Cold quarks stars from hot lattice QCD

Transcription

1 Cold quarks stars from hot lattice QCD Robert Schulze TU Dresden, FZ Dresden-Rossendorf with B. Kämpfer 1. hot lattice QCD and quasiparticles 2. quasiparticle model: going to μ > 0 3. cold quark stars Quarks stars from lattice QCD 1

2 Effective QPM quasiparticle model: = X Z d 4 = B/F Θ ( 2 ( ) (derived from 1-loop QCD) running/effective coupling Blaizot, Iancu, Rebhan: PRD 01 RS, Bluhm, Kämpfer: JPPNP 09 2 ( 2 )= ln( 2 ) =0 = Λ QCD - Bluhm, Kämpfer, RS, Seipt: EPJC 07 fit to -3 with fixed ( c): Ts, l, 0 Quarks stars from lattice QCD 2

3 At =0 quasiparticle model (QPM) fit to lattice results Bazavov et al.: PRD 09 Quarks stars from lattice QCD 3

4 state variables,,, ( -3 ),... effective coupling m = ¹ 0:?? Quarks stars from lattice QCD 4

5 Into the T- m -plane m > 0: stationary potential, self-consistent model impose Maxwell s relation = 2 + quasilinear PDE for G 2 (T, m ¹ 0): T-m-plane accessible 2 = Peshier, Kämpfer, Soff: PRC 00, PRD 02 caveat: for perfect solution collective excitations and damping terms necessary RS, Bluhm, Kämpfer: EPJ ST 08 Quarks stars from lattice QCD 5

6 Small chemical potential 0 i 6 test with p (T, m & 0) lattice data c (T) = 4 P ( ) strong interaction c (T) c 2 ( )= 1! strong interaction c (T) ( 4 ) ( ) 1 0 all lattice data from Allton et al.: PRD T/Tc 0.2 c T/Tc T/Tc Bluhm, Kämpfer, Soff: PLB 05 application in RHIC successful Bluhm, Kämpfer, RS, Seipt, Heinz: PRC 07 Quarks stars from lattice QCD 6

7 Isospin asymmetric QPM five chemical potentials + four side conditions equilibrium (e.g ; = + ) equilibrium in strangeness changing decays (e.g. Λ ; = ) muon decay (e.g ; = ) electric neutrality only one independent chemical potential = Quarks stars from lattice QCD 7

8 At =0 thermodynamic quantities well within perturbative predictions (Andersen, Strickland: PRD 02 Fraga et al.: NPA 02) hybrid approach needed individual contributions Quarks stars from lattice QCD 8

9 At =0 EOS: narrow range for all actions vacuum energy density dep. on lattice spacing asymptotics governed by lattice action good approximation = ( M V) 4 Quarks stars from lattice QCD 9

10 Pure quark stars solutions of TOV equations rather small and light ( -1 2 ) no twin candidates 0 RS, Kämpfer: arxiv: submitted to PRC Quarks stars from lattice QCD 10

11 Summary & Outlook QCD results mapped to large m, even =0 EOS for quark stars similar for all actions quark stars with rather smaller radii + masses outlook: hybrid stars full HTL quasiparticle model with Landau damping and collective modes EOS for FAIR/CBM Quarks stars from lattice QCD 11

12 Quarks stars static, spherical stellar objects = ( + )( +4 3 ) 2 (1 2 ) =4 2 TOV equations = ( ) EOS of the quark-gluon plasma from where? Quarks stars from lattice QCD

13 CJT formalism effective action Γ[ ] = Tr ln -1 +Tr ª + Γ 2 [ ] translation-invariant systems, no broken symmetries Ω Z = tr Tr ln -1 +Tr ª d 4 (2 ) 4 B( )Im ln -1 Π Z +2tr d 4 (2 ) 4 F( )Im ln -1 Σ Γ 2 Quarks stars from lattice QCD 13

14 2-loop QCD thermodynamics truncate G2 at 2-loop order self-energies of 1-loop order gauge invariance: hard thermal loops (HTL) Quarks stars from lattice QCD 14

15 Pressure ³ Ω + Ω expl. {z} Z n 0 o B/F qp + damping d 4 self-consistent formulation of the pressure = Ω := X entropy density = = X Z := X + Π Π = X d 4 o B/F nqp + damping Π Π ³ = P net quark density = Z F + n F qp + dampingo d 4 Ω + Ω expl. {z} 0 Quarks stars from lattice QCD 15

16 HTL self-energies Im P¹0 below the lightcone (solid lines) Π T / Π L / = / =0.5 Re(Π T ) Im(Π T ) light cone light cone Re(Π L ) Im(Π L ) / Σ + / ˆ =0.5 light cone Re(Σ + ) Im(Σ + ) / Landau damping Quarks stars from lattice QCD 16

17 Effective coupling fundamental parameter 2 ( 2 )= ln( 2 ) ³ ln[ln( 2 )] ln( 2 ) running coupling g 2 = Λ QCD =0 effective coupling G 2 = ( - ) QCD Quarks stars from lattice QCD 17

