Inferring the state of matter at neutron star interiors from

simulations of core-collapse supernovae ?

Tobias FischerUniversity of Wroclaw (Poland)

Bonn workshop on Formation and Evolution of Neutron Stars“Supernovae and Formation of Neutron stars”

Bonn (Germany), November 14th, 2016

General pictureCore-co l lapse supernova “converts” iron-core of massive star into (proto)neutron star

Binding energy gain available in form of neutrinos of all flavors

Strong gravity requires general relativity to solve:

“Supernova problem”:ejection of the stellar mantle

Formation of shock wave/shock stalling/shock revival (?)

Concept: Energy liberation from protoneutron star to standing shock

stellar core of a massive star

(weak gravity)

(proto)neutron star

�EG � 3− 6× 1053 erg −→ (νe, νe, νµ/τ , νµ/τ )

(� 9 M⊙)

(strong gravity)

Neutrino heating: (Bethe & Wilson (1985) ApJ 295, 14)

Ev = 3 – 6 x 1053 erg vs. Eexpl ~ 1050 – 1051 erg (ejecta kinetic energy)

Alternative scenarios:

Magnetic fields(Le Banc & Wilson (1970) ApJ 161, 542)

Sound waves (Burrows et al.,(2006) ApJ 640, 878)

High-density phase transition(Sagert & TF et al.,(2009) PRL 102, 081101)

Ferdman et al. (2014) MNRAS 443, 2183; (double pulsar system)

Kramer et al. (2005) 22nd Texas symposium(double pulsar system)

Low-mass progenitors and v-driven supernovaeRef. Minitial MCO MFe MNS fate

[M⊙] [M⊙] [M⊙] [M⊙][1] 8.8 1.376 – 1.3645 ± 0.0015 ECSN†,‡

[2] 8.75 1.368 – – ECSN/ONe WD-”- 8.8 1.371 – – ECSN/ONe WD[3] 7.5 1.088 – – ECSN/ONe WD-”- 8.0 1.171 – – ECSN/ONe WD-”- 8.5 1.271 – – ECSN/ONe WD-”- 8.75 1.345 – – ECSN/ONe WD[4] 2.7 1.41 – – ECSN/CCSN-”- 2.6 1.29 – – ECSN/ONe WD[5] 9.75 1.45 1.32(1.33) 1.35 ECSN/CCSN-”- 10.0 1.50 1.31(1.29) 1.36 CCSN[6] 9.6 1.377 1.297 ??? CCSN[7] 11.2 1.75 1.275 1.2906 CCSN�

[1] Nomoto (1984;1987)[2] Jones et al.(2013)[3] Woosley et al.(2015)[4] Tauris et al.(2015)[5] Suwa et al.(2015)[6] Melson et al.(2015),[7] Woosley et al.(2002)† Fischer et al.(2010)‡ Hudepohl et al.(2010),� Muller et al. (2012),Fischer et al.(2016)

baryon mass

PSR J1756–2251: 1.230± 0.007 M⊙

PSR J0737–3039B: 1.249± 0.001 M⊙

Low-mass neutron stars

Ferdman et al. (2014) MNRAS 443, 2183; (double pulsar system)

Kramer et al. (2005) 22nd Texas symposium(double pulsar system)

Low-mass progenitors and v-driven supernovaeRef. Minitial MCO MFe MNS fate

[M⊙] [M⊙] [M⊙] [M⊙][1] 8.8 1.376 – 1.3645 ± 0.0015 ECSN†,‡

[2] 8.75 1.368 – – ECSN/ONe WD-”- 8.8 1.371 – – ECSN/ONe WD[3] 7.5 1.088 – – ECSN/ONe WD-”- 8.0 1.171 – – ECSN/ONe WD-”- 8.5 1.271 – – ECSN/ONe WD-”- 8.75 1.345 – – ECSN/ONe WD[4] 2.7 1.41 – – ECSN/CCSN-”- 2.6 1.29 – – ECSN/ONe WD[5] 9.75 1.45 1.32(1.33) 1.35 ECSN/CCSN-”- 10.0 1.50 1.31(1.29) 1.36 CCSN[6] 9.6 1.377 1.297 ??? CCSN[7] 11.2 1.75 1.275 1.2906 CCSN�

