Research Projects

Equatorward migration of the Sun's magnetic field

Sunspots on the solar surface are one manifestation of the solar activity cycle. They tend to appear at mid-latitudes in the beginning of the cycle and tend to occur at low latitudes towards the end. This pattern is believed to be connected to the underlying toroidal magnetic field, which migrates equatorward during the cycle, see Figure 1 for an illustration.

Global spherical shell simulations of convectively driven magnetic field generation could only produce poleward migrating or constant magnetic fields (e.g. Gilman 1983, Brun et al. 2004, Nelson et al. 2013). Just recently, my collaborators and I were able to reproduce for the first time solar--like equatorward migrating magnetic fields (Käpylä et al. 2012, 2013), see Figure 2 for an illustration. Later on, we could relate this equatorward migration to the negative radial shear present in the simulations (Warnecke et al. 2014) following a simplified magnetic field propagation model (Parker-Yoshimura Rule, see Parker 1955, Yoshimura 1975). It turns out that this rule can explain the propagation of magnetic

fields surprisingly accurately in a variety of global simulations of convection (Warnecke et al 2015b). This result has important implications for the Sun: it constrains the region of magnetic field generation to the upper part of the convection zone, where the radial shear is negative.

Figure 1: Synoptic magnetogram of the solar magnetic field for the 3,5 cycles. It shows clearly the equatorward migration and polarity change of the magnetic field.

Figure 2: Solar-like equatorward migration of the magnetic field from a global simulation of magnetic field generation by convection in spherical shells. The toroidal magnetic field averaged over the azimuthal direction is shown as a function of latitude and time (Käpylä et al. 2012, 2013, Warnecke et al. 2014)

Formation of Flux Concentrations

Sunspots on the solar surface appear to be dark, because a strong magnetic field suppresses the convective heat transport. Although high-resolution observations of sunspots exist for the solar surface, the process leading to their formation is still debated. In the most accepted theory, it is believed that flux tubes rise from inside the Sun to the surface generating bipolar regions of sunspots ( e.g. Caligari et al.1995). This theory shows some difficulties and therefore alternative approaches have been developed, where flux concentrations are generated near the surface (Brandenburg et al. 2011, Stein & Nordlund 2012). One idea is that a hydromagnetic instability causes a spontaneous formation of sunspots. There, magnetic field suppresses locally turbulent pressure, leading to an inflow of material. These inflows drag along more magnetic fields, which then enhances the effect of suppressing the turbulent pressure. We were able to show that this effect can produce bipolar magnetic regions (Warnecke et al. 2013, 2015a). As seen in Figure 3, the two magnetic spots show some similarities to sunspots. These results have a large impact on the formation mechanism of sunspots and active regions as well as starspots.

Figure 3: Bipolar magnetic region. The normalized magnetic energy is shown at the corresponding surface. This illustrates the possibility to form bipolar magnetic flux concentrations by a turbulent hydromagnetic instability (Warnecke et al. 2013, 2015a).

Movie 1: Formation of a bipolar magnetic region. The normalized vertical magnetic field is shown at the corresponding surface (Warnecke et al. 2013, 2015a).

Spoke--like Differential Rotation With a NEAR--SURface shear layer

The Sun is rotating differentially, the equator faster than the poles. Furthermore, the solar differential rotation profile shows conical contours of constant rotation rate (Figure 4), which has been known since the advent of helioseismology (Schou et al. 1998). This technique, where one identifies discrete wave modes on the surface of the Sun and inverts their properties, allows measuring the velocity and temperature distribution inside the convection zone with high precision. Mean-field models, where velocity fluctuations are parameterized by transport coefficients, could successfully reproduce the solar differential rotation (e.g. Kitchatinov & Rüdiger 1995). However, direct numerical simulations (DNS) of turbulent convection had to impose a latitudinal entropy gradient or a sub-adiabatic layer to obtain spoke--like differential rotation (e.g. Miesch et al. 2006, Brun et al. 2011). For the first time I was able to produce a spoke-like differential rotation pattern in DNS, which was generated self-consistently in a global model of turbulent convection with a coronal envelope (Warnecke et al 2013). Additionally, and for the first time theses simulations could also produce a near-surface shear layer at low latitudes. This leads to the insight that the temperature structure at the surface is a very important ingredient to reproduce the correct rotation profile of the Sun (Warnecke al. 2015b). Additionally, the non-alignment of entropy and temperature gradients in the convection zone is responsible to achieve a non-cylindrical rotation profile. These results could confirm results from mean-field models and provide a new understanding of the generation of differential rotation in  global convection simulations.

Figure 4: The internal differential rotation of the Sun as obtained from helioseismology.

The bottom of the convection zone lies at r = 0.713 solar radii. Image courtesy of GONG.

Figure 5: The internal differential rotation of a global spherical shell simulation of convective driven dynamo. The rotation rate is normalized by the mean rotation rate (Warnecke et al 2013).

Coronal ejection driven by magnetic field generation

The generation of magnetic fields and the ejection of magnetized plasma from the Sun have been separated research fields in solar physics. We made in Warnecke et al. (2010) an attempt to combine these fields of research driven by two main reasons:

Firstly, for an effective production of magnetic field below the surface of the Sun, it is essential to transport magnetic helicity (dot product of magnetic vector potential and its magnetic field) to the surface and eventually out of the Sun. Coronal mass ejections are one promising way to do it (Blackman & Brandenburg 2003). Secondly, in the commonly used setup for modeling eruptions of coronal magnetic field and mass, an observed magnetic field and velocity configuration is taken for granted, neglecting underlying magnetic amplification mechanism, which actually generate these configurations. In Warnecke et al. (2010), we could already produce plasmoid ejections. With an improved model of Warnecke et al. (2011), we could generate self-consistent ejections, which have a similar shape than the observed solar coronal mass ejections, see Figure 7 for an illustration. In this simulation magnetic field gets ejected as a bipolar structure, in Figure 7 plotted as the current helicity density, which is a good proxy for helical magnetic at small scales.  Later in Warnecke et al. (2012), we was able to generate ejections driven by convectively generated magnetic fields, where the structure and shape of the ejected material was similar to that of earlier simulations. This approach of combining the region below the solar surface, where the magnetic field is generated and the solar corona is an innovative idea, which led to important insights into the coupling of the convection zone and the outer atmosphere of the Sun.

See more here.

Figure 6: Coronal Mass Ejections (CME) observed by LASCO@ SOHO

Figure 7: Illustration of a coronal ejection of current helicity. Current helicity is the dot product of the magnetic field and its current density representing twisted magnetic field structures. On the left hand side of the plot, the solar convection zone has a negative sign (dark blue) of current helicity in the northern hemisphere and a positive sign (light yellow) in the southern hemisphere. The right hand side shows the neutral (orange) coronal extension containing a bi-helical ejection of current helicity (yellow and blue) (Warnecke et al. 2011).