Discussing Patrick Motl's 2019 Simulations

May 1 (from Patrick)

Hi Joel,

I hope things are well for you and yours.

I did finally have a couple research students this semester that were able to slog their way into unix, programming, etc. far enough to do some useful things.

They ran two spherical bipolytropes with my old cylindrical code. These were n = 5 cores with n = 1 envelopes. No density discontinuity. One model is a little below the stability boundary in xi, the other is a little above the stability boundary.

What I can see from the evolutions, especially now that I made plots of the entropy, is that they are convectively unstable and that is just a mess with the core convecting into the envelope.

Did you happen to have any thoughts on what might be a better case to run? When I get done grading finals I am going to work through the equations with kappa set explicitly in the envelope so the entropy profile is flat and just live with whatever density discontinuity that gives me.

cheers, Patrick

May 4 (my response)

Patrick,

My initial response to your 1 May email follows. In an effort to make sure we are on the same page when referencing the structural properties and the stability properties of various configurations, my response includes links to various chapters/subsections of my online wiki-based book.

Thanks for pursuing this problem. I am still very interested in Its solution.

All the best, Joel

Chosen Initial Models

I presume that when you constructed your pair of initial (spherical) models, you used the analytically prescribed properties found in my chapter titled, "BiPolytrope with <math>n_c = 5</math> and <math>n_e=1</math>" and that when you reference the "stability boundary in <math>~\xi</math>" you are drawing from the summary (Table 3 and Figure 3) found near the end of this chapter in the subsection titled, "Stability Condition." In particular, based on the information contained in this chapter, I presume that you are assuming that the marginally unstable model along the <math>~\mu_e/\mu_c = 1</math> sequence is the configuration having the properties …

and that your pair of initial models have values of <math>~\xi_i</math> that are somewhat greater than and somewhat smaller than 2.416. If this does not properly describe your choice of initial models, please clarify.

Instability Toward Convection

In my chapter titled, "Axisymmetric Instabilities to Avoid," I discuss — among other things — the Schwarzschild Criterion. Toward the very end of this chapter, in a subsection titled, Modeling Implications and Advice, I specifically describe how convection might arise when modeling spherical polytropic configurations. Would you please read this short subsection and let me know whether you agree with my explanation or not?

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