with field strength will be found outside of sunspots/pores.
  • Is there a non-monotonic relation between photospheric brightness and magnetic field strength in solar plage regions? , D. Röhrbein, R. H. Cameron, M. Schüssler, A & A, Vol. 532, id. A140, 2011

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    Vortices in the solar atmosphere

    R. Moll, R. H. Cameron, M. Schüssler

    Where the magnetic field is weak, the upper photosphere is dominated by acoustic shocks. As the magnetic field increases the shocks are supressed and field-aligned vortices become dominant. Similar to the shocks, they heat the plasma and provide a possible chanel for transporting energy into the overlying chromosphere.

    Vortices in a weak plage simulation are aligned with the magnetic field which couple the different layers of the atmosphere.


  • Vortices in simulations of solar surface convection , R. Moll, R. H. Cameron, M. Schüssler, A & A, Vol. 533, id. A126, 2011
  • Vortices, shocks, and heting in the solar atmosphere: effect of a magnetic field , R. Moll, R. H. Cameron, M. Schüssler, A & A, Vol. 541, id. A68, 2012

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    The umbra

    M. Schüssler, A. Vögler (Univ. of Utrecht)

    The strong magnetic field (from 2000 G to more than 4000 G) in a sunspot umbra suppresses the normal granular convection. Simulations with the MURaM code have shown that the convective energy transport instead occurs in the form of narrow hot upflow plumes, which appear as bright patches before a dark background (see brightness image to the left, spatial scale in Mm). Their sizes, contrasts and lifetimes are similar to the observed properties of so-called `umbral dots'.

    The left panel shows the brightness, with the units on the axes being in Mm. The vertical velocity image (middle panel) taken near the level of optical depth unity shows that the upflows in the plumes (blue) are surrounded by narrow downflow channels (red). The strong expansion of the upflow plumes with height due to the pressure stratification leads to a strong expansion of the plumes and a concomitant reduction of the magnetic field strength (right panel) in the upper layers. Near optical depth unity, the hot material in the plume loses its buoyancy and piles up in a cusp-shaped structure, leading to the appearance of dark lanes in the brightness image.


  • Magnetoconvection in a Sunspot Umbra, Schüssler, M. & Vögler, V., ApJ, Volume 641, Issue 1, pp. L73-L76 (2006).

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    The penumbra

    M. Rempel, M. Schüssler, M. Knolker, R. H. Cameron

    Using comprehensive simuilations of the solar photosphere, the nature of the penumbra has been studied. Essentially the penumbra is the preferred form of convection in a strong, inclined magnetic field.
    Visualization of the structure of a fully 3d sunspot studied using comprehensive radiative magnetoconvection simulations.


  • Radiative Magnetohydrodynamic Simulation of Sunspot Structure, M. Rempel, M. Schüssler, M. Knölker, ApJ, Vol. 691, pp. 640-649, 2008
  • Penumbral Structure and Outflows in Simulated Sunspots, M. Rempel, M. Schüssler, R. Cameron, M. Knölker, Science, Vol. 325, pp. 171-174, 2009

    Active Regions

    M. Cheung (LMSAL, Palo Alto), M Schüssler, F. Moreno-Insertis (IAC, Tenerife/Spain)

    Magnetic fields exist over a wide range of length- and time-scales on the solar photosphere. We investigate the flux emergence process by carrying out realistic simulations of emerging flux tubes in the photosphere with the MURaM code. Since the effects of radiative transfer is included in our MURaM code, we are able to compare our simulation results with real photospheric observations of magnetic flux emergence.

    The picture on the left shows a transient dark lane marking the site of flux emergence. The properties of this dark lane are different from those of normal granulation. The animation to the right shows a synthetic greyscale `magnetogram' (white and black indicating the two opposite magnetic polarities) from the simulated emergence of a magnetic loop. The upper panel gives the original resolution of the simulation while the lower panel results after smearing with a Gaussian to be comparable with a typical ground-based observational result.


  • Solar Surface Emerging Flux Regions: A Comparative Study of Radiative MHD Modeling and Hinode SOT Observations, M. Cheung, M. Schüssler, T. D. Tarbell, A. M. Title, ApJ, Vol. 687, pp. 1373-1387, 2008
  • Magnetic flux emergence in granular convection: radiative MHD simulations and observational signatures, Cheung, M. C. M.; Schüssler, M.; Moreno-Insertis, F., Astron. Astrophys., 467, 703-719 (2007).
  • MURaM website

    Subphotospheric structures

    Subsurface structure of sunspots

    R. Cameron, H. Schunker, A. Pietarila, L. Gizon

    We have investigated the way in which waves propagating inside the Sun are affected by the presence of a sunspot. Our simulations nicely reproduce the observed helioseismic signature and indicate that most of the seismic signature is coming from the surface perturbation caused by the sunspot.
    Shown is an f-mode (suface gravity) after it has propagated trought a sunspot. The sunspot is centred at the origin and the waves are propagating from left to right. The lower half of the image shows the result of the calculation, the top half is the result from helioseismological measurements.


