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
******************************************************************************** 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.govmailto:James.A.Klimchuk@nasa.gov Homepage: http://science.gsfc.nasa.gov/sed/index.cfm?fuseAction=people.jumpBio&&am... No endorsement by NASA is implied for any correspondence related to my official role in professional organizations.
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Dear all:
Please find a recent paper on Asymmetries in Coronal Spectral Lines and Emission Measure Distribution, which Jim and Myself have recently submitted to ApJ. The abstract is appended below:
Abstract: It has previously been argued that 1. spicules do not provide enough preheated plasma to fill the corona, and 2. even if they did, additional heating would be required to keep the plasma hot as it expands upward. We here ad- dress the question of whether spicules play an important role by injecting plasma at cooler temperatures (< 2 MK), which then gets heated to coronal values at higher altitudes. We measure red-blue asymmetries in line profiles formed over a wide range of temperatures in the bright moss areas of two active regions. We derive emission measure distributions from the excess wing emission. We find that the asymmetries and emission measures are small and conclude that spicules do not inject an important (dominant) mass flux into the cores of active regions at temperatures > 0.6 MK (log T > 5.8). These conclusions apply not only to spicules, but to any process that suddenly heats and accelerates chromospheric plasma (e.g., a chromospheric nanoflare). The traditional picture of coronal heating and chromospheric evaporation appears to remain the most likely explanation of the active region corona.
Dear coronal loop explorers,
here a 2-part paper on scaling laws and statistical size distributions, accepted for publication in ApJ.
The datasets are M and X-class flares (observed with AIA), but a similar study could be conducted with heating events in coronal loops, if we believe that loops are heated individually and the heating events are considered as avalanche events in a self-organized criticality system.
Share and enjoy, Markus
Aschwanden,M.J., Zhang,J., and Liu,K. 2013, ApJ 774 (Sept 10, 2013 issue, in press) URL1="http://www.lmsal.com/~aschwand/eprints/2013_spatio1.pdf" Multi-Wavelength Observations of the Spatio-Temporal Evolution of Solar Flares with AIA/SDO: I. Universal Scaling Laws of Space and Time Parameters
Aschwanden,M.J. and Shimizu,T. 2013, ApJ (in press) URL1="http://www.lmsal.com/~aschwand/eprints/2013_spatio2.pdf" Multi-Wavelength Observations of the Spatio-Temporal Evolution of Solar Flares with AIA/SDO: II. Hydrodynamic Scaling Laws and Thermal Energies
____________________________________________ Dr. Markus J. Aschwanden Solar & Astrophysics Laboratory Lockheed Martin Advanced Techology Center Org. ADBS, Bldg. 252 3251 Hanover St., Palo Alto, CA 94304, USA Phone: 650-424-4001, FAX: 650-424-3994 URL: http://www.lmsal.com/~aschwand/ e-mail: aschwanden@lmsal.com _______________________________________
loops@solar.physics.montana.edu