[1] Nomoto (1984;1987)[2] Jones et al.(2013)[3] Woosley et al.(2015)[4] Tauris et al.(2015)[5] Suwa et al.(2015)[6] Melson et al.(2015),[7] Woosley et al.(2002)† Fischer et al.(2010)‡ Hudepohl et al.(2010),� Muller et al. (2012),Fischer et al.(2016)

PSR J1756–2251: 1.230± 0.007 M⊙

PSR J0737–3039B: 1.249± 0.001 M⊙

Podsiadlowski et al. (2005)

MG = 1.26378 M⊙

Constrains on the high-density EoS (?)

Low-mass neutron stars

Demorest et al. (2010) Nature 467, 1081Fonseca et al.(2016) arXiv:1603.00545 (nearly edge-on system with well-measured Shapiro time delay)

Antoniadis et al. (2013) Science 340(optical data and theoretical properties of companion white dwarf)

van Kerkwijk et al. (2010) ApJ 728, 8 (BWP)

Massive neutron stars

5 10 15 20 250

0.5

1

1.5

2

2.5

R [km]

M [

M ]

13 14 15 16log10( [g cm 3])

!

MMc

Mass-radius relation and central density

ρ0PSR J0348+0432: 2.01± 0.04 M⊙

PSR J1614–2230: 1.928± 0.017 M⊙

B1957–20: 2.4± 0.3 M⊙

Demorest et al. (2010) Nature 467, 1081Fonseca et al.(2016) arXiv:1603.00545 (nearly edge-on system with well-measured Shapiro time delay)

Antoniadis et al. (2013) Science 340(optical data and theoretical properties of companion white dwarf)

van Kerkwijk et al. (2010) ApJ 728, 8 (BWP)

Quark matter inside neutron stars

PSR J0348+0432: 2.01± 0.04 M⊙

PSR J1614–2230: 1.928± 0.017 M⊙

B1957–20: 2.4± 0.3 M⊙

Benic et al. (2015) A&A 577, 40A chance for high-mass twins ?

“commonly-employed” two-phase approach; sufficiently stiff quark matter EoS and strong 1st–oder phase transition

Radius difference of 1–2 km, observable? NICER...

hadronic branchquark branch

hadronic EoS

quar

k EoS

1st–orderphase transition

(Maxwell)

disconnected

large latent heat

EoS in supernova studiesSupernova relevant densities}

0

5

10

15

20

25

30

35

40

45

E/N

-mn

[MeV

]

0.0 0.05 0.1 0.15 0.2 0.25 0.3

n [fm-3]

0 1 2 3 4 5[1014 g cm-3]

DD2NL3TM1TMASFHoSFHxFSUgoldIUFSULS180LS220QB139 S0.7

Chiral EFT N3LO

ρ [1014 g cm−3]

nB [fm−3]

Neutron matter energy per nucleon

ρ [g cm−3]

T[M

eV]

T = 0.5 MeVnon-NSE

(time-dependent nuclear processes)

NSE

TF. et al.,(2011) ApJS 194, 39

“Supernova phase diagram”

L o w - d e n s i t y E o S w e l l constrained from χEFT

C a n w e u s e s u p e r n o v a simulations to constrain the supersaturation density EoS?

TF. et al.,(2014) EPJ A50, 46

EN−

mN

[MeV

]

Comparison in simulations

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.420

40

60

80

100

120

140

SFHoSFHxHS(TM1)LS(180)STOSQ155a03

Time after bounce (s)

shock radius

sphere radius

e

km

PNS collapse

Common mistake: many/all EoS parameters are different

Quantitative comparison difficult/impossible !

