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=Binary-driven | =Binary-driven Hypernovae= | ||
The material presented here builds on our separate discussion of [[Appendix/Ramblings/TurningPoints#Close_Binary_Stars|close binary stars]]. | The material presented here builds on our separate discussion of [[Appendix/Ramblings/TurningPoints#Close_Binary_Stars|close binary stars]]. | ||
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=Critique= | =Critique= | ||
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A. An excellent presentation regarding the classical "Fission Theory of Binary Stars" can be found in Lebovitz, N. R. (1972, ApJ, 175, p. 171) -- see especially the 2nd paragraph of section IV (pp. 176 - 177) where reference is made to the Jacobi bifurcation at e = 0.8127, and bifurcation to the "lower self-adjoint (LSA)" sequence at e = 0.9529. Both are points along the Maclaurin sequence where the the axisymmetric configuration is susceptible to deformation into a nonaxisymmetric (specifically, ellipsoidal) configuration: In the presence of viscous dissipation, the Jacobi bifurcation point is relevant; in the absence of viscosity, the LSA bifurcation point is relevant. In section 2 of their manuscript, Zhang and Ruffini focus on a "before fission" model that sits at the point along the Maclaurin sequence where the Jacobi sequence bifurcates. In the context of the precursor of long-GRBs, why have the authors focused on bifurcation to the Jacobi sequence instead of the LSA sequence? | A. An excellent presentation regarding the classical "Fission Theory of Binary Stars" can be found in Lebovitz, N. R. (1972, ApJ, 175, p. 171) -- see especially the 2nd paragraph of section IV (pp. 176 - 177) where reference is made to the Jacobi bifurcation at e = 0.8127, and bifurcation to the "lower self-adjoint (LSA)" sequence at e = 0.9529. Both are points along the Maclaurin sequence where the the axisymmetric configuration is susceptible to deformation into a nonaxisymmetric (specifically, ellipsoidal) configuration: In the presence of viscous dissipation, the Jacobi bifurcation point is relevant; in the absence of viscosity, the LSA bifurcation point is relevant. In section 2 of their manuscript, Zhang and Ruffini focus on a "before fission" model that sits at the point along the Maclaurin sequence where the Jacobi sequence bifurcates. In the context of the precursor of long-GRBs, why have the authors focused on bifurcation to the Jacobi sequence instead of the LSA sequence? | ||
B. In their effort to illustrate what the properties of an "after fission" binary system might be, Zhang and Ruffini pick: a system in which the mass ratio is 17/3; the more massive component is a Maclaurin spheroid; and the less massive component is a Jacobi ellipsoid. Why is this an appropriate "after fission" configuration? They seem to be suggesting that fission occurs precisely when the "before fission" CO_star evolves to the Jacobi bifurcation point and that it splits in such a way that one fission component lands on one equilibrium branch -- the Maclaurin sequence -- while the second lands on the other equilibrium branch -- the Jacobi sequence. This is quite different from the scenario that is suggested by the classical fission theory (see the following, | B. In their effort to illustrate what the properties of an "after fission" binary system might be, Zhang and Ruffini pick: a system in which the mass ratio is 17/3; the more massive component is a Maclaurin spheroid; and the less massive component is a Jacobi ellipsoid. Why is this an appropriate "after fission" configuration? They seem to be suggesting that fission occurs precisely when the "before fission" CO_star evolves to the Jacobi bifurcation point and that it splits in such a way that one fission component lands on one equilibrium branch -- the Maclaurin sequence -- while the second lands on the other equilibrium branch -- the Jacobi sequence. This is quite different from the scenario that is suggested by the classical fission theory (see the following, Note 1C). What is the physical justification for the scenario being proposed by Zhang and Ruffini? | ||
C. The classical fission theory is quantitatively well illustrated by Eriguchi, Y., and Hachisu, I. (1982, Progress of Theoretical Physics, 67, p. 844) -- see especially their Figure 1 -- and by Eriguchi, Y., Hachisu, I., and Sugimoto, D. (1982, Progress of Theoretical Physics, 67, p. 1068) -- see especially their Figs. 1, 3, and 4. Applying this classical theory to the physical scenario being investigated by Zhang and Ruffini, we would expect the following: After the axisymmetric CO_star encounters the Jacobi bifurcation point, the star should deform into an ellipsoidal configuration that becomes more and more elongated on a (slow) viscous timescale. Eventually, a point is encountered along the Jacobi sequence (a_2, a_3) = (0.2972, 0.2575) where a so-called dumbbell/binary sequence bifurcates from the Jacobi sequence; it is at this point that the configuration becomes susceptible to fission into a binary system with a mass ratio of unity. | C. The classical fission theory is quantitatively well illustrated by Eriguchi, Y., and Hachisu, I. (1982, Progress of Theoretical Physics, 67, p. 844) -- see