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__FORCETOC__ | __FORCETOC__ | ||
=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= | ||
== | ==Manuscript Review== | ||
===Overview=== | |||
It is not yet well-established what type of stellar configuration serves as the precursor to long-GRBs. Zhang and Ruffini argue that if you have a CO_star in orbit about a NS and assume that the angular rotation frequency of the CO_star is synchronous with its orbital frequency, there are situations in which the (core of the?) CO_star will be spinning sufficiently fast that it spontaneously undergoes fission. The authors imagine that the result will be a compact binary within a compact binary, opening the door for a rather exotic subsequent (hypernova?) explosion; an explosion that exhibits an emission/radiation signature that is more complex and more drawn out in time than that of a "simple" hypernova. | |||
At the heart of the authors' very speculative hypothesis is the suggestion that a CO_star can spontaneously undergo fission. The authors appear to be thinking that the classical fission theory of star formation is relevant to this problem. However, they present an inaccurate, as well as seriously incomplete, depiction of the classical fission theory [see our Notes 1A, 1B, and 1C, below]. | |||
Furthermore, the authors do not address serious questions that have been raised over the past 40+ years regarding the viability of the fission theory. Using numerical hydrodynamic techniques, various research groups have modeled the growth of non-axisymmetric structure in rapidly rotating protostellar clouds as well as in collapsing stellar cores. Nonlinear-amplitude bar-like and spiral-shaped structures develop, but fission into a binary system does not occur [see our Note 2, below]. | |||
Finally, the bulk of this manuscript (sections 2 and 3) describes efforts by the authors to develop, then use, a toy (algebraic) model to illustrate what the properties might be of a binary system that results from the fission of a CO_star. As is explained below [see our Note 3], there is nothing new (astrophysically or mathematically) in this presentation. At best, this portion of the manuscript should be significantly compressed; it should be modified to properly include citations to earlier works that have developed and used the same toy model; and -- again, at best -- it should be relegated to an appendix of a more substantive article. | |||
In summary, the authors present a highly speculative theory regarding precursors to long-GRBs but they provide no substantive arguments to back it up. My recommendation is that this manuscript by Zhang and Ruffini not be published in The Astrophysical Journal. | |||
===NOTES:=== | |||
[1] Is the classical "Fission Theory" relevant? | |||
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, 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. 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. | |||
[2] Is the classical concept of fission viable in any physical context? | |||
Over the past 40+ years, various modeling efforts have examined the onset and/or the nonlinear development of nonaxisymmetric structure in rapidly rotating configurations that are more realistic than the (incompressible) models considered by the classical fission hypothesis. All seem to indicate that the outcome is not fission. See, for example, Lebovitz, N. R. (1974, ApJ, 190, 121); or Tohline, J. E. (2002, Annual Review of Astronomy and Astrophysics, Vol. 40, 349) -- especially the section titled "Delayed Breakup" (pp. 367 - 374) -- or Ott, C. D. et al. (2005, ApJ, 625, L119). | |||
[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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The meat of this manuscript resides in sections 2 and 3. The authors illustrate, through a sequence of algebraic steps, how the physical parameters of the "after fission" binary system can be deduced from the (specified) parameters of the rapidly rotating "before fission" spheroidal configuration. This presentation is underwhelming. The relevant algebraic relations have appeared in various astrophysical publications for over 100 years -- see references, below, to Thomas & Tait (1867) and to Darwin (1906). By adopting relations from these earlier works, these two manuscript sections can be significantly reduced in length (and very likely combined); and, we would argue, Tables 3 and 4 should be omitted altogether. Given that there is nothing really new, here, we recommend that, at best, the meat of this manuscript should be relegated to the appendix of a paper that substantiates in a much more profound way why the core fission hypothesis. | The meat of this manuscript resides in sections 2 and 3. The authors illustrate, through a sequence of algebraic steps, how the physical parameters of the "after fission" binary system can be deduced from the (specified) parameters of the rapidly rotating "before fission" spheroidal configuration. This presentation is underwhelming. The relevant algebraic relations have appeared in various astrophysical publications for over 100 years -- see references, below, to Thomas & Tait (1867) and to Darwin (1906). By adopting relations from these earlier works, these two manuscript sections can be significantly reduced in length (and very likely combined); and, we would argue, Tables 3 and 4 should be omitted altogether. Given that there is nothing really new, here, we recommend that, at best, the meat of this manuscript should be relegated to the appendix of a paper that substantiates in a much more profound way why the core fission hypothesis. | ||
===Quantitative Model=== | ===Quantitative Model=== | ||
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Now assume that this CO star "fissions" into two component stars in orbit about one another, and that it does so while conserving total mass and total angular momentum. | Now assume that this CO star "fissions" into two component stars in orbit about one another, and that it does so while conserving total mass and total angular momentum. | ||
==Background== | |||
Let configuration #1 be a Maclaurin spheroid. Once the spheroid's eccentricity (e) has been specified, we know its dimensionless spin frequency [see note 1, below] and we know its dimensionless angular momentum [see note 2, below]. The configuration's spin frequency (Omega_0) and angular momentum (J_tot) can be expressed in physical units if, furthermore, the configuration's mass and spin period are specified. | |||
Let configuration #2 be a binary system that contains a pair of uniform-density spheres in circular orbit about one another; assume furthermore that both spheres have a spin frequency that is the same as (is synchronized with) the orbital frequency (Omega_f). Darwin (1906) provides an 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 note 3, below]. | |||
[1] See, for example, Eq. (6) on p. 78 of Chandrasekhar's EFE, or much earlier, Eq. (1) on p. 613 of Thomas & Tait (1867). | |||
[2] See, for example, Eq. (4.2) on p. 591 of Marcus, Press, & Teukolsky (1977). | |||
[3] See, for example, the expression for L_1 immediately following Eq. (1) on p. 165 of Darwin (1906). | |||
==Major Concern== | ==Major Concern== | ||
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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 | |