Disentangling the Entangled Linkages of Relative Magnetic Helicity

Magnetic helicity, $H$, measures magnetic linkages in a volume. The early theoretical development of helicity focused on magnetically closed systems in $\mathcal{V}$ bounded by $\mathcal{S}$. For magnetically closed systems, $\mathcal{V}\in\mathbb{R}^3=\mathcal{V}+\mathcal{V}^*$, no magnetic flux threads the boundary, $\hat{\boldsymbol{n}}\cdot\boldsymbol{B}|_\mathcal{S}=0$. Berger and Field (1984) and Finn and Antonsen (1985) extended the definition of helicity to relative helicity, $\mathcal{H}$, for magnetically open systems where magnetic flux may thread the boundary. Berger (1999,2003) expressed this relative helicity as two gauge invariant terms that describe the self helicity of magnetic field that closes inside $\mathcal{V}$ and the mutual helicity between the magnetic field that threads the boundary $\mathcal{S}$ and the magnetic field that closes inside $\mathcal{V}$. The total magnetic field that permeates $\mathcal{V}$ entangles magnetic fields that are produced by current sources $\boldsymbol{J}$ in $\mathcal{V}$ with magnetic fields that are produced by current sources $\boldsymbol{J}^*$ in $\mathcal{V}^*$. Building on this fact, we extend Berger's expressions for relative magnetic helicity to eight gauge invariant quantities that simultaneously characterize both of these self and mutual helicities and attribute their origins to currents $\boldsymbol{J}$ in $\mathcal{V}$ and/or $\boldsymbol{J}^*$ in $\mathcal{V}^*$, thereby disentangling the domain of origin for these entangled linkages. We arrange these eight terms into novel expressions for internal and external helicity (self) and internal-external helicity (mutual) based on their domain of origin. The implications of these linkages for interpreting magnetic energy is discussed and new boundary observables are proposed for tracking the evolution of the field that threads the boundary.Comment: 27 pages, 2 figure

Multi-fluid simulations of chromospheric magnetic reconnection in a weakly ionized reacting plasma

We present results from the first self-consistent multi-fluid simulations of chromospheric magnetic reconnection in a weakly ionized reacting plasma. We simulate two dimensional magnetic reconnection in a Harris current sheet with a numerical model which includes ion-neutral scattering collisions, ionization, recombination, optically thin radiative loss, collisional heating, and thermal conduction. In the resulting tearing mode reconnection the neutral and ion fluids become decoupled upstream from the reconnection site, creating an excess of ions in the reconnection region and therefore an ionization imbalance. Ion recombination in the reconnection region, combined with Alfv\'{e}nic outflows, quickly removes ions from the reconnection site, leading to a fast reconnection rate independent of Lundquist number. In addition to allowing fast reconnection, we find that these non-equilibria partial ionization effects lead to the onset of the nonlinear secondary tearing instability at lower values of the Lundquist number than has been found in fully ionized plasmas.These simulations provide evidence that magnetic reconnection in the chromosphere could be responsible for jet-like transient phenomena such as spicules and chromospheric jets.Comment: 8 Figures, 32 pages tota

The Dynamic Evolution of Solar Wind Streams Following Interchange Reconnection

Interchange reconnection is thought to play an important role in determining the dynamics and material composition of the slow solar wind that originates from near coronal hole boundaries. To explore the implications of this process we simulate the dynamic evolution of a solar wind stream along a newly-opened magnetic flux tube. The initial condition is composed of a piecewise continuous dynamic equilibrium in which the regions above and below the reconnection site are extracted from steady-state solutions along open and closed field lines. The initial discontinuity at the reconnection site is highly unstable and evolves as a Riemann problem, decomposing into an outward-propagating shock and inward-propagating rarefaction that eventually develop into a classic N-wave configuration. This configuration ultimately propagates into the heliosphere as a coherent structure and the entire system eventually settles to a quasi-steady wind solution. In addition to simulating the fluid evolution we also calculate the time-dependent non-equilibrium ionization of oxygen in real time in order to construct in situ diagnostics of the conditions near the reconnection site. This idealized description of the plasma dynamics along a newly-opened magnetic field line provides a baseline for predicting and interpreting the implications of interchange reconnection for the slow solar wind. Notably, the density and velocity within the expanding N-wave are generally enhanced over the ambient wind, as is the O7+/O6+ ionization ratio, which exhibits a discontinuity across the reconnection site that is transported by the flow and arrives later than the propagating N-wave

Simulations of Emerging Magnetic Flux. II. The Formation of Unstable Coronal Flux Ropes and the Initiation of Coronal Mass Ejections

We present results from three-dimensional magnetohydrodynamic simulations of the emergence of a twisted convection zone flux tube into a pre-existing coronal dipole field. As in previous simulations, following the partial emergence of the sub-surface flux into the corona, a combination of vortical motions and internal magnetic reconnection forms a coronal flux rope. Then, in the simulations presented here, external reconnection between the emerging field and the pre-existing dipole coronal field allows further expansion of the coronal flux rope into the corona. After sufficient expansion, internal reconnection occurs beneath the coronal flux rope axis, and the flux rope erupts up to the top boundary of the simulation domain (approximately 36 Mm above the surface).We find that the presence of a pre-existing field, orientated in a direction to facilitate reconnection with the emerging field, is vital to the fast rise of the coronal flux rope. The simulations shown in this paper are able to self-consistently create many of the surface and coronal signatures used by coronal mass ejection (CME) models. These signatures include surface shearing and rotational motions, quadrupolar geometry above the surface, central sheared arcades reconnecting with oppositely orientated overlying dipole fields, the formation of coronal flux ropes underlying potential coronal field, and internal reconnection which resembles the classical flare reconnection scenario. This suggests that proposed mechanisms for the initiation of a CME, such as "magnetic breakout," are operating during the emergence of new active regions

Distribution of Electric Currents in Solar Active Regions

There has been a long-lasting debate on the question of whether or not electric currents in solar active regions are neutralized. That is, whether or not the main (or direct) coronal currents connecting the active region polarities are surrounded by shielding (or return) currents of equal total value and opposite direction. Both theory and observations are not yet fully conclusive regarding this question, and numerical simulations have, surprisingly, barely been used to address it. Here we quantify the evolution of electric currents during the formation of a bipolar active region by considering a three-dimensional magnetohydrodynamic simulation of the emergence of a sub-photospheric, current-neutralized magnetic flux rope into the solar atmosphere. We find that a strong deviation from current neutralization develops simultaneously with the onset of significant flux emergence into the corona, accompanied by the development of substantial magnetic shear along the active region's polarity inversion line. After the region has formed and flux emergence has ceased, the strong magnetic fields in the region's center are connected solely by direct currents, and the total direct current is several times larger than the total return current. These results suggest that active regions, the main sources of coronal mass ejections and flares, are born with substantial net currents, in agreement with recent observations. Furthermore, they support eruption models that employ pre-eruption magnetic fields containing such currents.Comment: 6 pages, 5 figures, to appear in Astrophysical Journal Letter