Understanding the explosions of massive stars

Bernhard MüllerQueen's University Belfast

A. Betranhandy, C. Collins, D. Gay, S. Sim (QUB) C.Chan, A. Heger, J. Grimmett (Monash)

H. Andresen, R. Bollig, Th. Janka, T. Melson, E. Müller, A. Summa, M. Viallet (MPA)

core-collapsesupernovae

massive star

heavy elements

neutron stars & supernova remnants

gravitational waves neutrinos

Questions for supernova theory:● Which massive stars explode – NS vs

BH formation● Systematics of explosions (energy,

Nickel mass, etc.) & compact remnants● Impact on chemogalactic evolution● Etc.

Need to understand explosion mechanism(s) first

convection

shock oscillations

(“SASI”)

shock

he

atin

g

cool

ing

Explosion driven by neutrino heating & hydro instabilities

Magnetorotational mechanism likely needed for

small subset of CCSNe

Mechanism determines explosion

energy, kick, nucleosynthesis, etc.

on a time-scale of seconds

Progenitor develops iron core, become unstable to collapse

Rebound of core due to stiffening of EoS, shock forms & soon stalls

Neutrino-Driven Supernovae

● Stalled accretion shock still pushed outward to ~150km as matter piles up on the PNS, then recedes again

● Heating or gain region develops some tens of ms after bounce

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

● Big challenge: Show that this works!

convection

shock oscillations

(“SASI”)

shock

heat

ing

co

olin

g

Neutrino-Driven Supernovae

● Stalled accretion shock still pushed outward to ~150km as matter piles up on the PNS, then recedes again

● Heating or gain region develops ~50-100 ms after bounce

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

● Big challenge: Show that this works!

Entropy in 18 M⊙ star (no shock revival)

● Transition from accretion to explosion can be view as a critical phenomenon: no stationary accretion flow possible for sufficiently high luminosity (Burrows & Goshy 1993)

● Turbulent “pressure”, viscosity, mixing, etc. modify quasi-hydrostatic structure of gain region & enlarge shock radius (Murphy et al. 2012 & others) → J. Murphy's talk for detailed theory

● Heating in larger volume → reduction of critical luminosity by 20-30%

● Reduction depends on average “turbulent Mach number” (Müller & Janka 2015, Summa et al. 2016)

M M

L ⟨E2 ⟩

Model trajectories

More heating

Higher pre-shock ram pressure

explosion

The Role of Multi-D Effects

L ⟨E2 ⟩crit

L⟨E2 ⟩crit14 /3 ⟨Ma2⟩−3 /5

v turb~[ qrshock−r rgain]1 /3

Turbulent velocity (→ ⟨Ma⟩) regulated by avg. neutrino heating rate:

avg. heating rate per unitmass

Computational Challenges

● Multi-dimensionality of the flow

● Multi-scale problem

● Transition between the diffusion & free streaming regimes of the neutrinos → kinetic theory required → 6D problem (or more: flavour conversion)

● Nuclear & particle physics input partly undetermined

● Strong gravitational fields (GM/rc2≈0.1...0.2) & high velocities → relativistic effects important

● Need L & E to a few percent,

turbulent velocities to ~10% accuracy

● The most ambitious 3D models currently take ~50 million core hours

not to scale

several 100 km

~108km

Axisymmetric Models – Still Useful for Code Comparison

Summa et al. (2015)

O'Connor & Couch (2017)

● Huge spectrum of numerical approaches to the problem – from very simply to highly sophisticated

● Nonetheless, some 2D models with similar (not identical) input physics now appear to converge

Oakridge-B

Princeton

MPA/QUB

Burrows et al. (2016)

Oakridge-c

27 M⊙ Hanke et al. (2013)

Status in 2015:● Mixed record: failures or

delayed explosions compared to 2D

● Problem is forward turbulent cascade in 3D → (mostly) smaller turbulent Mach number

● Still no proof that mechanism is robust in 3D

20 M⊙ Melson et al. (2015)

15 M⊙ Lentz et al. (2015)

Problems: Shock revival by the -driven mechanism in 3D

Or with simpler schemes: e.g. IDSA+leakage Takiwaki et al. (2014)

Failure in 3D

2D 3D

Simplified 3D “light-bulb” model from Hanke et al. (2012):Turbulent convection in 2D and 3D

shock

shock

entropy snapshots

Possible Solutions: Neutrino Opacities

Melson et al. (2015)

