Small-scale dynamo magnetism as the driver for heating the solar atmosphere

Journal name:
Nature
Volume:
522,
Pages:
188–191
Date published:
DOI:
doi:10.1038/nature14478
Received
Accepted
Published online

The long-standing problem of how the solar atmosphere is heated has been addressed by many theoretical studies, which have stressed the relevance of two specific mechanisms, involving magnetic reconnection and waves, as well as the necessity of treating the chromosphere and corona together1, 2, 3, 4, 5, 6, 7. But a fully consistent model has not yet been constructed and debate continues, in particular about the possibility of coronal plasma being heated by energetic phenomena observed in the chromosphere2, 3, 8, 9, 10, 11. Here we report modelling of the heating of the quiet Sun, in which magnetic fields are generated by a subphotospheric fluid dynamo intrinsically connected to granulation. We find that the fields expand into the chromosphere, where plasma is heated at the rate required to match observations (4,500 watts per square metre) by small-scale eruptions that release magnetic energy and drive sonic motions. Some energetic eruptions can even reach heights of 10 million metres above the surface of the Sun, thereby affecting the very low corona. Extending the model by also taking into account the vertical weak network magnetic field allows for the existence of a mechanism able to heat the corona above, while leaving unchanged the physics of chromospheric eruptions. Such a mechanism rests on the eventual dissipation of Alfvén waves generated inside the chromosphere and that carry upwards the required energy flux of 300 watts per square metre. The model shows a topologically complex magnetic field of 160 gauss on the Sun’s surface, agreeing with inferences obtained from spectropolarimetric observations12, 13, 14, chromospheric features (contributing only weakly to the coronal heating) that can be identified with observed spicules9 and blinkers10, 11, and vortices that may be possibly associated with observed solar tornadoes8.

At a glance

Figures

  1. Magnetic field and Poynting flux.
    Figure 1: Magnetic field and Poynting flux.

    a, Intensity of the total (black line), vertical component (blue) and current-free (green) magnetic field. b, Time averaged Poynting flux in the photosphere (red shading), chromosphere (orange) and corona (yellow) computed without (blue) and with (dashed blue) the presence of the large-scale vertical magnetic field (mimicking the supergranulation network). c, Selected field lines of the global magnetic configuration at time t = 52.17 min and characteristic features of its complex topology: a vertical twisted flux tube associated with a core of vortices/torsional motions (boxed area V), a twisted flux rope (TFR), and features that characterize the connection of the magnetic flux tubes to the photosphere, namely concentrated legs (CL) and bifurcating legs (BL). dg, Horizontal cuts of the vertical component of the magnetic field in the low photosphere (d, also background image in c), at the bottom of the chromosphere (e), and in the middle (f) and high (g) chromosphere.

  2. Twisted flux rope eruption.
    Figure 2: Twisted flux rope eruption.

    a–c, Vertical cuts at constant x of the logarithm of the square of the modulus of the electric current density (expressed in non-dimensional code units). a, The TFR section (boxed) clearly shows that its eruption is associated with opening of the configuration, with current layers structuring the atmosphere at those heights and above (see Supplementary Video 3). d–f, Selected field lines showing the evolution of the TFR seen in Fig. 1c, starting from the same time (52.17 min). The background image represents the vertical component of the magnetic field at z = 1,500 km, which appears to be organized in stronger ‘spots’ and can reach locally 30 G. d, e, The chromospheric trace of the TFR is associated with footpoints FP1 and FP2. Flux changes occur at its chromospheric ‘feet’ FP2 as seen from d to e. They imply topological constraints leading to the eruption of the TFR shown at two particular times in boxes E1 and E2 drawn in e and f, respectively.

  3. Torsional motions and Poynting vertical flux.
    Figure 3: Torsional motions and Poynting vertical flux.

    a, b, Horizontal slice of the horizontal component of the velocity field at two heights showing persistence of vortex/torsional motions with altitude when the vertical background field of 5 G is added. c, Horizontal slice at the same heights as in b of the vertical component of the velocity field associated with jet-like features forming in the regions free of vortices near the separatrices. d, z-component of the Poynting vector computed at the same heights as in b. There is clearly a correlation between the regions where it takes its largest values and the vortex/torsional motions shown in a and b. A large amount of energy is transported towards the upper corona through Alfvén waves. The labelled boxes show characteristic magnetic features: twisted flux rope (TFR), cusped flux tube (CFT) with coronal streamer-like shape, and vertical twisted flux tube (VTFT) guiding Alfvén waves.

