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
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
EQUATION OF STATE IN CCSNE ➤ Multi-component system: electrons, photons, nuclei, free nucleons, pions, etc ➤ Large range of thermodynamic conditions: ➤ Electron fraction Y e = 0 → 1 ➤ Density n = 0 → 10 15 g/cm 3 ➤ Temperature T = 0 → 150 MeV ➤ Problems persist… ➤ Phenomenological approaches necessary ➤ Uncertainties in nuclear data ➤ Neutron stars want sti ff EoS, supernovae want soft EoS
NUCLEAR EQUATIONS OF STATE FOR ASTROPHYSICAL SIMULATIONS Relativistic Density Mean Field: Liquid Drop Functional G. Shen et al, H. Model: Theory: Shen et al, Lattimer & Swesty Hempel et al, etc ????
NUCLEAR EQUATIONS OF STATE FOR ASTROPHYSICAL SIMULATIONS Density Functional Relativistic Theory: Mean Field: Liquid Drop Notre Dame- G. Shen et al, H. Model: Livermore Shen et al, Lattimer & Swesty Hempel et al, etc ➤ Harness existing DFT models for astrophysical simulations
WHAT WE DID ➤ Developed Notre Dame- Livermore Equation of State 100 LS220 ➤ DFT approach with three- Shen NDL - GsKI Pressure (MeV/fm ) T = 10 MeV 80 -3 NDL - KDE0v1 body forces NDL - LNS Y e = 0.3 60 ➤ Transition 0.1 n 0 → n 0 40 ➤ Includes pions ➤ First order or crossover 20 transition to QGP 0 0 0.1 0.2 0.3 -3 Denisty (fm ) ➤ Explored EoS dependence of CCSNe Olson et al (in prep)
REGIONS OF HADRONIC EOS Below n 0 : Above n 0 : ➤ NSE Transition to ➤ 9 element ➤ Skyrme force QGP? nuclear ➤ Pions network ➤ “Pasta” Repulsive Ravenhall, Pethick, & Wilson 3-body force Soft again? Lattimer & Swesty Soft Stiff
ABOVE n 0 QGP Phase transition? F tot = F Skyrme + F therm + F π + F el+rad + 8 . 79 MeV u,d (massless) s (massive) QGP modeled using MIT Bag model: X ( Ω i q 0 + Ω i Ω = q 2 ) + Ω g 0 + Ω g 2 + BV i 165 ≤ B 1 / 4 ≤ 240 MeV F therm → Ω ( n, T ) − Ω ( n, T = 0) McLerran (1986)
PIONS Pions (and other resonances) soften EoS 0.25 Charge fraction Y p at high T 0.2 Y π 0.15 0.1 Y e 0.05 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -3 Density (fm ) Olson et al (in prep)
2.5 GsKI J0348+0432 GsKII KDE0 2 LNS MSL0 NRAPR Mass (M ) Ska25s20 ⦿ 1.5 Ska35s20 SKRA SkT1 SkT2 SkT3 1 Skxs20 SQMC650 SQMC700 SV-sym32 0.5 Olson et al (2016) 0 8 9 10 11 12 13 14 15 Radius (km) Olson et al (in prep)
LIVERMORE SUPERNOVA MODEL General relativistic spherically symmetric supernova model 10 10 ➤ Flux limited diffusion 9 10 scheme Radius (cm) 8 10 ν e , ¯ ν e , ν x 7 ➤ Explodes via enhanced 10 convection below 6 10 neutrinosphere 5 10 0 2 4 6 8 Time post-bounce (s)
EOS DEPENDENCE OF CCSNE 52 10 Bowers & Wilson GSkI Kinetic energy (ergs) GSkII KDE0v1 LNS MSL0 NRAPR Ska25s20 51 Ska35s20 10 SKRA SkT1 SkT2 SkT3 Skxs20 SQMC650 SQMC700 SV-sym32 50 10 0 0.1 0.2 -0.05 0.05 0.15 0.25 Time post-bounce (s) Olson et al (in prep)
EOS DEPENDENCE OF CCSNE Bowers & Wilson GSkI GSkII Luminosity (ergs/s) 53 KDE0v1 10 LNS MSL0 NRAPR Ska25s20 Ska35s20 SKRA SkT1 SkT2 52 SkT3 10 Skxs20 SQMC650 SQMC700 SV-sym32 51 10 -0.05 0 0.05 0.1 0.15 0.2 0.25 Time post-bounce (s) Olson et al (in prep)
MIXED PHASE GSI
MIXED PHASE ? GSI
QGP MIXED PHASE 0 1 χ Hadronic Quark-Gluon Plasma χ = V Q / ( V Q + V H ) Assume: QGP modeled using MIT Bag model: Pressure equilibrium Global charge & baryon number X ( Ω i q 0 + Ω i Ω = q 2 ) + Ω g 0 + Ω g 2 + BV conservation i Figure from J.P . Olson
MIXED PHASE: SAGERT RESULTS ➤ Secondary collapse to QGP results in second shock ➤ Successful explosion in 1D ➤ Distinct neutrino emission Sagert et al (2009)
MAXIMUM MASS DEPENDS ON BAG CONSTANT 2.5 None 1/4 B = 180 MeV 1/4 B = 190 MeV 2 1/4 B = 200 MeV 1/4 B = 210 MeV No 2-loop Mass (M ) ⦿ 1.5 Need B 1/4 ≥ 190 1 0.5 0 8 9 10 11 12 13 14 15 Radius (km) Olson et al (in prep)
QGP MIXED PHASE 0.6 Y p Y q 0.4 χ = 0 . 9 χ = 0 . 7 0.2 χ = 0 . 5 T = 10 MeV 0 χ = 0 . 3 Y e = 0.3 -0.2 χ = 0 . 1 -0.4 0 0.5 1 1.5 2 2.5 3 Density (fm ) -3 Pure Pure Mixed QGP hadronic phase
QGP MIXED PHASE 120 Quark 100 phase Temperature (MeV) 80 Mixed 60 phase Hadronic phase 40 20 -3 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Density (fm ) -3 Olson et al (in prep)
MIXED PHASE: PRESSURE 1400 Y = 0.1 Y = 0.25 Pressure (MeV/fm ) Y = 0.4 1200 1000 800 600 400 200 0 0 0.5 1 1.5 2 2.5 3 -3 Density (fm ) Olson et al (in prep)
QGP MIXED PHASE 2.4 T = 10 MeV T = 25 MeV T = 50 MeV 2.2 Secondary Adiabatic index collapse? 2 1.8 1.6 1.4 (Effective) 1.2 1 0 0.5 1 1.5 2 2.5 3 -3 Density (fm ) Olson et al (in prep)
QGP MIXED PHASE 2.4 T = 10 MeV T = 25 MeV Coming soon: T = 50 MeV 2.2 Secondary Adiabatic index collapse! 2 1.8 SN simulations! 1.6 1.4 (Effective) 1.2 1 0 0.5 1 1.5 2 2.5 3 -3 Density (fm ) 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?
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