Y. Q. Hu

Influence of heavy ions on the high‐speed solar wind

We present the results of a parameter study of the influence of heavy ions on the background solar wind, choosing doubly ionized helium, or alpha particles, and O+6, as examples. Using a three-fluid solar wind model, we keep the input parameters to the electrons and protons unchanged and investigate the effects of changing the input energy flux to the heavy ions and their coronal abundance, i.e., their abundance at 1 Rs, on the background electron-proton solar wind. Our results confirm earlier studies that alpha particles can have a dramatic effect on the thermodynamic and flow properties of the protons in the solar wind. The maximum coronal abundance for which the changes in the energy input to the heavy ions has no effect on the protons is 5 × 10−4 for the alphas and 5 × 10−5 for the oxygen ions, which are well below the photospheric values. For larger coronal abundances, the sensitivity of the changes of the flow speed and proton mass flux to changes in the energy input to the heavy ions increases sharply with increasing abundance. When the heavy ions are not heated, the increase in the coronal abundance leads to an increase in flow speed, a decrease in proton mass flux, and an increase in proton temperature at 1 AU. However, as the heat input to the heavy ions increases, the dependence of these parameters on the abundance goes through a transition and starts to follow the opposite pattern, namely a decrease in flow speed and proton temperature at 1 AU, and an increase in proton mass flux. This study shows that, for currently known photospheric elemental abundances, the flow properties of heavy ions cannot be investigated independently of those of the bulk proton-electron solar wind. The effect of heavy ions on the electron-proton bulk solar wind is determined primarily by the collisions occurring very close to the coronal base. Hence including physical processes responsible for the preferential heating of heavy ions to temperatures exceeding those of protons in the inner corona cannot be done without considering the subsequent implications for the protons and electrons in a self-consistent manner.

Catastrophic Eruption of Magnetic Flux Rope in the Corona and Solar Wind With and Without Magnetic Reconnection

It is generally believed that the magnetic free energy accumulated in the corona serves as a main energy source for solar explosions such as coronal mass ejections (CMEs). In the framework of the flux rope catastrophe model for CMEs, the energy may be abruptly released either by an ideal magnetohydrodynamic (MHD) catastrophe, which belongs to a global magnetic topological instability of the system, or by a fast magnetic reconnection across preexisting or rapidly developing electric current sheets. Both means of magnetic energy release are thought to be important to CME dynamics. To disentangle their contributions, we construct a flux rope catastrophe model in the corona and solar wind and compare different cases in which we either prohibit or allow magnetic reconnection to take place across rapidly growing current sheets during the eruption. It has been demonstrated that CMEs, even fast ones, can be produced taking the ideal MHD catastrophe as the only process of magnetic energy release. Nevertheless, the eruptive speed can be significantly enhanced after magnetic reconnection sets in. In addition, a smooth transition from slow to fast eruptions is observed when increasing the strength of the background magnetic field, simply because in a stronger field there is more free magnetic energy at the catastrophic point available to be released during an eruption. This suggests that fast and slow CMEs may have an identical driving mechanism.

A 2.5-dimensional Ideal Magnetohydrodynamic Model for Coronal Magnetic Flux Ropes

Coronal magnetic flux ropes are closely related to various solar active phenomena such as prominences, flares, and coronal mass ejections. Using a 2.5-dimensional (2.5-D), time-dependent ideal MHD model in Cartesian coordinates, a numerical study is carried out to find the equilibrium solution associated with a magnetic flux rope in the corona, which is assumed to emerge as a whole from the photosphere. The rope in equilibrium is characterized by its geometrical features such as the height of the axis, the half-width of the rope, and the length of the vertical current sheet below the rope, and its magnetic properties such as the axial and annular magnetic fluxes and the magnetic helicity as well, which are conserved quantities of the rope in the frame of ideal MHD. It is shown that, for a given bipolar ambient magnetic field, the magnetic flux rope is detached from the photosphere, leaving a vertical current sheet below, when its axial magnetic flux, annular magnetic flux, or magnetic helicity exceeds a certain critical value. The magnetic field is nearly force free in the rope but not in the prominence region, where the Lorentz force takes an important role in supporting the prominence appearing below the rope axis. The geometrical features of the rope vary smoothly with its magnetic properties, and no catastrophe occurs, a similar conclusion to that reached by Forbes & Isenberg for magnetic flux ropes of large radius.

