GENERALIZED DENSITY FUNCTIONAL EQUATION OF STATE FOR SUPERNOVA & - - PowerPoint PPT Presentation
GENERALIZED DENSITY FUNCTIONAL EQUATION OF STATE FOR SUPERNOVA & NEUTRON STAR SIMULATIONS MacKenzie Warren J.P . Olson, M. Meixner, & G. Mathews Symposium on Neutron Stars in the Multimessenger Era Ohio University May 24th, 2016
MacKenzie Warren
J.P . Olson, M. Meixner, & G. Mathews Symposium on Neutron Stars in the Multimessenger Era Ohio University May 24th, 2016
MacKenzie Warren
J.P . Olson, M. Meixner, & G. Mathews Symposium on Neutron Stars in the Multimessenger Era Ohio University May 24th, 2016
EQUATION OF STATE IN CCSNE
➤ Multi-component system: electrons, photons, nuclei, free
nucleons, pions, etc
➤ Large range of thermodynamic conditions: ➤ Electron fraction Ye = 0 →1 ➤ Density n = 0 → 1015 g/cm3 ➤ Temperature T = 0 → 150 MeV ➤ Problems persist… ➤ Phenomenological approaches necessary ➤ Uncertainties in nuclear data ➤ Neutron stars want stiff EoS, supernovae want soft EoS
NUCLEAR EQUATIONS OF STATE FOR ASTROPHYSICAL SIMULATIONS
Lattimer & Swesty
Shen et al, Hempel et al, etc
????
NUCLEAR EQUATIONS OF STATE FOR ASTROPHYSICAL SIMULATIONS
Lattimer & Swesty
Shen et al, Hempel et al, etc
Notre Dame- Livermore
➤ Harness existing
DFT models for astrophysical simulations
WHAT WE DID
➤ Developed Notre Dame-
Livermore Equation of State
➤ DFT approach with three-
body forces
➤ Transition 0.1 n0 → n0 ➤ Includes pions ➤ First order or crossover
transition to QGP
➤ Explored EoS dependence of
CCSNe
0.1 0.2 0.3
Denisty (fm )
20 40 60 80 100
Pressure (MeV/fm )
LS220 Shen NDL - GsKI NDL - KDE0v1 NDL - LNS
T = 10 MeV Ye = 0.3
Olson et al (in prep)
REGIONS OF HADRONIC EOS
➤ NSE ➤ 9 element
nuclear network
➤ “Pasta”
➤ Skyrme force ➤ Pions
Soft Repulsive 3-body force Stiff Soft again?
Ravenhall, Pethick, & Wilson Lattimer & Swesty
ABOVE n0
QGP modeled using MIT Bag model:
Ω = X
i
(Ωi
q0 + Ωi q2) + Ωg0 + Ωg2 + BV
McLerran (1986)
QGP Phase transition?