2D

3Dwith strangeness

corrections

without

shock

● Uncertainties concerning in-medium effects above ~1012g/cm3 could affect L and E on

the percent level

● Testing this is difficult without better microscopic calculations of cross-sections

● Melson et al. (2015) mimicked this by increasing the strangeness contribution to neutral current scattering

● Faster neutron star contraction slightly increases L and E → shock revival in

marginal model

● New virial fit of Horowitz et al. (2017) for axial vector coupling below nuclear density:

● Small effect size, at least in 1D models (Horowitz et al. 2017; A. Betranhandy, Masters thesis)

● Cannot reprorduce large effects claimed by Burrows et al. (2017) and Radice et al. (2017)

0.0 0.1 0.2 0.3 0.4 0.5Time after bounce [s]

Horowitz et al. (2017)

Hea

ting

rate

[foe

/s]

Virial correctionsNo correlations

Axial coupling off

Time [s](A. Betranhandy, thesis)

Rapid Rotation and Neutrino-Driven Explosions● May be conducive to shock revival

in -driven explosions (even without magnetic fields)

● Key is smaller binding energy of gain region and smaller pre-shock ram pressure

→less neutrino heating required to unbind gain region, larger shock radius (Janka, Summa & Melson 2016)

● Moreover: spiral SASI mode transitions to rapidly growing low-T/W instability at extreme rotation rates (Takiwaki et al. 2016)

● But would require ~1ms NS spin period

Janka et al. (2016)

Kotake et al. (2016)shock

● Some interior shells in progenitor convective at collapse → impact on instabilities during SN (Couch&Ott 2014, Müller & Janka 2015?

● Expected effect of injection of extra turbulent kinetic energy:

● Mixing length theory and linear theory: Maconv~0.1 and ℓ~2-4 in some (not all!) progenitors

Seed Perturbations for Boosting Convection/SASI

Lcrit

Lcrit

~24×Maconv

multipole order ℓ(Müller et al. 2016, cp. also Abdikamalov et al. 2016)

O burnshere

O mass fraction

Radial velocity

log

lateral velocity

High ram pressure

Low rampressure

Müller & Janka (2015)

Pram/Pram~Maconv (cp. Lai & Goldreich 2000) → “forced shock deformation”

colla

pse

Couch et al. (2015): 15 M⊙ Si burning

in 3D octant

Müller et al. (2016): 18 M⊙, O burning

4 solid angle

Si mass fraction in O shell

● Some interior shells in progenitor convective at collapse → impact on instabilities during SN (Couch&Ott 2014, Müller & Janka 2015)?

● Expected effect of injection of extra turbulent kinetic energy:

● Mixing length theory and linear theory: Maconv~0.1 and ℓ~2-4 in some (not all!) progenitors

● 3D simulations of shell burning needed to obtain initial conditions (Couch et al. 2015, Müller et al. 2016)

Seed Perturbations for Boosting Convection/SASI

Lcrit

Lcrit

~24×Maconv

multipole order ℓ(Müller et al. 2016, cp. also Abdikamalov et al. 2016)

1D progenitor (with tiny artificial seed perturbations)

3D initial conditions

Impact of 3D Initial Conditions in Multi-Group Neutrino Hydrodynamics Simulations

Red: Si-rich ashesCyan: Outer O shell boundaryGrey: Si core

min./avg./max. shock radius

Neutrino-heated bubbles in ensuing supernova (red/yellow)

● “Perturbation-aided” neutrino-driven mechanism quite efficient in first comparisons with multi-group neutrino transport (Müller 2016, Müller et al. 2017)

● Beware selection bias!● Forced shock deformation imprints O

shell asymmetries on explosion

3D vs. 1D initial conditions for 18M⊙

progenitor

Red: Si-rich ashesCyan: Outer O shell boundaryGrey: Si core

min./avg./max. shock radius

3D vs. 1D initial conditions for 18M⊙

progenitor

● “Perturbation-aided” neutrino-driven mechanism quite efficient in first comparisons with multi-group neutrino transport (Müller 2016, Müller et al. 2017)

● Beware selection bias!● Forced shock deformation imprints O

shell asymmetries on explosion

Perturbation-Aided Mechanism not a Panacea

Credit: A. Heger (2sn.org)

Müller et al. (2016): 18 M⊙, O burning

Si mass fraction in O shell● Tremendous variations in shell configuration (more complex than “compactness”)● Exploration of parameter space & better treatment of most advanced burning

stages (Si) needed in 3D models of shell burning● Effect size ranges from huge (Müller et al. 2017, 18M⊙) to small (Couch et al.

