<?xml version="1.0" encoding="UTF-8"?> <!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> <title>Case A</title> <link rel="stylesheet" type="text/css" href="style.css" /> <style type="text/css"> /*<![CDATA[*/ span.c9 {font-size: 120%} span.c8 {font-family: arial,helvetica; font-size: 120%} p.c7 {font-size: 80%; text-align: center} span.c6 {font-size: 60%} p.c5 {text-align: center} p.c4 {font-size: 144%; font-weight: bold; text-align: center} p.c3 {font-family: arial,helvetica; font-size: 144%; text-align: center} p.c2 {text-align: left}Fig. 2-1 Colormap for density profile at t/M = 0 span.c1 {font-family: arial,helvetica; font-size: 248%} /*]]>*/ </style> <script type="text/javascript" src="js/prototype.js"></script> <script type="text/javascript" src="js/scriptaculous.js?load=effects,builder"></script> <script type="text/javascript" src="js/lightbox.js"></script> <link rel="stylesheet" href="css/lightbox.css" type="text/css" media="screen" /> <script type="text/javascript" src="http://code.jquery.com/jquery-latest.min.js"></script> <link rel="stylesheet" href="fancybox/source/jquery.fancybox.css?v=2.1.5" type="text/css" media="screen" /> <script type="text/javascript" src="fancybox/source/jquery.fancybox.pack.js?v=2.1.5"></script> <script type="text/javascript" src="/fancybox/source/helpers/jquery.fancybox-media.js?v=1.0.6"></script> <script src="http://www.youtube.com/player_api"></script> <script type="text/javascript"> function onPlayerReady(event) { event.target.playVideo(); } // The API will call this function when the page has finished downloading the JavaScript for the player API function onYouTubePlayerAPIReady() { // Initialise the fancyBox after the DOM is loaded $(document).ready(function() { $(".fancybox") .attr('rel', 'gallery') .fancybox({ openEffect : 'none', closeEffect : 'none', nextEffect : 'none', prevEffect : 'none', padding : 0, margin : [20, 60, 20, 60], beforeShow : function() { // Find the iframe ID var id = $.fancybox.inner.find('iframe').attr('id'); // Create video player object and add event listeners var player = new YT.Player(id, { events: { 'onReady': onPlayerReady, } }); } }); }); } </script> </head> <body text="#000000" bgcolor="#bfbfbf" link="#000088" vlink="#880088"> <div class="textbox"> <p align="left"> <font face="arial,helvetica" size="+5"> <i>Case A</i><br> </font> <img src="img/hrule.gif"><br> </div> <p align="center"><font face="arial,helvetica" size="+2"> <a href="#intro">Introduction</a><br> <a href="#evolution">Evolution of Density Profile</a><br> <a href="#velevolution">Evolution of Density Profile with Velocity Field</a><br> <a href="#waveform">Evolution of Gravitational Radiation Profile</a><br> <a href="#parameters">Final Black Hole Parameters</a><br></font> </font> <hr size="1" color="black" width="75%" noshade> <a name="intro"></a><p align="center"><font size="+2"><b>Introduction</b></font> <p align="center"> <img src="img/A_0000.png" border="1"><br> <i>Fig. 1-1 Initial Configuration of Binary</i> <div class="textbox"><p align="left"> Evolution is performed on an AMR (Adaptive Mesh Refinement) grid. The outermost grid is 394&nbsp;M&nbsp;x&nbsp;394&nbsp;M, the innermost refinement level for the BH is 2.8&nbsp;M&nbsp;x&nbsp;2.8&nbsp;M and the innermost refinement level for the NS is 3.3&nbsp;M&nbsp;x&nbsp;3.3&nbsp;M. Here M is the total (ADM) mass of the intial system. The innermost resolution is &Delta;X<sub>min</sub>/M&nbsp;=&nbsp;1/32.5 while the outermost is &Delta;X<sub>max</sub>/M&nbsp;=&nbsp;3.94. In this simulation, the initial binary coordinate separation is <span class="equation">D<sub>0</sub>/M = 8.81</span>, the initial angular momentum of the system is <span class="equation">J/M<sup>2</sup> = 0.702</span>, the mass ratio is <span class="equation">M<sub>BH</sub>:M<sub>NS</sub>&nbsp;=&nbsp;3:1</span>, and the black hole spin parameter is <span class="equation">J<sub>BH</sub>/M<sub>BH</sub><sup>2</sup>&nbsp;=&nbsp; 0.00</span>. (Note: The open circle in the lower right-hand corner of the above figure is a clock.)