Xudong Sun1, for the CGEM Collaboration
1. W. W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA 94305-4085
The lower solar corona is dominated by magnetic fields that power explosive events which, in turn, can disturb the near-Earth environment by causing extreme space weather. The CGEM (Coronal Global Evolutionary Model) project (PI: G. Fisher) is developing a new coronal model driven by observations of the photospheric magnetic field to better understand and describe its dynamics. We describe our first data product: the Lorentz force estimate1 based on HMI active region (AR) vector magnetograms.
The total Lorentz force acting on a plasma at and above the photosphere may be estimated using a surface integral of the photospheric magnetic field2. The vertical component Fz, for example, is proportional to the integrated horizontal field squared minus the vertical field squared (Bh2-Bz2). Such estimates can be useful in diagnosing the coronal plasma dynamics.
Recent HMI observations have shown that Bh generally increases near the polarity inversion line during major eruptive events3. The value of Fz thus exhibits a jump, resulting in a Lorentz force impulse. One may infer the mass of the ejecta from the time-difference of Fz, assuming the impulse provides the initial momentum2. The change of torque from the horizontal Lorentz force Fh has also been linked to the sudden angular velocity change of rotating sunspots during a large flare4.
Figure 1 Maps for SHARP 377 (NOAA AR 11158) on 2011 Feb 15. Weak-field regions are masked out and shown as white; only the central part of the AR is shown. (a) Vector magnetic field map for 01:36 UT, right before the X-class flare. (b) Vertical Lorentz-force map, Fz, for 01:36 UT. Values are calculated as (Bh2-Bz2)dA, where dA is the pixel area (~1.3*1015 cm2). (c) Map of differences in Fz between post-flare (02:36 UT) and pre-flare (01:36 UT) data. A large increase is seen near the central polarity inversion line at around (34,-20).
We compute the Lorentz force every 12 minutes for each Space-weather HMI Active Region Patch (SHARP, ref. ). Results are provided as 1) maps of the integrand (e.g., (Bh2-Bz2)dA) as “force density”; 2) various integrated indices, both over the whole image and over the strong-field pixels only (see Table 1 of ref. ). Figure 1 shows an example of the Fz maps for AR 11158, which produced an X-class flare at 01:44 UT on Feb 15, 2011. Figure 2 shows a time profile of the indices during the flare and over several days.
Figure 2 Evolution of the integrated Lorentz forces for SHARP 377 (NOAA AR 11158). (a) Vertical Lorentz force Fz integrated over strong-field pixels (index name TOTFZ1) during the X-class flare. The rapid, permanent Bh increase leads to the Fz increase. The Fz decreases in the peripheral regions (Fig 1(c)), and the total returns to the pre-flare value within an hour. (b) Three Lorentz-force components in strong-field pixels over five days. A six-hour periodicity caused by spacecraft velocity is obvious. The east-west component Fx (TOTFX1) appears to scale linearly with the AR longitude. The flare signal is small compared to the systematic periodic uncertainties.
We note that these estimates should be interpreted with care. As shown in Figure 2, the periodic variations caused by the spacecraft’s orbital velocity are larger than the flare signal; evolution of the AR also contributes. Generally speaking, only values differenced during eruptive events (e.g. tens of minutes) are physically meaningful. The Fx component also displays a longitudinal dependence that is not well understood. Investigation is underway.
The data are now available through the JSOC website (data series name cgem.Lorentz) like other HMI data. For a detailed description of the content, usage, and known uncertainties, please refer to reference .
 Sun, X. for the CGEM team, 2014, arXiv: 1405.7353, http://arxiv.org/abs/1405.7353
 Fisher, G. H., Bercik, D. J., Welsch, B. T., & Hudson, H. S. 2012, Solar Phys, 277, 59
 Sun, X., Hoeksema, J. T., Liu, Y., et al., 2012, ApJ, 748, 77
 Wang, S., Liu, C., Deng, N., & Wang, H., 2014, ApJ Lett, 782, L31
 Bobra, M. G., Sun, X., Hoeksema, J. T., et al., 2014, Solar Phys., doi: 10.1007/s11207-014-0529-3