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Dear Piet,<div><br class="webkit-block-placeholder"></div><div>Congratulations to the new analytical paper on loop profiles.</div><div>I just came back from a 3-week trip to France and saw your</div><div>new paper which I am going to read. Incidentally, I also worked</div><div>on some analytical approximations for loop profiles as well as</div><div>time profiles of heated and cooling loops. Perhaps we can compare</div><div>some of the analytical solutions in both papers. I think the two</div><div>papers are quite complementary, but I had the same motivation,</div><div>to derive some analytical expressions that provide simple tools</div><div>for rapid forward modeling of loops observed by XRT and AIA.</div><div>You probably have also seen Jim Klimchuk's EBTEL paper which</div><div>also goes in this direction (just accepted by ApJ). I give you</div><div>the URL of my preprint below and we could think if a comparison</div><div>of some cases could be useful to corroborate each others approach.</div><div><br class="webkit-block-placeholder"></div><div>Cheers,</div><div>Markus</div><div><br class="webkit-block-placeholder"></div><div> <span class="Apple-style-span" style="font-family: Times; font-size: 16px; ">Aschwanden,M.J. and Tsiklauri, D. 2008, The Astrophysical Journal, ... (subm)</span></div><p style="margin: 0.0px 0.0px 16.0px 0.0px"><font face="Times" size="5" style="font: 16.0px Times"> <a href="http://www.lmsal.com/~aschwand/eprints/2008_hydroapprox.pdf"><font color="#541a8c" style="color: #541a8c"><u>URL1="http://www.lmsal.com/~aschwand/eprints/2008_hydroapprox.pdf"</u></font></a> <br> </font><font face="Times" size="5" style="font: 18.0px Times">Analytical approximations in explicit form for the hydrodynamic evolution of heated and cooling coronal loops</font></p><div><br><div><div>On Apr 16, 2008, at 10:25 AM, Petrus Martens wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Folks,</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><span class="Apple-converted-space"> </span>I submitted the following paper to ApJ and put a copy on Astro-Ph:</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Article-id: 0804.2241. <span class="Apple-converted-space"> </span>Its main purpose was to develop the tools</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">for rapid forward modeling of loops observed by XRT and AIA.</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><span class="Apple-converted-space"> </span>Best regards,</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><span class="Apple-converted-space"> </span>Piet</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Scaling Laws and Temperature Profiles for Solar and Stellar Coronal<span class="Apple-converted-space"> </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Loops with Non-uniform Heating</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">P.C.H. Martens</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Abstract:</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">The bulk of solar coronal radiative loss consists of soft X-ray emission<span class="Apple-converted-space"> </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">from quasi-static loops at the cores of Active Regions.<span class="Apple-converted-space"> </span>In order to<span class="Apple-converted-space"> </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">develop diagnostics for determining the heating mechanism of these loops<span class="Apple-converted-space"> </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">from observations by coronal imaging instruments, I have developed<span class="Apple-converted-space"> </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">analytical solutions for the temperature structure and scaling laws of<span class="Apple-converted-space"> </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">loop strands for a wide range of heating functions, including footpoint<span class="Apple-converted-space"> </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">heating, uniform heating, and heating concentrated at the loop apex. Key<span class="Apple-converted-space"> </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">results are that the temperature profile depends only weakly on the<span class="Apple-converted-space"> </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">heating distribution -- not sufficiently to be of significant diagnostic<span class="Apple-converted-space"> </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">value --<span class="Apple-converted-space"> </span>and that the scaling laws survive for this wide range of<span class="Apple-converted-space"> </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">heating distributions, but with the constant of proportionality in the<span class="Apple-converted-space"> </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">RTV scaling law ($P_{0}L\, \thicksim\, T_{max}^3$) depending on the<span class="Apple-converted-space"> </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">specific heating function.<span class="Apple-converted-space"> </span>Furthermore, quasi-static analytical<span class="Apple-converted-space"> </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">solutions do not exist for an excessive concentration of heating near<span class="Apple-converted-space"> </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">the loop footpoints, a result in agreement with recent numerical<span class="Apple-converted-space"> </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">simulations.<span class="Apple-converted-space"> </span>It is demonstrated that a generalization of the solutions<span class="Apple-converted-space"> </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">to the case of a strand with a variable diameter leads to only<span class="Apple-converted-space"> </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">relatively small correction factors in the scaling laws and temperature<span class="Apple-converted-space"> </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">profiles for constant diameter loop strands.<span class="Apple-converted-space"> </span>A quintet of leading<span class="Apple-converted-space"> </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">theoretical coronal heating mechanisms is shown to be captured by the<span class="Apple-converted-space"> </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">formalism of this paper, and the differences in thermal structure<span class="Apple-converted-space"> </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">between them may be verified through observations.<span class="Apple-converted-space"> </span>Preliminary results<span class="Apple-converted-space"> </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">from full numerical simulations demonstrate that, despite the<span class="Apple-converted-space"> </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">simplifying assumptions, the analytical solutions from this paper are<span class="Apple-converted-space"> </span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">stable and accurate.</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">--------------------------------------------------------------------</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><span class="Apple-converted-space"> </span>Piet Martens<span class="Apple-converted-space"> </span>Tel: <span class="Apple-converted-space"> </span>617-496-7769</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><span class="Apple-converted-space"> </span>Center for Astrophysics <span class="Apple-converted-space"> </span>Fax: <span class="Apple-converted-space"> </span>617-496-7577</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><span class="Apple-converted-space"> </span>60 Garden Street, MS 58 <span class="Apple-converted-space"> </span>Cell:<span class="Apple-converted-space"> </span>617-999-0353</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><span class="Apple-converted-space"> </span>Cambridge, MA 02138<span class="Apple-tab-span" style="white-space:pre"> </span> <span class="Apple-converted-space"> </span><a href="mailto:pmartens@cfa.harvard.edu">pmartens@cfa.harvard.edu</a></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">--------------------------------------------------------------------</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">_______________________________________________</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Loops mailing list</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><a href="mailto:Loops@solar.physics.montana.edu">Loops@solar.physics.montana.edu</a></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><a href="https://mithra.physics.montana.edu/mailman/listinfo/loops">https://mithra.physics.montana.edu/mailman/listinfo/loops</a></div> </blockquote></div><br><div> <span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 14px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0; "><span class="Apple-style-span" style="border-collapse: separate; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; -webkit-text-decorations-in-effect: none; text-indent: 0px; -webkit-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><span class="Apple-style-span" style="border-collapse: separate; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; -webkit-text-decorations-in-effect: none; text-indent: 0px; -webkit-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><span class="Apple-style-span" style="border-collapse: separate; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; -webkit-text-decorations-in-effect: none; text-indent: 0px; -webkit-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><div>____________________________________________</div><div>Dr. Markus J. Aschwanden</div><div>Solar & Astrophysics Laboratory</div><div>Lockheed Martin Advanced Techology Center</div><div>Org. ADBS, Bldg. 252</div><div>3251 Hanover St., Palo Alto, CA 94304, USA</div><div>Phone: 650-424-4001, FAX: 650-424-3994</div><div>URL: <a href="http://www.lmsal.com/~aschwand/">http://www.lmsal.com/~aschwand/</a></div><div>e-mail: <a href="mailto:aschwanden@lmsal.com">aschwanden@lmsal.com</a></div><div>_______________________________________</div><div>____________________________________</div><br class="Apple-interchange-newline"></span></span></span></span><br class="Apple-interchange-newline"> </div><br></div></body></html>