Evidence that the X-Ray Plasma in Microflares is in a Sequence of Subresolution Magnetic Tubes

We analyze the cooling of the X-ray emitting thermal plasma in microflares observed in active regions by the Yohkoh Soft X-ray Telescope. A typical microflare appears to be a transient brightening of an entire small magnetic loop, often having a diameter near the limit of resolution (approximately 2 x 10(exp 8) cm) (Shimizu 1995, PASJ, 47, 251). The X-ray plasma in the loop cools by emission of XUV radiation and by heat conduction to the cooler plasma at the feet of the loop. The cooling rate is determined by the plasma temperature and density and the loop length. The plasma density is determined from the observed X-ray brightness of the loop in combination with the temperature, the loop diameter, and the filling factor. The filling factor is the volume fraction of the loop occupied by the subset of magnetic tubes that is filled by the X-ray plasma and that contains practically all of the X-ray plasma present in the microflare loop. Taking typical values from the hundreds of microflares measured by Shimizu (1995) (X-ray brightness through the thin aluminum filter approximately 4 x 10(exp 3) DN/s/pixel, lifetime approximately 5 min, temperature approximately 6 x 10(exp 6) K, loop length approximately 10(exp 9) cm, loop diameter approximately 3 x 10(exp 8) cm), we find that for filling factors greater than approximately 1% (1) the cooling time is much shorter than the duration of the microflare, and (2) conductive cooling strongly dominates over radiative cooling. Because the cooling time is so short and because the conductive heat flux goes mainly into increasing the plasma density via chromospheric evaporation, we are compelled to conclude that (1) heating to X-ray temperatures continues through nearly the entire life of a microflare, (2) the heating keeps changing to different field lines, so that any one magnetic tube in the sequence of heated tubes emits X-rays only briefly in the life of the microflare, and (3) at any instant during the microflare the tubes filled with X-ray plasma occupy only a small fraction (less than approximately 10%) of the microflare loop. Hence, we expect that coronal X-ray images with spatial resolution 2-3 times better than from Yohkoh will show plenty of rapidly changing filamentary substructure in microflares.