Simulations of stellar collapses toblack holes: influence of hyperonsJérôme Novak (Jerome.Novak@obspm.fr)
Laboratoire Univers et Théories (LUTH)
CNRS / Observatoire de Paris / Université Paris-Diderot
Peres, Oertel & Novak,
Phys. Rev. D 87, 043006 (2013)

Supernovae & Gamma-Ray Bursts 2013, YITP Kyoto
University, October, 15th 2013

Plan

1

Numerical model

2

Equation of state

3

Parameters

4

ResultsPlan

1

Numerical model

2

Equation of state

3

Parameters

4

ResultsPlan

1

Numerical model

2

Equation of state

3

Parameters

4

ResultsPlan

1

Numerical model2Equation of state

3Parameters

4Results

Context
How do stellar black holes form?

Stellar-mass black holes form in the collapse of massivestars
Beginning of collapse triggered by mass-limit of iron core
Collapse & bounce, then collapse of the proto-neutron star
triggered by accretion⇒very similar scenario to core-collapse supernova⇒central engine for gamma-ray bursts (collapsar model)
0.02

bolometricluminosity0

Vincent et al. (2012)

Context
Collapse to black hole from stellar progenitor has already beenstudied (e.g. Sumiyoshi et al. (2007), Fischer et al. (2009),
O’Connor & Ott (2011), Ugliano et al. (2012). . . ).
17250

10162001015

temperature [MeV]

central density [g/cm3]

10141010131012
1011

150

100

50

1010109

0.0

0.5

1.00

1.5

time after bounce [sec]0.00.51.0

1.5

time after bounce [sec]40Mprogenitor, from Sumiyoshi et al. (2007)⇒much higher densities (above nuclear saturation density) andtemperatures (tens of MeV) than in supernova simulations.

Aims. . .
High density & temperature conditions ⇒additional particlesshould appear (observed on Earth).
How many “exotic” particles could appear on the way tothe black hole?
What is their influence on the collapse?
What is their observational signature? (neutrinos,gravitational waves)
Reverse question:
Can we infer nuclear matter composition from observationsof black hole formation?

LIGO

Virgo

KAGRA

Numerical modelPhysical framework
Spherical or axial symmetry (1D/2D runs).
Relativistic hydrodynamics, with perfect-fluid stress-energy
tensor.
General relativity in 3+1 formulation. Isotropic gauge for
1D, conformally-flat condition (CFC) in 2D.
Apparent horizon finder (Lin & Novak 2007).
Microphysical equation of state from Oertel et al. (2012).
Deleptonization and neutrino leakage.
Gravitational waves extracted with the modified
quadrupole formula (2D).

Numerical tools

CoCoNuT code (Dimmelmeier et al. 2005):

Potentially 3D code, but used only in 1D or 2D (not fullyparallel, yet);high resolution-shock capturing schemes for the relativistichydrodynamics (e.g. Font 2008)⇒conservative-formhydrodynamic equations;multi-domain pseudo-spectral methods for the solution ofEinstein equations (e.g. Grandclément & Novak 2009)⇒non-linear coupled elliptic system;
interpolation and filtering to avoid Gibbs phenomenon.

Neutrino leakage
Only one opaque (⇒fluid) zone and one transparent(⇒free-streaming) zone (e.g. van Riper et al. 1981)
No transport, cheap in CPU time, but number ofapproximations and drawbacks
No semi-transparent regime, no self-consistent heating⇒not good to revive the shock.
⇒computation of “optical” depth for three species of neutrinos:
νe , ν̄e , νx . Loss of energy & momentum taken into account.

Creation processes

Opacity processes

p + e− → νe + n(A, Z)+e− → (A, Z −1)+νee− + e+ → νi + ν̄i

νi + N → νi + Nγ̃ → νi + ν̄iν̄e + p → n + e+

νi + (A, Z) → νi + (A, Z)
νe + n → p + e−

Equation of stateNuclear model
Nucleon - nucleon interaction uncertain and difficult to model:
use different interactions.

Model by Lattimer & Swesty (1991)
Effective (Skyrme-type) model for the nucleon-nucleon
interaction
Constituents: n, p, e− , e+ , γ, α, AIncompressibility K = 220 MeV.
⇒ other parameters involved: B, J, K 0 , L, constrained by
nuclear experiments, but defined at saturation density n0 andfor symmetric matter.
⇒ one of the two mainly used EoSs, other: Shen et al. (1998),
based on a relativistic mean field model.

Additional particles
Oertel et al. (2012), Gulminelli et al. (2012)

Particle accelerators and heavy-ion colliders show the presenceof pions and hyperons at high densities and temperatures.
⇒ these “additional” particles should appear in core-collapse
phenomena

EoS LS220+hyperons
EoS LS220+pions
Pions π − , π 0 , π +free gasΛ hyperons
interactions adapted fromBalberg & Gal (1997)
contains a first order phasetransition to hyperonic matter

Hadronic interaction different from previous studies withadditional particles (Sumiyoshi et al. 2009, Shen et al. 2011),
where a relativistic mean field model was used.