  4. Temperature and density profiles.
    Extended Data Fig. 1: Temperature and density profiles.

    Shown are profiles of the temperature (blue), which is kept fixed during the simulation, and of the initial density profile (black), using the same colour code as in Fig. 1a for the various layers of the atmosphere.

  5. Parallel currents profile.
    Extended Data Fig. 2: Parallel currents profile.

    Shown is the profile of the average value of the parameter α associated with the electric currents running along field lines. This quantity appears to take high values in the confined lower and middle parts of the chromosphere. We use the same colour code as in Fig. 1b for the various layers of the atmosphere.

  6. Current-free magnetic configuration.
    Extended Data Fig. 3: Current-free magnetic configuration.

    Figure shows selected field lines of an idealized magnetic configuration which is current-free and has the same distribution of vertical component in the photosphere {z = 0} as the field shown in Fig. 1c (at time t = 52.17 min). The footpoints used to launch the field lines (from various planes) are the same as those used in Fig. 1c. Although often used in simple models of the quiet Sun, this kind of current-free configuration is very different from the one produced by our model. In particular, it does not exhibit, either in the chromosphere or above, many of the characteristic features (such as shear and twist) of large magnetic energy and electric current density.

  7. Pre-eruptive flow structure.
    Extended Data Fig. 4: Pre-eruptive flow structure.

    a, Horizontal velocity (vx, vy) computed at the top of the chromosphere (z = 2 Mm) at the same time (t = 52.17 min) as the configuration of Figs 1c and 2d. The flow pattern is clearly organized in regions containing vortex/torsional motions and other ones that are more ‘calm’. The feet of the TFR of Fig. 2d are located at the periphery of those flows. b, Zoom on one vortex/torsional flow structure V, just above the one shown on Fig. 1c, g, with the norm of (vx, vy) as background. c, Horizontal slice of the vertical component vz of the velocity at z = 3 Mm, where vz starts to show red and blue shifts in the vortex/torsional feature V, while vz is mostly negative below this height. Other boxed features, located at the same places as in a, are shown for information.d, Vertical slice of vz in the plane x = 6 Mm. Downward motions associated with CL almost reach the photosphere.

  8. Eruptive flow structure.
    Extended Data Fig. 5: Eruptive flow structure.

    a, Horizontal velocity computed at the top of the chromosphere (z = 2 Mm) at the same time (t = 63.50 min, that is, during the eruption phase) as the magnetic configuration of Fig. 2f. The eruptive area (E2) becomes free of vortex/torsional motions, which are still present elsewhere, as in the vortex/torsional feature (V) and concentrated legs (CL). Large vertical flows associated with the eruption of the TFR are correlated with a positive vertical component vz shown as a horizontal slice in b and as a vertical slice in c.

  9. Magnetic configuration with the addition of the background magnetic field.
    Extended Data Fig. 6: Magnetic configuration with the addition of the background magnetic field.

    Shown are selected field lines of the magnetic configuration at time t = 72.42 min (as in Fig. 3) corresponding to the case where a background vertical magnetic field of 5 G is added to mimic the effects of the supergranulation network. Several characteristic features are represented above an isosurface of the temperature fluctuations coloured with the vertical component of the magnetic field. They confirm and extend those of Fig. 1c: twisted flux rope (TFR), cusped flux tube (CFT) with coronal streamer-like shape, vertical twisted flux tube (VTFT) guiding Alfvén waves, and magnetic arcades (MA). The structures coloured in grey and green, respectively, are VTFT.

