Hydrodynamic Mechanism for Clumping along the Equatorial Rings of SN1987A and Other Stars

An explanation for the origin and number of clumps along the equatorial ring of Supernova 1987A has eluded decades of research. Our linear analysis and hydrodynamic simulations of the expanding ring prior to the supernova reveal that it is subject to the Crow instability between vortex cores. The dominant wave number is remarkably consistent with the number of clumps, suggesting that the Crow instability stimulates clump formation. Although the present analysis focuses on linear fluid flow, future nonlinear analysis and the incorporation of additional stellar physics may further elucidate the remnant structure and the evolution of the progenitor and other stars.

Figure 1

Hot spots along the equatorial ring of SN1987A [5, 11] (a) and pinch-off of isolated vortex structures from a radially expanding vortex dipole in water [12] (b). Images are reproduced with permission.

Figure 2

Schematic of the stability analysis parameters. Red arrows indicate the direction of the dipole expansion.

Figure 3

Mach (blue dashed), Reynolds (yellow solid), and Knudsen (orange dotted) numbers versus radius. The teal shaded region satisfies $M<0.3$, $\mathrm{Re}>{10}^3$, and $\mathrm{Kn}<{10}^{-3}$.

Figure 4

The growth rate (a) and perturbation amplitude (b) of the symmetric mode versus wave number and time. The red X denotes the time and wave number when the maximum perturbation equals the core separation distance.

Figure 5

Isosurfaces of mass fraction (left) and $Q$ criterion (right) at times $t\mathrm{\Gamma }/R_0^2\in (0,0.1,0.7)$, which increase with increasing radius.