<br></div><br></div> <hr size="1" color="black" width="75%" noshade> <a name="evolution"></a><p align="center"><font size="+2"><b>Evolution of the Density Profile</b></font><div class="textbox"> <p align="left"> In the clip from the equatorial plane, the rest-mass density of the neutron star is plotted on a logarithmic scale normalized to the initial central density. The gravitational field is evolved via the BSSN scheme using "moving puncture" gauge conditions. The relativistic hydrodynamic equations are solved using a high-resolution shock-capturing (HRSC) method. <p align="left"> After two orbits the density contours are for the most part undisturbed. After 3.5 orbits the first few density contours have crossed into the apparent horizon. The NS tail deforms into a quasistationary disk, as the bulk of the matter is all accreted onto the hole in a few periods.<br><br> <p align="left"></div> <p align="center"> <table align="center" border="0" cellspacing="0" cellpadding="5"> <tr align="center" valign="top"> <td align="center"> <img src="img/Case_A_colorbar.png" border="1"><br> <i>Fig. 2-1 Color code for density profile</i> <td align="center"> <img src="img/A_0295.png" border="1"><br> <i>Fig. 2-2 Density Profile at t/M = 530</i> </td></tr><tr align="center" valign="top"> <td align="center"> <img src="img/A_0390.png" border="1"><br> <i>Fig. 2-3 Density Profile at t/M = 700</i> <td align="center"> <img src="img/A_0491.png" border="1"><br> <i>Fig. 2-4 Density Profile at t/M = 882</i> </td> </tr> </table> <div class="clip"><p align="center"><a href="http://www.youtube.com/embed/bUQkRzLSFhQ?enablejsapi=1&wmode=opaque&rel=0" class="fancybox fancybox.iframe">Play Online</a></div> <p align="center"><font size"+2"><a href="clips/A_dens.mov">Download MPEG-4 (35.2 MB)</a></font><br> <hr size="1" color="black" width="75%" noshade> <a name="velevolution"></a><p align="center"><font size="+2"><b>Evolution of Density Profile with Velocity Field</b></font><div class="textbox"> <p align="left"></div> <p align="center"> <table align="center" border="0" cellspacing="0" cellpadding="5"> <tr align="center" valign="top"> <td align="center"> <img src="img/A_vel_0000.png" border="1"><br> <i>Fig. 3-1 Density Profile at t = 0</i> <td align="center"> <img src="img/A_vel_0295.png" border="1"><br> <i>Fig. 3-2 Density Profile at t = 530</i> </td></tr><tr align="center" valign="top"> <td align="center"> <img src="img/A_vel_0390.png" border="1"><br> <i>Fig. 3-3 Density Profile t/M = 700</i> <td align="center"> <img src="img/A_vel_0491.png" border="1"><br> <i>Fig. 3-4 Density Profile at t/M = 882</i> </td> </tr> </table> <div class="clip"><p align=center><a href="http://www.youtube.com/embed/pIyOUKUaD8k?enablejsapi=1&wmode=opaque&rel=0" class="fancybox fancybox.iframe">Play Online</a></div> <p align="center"><font size"+2"> <a href="clips/A_vel.mov">Download MPEG-4 (20.0 MB)</a></font><br> <hr size="1" color="black" width="75%" noshade> <a name="waveform"></a><p align="center"><font size="+2"><b>Evolution of Gravitational Radiation Profile<br></b></font> <div class="textbox"> <p align="left"> The gravitational wavetrain from a compact binary system may be separated into three qualitatively different phases: the inspiral, merger, and ringdown. During the inspiral phase, which takes up most of the binary's lifetime, gravity wave emission gradually reduces the binary separation. The merger phase of the gravitational wavetrain is characterized by tidal disruption of the neutron star. Finally, ringdown radiation is emitted as the distorted black hole settles down to Kerr-like equilibrium (Note: Only in the case of a vacuum spacetime does the spinning BH obey the Kerr solution. The BHs formed here are surrounded by gaseous disks with small, but nonnegligible, rest mass). Both polarization modes (h<sub>+</sub> and h<sub>x</sub>) are shown. Total energy conservation is obeyed to within 0.02%. Total angular momentum conservation is obeyed to within 2.2%.