Standing Accretion Shock Instability (SASI): The Sloshing That Revives a Supernova

What SASI Is: A Stalled Shock That Won't Sit Still

When an iron core exceeding the Chandrasekhar limit (~1.4 M_sun) collapses, the inner core bounces at nuclear density and launches a shock wave outward. That shock loses energy to photodissociating iron and to neutrino losses, and within milliseconds it stalls — becoming a nearly stationary "standing accretion shock" at roughly 100–200 km while matter keeps raining down through it at ~0.1–1 M_sun per second.

SASI is the discovery that this standing shock is not stable. Small perturbations of the shock surface grow exponentially into large-scale, coherent oscillations. In axisymmetric (2D) simulations the dominant pattern is an ℓ = 1 dipole: the shock sloshes up and down the symmetry axis. In full 3D, spiral (m = ±1) modes emerge, with the deformed shock rotating around the proto-neutron star.

• It is global, not local — it moves the entire shock, not just bubbles behind it.
• It is oscillatory, with a well-defined period, unlike chaotic convection.
• It grows on the advection timescale from shock to neutron-star surface.

The Mechanism: An Advective-Acoustic Feedback Loop

The favored explanation, developed by Thierry Foglizzo and collaborators (2002, 2006, 2007), is the advective-acoustic cycle. It is a self-amplifying feedback loop between two ways information travels in the post-shock flow:

• A ripple on the shock creates entropy and vorticity perturbations that are carried inward (advected) with the settling flow toward the proto-neutron star.
• When these perturbations decelerate sharply near the dense neutron-star surface (~30–100 km), they generate acoustic (pressure) waves that travel back outward.
• The returning sound wave hits the shock and displaces it again — larger than before, closing an amplifying cycle.

The oscillation period is set by the sum of the advection time inward plus the sound-crossing time back out: roughly τ_SASI ≈ τ_adv + τ_ac. A competing "purely acoustic" mechanism has been proposed, but numerical experiments and the analytic toy models of Foglizzo, Guilet, and Sato favor the advective-acoustic interpretation as the dominant driver.

Characteristic Numbers and a Worked Estimate

Consider a typical stalled-shock configuration: shock radius R_s ≈ 150 km, proto-neutron-star radius R_ns ≈ 50 km. In the subsonic post-shock region the flow settles inward at a fraction of the local sound speed, so the inward advection time is of order:

τ_adv ≈ (R_s − R_ns) / ⟨v_adv⟩ ≈ 100 km / (few × 10³ km/s) ≈ 10–30 ms.

The acoustic return leg is faster (sound speed is tens of thousands of km/s in the hot post-shock gas), so the SASI period is dominated by advection and lands near ~30–50 ms, i.e. a frequency of ~20–100 Hz. Key characteristic values:

• Post-bounce onset: ~100–200 ms, once the shock has stalled.
• Duration of strong SASI: ~100–200 ms before convection or explosion takes over.
• Growth: exponential, with e-folding times of a few tens of ms.
• Shock excursions: tens of km, comparable to the mean shock radius itself.

A key dimensionless control parameter is χ, the ratio of the advection time through the gain region to the local convective growth time; χ ≳ 3 favors convection, while smaller χ favors SASI.

How SASI Is Detected: Neutrinos and Gravitational Waves

No supernova since 1987 has been close enough to test SASI directly, but two "multimessenger" channels would carry its fingerprint from the next Galactic core-collapse event:

• Neutrinos. As the sloshing shock periodically funnels accreting matter onto the proto-neutron star, the neutrino luminosity and mean energy are modulated. Simulations predict luminosity variations of tens of percent and mean-energy swings of ~1 MeV, with most power at typical SASI frequencies of ~20–100 Hz. Detectors like Super-Kamiokande / Hyper-Kamiokande and IceCube could resolve this quasi-periodic flicker for a supernova within ~10 kpc — and the modulation is strongest for an observer looking along the sloshing axis.
• Gravitational waves. The same accretion pulses striking the PNS surface produce a quasi-periodic GW signal. Kuroda, Kotake & Takiwaki (2016) identified a distinctive SASI GW component around ~100–200 Hz that is correlated with the neutrino modulation — a joint detection would be a smoking gun. This sits below the higher-frequency (~few hundred Hz to kHz) proto-neutron-star g-mode emission.

SASI Versus Its Cousins: Convection, Rotation, and Spiral Modes

SASI shares the gain region with neutrino-driven convection, and which one dominates depends on the progenitor and heating. Convection is a local, buoyancy-driven overturn (Ledoux-unstable negative entropy gradient) that produces small-scale turbulent plumes; SASI is a global, advective-acoustic oscillation. When the parameter χ ≳ 3, convection tends to win; compact configurations with long advection times and modest heating favor SASI.

• Spiral versus sloshing: In 3D the ℓ = 1 sloshing can organize into a rotating spiral mode carrying angular momentum. Blondin & Mezzacappa (2007) showed spiral SASI can spin up an initially non-rotating core, potentially giving the neutron star a birth period of ~50 ms to 1 s — a possible origin of pulsar spins.
• Rotation: Rapid progenitor rotation expands the gain region and can push a SASI-dominated core toward a convection-dominated regime.
• Not a MHD or magnetorotational instability: SASI is purely hydrodynamic; it needs no magnetic field, distinguishing it from the magnetorotational instability invoked in magnetar/collapsar models.

Why It Matters, Famous Cases, and Open Questions

SASI is a central piece of the modern delayed neutrino-driven explosion mechanism. By sloshing the shock outward and enlarging its average radius, it lengthens the dwell time of gas in the gain region, where neutrinos deposit energy — pushing marginal models over the threshold to explode (e.g. Marek & Janka 2009; Müller, Janka & Marek). It also naturally imprints the large-scale asymmetries seen in supernova remnants and can help explain neutron-star kicks and spins.

• SN 1987A — the nearest supernova in centuries — shows a strikingly asymmetric, clumpy ejecta and ⁴⁴Ti distribution consistent with a large-scale, SASI-and-convection-driven engine. Its neutrino burst (~10 s, ~24 events across Kamiokande-II, IMB and Baksan) predated the detectors that could have resolved SASI modulation.
• Laboratory analog: Foglizzo's SWASI shallow-water experiment reproduces the sloshing and spiral modes in a water tank, a rare tabletop demonstration of a supernova-scale instability.

Open questions remain: the relative importance of SASI versus convection across progenitor masses, the exact mechanism debate (advective-acoustic versus purely acoustic), and how strongly 3D effects, rotation, and the equation of state shape the outcome. A well-observed Galactic supernova would resolve much of this.

SASI versus neutrino-driven convection: the two instabilities competing behind the stalled supernova shock

Property	SASI	Neutrino-driven convection
Physical driver	Advective-acoustic cycle (amplified feedback loop)	Buoyancy in a negative-entropy gradient (Ledoux unstable)
Spatial scale	Global, low-order (ℓ = 1, 2; spiral)	Small-scale, high-ℓ plumes and bubbles
Character	Coherent, oscillatory / quasi-periodic	Chaotic, turbulent overturn
Favored when	Long advection time, small shock radius, low heating	χ ≳ 3, larger gain region, strong heating
Timescale	Advection time shock→PNS, ~10–50 ms period	Convective growth time, few ms e-foldings
Key signature	Quasi-periodic neutrino & GW modulation (~50–100 Hz)	Broadband GW noise, stochastic neutrino flicker