Difference between revisions of "User:Tohline/SSC/Stability/BiPolytropes"
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We expect the content of this chapter — which examines the relative stability of bipolytropes — to parallel in many ways the content of an [[User:Tohline/SSC/Stability/InstabilityOnsetOverview#Marginally_Unstable_Pressure-Truncated_Gas_Clouds|accompanying chapter in which we have successfully analyzed the relative stability of pressure-truncated polytopes]]. Figure 1, shown here on the right, has been copied from that separate discussion. The curves show the mass-radius relationship for pressure-truncated model sequences having a variety of polytropic indexes, as labeled, over the range <math>3 \le n \le \infty</math>. On each sequence, the green filled circle identifies the model with the largest mass. We have shown that | We expect the content of this chapter — which examines the relative stability of bipolytropes — to parallel in many ways the content of an [[User:Tohline/SSC/Stability/InstabilityOnsetOverview#Marginally_Unstable_Pressure-Truncated_Gas_Clouds|accompanying chapter in which we have successfully analyzed the relative stability of pressure-truncated polytopes]]. Figure 1, shown here on the right, has been copied from that separate discussion. The curves show the mass-radius relationship for pressure-truncated model sequences having a variety of polytropic indexes, as labeled, over the range <math>3 \le n \le \infty</math>. On each sequence, the green filled circle identifies the model with the largest mass. We have shown that the oscillation frequency of the fundamental-mode of radial oscillation is precisely zero for each one of these maximum-mass models. As a consequence, we know that each green circular marker identifies the point along its associated sequence that separates dynamically stable from dynamically unstable models. | ||
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Revision as of 03:54, 2 November 2018
Marginally Unstable Bipolytropes
Our aim is to determine whether or not there is a relationship between equilibrium models at turning points along bipolytrope sequences and bipolytropic models that are marginally (dynamically) unstable toward collapse (or dynamical expansion).
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 of Pressure-Truncated Polytropes |
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We expect the content of this chapter — which examines the relative stability of bipolytropes — to parallel in many ways the content of an accompanying chapter in which we have successfully analyzed the relative stability of pressure-truncated polytopes. Figure 1, shown here on the right, has been copied from that separate discussion. The curves show the mass-radius relationship for pressure-truncated model sequences having a variety of polytropic indexes, as labeled, over the range <math>3 \le n \le \infty</math>. On each sequence, the green filled circle identifies the model with the largest mass. We have shown that the oscillation frequency of the fundamental-mode of radial oscillation is precisely zero for each one of these maximum-mass models. As a consequence, we know that each green circular marker identifies the point along its associated sequence that separates dynamically stable from dynamically unstable models.
See Also
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