An Introduction to Modern Astrophysics · Problem 11.13
The Interstellar Medium and Star Formation — Carroll & Ostlie
Physics — Astrophysics · solar-flare-energy
Problem
Assume that a large solar flare erupts in a region where the magnetic field strength is 0.03 T and that it releases 1025 J in one hour.
(a) What was the magnetic energy density in that region before the eruption began?
(b) What minimum volume would be required to supply the magnetic energy necessary to fuel the flare?
(c) Assuming for simplicity that the volume involved in supplying the energy for the flare eruption was a cube, compare the length of one side of the cube with the typical size of a large flare.
(d) How long would it take an Alfv\'{e}n wave to travel the length of the flare?
(e) What can you conclude about the assumption that magnetic energy is the source of solar flares, given the physical dimensions and timescales involved?