TY - JOUR AU - Singh, Kamal Krishan AU - Saini, Seema AU - Kumar, Sunil PY - 2023/02/28 Y2 - 2024/03/28 TI - Local Stability and Structure of a Differentially Rotating Star of Non- Uniform Density JF - Journal of Graphic Era University JA - JGEU VL - 7 IS - 1 SE - Articles DO - UR - https://riverpublishersjournal.com/index.php/JGEU/article/view/67 SP - 29-40 AB - <p><span id="page3R_mcid16" class="markedContent"><span dir="ltr" style="left: calc(var(--scale-factor)*72.02px); top: calc(var(--scale-factor)*307.37px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif;" role="presentation">A</span> <span dir="ltr" style="left: calc(var(--scale-factor)*82.46px); top: calc(var(--scale-factor)*307.37px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.917815);" role="presentation">method is proposed to compute the</span> <span dir="ltr" style="left: calc(var(--scale-factor)*229.25px); top: calc(var(--scale-factor)*307.37px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.936265);" role="presentation">theoretical estimation of</span> <span dir="ltr" style="left: calc(var(--scale-factor)*331.03px); top: calc(var(--scale-factor)*307.37px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.899015);" role="presentation">physical parameters</span> <span dir="ltr" style="left: calc(var(--scale-factor)*414.43px); top: calc(var(--scale-factor)*307.37px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.968755);" role="presentation">and stability of differential</span><br role="presentation"><span dir="ltr" style="left: calc(var(--scale-factor)*72.02px); top: calc(var(--scale-factor)*318.89px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.942886);" role="presentation">rotation for</span> <span dir="ltr" style="left: calc(var(--scale-factor)*119.30px); top: calc(var(--scale-factor)*318.89px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.921958);" role="presentation">polytropic stars</span> <span dir="ltr" style="left: calc(var(--scale-factor)*183.38px); top: calc(var(--scale-factor)*318.89px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.921136);" role="presentation">including mass variation</span><span dir="ltr" style="left: calc(var(--scale-factor)*281.33px); top: calc(var(--scale-factor)*318.89px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif;" role="presentation">.</span> <span dir="ltr" style="left: calc(var(--scale-factor)*286.25px); top: calc(var(--scale-factor)*318.89px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.943033);" role="presentation">The law of differential rotation</span> <span dir="ltr" style="left: calc(var(--scale-factor)*411.67px); top: calc(var(--scale-factor)*318.89px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.893416);" role="presentation">is assumed to be in the form</span></span><span id="page3R_mcid17" class="markedContent"><span dir="ltr" style="left: calc(var(--scale-factor)*183.85px); top: calc(var(--scale-factor)*331.12px); font-size: calc(var(--scale-factor)*6.87px); font-family: sans-serif; transform: rotate(0.000026371deg);" role="presentation">4</span><br role="presentation"><span dir="ltr" style="left: calc(var(--scale-factor)*173.51px); top: calc(var(--scale-factor)*339.32px); font-size: calc(var(--scale-factor)*6.87px); font-family: sans-serif; transform: rotate(0.000026371deg);" role="presentation">3</span><br role="presentation"><span dir="ltr" style="left: calc(var(--scale-factor)*151.55px); top: calc(var(--scale-factor)*331.12px); font-size: calc(var(--scale-factor)*6.87px); font-family: sans-serif; transform: rotate(0.000026371deg);" role="presentation">2</span><br role="presentation"><span dir="ltr" style="left: calc(var(--scale-factor)*141.02px); top: calc(var(--scale-factor)*339.32px); font-size: calc(var(--scale-factor)*6.87px); font-family: sans-serif; transform: rotate(0.000026371deg);" role="presentation">2</span><span dir="ltr" style="left: calc(var(--scale-factor)*119.36px); top: calc(var(--scale-factor)*339.32px); font-size: calc(var(--scale-factor)*6.87px); font-family: sans-serif; transform: rotate(0.000026371deg);" role="presentation">1</span><br role="presentation"><span dir="ltr" style="left: calc(var(--scale-factor)*82.95px); top: calc(var(--scale-factor)*331.12px); font-size: calc(var(--scale-factor)*6.87px); font-family: sans-serif; transform: rotate(0.000026371deg);" role="presentation">2</span> <span dir="ltr" style="left: calc(var(--scale-factor)*97.70px); top: calc(var(--scale-factor)*332.66px); font-size: calc(var(--scale-factor)*11.77px); font-family: sans-serif; transform: rotate(0.000026371deg);" role="presentation">)</span><span dir="ltr" style="left: calc(var(--scale-factor)*88.15px); top: calc(var(--scale-factor)*332.66px); font-size: calc(var(--scale-factor)*11.77px); font-family: sans-serif; transform: rotate(0.000026371deg);" role="presentation">(</span> <span dir="ltr" style="left: calc(var(--scale-factor)*177.95px); top: calc(var(--scale-factor)*332.66px); font-size: calc(var(--scale-factor)*11.77px); font-family: