fl210.metcalf04 Posted: 17-Jul-95 Updated: 16-Sep-95 Events specified: N/A
T. Metcalf Institute for Astronomy, Univeristy of Hawaii
G. Fisher Space Sciences Laboratory, University of California, Berkeley
In a recent paper, Hawley et al. derived a scaling law relating the length of a flaring coronal loop to the loop apex temperature and to the rise and decay time of the x-ray flare. The scaling law was used in the study of a stellar flare on AD Leonis. This scaling law is important for the interpretation of stellar flare data. However, since there is no way to test the law for stellar flares it should be tested against solar data.
We propose to use SXT data to test the Hawley-Fisher scaling law. We will measure the loop length and temperature, as well as the x-ray rise and decay time, for a large number of flaring loops in the SXT database. We will concentrate on flares with simple geometries in which individual flaring loops can be identified. With these data, we will determine the validity of the H-F scaling law.
Reference
Hawley, S. L. et al, "Simultaneous EUVE and Optical Observations of AD Leonis: Evidence for Large Coronal Loops and the Neupert Effect in Stellar Flares", Ap.J, in press (Nov. 1, 1995)
Update 16-Sep-95
This work has been completed. We have verified the loop length estimator have submitted a paper to ApJ describing the results. The abstract of the paper follows:
We compare the lengths of coronal loops observed on the Sun using the SXT telescope on {\it Yohkoh} with those predicted from the theoretical model of Hawley {\it et al}. This model relates the temporal behavior of coronal emission observed during flares on active stars to the length of the loops undergoing flaring. In that model, the footpoint-to-footpoint loop length $2L$ (measured in km) should obey the relationship $2L \simeq .01 \ Y$, where $Y = 1.26 \tau_r^{3/7}\ \tau_d^{4/7} T_A^{1/2}$, $\tau_r$ is the ``rise time'' (s) from flare onset to flare peak, $\tau_d$ is the ``decay time'' (s) from flare peak to the time when the emission measure is 25\% of its peak value, and $T_A$ (K) is the temperature at the top of the loop at flare peak. The observations show a strong correlation between $2L$ and $Y$, with the theoretical relationship consistent with observed loop lengths in most cases. For a few loops, the theoretical model tends to somewhat overpredict the loop length. When the observed loop lengths are fitted to a single power law relationship in $Y$, we find the data are best fit by $\log 2L = \log (0.44\pm 0.06) + (0.75\pm 0.05)\log Y\ $. We offer no quantitative theoretical justification for this relationship, but we do suggest several reasons why the Hawley {\it et al} model overpredicts loop lengths in some cases.