Variations in the Solar Coronal Rotation with Altitude – Revisited

Here we report an in-depth reanalysis of an article by Vats et al. (Astrophys. J. 548, L87, 2001) that was based on measurements of differential rotation with altitude as a function of observing frequencies (as lower and higher frequencies indicate higher and lower heights, respectively) in the solar corona. The radial differential rotation of the solar corona is estimated from daily measurements of the disc-integrated solar radio flux at 11 frequencies: 275, 405, 670, 810, 925, 1080, 1215, 1350, 1620, 1755, and 2800 MHz. We use the same data as were used in Vats et al. (2001), but instead of the twelfth maxima of autocorrelograms used there, we use the first secondary maximum to derive the synodic rotation period. We estimate synodic rotation by Gaussian fit of the first secondary maximum. Vats et al. (2001) reported that the sidereal rotation period increases with increasing frequency. The variation found by them was from 23.6 to 24.15 days in this frequency range, with a difference of only 0.55 days. The present study finds that the sidereal rotation period increases with decreasing frequency. The variation range is from 24.4 to 22.5 days, and the difference is about three times larger (1.9 days). However, both studies give a similar rotation period at 925 MHz. In Vats et al. (2001) the Pearson’s factor with trend line was 0.86, whereas present analysis obtained a \({\sim}\,0.97\) Pearson’s factor with the trend line. Our study shows that the solar corona rotates more slowly at higher altitudes, which contradicts the findings reported in Vats et al. (2001).     

Reconstruction of the North–South Solar Asymmetry with a Kuramoto Model

This paper applies a Kuramoto model of coupled oscillators to investigate the north–south (N–S) solar asymmetry and properties of meridional circulation. We focus our study on the asymmetry of the 11-year phase, which is slight but persistent: only two changes of sign (around 1928 and 1968) are observed in the past century. We present a model of two non-linear coupled oscillators that links the hemispheric phase asymmetry of sunspots with the asymmetry of the meridional flow. We use a Kuramoto model with evolving frequencies and constant symmetric coupling to show how asymmetry in meridional circulation could produce a persistent phase lead of one solar hemisphere over the other. We associate the natural frequencies of the two oscillators with the velocities of the meridional flow cells in the northern and southern hemispheres. We assume the respective circulations to be independent and estimate the value of the relevant cross-equatorial coupling by the coupling coefficient in the Kuramoto model. We find that a persistent N–S asymmetry of sunspots and the change of the leading hemisphere could indeed both be the result of the evolving frequencies of meridional circulation; the necessary asymmetry of the meridional flow may be small; and the cross-equatorial coupling has an intermediate range value. Possible applications of these results in solar dynamo models are discussed.     

The Interaction of Successive Coronal Mass Ejections: A Review

We present a review of the different aspects associated with the interaction of successive coronal mass ejections (CMEs) in the corona and inner heliosphere, focusing on the initiation of series of CMEs, their interaction in the heliosphere, the particle acceleration associated with successive CMEs, and the effect of compound events on Earth’s magnetosphere. The two main mechanisms resulting in the eruption of series of CMEs are sympathetic eruptions, when one eruption triggers another, and homologous eruptions, when a series of similar eruptions originates from one active region. CME?–?CME interaction may also be associated with two unrelated eruptions. The interaction of successive CMEs has been observed remotely in coronagraphs (with the Large Angle and Spectrometric Coronagraph Experiment – LASCO – since the early 2000s) and heliospheric imagers (since the late 2000s), and inferred from in situ measurements, starting with early measurements in the 1970s. The interaction of two or more CMEs is associated with complex phenomena, including magnetic reconnection, momentum exchange, the propagation of a fast magnetosonic shock through a magnetic ejecta, and changes in the CME expansion. The presence of a preceding CME a few hours before a fast eruption has been found to be connected with higher fluxes of solar energetic particles (SEPs), while CME?–?CME interaction occurring in the corona is often associated with unusual radio bursts, indicating electron acceleration. Higher suprathermal population, enhanced turbulence and wave activity, stronger shocks, and shock?–?shock or shock?–?CME interaction have been proposed as potential physical mechanisms to explain the observed associated SEP events. When measured in situ, CME?–?CME interaction may be associated with relatively well organized multiple-magnetic cloud events, instances of shocks propagating through a previous magnetic ejecta or more complex ejecta, when the characteristics of the individual eruptions cannot be easily distinguished. CME?–?CME interaction is associated with some of the most intense recorded geomagnetic storms. The compression of a CME by another and the propagation of a shock inside a magnetic ejecta can lead to extreme values of the southward magnetic field component, sometimes associated with high values of the dynamic pressure. This can result in intense geomagnetic storms, but can also trigger substorms and large earthward motions of the magnetopause, potentially associated with changes in the outer radiation belts. Future in situ measurements in the inner heliosphere by Solar Probe+ and Solar Orbiter may shed light on the evolution of CMEs as they interact, by providing opportunities for conjunction and evolutionary studies.     