  • Constructing Semi-Empirical Sunspot Models for Helioseismology Modeling the Subsurface Structure of Sunspots , R. H. Cameron, L. Gizon, H. Schunker, A. Pietarila, Solar Phys., Vol. 268, pp. 293-308, 2011
  • Helioseismology of sunspots: confronting observations with three-dimensional MHD simulations of wave propagation, R. Cameron, L. Gizon, T. L. Duvall, Solar Phys., Vol 251, pp. 291-308, 2008

    Dynamics of the Sun's large-scale magnetic field

    The generation of toroidal field and the Babcock-Leighton dynamo

    R. Cameron, M. Schüssler

    We have applied Stokes theorem, combined with Hales law, to show that the large-scale toroidal field which produces sunspots is produced by the Babcock-Leighton dynamo mechanism.

    Shown is the contour used in determining the generation of toroidal field in each hemisphere using Stokes theorem.


  • The crucial role of surface magnetic fields for the solar dynamo, R. Cameron, M. Schüssler, Science, Vol. 347, 1333, 2015

    From the photosphere to the heliosphere

    Baumann, I., J. Jiang, R. Cameron, D.Schmitt, M. Schüssler

    We aim to model the heliospheric magnetic field, especially near the earth, using the historical sunspot record. This will allow us to reconstruct the heliospheric field back to the end of the Maunder minimum. The sunspot record is used as input data, and is evolved using the Surface Flux Transport model. The heliospheric field is then obtained using the Current Sheet Source Surface model.

    Upper panel: The temporal evolution of polar field, solar surface total flux density and open flux density. Lower panel: The temporal evolution of the solar surface field distribution from the SFT simulation and the location of the open flux.


  • Modeling the Sun's open magnetic flux and heliospheric current sheet, J. Jiang, R. H. Cameron, D. Schmitt, M. Schüssler, ApJ, Vol. 709, pp. 301-307, 2010
  • Modeling the Sun's open magnetic flux, Schüssler, M. & Baumann, I., Astron. Astrophys. 459, 945-953 (2006).

    Magnetic flux transport on the Sun

    I. Baumann, D.Schmitt, M. Schüssler, S.K. Solanki, J. Jiang, R. Cameron

    Active regions emerge on the photosphere as bipolar magnetic regions in the low-latitude sunspot-belts. The magnetic flux is dispersed by supergranular convective motions and meridional circulation. The differential rotation rate of the sun leads to a shearing of the flux pattern. The transport equation is derived from the induction equation resulting from the MHD-Approximation.
    We have also extended the model to include the effect of the cycle-related inflows into the activity region belts. This makes the SFT model nonlinear and provides an appealing explanation for the activity levels for cycles 13 to 21.

    Longitude averaged latitude-time diagram of the magnetic flux (upper panel), unsigned magnetic flux (middle panel) and meridional flow (lower panel) from the non-linear Surface Flux Transport model.


  • Are the strength of solar cycles determined by converging flows towards the activity belts? , R. H. Cameron, M. Schüssler, A&A (accepted)
  • The effect of activity-related meridional flow modulation on the strength of the solar polar magnetic field, J. Jiang, E. Isik, R. H. Cameron, D. Schmitt, M. Schüssler, ApJ, Vol. 714, pp. 597-602, 2010
  • A necessary extension of the surface flux transport model, Baumann, I., Schmitt, D. and Schüssler, M., Astron. Astrophys., 446, 307-314 (2006).
  • Evolution of the large-scale magnetic field on the solar surface: a parameter study, I. Baumann, D. Schmitt, M. Schüssler, and S. K. Solanki, Astron. & Astrophys., 426, 1075-1091 (2004).

    Flux Transport Dynamo modelling

    D.Schmitt, J. Jiang, E. Isik, R. Cameron

    We have began using the Flux Transport Dynamo framework to extend the results we have obtained using the SFT model to study the evolution of the field beneath the photosphere. Our results have in particular shown that reasonably strong magnetic pumping is required to match the (surface) observations.

    Poloidal field lines and toroidal field (blue/red) for cycle 19 froma FTD simulation including magnetic pumping and cycle-depenedent sunspot group tilt angles..

  • Surface flux evolution constraints for flux transport dynamo , R. H. Cameron, D. Schmitt, J. Jiang, E. Isik, A & A, Vol. 542, id. A127, 2012

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    Stellar magnetism

    Comprehensive simulations of stellar photospheres

    B. Beeck, R. H. Cameron, M. Schüssler, A. Reiners (Univ. Göttingen)

    We set up a series of six local-box simulations of cool main-sequence stars (6900 K ≥ Teff3680 K). For each set of stellar parameters, we have run one non-magnetic as well as three magnetic simulations with an imposed vertical magnetic field strength of 20 G, 100 G, and 500 G. For the non-magnetic simulations, we analysed the overall stratification, the granule sizes and life times as well as the impact of the convective flows on the limb darkening and on shapes of synthesised spectral line profiles (Beeck et al., 2013a, 2013b)

    (Teff = 6890 K, log g [cgs] = 4.301)
    (Teff = 5760 K, log g [cgs] = 4.438)
    (Teff = 4370 K, log g [cgs] = 4.699)
    (Teff = 3690 K, log g [cgs] = 4.826)
    Snapshots of the vertical bolometric intensity four non-magnetic stellar simulations. In all images the grey scale saturates at ± 2 σ, i. e. twice the standard deviation of the intensity. Note the significant difference of the length scale of the granules.

