A Simple Approach to the Supernova Progenitor-Explosion Connection

Bernhard Müller Queen's University Belfast Monash

Alexander Heger, David Liptai, Joshua Cameron (Monash University) Many potential/indirect observables from core-collapse supernovae, but some of the most direct ones (explosion energies, remnant masses) are heavy elements challenging for SN theory!

massive star

core-collapse supernovae

neutron stars & gravitational waves neutrinos supernova remnants

The neutrino-driven mechanism in its modern flavour shock ● Stalled accretion shock still oscillations (“SASI”) pushed outward to ~150km as matter piles up on the PNS, then recedes again convection

● Heating or gain region

g develops some tens of ms n i t g a n after bounce e li h o

o  c

● Convective overturn & shock  oscillations “SASI” enhance the efficiency of -heating, shock which finally revives the shock

● Big challenge: Show that this works! Status of 3D Neutrino Hydrodynamics Models with Multi-Group Transport First-principle 3D models:

● Mixed record, some failures

● Some explosions, delayed compared to 2D

● Models close to the threshold So what is missing? 27 M Hanke et al. (2013) 2 3/5 2 −3/5 ⊙ ● Lcrit ∝M˙ M  14 Ma /3

● → Increase neutrino heating or Reynolds stresses

● Unknown/undetermined microphysics (e.g. Melson et al. 2015)?

● 20 M Melson et al. (2015) Lower explosion threshold in ⊙ SASI-dominated regime (Fernandez 2015)? 15 M⊙ Lentz et al. (2015) ● Better 1D/multi-D progenitor Or with simpler schemes: e.g. IDSA+leakage Takiwaki et al. (2014) models? Challenge: Connecting to Observables Several 50 diagnostic 10 erg with explosion sustained energy accretion

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1 a 0 k 2 ( n Pejcha & Prieto (2015): Explosion energies a J vs. Nickel masses

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accretion n

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Hard to reach several 1050erg in many 2D simulations – considerable accretion needed Schwab & Podsiadlowski (2010): inferred neutron star birth mass distribution (beware → high neutron star masses selection effects...) A Time-Scale Problem Explosion energies

Neutron star )

5 masses (baryonic) 1 0 2 (

r e l l ü M

O'Connor & Couch (2015, submitted) shock revival: Accretion can last well bounce ~a few 0.1s 1s beyond 1s!

explosion energy/neutron star mass determined 2D Long-Time Models not Adequate

2D 3D Shock trajectories

Explosion energies Kelvin-Helmholtz instability suppressed

Neutron star Müller (2015) masses (baryonic)

Long-time simulations with multi-group feasible in 2D but post-explosion dynamics is artificial (more 3D than before explosion): accretion lasts too long, growth of explosion energy inhibited Long-time evolution in 2D: Cp. Raph Hix' question about the end of the explosion Predicting Supernova Explosion Properties First-principle simulations vs. parameterised models

20 M⊙ Melson et al. (2015) Müller (2015) Ugliano et al. (2012) First-principle simulations: ● Physics captured as accurately as Parameterised 1D hydro models:: possible (neutrino transport, 3D ● Trigger explosion artificially (e.g. effects, nuclear equation of state...) enhanced neutrino heating) ● ● Cost: up to 50M core-h for 0.5s Reasonably fast → Systematic studies of explosion ● Require calibration: prediction or properties in 3D currently unfeasible “postdiction” ● Explosions are not 1D

Recent Phenomenological Models ● Analytic + hybrid approaches (Fryer et al. 2012, Pejcha & Thompson 2015, Suwa et al. 2016)

● 1D simulations

● O'Connor & Ott (2010): leakage + heating

Regions of NS/BH formation: O'Connor ● Ugliano et al. (2012), Ertl et al. (2015), & Ott (2010) Sukhbold et al. (2015): grey transport + 1 or 2 calibration points

● Perego et al. (2015): PUSH – extra heating by /-neutrinos in 1D

● Results

● Variegated landscape of BH/NS

formation above ~18M⊙

● Empirical parameters for “explodability” (compactness, Ertl- Ugliano et al. (2012) Janka criterion) Why another parameterised model?

● How robust is the landscape of neutron star/black hole formation? (e.g. are the islands of NS/BH formation just due to stochastic variations in the progenitors)

● 1D hydro cannot capture simultaneous ejection and accretion (→ important for energetics)

● Make connection to multi-D dynamics more manifest

● Quick tool for evaluating changes in stellar evolution models desirable → Condense findings from recent multi-D models into a (largely) analytic approach?

