Quark EOS Phase transition Outlook A new RMF based quark-nuclear matter EoS for applications in astrophysics and heavy-ion collisions Niels-Uwe Friedrich Bastian Uniwersytet Wroc� lawski, Instytut Fizyki Teoretycznej 24. February 2016
Quark EOS Phase transition Outlook Comparition to current EOS 1 2 1A.S. Khvorostukhin, V.V. Skokov, V.D. Toneev, K. Redlich, Eur.Phys.J.C 48 :531-543,2006 2Y. B. Ivanov, V. N. Russkikh and V. D. Toneev, Phys. Rev. C 73 (2006) 044904
Quark EOS Phase transition Outlook three points to improve more general density functional for self-energies with vector and scalar density dependencies
Quark EOS Phase transition Outlook three points to improve more general density functional for self-energies with vector and scalar density dependencies HTL only applicable for T > 2 T c , so not for the phase-transition to high masses suppress the quark sector. was compensated for T-axes, but leads to way to high transition densities at T = 0 (8 n 0 )
Quark EOS Phase transition Outlook three points to improve more general density functional for self-energies with vector and scalar density dependencies HTL only applicable for T > 2 T c , so not for the phase-transition to high masses suppress the quark sector. was compensated for T-axes, but leads to way to high transition densities at T = 0 (8 n 0 ) orientation on astrophysical constraints (e.g. two solar mass neutron stars)
Quark EOS Phase transition Outlook three points to improve more general density functional for self-energies with vector and scalar density dependencies HTL only applicable for T > 2 T c , so not for the phase-transition to high masses suppress the quark sector. was compensated for T-axes, but leads to way to high transition densities at T = 0 (8 n 0 ) orientation on astrophysical constraints (e.g. two solar mass neutron stars) improvements in the low temperature / high density regime
Quark EOS Phase transition Outlook density functional approach with tdyn consistency start with approach for grand canonical potential density d 3 p � � T ln[1 + e (˜ E + i − µ i ) / T ] + T ln[1 + e (˜ � E − i + µ i ) ω = − U − g i (2 π ) 3 i
Quark EOS Phase transition Outlook density functional approach with tdyn consistency start with approach for grand canonical potential density d 3 p � � T ln[1 + e (˜ E + i − µ i ) / T ] + T ln[1 + e (˜ � E − i + µ i ) ω = − U − g i (2 π ) 3 i with the quasiparticle/antilparticle energy � p 2 + ( m i − S i ) 2 ± V i E ± ˜ = i one can introduce an effective mass M i = m − S and an effective chemical potential ˜ µ i = µ i − V i with self-energies S i = ∆ m i + m R V i = ∆ E i + E R i i
Quark EOS Phase transition Outlook density functional approach with tdyn consistency start with approach for grand canonical potential density d 3 p � � T ln[1 + e (˜ E + i − µ i ) / T ] + T ln[1 + e (˜ � E − i + µ i ) ω = − U − g i (2 π ) 3 i with the quasiparticle/antilparticle energy � p 2 + ( m i − S i ) 2 ± V i E ± ˜ = i one can introduce an effective mass M i = m − S and an effective chemical potential ˜ µ i = µ i − V i with self-energies S i = ∆ m i + m R V i = ∆ E i + E R i i rearrangement contributions U , m R i , E R ensure consistency i
Quark EOS Phase transition Outlook density functional approach with tdyn consistency derivation of rearrangement to preserve thermodynamical consistency the definition of the particle density d 3 p n i = ∂ p � 1 = g i 1 + e ( √ (2 π ) 3 ∂µ i p 2 − M i − ˜ µ i ) / T must be ensured by an appropriate set of rearrangement contributions
Quark EOS Phase transition Outlook density functional approach with tdyn consistency derivation of rearrangement to preserve thermodynamical consistency the definition of the particle density d 3 p n i = ∂ p � 1 = g i 1 + e ( √ (2 π ) 3 ∂µ i p 2 − M i − ˜ µ i ) / T must be ensured by an appropriate set of rearrangement contributions this leads us to the differential equation � � ∂ E R ∂ m R ∂ U ∂ ∆ E j ∂ ∆ m j j j � − n s − n s = + n j n j j j ∂µ i ∂µ i ∂µ i ∂µ i ∂µ i j
