The influence of non-uniform solar wind expansion on the angular momentum loss from the Sun

The influence on the rate of angular momentum loss from the Sun of magnetic geometries which are not spherically symmetric is estimated. Departures from spherical symmetry are expected to influence significantly the loss rate by two effects - the presence of closed magnetic field regions with no loss and also the variability in the radial distance to the Alfvénic point, as stressed by Mestel (1968).The loss rate is calculated for an MHD solar wind model with a solar magnetic field whose normal component at the surface is that of a north-south dipole. In contrast to Mestel's work, where the field was assumed dipolar within a certain surface and radial outside, the coupling between the solar wind and magnetic field is here taken into account exactly. For equivalent boundary conditions at the surface, the resulting field configuration yields an angular momentum loss rate which is only 15% of that for the monopole field normally used in angular momentum loss estimates. If, instead of equating boundary conditions at the Sun, one equates the two losses at the equator to that observed at 1 AU by spacecraft, then the ratio of the total loss for the distended dipole to that for the monopole is about 40%.On Leave from the Department of Applied Mathematics, The University, St. Andrews, Scotland.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Gas-magnetic field interactions in the solar corona

It is evident from eclipse photographs that gas-magnetic field interactions are important in determining the structure and dynamical properties of the solar corona and interplanetary medium. Close to the Sun in regions of strong field, the coronal gas can be contained within closed loop structures. However, since the field in these regions decreases outward rapidly, the pressure and inertial forces of the solar wind eventually dominate and distend the field outward into interplanetary space. The complete geometrical and dynamical state is determined by a complex interplay of inertial, pressure, gravitational, and magnetic forces. The present paper is oriented toward the understanding of this interaction. The helmet streamer type configuration with its associated neutral point and sheet currents is of central importance in this problem and is, therefore, considered in some detail.Integration of the relevant partial differential equations is made tractable by an iterative technique consisting of three basic stages, which are described at length. A sample solution obtained by this method is presented and its physical properties discussed.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The formation of solar prominences by magnetic reconnection and condensation

A model for solar quiescent prominences nested in a Figure 8 magnetic field topology is developed. This topology is argued to be the natural consequence of the distention of bipolar regions upward into the corona. If this distention is slow enough so that hydrostatic equilibrium holds approximately along the field lines, the transverse gas pressure forces fall exponentially with height whereas the inward Lorentz forces fall as a power law. At a low height in the corona, the pressure forces cannot balance the Lorentz forces provided the field lines remain tied to the photosphere and an inward collapse with subsequent reconnection at the point of closest approach should occur. Because of initial shear in the magnetic field, the reconnection would produce isolated helices above the point of reconnection since field lines would not interact with themselves but with their neighbors. This resulting topology produces a field above the elevated neutral line which is opposite in polarity to that of the photospheric field as in the current sheet models of Kuperus and Tandberg-Hanssen (1967). Raadu and Kuperus (1973), Kuperus and Raadu (1974), and Raadu (1979) and in agreement with recent observations of Leroy (1982), and Leroy et al. (1983).Assuming the isolated helices formed by reconnection are insulated from coronal thermal conduction and heating, the radiative cooling process and condensation is considered for the temperature range of 10⁴-6000 K. This condensation results in a steady downflow to the bottom of the helices as the temperature scale-height falls, thus forming a dense, cool, prominence at the bottom of the helical configuration resting on the elevated neutral line with the remainder of the helix being essentially evacuated of material. We identify this neutral line at the bottom of the prominence with the sharp lower edge often seen when viewing quiescent prominences side-on and the evacuated helix with the coronal cavity observed around prominences when seen during total eclipses.Downflow speeds associated with the condensation process are calculated for prominence temperatures and yield velocities in the range of the observed downflows of about 1 km s^–1.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The ‘melon-seed’ mechanism and coronal transients

