Hi Piet,
I am just reading your new paper on analytical solutions of loop profiles, which overlaps and complements my new paper on analytical approximations of loop dynamics. Here a few overlapping aspects:
(1) In Eq.(28) you show that the RTV scaling law survives in your analytical solution, which fully agrees with my finding (Eq.81-82 in my paper), even for different non-uniform heating functions. For the constant of proportionality, I find also slightly different values for different heating functions (Eq.82), basically scaling with the Mach number of the upflows.
(2) Also the second scaling law (your Eq.31) is reproduced in my paper in an equivalent way (Eq. 20 in my paper), with slightly different values for the constant for non-uniform heating.
(3) The expression for the loop top temperature (your Eq.35) is also reproduced in Eq.23 in my paper.
(4) Your analytical solutions for the temperature profiles (Fig.3 in your paper) are nearly identical to the approximations I derive in my paper (Fig.2), for uniform as well as non-uniform heating.
So, all the overlapping parts in your and my paper seems to agree quite well, although my approach is based on some approximations (such as neglecting the radiative loss during the heating phase). On the other side, my approach is complementary in the sense that it gives also an approximation for the density profile n(s), as well as for the time evolution of temperature T(s,t) and density n(s,t) during the heating and cooling phase. So, both papers provide some analytical tools in a complementary way, which might be useful for quick forward-modeling of loops observed with Hinode and/or STEREO.
Congrats, again, to your very useful analytical study. Cheers,
Markus
____________________________________________ 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 _______________________________________