Videos

  1. Dynamo solution seen at the Sun’s surface
    Video 1: Dynamo solution seen at the Sun’s surface
    Temperature (left panel) and vertical component of the magnetic field (right panel) produced by the sub-surface dynamo model. The temperature is structured at the granulation scale while the magnetic field exhibits both granulation scale and mesoscale features. The magnetic field evolution clearly shows that flux cancellation of magnetic concentrations of opposite polarities occurs frequently all along the evolution.
  2. Flows and electric currents
    Video 2: Flows and electric currents
    Horizontal slice, taken at height z=2000 km, of the horizontal velocity field, with in background the square of the norm of the electric current density (expressed in non dimensional code units) predicted by the model. This reveals the presence of many current sheets structuring the atmosphere and bounding vortex/torsional motions.
  3. Time evolution seen through electric currents
    Video 3: Time evolution seen through electric currents
    Vertical slice, taken at x=6 Mm, of the square of the norm of the electric current density (expressed in non dimensional code units) predicted by the model. This reveals again the presence of many current sheets, small scale dynamics in the region of strong confinement of the magnetic field in the low chromosphere, in response to the flux changes seen in Video 1, as well as larger scale eruptions, as the one shown on Fig. 2.
  4. Jet like events
    Video 4: Jet like events
    Evolution of the vertical component of the velocity field, seen as a vertical slice during the simulation, when a larger scale vertical magnetic field of 5 G is present in the atmosphere. Jet like events occur repeatedly and reach the corona guided by the vertical magnetic field (Extended Data Figure 6).
  5. Dynamics of electric currents
    Video 5: Dynamics of electric currents
    Evolution of the electric current density in a vertical slice during the simulation when a larger scale vertical magnetic field of 5 G is present in the atmosphere. Up to the chromosphere, the magnetic field is still strongly confined as in the case without an added background magnetic field (Video 3), while above, eruptions and jet like events feed the corona, guided by the main vertical magnetic field (Extended Data Figure 6) close to the separatrix surfaces.
  6. Complexity near the transition region
    Video 6: Complexity near the transition region
    Observations at 1400 A° made on the west side of the solar limb by the IRIS mission on 2013-12-09 at 23:33 UT, with a cadence of 18.8 seconds between images. The video shows characteristic structures and their evolution on a time scale corroborating the results of our simulations. We have used data downloaded from http://iris.lmsal.com and processed them with help of standard solar packages, including the IRIS IDL routines available at http://www.lmsal.com/solarsoft/.

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Author information

Affiliations

  1. Centre de Physique Théorique, Ecole Polytechnique, CNRS, F-91128 Palaiseau Cedex, France

    • Tahar Amari &
    • Jean-François Luciani
  2. AIM – Unité Mixte de Recherche CEA – CNRS – Université Paris VII, UMR no. 7158, Centre d’Etudes de Saclay, F-91191 Gif sur Yvette Cedex, France

    • Jean-Jacques Aly

Contributions

T.A. and J.-F.L. planned the various calculations, and discussed the results with J.-J.A. The manuscript was written by T.A., J.-F.L. and J.-J.A.

Competing financial interests

The authors declare no competing financial interests.

Corresponding author

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Author details

Extended data figures and tables

Extended Data Figures

  1. Extended Data Figure 1: Temperature and density profiles. (181 KB)

    Shown are profiles of the temperature (blue), which is kept fixed during the simulation, and of the initial density profile (black), using the same colour code as in Fig. 1a for the various layers of the atmosphere.

  2. Extended Data Figure 2: Parallel currents profile. (169 KB)

    Shown is the profile of the average value of the parameter α associated with the electric currents running along field lines. This quantity appears to take high values in the confined lower and middle parts of the chromosphere. We use the same colour code as in Fig. 1b for the various layers of the atmosphere.

  3. Extended Data Figure 3: Current-free magnetic configuration. (481 KB)

    Figure shows selected field lines of an idealized magnetic configuration which is current-free and has the same distribution of vertical component in the photosphere {z = 0} as the field shown in Fig. 1c (at time t = 52.17 min). The footpoints used to launch the field lines (from various planes) are the same as those used in Fig. 1c. Although often used in simple models of the quiet Sun, this kind of current-free configuration is very different from the one produced by our model. In particular, it does not exhibit, either in the chromosphere or above, many of the characteristic features (such as shear and twist) of large magnetic energy and electric current density.