Estimating Solar Flux Density at Low Radio Frequencies Using a Sky Brightness Model

Sky models have been used in the past to calibrate individual low radio frequency telescopes. In this article we generalize this approach from a single antenna to a two element interferometer, and formulate the problem in a way that allows us to estimate the flux density of the Sun using the normalized cross-correlations (visibilities) measured on a low resolution interferometric baseline. For wide field-of-view instruments, typically the case at low radio frequencies, this approach can provide robust absolute solar flux calibration for well characterized antennas and receiver systems. It can provide a reliable and computationally lean method for extracting parameters of physical interest using a small fraction of the voluminous interferometric data, which can be computationally prohibitively expensive to calibrate and image using conventional approaches. We demonstrate this technique by applying it to data from the Murchison Widefield Array and assess its reliability.     

Meridional Motion and Reynolds Stress from Debrecen Photoheliographic Data

The Debrecen Photoheliographic Data catalogue is a continuation of the Greenwich Photoheliographic Results providing daily positions of sunspots and sunspot groups. We analyse the data for sunspot groups focussing on meridional motions and transfer of angular momentum towards the solar equator. Velocities are calculated with a daily shift method including an automatic iterative process of removing the outliers. Apart from the standard differential rotation profile, we find meridional motion directed towards the zone of solar activity. The difference in measured meridional flow in comparison to Doppler measurements and some other tracer measurements is interpreted as a consequence of different flow patterns inside and outside of active regions. We also find a statistically significant dependence of meridional motion on rotation velocity residuals confirming the transfer of angular momentum towards the equator. Analysis of horizontal Reynolds stress reveals that the transfer of angular momentum is stronger with increasing latitude up to about \(40^{\circ}\), where there is a possible maximum in absolute value.     

Changing Relationships Between Sunspot Number,Total Sunspot Area and $F_{10.7}$ in Cycles 23 and 24

This article is an update of a study (Tapping and Valdès in Solar Phys. 272, 337, 2011) made in the early part of Cycle 24 using an intercomparison of various solar activity indices (including sunspot number and the 10.7 cm solar radio flux), in which it was concluded that a change in the relationship between photospheric and chromospheric/coronal activity took place just after the maximum of Cycle 23 and continued into Cycle 24. Precursors (short-term variations) were detected in Cycles 21 and 22. Since then the sunspot number index data have been substantially revised. This study is intended to be an update of the earlier study and to assess the impact of the revision of the sunspot number data upon those conclusions. This study compares original and revised sunspot number, total sunspot area, and 10.7 cm solar radio flux. The conclusion is that the transient changes in Cycles 21 and 22, and the more substantial change in Cycle 23, remain evident. Cycle 24 shows indications that the deviation was probably another short-term one.     

Forbush Decrease: A New Perspective with Classification

Sudden short-duration decreases in cosmic ray flux, known as Forbush decreases (FDs), are mainly caused by interplanetary disturbances. A generally accepted view is that the first step of an FD is caused by a shock sheath and the second step is due to the magnetic cloud (MC) of the interplanetary coronal mass ejection (ICME). This simplistic picture does not consider several physical aspects, such as whether the complete shock sheath or MC (or only part of these) contributes to the decrease or the effect of internal structure within the shock-sheath region or MC. We present an analysis of 16 large (\({\geq}\,8 \%\)) FD events and the associated ICMEs, a majority of which show multiple steps in the FD profile. We propose a reclassification of FD events according to the number of steps observed in their respective profiles and according to the physical origin of these steps. This study determines that 13 out of 16 major events (\({\sim}\,81\%\)) can be explained completely or partially on the basis of the classic FD model. However, it cannot explain all the steps observed in these events. Our analysis clearly indicates that not only broad regions (shock sheath and MC), but also localized structures within the shock sheath and MC have a significant role in influencing the FD profile. The detailed analysis in the present work is expected to contribute toward a better understanding of the relationship between FD and ICME parameters.     

