On the Lorentz Force and Torque of Solar Photospheric Emerging Magnetic Fields

Abstract

Magnetic flux generated and intensified by the solar dynamo emerges into the solar atmosphere, forming active regions (ARs) including sunspots. Existing theories of flux emergence suggest that the magnetic flux can rise buoyantly through the convection zone but is trapped at the photosphere, while its further rising into the atmosphere resorts to the Parker buoyancy instability. To trigger such an instability, the Lorentz force in the photosphere needs to be as large as the gas pressure gradient to hold up an extra amount of mass against gravity. This naturally results in a strongly non-force-free photosphere, which is indeed shown in typical idealized numerical simulations of flux tube buoyancy from below the photosphere into the corona. Here we conduct a statistical study of the extents of normalized Lorentz forces and torques in the emerging photospheric magnetic field with a substantially large sample of Solar Dynamics Observatory/Helioseismic and Magnetic Imager vector magnetograms. We found that the photospheric field has a rather small Lorentz force and torque on average, and thus is very close to a force-free state, which is not consistent with theories as well as idealized simulations of flux emergence. Furthermore, the small extents of forces and torques seem not to be influenced by the emerging AR's size, the emergence rate, or the nonpotentiality of the field. This result puts an important constraint on future development of theories and simulations of flux emergence.

Data-driven modeling of solar coronal magnetic field evolution and eruptions

“…On the other hand, the observed photospheric field for flux-emerging ARs from SDO/HMI has been found to be much closer to force free than the FES data, as demonstrated recently by Duan et al. 171 They conducted a statistical study of the normalized Lorentz forces and torques with a substantially large sample of 3,536 vector magnetograms from 51 ARs taken by SDO/HMI over the period of 2010–2019. These ARs were selected as having significant flux emergence during their passage on the solar disk within in longitude from the Sun’s central meridian.…”

The Force-freeness of the Solar Photosphere: Revisit with New Approach and Large Data Sets

“…From the right panels of Figure 3, we can also see that, although the mean values of F z /F p decrease from −0.021 in the R = 0 panel to −0.210 in the R = 4 panel, the distributions of the histograms do not change much. Note that in previous studies (Moon et al 2002;Tiwari 2012;Duan et al 2020) where the authors claimed that their data are nearly force-free, some of their |F z /F p | show values larger than 0.1. So in terms of the distribution of histograms, our results do not differ very much from most of the previous publications.…”

“…At the same time, "many nonlinear force-free coronal-field extrapolations based directly on the photospheric vector magnetograms generally agrees with each other to some extent" (Duan et al 2020) cannot be used as proof that the photospheric magnetic field is close to being force-free. However, using the observed force-freeness to test and constrain flux emergence models and simulations is indeed a very interesting practice.…”

“…They found that only about 25% of the magnetograms can be considered as close to being forcefree, i.e., most (75%) of the photospheric magnetic fields are not force-free. Yet when Duan et al (2020) studied a sample of 3536 Helioseismic and Magnetic Imager (HMI)/Solar Dynamics Observatory (SDO) magnetograms of 51 flux emerging active regions, they concluded that the emerging active regions are "very close to a force-free state, which is not consistent with theories as well as idealized simulations of flux emergence." Different from the above studies that directly applied Equations (2)-( 5) to observed magnetograms and gave their respective conclusions, Zhang et al (2017) tried to reconcile the differences in the results of previous studies by carrying out a systematic study on how the instrumental effects could influence the judgment of the force-freeness.…”

Structural evolution of a magnetic flux rope associated with a major flare in the solar active region 12205

“…Observations show that non-radial eruptions are frequent in filament eruptions (McCauley et al 2015), some of which significantly deviates from the vertical direction. We propose a more universal method to compute the decay index along an oblique line matching the eruption direction (Duan et al 2019), having applied it in many studies (Jiang et al 2019;Duan et al 2020Duan et al , 2021b. Briefly speaking, for an MFR, we cut through the middle of the rope axis (often at its apex) with a vertical slice in perpendicular direction to the rope axis.…”