  4. Extended Data Figure 4: Pre-eruptive flow structure. (494 KB)

    a, Horizontal velocity (vx, vy) computed at the top of the chromosphere (z = 2 Mm) at the same time (t = 52.17 min) as the configuration of Figs 1c and 2d. The flow pattern is clearly organized in regions containing vortex/torsional motions and other ones that are more ‘calm’. The feet of the TFR of Fig. 2d are located at the periphery of those flows. b, Zoom on one vortex/torsional flow structure V, just above the one shown on Fig. 1c, g, with the norm of (vx, vy) as background. c, Horizontal slice of the vertical component vz of the velocity at z = 3 Mm, where vz starts to show red and blue shifts in the vortex/torsional feature V, while vz is mostly negative below this height. Other boxed features, located at the same places as in a, are shown for information.d, Vertical slice of vz in the plane x = 6 Mm. Downward motions associated with CL almost reach the photosphere.

  5. Extended Data Figure 5: Eruptive flow structure. (259 KB)

    a, Horizontal velocity computed at the top of the chromosphere (z = 2 Mm) at the same time (t = 63.50 min, that is, during the eruption phase) as the magnetic configuration of Fig. 2f. The eruptive area (E2) becomes free of vortex/torsional motions, which are still present elsewhere, as in the vortex/torsional feature (V) and concentrated legs (CL). Large vertical flows associated with the eruption of the TFR are correlated with a positive vertical component vz shown as a horizontal slice in b and as a vertical slice in c.

  6. Extended Data Figure 6: Magnetic configuration with the addition of the background magnetic field. (486 KB)

    Shown are selected field lines of the magnetic configuration at time t = 72.42 min (as in Fig. 3) corresponding to the case where a background vertical magnetic field of 5 G is added to mimic the effects of the supergranulation network. Several characteristic features are represented above an isosurface of the temperature fluctuations coloured with the vertical component of the magnetic field. They confirm and extend those of Fig. 1c: twisted flux rope (TFR), cusped flux tube (CFT) with coronal streamer-like shape, vertical twisted flux tube (VTFT) guiding Alfvén waves, and magnetic arcades (MA). The structures coloured in grey and green, respectively, are VTFT.

Supplementary information

Video

  1. Video 1: Dynamo solution seen at the Sun’s surface (23.66 MB, Download)
    Temperature (left panel) and vertical component of the magnetic field (right panel) produced by the sub-surface dynamo model. The temperature is structured at the granulation scale while the magnetic field exhibits both granulation scale and mesoscale features. The magnetic field evolution clearly shows that flux cancellation of magnetic concentrations of opposite polarities occurs frequently all along the evolution.
  2. Video 2: Flows and electric currents (27.98 MB, Download)
    Horizontal slice, taken at height z=2000 km, of the horizontal velocity field, with in background the square of the norm of the electric current density (expressed in non dimensional code units) predicted by the model. This reveals the presence of many current sheets structuring the atmosphere and bounding vortex/torsional motions.
  3. Video 3: Time evolution seen through electric currents (25.47 MB, Download)
    Vertical slice, taken at x=6 Mm, of the square of the norm of the electric current density (expressed in non dimensional code units) predicted by the model. This reveals again the presence of many current sheets, small scale dynamics in the region of strong confinement of the magnetic field in the low chromosphere, in response to the flux changes seen in Video 1, as well as larger scale eruptions, as the one shown on Fig. 2.
  4. Video 4: Jet like events (13.61 MB, Download)
    Evolution of the vertical component of the velocity field, seen as a vertical slice during the simulation, when a larger scale vertical magnetic field of 5 G is present in the atmosphere. Jet like events occur repeatedly and reach the corona guided by the vertical magnetic field (Extended Data Figure 6).
  5. Video 5: Dynamics of electric currents (18.67 MB, Download)
    Evolution of the electric current density in a vertical slice during the simulation when a larger scale vertical magnetic field of 5 G is present in the atmosphere. Up to the chromosphere, the magnetic field is still strongly confined as in the case without an added background magnetic field (Video 3), while above, eruptions and jet like events feed the corona, guided by the main vertical magnetic field (Extended Data Figure 6) close to the separatrix surfaces.
  6. Video 6: Complexity near the transition region (10.43 MB, Download)
    Observations at 1400 A° made on the west side of the solar limb by the IRIS mission on 2013-12-09 at 23:33 UT, with a cadence of 18.8 seconds between images. The video shows characteristic structures and their evolution on a time scale corroborating the results of our simulations. We have used data downloaded from http://iris.lmsal.com and processed them with help of standard solar packages, including the IRIS IDL routines available at http://www.lmsal.com/solarsoft/.

Additional data