134. The First Numerical Modeling of Spontaneous Generation of δ-sunspots

Contributed by Shin Toriumi. Posted on December 17, 2019

Shin Toriumi1 & Hideyuki Hotta2

1. Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210, Japan
2. Department of Physics, Graduate School of Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan

Here we report on the first numerical simulation in which a magnetic flux tube in turbulent background convection emerges to the photosphere and self-consistently builds up δ-sunspot, the most flare-productive category of sunspots[1].

Observations have revealed that major solar flares and coronal mass ejections tend to emanate from complex-shaped active regions[2]. Among others, δ-spots, where umbrae of positive and negative polarities are placed so closely that they share a common penumbra, are known to cause the strongest events in history[3]. However, because the solar interior is inaccessible to optical observations, how subsurface magnetic flux emerges to the surface and produces such flare-prone regions remains one of the mysteries of the flare studies. Although a multitude of numerical simulations that mimic flux emergences from the interior have been conducted, most of them are highly idealized models in which the flux is arbitrarily endowed with complexity or forcibly injected into the computational domain.

In this study, by utilizing state-of-the-art radiative MHD code R2D2[4], we succeed in the first-ever modeling of the convection-driven flux emergence and the resultant spontaneous generation of flare-productive sunspots. To investigate the process that a magnetic flux is elevated by this realistic thermal convection, we set a computational box that stretches down to -140 Mm with thermal convection of various scales from 100 Mm sized cells to surface granules, and placed a flux tube at -16.7 Mm without any artificial triggering of buoyant emergence. It was found that large-scale convective upflows elevate the flux to the photosphere at two sections and produce a pair of emerging bipoles (Figure 1). The spots of opposite polarities collide against each other to eventually generate δ-spots.

Figure 1| Generation of δ-sunspots. From left to right, intensity, magnetic field strength (white and black indicate positive and negative polarities, respectively), and field strength on the vertical cross-section at 32 hours (upper row) and 42 hours (lower row). A pair of bipoles (P1-N1 and P2-N2) collide to produce δ-spots N1-P2 and N2-P1.

Between the positive and negative polarities, strongly sheared polarity inversion lines are created by counter-streaming flows, which are excited due to the Lorentz force of rotating sunspots. Above the polarity inversion line, a helical magnetic structure (magnetic flux rope: Figure 2) is created in response to the rotational motions in the photosphere. All these structures (i.e., the δ-spots, sheared polarity inversion lines, rotating spots, and flux rope structures) are the key ingredients of the active regions prone to major flare eruptions.

Figure 2| Strongly twisted magnetic field lines are created in the atmosphere above the δ-spots. This structure is called a magnetic flux rope, which may be ejected into the interplanetary space once a flare eruption occurs.

We find that the δ-spot formation in this model follows the multi-buoyant segment scenario, suggested in the previous idealized simulations [e.g., Ref 5]. Moreover, the δ-spot is generated as a natural consequence of interaction between magnetic flux and turbulent convection, suggesting that the δ-spot formation and the resultant flare eruptions may be stochastically determined processes.


[1] Toriumi, S., & Hotta H., 2019, ApJL, 886, L21
[2] Toriumi, S. & Wang, H., 2019, LRSP, 16, 3
[3] Sammis, I., Tang, F., & Zirin, H., 2000, ApJ, 540, 583
[4] Hotta, H., Iijima, H., & Kusano, K., 2019, Sci Adv, 5, 2307
[5] Toriumi, S., Iida, Y., Kusano, K., Bamba, Y., & Imada, S., 2014, Solar Phys, 289, 3351

One comment on “The First Numerical Modeling of Spontaneous Generation of δ-sunspots

  1. Xudong Sun

    Shin, I really like the work. Wish it were a bit longer.

    Also, “fortuitous” is a good word when an extraordinary phenomenon emerges from a stochastically determined process 🙂


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