u,d (massless) s (massive)
165 ≤ B1/4 ≤ 240 MeV Ftherm → Ω(n, T) − Ω(n, T = 0) Ftot = FSkyrme + Ftherm + Fπ +Fel+rad + 8.79 MeV
PIONS
0.2 0.3 0.4 0.5 0.6 0.7 0.8
Density (fm )
0.05 0.1 0.15 0.2 0.25
Pions (and other resonances) soften EoS at high T
Charge fraction Yp Yπ Ye
Olson et al (in prep)
Olson et al (2016)
8 9 10 11 12 13 14 15
Radius (km)
0.5 1 1.5 2 2.5
Mass (M )
GsKI GsKII KDE0 LNS MSL0 NRAPR Ska25s20 Ska35s20 SKRA SkT1 SkT2 SkT3 Skxs20 SQMC650 SQMC700 SV-sym32
⦿
J0348+0432
Olson et al (in prep)
LIVERMORE SUPERNOVA MODEL
2 4 6 8 Time post-bounce (s) 10
5
10
6
10
7
10
8
10
9
10
10
Radius (cm)
General relativistic spherically symmetric supernova model
➤ Flux limited diffusion
scheme
➤ Explodes via enhanced
convection below neutrinosphere
νe, ¯ νe, νx
EOS DEPENDENCE OF CCSNE
0.05 0.1 0.15 0.2 0.25
Time post-bounce (s)
10
50
10
51
10
52
Kinetic energy (ergs)
Bowers & Wilson GSkI GSkII KDE0v1 LNS MSL0 NRAPR Ska25s20 Ska35s20 SKRA SkT1 SkT2 SkT3 Skxs20 SQMC650 SQMC700 SV-sym32
Olson et al (in prep)
EOS DEPENDENCE OF CCSNE
0.05 0.1 0.15 0.2 0.25
Time post-bounce (s)
10
51
10
52
10
53
Luminosity (ergs/s)
Bowers & Wilson GSkI GSkII KDE0v1 LNS MSL0 NRAPR Ska25s20 Ska35s20 SKRA SkT1 SkT2 SkT3 Skxs20 SQMC650 SQMC700 SV-sym32
Olson et al (in prep)
MIXED PHASE
GSI
MIXED PHASE
GSI
QGP MIXED PHASE
1 χ
Quark-Gluon Plasma Hadronic
Figure from J.P . Olson
χ = VQ/(VQ + VH)
Assume: Pressure equilibrium Global charge & baryon number conservation QGP modeled using MIT Bag model: Ω = X
i
(Ωi
q0 + Ωi q2) + Ωg0 + Ωg2 + BV
MIXED PHASE: SAGERT RESULTS
Sagert et al (2009)
➤ Secondary collapse to QGP
results in second shock
➤ Successful explosion in 1D ➤ Distinct neutrino emission
MAXIMUM MASS DEPENDS ON BAG CONSTANT
8 9 10 11 12 13 14 15
Radius (km)
0.5 1 1.5 2 2.5
Mass (M )
None B = 180 MeV B = 190 MeV B = 200 MeV B = 210 MeV No 2-loop
⦿
1/4 1/4 1/4 1/4Need B1/4 ≥190
Olson et al (in prep)
0.5 1 1.5 2 2.5 3
Density (fm )
0.2 0.4 0.6 Y Y
p q
χ = 0.1 χ = 0.3 χ = 0.5 χ = 0.7 χ = 0.9
Pure hadronic Mixed phase Pure QGP
T = 10 MeV Ye = 0.3
QGP MIXED PHASE
QGP MIXED PHASE
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Density (fm )
20 40 60 80 100 120
Temperature (MeV)
Hadronic phase Mixed phase Quark phase
Olson et al (in prep)
MIXED PHASE: PRESSURE
0.5 1 1.5 2 2.5 3
Density (fm )
200 400 600 800 1000 1200 1400
Pressure (MeV/fm )
Y = 0.1 Y = 0.25 Y = 0.4
Olson et al (in prep)
QGP MIXED PHASE
0.5 1 1.5 2 2.5 3
Density (fm )
1 1.2 1.4 1.6 1.8 2 2.2 2.4
Adiabatic index
T = 10 MeV T = 25 MeV T = 50 MeV
Secondary collapse? (Effective)
Olson et al (in prep)
QGP MIXED PHASE
0.5 1 1.5 2 2.5 3
Density (fm )
1 1.2 1.4 1.6 1.8 2 2.2 2.4
Adiabatic index
T = 10 MeV T = 25 MeV T = 50 MeV
Secondary collapse! (Effective)
Olson et al (in prep)
IN CONCLUSION…
➤ New nuclear EoS for use in CCSNe
simulations
➤ EoS will be publicly available ➤ Updates: ➤ Add kaons, hyperons, etc… ➤ Improve pasta phases ➤ Continued study of EoS dependence of
CCSNe
➤ Convection ➤ QGP phase transition possible with new
NDL EoS
➤ Secondary collapse may lead to
successful explosion (Sagert et al 2009)
➤ Observables?