A two‐dimensional Alfvén wave–driven solar wind model with proton temperature anisotropy

[i] We present the first two-dimensional (2-D) Alfven wave turbulence-driven solar wind model which takes the proton temperature anisotropy into account. While the modeled proton temperature anisotropy in the fast solar wind is established in the inner corona and yields T∥ p /T⊥p = 0.57 at 1 AU, which is comparable to measured values, T∥ p and T⊥ p are only about half the observed values. In the slow wind, on the other hand, the modeled values for T∥ p and T⊥ p as well as their ratio are close to those measured in interplanetary space. Curiously, the dip in the velocity that develops near the cusp at the top of the helmet streamer reduces the effect of transverse expansion and leads to a realistic electron temperature in the slow wind at 1 AU, although no explicit external heating is applied to electrons. Comparison with models with and without proton temperature anisotropy shows that by allowing the proton temperature anisotropy to develop, the average proton temperature is lower than the isotropic case primarily because of the cooling in the direction parallel to the magnetic field. These results imply that ion cyclotron resonance models with isotropic proton temperature are somewhat optimistic in assessing the role of Alfven wave turbulence in driving the fast solar wind. Inclusion of the temperature anisotropy of protons and proton thermal conduction are necessary for any physically realistic model.

Formation of Minor-Ion Charge States in the Fast Solar Wind: Roles of Differential Flow Speeds of Ions of the Same Element

To investigate the possibility of differential flow speeds between ions of the same element and their roles in the determination of ionic fractions, this paper extends our latest minor-ion model to a five-fluid model, describing the behavior of five species of minor ions of one given element in the fast solar wind. We solve the five sets of mass, momentum, and energy equations simultaneously to include the effects of ionization, recombination, and heating. The five species of minor ions are taken as test particles flowing in a background plasma consisting of electrons, protons, and alpha particles. The parameters of the background gas are calculated using a previous three-fluid wave-driven magnetohydrodynamic model for the fast solar wind. These background parameters are modeled as closely as possible to observed values. Using this background of fast solar wind parameters, the five-fluid minor-ion model has no problem reproducing the frozen-in charge-state distributions observed in the fast solar wind for C and O ions, while the modeled ionic fractions of Si, Mg, and Fe show significant shifts to lower charge states compared with the observed values. It is found that the majority of C and O ions are frozen-in below 1.2 solar radii, while most Si, Mg, and Fe ions are frozen-in beyond 1.3-1.5 solar radii. Comparing the cases with and without differential flows shows that even though differential flow speeds between ions of the same element do develop beyond a certain heliocentric distance (e.g., 1.2 solar radii for Si ions), they cannot account for the high ion charge states observed in situ.

Force Balance Analysis of a Coronal Magnetic Flux Rope in Equilibrium or Eruption

Based on a flux rope catastrophe model for coronal mass ejections (CMEs), we calculate the Lorentz forces acting on the rope in equilibrium or eruption in the background field, which is taken to be either a partially open bipolar field or a closed quadrupolar field. The forces, including upward lifting and downward pulling ones, are exerted by the coronal currents inside and outside the rope, as well as the potential field, which has the same normal component distribution on the photosphere as the background field. The resultant of forces vanishes for a rope in equilibrium. For both cases with different background fields, the primary lifting force is provided by the azimuthal current inside the rope and its image below the photosphere. It is mainly balanced by the pulling force produced by the background potential field when the rope is in equilibrium. During an eruption of the rope caused by catastrophe, the two predominant forces mentioned above decrease rapidly with the ascent of the rope. In the meantime, the vertical and/or transverse current sheets and their images, which form and develop along with the rope eruption, contribute additional and significant pulling (or restoring) forces that decelerate the rope. When fast magnetic reconnection takes place across these current sheets, the restoring force provided by the sheets will be greatly reduced, which may play an important role in the dynamics of the rope. The implication of such a conclusion in the acceleration of CMEs is briefly discussed.

