Joel2: Created page with "FORCETOC =Radial Oscillations of Polytropic Spheres= ===Adiabatic (Polytropic) Wave Equation=== Copied from here … In an accompanying discussion, we derived the so-called,
'''Adiabatic Wave''' (or ''Radial Pulsation'') '''Equation'''
{{Math/EQ_RadialPulsation01}}
=BiPolytrope..."

2024-07-16T00:01:08Z

Created page with "__FORCETOC__  =Radial Oscillations of Polytropic Spheres= ===Adiabatic (Polytropic) Wave Equation=== Copied from here … In an accompanying discussion, we derived the so-called, <div align="center" id="2ndOrderODE"> <font color="#770000">'''Adiabatic Wave''' (or ''Radial Pulsation'') '''Equation'''</font><br /> {{Math/EQ_RadialPulsation01}} </div> =BiPolytrope..."

New page

__FORCETOC__

=Radial Oscillations of Polytropic Spheres=

===Adiabatic (Polytropic) Wave Equation===

Copied from [[SSC/Stability/Polytropes|here]] …

In an [[SSC/Perturbations#2ndOrderODE|accompanying discussion]], we derived the so-called,

<div align="center" id="2ndOrderODE">
<font color="#770000">'''Adiabatic Wave''' (or ''Radial Pulsation'') '''Equation'''</font><br />

{{Math/EQ_RadialPulsation01}}
</div>

=BiPolytrope with n<sub>c</sub> = 5 and n<sub>e</sub> = 1=

Copied from [[SSC/Structure/BiPolytropes/Analytic51|here]] …
Here we construct a [[SSC/Structure/BiPolytropes#BiPolytropes|bipolytrope]] in which the core has an <math>~n_c=5</math> polytropic index and the envelope has an <math>~n_e=1</math> polytropic index. This system is particularly interesting because the entire structure can be described by closed-form, analytic expressions. In deriving the properties of this model, we will follow the [[SSC/Structure/BiPolytropes#Solution_Steps|general solution steps for constructing a bipolytrope]] that we have outlined elsewhere.

=See Also=

{{ SGFfooter }}

Appendix/Ramblings/51BiPolytropeStability/CleanMethodicalExaminatioin - Revision history