especially their Figure 1 -- and by Eriguchi, Y., Hachisu, I., and Sugimoto, D. (1982, Progress of Theoretical Physics, 67, p. 1068) -- see especially their Figs. 1, 3, and 4. Applying this classical theory to the physical scenario being investigated by Zhang and Ruffini, we would expect the following: After the axisymmetric CO_star encounters the Jacobi bifurcation point, the star should deform into an ellipsoidal configuration that becomes more and more elongated on a (slow) viscous timescale. Eventually, a point is encountered along the Jacobi sequence (a_2, a_3) = (0.2972, 0.2575) where a so-called dumbbell/binary sequence bifurcates from the Jacobi sequence; it is at this point that the configuration becomes susceptible to fission into a binary system with a mass ratio of unity. The scenario presented by Zhang and Ruffini regarding the manner in which fission occurs is quite different from the classical theory; the authors should explain why. | ||
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[3] | [3] Authors should acknowledge earlier examples of toy model. | ||
The authors' "Before Fission" configuration is a Maclaurin spheroid. For over 100 years, we have known what the expression is for the spheroid's dimensionless spin frequency [see reference 3A, below], for any value of the spheroid's eccentricity (e) -- not just the limited set of values picked for illustration purposes by the authors. Similarly, the community has had access to an analytic expression for the configuration's dimensionless angular momentum [see reference 3B, below]. The configuration's spin frequency (Omega_0) and angular momentum (J_tot) can furthermore be expressed in physical units if the configuration's mass and spin period are specified. | |||
The authors' "After Fission" configuration is a binary system that contains a pair of uniform-density, uniformly rotating objects in circular orbit about one another; they assume furthermore that both stars have a spin frequency that is the same as (is synchronized with) the orbital frequency (Omega_f). Over a century ago, Darwin (1906) provided a general expression for this system's dimensionless total angular momentum, in terms of the binary's mass ratio and the ratio of the radius of each star to the orbital separation [see reference 3C, below]. Darwin assumed that both stars are spherical, whereas Zhang and Ruffini have assumed that one is a Maclaurin spheroid and the other is a Jacobi ellipsoid; in the context of the "toy model" being offered by the authors, this is a subtle and negligible difference. | |||
Why don't the authors provide these much more general expressions to the reader and, at the same time, acknowledge that there is nothing particularly new about the toy model that they have adopted. | |||
Relevant References ... | |||
A. See, for example, Eq. (6) on p. 78 of Chandrasekhar's EFE, or much earlier, Eq. (1) on p. 613 of Thomas, W. and Tait, P. G. (1867, Treatise on Natural Philosophy, Vol. I). | |||
B. See, for example, Eq. (4.2) on p. 591 of Marcus, P. S., Press, W. H., and Teukolsky, S. A. (1977, ApJ, 214, 584). | |||
C. See, for example, the expression for L_1 immediately following Eq. (1) on p. 165 of Darwin, G. H. (1906, Philosophical Transactions of the Royal Society A, Vol. 206, 161). | |||
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==Other== | |||
=== | ===Trial Pieces=== | ||
As a case in point, their toy model "before fission" is a (10 solar-mass) Maclaurin spheroid; next, they envision that fission occurs when the initial CO_star is rotating sufficiently fast that its eccentricity places it at the point along the Maclaurin sequence where the Jacobi sequence bifurcates (e = 0.8127); finally, their toy model "after fission" is a (1.5 solar-mass) Jacobi ellipsoid paired with an 8.5 solar-mass Maclaurin spheroid; . This is inaccurate depiction of the classical fission theory [see note 1, below]. | As a case in point, their toy model "before fission" is a (10 solar-mass) Maclaurin spheroid; next, they envision that fission occurs when the initial CO_star is rotating sufficiently fast that its eccentricity places it at the point along the Maclaurin sequence where the Jacobi sequence bifurcates (e = 0.8127); finally, their toy model "after fission" is a (1.5 solar-mass) Jacobi ellipsoid paired with an 8.5 solar-mass Maclaurin spheroid; . This is inaccurate depiction of the classical fission theory [see note 1, below]. | ||
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<li>Ill-advised to refer to the ''new'' NS as "νNS" because, in this context, readers might reasonably associate the greek letter, ν, with neutrinos. </li> | <li>Ill-advised to refer to the ''new'' NS as "νNS" because, in this context, readers might reasonably associate the greek letter, ν, with neutrinos. </li> | ||
</ol> | </ol> | ||
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=See Also= | =See Also= | ||
Latest revision as of 12:59, 4 July 2023
Binary-driven Hypernovae
The material presented here builds on our separate discussion of close binary stars.
HIDDEN as of 4 July 2023.
See Also
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Appendices: | VisTrailsEquations | VisTrailsVariables | References | Ramblings | VisTrailsImages | myphys.lsu | ADS | |