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<!DOCTYPE html>
<!-- Style adapted from https://startbootstrap.com/themes/freelancer/ -->
<html lang="en">
<!--#include virtual="includes/head.inc" -->
<body id="page-top">
<nav class="navbar navbar-expand-lg bg-secondary fixed-top" id="mainNav">
<div class="container"><a class="navbar-brand js-scroll-trigger" href="#page-top">PhotoDissociation Region Toolbox</a>
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MODELS
</a>
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<li><a class="dropdown-item" href="/models.html">PDR Code Descriptions</a></li>
<li><a class="dropdown-item" href="/models/index.html">Model Plots & FITS Files</a></li>
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<header class="mymasthead bg-primary text-white text-center">
<div class="container d-flex flex-column">
<!-- Masthead Subheading-->
<h1 class="pre-wrap mymasthead-heading font-weight-bold mb-0">PDR Model Codes Used in the Toolbox</h1>
<br>
<div class="row mxauto">
<div class="col p3"></div>
<div class="col p3">
<button type="button" class="btn btn-light">
<a class="mya" href="#wolfirekaufman">Wolfire/Kaufman</a>
</button>
</div>
<div class="col p3">
<button type="button" class="btn btn-light">
<a class="mya" href="#kosmatau">KOSMA-tau</a>
</button>
</div>
<div class="col p3">
<button type="button" class="btn btn-light">
<a class="mya" href="#alternate">Bring Your Own</a>
</button>
</div>
<div class="col p3"></div>
</div>
<a name="wolfirekaufman">
<br>
<hr>
<h2>Wolfire/Kaufman Models</h2>
<p class="myp">
The Wolfire/Kaufman models are primarily based on the work of
<a class="mya" href="http://adsbit.harvard.edu/cgi-bin/nph-iarticle_query?1985ApJ...291..722T">Tielens & Hollenbach 1985;</a>
<a class="mya" href="http://adsbit.harvard.edu/cgi-bin/nph-iarticle_query?1990ApJ...358..116W">
Wolfire et al. 1990;
</a>
<a class="mya" href='http://adsbit.harvard.edu/cgi-bin/nph-iarticle_query?1991ApJ...377..192H'>
Hollenbach et al. 1991;
</a>
<a class="mya" href="http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1999ApJ...527..795K">Kaufman et al. 1999</a>;
and <a class="mya" href="https://ui.adsabs.harvard.edu/abs/2006ApJ...644..283K/abstract">Kaufman et al. 2006</a>.
For a given set of gas phase elemental abundances and grain properties,
each model is described by a constant H nucleus number density,
<span class="math">\(n\)</span>, or constant thermal pressure,
<span class="math">\(P_{th}\)</span>,
and incident far-ultraviolet intensity
<span class="math">\(G_0\)</span>.
The models solve for the
chemical balance, thermal equilibrium, and radiation transfer through
a PDR layer. Our treatment updates previous results
to use recent values of atomic and molecular data, current chemical
rate coefficients, and grain photolectric heating rates.
There are two versions of the "WK" model data sets ("ModelSets") available: 2006 and 2020. We recommend you use the 2020 version as they contain updated physics and chemistry.
There are a number model data sets ("ModelSets") currently available in PDR Toolbox.
The Wolfire/Kaufman constant density ModelSets present spectral line and continuum intensity ratios
as a function of
<span class="math notranslate nohighlight">\(G_0\)</span> and
<span class="math notranslate nohighlight">\(n\)</span>.
In a future release, we will add
constant thermal pressure ModelSets which present the intensity ratios as a function of
<span class="math notranslate nohighlight">\(G_0\)</span>
and thermal pressure <span class="math notranslate nohighlight">\(P_{th}\)</span>.
The PDR Toolbox can also support <a class="mya" href="#alternate">importing the external models of your choice</a>, provided they are stored in the right format.
</p>
<p class="myp">
The ratio plots are used to determine the beam averaged values of
<span class="math notranslate nohighlight">\(G_0\)</span> and <span class="math notranslate nohighlight">\(n\)</span>.
Note that <span class="math notranslate nohighlight">\(n\)</span> is the H nucleus density (cm<sup>-3</sup>).
so that the maximum abundance of H<sub>2</sub>, for example, is
<span class="math notranslate nohighlight">\(n(H_2)= 0.5~n\)</span>.
