Brendan Krueger CEA Saclay 2013 October 18 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
Brendan Krueger | CEA Saclay
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
Brendan Krueger | CEA Saclay
gain region
cooling region
neutrinosphere
shock
gain radius
supersonic infall
gain region
cooling region
PNS
shock
gain radius
supersonic infall
Neutrino heating mechanism Reabsorb suffi cient
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
Brendan Krueger | CEA Saclay 6
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
Brendan Krueger | CEA Saclay 7
Discovered by Blondin et al. (2003) in a simplifi ed context
Since 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
Brendan Krueger | CEA Saclay 8
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
Brendan Krueger | CEA Saclay 9
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
Brendan Krueger | CEA Saclay 10
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)
Diffi cult to distinguish SASI from convection in nonlinear regime using naïve spherical-harmonic decomposition
CONVECTION I: BACKGROUND
Brendan Krueger | CEA Saclay 11
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
Brendan Krueger | CEA Saclay 12
Diff erent 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 physics
SASI can lead to gravitational wave emission: Marek et al. (2009), Murphy et al. (2009)
Neutrino emission from CC SNe could depend on fl ow dynamics
Diff erent shock evolution (asymmetry)Dimensionality of simulations could be signifi cant for
diff erent 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
Brendan Krueger | CEA Saclay
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
14
THE BIG QUESTIONS
Brendan Krueger | CEA Saclay 15
The linear theory provides a good predictionThere is evidence that nonlinear eff ects 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
Brendan Krueger | CEA Saclay 16
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
Brendan Krueger | CEA Saclay 17
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
Brendan Krueger | CEA Saclay 18
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 fl ow
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
Brendan Krueger | CEA Saclay 19
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
Brendan Krueger | CEA Saclay 20
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
Brendan Krueger | CEA Saclay 21
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
Brendan Krueger | CEA Saclay 22
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 suffi ciently that a simple trajectory is not predictive
BUBBLE TEST
Brendan Krueger | CEA Saclay 23
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
Brendan Krueger | CEA Saclay 24
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
Brendan Krueger | CEA Saclay 25
Continue refining the study of a buoyancy criterionDetermine whether a buoyant bubble is suffi cient 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
Brendan Krueger | CEA Saclay 26
We are exploring the nonlinear behavior of convection in CC SNe
A simple bubble trajectory seems to miss multidimensional eff ects 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