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Feb 26, 2023 146 likes •418 views

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

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SLIDE 1

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
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SLIDE 2

Quark EOS Phase transition Outlook

Comparition to current EOS1 2

1A.S. Khvorostukhin, V.V. Skokov, V.D. Toneev, K. Redlich, Eur.Phys.J.C48:531-543,2006

  • 2Y. B. Ivanov, V. N. Russkikh and V. D. Toneev, Phys. Rev. C 73 (2006) 044904
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SLIDE 3

Quark EOS Phase transition Outlook

three points to improve

more general density functional for self-energies with vector and scalar density dependencies

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SLIDE 4

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 > 2Tc, 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 (8n0)

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SLIDE 5

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 > 2Tc, 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 (8n0)

  • rientation on astrophysical constraints (e.g. two solar mass

neutron stars)

slide-6
SLIDE 6

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 > 2Tc, 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 (8n0)

  • rientation on astrophysical constraints (e.g. two solar mass

neutron stars) improvements in the low temperature / high density regime

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SLIDE 7

Quark EOS Phase transition Outlook

density functional approach with tdyn consistency

start with approach for grand canonical potential density ω = −U −

  • i

gi

  • d3p

(2π)3

  • T ln[1 + e(˜

E +

i −µi)/T] + T ln[1 + e(˜

E −

i +µi)

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SLIDE 8

Quark EOS Phase transition Outlook

density functional approach with tdyn consistency

start with approach for grand canonical potential density ω = −U −

  • i

gi

  • d3p

(2π)3

  • T ln[1 + e(˜

E +

i −µi)/T] + T ln[1 + e(˜

E −

i +µi)

with the quasiparticle/antilparticle energy ˜ E ±

i

=

  • p2 + (mi − Si)2 ± Vi
  • ne can introduce an effective mass Mi = m − S and an

effective chemical potential ˜ µi = µi − Vi with self-energies Si = ∆mi + mR

i

Vi = ∆Ei + E R

i

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SLIDE 9

Quark EOS Phase transition Outlook

density functional approach with tdyn consistency

start with approach for grand canonical potential density ω = −U −

  • i

gi

  • d3p

(2π)3

  • T ln[1 + e(˜

E +

i −µi)/T] + T ln[1 + e(˜

E −

i +µi)

with the quasiparticle/antilparticle energy ˜ E ±

i

=

  • p2 + (mi − Si)2 ± Vi
  • ne can introduce an effective mass Mi = m − S and an

effective chemical potential ˜ µi = µi − Vi with self-energies Si = ∆mi + mR

i

Vi = ∆Ei + E R

i

rearrangement contributions U, mR

i , E R i

ensure consistency

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SLIDE 10

Quark EOS Phase transition Outlook

density functional approach with tdyn consistency

derivation of rearrangement

to preserve thermodynamical consistency the definition of the particle density ni = ∂p ∂µi = gi

  • d3p

(2π)3 1 1 + e(√

p2−Mi−˜ µi)/T

must be ensured by an appropriate set of rearrangement contributions

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SLIDE 11

Quark EOS Phase transition Outlook

density functional approach with tdyn consistency

derivation of rearrangement

to preserve thermodynamical consistency the definition of the particle density ni = ∂p ∂µi = gi

  • d3p

(2π)3 1 1 + e(√

p2−Mi−˜ µi)/T

must be ensured by an appropriate set of rearrangement contributions this leads us to the differential equation ∂U ∂µi =

  • j
  • nj

∂∆Ej ∂µi + nj ∂E R

j

∂µi − ns

j

∂∆mj ∂µi − ns

j

∂mR

j

∂µi

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SLIDE 12

Quark EOS Phase transition Outlook

density functional approach with tdyn consistency

derivation of rearrangement

  • ne solution,provided by Stefan Typel (but slightly altered), is

E R

i

=

  • j

nj ∂∆Ej ∂ni −

  • j

ns

j

∂∆mj ∂ni mR

i = −

  • j

nj ∂∆Ej ∂ns

i

+

  • j

ns

j

∂∆mj ∂ns

i

U =

  • i

niE R

i −

  • i

ns

i mR i

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SLIDE 13

Quark EOS Phase transition Outlook

density functional approach with tdyn consistency

derivation of rearrangement

  • ne solution,provided by Stefan Typel (but slightly altered), is

E R

i

=

  • j

nj ∂∆Ej ∂ni −

  • j

ns

j

∂∆mj ∂ni mR

i = −

  • j

nj ∂∆Ej ∂ns

i

+

  • j

ns

j

∂∆mj ∂ns

i

U =

  • i

niE R

i −

  • i

ns

i mR i

now we are coming to an concrete example

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SLIDE 14

Quark EOS Phase transition Outlook

Stringflip modell

confinement potential with effects of pauli quenching34 ∆mi = −C q · (ns)1/3 − Dq · (ns)−1/3 ∆Ei = aqn + bqn3 with the density dependent Dq = Dq(ns).