The values of <span class="math notranslate nohighlight">\(G_0\)</span> and <span class="math notranslate nohighlight">\(n\)</span>
are obtained by <a class="mya" href="http://pdrtpy.readthedocs.io">fitting the observations to the model space.</a>
Required are at least
two observations of line intensity ratios or
one line intensity ratio and the ratio of the [C II] + [O I]
intensity to the infrared dust continuum emission <span class="math notranslate nohighlight">\(I_{FIR}\)</span>.
More than two observed ratios will of course do a better job of determining unique <span class="math notranslate nohighlight">\(G_0\)</span> and <span class="math notranslate nohighlight">\(n\)</span>.
<!-- We have also provided
a diagnostic plot combining the [C II]/[O I] and ([C II]+[O I])/FIR
ratios as in Wolfire, Tielens, & Hollenbach 1990.
-->
</p>
<p class="myp">
It is important
to correct for the different beam area filling factors for various species.
For example, diffuse [C II] emission may fill the observing beam whereas
[O I] emission may arise from a smaller, high density and high temperature
region. In such a case, it would not be appropriate to take the ratio
of observed fluxes for fitting. Instead the ratio of intensities
should be used or the ratio of fluxes corrected for the separate emitting
solid angles. Note also that the ([C II] + [O I])/<span class="math notranslate nohighlight">\(I_{FIR}\)</span> model ratios
are for a single face-on PDR. For the case of active regions of galaxies,
or where there may be many clouds contained within the beam,
the FIR continuum is observed from both the near and far side of the cloud.
Thus, the observed ratio should be multiplied by a factor 2 (or
equivalently the model values should be divided by 2).
</div>
</header>
<section class="mypage-section bg-primary text-white mb-0" id="modelspecifics">
<div class="container">
<div class="text-center">
<h2 class="mypage-section-heading d-inline-block text-white">WK Model Specifics</h2>
</div>
<div class="row">
<div class="col-lg-7 ml-auto">
<h4>2020 Models</h4>
<p class="myp">
These model data start with the 2006 PDR model code and add improved physics and chemistry. Critical updates include those discussed in
<a class="mya" href="https://ui.adsabs.harvard.edu/abs/2016ApJ...826..183N/abstract">Neufeld & Wolfire 2016</a>, plus photo rates from
<a class="mya" href="https://ui.adsabs.harvard.edu/abs/2017A%26A...602A.105H/abstract">Heays et al. 2017</a>, oxygen chemistry rates from
<a class="mya" href="https://ui.adsabs.harvard.edu/abs/2018ApJ...856..100K/abstract">Kovalenko et al. 2018</a> and
<a class="mya" href="https://ui.adsabs.harvard.edu/abs/2018ApJ...854...25T/abstract">Tran et al. 2018</a>,
and carbon chemistry rates from
<a class="mya" href="https://ui.adsabs.harvard.edu/abs/2019MNRAS.487.3427D/abstract">Dagdigian 2019</a>. We have also implemented new collisional
excitation rates for [O I] from
<a class="mya" href="https://ui.adsabs.harvard.edu/abs/2018MNRAS.474.2313L/abstract">Lique et al. 2018</a> (and Lique private
communication) and have included <sup>13</sup>C chemistry along with the
emitted line intensities for [<sup>13</sup>C II] and <sup>13</sup>CO. In Box 1, we show the currently available spectral lines and those we expect to deploy later in the project. In addition, we will compute ModelSets for a full range of metallicity <span class="math">\(Z\)</span>.
</p>
</p><p class="myp">
In <a class="mya" href="https://pdrtpy.readthedocs.io">pdrtpy</a>, these are referred to as the <i>wk2020</i> ModelSet.
</p>
<h4>2006 Models</h4>
<p class="myp">
<a class="mya" href="/models/wk2006/index.html">These models</a>
are identical to those available in the "classic" web-based PDR Toolbox. They have metallicity <span class="math">\(Z=1\)</span>,
and contain [C I], [C II], [O I], Fe, Si, H<sub>2</sub> lines and the <sup>12</sup>CO ladder up to <span class="math">\(J=14\rightarrow 13\)</span>. For some lines, <span class="math">\(Z=3\)</span> is also available.
</p><p class="myp">
In <a class="mya" href="https://pdrtpy.readthedocs.io">pdrtpy</a>, these are referred to as the <i>wk2006</i> ModelSet.
