Effect of Rotation on the Stability of a Stalled Cylindrical Shock and Its Consequences for Core‐Collapse Supernovae

Abstract

A perturbative analysis is used to investigate the effect of rotation on the instability of a steady accretion shock (SASI) in a simple toy model, in view of better understanding supernova explosions in which the collapsing core contains angular momentum. A cylindrical geometry is chosen for the sake of simplicity. Even when the centrifugal force is very small, rotation can have a strong effect on the nonaxisymmetric modes of SASI by increasing the growth rate of the spiral modes rotating in the same direction as the steady flow. Counterrotating spiral modes are significantly damped, while axisymmetric modes are hardly affected by rotation. The growth rates of spiral modes have a nearly linear dependence on the specific angular momentum of the flow. The fundamental one-armed spiral mode (m ¼ 1) is favored for small rotation rates, whereas stronger rotation rates favor the mode m ¼ 2. A WKB analysis of higher harmonics indicates that the efficiency of the advective-acoustic cycles associated with spiral modes is strongly affected by rotation in the same manner as low-frequency modes, whereas the purely acoustic cycles are stable. These results suggest that the linear phase of SASI in rotating core-collapse supernovae naturally selects a spiral mode rotating in the same direction as the flow, as observed in the three-dimensional numerical simulations of Blondin and Mezzacappa. This emphasizes the need for a three-dimensional approach to rotating core collapse, before conclusions on the explosion mechanisms and pulsar kicks can be drawn.

Three‐Dimensional Simulations of Standing Accretion Shock Instability in Core‐Collapse Supernovae

“…On the other hand, differences do show up, for example, if random perturbations are added to the nonradial velocity components; this case is important in discussing the origin of pulsar spins proposed by Blondin & Mezzacappa (2007), and will be the subject of a forthcoming paper ( W. Iwakami et al 2008). We also note that the symmetry between m ¼ 1 and À1 modes is naturally removed if the unperturbed accretion flow is rotating (see Yamasaki & Foglizzo 2008). All the models presented in this paper are summarized in Table 1.…”

Self-Sustained Asymmetry of Lepton-Number Emission: A New Phenomenon During the Supernova Shock-Accretion Phase in Three Dimensions

“…It was unambiguously identified in 2D hydrodynamical simulations of idealized, adiabatic (and thus non-convective) postshock accretion flows (Blondin, Mezzacappa, & DeMarino 2003). SASI was found to possess the highest growth rates for the lowest-order (dipole and quadrupole) spherical harmonics (Blondin & Mezzacappa 2006;Foglizzo et al 2007;Iwakami et al 2008) and to give rise to spiral-mode mass motions in 3D simulations (Blondin & Mezzacappa 2007;Iwakami et al 2009;Fernández 2010;Hanke et al 2013) or in 2D setups without the constraint of axisymmetry (Blondin & Mezzacappa 2007;Yamasaki & Foglizzo 2008;Foglizzo et al 2012). The instability can be explained by an advectiveacoustic cycle of amplifying entropy and vorticity perturbations in the cavity between accretion shock and PNS surface (Foglizzo 2002;Foglizzo et al 2007;Scheck et al 2008; and has important consequences for NS kicks (Scheck et al 2004Nordhaus et al 2010bNordhaus et al , 2012Wongwathanarat, Janka, & Müller 2010, 2013 and spins (Blondin & Mezzacappa 2007;Rantsiou et al 2011;Guilet & Fernández 2013), quasi-periodic neutrino emission modulations (Marek, Janka, & Müller 2009;Lund et al 2010;Tamborra et al 2013), and SN gravitational-wave signals (Marek, Janka, & Müller 2009;Murphy, Ott, & Burrows 2009;).…”

Three-dimensional neutrino-driven supernovae: Neutron star kicks, spins, and asymmetric ejection of nucleosynthesis products

“…It is possible that faster NS rotation requires the progenitor core to rotate (e.g., Heger et al 2005;Ott et al 2006). In a rotating environment, however, the growth of SASI spiral modes will be severely altered and potentially fostered (Blondin & Mezzacappa 2007;Yamasaki & Foglizzo 2008;Iwakami et al 2009), and three-dimensional simulations are therefore indispensable to make predictions for the connection between progenitor and NS rotation. Fryer & Kusenko (2006) pointed out that ejecta asymmetries could be used to distinguish between different theoretical suggestions for the kick mechanism.…”