Neutron star mass constraints
Classical result: with hyperons, maximum neutron starmass ∼ 1.4M .
⇒Absolutely incompatible with observations :Mass constraint
M = 2.01 ± 0.04 M Antoniadis et al. (2013)
M = 1.97 ± 0.04 M Demorest et al. (2010)
Solutions:
Stiffen (modify) the EOS, with short-range repulsion via
Y Y interaction
Let quarks appear early enough. . .
In our cases, static neutron stars computed with T = 0 and
β-equilibrium:
EoS LS220+pions maximal mass: M = 1.95 M
EoS LS220+hyperons maximal mass: M = 1.91 M

Parameters & Initial models

Initial setup
Progenitor
From Woosley et al. (2002), 40M
ZAMS and 10−4 × solar metallicity

Leakageβ-equilibrium density 1.2 × 1012 g.cm−2
ν escape time tesc = 3(Rν−sphere − r)τ
power lost by the fluid in the trappedYν
regime QE = −1.1 hν itescEoS
Values of the parameters for Y − N andY − Y interactions compatible withhyperonic data and PSR J 1614-2230(marginally).

Black hole formation

Spherical symmetry
with pions
8LS220+π EoS
LS220 EoS
AH time7
ρc [1014 g.cm-3]

6Maximum pion
fraction Yπ− = 0.13
at the onset of BH
collapse

5432Yπ− > Yπ0 > Yπ+ at
all times

10-1000100200t [ms]300400500

The PNS with LS220+π EoS is slightly more compressible
More compressible means less pressure → cannot hold asmuch mass as LS220 → less time post bounce accreting
mass and maximum mass smaller
PNS baryonic masses at BH collapse : 2.55 M withLS220, 2.49 M with LS220+πSpherical symmetry
Λ EoS
AH timewith hyperons

ρc [1014 g.cm-3]

20

PNS baryonic massat BH collapse :2.00 M

151050-20020

406080t [ms]

100120140

Maximum of Λ
hyperon fraction
YΛ = 0.41 at theonset of BH collapse

Presence of a phase transition to hyperonic matter (relatedto the high accretion rate)
The PNS oscillates after the phase transition (PNSfundamental modes)
Oscillations are resolved in time and stay when increasing
the resolution

Phase transition
0.25

120.2

110.15onset
half-wayendYΛρc [1014 g.cm-3]

Spherical symmetry
13100.1

90.05
0860

65

70
t [ms]

75

80

02

468r [km]Phase transition only reached for progenitors with highmass accretion rate (low metallicity),
Induces a “mini-collapse” followed by oscillations of thePNS,
No second shock wave as in simulations with phasetransition to quark matter (Sagert et al. 2009).

10Phase transition
Rotational symmetry

2D in axisymmetry
Progenitor rotation profile : slow and differential
All other settings similar to 1D settings

LS220+Λ EoS, 1D
LS220+Λ EoS, 2D

ρc [1014 g.cm-3]

20

15

105

0-100

-50

050
100
t [ms]

150

200

Gravitational waves
With the modified quadrupole formuladE/df [10−7 M c2 .Hz−1 ]

4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
100

1000
Frequency [Hz]

Blank
Blank

10000

Gravitational waves
With the modified quadrupole formula

1.6

LS220 EoSLS220+Λ EoS

4LS220 ×5
LS220+Λ
AH time

1.4

3.5

1.2

EGW [10−3 M c2 ]dE/df [10−7 M c2 .Hz−1 ]

4.5

32.5
2
1.5

10.8
0.6
0.4

10.2

0.5

000
100

1000

10000

100

200

300

400

500

time [ms]Frequency [Hz]Phase transition induces higher frequency and higher amplitude
waves

600

Summary / Outlook
EoS for core-collapse based on Lattimer & Swesty (1991),
with additional particles (π, Λ), compatible with recent
observations of 2M neutron stars.
Softens the PNS, which collapses more rapidly andeventually undergoes a phase transition to hyperonicmatter.
Phase transition “softened” in 2D simulations⇒implications for QGP phase transition?
Possibly observable with gravitational waves.
Improvement of resolution in 2D
Better (full?) neutrino transport (Peres et al.
arXiv:1307.1666)

Summary / Outlook
EoS for core-collapse based on Lattimer & Swesty (1991),
with additional particles (π, Λ), compatible with recent
observations of 2M neutron stars.
Softens the PNS, which collapses more rapidly andeventually undergoes a phase transition to hyperonicmatter.
Phase transition “softened” in 2D simulations⇒implications for QGP phase transition?
Possibly observable with gravitational waves.
Improvement of resolution in 2D
Better (full?) neutrino transport (Peres et al.
arXiv:1307.1666)

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