18 Lattice QCD lattice results: availability limited one answer: quasiparticle model - self-consistency allows mapping to = 0 - ensure stability and charge neutrality Quarks stars from lattice QCD

19 m = 0 m = 0: adjust to QCD Ts, l fixed G 2 (T, m = 0) T s = 0: 3 Quarks stars from lattice QCD 19

20 Influence of coll. modes + m = 0 individual entropy contributions Landau damping large close to T c, decreases for higher temperatures Quarks stars from lattice QCD 20

21 Thermodynamic bulk variables entropy density and net quark density RS, Bluhm, Kämpfer: PPNP 09 increase with chemical potential Quarks stars from lattice QCD 21

22 Thermodynamic bulk variables pressure and energy density small area of negative pressure no problems for RHIC, LHC, SPS, FAIR natural limit of stability for quark stars (CFL?) Quarks stars from lattice QCD 22

23 EOS for RHIC and LHC EOS for LHC, RHIC b 0 crossover 1 st order Quarks stars from lattice QCD 23

24 Comparison with the experiment calculate elliptic flow using relativistic hydro code compare with experimental data (RHIC) Bluhm, Kämpfer, RS, Seipt, Heinz: PRC 07 Quarks stars from lattice QCD 24

25 Compact stellar matter Tolman-Oppenheimer-Volkov equations b -equilibrium by d, s «u, l, n l m l from charge neutrality compare with bag-like EOS 4 = +4 strong dependence on critical temperature Quarks stars from lattice QCD 25

26 Summary & Outlook 2-loop G 2 + eff. coupling G 2 HTL QPM QCD results describable; used as input large m accessible due to self-consistency EOS for heavy ion collision experiments available quark stars with even smaller radii than bag model outlook: hydro for SPS,FAIR critical endpoint Kämpfer, Bluhm, RS, Seipt: NPA 06 Quarks stars from lattice QCD 26

27 Backup influence of a Quarks stars from lattice QCD 27

28 EOS for SPS PRELIMINARY SPS / q» Quarks stars from lattice QCD 28

29 More effects of collective excitations collective modes neg. entropy contrib. / c / c situation improves Quarks stars from lattice QCD 29

30 More effects of Landau damping only minor contribution at m = 0 essential for m > 0 / c without collective modes without Landau damping full HTL / c Quarks stars from lattice QCD 30

31 Results for the pressure (2) pressure cuts Quarks stars from lattice QCD 31

32 EOS for Nf = 2 +1 RHIC, LHC: =0 Bernard 0.2 Bernard 0.1 Karsch Aoki Kämpfer, Bluhm, RS, Seipt, Heinz: NPA'05 Bluhm, Kämpfer, RS, Seipt, Heinz: PRC'07 Quarks stars from lattice QCD 32

33 file:///d:/dokumente/fzr/vortraege/ %20-%20orsay/eos_interpolation_gsv32epsconvwmvprev.eps QCD Matter under Extreme Conditions, Hirschegg 2010 Predictions for LHC LHC Pb+Pb collisions - conservative guess: 0 =330fm -3 =5 2fm 0 =0 6fm 0 =515M V higher initial temperature flatter p T spectra smaller 2 Quarks stars from lattice QCD 33

34 More LHC predictions initial parameters translate to 0 =127G V 0 =42 G V fm 3 0 =515M V LHC: higher initial temperature longer fireball lifetime stronger radial flow pt spectra flat Quarks stars from lattice QCD 34

35 More full HTL quasiparticle model now: Im P¹0 + collective excitations = + = +( ) = R ( ) (ImΠ( )) {z } ˆ= ( ) := - 1 := ImΠ Re ³ -1 2 ( ) (1+ 2 ( )) + 2 (- ) 2 (1+ 2 (- )) 2 Quarks stars from lattice QCD 35

36 Backup file:///d:/dokumente/fzr/qpm/_ergebnisse/ %20-%20char%20neuer%20fit/isentropen/tc=166mev%20fuer%20vortrag/pse_graph255vs85.eps model describes all available quantities: Quarks stars from lattice QCD 36

37 A family of EOS s interpolate between hadron gas and QPM description lin. interpol. fixed sound waves Quarks stars from lattice QCD 37

38 Backup: Inclusion of widths Peshier: Im P=2gw 4 BW,, [ -1 ] 2 Γ= =0.2,, =0.1,, =1.0,, =2.0 BW ansatz F(w,k) BW(m) Z ( )= / d ( )BW( Γ) Quarks stars from lattice QCD 38

39 Backup: Distributed quasiparticle model fixed parameters, vary G Γ=0.01G V Γ=0.10G V Γ=1.00G V / c / c / c / c adjustment to lattice Γ =0 01 G V 0.0 / c / c SB limit 20 / dqp with Γ=0.01G V [Kar07] lat =0.952 eqp [Kar07] lat = / / Quarks stars from lattice QCD 39

40 Backup: Distributed quasiparticle model II bias adjustment 12 Γ! =1G V SB limit / dqp with Γ=1.00G V [Kar07] lat =0.667 eqp [Kar07] lat = / / Quarks stars from lattice QCD 40