Determination of magnetic helicity content of solar active regions from SOHO/MDI magnetograms

Abstract

Chae (2001) first proposed a method of self-consistently determining the rate of change of magnetic helicity using a time series of longitudinal magnetograms only, such as taken by SOHO/MDI. Assuming that magnetic fields in the photosphere are predominantly vertical, he determined the horizontal component of velocity by tracking the displacements of magnetic flux fragments using the technique of local correlation tracking (LCT). In the present paper, after briefly reviewing the recent advance in helicity rate measurement, we argue that the LCT method can be more generally applied even to regions of inclined magnetic fields. We also present some results obtained by applying the LCT method to the active region NOAA 10365 under emergence during the observable period, which are summarized as follows. (1) Strong shearing flows were found near the polarity inversion line that were very effective in helicity injection. (2) Both the magnetic flux and helicity of the active region steadily increased during the observing period, and reached 1.2 × 1022 Mx and 8 ×1042 Mx2, respectively, 4.5 days after the birth of the active region. (3) The corresponding ratio of the helicity to the square of the magnetic flux, 0.05, is roughly compatible with the values determined by other studies using linear-force-free modeling. (4) A series of flares took place while the rate of helicity injection was high. (5) The choice of a smaller window size or a shorter time interval in the LCT method resulted in a bigger value of the LCT velocity and a bigger value of the temporal fluctuation of the helicity rate. (6) Nevertheless when averaged over a time period of about one hour or longer, the average rate of helicity became about the same within about 10%, almost irrespective of the chosen window size and time interval, indicating that short-lived, fluctuating flows may be insignificant in transferring magnetic helicity. Our results suggest that the LCT method may be applied to 96-minute cadence full-disk MDI magnetograms or other data of similar kind, to provide a practically useful, if not perfect, way of monitoring the magnetic helicity content of active regions as a function of time.