[Loops] comments on new loop paper and comparison with my paper

[Markus J. Aschwanden]

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 at lmsal.com
_______________________________________



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