2015), maybe nil in some stars● Especially Si shell often inactive at collapse (Collins, Müller & Heger in prep.) ● Need to consider long-term effect of convective boundary mixing on SN

progenitors

Growth of O shell by turbulent entrainment

(fed by ~10% of convective luminosity)

Exploring Variations in Shell DynamicsQuiescent shell,O almost delpeted

reignites

Encroachment intoO/Ne shell

O mass fraction

velocity

Ignition of unburned shell & convective encroachment in 12.5M8 progenitor (Mueller 2016)

Also observed in 1D model, but could such events sometimes give rise to surface phenomena (pre-SN outbursts?)

Pejcha & Prieto (2015): Explosion energies vs. Nickel massesaccretion

outflow

Schwab & Podsiadlowski (2010): inferred neutron star birth mass distribution (beware selection effects...)

Bridging the Gap to Observations

Ongoing accretion onto proto-neutron star → energetics only determined

after several seconds

observa tions

simulati ons

Janka et al. (2012)

diagnostic explosion

energy

only ~3×1049erg

The “Energy Problem” of Successful 2D Models

O'Connor & Couch (2015, arXiv:1511.07443)

Bruenn et al. (2016): Only 2D models with “acceptable”

explosion energies

3D Effects Helpful After Shock Revival!

spin period of ~20msSimulations no longer off in explosion energy

by factor of ~10 (cp. also 2D models of Bruenn et al. 2016, Burrows et al. 2016)

Müller, Melson, Heger & Janka (2017)

Mgrav=1.67M⊙

Robust Growth of Explosion Energy in 3D

dEexpl/dt ~ outflow rate× nuclear recombination energy

Outflow rate vs. neutrino heating/binding energy at gain radius

Efficient turbulent mixing between downflows & outflows in 3D

→ heating need not lift ejecta out from deep in the potential of the neutron star→ limits growth of neutron star mass

Distribution of turnaround radii of neutrino-driven ejecta

● Extant simulations are on the margin between explosion and failure in 3D (which is OK)... and show “qualitative convergence” in 2D

● Several promising ideas for robust neutrino-driven explosion models:

● Unknown/undetermined microphysics (e.g. Melson et al. 2015, Burrows et al. 2016)

● Convective seed perturbations for “perturbation-aided” mechanism (Couch et al. 2015, Mueller 2016)

● Rotation (Janka et al. 2016, Takiwaki et al. 2016)

● Lower explosion threshold in SASI-dominated regime (Fernandez 2015)?

● Solution is likely a combination of several effects & better modelling (neutrino transport, resolution...)

● First long-term 3D runs start to give plausible explosion properties – need more & better models to see whether we get “typical” explosions

● We still need phenomenological approaches to understand the whole population of CCSNe (see T. Ertl's talk), but can now use long-time 3D models to improve these

Modelling Neutrino-Driven Explosions: Summary

core-collapsesupernovae

massive starneutron stars &

supernova remnants

gravitational waves neutrinos

Gravitational Waves from Supernovae(replacement for S. Gossan)

h~2G

c4 r

d 2 I

dt 2~ 2G

c4 rM R2 f 2

dimensionless strain distance

mass quadrupole moment (transverse-

trace free component)

mass involved

radius typical frequency

Gravitational Waves from Core-Collapse Supernovae

Rotational collapse Convection & SASI

Other triaxial instabilities (low T/W, r-mode)

Asymmetry parameter

Scheidegger et al. (2010)

Rotational Collapse

Bounce signal (Dimmelmeier et al. 2008): very regular shape, amenable to template-based searches, frequency of ~750 Hz determined fundamental quadrupole mode of proto-neutron star (Fuller et al. 2015)

rotating 15M8 model of Heger, Woosley & Spruit (2005)(2D simulation)

peak from rotational collapse

Most cores of massive stars expected to rotate slowly!

Bounce signal subdominant for the “typical” slowly rotating SN progenitor

8.1 M8, Z=10-

4Z8

9.6 M8, Z=0 11.2 M8

15 M8 27 M825 M8

(no explosion!)