Suggestion: only supersaturation density EoS is affected; all other nuclear matter properties remain unchanged

Steiner et al.(2013) ApJ 774,17

Supersaturation density

1 1.5 2 2.5 3 3.50

2

4

6

8

10

12

14

[1014 g cm 3]

P [M

eV fm

3 ]

HS(DD2 EV) (v = +8.0) HS(DD2) ref. EOS (v=0) HS(DD2 EV) (v = 3.0)

0.08 0.1 0.12 0.14 0.16 0.18 0.2nB [fm 3]

0

2 3 4 5 60.60.81.01.21.4

c s [c]

T = 3 MeVYe = 0.3

stiff

soft

ref. E

oS

Geometric excluded volume approach; modifying the available volume:

Vi = V φi

φi = 1−�

j

vjnj

Excluded volume parameter:v ≡ vn = vp

φ(ρ; v) = exp�−v|v|

2(ρ− ρ0)

2�

(Gauss-functional)

DD2 – RMF parameters:K = 243 MeVS = 31.67 MeVL = 55.04 MeV

Ref. EoS in agreement with nuclear constraints (e.g. χEFT and nuc lear masses) and massive neutron stars !

TF (2016) EPJA 52, 54

TF (2016) EPJA 52, 54

0.1 0 0.1 0.2 0.3 0.4 0.50

0.5

1

1.5

2

2.5

3

3.5

4

4.5

t tbounce [s]

cent

ral [

10

g c

m14

3 ]

HS(DD2 EV) (v = +8.0) HS(DD2) ref. case (v=0) HS(DD2 EV) (v = 3.0)

0 0.1 0.2 0.3 0.4

8

10

12

14

16

18

20

T cen

tral

[MeV

]

Central density and temperature

ref. EoS

stiff

soft

Geometric excluded volume approach; modifying the available volume:

Vi = V φi

φi = 1−�

j

vjnj

Excluded volume parameter:v ≡ vn = vp

φ(ρ; v) = exp�−v|v|

2(ρ− ρ0)

2�

(Gauss-functional)

La rge va r ia t i ons i n the supernova-core properties

Supernova evolution

TF (2016) EPJA 52, 54

0.1 0.2 0.3 0.40

1

2

3

4

5

6

7

L [

1052

erg

s1 ]

!e

!e

!µ/!

0 0.1 0.2 0.3 0.4 0.56789

1011121314151617

t tbounce [s]

E

[MeV

]

!e

!e

!µ/!

!µ/!

HS(DD2 EV) (v = +8.0)HS(DD2) ref. case (v=0) HS(DD2 EV) (v = 3.0)

0.0 0.1 0.2 0.3 0.4 0.5t – tbounce [s]

TF (2016) EPJA 52, 54

Geometric excluded volume approach; modifying the available volume:

Vi = V φi

φi = 1−�

j

vjnj

Excluded volume parameter:v ≡ vn = vp

φ(ρ; v) = exp�−v|v|

2(ρ− ρ0)

2�

(Gauss-functional)

Supernova evolution

Supernova evolution, incl. neutrino signal, is insensitive to supersaturation density EoS

TF (2016) EPJA 52, 54

0.1 0.2 0.3 0.40

1

2

3

4

5

6

7

L [

1052

erg

s1 ]

!e

!e

!µ/!

121314151617

[M

eV]

!e

!µ/!

!µ/!

HS(DD2 EV) (v = +8.0)HS(DD2) ref. case (v=0) HS(DD2 EV) (v = 3.0)

0.0 0.1 0.2 0.3 0.4 0.5t – tbounce [s]

TF (2016) EPJA 52, 54

Geometric excluded volume approach; modifying the available volume:

Vi = V φi

φi = 1−�

j

vjnj

Excluded volume parameter:v ≡ vn = vp

φ(ρ; v) = exp�−v|v|

2(ρ− ρ0)

2�

(Gauss-functional)

Supernova evolution

Supernova evolution, incl. neutrino signal, is insensitive to supersaturation density EoS

Thank

s for

your a

ttenti

onIn collaboration with:W. NewtonG. RöpkeF.-K. ThielemannY. SuwaS. TypelM. R. WuD. Voskresensky

S. BenicD. BlaschkeM. HempelC. HorowitzT. KlähnM. LiebendörferK. LangankeA. LohsG. Martínez-Pinedo