GENERALIZED DENSITY FUNCTIONAL EQUATION OF STATE FOR SUPERNOVA & NEUTRON STAR SIMULATIONS MacKenzie Warren J.P. Olson, M. Meixner, & G.
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1 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
2 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
3 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 = g/cm 3 Temperature T = MeV Problems persist Phenomenological approaches necessary Uncertainties in nuclear data Neutron stars want stiff EoS, supernovae want soft EoS
4 NUCLEAR EQUATIONS OF STATE FOR ASTROPHYSICAL SIMULATIONS Liquid Drop Model: Lattimer & Swesty Relativistic Mean Field: G. Shen et al, H. Shen et al, Hempel et al, etc Density Functional Theory:????
5 NUCLEAR EQUATIONS OF STATE FOR ASTROPHYSICAL SIMULATIONS Density Liquid Drop Model: Lattimer & Swesty Relativistic Mean Field: G. Shen et al, H. Shen et al, Hempel et al, etc Functional Theory: Notre Dame- Livermore Harness existing DFT models for astrophysical simulations
6 WHAT WE DID 100 Developed Notre Dame- Livermore Equation of State -3 Pressure (MeV/fm ) LS220 Shen NDL - GsKI NDL - KDE0v1 NDL - LNS T = 10 MeV Ye = Denisty (fm ) Olson et al (in prep) DFT approach with threebody forces Transition 0.1 n 0 n 0 Includes pions First order or crossover transition to QGP Explored EoS dependence of CCSNe
7 REGIONS OF HADRONIC EOS Below n0: NSE 9 element nuclear network Pasta Ravenhall, Pethick, & Wilson Lattimer & Swesty Above n0: Skyrme force Pions Repulsive 3-body force Transition to QGP? Soft again? Soft Stiff
8 ABOVE n 0 F tot = F Skyrme + F therm + F +F el+rad MeV QGP Phase transition? u,d (massless) s (massive) QGP modeled using MIT Bag model: = X i ( i q0 + i q2)+ g0 + g2 + BV 165 apple B 1/4 apple 240 MeV F therm! (n, T ) (n, T = 0) McLerran (1986)
9 PIONS Pions (and other resonances) soften EoS at high T Charge fraction Yp Yπ Ye Density (fm ) Olson et al (in prep)
10 Mass (M ) J GsKI GsKII KDE0 LNS MSL0 NRAPR Ska25s20 Ska35s20 SKRA SkT1 SkT2 SkT3 Skxs20 SQMC650 SQMC700 SV-sym32 0 Olson et al (2016) Radius (km) Olson et al (in prep)
11 LIVERMORE SUPERNOVA MODEL General relativistic spherically symmetric supernova model Radius (cm) Time post-bounce (s) Flux limited diffusion scheme e, e, x Explodes via enhanced convection below neutrinosphere
12 EOS DEPENDENCE OF CCSNE Kinetic energy (ergs) Bowers & Wilson GSkI GSkII KDE0v1 LNS MSL0 NRAPR Ska25s20 Ska35s20 SKRA SkT1 SkT2 SkT3 Skxs20 SQMC650 SQMC700 SV-sym Time post-bounce (s) Olson et al (in prep)
13 EOS DEPENDENCE OF CCSNE Luminosity (ergs/s) Bowers & Wilson GSkI GSkII KDE0v1 LNS MSL0 NRAPR Ska25s20 Ska35s20 SKRA SkT1 SkT2 SkT3 Skxs20 SQMC650 SQMC700 SV-sym Time post-bounce (s) Olson et al (in prep)
14 MIXED PHASE GSI
15 MIXED PHASE? GSI
16 QGP MIXED PHASE 0 1 χ Quark-Gluon Plasma Hadronic Assume: Pressure equilibrium Global charge & baryon number conservation = V Q /(V Q + V H ) QGP modeled using MIT Bag model: = X i ( i q0 + i q2)+ g0 + g2 + BV Figure from J.P. Olson
17 MIXED PHASE: SAGERT RESULTS Secondary collapse to QGP results in second shock Successful explosion in 1D Distinct neutrino emission Sagert et al (2009)
18 MAXIMUM MASS DEPENDS ON BAG CONSTANT 2.5 Mass (M ) Need B 1/4 190 None 1/4 B = 180 MeV 1/4 B = 190 MeV 1/4 B = 200 MeV 1/4 B = 210 MeV No 2-loop Radius (km) Olson et al (in prep)
19 QGP MIXED PHASE 0.6 Y Y p q =0.5 =0.9 =0.7 =0.1 =0.3 T = 10 MeV Y e = Density (fm ) Pure hadronic Mixed phase Pure QGP
20 QGP MIXED PHASE 120 Temperature (MeV) Hadronic phase Mixed phase Quark phase Density (fm ) Olson et al (in prep)
21 MIXED PHASE: PRESSURE Pressure (MeV/fm ) Y = 0.1 Y = 0.25 Y = Density (fm ) Olson et al (in prep)
22 QGP MIXED PHASE Adiabatic index Secondary collapse? T = 10 MeV T = 25 MeV T = 50 MeV (Effective) Density (fm ) Olson et al (in prep)
23 QGP MIXED PHASE Adiabatic index (Effective) T = 10 MeV T = 25 MeV T = 50 MeV Coming Secondary soon: collapse! SN simulations! Density (fm ) Olson et al (in prep)
24 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?
25 THANK YOU!
26
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