  • 3G. Ropke, D. Blaschke and H. Schulz, Phys. Rev. D 34 (1986) 3499.

4Yukalov, Yukalova, Physica A 243 (1997) 382-414

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SLIDE 15

Quark EOS Phase transition Outlook

Stringflip modell

confinement potential with effects of pauli quenching34 ∆mi = −C q · (ns)1/3 − Dq · (ns)−1/3 ∆Ei = aqn + bqn3 with the density dependent Dq = Dq(ns). The rearrangement contributions E R

i

=

  • aq + 3bqn2

n = E R mR

i =

  • −C q

3 (ns)−2/3 + Dq 3 (ns)−4/3 − Dq′ · (ns)−1/3

  • ns = mR

U = nE R − nsmR

  • 3G. Ropke, D. Blaschke and H. Schulz, Phys. Rev. D 34 (1986) 3499.

4Yukalov, Yukalova, Physica A 243 (1997) 382-414

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SLIDE 16

Quark EOS Phase transition Outlook

resulting eos

pressure over baryon chemical potential

500 1000 1500 2000 100 200 300 400 500 600 700 D=000.0, exvol=0.0 D=200.0, exvol=0.00 D=200.0, exvol=0.01 D=200.0, exvol=0.10 D=200.0, exvol=1.00 D=200.0, exvol=1.0,a=b=0.05

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SLIDE 17

Quark EOS Phase transition Outlook

resulting eos

neutron star eos

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SLIDE 18

Quark EOS Phase transition Outlook

resulting eos

neutron star configurations

8 9 10 11 12 13 14 Radius [Rsolar] 0.5 1 1.5 2 2.5 Mass [Msolar]

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SLIDE 19

Quark EOS Phase transition Outlook

resulting eos

symmetric matter

0.5 1 1.5 2 2.5 n [fm

  • 3]
  • 200

200 400 600 800 1000 1200 P [MeV/fm

3]

T = 0 T = 150 MeV

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SLIDE 20

Quark EOS Phase transition Outlook

Outlook

what to do next?

systematic calculation and analysis of the current eos’

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SLIDE 21

Quark EOS Phase transition Outlook

Outlook

what to do next?

systematic calculation and analysis of the current eos’ implement all temperature effects (antiparticles, pions . . . )

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SLIDE 22

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

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SLIDE 23

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!

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SLIDE 24

Quark EOS Phase transition Outlook

Phase transition

bare models

500 600 700 800 900 1000 1100 1200 1300 1400 1500 50 100 150 200 250 p / MeV fm-3 hNJL DD2 500 600 700 800 900 1000 1100 1200 1300 1400 1500 µn 100 200 300 M / MeV T=0 T=40MeV T=50MeV

hNJL Chiral Transition

η02 = 0.08 ; η04 = 5.0 ; symmetric chiral pt deconfinement pt

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SLIDE 25

Quark EOS Phase transition Outlook

Phase transition

including bag constant

500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000

  • 50

50 100 150 200 250 300 350 400 450 500 550 600 p / MeV fm-3 hNJL - 160 MeV fm-3 DD2 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 µn 100 200 300 M / MeV T=0 T=40MeV T=50MeV

hNJL Chiral Transition

η02 = 0.08 ; η04 = 5.0 ; symmetric

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SLIDE 26

Quark EOS Phase transition Outlook

Phase transition

  • ver density

0.5 1 1.5 2 n / fm-3 500 1000 1500 2000 p / MeV T = 0 MeV T = 100 MeV B = 160 MeV fm-3 Hadrons Quarks

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SLIDE 27

Quark EOS Phase transition Outlook

Phase transition

phase diagram

500 1000 1500 2000 2500 3000 µ / MeV 50 100 150 200 T / MeV 160 180 200

hNJL DD2 phase diagram with bag constants

sym η2=0.08 und η2=5.0