Relativistic Milne-Eddington Type Solutions with a Variable Eddington Factor for Relativistic Spherical Winds

<table>Eddington factor <svg height="13.4875" id="M157" style="vertical-align:-2.34499pt" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.4875)">
<g transform="translate(72,-61.21)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑓</tspan>
</text>
</g>
</g>
</svg> appropriate for the LTE case as a function of the optical depth <svg height="6.8874998" id="M158" style="vertical-align:-0.0627pt" version="1.1" viewbox="0 0 8.125 6.8874998" width="8.125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,6.8875)">
<g transform="translate(72,-66.49)">
<text transform="matrix(1,0,0,-1,-71.95,66.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜏</tspan>
</text>
</g>
</g>
</svg> for the various values of the flow speed <svg height="13.425" id="M159" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 8.8500004 13.425" width="8.8500004" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.425)">
<g transform="translate(72,-61.26)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝛽</tspan>
</text>
</g>
</g>
</svg>. The values of <svg height="13.425" id="M160" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 8.8500004 13.425" width="8.8500004" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.425)">
<g transform="translate(72,-61.26)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝛽</tspan>
</text>
</g>
</g>
</svg> are from 0 to 0.9 in steps of 0.1 from bottom to top.</table>

Advances in Astronomy

fig3

Figure 3

Figure 3: Relativistic Milne-Eddington Type Solutions with a Variable Eddington Factor for Relativistic Spherical Winds 