The Onset of Neutrino-Driven Convection in Core-Collapse Supernovae

Brendan Krueger

CEA Saclay2013 October

18

THE ONSET OF NEUTRINO-DRIVEN CONVECTION IN

CORE-COLLAPSE SUPERNOVAE

Brendan Krueger | CEA Saclay 2

Background Structure of CC SNe in the stalled-shock phase Instabilities in CC SNe

Convective instability Standing accretion shock instability

Research at CEA The big picture A simple model Predictions Hydrodynamics

Were do we go from here?Summary & Conclusions

OUTLINE

Brendan Krueger | CEA Saclay

Convection vs. SASI in CC SNe

3

BACKGROUND


Above the proto-neutron star matter is cooling from neutrino emission

Neutrino emission weakens farther out until the gain radius

Above the gain radius is the gain region, where a fraction of the neutrinos are re-absorbed

Gain region is bounded by the stalled shock

Outward of the shock matter is infalling supersonically

4

POST-BOUNCE CC SNE STRUCTURE

gain region

cooling region

PNS

shock

gain radius

supersonic infall


gain region

cooling region

neutrinosphere

shock

gain radius

supersonic infall

gain region

cooling region

PNS

shock

gain radius

supersonic infall

Neutrino heating mechanism Reabsorb sufficient

neutrinos in the gain region

Re-energize the shock Wilson (1985), Bethe &

Wilson (1985), Bethe (1990), Janka et al. (2007)

Magnetorotational Rapid rotator Burrows et al. (2007)

5

POST-BOUNCE CC SNE STRUCTURE


Several may existNot mutually exclusive (e.g., Guilet et al. 2010)Two very important:

Convective instability Standing Accretion Shock Instability (SASI)

Generally believed that one of these two will dominate dynamics of the gain region

INSTABILITIES IN THE GAIN REGION


Discovered by Blondin et al. (2003) in a simplified contextSince observed in variety of simulations: e.g., Blondin &

Mezzacappa (2006, 2007), Ohnishi et al. (2006), Scheck et al. (2008), Iwakami et al. (2008, 2009), Fernández & Thompson (2009), Fernández (2010), Müller et al. (2012), Hanke et al. (2013)

Studied analytically: Foglizzo et al. (2006, 2007), Blondin & Mezzacappa (2006), Yamasaki & Yamada (2007), Fernández & Thompson (2009) Blondin & Mezzacappa (2006) suggest SASI is purely-acoustic Sato et al. (2009) and Guilet & Foglizzo (2012) provide evidence

for an advective-acoustic cycleDemonstrated experimentally in a shallow-water analogue

of CC SNe: Foglizzo et al. (2012)

SASI I: BACKGROUND


Perturbations in the shock front create perturbations of entropy and vorticity in the flow

Perturbations advect downward

Deceleration of perturbations generates acoustic wave

Acoustic wave perturbs shock front

SASI II: ADVECTIVE-ACOUSTIC CYCLE

acoustic wave

entropy-vorticitywave


Generally dominated by low-order (l=1,2) modes l=1, m=0: sloshing l=1, m=±1: spiral

Increase dwell time Increases energy gain

from neutrino absorption

Push shock outwardMay give neutron

star a “kick”Spiral modes may

redistribute angular momentum and “spin up” neutron star

SASI III: PROPERTIES


Seen in numerous CC SN simulations: e.g. Herant et al. (1992, 1994), Burrows et al. (1995), Janka & Müller (1995, 1996), Fryer & Heger (2000), Ott et al. (2013), Murphy et al. (2013)

Studied analytically: Foglizzo et al. (2006)Generally higher-order modes (l~5-7)

Convection may cause low-order modes (especially in 2D): Burrows et al. (2012), Dolence et al. (2013)

Difficult to distinguish SASI from convection in nonlinear regime using naïve spherical-harmonic decomposition

CONVECTION I: BACKGROUND


Due to negative entropy gradient, the gain region is unstable to convection

May be stabilized through advection: Foglizzo et al. (2006) Compare the advection time across the gain region and the

growth rate of convective modes Foglizzo’s χ parameter: χ > 3 is unstable to convection

CONVECTION II: STABILIZATION


Different behavior results from these two instabilitiesSASI has the potential to generate high-velocity and/or fast-

rotating neutron stars (through sloshing and spiral modes)Convection requires much more focus on heating (i.e.,

neutrino transport) to capture the driving physicsSASI can lead to gravitational wave emission: Marek et al.

(2009), Murphy et al. (2009)Neutrino emission from CC SNe could depend on flow

dynamicsDifferent shock evolution (asymmetry)Dimensionality of simulations could be significant for

different reasons Convection: inverse cascade in 2D vs. forward cascade in 3D SASI: tendency towards sloshing in 2D vs. spiral in 3D

SASI VS. CONVECTION

13Brendan Krueger | CEA Saclay

Research from CEA Saclay

NONLINEAR BEHAVIOR OF CONVECTION


What can we learn about instabilities in the gain region of a collapsing massive star?

