During the past year we have continued our work on twisted active region flux tubes. Our two most notable accomplishments have been the development of a theoretical model which explains the amounts of twist observed for most active regions, and our work on the kink instability pertaining to the highly twisted, so-called ``Delta spot'' active regions, responsible for the largest solar flares.
Recent work by Pevtsov, Canfield and Metcalf suggests that active regions emerge from the solar interior in a twisted state, with a weak dependence upon latitude superimposed upon a high degree of scatter. During a visit to UC Berkeley's Space Sciences Laboratory during the Summer of 1997, Dr. Dana Longcope led an investigation into the origins of twist in active regions. We propose that this twist is imparted to the flux through its interaction with turbulent motions in the solar convection zone. This process, which we call the ``Sigma Effect'', operates on isolated magnetic flux tubes subjected to buffeting by turbulence with a nonvanishing kinetic helicity. The Sigma effect leads to twist of the same sense inferred from observation and opposite to that predicted by the so-called ``alpha effect'', which is presumed by many to be responsible for the solar dynamo. A series of numerical calculations were performed to estimate the importance of the Sigma effect in the solar convection zone. The results compare favorably with observations of both the weak latitudinal dependence and the level of scatter. We find a further relationship with the magnetic flux in active regions that can be tested with future observations.
This work was carried out by Dr. Longcope during his visit to Berkeley, Dr. Fisher, and Dr. Alex Pevtsov of Montana State University. A paper describing this work is in press in the Astrophysical Journal.
We have also continued our investigation of the helical kink instability as it relates to the evolution of active region scale magnetic flux tubes in the solar interior. Rising flux loops with helical kinks superposed may explain the observed rotational behavior of emerging delta spot regions. We studied time evolution of the kink using a 3d MHD code on the Naval Research Laboratory's CM5. We have found that highly twisted flux tubes subjected to multiple unstable kink modes will develop concentrated kinks where the modes of differing wavenumber interfere constructively. In the nonlinear regime the flux tube reconnects with itself to form a structure which looks very much like a Delta spot active region.
This work is being carried out by UCB Physics Graduate Student Mark G. Linton, as a collaboration with Dr. R. B. Dahlburg of NRL, Fisher (SSL), Dana Longcope (SSL and Montana State Univ.), and Dr. Yuhong Fan (HAO/NCAR). Two papers describing this work were submitted, one of which is now in press.
Dr. Christopher M. Johns-Krull arrived in our group in Berkeley in August 1997. He is interested in activity in the Sun and on other active stars. During the past year, Dr. Johns-Krull has worked primarily on problems involving the direct measurement of magnetic field strength and filling factors on the surfaces of late-type main sequence and pre-main sequence stars. Such measurements rely on detailed analysis of line profiles, which can be strongly affected by the ubiquitous lines of TiO present in photospheric spectra. Valenti, Piskunov, and Johns-Krull (1998) have determined wavelength corrections for several strong gamma bands of TiO and show that regions of the optical spectrum of M dwarfs can be well modeled at high spectral resolution. Using these improved line data and additional infrared spectra, Johns-Krull, Valenti, and Koresko (1998) have measured the magnetic field through Zeeman broadening of line profiles for the first time on a T Tauri star. Additionally, at the Protostars and Planets IV conference held this July, Dr. Johns-Krull presented the first unambiguous measurements of circular polarization resulting from magnetic fields on a slowly rotating late-type pre-main sequence star.
While magnetic fields are known to play the primary role in heating the Sun's corona, the heating mechanism(s) remain poorly understood. We employ a new approach to studying coronal heating by comparing the spatially integrated radiative output of the corona in active regions with ``global'' magnetic variables computed from vector magnetograms. Our strategy is to examine as diverse a sample of active regions as possible, and see which, if any, global magnetic quantities provide a good predictor for coronal heating.
X-ray luminosities are measured with the SXT telescope on Yohkoh (Tsuneta et al 1991 Sol. Phys. 136, p. 37) using the thin aluminum filter; vector magnetograms were taken with the Haleakala Stokes Polarimeter (Mickey et al 1985 Sol. Phys. 97, p. 223) at the University of Hawaii's Mees Solar Observatory. Global (spatially integrated) magnetic quantities in our study include the total unsigned magnetic flux, the integral of the absolute vertical current density, the integral of the square of the vertical magnetic field, and the integral of the square of the transverse components of the magnetic field.