sans-serif; transform: rotate(0.000026371deg);" role="presentation">s</span><span dir="ltr" style="left: calc(var(--scale-factor)*167.78px); top: calc(var(--scale-factor)*332.66px); font-size: calc(var(--scale-factor)*11.77px); font-family: sans-serif; transform: rotate(0.000026371deg);" role="presentation">b</span><span dir="ltr" style="left: calc(var(--scale-factor)*145.65px); top: calc(var(--scale-factor)*332.66px); font-size: calc(var(--scale-factor)*11.77px); font-family: sans-serif; transform: rotate(0.000026371deg);" role="presentation">s</span><span dir="ltr" style="left: calc(var(--scale-factor)*135.05px); top: calc(var(--scale-factor)*332.66px); font-size: calc(var(--scale-factor)*11.77px); font-family: sans-serif; transform: rotate(0.000026371deg);" role="presentation">b</span><span dir="ltr" style="left: calc(var(--scale-factor)*114.18px); top: calc(var(--scale-factor)*332.66px); font-size: calc(var(--scale-factor)*11.77px); font-family: sans-serif; transform: rotate(0.000026371deg);" role="presentation">b</span><span dir="ltr" style="left: calc(var(--scale-factor)*92.64px); top: calc(var(--scale-factor)*332.66px); font-size: calc(var(--scale-factor)*11.77px); font-family: sans-serif; transform: rotate(0.000026371deg);" role="presentation">s</span> <span dir="ltr" style="left: calc(var(--scale-factor)*159.02px); top: calc(var(--scale-factor)*332.66px); font-size: calc(var(--scale-factor)*11.77px); font-family: sans-serif; transform: rotate(0.000026371deg);" role="presentation"></span><span dir="ltr" style="left: calc(var(--scale-factor)*126.28px); top: calc(var(--scale-factor)*332.66px); font-size: calc(var(--scale-factor)*11.77px); font-family: sans-serif; transform: rotate(0.000026371deg);" role="presentation"></span><span dir="ltr" style="left: calc(var(--scale-factor)*104.82px); top: calc(var(--scale-factor)*332.66px); font-size: calc(var(--scale-factor)*11.77px); font-family: sans-serif; transform: rotate(0.000026371deg);" role="presentation"></span><br role="presentation"><span dir="ltr" style="left: calc(var(--scale-factor)*73.11px); top: calc(var(--scale-factor)*332.12px); font-size: calc(var(--scale-factor)*12.47px); font-family: sans-serif; transform: rotate(0.000026371deg);" role="presentation"></span></span><span id="page3R_mcid18" class="markedContent"><br role="presentation"><span dir="ltr" style="left: calc(var(--scale-factor)*190.01px); top: calc(var(--scale-factor)*333.77px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif;" role="presentation">,</span> <span dir="ltr" style="left: calc(var(--scale-factor)*194.81px); top: calc(var(--scale-factor)*333.77px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif;" role="presentation">t</span><span dir="ltr" style="left: calc(var(--scale-factor)*197.57px); top: calc(var(--scale-factor)*333.77px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.920875);" role="presentation">he angular velocity of r</span><span dir="ltr" style="left: calc(var(--scale-factor)*289.97px); top: calc(var(--scale-factor)*333.77px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.92111);" role="presentation">otation (ω) is a function of</span> <span dir="ltr" style="left: calc(var(--scale-factor)*397.39px); top: calc(var(--scale-factor)*333.77px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.908659);" role="presentation">distance (s) of the fluid element</span><br role="presentation"><span dir="ltr" style="left: calc(var(--scale-factor)*72.02px); top: calc(var(--scale-factor)*348.89px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.933911);" role="presentation">from the axis of rotation</span><span dir="ltr" style="left: calc(var(--scale-factor)*169.34px); top: calc(var(--scale-factor)*348.89px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif;" role="presentation">.</span> <span dir="ltr" style="left: calc(var(--scale-factor)*174.38px); top: calc(var(--scale-factor)*348.89px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(1.02);" role="presentation">Utilizing</span> <span dir="ltr" style="left: calc(var(--scale-factor)*212.57px); top: calc(var(--scale-factor)*348.89px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif;" role="presentation">t</span><span dir="ltr" style="left: calc(var(--scale-factor)*215.45px); top: calc(var(--scale-factor)*348.89px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.843162);" role="presentation">he</span> <span dir="ltr" style="left: calc(var(--scale-factor)*227.33px); top: calc(var(--scale-factor)*348.89px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.89605);" role="presentation">concepts of Roche</span><span dir="ltr" style="left: calc(var(--scale-factor)*301.37px); top: calc(var(--scale-factor)*348.89px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif;" role="presentation">-</span> <span dir="ltr" style="left: calc(var(--scale-factor)*307.25px); top: calc(var(--scale-factor)*348.89px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.911075);" role="presentation">equipotential