Expert: Philip A. Stahl - 2/26/2009

Question
What is the difference between the different flare time scales: the conductive, radiative, and acoustic? Can you provide basic equations that give these? (Not a HW problem!)

Answer
Hello,

The three time scales to which you refer (for LOOP flares of some length, L) can be given in theoretical and empirical equations.

For the conduction time scale (t_c):

Theoretical:  t_c = (pL^2)/(y - 1) kT

Empirical:  t_c =  (4 x 10^-12) n_e L^2/  T ^5/2

In the preceding, p is the pressure, L the length, y the ratio of specific heats (e.g. for an ideal gas, y = 5/3), k is the conductivity, and T the temperature.

In the empirical formula, n_e is the electron number density.

For the radiative time scale (t_r):

Theoretical:  t_r = p/ (y - 1) n_e^2 Q

Empirical: t_r = (4 x 10^6) T^2/ n_e

where Q is a radiative emission parameter.

For the acoustic- sound time scale (t_s):


Theoretical:  t_s = L/c_s

Empirical: t_s =  (6 x 10^-3) L/ T^1/2


where c_s is the ion sound speed

Of course, these do not always work out to what is projected. For example, for the loop desingated 'BC' in AR 2776 (which appeared around Nov. 4, 1980) the value for c_s ~ 3 x 10^5 m/s and L =  9.3 x 10^8 m

the value comes to nearly one hour for t_s although the projected value is typically on the order of 100s.

So, one does need to be aware of divergences from what is usually expected.

Hope this is useful!