I was asked to define the cooling time, t_cool, in my last e-mail. Sorry, I should have done this. It is the thermal energy density divided by the energy loss rate:
t_cool = (3/2) P / R_loss ,
where P is the pressure. When thermal conduction dominates the cooling, as is the case early in a nanoflare event, the loss rate is approximately
R_loss = (2/7) kappa_0 T^(7/2) / L^2 ,
where T is the peak temperature in the strand, and L is the distance between the location of the peak and the chromosphere (typically the loop half length). Generally speaking, temperature decreases according to
T(t) = T_0 exp(-t / t_cool) .
I assumed this in getting the percentage temperature variations in the original e-mail.
Cheers,
Jim
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James A. Klimchuk
NASA Goddard Space Flight Center
Solar Physics Lab, Code 671
Bldg. 21, Rm. 158
Greenbelt, MD 20771
USA
Phone: 1-301-286-9060
Fax: 1-301-286-7194
E-mail: James.A.Klimchuk@nasa.gov
Homepage: http://science.gsfc.nasa.gov/sed/index.cfm?fuseAction=people.jumpBio&&iPhonebookId=15844
No endorsement by NASA is implied for any correspondence related to my official role in professional organizations.
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