[Loops] cooling time

[Klimchuk, James A. (GSFC-6710)]

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
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E-mail:  James.A.Klimchuk at nasa.gov<mailto:James.A.Klimchuk at nasa.gov>
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No endorsement by NASA is implied for any correspondence related to my official role in professional organizations.

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