We find that the X-ray luminosity Lx is best correlated with the total unsigned magnetic flux Phi. While other global quantities also correlate with the X-ray luminosity, we find that these correlations can be explained entirely by their own correlations with Phi, and when these correlations are accounted for, there is no significant residual correlation of Lx with any other variables. We also find the specific flux dependence of Lx is consistent with Longcope's ``Minimum Current Corona'' picture of coronal heating via reconnection near separator loops.
This work is being carried out by Fisher (SSL), Longcope (SSL and Montana State U.) T. R. Metcalf (Lockheed Palo Alto), and A. A. Pevtsov (Montana State U.) This work has been submitted for publication in the Astrophysical Journal and is now in press.
The launch of spacecraft such as SOHO and Solar-B, and the advent of new high spectral resolution optical solar observations (e.g. Johns-Krull et al 1997 Ap. J., 112, 221.) greatly increase the number of available spectral lines and continua which can be used to understand heating in the chromosphere, transition region, and corona. However, computation of radiative diagnostics, whether in the optically thin regime or through non-LTE radiation transfer calculations, requires accurate, and sometimes extensive atomic data. Since the accuracy of any spectral predictions are dependent upon the accuracy of the atomic data, we embarked upon, and have nearly completed, an ambitious effort (dubbed the ``Berkeley-Livermore Atomic Models'' [BLAM] project) to provide extensive atomic models of all ion stages of the 11 most abundant elements of the Sun. Our dataset is unique in that there is no bias toward any particular wavelength range or temperature, and it is intended to be as comprehensive and self-consistent as possible. We seek to provide extremely detailed atomic models for all of the important absorbers and radiators in the outer atmosphere of the Sun.
The BLAM project is being carried out primarily by D. Tod Woods, and consists of two parts. First, we perform extensive calculations using a suite of atomic physics codes available at Lawrence Livermore National Laboratory (LLNL), in collaboration with J. K. Nash (LLNL). The second part of the project is to incorporate other work which we consider better than our own into the data base, particularly for the collisional processes. Our calculations are based upon generating wave functions using a Multi-Configuration Dirac-Fock technique. We then compute the energy levels, oscillator strengths, and autoionization rates. We also compute in a more approximate manner the collisional excitation, photoionization, and collisional ionization cross sections. The only physical processes which we do not compute directly are dielectronic recombination (due to the large number of doubly excited states which must be enumerated to obtain accurate results) and charge exchange. We rely solely on the literature for these processes. The extent of the BLAM dataset is outlined in Table 1 where we list the ion stages covered, the total level count, and the number of bound-bound radiative transition rates computed (including electric dipole, magnetic dipole, and electric quadrupole transitions). The number of collision cross sections calculated is of the same order. To date we have completed calculations for all ion stages of the elements H, He, C, N, O, Ne, Mg, Si, S, Ca, and Fe. The model for a given ion can be quite extensive. For neutral iron alone, our model has over 5000 levels. We have also included many inner shell vacant states in our models to allow us to properly absorb the intense X-ray emission which is sometimes emitted in very large flares.
| Element | Ion Stages | Level Count | No. Bound-Bound Transitions |
|---|---|---|---|
| H | I | 20 | 190 |
| He | I-II | 39 | 270 |
| C | I-VI | 272 | 8.9 x 103 |
| N | I-VII | 438 | 2.48 x 104 |
| O | I-VIII | 672 | 5.27 x 104 |
| Ne | I-X | 3386 | 1.10 x 106 |
| Mg | I-XII | 1078 | 8.20 x 104 |
| Si | I-XIV | 2629 | 3.54 x 105 |
| S | I-XIV | 4529 | 1.09 x 106 |
| Ca | I-XX | 6799 | 1.83 x 106 |
| Fe | I-XXVI | 32770 | 3.10 x 107 |
The BLAM project differs from others such as the OPACITY and IRON projects in several respects. From a computational standpoint, our results differ in that we compute the structure including relativistic effects in intermediate coupling, whereas both of the above projects assume LS coupling. We also differ from the OPACITY and IRON projects in that we are concerned with a combination of physical processes (i.e. collisional and radiative) and a number of elements. Neither of these projects addresses all of these issues. Finally, our project differs from others in that we do not rely solely on our own computations. By far the most time consuming part of this project is including the best results (whether experimental or theoretical) from the literature in our models. The end result is a single source for all of the atomic data needed by the solar community. We hope to make the data available to the solar physics community sometime within the next year.