<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <title>wpwaCDM — Astropy v0.2.4</title> <link rel="stylesheet" href="../_static/bootstrap-astropy.css" type="text/css" /> <link rel="stylesheet" href="../_static/pygments.css" type="text/css" /> <script type="text/javascript"> var DOCUMENTATION_OPTIONS = { URL_ROOT: '../', VERSION: '0.2.4', COLLAPSE_INDEX: false, FILE_SUFFIX: '.html', HAS_SOURCE: true }; </script> <script type="text/javascript" src="../_static/jquery.js"></script> <script type="text/javascript" src="../_static/underscore.js"></script> <script type="text/javascript" src="../_static/doctools.js"></script> <script type="text/javascript" src="../_static/sidebar.js"></script> <link rel="shortcut icon" href="../_static/astropy_logo.ico"/> <link rel="top" title="Astropy v0.2.4" href="../index.html" /> <link rel="up" title="Cosmological Calculations (astropy.cosmology)" href="../cosmology/index.html" /> <link rel="next" title="Astrostatistics Tools (astropy.stats)" href="../stats/index.html" /> <link rel="prev" title="wCDM" href="astropy.cosmology.core.wCDM.html" /> </head> <body> <div class="topbar"> <a class="brand" title="Documentation Home" href="../index.html"></a> <ul> <li><a class="homelink" title="AstroPy Homepage" href="http://www.astropy.org"></a></li> <li><a title="General Index" href="../genindex.html">Index</a></li> <li><a title="Python Module Index" href="../py-modindex.html">Modules</a></li> <li> <form action="../search.html" method="get"> <input type="text" name="q" placeholder="Search" /> <input type="hidden" name="check_keywords" value="yes" /> <input type="hidden" name="area" value="default" /> </form> </li> </ul> </div> <div class="related"> <h3>Navigation</h3> <ul> <li class="right"> <a href="../stats/index.html" title="Astrostatistics Tools (astropy.stats)"> next » </a> </li> <li class="right"> <a href="astropy.cosmology.core.wCDM.html" title="wCDM"> « previous </a> | </li> <li> <a href="../index.html">Astropy v0.2.4</a> » </li> <li><a href="../cosmology/index.html" accesskey="U">Cosmological Calculations (<tt class="docutils literal"><span class="pre">astropy.cosmology</span></tt>)</a> »</li> <li>wpwaCDM</li> </ul> </div> <div class="document"> <div class="documentwrapper"> <div class="bodywrapper"> <div class="body"> <div class="section" id="wpwacdm"> <h1>wpwaCDM<a class="headerlink" href="#wpwacdm" title="Permalink to this headline">¶</a></h1> <dl class="class"> <dt id="astropy.cosmology.core.wpwaCDM"> <em class="property">class </em><tt class="descclassname">astropy.cosmology.core.</tt><tt class="descname">wpwaCDM</tt><big>(</big><em>H0</em>, <em>Om0</em>, <em>Ode0</em>, <em>wp=-1.0</em>, <em>wa=0.0</em>, <em>zp=0</em>, <em>Tcmb0=2.725</em>, <em>Neff=3.04</em>, <em>name='wpwaCDM'</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L1667" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link"> [edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#wpwaCDM"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.wpwaCDM" title="Permalink to this definition">¶</a></dt> <dd><p>Bases: <a class="reference internal" href="astropy.cosmology.core.FLRW.html#astropy.cosmology.core.FLRW" title="astropy.cosmology.core.FLRW"><tt class="xref py py-class docutils literal"><span class="pre">astropy.cosmology.core.FLRW</span></tt></a></p> <p>FLRW cosmology with a CPL dark energy equation of state, a pivot redshift, and curvature.</p> <p>The equation for the dark energy equation of state uses the CPL form as described in Chevallier & Polarski Int. J. Mod. Phys. D10, 213 (2001) and Linder PRL 90, 91301 (2003), but modified to have a pivot redshift as in the findings of the Dark Energy Task Force (Albrecht et al. arXiv:0901.0721 (2009)): <span class="math">w(a) = w_p + w_a (a_p - a) = w_p + w_a( 1/(1+zp) - 1/(1+z) )</span>.