[Loops] New loop paper

[Petrus Martens]

Hey Markus,

    Thanks for the kind words.  Right now I am focusing on the
numerical verification mentioned in the paper, plus, most important,
on supporting Trae in the final writing for his thesis -- that
mostly concerns flaring loops.

    I hope we can get together sometime at a meeting and compare
notes.  Perhaps some future Santorini-like meeting to move into
the XRT/AIA era.

    Cheers,

    Piet


Markus J. Aschwanden wrote:
> 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"_ 
> <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 
>> <mailto: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 <mailto:aschwanden at lmsal.com>
> _______________________________________
> ____________________________________
> 
> 
> 
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