Quark EOS Phase transition Outlook density functional approach with tdyn consistency derivation of rearrangement one solution,provided by Stefan Typel (but slightly altered), is ∂ ∆ E j ∂ ∆ m j � � E R n s = n j − i j ∂ n i ∂ n i j j ∂ ∆ E j ∂ ∆ m j � � m R n s i = − n j + j ∂ n s ∂ n s i i j j � � n i E R n s i m R U = i − i i i
Quark EOS Phase transition Outlook density functional approach with tdyn consistency derivation of rearrangement one solution,provided by Stefan Typel (but slightly altered), is ∂ ∆ E j ∂ ∆ m j � � E R n s = n j − i j ∂ n i ∂ n i j j ∂ ∆ E j ∂ ∆ m j � � m R n s i = − n j + j ∂ n s ∂ n s i i j j � � n i E R n s i m R U = i − i i i now we are coming to an concrete example
Quark EOS Phase transition Outlook Stringflip modell confinement potential with effects of pauli quenching 34 ∆ m i = − C q · ( n s ) 1 / 3 − D q · ( n s ) − 1 / 3 ∆ E i = a q n + b q n 3 with the density dependent D q = D q ( n s ). 3G. Ropke, D. Blaschke and H. Schulz, Phys. Rev. D 34 (1986) 3499. 4Yukalov, Yukalova, Physica A 243 (1997) 382-414
Quark EOS Phase transition Outlook Stringflip modell confinement potential with effects of pauli quenching 34 ∆ m i = − C q · ( n s ) 1 / 3 − D q · ( n s ) − 1 / 3 ∆ E i = a q n + b q n 3 with the density dependent D q = D q ( n s ). The rearrangement contributions a q + 3 b q n 2 � E R n = E R � = i − C q 3 ( n s ) − 2 / 3 + D q � � n s = m R 3 ( n s ) − 4 / 3 − D q ′ · ( n s ) − 1 / 3 m R i = U = nE R − n s m R 3G. Ropke, D. Blaschke and H. Schulz, Phys. Rev. D 34 (1986) 3499. 4Yukalov, Yukalova, Physica A 243 (1997) 382-414
Quark EOS Phase transition Outlook resulting eos pressure over baryon chemical potential 700 D=000.0, exvol=0.0 D=200.0, exvol=0.00 D=200.0, exvol=0.01 600 D=200.0, exvol=0.10 D=200.0, exvol=1.00 D=200.0, exvol=1.0,a=b=0.05 500 400 300 200 100 0 500 1000 1500 2000
Quark EOS Phase transition Outlook resulting eos neutron star eos
Quark EOS Phase transition Outlook resulting eos neutron star configurations 2.5 2 1.5 Mass [M solar ] 1 0.5 0 8 9 10 11 12 13 14 Radius [R solar ]
Quark EOS Phase transition Outlook resulting eos symmetric matter 1200 1000 800 3 ] P [MeV/fm 600 400 T = 0 T = 150 MeV 200 0 -200 0 0.5 1 1.5 2 2.5 -3 ] n [fm
Quark EOS Phase transition Outlook Outlook what to do next? systematic calculation and analysis of the current eos’
Quark EOS Phase transition Outlook Outlook what to do next? systematic calculation and analysis of the current eos’ implement all temperature effects (antiparticles, pions . . . )
Quark EOS Phase transition Outlook Outlook what to do next? systematic calculation and analysis of the current eos’ implement all temperature effects (antiparticles, pions . . . ) development of more systematic approach of phasetransition via cluster virial expansion
Quark EOS Phase transition Outlook Outlook what to do next? systematic calculation and analysis of the current eos’ implement all temperature effects (antiparticles, pions . . . ) development of more systematic approach of phasetransition via cluster virial expansion thank you for your attention!
Quark EOS Phase transition Outlook Phase transition bare models hNJL Chiral Transition η02 = 0.08 ; η04 = 5.0 ; symmetric 250 300 200 T=0 deconfinement pt T=40MeV T=50MeV 200 150 p / MeV fm -3 M / MeV 100 chiral pt 100 hNJL DD2 50 0 0 500 500 600 600 700 700 800 800 900 900 1000 1000 1100 1100 1200 1200 1300 1300 1400 1400 1500 1500 µ n
Quark EOS Phase transition Outlook Phase transition including bag constant hNJL Chiral Transition η02 = 0.08 ; η04 = 5.0 ; symmetric 600 550 300 500 450 T=0 T=40MeV 400 T=50MeV 350 200 p / MeV fm -3 M / MeV 300 250 200 100 150 100 hNJL - 160 MeV fm -3 50 DD2 0 0 -50 500 500 600 600 700 700 800 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 µ n
Quark EOS Phase transition Outlook Phase transition over density B = 160 MeV fm -3 2000 T = 0 MeV T = 100 MeV 1500 p / MeV 1000 500 Quarks Hadrons 0 0 0.5 1 1.5 2 n / fm -3
Quark EOS Phase transition Outlook Phase transition phase diagram hNJL DD2 phase diagram with bag constants sym η 2 =0.08 und η 2 =5.0 200 160 180 200 150 T / MeV 100 50 0 0 500 1000 1500 2000 2500 3000 µ / MeV
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