and</span> <span dir="ltr" style="left: calc(var(--scale-factor)*379.03px); top: calc(var(--scale-factor)*348.89px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.902888);" role="presentation">averaging</span> <span dir="ltr" style="left: calc(var(--scale-factor)*421.03px); top: calc(var(--scale-factor)*348.89px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.887145);" role="presentation">approach</span> <span dir="ltr" style="left: calc(var(--scale-factor)*460.42px); top: calc(var(--scale-factor)*348.89px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(1.00439);" role="presentation">of</span> <span dir="ltr" style="left: calc(var(--scale-factor)*471.22px); top: calc(var(--scale-factor)*348.89px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif;" role="presentation">(</span><span dir="ltr" style="left: calc(var(--scale-factor)*474.58px); top: calc(var(--scale-factor)*348.89px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.91901);" role="presentation">Kippenhahn</span><br role="presentation"><span dir="ltr" style="left: calc(var(--scale-factor)*72.02px); top: calc(var(--scale-factor)*360.41px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.923597);" role="presentation">and Thomas, 1970)</span> <span dir="ltr" style="left: calc(var(--scale-factor)*155.66px); top: calc(var(--scale-factor)*360.41px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.949902);" role="presentation">in a manner, earlier used by</span> <span dir="ltr" style="left: calc(var(--scale-factor)*276.17px); top: calc(var(--scale-factor)*360.41px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif;" role="presentation">(</span><span dir="ltr" style="left: calc(var(--scale-factor)*279.53px); top: calc(var(--scale-factor)*360.41px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif;" role="presentation">S</span><span dir="ltr" style="left: calc(var(--scale-factor)*285.05px); top: calc(var(--scale-factor)*360.41px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.957294);" role="presentation">aini,</span> <span dir="ltr" style="left: calc(var(--scale-factor)*306.29px); top: calc(var(--scale-factor)*360.41px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.953117);" role="presentation">et al.</span><span dir="ltr" style="left: calc(var(--scale-factor)*326.95px); top: calc(var(--scale-factor)*360.41px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.952333);" role="presentation">, 2012)</span> <span dir="ltr" style="left: calc(var(--scale-factor)*360.19px); top: calc(var(--scale-factor)*360.41px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.963901);" role="presentation">to incorporate the effects of differential</span><br role="presentation"><span dir="ltr" style="left: calc(var(--scale-factor)*72.02px); top: calc(var(--scale-factor)*371.93px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.956464);" role="presentation">rotation on the equilibrium structure of polytropic stellar models.</span> <span dir="ltr" style="left: calc(var(--scale-factor)*343.39px); top: calc(var(--scale-factor)*371.93px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.964295);" role="presentation">The inner structure of differentiall</span><span dir="ltr" style="left: calc(var(--scale-factor)*483.94px); top: calc(var(--scale-factor)*371.93px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif;" role="presentation">y</span> <span dir="ltr" style="left: calc(var(--scale-factor)*492.22px); top: calc(var(--scale-factor)*371.93px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.939351);" role="presentation">rotating</span><br role="presentation"><span dir="ltr" style="left: calc(var(--scale-factor)*72.02px); top: calc(var(--scale-factor)*383.33px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.941023);" role="presentation">polytropic models of</span> <span dir="ltr" style="left: calc(var(--scale-factor)*158.06px); top: calc(var(--scale-factor)*383.33px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif;" role="presentation">a</span> <span dir="ltr" style="left: calc(var(--scale-factor)*165.14px); top: calc(var(--scale-factor)*383.33px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.909069);" role="presentation">star is demonstrated by calculating various physical parameters for</span> <span dir="ltr" style="left: calc(var(--scale-factor)*435.91px); top: calc(var(--scale-factor)*383.33px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.919773);" role="presentation">suitable combination</span><span dir="ltr" style="left: calc(var(--scale-factor)*519.58px); top: calc(var(--scale-factor)*383.33px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif;" role="presentation">s</span><br role="presentation"><span dir="ltr" style="left: calc(var(--scale-factor)*72.02px); top: calc(var(--scale-factor)*394.85px); font-size: calc(var(--scale-factor)*9.96px); font-family: sans-serif; transform: scaleX(0.887764);" role="presentation">of parameters</span></span></p> ER -