</p>
</div><!-- col-->
<div class="col-lg-5 ml-auto">
<div class="card-transparent">
<a href="images/pdrttable.png"><img class="card-img-top" style="margin:0em 1em 1em 1em;border:3px;" src="images/pdrttable.png" align="left" width="80%" alt="Spectral lines modeled in PDRT"></a>
<div class="card-body"><p class="card-text" style="font-variant: small-caps;text-align:left">Current and future spectral line and metallicity coverage of the PDR Toolbox.</p></div>
</div> <!-- card -->
</div> <!-- col-->
</div> <!-- row -->
<a name="parameters">
<h4><center>WK Model Parameters</center></h4>
<p class="myp">
Our
<a class="mya" href="/models/wk2006/index.html">2006 models</a>
use the standard parameters from <a class="mya" href="http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1999ApJ...527..795K">Kaufman et al. 1999</a>. Changes for the
<a class="mya" href="#2020">2020 models</a> are listed below.
The formation rate of H<sub>2</sub> goes as
<span class="math notranslate nohighlight">\(R_{form}~n_{HI}~n\)</span>.
The PAH abundance <span class="math notranslate nohighlight">\(X_{PAH}=n_{PAH}/n\)</span>.
<!-- Gas Phase abundances of C, O, Si, S, Fe, Mg are from Savage & Sembach 1996 -->
</p>
<table class="table table-striped" bgcolor="white">
<caption class="tablecaption"><h6>Parameters for 2006 Models</h6></caption>
<thead>
<tr><th>Parameter</th>
<th>Symbol</th>
<th>Value</th>
</tr>
</thead>
<tbody>
<tr>
<td>Turbulent Doppler velocity</td>
<td><span class="math notranslate nohighlight">\(\delta v_D\)</span></td>
<td>1.5 km s<sup>-1</sup></td>
</tr>
<tr>
<td>Carbon abundance</td>
<td><span class="math notranslate nohighlight">\(X_C\)</span></td>
<td><span class="math notranslate nohighlight">\(1.4\times10^{-4}\)</span></td>
</tr>
<tr>
<td>Oxygen abundance</td>
<td><span class="math notranslate nohighlight">\(X_O\)</span></td>
<td><span class="math notranslate nohighlight">\(3.0\times10^{-4}\)</span></td>
</tr>
<tr>
<td>Silicon abundance</td>
<td><span class="math notranslate nohighlight">\(X_{Si}\)</span></td>
<td><span class="math notranslate nohighlight">\(1.7\times10^{-6}\)</span></td>
</tr>
<tr>
<td>Sulfur abundance</td>
<td><span class="math notranslate nohighlight">\(X_{S}\)</span></td>
<td><span class="math notranslate nohighlight">\(2.8\times10^{-5}\)</span></td>
</tr>
<tr>
<td>Iron abundance</td>
<td><span class="math notranslate nohighlight">\(X_{Fe}\)</span></td>
<td><span class="math notranslate nohighlight">\(1.7\times10^{-7}\)</span></td>
</tr>
<tr>
<td>Magnesium abundance</td>
<td><span class="math notranslate nohighlight">\(X_{Mg}\)</span></td>
<td><span class="math notranslate nohighlight">\(1.1\times10^{-6}\)</span></td>
</tr>
<tr>
<td>Dust abundance relative to diffuse ISM</td>
<td><span class="math notranslate nohighlight">\(\delta_d\)</span></td>
<td>1</td>
</tr>
<tr>
<td>FUV dust absorption/visual extinction</td>
<td><span class="math notranslate nohighlight">\(\delta_{UV}\)</span></td>
<td>1.8</td>
</tr>
<tr>
<td>Dust visual extinction per H</td>
<td><span class="math notranslate nohighlight">\(\sigma_V\)</span></td>
<td><span class="math notranslate nohighlight">\(5\times10^{-22}\)</span> cm<sup>-2</sup></td>
</tr>
<tr>
<td>Formation rate of H<sub>2</sub> on dust</td>
<td><span class="math notranslate nohighlight">\(R_{form}\)</span></td>
<td><span class="math notranslate nohighlight">\(3\times10^{-17}\)</span> s<sup>-1</sup></td>
</tr>
<tr>
<td>PAH abundance</td>
<td><span class="math notranslate nohighlight">\(X_{PAH}\)</span></td>
<td><span class="math notranslate nohighlight">\(5\times10^{-7}\)</span></td>
</tr>
<tr>
<td>Cloud H density</td>
<td><span class="math notranslate nohighlight">\(n\)</span></td>
<td><span class="math notranslate nohighlight">\(10^{1} - 10^{7}\)</span> cm<sup>-3</sup></td>
</tr>
<tr>