</p> <p class="rubric">Examples</p> <div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">astro.cosmology</span> <span class="kn">import</span> <span class="n">wpwaCDM</span> <span class="gp">>>> </span><span class="n">cosmo</span> <span class="o">=</span> <span class="n">wpwaCDM</span><span class="p">(</span><span class="n">H0</span><span class="o">=</span><span class="mi">70</span><span class="p">,</span><span class="n">Om0</span><span class="o">=</span><span class="mf">0.3</span><span class="p">,</span><span class="n">Ode0</span><span class="o">=</span><span class="mf">0.7</span><span class="p">,</span><span class="n">wp</span><span class="o">=-</span><span class="mf">0.9</span><span class="p">,</span><span class="n">wa</span><span class="o">=</span><span class="mf">0.2</span><span class="p">,</span><span class="n">zp</span><span class="o">=</span><span class="mf">0.4</span><span class="p">)</span> </pre></div> </div> <p>The comoving distance in Mpc at redshift z:</p> <div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">dc</span> <span class="o">=</span> <span class="n">cosmo</span><span class="o">.</span><span class="n">comoving_distance</span><span class="p">(</span><span class="n">z</span><span class="p">)</span> </pre></div> </div> <p class="rubric">Attributes Summary</p> <table border="1" class="longtable docutils"> <colgroup> <col width="10%" /> <col width="90%" /> </colgroup> <tbody valign="top"> <tr class="row-odd"><td><a class="reference internal" href="#astropy.cosmology.core.wpwaCDM.wa" title="astropy.cosmology.core.wpwaCDM.wa"><tt class="xref py py-obj docutils literal"><span class="pre">wa</span></tt></a></td> <td>Negative derivative of dark energy equation of state w.r.t.</td> </tr> <tr class="row-even"><td><a class="reference internal" href="#astropy.cosmology.core.wpwaCDM.wp" title="astropy.cosmology.core.wpwaCDM.wp"><tt class="xref py py-obj docutils literal"><span class="pre">wp</span></tt></a></td> <td>Dark energy equation of state at the pivot redshift zp</td> </tr> <tr class="row-odd"><td><a class="reference internal" href="#astropy.cosmology.core.wpwaCDM.zp" title="astropy.cosmology.core.wpwaCDM.zp"><tt class="xref py py-obj docutils literal"><span class="pre">zp</span></tt></a></td> <td>The pivot redshift, where w(z) = wp</td> </tr> </tbody> </table> <p class="rubric">Methods Summary</p> <table border="1" class="longtable docutils"> <colgroup> <col width="10%" /> <col width="90%" /> </colgroup> <tbody valign="top"> <tr class="row-odd"><td><a class="reference internal" href="#astropy.cosmology.core.wpwaCDM.de_density_scale" title="astropy.cosmology.core.wpwaCDM.de_density_scale"><tt class="xref py py-obj docutils literal"><span class="pre">de_density_scale</span></tt></a>(z)</td> <td>Evaluates the redshift dependence of the dark energy density.</td> </tr> <tr class="row-even"><td><a class="reference internal" href="#astropy.cosmology.core.wpwaCDM.w" title="astropy.cosmology.core.wpwaCDM.w"><tt class="xref py py-obj docutils literal"><span class="pre">w</span></tt></a>(z)</td> <td>Returns dark energy equation of state at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</td> </tr> </tbody> </table> <p class="rubric">Attributes Documentation</p> <dl class="attribute"> <dt id="astropy.cosmology.core.wpwaCDM.wa"> <tt class="descname">wa</tt><a class="reference internal" href="../_modules/astropy/cosmology/core.html#wpwaCDM.wa"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.wpwaCDM.wa" title="Permalink to this definition">¶</a></dt> <dd><p>Negative derivative of dark energy equation of state w.r.t. a</p> </dd></dl> <dl class="attribute"> <dt id="astropy.cosmology.core.wpwaCDM.wp"> <tt class="descname">wp</tt><a class="reference internal" href="../_modules/astropy/cosmology/core.html#wpwaCDM.wp"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.wpwaCDM.wp" title="Permalink to this definition">¶</a></dt> <dd><p>Dark energy equation of state at the pivot redshift zp</p> </dd></dl> <dl class="attribute"> <dt id="astropy.cosmology.core.wpwaCDM.zp"> <tt class="descname">zp</tt><a