Adopting the point of view that a coronal transient is a defined magnetic structure, it must be diamagnetic with respect to the external ambient magnetic field, i.e., the external field lines cannot penetrate the structure. If this is so, an integral approach involving only external forces can be very useful for studying the conditions for acceleration and large-scale dynamical behavior of the transient.After a discussion of a suggested transient configuration based upon observations of prominences, flare loops, and transient - filament relative orientations observed by Trottet and MacQueen (1980), we demonstrate the diamagnetic approach to this problem through a particularly simplified model. Necessary conditions for upward acceleration of the transient are discussed in some detail. One such plausible initiation mechanism is shown to be a constriction of the structure near its base by the external forces. This mechanism not only can provide the upward acceleration for the transient but is also compatible with the observation of hot rising flare loops during two-ribbon flare which show evidence for magnetic reconnection.We have studied the equilibrium conditions and dynamical behavior of the transient using this mechanism for two limiting cases - that in which the gas pressure in the structure dominates over the magnetic pressure and that in which the magnetic pressure dominates. For both cases, the required equilibrium conditions are compatible with observed coronal parameters. The dynamical behavior upon inward constriction, however, resembles the observed characteristics for transients best for the magnetically dominated case. For example, in the pressure-dominated case, the required temperatures for acceleration appear somewhat high being in excess of about 1.9 × 10⁶ K. If, in addition, the internal temperature declines adiabatically during the outward motion, the structure does not reach inifinity unless its initial temperature exceeds about 3 × 10⁶ K but stops a some radial distance, returns to the Sun only to be accelerated outward again in the same fashion. The rather stringent requirements on internal temperature for the pressure-dominated case in addition to the expectation that pressure-dominated transients should evolve into a thin pencil shape instead of maintaining an approximately self-similar profile as observed are strong arguments in favor of the magnetically dominated case.Based upon the above results, we suggest that the reconnection process evidenced in two-ribbon flares may not necessarily be the result of the relaxation of a locally open field configuration produced by the transient as described by Kopp and Pneuman (1976) but, instead, that the acceleration of the transient and the two-ribbon flare both may be produced by a common force, namely that provided by the constricting effect of the external magnetic field displaced by the presence of the structure.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Magnetic reconnection in the corona and the loop prominence phenomenon

Many classes of transient solar phenomena, such as flares, flare sprays, and eruptive prominences, cause major disruptions in the magnetic geometry of the overlying corona. Typically, the results from Skylab indicate that pre-existing closed magnetic loops in the corona are torn open by the force of the disruption. We examine here some of the theoretical consequences to be expected during the extended relaxation phase which must follow such events. This phase is characterized by a gradual reconnection of the outward-distended field lines. In particular, the enhanced coronal expansion which occurs on open field lines just before they reconnect appears adequate to supply the large downward mass fluxes observed in Ha loop prominence systems that form during the post-transient relaxation. In addition, this enhanced flow may produce nonrecurrent high speed streams in the solar wind after such events. Calculations of the relaxation phase for representative field geometries and the resulting flow configurations are described.New address: Los Alamos Scientific Laboratory, Los Alamos, N.M. 87545, U.S.A.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Coronal streamers

The geometrical and dynamical structure of a corona consisting of streamer and interstreamer regions is examined. The present paper is an extension of previous works of this series in that energy transport processes are included in the theoretical framework of the model. Under specified conditions at some reference level above the coronal base, the structure at larger distances is determined by simultaneous integration of the continuity, momentum, and energy equations for each region subject to the condition for a lateral balance of magnetic and gas pressure at all levels. Outward thermal conduction and convection by the solar wind are assumed to be the processes contributing to the energy balance of each region, the magnetic field effectively thermally insulating one region from the other.Numerical results are presented for situations representative of the solar corona. Regions occupied by streamers are found to have higher densities than their surroundings at all distances from the sun. For a given density at the coronal base, the density at the orbit of earth is lower in both the streamer and interstreamer region than that predicted for radial flow. The density enhancement increases outward to a maximum value at a distance of several solar radii. In addition, beyond a distance of a few radii streamers are characterized by higher expansion velocities and lower temperatures than their immediate surroundings. Similar to the case of radial flow, supersonic solutions exist only for base densities below a certain value, which depends upon the specified base temperature and magnetic field distribution. The general features illustrated by these models are expected to persist in the advent of more sophisticated multi-region models.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

A sheet-current approach to coronal-interplanetary modeling

The most pertinent effect of the currents in the coronal-interplanetary space is their alteration of the magnetic topology to form configurations of open field lines. The important currents seem to be those in the neighborhoods of the interfaces between closed and open field lines or between oppositely directed open field lines in the coronal helmet-streamer structures. Thus, the coronal-interplanetary space may be regarded as being partitioned by current-sheets into several piecewise current-free regions. These current sheets overlie the photospheric neutral lines, where the vertical component of the magnetic field reverses its polarity on the solar surface. But, their locations and strengths are determined by force balance between the magnetic field and the gas pressure in the coronal-interplanetary space. Since the pressure depends on the flow velocity of the solar wind and the solar wind channels along magnetic flux tubes, there is a strong magnetohydrodynamic coupling between the magnetic field and the solar wind. The sheetcurrent approach presented in this paper seems to be a reasonable way to account for this complicated interaction.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The rotation of magnetic loop systems in the solar atmosphere

