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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)
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)
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