Breno Raphaldini, Mausumi Dikpati, Scott W. McIntosh
High Altitude Observatory, NCAR, 3080 Center Green Drive, Boulder, CO 80301, USA
Perhaps, the most obvious organized pattern in the spatio-temporal evolution of the observed photospheric magnetic field is the latitudinal migration of the magnetic activity from middle to low latitudes as the solar cycle progresses. This process is known as the butterfly diagram and is understood in terms of the evolution of the solar dynamo cycle. Less obvious but equally important is the organization of the non-axisymmetric of the magnetic fields in the form of preferred longitudes and activity nests, implying an arrangement of emerging magnetic fields around slowly drifting longitudes. The physical origin of these structures is not well understood, but their organized nature suggests the existence of an underlying deterministic mechanism rather than a result of more stochastic phenomena such as fully developed turbulence.
In recent years an increasing amount of evidence points to the crucial role of magnetically-modified Rossby waves in several solar phenomena[1,2]. Rossby waves are large scale vortical oscillations that arise in rotating fluid/plasma systems as a result of the Coriolis force, being one of the most fundamental physical mechanisms in the understanding of Earths’s climate and weather. In Earth’s atmosphere one of their effects is to organize the spatial temporal formation of clouds and consequently rainfall and storms. Rays (paths) along which Rossby waves propagate are the origin of atmospheric stormtracks and teleconnection patterns[3].
Different from Rossby waves that occur in Earth’s atmosphere and oceans, Rossby waves that arise in the Sun are probably significantly impacted by the strong magnetic fields in the solar interior. Among all the locations that can support different kinds of Rossby waves in the Sun, such as the radiative zone, the tachocline, the bulk of the convection zone, and the top of the convection zone, the tachocline one is the strongest candidate to interact with the dynamo-generated magnetic fields. The reasons for this are that the tachocline provides the stratification necessary to favor the formation of large-scale patterns, and that it supports strong dynamo-generated toroidal fields.
Given that atmospheric Rossby waves provide this organizing mechanism for localized convective phenomena such as cloud formation and storms, is it possible that Solar Rossby waves have a similar effect in the organization of localized magnetic field structures such as active regions?
In order to investigate this, we utilized MDI and HMI synoptic maps from 1999 to 2022 to quantify the degree of organization and drift velocity of magnetic field structures (primarily dominated by activity nests). To quantify the organization of these magnetic fields structures we utilize tools from information theory. The primary quantity in information theory is the Shannon Entropy (SE), which provides a measure of organization/randomness in random processes/fields. The lower the SE, the more organized is the process in question.
Figure 1| Comparison of the evolution of the Shannon Entropy and the average magnetic field at selected latitudes.
We calculated the evolution of Shannon entropy for strips magnetic field profiles around ±40°, ±30°, ±20°, ±10°, and at the equator. The evolution of the SE for each of these latitudes is presented in Fig.1, showing an anti-correlation between the level of activity and the entropy. This means that the closer the given latitude is to its peak in activity, the more organized is the magnetic field profile. This highlights the organized nature of the magnetic fields in active regions.
Figure 2| Comparison of the latitudinal evolution of the Shannon entropy of the longitudinal magnetic field profiles with the Butterfly diagram for the respective mean magnetic field intensity.
We also investigate how the SE of the magnetic field profiles varies in latitude. The calculation of the SE continuously in space (for each latitude grid point) is presented in in Fig.2, and reveals an interesting fact: the SE follows the butterfly-diagram pattern, with organization being highest at approximately ±35° and propagating towards the equator as the cycle evolves.
Figure 3| Comparison of the drift velocities derived for selected latitudes with the local photospheric differential rotation revealing that the drift velocity is consistently more negative that the differential rotation.
Finally, we quantify the velocity at which these structures propagate by maximizing the correlation between consecutive (in time) magnetic field profiles. The average (in time) result shows that these structures drift at a speed that is slightly more negative than the local differential rotation (20-30m/s less that the differential rotation rate), which is consistent with the phase velocity of Rossby waves with low wavenumbers. The results are shown in Fig.3, suggesting Rossby waves as strong candidates for the occurrence of organized structures such as activity nests and preferred longitudes.
In summary, we have studied the evolution of the spatio-temporal organization of solar magnetic fields on long timescales and suggested that Rossby waves can be the primary driver of activity nests and preferred longitudes. This also suggests an interesting analogy between the magnetic activity of the Sun and Earth’s weather, with Rossby waves mediating the organization of rainfall and storms on the Earth, and patterns of active regions in the Sun. This also opens perspectives in terms of monitoring solar Rossby waves and the predictability of solar activity on intermediate timescales. Further details can be found in Ref. [4].
References
[1]Dikpati, M., McIntosh, S. W., Bothun, G., et al. 2018, ApJ, 853, 144.
[2]Raphaldini, B., Seiji Teruya, A., Raupp, C. F. M., et al. 2019, ApJ, 887, 1.
[3]Boers, N., Goswami, B., Rheinwalt, A., et al. 2019, Nature, 566, 373.
[4]Raphaldini, B., Dikpati, M., & McIntosh, S. W. 2023, ApJ, 953, 156.