Eclipse photographs indicate that large regions of the inner solar corona are confined in various types of closed magnetic configurations and, as a result, do not participate in the general solar wind expansion. In this paper, the rotation of initially poloidal loop configurations of this type, as influenced by differential rotation of the footpoints, is investigated. The analysis is restricted to axially symmetric fields and it is assumed that the toroidal magnetic field induced by differential rotation is small as compared to the initial poloidal field. This restricts the validity of the analysis to times less than about one month.The most interesting physical situation is that of flux tubes existing in one solar hemisphere only, one end of the tube being fixed in the photosphere at a higher latitude than the other. As a consequence, the lower end of the tube rotates at a faster rate than the upper end. Solution of the pertinent equations reveals that the angular velocity measured along a field line increases monotonically from its value at the poleward footpoint to that at the lower footpoint. The variation of angular velocity along the field depends upon the field geometry only and is not directly related to the variation of angular velocity along the solar surface between the footpoints. Depending upon the field configuration, both outward radial increases and decreases are possible. Using the Newton and Nunn model for the surface differential rotation rate, the angular velocity distribution on two particularly simple types of closed magnetic loop systems is determined analytically. It is shown that the angular velocity increases outward in the polar regions but decreases outward near the equator - leading to a decrease in differential rotation with height.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Solar flares as resulting from the temporary interruption of energy flow to the corona: A case of hydromagnetic resonance

The hypothesis that solar flares may be caused by a choking off of the normal energy flux to the corona by the strong closed magnetic fields of a plage is examined. If the energy flux into a plage from the photosphere is of the order of 10⁸ ergs/cm² sec, and if a substantial fraction of this energy is carried in the form of Alfvén waves, then the rate of dissipation of the waves is slower than the rate at which energy is injected. Since the waves must propagate along the magnetic field and cannot reenter the photosphere, they must remain within the plage; hence, the magnetic and kinetic energy in a small-scale motion (either waves, turbulence, or high-energy particles) must increase with time, eventually causing disruption of the volume when the small-scale energy density exceeds the energy in the mean field. It is believed that the unusually broad wings in the emission lines represent evidence of this phenomenon. The accumulation of waves is manifested as a resonance which occurs initially only at discrete locations in the magnetic field, but later is expected to involve the whole flare volume. The response of a typical volume of flare dimensions due to a trapping of the normal wave supply to the corona is studied through use of the virial equation. For magnetic fields typical of a plage, the region expands in a time scale of 10²–10³ sec, with a velocity in the neighborhood of 10–20 km/sec. Small-scale velocities within the region, however, have reached 100–300 km/sec, indicating that almost all the energy in the flare resides in small-scale forms. The energy density of the flare region exhibits a behavior much more explosive than the expansion rate. There is a rapid rise to maximum in 10² sec or less, and a slow subsequent decline taking about 10³–10⁴ sec due to the dilution of energy caused by expansion of the region. The predicted temporal behavior of the energy density coincides qualitatively with the light curves observed during flares, and it is suggested that the rise and decline of the energy density is to be associated with the optical flare. The total flare is defined as the time required for the energy density of the chromosphere and corona to return to the pre-flare state. During this time (about one hour) a large flare can derive the necessary 10³² ergs from normal photospheric energy output.     

Energetics of two-ribbon solar flares

A theory of two-ribbon solar flares is presented which identifies the primary energy release site with the tops of the flare loops. The flare loops are formed by magnetic reconnection of a locally opened field configuration produced by the eruption of a pre-flare filament. Such eruptions are commonly observed about 15 min prior to the flare itself. It is proposed that the flare loops represent the primary energy release site even during the earliest phase of the flare, i.e., the flare loops are in fact the flare itself.Based upon the supposition that the energy release at the loop tops is in the form of Joulean dissipation of magnetic energy at the rising reconnection site, a quantitative model of the energy release process is developed based upon an analytic reconnecting magnetic field geometry believed to represent the basic process. Predicted curves of energy density vs time are compared with X-ray observations taken aboard Skylab for the events of 29 July, 13 August, and 21 August in 1973. Considering the crudity of the model, the comparisons appear reasonable. The predicted field strengths necessary to produce the observed energy density curves are also reasonable, being in the range 100–1000 G.The National Center for Atmospheric Research is sponsored by the National Science Foundation.