Can we use this information to develop criteria for when a particular instability will dominate the post-shock dynamics?

We have started with convection We also have a study of nonlinear effects relating to SASI in

progress, currently being led by a graduate student, and we hope to be seeing new results soon

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THE BIG QUESTIONS


The linear theory provides a good predictionThere is evidence that nonlinear effects could be

important under some circumstances (e.g., Scheck et al. 2008)

Can we determine a criterion for the non-linear triggering of buoyancy-induced turbulence? Step 1: When is the flow unstable? For example: When is a

bubble buoyant against advection? Step 2: When does a buoyant bubble lead to convective

instability and/or turbulence?

BREAK DOWN THE PROBLEM


Simplify to the minimal physics necessary to capture buoyant instabilities analogous to what is seen in the gain region of CC SNe

Cartesian geometryIdeal ϒ-law equation

of state ϒ = 4/3

Define a buoyant layer Shape function s(x)

Analytic heating function H = H0 (ρ/ρ0) s(x)

Gravitational acceleration g = g0 s(x)

SIMPLIFIED MODEL


Small perturbations grow (unstable) or decay (stable) exponentially

Unstable modes bounded by kmin = 0 and hkmax ~ χ kmax(χ=2) = kmin = 0 : no unstable modes for χ < 2

Fastest-growing mode: kpeak = kpeak(χ)Confirmed using hydrodynamic simulations

LINEAR THEORY


Scheck et al. (2008)Change in velocity due to

buoyancy:(~0.2%)

No mention of heating Adiabatic bubble No reference to the

background entropy gradientNo mention of drag from

rising against accretion flow

Fernández et al. (2013)

Balance of gravitational, buoyant, and drag forces:

No mention of heating Adiabatic bubble No reference to the background

entropy gradient No mention of the size of the

gain region Criterion on constant

velocity, not buoyancy

CURRENT CRITERIA

Neither details the relationship between a rising bubbleand the development of turbulent convection


Attempt to improve the physics of previous estimatesNumerically integrate the equations of motionBegin with an adiabatic bubble and no drag force

Approximates the inputs to the Scheck et al. (2008) criterion

Add drag force and heating of the bubbleResults

Heating had very minimal effect Drag force caused the bubble to reach an equilibrium

position instead of escaping to infinity and is thus more physical, but changed the critical value very little

Net result is a critical value within an order of magnitude of the Scheck et al. (2008) and Fernández et al. (2013) predictions for our model

MODIFIED CRITERION


Same model as previously describedRAMSES fluid dynamics code

Parallel (MPI) AMR

We are using a uniform-grid version to avoid overhead MHD algorithm based on the MUSCL method

No magnetic field yet; that is on the to-do list

HYDRODYNAMIC SIMULATIONS


Add a bubble to the upstream flow Low-density/high-entropy, pressure equilibrium Varied the density contrast to explore (in)stability limit

Result: Density contrast must be approximately 100 times what

was given by the bubble trajectory models

BUBBLE TEST


Why? Appears to be largely due to multidimensional effects that a

simple trajectory will not capture Upon entering the buoyant region, the bubble flattens, then

splits into two counter-rotating bubbles (would be a ring in 3D)

This splitting lowers the density contrast The rotating flows will dissipate, further lowering the

density contrast For an isolated bubble, multidimensional effects appear to

modify the situation sufficiently that a simple trajectory is not predictive

BUBBLE TEST


Critical density contrast depends on χ Lower value of χ is more stable

Resolution Dissipation is partly physical, partly numerical Some increase in the buoyancy of bubbles is seen at higher

resolution A large number of grid cells may be required to capture

small perturbations, meaning they would be artificially dissipated in many simulations

BUBBLE TEST


Are small, localized perturbations the expectation?Consider, as an example, a SASI-like oscillation in the

shock front Result would not be a single, localized bubble The rotating flows resulting from a single bubble would

likely not occur Potentially will behave more in line with the predictions

from the bubble trajectory models

OTHER PERTURBATIONS


Continue refining the study of a buoyancy criterionDetermine whether a buoyant bubble is sufficient to

initiate convection and turbulence If not: Is there a stronger criterion we can determine that

will initiate turbulence?Three dimensions

Convection is known to be difference in 2D and 3D due to the inverse cascade. 2D simulations can explore more effectively due to the lower computing cost, but 3D simulations will be necessary to confirm any conclusions

“Missing” physics Are any of the physical ingredients we removed important?

NEXT STEPS


We are exploring the nonlinear behavior of convection in CC SNe

A simple bubble trajectory seems to miss multidimensional effects that are important to the buoyancy of bubbles

Critical density contrasts as predicted by bubble trajectories tend to overestimate the capacity of bubbles to become nonlinearly unstable

Still a work in progressWe hope to tie in similar work on the SASI in order to

develop a coherent picture of the instabilities that govern dynamics in the gain region

CONCLUSIONS

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The Onset of Neutrino-Driven Convection in Core-Collapse Supernovae

Documents