class="reference internal" href="../_modules/astropy/cosmology/core.html#wpwaCDM.zp"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.wpwaCDM.zp" title="Permalink to this definition">¶</a></dt> <dd><p>The pivot redshift, where w(z) = wp</p> </dd></dl> <p class="rubric">Methods Documentation</p> <dl class="method"> <dt id="astropy.cosmology.core.wpwaCDM.de_density_scale"> <tt class="descname">de_density_scale</tt><big>(</big><em>z</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L1781" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link"> [edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#wpwaCDM.de_density_scale"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.wpwaCDM.de_density_scale" title="Permalink to this definition">¶</a></dt> <dd><p>Evaluates the redshift dependence of the dark energy density.</p> <table class="docutils field-list" frame="void" rules="none"> <col class="field-name" /> <col class="field-body" /> <tbody valign="top"> <tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>z</strong> : array_like</p> <blockquote> <div><p>Input redshifts.</p> </div></blockquote> </td> </tr> <tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>I</strong> : ndarray, or float if input scalar</p> <blockquote class="last"> <div><p>The scaling of the energy density of dark energy with redshift.</p> </div></blockquote> </td> </tr> </tbody> </table> <p class="rubric">Notes</p> <p>The scaling factor, I, is defined by <span class="math">\rho(z) = \rho_0 I</span>, and in this case is given by</p> <div class="math"> <p><span class="math">a_p = \frac{1}{1 + z_p} I = \left(1 + z\right)^{3 \left(1 + w_p + a_p w_a\right)} \exp \left(-3 w_a \frac{z}{1+z}\right)</span></p> </div></dd></dl> <dl class="method"> <dt id="astropy.cosmology.core.wpwaCDM.w"> <tt class="descname">w</tt><big>(</big><em>z</em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/cosmology/core.py#L1752" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link"> [edit on github]</span></a><a class="reference internal" href="../_modules/astropy/cosmology/core.html#wpwaCDM.w"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.cosmology.core.wpwaCDM.w" title="Permalink to this definition">¶</a></dt> <dd><p>Returns dark energy equation of state at redshift <tt class="xref py py-obj docutils literal"><span class="pre">z</span></tt>.</p> <table class="docutils field-list" frame="void" rules="none"> <col class="field-name" /> <col class="field-body" /> <tbody valign="top"> <tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>z</strong> : array_like</p> <blockquote> <div><p>Input redshifts.</p> </div></blockquote> </td> </tr> <tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>w</strong> : ndarray, or float if input scalar</p> <blockquote class="last"> <div><p>The dark energy equation of state</p> </div></blockquote> </td> </tr> </tbody> </table> <p class="rubric">Notes</p> <p>The dark energy equation of state is defined as <span class="math">w(z) = P(z)/\rho(z)</span>, where <span class="math">P(z)</span> is the pressure at redshift z and <span class="math">\rho(z)</span> is the density at redshift z, both in units where c=1. Here this is <span class="math">w(z) = w_p + w_a (a_p - a)</span> where <span class="math">a = 1/1+z</span> and <span class="math">a_p = 1 / 1 + z_p</span>.</p> </dd></dl> </dd></dl> </div> </div> </div> </div> <div class="sphinxsidebar"> <div class="sphinxsidebarwrapper"><h3>Page Contents</h3> <ul> <li><a class="reference internal" href="#">wpwaCDM</a></li> </ul> </div> </div> <div class="clearer"></div> </div> <footer class="footer"> <p class="pull-right"> <a href="../_sources/_generated/astropy.cosmology.core.wpwaCDM.txt" rel="nofollow">Page Source</a> <a href="#">Back to Top</a></p> <p> © Copyright 2011-2013, The Astropy Developers.<br/> Created using <a href="http://sphinx.pocoo.org/">Sphinx</a> 1.1.3. Last built 22 Oct 2013. <br/> </p> </footer> </body> </html>