“onset” of explosion

The Post-Bounce & Explosion Phase

Müller, Janka & Marek (2013)General trends from 2D models:

● Emission stronger for more massive progenitors (massive Si and O shells)● Peak activity around onset of explosion (weaker emission w/o explosion)

29

Structure of the GW Spectrum

time-integrated spectrum, 15M8

Signal seems to contain a lot of broad-band noise, but there is a well-defined and sharp frequency structure underneath:

● Better time-frequency analysis helps!

● Normalized wavelet spectrogram clearly shows evolution of typical frequency

zooming in on an exemplary time interval...

30

Structure of the GW Spectrum

“prompt convection”

Increasing PNS surface g-mode

frequency

time-integrated spectrum, 15M8

normalized wavelet spectrogram, 15M8

23zooming in on an exemplary

time interval...

Signal seems to contain a lot of broad-band noise, but there is a well-defined and sharp frequency structure underneath:

● Better time-frequency analysis helps!

● Normalized wavelet spectrogram clearly shows evolution of typical frequency

GR : f B2=d c2

dr

h4c s2

dS r dr

Newtonian : f B2=d dr

1

cs2

dS r dr

downflow

● Gravitational wave emission due to “ringing” in the neutron star surface region (Murphy et al. 2009, Müller et 2013)

● Typical frequency ~ buoyancy-frequency fb (l=2 g-mode) in convectively stable layer below the gain region

● GR correction factors matter!

● Relation to neutron star properties:

Gradient of potential

density

Schwarzschild discriminant

sound speed

f peak≈1

2GM

R2 1.1mn⟨E⟩ 1−GMRc2

2

The GW Spectrum

neutron mass

electron antineutrino mean energy ~ neutron

star surface temperature

neutron star mass

neutron star radius

GW Spectrograms from 3D Models

SASI episodes

Still see g-mode, but weaker & predominantly excited by PNS convection

non-

expl

odi

ngex

plod

ing

Enhanced emission after explosion

Andresen et al. (2017)New low-frequency features during SASI phases

33

New Low-Frequency Component in 3D

Kuroda, Kotake & Takiwaki (2016)

● Low-frequency emission at 100-200 Hz correlated with SASI activity● Even more impressive in Kuroda, Kotakte & Takiwaki (2016) for model

with SFHx equation of state (very compact neutron star)● Frequency also similar to SASI frequency, but what is the precise

relationship● Could this feature allow a direct detection of SASI & measurement of its

frequency?

Frequency of surface g-mode

Detectability & Signal Inversion

Core-collapse supernovae in

this region

Signal from convection: √S/N in wavelet spectrogram, distance of Crab supernova (Einstein

Telescope)

=70°, =210°

Hayama et al. (2015): theoretical & noisy spectrograms at 10kpc for triaxial instability

PCA

Bayesian model selection

● Obvious structures in detected signal only for strong sources or nearby events ● Statistical analysis methods can distinguish signal type with Galaxy (Powell et al. 2017, Gossan et al. 2016), Logue et al. 2012)

Rotational Collapse: Parameter Estimation

Abdikamlov et al. (2014): Inferred=T/W in progenitor coe from prospective signal

Regular character helps detection (matched filtering...)

Detectability limit: of order ~40kpc for Advanced LIGO for initial core rotation periods of ~seconds (see, e.g., Logue et al. 2012, Hayama et al. 2015, Gossan et

al. 2016)

At ~10kpc, the initial period can be constrained to within ~20% (Abdikamalov

et al. 2014)

Conclusions● Bounce signal: promising quantitative diagnostic for

rapid rotation in nearby supernovae

→ will constrain core rotation for Galactic SN● GW signal from convection & SASI:

● Information content is considerable (especially if combined with neutrino detection)→ PNS mass, radius

● But weakness of signal is challenging● Can distinguish emission scenarios (convection vs. rotational

bounce) but need to update Bayesian model selection to include recent 3D models

● Can we better characterise the features of the predicted GW signals to aid detection?

● Need to deepen links between SN modelling & GW community (Advisory Board “OneVoice” established)

Thank you!

Predicting Supernova Explosion Properties

20 M⊙ Melson et al. (2015)

First-principle simulations:● Physics captured as accurately

as possible (neutrino transport, 3D effects, nuclear equation of state...)

