LSUsimulations

"Fission" Simulations at LSU

This chapter essentially replicates an earlier html-based discussion.

Simulations Performed by John Cazes

Here we summarize the results of numerical simulations that John Cazes performed as part of his doctoral dissertation research, which was completed in 1999. A portion of this work has been published by 📚 J. E. Cazes & J. E. Tohline (2000, ApJ, Vol 532, Issue 2, pp. 1051 - 1068) in an article titled, "Self-Gravitating Gaseous Bars.   I. Compressible Analogs of Riemann Ellipsoids with Supersonic Internal Flows."

Model A

Table 1 extracted from p. 1057 of J. E. Cazes & J. E. Tohline (2000) Self-gravitating Gaseous Bars.   I. Compressible Analogs of Riemann Ellipsoids with Supersonic Internal Flows The Astrophysical Journal, Vol 532, Issue 2, pp. 1051 - 1068

The initial configuration of "Model A" is an axisymmetric,

$n=\frac{3}{2}$

polytrope with differential rotation prescribed in such a way that the angular momentum as a function of cylindrical radius,

$\varpi$

, has the same function as a uniformly rotating,

$n=0$

polytrope — that is, the same as a Maclaurin spheroid. This is a rotation profile originally introduced by 📚 R. Stoeckly (1965, ApJ, Vol. 142, pp. 208 - 228). With this in mind, it is clear that "Model A" sits on the so-called

$n^{\prime }=0$

sequence, as introduced by 📚 J. P. Ostriker & J. W.-K. Mark (1968, ApJ, Vol. 151, pp. 1075 - 1088), and as implemented, for example, by 📚 P. Bodenheimer & J. P. Ostriker (1973, ApJ, Vol. 180, pp. 159 - 170), and by 📚 B. K. Pickett, R. H. Durisen, & G. A. Davis (1996, ApJ, Vol. 458, pp. 714 - 738). (See our additional discussion of Simple Rotation Profiles.)

The initial values of various "Model A" parameters are provided in the second column of numbers in Table 1 (p. 1057) of 📚 Cazes & Tohline (2000) — this table has been reprinted here, on the right. For example, the ratio of the maximum density to the mean density of the model is, ${\rho }_{\mathrm{m}\mathrm{a}\mathrm{x}}/\overline{\rho }=5.66$; and the ratio of rotational kinetic energy to the absolute value of the gravitational potential energy, $T_{\mathrm{r}\mathrm{o}\mathrm{t}}/|W|=0.30$. For comparison — see the first column of numbers — in a nonrotating, spherically symmetric $n=\frac{3}{2}$ polytrope, ${\rho }_{\mathrm{m}\mathrm{a}\mathrm{x}}/\overline{\rho }=5.99$ and $T_{\mathrm{r}\mathrm{o}\mathrm{t}}/|W|=0.0$.

1^st Video

Our initially axisymmetric "Model A" configuration is dynamically unstable toward the development of a so-called bar-mode instability; actually, the unstable eigenfunction has a slight two-armed spiral character. The icon shown here, on the left, links to a YouTube video that shows the nonlinear development of this instability.

Model A Barmode Instability YouTube video:  BhRUqZe0Ly4

Resolution …

• Radial:   Model A was evolved on a cylindrical grid that contained 128 radial zones, but the equatorial radius of the initial axisymmetric model extended out to only zone 53. Hence, ample room was allowed for radial expansion of the model as it deformed into a bar-like configuration.
• Vertical:   Although the model was initially quite flat — with a pole-to equatorial ratio of $0.5$, meaning that the vertical extent above its equatorial plane was substantially less than 53 vertical zones — it was evolved on a grid that contained 128 vertical zones in this "northern" hemisphere.

See Also