Estimates of thermal nucleation of quark matter during bounce

Transcription

1 Estimates of thermal nucleation of quark matter during bounce Bruno Mintz 1 Eduardo Fraga 1, Giuseppe Pagliara 2 and Jürgen Schaffner Bielich 2 (1) Universidade Federal do Rio de Janeiro (2) Ruprecht Karls Universität Heidelberg

2 Outline Introduction: nuclear quark phase transition in dense matter Dynamics: thermal nucleation (over)estimates Conclusions

3 Introduction Asymptotic freedom is a well known feature of the strong force. During bounce in a CCSN, the deep core of a PNS can reach very high densities ~ n 0. (n 0 : nuclear saturation density) [e.g.: Sagert et al. PRL 102, (2009)].

4 Introduction Asymptotic freedom is a well known feature of the strong force. During bounce in a CCSN, the deep core of a PNS can reach very high densities ~ n 0. (n 0 : nuclear saturation density) [e.g.: Sagert et al. PRL 102, (2009)]. Are such densities high enough to set quarks free? The high density during the bounce can trigger a hadron quark phase transition: formation of stellar quark matter! [Sagert and Pagliara (2008)] [Ruester et al.: arxiv:hep ph/ ]

5 Introduction Asymptotic freedom is a well known feature of the strong force. During bounce in a CCSN, the deep core of a PNS can reach very high densities ~ n 0. (n 0 : nuclear saturation density) [e.g.: Sagert et al. PRL 102, (2009)]. Are such densities high enough to set quarks free? The high density during the bounce can trigger a hadron quark phase transition: formation of stellar quark matter! [Sagert and Pagliara (2008)] [Ruester et al.: arxiv:hep ph/ ]

6 Introduction Phase transition from hadronic matter to quark matter at high densities: 1 st order phase transition critical density/temperature.

7 Introduction Phase transition from hadronic matter to quark matter at high densities: 1 st order phase transition critical density/temperature. But: simply reach n c is not enough for the transition to occur it takes some time dynamical effects! Dynamics of 1 st order PhT: bubble nucleation (close to the coexistence line) or spinodal decomposition (far from it).

8 Introduction Early post bounce: high density and temperature T central (Bounce)~20MeV n central (Bounce)~ n 0 thermally activated nucleation possible formation of quark matter at this stage may possibly proceed via thermal nucleation of bubbles. Formation of bubbles time scale. Given the physical scales at bounce, is there enough time for a hadron quark phase transition to occur via thermal nucleation?

9 Thermal nucleation Given a density n>n c, the nucleation rate of critical bubbles per unit time per unit volume is given by Fc : free energy shift (critical bubble) T: temperature F is given in the thin wall approximation R c is the surface tension and p is the (bulk) pressure difference between the quark and hadron phases at a given density.

10 Thermal nucleation Main ingredients of the nucleation rate: Equations of state for nuclear and quark matter Temperature, baryon and lepton density Surface tension of the nuclear/quark interface 'Nucleation time': time to form one critical bubble of quark matter inside a volume of constant (T, n). We take V=1km 3, which leads to an overestimate of nucleation rates. to be compared with bounce time scale.

11 Equation of state Nuclear EoS (no hyperons): RMF, with the TM1 parameter set [arxiv:nucl th/ ]. Quark EoS (free fermions): (a) u, d quarks + electrons and e neutrinos (all massless) (b) u, d massless, s massive + electrons and e neutrinos We choose the bag constant B such that n c = 1.5n 0. Electric neutrality and beta equilibrium are enforced in both phases.

12 Equation of state Pressure vs. baryon density (n c =1.5n 0 )

13 Preliminary Results

14 Nucleation rates 'u d matter': no strangeness created in nucleation time scale

15 Nucleation rates Fast strangeness production [m s = 200 MeV]

16 Conclusions There is a clear hierarchy of parameters for the nucleation rate Surface tension Strange quark mass Temperature Our estimates if there is a phase transition during the bounce of a CCSN, the surface tension of the nuclear/quark matter interface is probably not larger than 20 MeV/fm 2. The existence (or not!) of a phase transition during the bounce may help to constrain parameters of the phase diagram of strong interactions.

17 Conclusions There is a clear hierarchy of parameters for the nucleation rate Surface tension Strange quark mass Temperature Our estimates if there is a phase transition during the bounce of a CCSN, the surface tension of the nuclear/quark matter interface is probably not larger than 20 MeV/fm 2. The existence (or not!) of a phase transition during the bounce may help to constrain parameters of the phase diagram of strong interactions.

18 Next steps Check if EoS is compatible with observed SN remnant mass. Different equations of state. Consider PNS density profile n(r). Consider time window of high compression (n>n c ). Calculate exact (numerical) nucleation rates (to compare with overestimate).

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