Catastrophe of Coronal Flux Rope in Unsheared and Sheared Bipolar Magnetic Fields

This article investigates the catastrophic behavior of a preexisting coronal magnetic flux rope embedded in a dipolar or partially open bipolar background field, which is either unsheared or sheared with a given footpoint displacement of magnetic field lines. It is found that in the unsheared background field the catastrophic energy threshold decreases slightly with increasing extent of opening of the background field and increasing annular flux or decreasing axial flux of the flux rope, varying in the range between 1.08 and 1.1 times the magnetic energy of the corresponding fully open field. As the background field is sheared, on the other hand, catastrophe may be triggered by shear provided that the presheared magnetic energy of the system is high enough. The catastrophic energy threshold is almost invariant but then increases monotonically with the increase of the presheared magnetic energy of the system, and it is bounded above by the energy of the corresponding flux rope system associated with an unsheared background field.

Ion Effective Temperatures in Polar Coronal Holes: Observations versus Ion-Cyclotron Resonance

The resonant cyclotron interaction between ion-cyclotron waves and solar wind species is considered nowadays to be a strong candidate for heating and acceleration of protons, α-particles, and heavy ions. A crucial physical parameter for determining the amount and the location of significant heating and acceleration, which the different solar wind ions receive from the waves in the frame of the ion-cyclotron mechanism, is their charge-to-mass ratio q/m. Therefore, comparisons of ion temperatures derived from spectroscopic observations and calculated by ion-cyclotron models, for ions that span a broad range in q/m, would provide a rigorous test for such models. By using an ion-cyclotron model, we calculate the effective temperatures for 10 different ions that cover the range 0.16-0.37 in q/m. Effective temperatures correspond to unresolved thermal motions and wave motions. The good agreement between our calculations, based on the specific mechanism that we employed here (ion-cyclotron resonance) and on spectroscopic observations of effective temperatures in polar coronal holes, provides support that the above mechanism accounts for the energetics and kinematics of fast solar wind heavy ions. However, such an agreement does not prove that other potential mechanisms can be excluded.

Two energy release processes for CMEs: MHD catastrophe and magnetic reconnection

Abstract It remains an open question how magnetic energy is rapidly released in the solar corona so as to create solar explosions such as solar flares and coronal mass ejections (CMEs). Recent studies have confirmed that a system consisting of a flux rope embedded in a background field exhibits a catastrophic behavior, and the energy threshold at the catastrophic point may exceed the associated open field energy. The accumulated free energy in the corona is abruptly released when the catastrophe takes place, and it probably serves as the main means of energy release for CMEs at least in the initial phase. Such a release proceeds via an ideal MHD process in contrast with nonideal ones such as magnetic reconnection. The catastrophe results in a sudden formation of electric current sheets, which naturally provide proper sites for fast magnetic reconnection. The reconnection may be identified with a solar flare associated with the CME on one hand, and produces a further acceleration of the CME on the other. On this basis, several preliminary suggestions are made for future observational investigations, especially with the proposed Kuafa satellites, on the roles of the MHD catastrophe and magnetic reconnection in the magnetic energy release associated with CMEs and flares.

DOWNWARD CATASTROPHE OF SOLAR MAGNETIC FLUX ROPES

2.5D time-dependent ideal magnetohydrodynamic (MHD) models in Cartesian coordinates were used in previous studies to seek MHD equilibria involving a magnetic flux rope embedded in a bipolar, partially open background field. As demonstrated by these studies, the equilibrium solutions of the system are separated into two branches: the flux rope sticks to the photosphere for solutions at the lower branch but is suspended in the corona for those at the upper branch. Moreover, a solution originally at the lower branch jumps to the upper, as the related control parameter increases and reaches a critical value, and the associated jump is here referred to as upward catastrophe. The present paper advances these studies in three aspects. First, the magnetic field is changed to be force-free. The system still experiences an upward catastrophe with an increase in each control parameter. Secondly, under the force-free approximation, there also exists a downward catastrophe, characterized by a jump of a solution from the upper branch to the lower. Both catastrophes are irreversible processes connecting the two branches of equilibrium solutions so as to form a cycle. Finally, the magnetic energy in the numerical domain is calculated. It is found that there exists a magnetic energy release for both catastrophes. The Amp`{e}res force, which vanishes everywhere for force-free fields, appears only during the catastrophes and does a positive work, which serves as a major mechanism for the energy release. The implications of the downward catastrophe and its relevance to solar activities are briefly discussed.