[Loops] New loop paper

[Markus J. Aschwanden]

Dear Piet,

Congratulations to the new analytical paper on loop profiles.
I just came back from a 3-week trip to France and saw your
new paper which I am going to read. Incidentally, I also worked
on some analytical approximations for loop profiles as well as
time profiles of heated and cooling loops. Perhaps we can compare
some of the analytical solutions in both papers. I think the two
papers are quite complementary, but I had the same motivation,
to derive some analytical expressions that provide simple tools
for rapid forward modeling of loops observed by XRT and AIA.
You probably have also seen Jim Klimchuk's EBTEL paper which
also goes in this direction (just accepted by ApJ). I give you
the URL of my preprint below and we could think if a comparison
of some cases could be useful to corroborate each others approach.

Cheers,
Markus

  Aschwanden,M.J. and Tsiklauri, D. 2008, The Astrophysical  
Journal, ... (subm)
URL1="http://www.lmsal.com/~aschwand/eprints/2008_hydroapprox.pdf"
Analytical approximations in explicit form for the hydrodynamic  
evolution of heated and cooling coronal loops


On Apr 16, 2008, at 10:25 AM, Petrus Martens wrote:

> Folks,
>
>     I submitted the following paper to ApJ and put a copy on Astro-Ph:
> Article-id: 0804.2241.   Its main purpose was to develop the tools
> for rapid forward modeling of loops observed by XRT and AIA.
>
>     Best regards,
>
>     Piet
>
>
> Scaling Laws and Temperature Profiles for Solar and Stellar Coronal
> Loops with Non-uniform Heating
>
> P.C.H. Martens
>
> Abstract:
>
> The bulk of solar coronal radiative loss consists of soft X-ray  
> emission
> from quasi-static loops at the cores of Active Regions.  In order to
> develop diagnostics for determining the heating mechanism of these  
> loops
> from observations by coronal imaging instruments, I have developed
> analytical solutions for the temperature structure and scaling laws of
> loop strands for a wide range of heating functions, including  
> footpoint
> heating, uniform heating, and heating concentrated at the loop  
> apex. Key
> results are that the temperature profile depends only weakly on the
> heating distribution -- not sufficiently to be of significant  
> diagnostic
> value --  and that the scaling laws survive for this wide range of
> heating distributions, but with the constant of proportionality in the
> RTV scaling law ($P_{0}L\, \thicksim\, T_{max}^3$) depending on the
> specific heating function.  Furthermore, quasi-static analytical
> solutions do not exist for an excessive concentration of heating near
> the loop footpoints, a result in agreement with recent numerical
> simulations.  It is demonstrated that a generalization of the  
> solutions
> to the case of a strand with a variable diameter leads to only
> relatively small correction factors in the scaling laws and  
> temperature
> profiles for constant diameter loop strands.  A quintet of leading
> theoretical coronal heating mechanisms is shown to be captured by the
> formalism of this paper, and the differences in thermal structure
> between them may be verified through observations.  Preliminary  
> results
> from full numerical simulations demonstrate that, despite the
> simplifying assumptions, the analytical solutions from this paper are
> stable and accurate.
>
>
>
> --------------------------------------------------------------------
>   Piet Martens              Tel:   617-496-7769
>   Center for Astrophysics   Fax:   617-496-7577
>   60 Garden Street, MS 58   Cell:  617-999-0353
>   Cambridge, MA 02138	   pmartens at cfa.harvard.edu
> --------------------------------------------------------------------
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____________________________________________
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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