    The magnetic simulations revealed that the structure of small-scale magnetic flux concentrations substantially differs between solar-type and M-type stars. In Sun-like stars, small concentrations of magnetic flux in simulations with an average vertical field strength of up to 500 G mostly correspond to structures of enhanced intensity whereas, on M-type stars, these structures are mostly darker than the non-magnetic environment (Beeck et al., 2011). This different appearance is caused by the different radius-to-depth ratio of the optical surface depression caused by the magnetic flux tubes. In the Sun, the efficient convective collapse of thin flux tubes produces strongly evacuated structures with a low radius-to-depth ratio, which can be efficiently heated radiatively from the sidewalls. On M dwarfs the convective collapse is less efficient leading to much shallower depressions in the optical surface, with little radiative heating from their (small) walls (Beeck et al., 2015a).

    Comparison of the vertical bolometric intensity of snapshots from the G2V (=solar) and the M2V simulations both with an average vertical field of 500 G. The grey scale saturates at ± 2.5 σ, i. e. 2.5 times the standard deviation of the intensity. In the solar case, most of the magnetic flux concentrations appear bright (only the largest are dark), all flux concentrations on the M-star simulation have a significantly lower intensity than the unmagnetised parts of the surface.

    The impact of the magnetic field on the atmospheric structure leads to a strong correlation of velocity field, magnetic field and the radiation field, which leaves imprints in spectral line profiles. For some representative line profiles synthetic, line profiles were calculated. In many cases the line broadening by virtue of the Zeeman effect is opposed by a magnetically induced line weakening, which is caused by a strong reduction of the line opacities in magnetic small-scale structures (Beeck et al., 2015b). As these spectral lines are used for the detection and measurement of stellar magnetic fields, it is necessary to take effects like this into account in the interpretation of observations.

    Local vertical spectral line profiles for four points in a snapshot of the K0V-star simulation with 500 G average vertical field-strength. Points 1 and 2 are in an unmagnetised upflow and downflow, respectively. The height dependence of the velocity leads to asymmetries in the line profile. Points 3 and 4 are in a bright and dark magnetic structure respectively. By virtue of the Zeeman effect both spectral lines are split, however, due to the strongly modified thermodynamical structure, the opacity of the lines is also changed: the Fe line is weakened in the dark structure while the Ti line is weakened in the bright structure. The severe weakening of the Ti line is mostly due to ionisation of Ti I in the hot (bright) magnetic structure and will lead to a strong underestimation of the magnetic field from the disc-integrated spectral line profile (if a substantial fraction of the field is distriubuted over the stellar surface in form of small bright magnetic features).


    Coupled models of generation, emergence, and surface evolution of stellar magnetic flux

    E. Isik, D. Schmitt, M. Schüssler

    We develop a model which connects the missing link between deep-seated dynamos and the evolving surface flux in cool stars. The link, which is hitherto not included in any dynamo model, is the buoyant rise of magnetic flux tubes from the dynamo layer throughout the entire convection zone. We choose toroidal flux tubes with a spatial probability distribution determined by the mean toroidal magnetic field generated by a cyclic dynamo. As a first example, we use a thin-layer alpha-omega dynamo (Schüssler & Schmitt 1989) with Sun-like shear in the convective overshoot region. We carry out numerical simulations of the rise of Parker-unstable flux tubes (Caligari et al. 1995), which in turn determine the latitudes and the tilt angles of the emerging flux loops. This information is then put into a surface flux transport model (Baumann et al. 2004, 2006) with Sun-like differential rotation, meridional flow, and turbulent supergranular diffusion. In this part, we simulate the evolution of bipolar magnetic regions, which emerge with a Sun-like area distribution and with tilt angles and emergence latitudes determined by rising flux tubes.

    The figure on the left panel shows a comparison of the generated toroidal field pattern in the overshoot region (contours) and the emerging flux tubes on the surface (dots), for a star having solar internal structure but rotating 2.7 times faster than the Sun, hence representing somewhat a "younger Sun". The time-latitude diagram on the right-hand panel shows the surface evolution of longitudinally averaged magnetic flux density. The polar fields are about 20-30 times stronger than in the Sun, and the cyclic dynamo is no longer visible in the variation of magnetic flux integrated over the entire surface.


  • A coupled model of magnetic flux generation and transport in stars, Isik, E.; Schmitt, D.; Schüssler, M., Astron. Nachr., 328, 1111

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