Estimation and limits of MHD simulations forpredicting extreme events

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Abstract
Many questions must be answered before understanding the rela- tionship between the emerging magnetic flux through the solar surface and the extreme geoeffective events. Which threshold determines the onset of the eruption? What is the upper limit in energy for a flare? Is the size of the sunspot the only criterion to get extreme solar events? Based on observations of previous solar cycles and theory, the main ingredients for getting X-ray classflares and large interplanetary Coronal Mass Ejections, e.g., the built-up of theelectric current in the corona, are presented, as are the existence of magnetic freeenergy, magnetic energy/helicity ratio, twist, and stress in active regions. Theupper limit of solar energy in the space research era, and the possible chancesof getting super-flares and extreme solar events, can be predicted using MHDsimulations of coronal mass ejections. For eruptive flares with CMEs or confinedflares, magnetic solar energy is discussed in this context, along with data-drivenMHD simulations of the May 2024 events. We show the consistency between thedata-initiated realistic simulation of the May 2024 big event and energy scalingsfrom an idealised simulation of a bipolar eruption. The estimated free magneticenergy did not surpass 5.2 * 1032 erg. Good arrival time predictions (< 3 hours)are achieved with the EUHFORIA simulation with the cone model. We notethe interest in coupling all the chains of codes from the Sun to the Earth anddeveloping different approaches to test the results.

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