Deciphering the Deep Origin of Active Regions via Analysis of Magnetograms

Abstract

In this work, we derive magnetic toroids from surface magnetograms by employing a novel optimization method, based on the trust region reflective algorithm. The toroids obtained in this way are combinations of Fourier modes (amplitudes and phases) with low longitudinal wavenumbers. The optimization also estimates the latitudinal width of the toroids. We validate the method using synthetic data, generated as random numbers along a specified toroid. We compute the shapes and latitudinal widths of the toroids via magnetograms, generally requiring several m's to minimize residuals. A threshold field strength is chosen to include all active regions in the magnetograms for toroid derivation, while avoiding non-contributing weaker fields. Higher thresholds yield narrower toroids, with an m = 1 dominant pattern. We determine the spatiotemporal evolution of toroids by optimally weighting the amplitudes and phases of each Fourier mode for a sequence of five Carrington Rotations (CRs) to achieve the best amplitude and phases for the middle CR in the sequence. Taking more than five causes “smearing” or degradation of the toroid structure. While this method applies no matter the depth at which the toroids actually reside inside the Sun, by comparing their global shape and width with analogous patterns derived from magnetohydrodynamic (MHD) tachocline shallow water model simulations, we infer that their origin is at/near the convection zone base. By analyzing the “Halloween” storms as an example, we describe features of toroids that may have caused the series of space weather events in 2003 October–November. Calculations of toroids for several sunspot cycles will enable us to find similarities/differences in toroids for different major space weather events.

Accounting for differential rotation in calculations of the Sun’s angular momentum-loss rate

“…Some strong magnetic features, however, appear to rotate around every 25.4 days (otherwise referred to as the Carrington rotation period). Whether this relates to the anchoring of magnetic field in the interior (Gilman 1983;Miesch et al 2008;Brun et al 2004;Nelson et al 2013;Dikpati et al 2021;Käpylä 2022;Brun et al 2022), or the role of the near surface shear layer in sculpting the toroidal flux before emergence (as discussed in Brandenburg 2005), is unclear. Generally, magnetic features at the top of the convection zone are still subject to differential rotation, but this can be less that would be expected from the observed rate at the photosphere (see Gigolashvili et al 2013), and depends on their field strength and surface area (Imada & Fujiyama 2018).…”

Simulating Properties of “Seasonal” Variability in Solar Activity and Space Weather Impacts

“…Simulations of TNO for narrow toroidal magnetic bands of latitudinal widths of 10-degree were studied in detail by Dikpati et al (2017Dikpati et al ( , 2018aDikpati et al ( , 2018b. Very recently nonlinear magnetohydrodynamics of a slightly wider band of 14-degree latitudinal width have been studied in the context of understanding the features of Halloween storm of 2003 (see, e.g., figures 12-14 of Dikpati et al, 2021). We focus here in the magnetohydrodynamics of a much broader magnetic band of latitudinal widths of 30-degree, for example.…”

Deciphering the Pre–solar-storm Features of the 2017 September Storm From Global and Local Dynamics

“…These are mostly generated from global MHD instabilities (Dziembowski & Kosovichev 1987;Gilman & Fox 1997;Zaqarashvili et al 2010a;Raphaldini & Raupp 2015;Dikpati et al 2018a). Their signatures are observed in the solar magnetic patterns at the solar surface, in the spatial distribution of ARs (Dikpati et al 2021), and at the corona, in the evolution of bright point densities (McIntosh et al 2017) and in the longitude drift of long-lived coronal holes (Harris et al 2022). It is to be noted that there can be other Rossby waves which can interact with mean magnetic fields.…”

“…Studies of plasma flows in flux emergence simulations on the other hand show that it is possible to predict new emergences within 10 hr of advance (Silva et al 2023). On the other hand, the global pattern of the toroid, the strong reservoir of magnetic field stored at depth in the Sun and from which ARs emerge, can provide certain features indicative of the occurrence of big solar storms (Dikpati et al 2021).…”

“…Having discussed the important roles a class of solar Rossby waves play in organizing longitude distribution of ARs (see also Teruya et al 2022;Raphaldini et al 2023), analogous to the way atmospheric Rossby waves play for terrestrial weather patterns, we explore prestorm feature analysis from solar Rossby wave dynamics. Dikpati et al (2021) derived toroid patterns by fitting low-order longitudinal modes to synoptic magnetogram maps. When applied to a prestorm configuration, namely the "Halloween Storms" of 2003, which originated from an X-45 class flare (Thomson et al 2004), the wavy toroid patterns in the northern and southern hemispheres were found to tip away from each other at certain longitudes, and consequently at certain other longitudes the north and south toroids were found to come closer to each other.…”