We present a method newly developed at the Astrophysikalisches Institut Potsdam (AIP) for determining the structure and the strength of coronal magnetic fields during the late phase of solar flares.

Fiber bursts

Fiber bursts are a spectral fine structure occuring in some type IV radio burst continua. Here we assume that the fiber bursts are excited by whistler waves and their interaction with nonthermal electrons trapped in a magnetic loop. The model is referenced in detail in the full paper (Aurass, H., Rausche, G., Mann, G., Hofmann, A.: Astron. Astrophys. 435, 1137, 2005). It is important to know that the whistler waves propagate dominantly parallel to the magnetic field under coronal conditions.

For the analysis we use dynamic radio spectra (regular AIP observations), Nançay Radio Heliograph data (Courtesy: Observatory Paris-Meudon, France), and SOHO-MDI photospheric field data (Solar and Heliospheric Observatory, Michelson Doppler Imager, courtesy: NASA/ESA).

Method

From the radio spectrum (first image, right panel) we derive the frequency drift rate and the instantaneous bandwidth of fiber bursts. Applying the whistler wave dispersion law we find from the spectral data an estimate of the magnetic field strength in the fiber burst source volume.

From the radio images we must find the 2D fiber burst source sites at least at 2 frequencies, in projection on the solar disc. From the SOHO-MDI magnetogram we compute the (potential or force-free) extrapolation of the magnetic field in the corona.

Comparing the 3D set of extrapolated field lines with the radio images of the fiber bursts a subset of field lines is selected, crossing the radio source at the Nancay imaging frequencies (first image, left panel). Next, we change the density model – and thus vary the height of a given observing frequency – until we obtain the best coincidence of the field strength derived from the “fiber burst source fieldlines” and from the spectral data (independently).

Right panel: AIP radio spectrum with fiber bursts (dark features indicate bright emission). The abscissa is the time (60 s) and the ordinate is the observing frequency corresponding (by an electron density model) with the height above the photosphere.

Left panel: Part of a SOHO-MDI magnetogram, red and blue: magnetic north and south polarity. Thin arcs: magnetic field lines passing all fiber burst source sites (the boxes assigned by arrows with the observing frequency). We have plotted a perspective view using a 3.5 times Newkirk coronal density model. Thick line (magenta): the average fiber burst field line for a certain time interval during the flare.

Example

As an example we have studied the evolution of the 7 April 1997 14 UT event. In this case, the evolution of the postflare loop magnetic field can be observed within one hour after the onset of the impulsive flare phase. The colored magnetic field lines (yellow, magenta, green) are selected as characterizing the evolution of the eruption in the time intervals 15, 30, and 40 min after the onset of the impulsive flare energy release.

Yohkoh soft X-ray image of the flaring active region (N–upwards, W–to the right) with superposed potential field lines (grey) and overplotted flare-activated field lines selected by means of the fiber burst radio sources. Yellow line – 15 min after flare start, magenta – 30 min, green – 40 min after onset.

The magnetic field strength, measured along the same field lines, can be given as a function of height above the photosphere: Measured coronal magnetic field strength along the flare-activated field lines (PFL) versus height over the photosphere. Same color code as in the first image. Red dots give the average field strength in the active region (potential field). Red curve (DM) is the mean active region magnetic field after the Dulk and McLean model.

For comparison, we give here the widely accepted model of the active region coronal magnetic field (‘DM’) after Dulk and McLean (Solar Phys. 57, 279, 1978). For the analyzed event, the field strength in postflare loops is roughly one order of magnitude lower than the model field strength. As a confirmation of the results we can reconstruct from the selected activated field regions the spreading speed of the postflare loop footpoints, which is in agreement with the independent measurements from the soft X-ray and Ultra-Violet coronal images (Yohkoh and SOHO spacecrafts).

According to our knowledge this result is the first direct measurement of coronal magnetic fields underneath an erupting flux rope and it is relevant for flare models and for diagnostics of coronal loops by MHD waves.