Nonequilibrium Processes in the Solar Corona,Transition Region,Flares, and Solar Wind <Emphasis Type="Italic">(Invited Review)</Emphasis>

We review the presence and signatures of the non-equilibrium processes, both non-Maxwellian distributions and non-equilibrium ionization, in the solar transition region, corona, solar wind, and flares. Basic properties of the non-Maxwellian distributions are described together with their influence on the heat flux as well as on the rates of individual collisional processes and the resulting optically thin synthetic spectra. Constraints on the presence of high-energy electrons from observations are reviewed, including positive detection of non-Maxwellian distributions in the solar corona, transition region, flares, and wind. Occurrence of non-equilibrium ionization is reviewed as well, especially in connection to hydrodynamic and generalized collisional-radiative modeling. Predicted spectroscopic signatures of non-equilibrium ionization depending on the assumed plasma conditions are summarized. Finally, we discuss the future remote-sensing instrumentation that can be used for the detection of these non-equilibrium phenomena in various spectral ranges.     

On the Collision Nature of Two Coronal Mass Ejections: A Review

Observational and numerical studies have shown that the kinematic characteristics of two or more coronal mass ejections (CMEs) may change significantly after a CME collision. The collision of CMEs can have a different nature, i.e. inelastic, elastic, and superelastic processes, depending on their initial kinematic characteristics. In this article, we first review the existing definitions of collision types including Newton’s classical definition, the energy definition, Poisson’s definition, and Stronge’s definition, of which the first two were used in the studies of CME–CME collisions. Then, we review the recent research progresses on the nature of CME–CME collisions with the focus on which CME kinematic properties affect the collision nature. It is shown that observational analysis and numerical simulations can both yield an inelastic, perfectly inelastic, merging-like collision, or a high possibility of a superelastic collision. Meanwhile, previous studies based on a 3D collision picture suggested that a low approaching speed of two CMEs is favorable for a superelastic nature. Since CMEs are an expanding magnetized plasma structure, the CME collision process is quite complex, and we discuss this complexity. Moreover, the models used in both observational and numerical studies contain many limitations. All of the previous studies on collisions have not shown the separation of two colliding CMEs after a collision. Therefore the collision between CMEs cannot be considered as an ideal process in the context of a classical Newtonian definition. In addition, many factors are not considered in either observational analysis or numerical studies, e.g. CME-driven shocks and magnetic reconnections. Owing to the complexity of the CME collision process, a more detailed and in-depth observational analysis and simulation work are needed to fully understand the CME collision process.     

CME Velocity and Acceleration Error Estimates Using the Bootstrap Method

The bootstrap method is used to determine errors of basic attributes of coronal mass ejections (CMEs) visually identified in images obtained by the Solar and Heliospheric Observatory (SOHO) mission’s Large Angle and Spectrometric Coronagraph (LASCO) instruments. The basic parameters of CMEs are stored, among others, in a database known as the SOHO/LASCO CME catalog and are widely employed for many research studies. The basic attributes of CMEs (e.g. velocity and acceleration) are obtained from manually generated height-time plots. The subjective nature of manual measurements introduces random errors that are difficult to quantify. In many studies the impact of such measurement errors is overlooked. In this study we present a new possibility to estimate measurements errors in the basic attributes of CMEs. This approach is a computer-intensive method because it requires repeating the original data analysis procedure several times using replicate datasets. This is also commonly called the bootstrap method in the literature. We show that the bootstrap approach can be used to estimate the errors of the basic attributes of CMEs having moderately large numbers of height-time measurements. The velocity errors are in the vast majority small and depend mostly on the number of height-time points measured for a particular event. In the case of acceleration, the errors are significant, and for more than half of all CMEs, they are larger than the acceleration itself.