● Cost: up to 50M core-h for 0.5s→ Systematic studies of explosion properties in 3D currently unfeasible

Ugliano et al. (2012)

Parameterised 1D hydro models (Ugliano et al. 2012, Sukhbold et al. 2016, Perego et al. 2016)

● Trigger explosion artificially (e.g. enhanced neutrino heating)

● Reasonably fast● Require calibration: prediction or

“postdiction”● Explosions are not 1D

Can we do without simulations altogether?

First-principle simulations parameterisedmodels

vs.

Back from 3D to a Phenomenological Supernova Model – Pre-Explosion Phase

convection

shock oscillations

(“SASI”)

shock

he

atin

g

cool

ing

Roughly hydrostatic, corrections from turbulent pressure

Shock: jump conditions

Supersonic infall (~free-fall velocity)

Neutron star surface:contracting “hard” inner boundary

rsh∝L E

2 4/9 rNS16 /9

˙M 2/3M 1/3 143⟨Ma2⟩

Still some free parameters, but these are physically relevant efficiency factors, time-scales, etc...

multi-D effects (see Müller & Janka 2015, Summa et al. 2015)

Neutrino emission:

Lacc=GM M /2R

Lcore≈Ebind / tcool

rsh, L, E ...→ criticality

parameter for explosive runaway → time of shock revival & “initial mass cut”

accretion

outflow M out

M in

M out≈Q

∣ebind,gain∣; Q=acc M in

E expl≈6 Mev /mnucleon×M outebind,preeburnM sh

2D3D

dEexpl /dth M out

Total enthalpy

Total energy

Estimate from pre-explosion phase

vsh∝E expl/M ej1 /2M ej / r

30.19

v post=−1/v sh≈vesc

Estimate end of accretion (Marek & Janka 2009):

Shock velocity from formula of Matzner & McKee (1999)

→ growth of explosion energy, amount of residual accretion, neutron star mass

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

Explosion Phase

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

● Ertl criterion: 94% of models

● Obtainable with parameters compatible (by and large) with multi-D simulations

● General pattern robust against parameter variations – not the precise values!

explosion energy

black hole mass

neutron star mass

Iron group elements

Explosion properties for ~2000 KEPLER stellar evolution models:

Islands of BH/NS formation are no statistical flukes

ResultsExplosion energy vs. Nickel mass

Explosion energy vs. ejecta mass

Clump from MZAMS~17M⊙ –

maybe affected by fallback

red/blue: fits to observational date from Pejcha & Prieto (2015)

● 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

● Ertl criterion: 94% of models

● Observed correlation between MNi and Eexpl (Hamuy 2003) and Mej and Eexpl (Poznanski 2013, Chugai & Utrobin 2014, Pejcha & Prieto 2015)

Potential Conflicts?

Observa

t ions (Sc hw

ab &

P

odsia

dl ow

ski 20 10

) – ma

inly N

S/N

S b inaries

Distribution of NS birth masses

Standard scenario(s) (as Sukhbold et al. 2015, etc.) fits more or less for● Explosion energetics (except

hypernovae)

● Nickel mass

● NS masses (though peaks may not exactly agree)

● Sukhbold et al. (2015) also get decent population-integrated nucleosynthesis

But...

Potential Conflicts?

Cumulative distribution function of inferred progenitor masses from Smartt (2015)

turb=1.15,expl=3

Observa

t ions (Sc hw

ab &

P

odsia

dl ow

ski 20 10

) – ma

inly N

S/N

S b inaries

BH formation above ~19M8 can be accommodated with plausible parameter choices – but conflict with NS mass distribution & GCE?

Some of the observational constraints may be “soft” (selection effects for NS masses,...) but tensions still warrant explanation

Very high NS masses

Looks not too bad

explosion energy

black hole mass

neutron star mass

Iron group elements

Estimated explosion properties for ~2000 KEPLER stellar evolution models:

Variegated landscape of NS and BH formation (similar to Ugliano et al. 2012,

Sukhbold et al. 2016)

Explosion energy vs. ejecta mass

Weak explosions affected by fallback?

(PhD thesis of C. Chan)

Comparison to observed correlations (red, blue) as reconstructed by Pejcha & Prieto

(2015)

First step to explain neutron star mass distribution, mass limits for

SN explosions, correlations of explosion properties...

(caveats as for all phenomenological approaches)