Back from 3D to a Phenomenological Supernova Model – Pre-Explosion Phase shock Supersonic infall (~free-fall velocity) oscillations (“SASI”) Shock: jump conditions shock

Roughly hydrostatic, convection corrections from turbulent pressure

g Neutrino emission: n i t g Neutron star surface: a n L GM M˙ 2R e li acc= /  contracting “hard” inner h o

o  c boundary Lcore≈E bind / tcool 

2 4/9 16/9  L E  r NS 4 2 rsh ∝ 1 〈 Ma 〉 M˙2/3 M 1/3  3 

rsh, L, E ...→ criticality multi-D effects (see parameter for explosive Müller & Janka 2015, runaway → time of shock Summa et al. 2015) revival & “initial mass cut” Still some free parameters, but these are physically relevant efficiency factors, time-scales, etc... Explosion Phase 2D dE /dt expl 3D h M˙ out accretion

M˙ in

outflow

M˙ out Total enthalpy Total energy

Estimate end of accretion (Marek & Janka 2009):

v post=−1/vsh≈vesc

Q˙  Shock velocity from formula M˙ out≈ ;Q˙ =acc M˙ in of Matzner & McKee (1999) ∣ebind,gain∣ 1/2 3 0.19 vsh ∝E expl/ M ej M ej / r  E˙ expl≈6 Mev/mnucleon×M˙ outebind,preeburn M˙ sh Estimate from pre-explosion phase → growth of explosion energy, amount of residual accretion, neutron star mass

(another >40 equations omitted, see Müller, Heger, Liptai & Cameron 2016, arxiv:1602.05956) Results

● Islands of explodability at high explosion energy M>20 M8 (similar to previous work)

● Decent agreement with empirical explodability criteria, especially if we consider only shock revival: black hole mass ● Compactness parameter: 93% of models

● Ertl criterion: 94% of models neutron star mass ● Obtainable with parameters compatible (by and large) with multi-D simulations Iron group elements

Explosion properties for ~2000 KEPLER stellar evolution models: Islands of BH/NS formation are no statistical flukes Explosion energy vs. Nickel mass Results

● Islands of explodability at high M>20 M8 (similar to previous work)

● Decent agreement with empirical explodability criteria, especially if we consider only shock revival:

● Compactness parameter: 93% of models Explosion energy ● Ertl criterion: 94% of models vs. ejecta mass

● Observed correlation between MNi and Eexpl (Hamuy 2003) and Mej and Eexpl (Poznanski 2013, Chugai & Utrobin 2014, Pejcha & Prieto Affected by 2015) fallback? red/blue: fits to observational date from Pejcha & Prieto (2015) Work left for everyone...

Explosion energy Corridor of 0.3dex in Nickel mass: vs. Nickel mass ● Estimate from analytic model is shaky (based on ignition temperatures) ● 1D hydro needed for more reliable Ni mass & detailed nucleosynthesis

Explosion energy vs. ejecta mass

Correlation of Eexpl and Mej ● Clump of low-energy explosions at high M due to lack of fallback ej fallback? treatment? (→ 1D/multi-D hydro) ● How robust are the observed correlations?

red/blue: fits to observational date from Pejcha & Prieto (2015) Is this landscape robust?

: shock compression ratio → affects exp turb: shock expansion due to turbulent post-shock velocity and termination of stresses → affects critical luminosity for accretion explosion

Parameter variations largely tantamount to rescaling of Eexpl and Mni and/or shift of boundaries between NS/BH formation regions → underlying landscape of explodability & potentially attainable energies is robust (exception: change in neutron star cooling time) turb=1.15,expl=3 Looks not Conflicts: Upper mass too bad limit for NS formation?

Very high NS masses

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Cumulative distribution function of inferred progenitor o

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0 BH formation above ~19M can be accommodated r

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with plausible parameter choices – but conflict with a

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NS mass distribution & GCE (cp. Falk Herwig's talk)? &

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y Some of the observational constraints may be “soft” (selection effects for NS masses,...) but tensions still warrant explanation Conclusions & Outlook ● Analytic model for explosion properties directly from progenitor structure?

● strength: simple model for simultaneous accretion/ejection

● weakness: no good fallback model, etc.

● Complementary approach to previous 1D models

● Findings largely corroborate parametric 1D models – but extent of BH/NS can't be pinned down precisely

● Natural explanation for Mej-Eexpl correlation (cp. Nakamura et al. 2015 in 2D) – little change in “explodability”

● Suggests our 3D models will go in the right direction – once we can compute long enough...

● How to better capture multi-D hydro in phenomenological models (SASI, seed perturbations)?

● How to reconcile different observational constraints (from light curve/spectral modelling, progenitor observations, remnant masses, GCE) with each other?