</div> <div class="textbox"> <p align="left"></div> <p align="center"> <table align=center border="0" cellspacing="0" cellpadding="5"> <tr align="center" valign="top"> <td align="center"> <img src="img/A_Hplus_0750.png" border="1"><br> <i>Fig. 4-1 h<sub>+</sub> Profile</i> <td align="center"> <img src="img/A_Hx_0750.png" border="1"><br> <i>Fig. 4-2 h<sub>x</sub> Profile</i> </td></tr><tr align="center" valign="top"> </tr> </table> <div class="clip"><p align=center><a href="http://www.youtube.com/embed/vluAL03xQ_g?enablejsapi=1&wmode=opaque&rel=0" class="fancybox fancybox.iframe">Play Online</a></div> <p align="center"><font size"+2"> <a href="clips/A_Hplus.mov">Download MPEG-4 (21.9 MB)</a></font> <div class="clip"><p align=center><a href="http://www.youtube.com/embed/6ZyGzB5q6OE?enablejsapi=1&wmode=opaque&rel=0" class="fancybox fancybox.iframe">Play Online</a></div> <p align="center"><font size"+2"> <a href="clips/A_Hx.mov">Download MPEG-4 (14.4 MB)</a></font><br> <p align="center"> <img src="img/A_H_1.png" border="1"><br> <i>Fig. 4-3 h<sub>+</sub> in orbital plane</i> <div class="clip"><p align=center><a href="http://www.youtube.com/embed/YvOUr5zMlaU?enablejsapi=1&wmode=opaque&rel=0" class="fancybox fancybox.iframe">Play Online</a></div> <p align="center"><font size"+2"> <a href="clips/A_Hplus1.mov">Download MPEG-4 (28.2 MB)</a></font><br> <hr size="1" color="black" width="75%" noshade> <a name="parameters"></a> <p align="center"> <font size="+2"><b>Final Black Hole Parameters</b></font> <div class="textbox"> <p align="left">Listed in the table below is the dimensionless spin of the Kerr-like black hole at the end of our simulation. Also shown are the radiated energy, angular momentum, and linear recoil velocity resulting from gravitational wave emission. Additional parameters for the disk are given in the film clip. </div> <p align="center"> <table align="center" border="1" bordercolor="black" bordercolorlight="black" bordercolordark="black" cellpadding="3" cellspacing="0"> <tr><td width="200">J<sub>BH</sub>/M<sup>2</sup><sub>BH</sub></td><td>0.559</td> </tr> <tr><td>&Delta J<sub>GW</sub>/J</td><td>17.4%</td></tr> <tr><td>&Delta E<sub>GW</sub>/M</td><td>0.93%</td></tr> <tr><td>Recoil velocity</td><td>33 km/s</td></tr> </table> <div class="clip"><p align=center><a href="http://www.youtube.com/embed/GBfGroJf5DE?enablejsapi=1&wmode=opaque&rel=0" class="fancybox fancybox.iframe">Play Online</a></div> <p align="center"><font size"+2"> <a href="clips/A_final.mov">Download MPEG-4 (4.6 MB)</a></font><br> <hr size="1" color="black" width="75%" noshade> <div class="textbox"><p align="center"><a href=".">Back to Index</a> <p align="center"><font size="-1">last updated 15 December by aakhan3</font><p align="center"> <p align="center"> <table align="center" border=0> <tr> <td valign="center" align="left"><a href="/CTA/"> <img height="32" src="img/small_logo.gif" width="51" border="0"></a> </td> <td valign="center" align="middle"><font face="arial,helvetica" size="+1"> <i>Center for Theoretical Astrophysics---University of Illinois at Urbana-Champaign</i><br> </font><br> <font size="+1"><b> <A HREF="../../index.html">Home</A> | <A HREF="../../research/groups.html">Research</A> | <A HREF="../../events/activities.html">Activities</A> | <A HREF="../../faculty/faculty.html">Faculty</A> | <A HREF="../../postdocs/postdocs.html">Postdocs</A> | <A HREF="../../graduate/graduate.html">Graduate</A> | <A HREF="../../undergrad/undergrad.html">Undergraduate</A> | <A HREF="../../IRG/movies.html">Movies</A> </b></font> </td> </tr> </table> </div> </body> </html>