Research example:
Distribution of the coronal energy input
in space, time and energy

We investigate the spatial and temporal evolution of the heating of the corona of a cool star such as our Sun in a three-dimensional magneto-hydrodynamic (3D MHD) model. For this we solve the 3D MHD problem numerically in a box representing part of the (solar) corona. The self-consistent heating mechanism is based on the braiding of magnetic field lines rooted in the convective photosphere. Magnetic stress induced by photospheric motions leads to currents in the atmosphere that heat the corona through Ohmic dissipation.

While the horizontally averaged quantities, such as heating rate, temperature, or density, are relatively constant in time, the simulated corona is highly variable and dynamic, on average reaching the temperatures and densities as found in observations. The strongest heating per particle is found in the transition region from the chromosphere to the corona. The heating is concentrated in current sheets roughly aligned with the magnetic field and is transient in time and space. This supports the idea that numerous small heating events heat the corona, often referred to as nanoflares.

click on image for a larger version
In the above image the left panel shows the distribution of the energy realeases as a function of eenergy. The distribution is close to a power law, with a prominent knee around 1017 J (=1024 ergs). Below the knee the slope is flatter than -2, above the knee it is steeper than -2. Consequently the major part of the energy is deposited around the knee. This is emphasized by the right panel which shows a clear peak of the energy input into the corona near energies of 1017 J. This energy roughly coincides with the energy for nanoflares as predicted by Parker (1983).

click on image for a larger version

In the model we can also investigate the energy input along individial field lines. The above figure shows just one example. Here as a function of the loop length and in time we shows the heating ratem, temperature and vertical velocity. This shows that the heat input along each fieldline (on average) drops with hight, and in particular that the heat input in one loop can be steady in one leg and bursty in the other leg. The middle and right panel show the response of the corona to this heating rate, i.e., when the plasam is heated it gets hotter and material is evaporated from the chromosphere. Thus this 3D model captures also the thermal evolution as found before in 1D loop models.

More inforation can be found in the following publications:

Nanoflare statistics in an active region 3D MHD coronal model
Bingert S., Peter H. (2013) A&A 550, A30
Link to ADS

Intermittent heating in the solar corona employing a 3D MHD model
Bingert S., Peter H. (2011) A&A 530, A112
Link to ADS