<td>Incident UV flux</td>
<td><span class="math notranslate nohighlight">\(G_0\)</span></td>
<td><span class="math notranslate nohighlight">\(10^{-0.5} - 10^{6.5}\)</span> Habing</td>
</tr>
</tbody>
</table>
<a name="2020">
<table class="table table-striped" width="100%" bgcolor="white">
<caption class="tablecaption"><h6>Parameters for 2020 Models Changed from 2006</h6></caption>
<thead>
<tr><th>Parameter</th>
<th>Symbol</th>
<th>Value</th>
</tr>
</thead>
<tbody>
<tr>
<td>Carbon abundance</td>
<td><span class="math notranslate nohighlight">\(X_C\)</span></td>
<td><span class="math notranslate nohighlight">\(1.6\times10^{-4}\)</span></td>
</tr>
<tr>
<td>Oxygen abundance</td>
<td><span class="math notranslate nohighlight">\(X_O\)</span></td>
<td><span class="math notranslate nohighlight">\(3.2\times10^{-4}\)</span></td>
</tr>
<tr>
<td>Dust visual extinction per H</td>
<td><span class="math notranslate nohighlight">\(\sigma_V\)</span></td>
<td><span class="math notranslate nohighlight">\(5.26\times10^{-22}\)</span> cm<sup>-2</sup></td>
</tr>
<tr>
<td>Formation rate of H<sub>2</sub> on dust</td>
<td><span class="math notranslate nohighlight">\(R_{form}\)</span></td>
<td><span class="math notranslate nohighlight">\(6\times10^{-17}\)</span> s<sup>-1</sup></td>
</tr>
<tr>
<td>PAH abundance</td>
<td><span class="math notranslate nohighlight">\(X_{PAH}\)</span></td>
<td><span class="math notranslate nohighlight">\(2\times10^{-7}\)</span></td>
</tr>
</tbody>
</table>
</div>
</section>
<a name="kosmatau">
<section class="mypage-section bg-primary text-white mb-0" id="kosmatau">
<div class="container">
<div class="text-center">
<h2 class="mypage-section-heading d-inline-block text-white">KOSMA-tau Models</h2>
</div>
<p class="myp">
The <a class="mya" href="https://astro.uni-koeln.de/stutzki/research/kosma-tau">KOSMA-tau models</a>
This KOSMA-tau code was developed from an earlier PDR code, written
by A. Sternberg from Tel Aviv University in Israel (Sternberg &
Dalgarno 1989; Sternberg & Dalgarno 1995). His original code uses
a plane-parallel geometry and was updated to employ spherical geometry
(Gierens, Stutzki and Winnewisser 1992; Köster et al. 1994; Störzer,
Stutzki and Sternberg 1996; Zielinsky, Stutzki & Störzer 2000).
</p>
<p class="myp">
The KOSMA-tau models come in "clumpy" and "non-clumpy" variety, with 3.1
≤R<sub>V</sub> ≤ 5.5 depending on the model. For the non-clumpy
models, the mass parameter is the mass of the spherical clump. The
density profile and the mass determine the clump radius and the total
A<sub>V</sub> to the clump center. In the clumpy models there are three
mass parameters. The main mass parameter in the clumpy models is the total
(ensemble) mass of all clumps which are distributed according to a power
law with the mass range [M<sub>low</sub>, M<sub>up</sub>]. Typically the
upper and lower masses are fixed and the total mass is varied.
</p>
<p class="myp">
For more information about these models, see the
<a class="mya" href="https://astro.uni-koeln.de/stutzki/research/kosma-tau">KOSMA-tau website.</a>
</p>
</div>
</section>
<a name="alternate">
<section class="mypage-section bg-primary text-white mb-0" id="alternatemodels">
<div class="container">
<div class="text-center">
<h2 class="mypage-section-heading d-inline-block text-white">Using Alternate Models</h2>
</div>
<p class="myp">
This feature is not fully implemented yet, but it can be used
with a little extra work on your part. To be imported in
to PDRT, model files must be in FITS format and must follow <a
class="mya" href="docs/PDRT_Model_Standards.pdf"> our given standards.</a>
If you would like to try and use alternate models, please <a class="mya" href="mailto:[email protected]">contact Marc Pound.</a>
</p>
</div>
</section>
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