The scenario of two families of compact The scenario of two families - PowerPoint PPT Presentation

The scenario of two families of compact The scenario of two families of compact stars: burning of hadronic stars stars: burning of hadronic stars Giuseppe Pagliara Giuseppe Pagliara Dipartimento di Fisica e Scienze della Terra, Universita' di Ferrara & Dipartimento di Fisica e Scienze della Terra, Universita' di Ferrara & INFN Ferrara, Italy INFN Ferrara, Italy Kyoto 27/10/2016 Kyoto 27/10/2016

Outline Outline -) Under the assumption of absolute -) Under the assumption of absolute stability of strange quark matter: stability of strange quark matter: modeling the process of conversion of modeling the process of conversion of hadronic stars into quark stars hadronic stars into quark stars -) Motivation: two families of compact -) Motivation: two families of compact stars from observations? stars from observations?

Strange quark matter hypothesis Strange quark matter hypothesis (Bodmer 71- Terazawa 79 - Witten 84) (Bodmer 71- Terazawa 79 - Witten 84) Hyp: “three flavor beta-stable quark Hyp: “three flavor beta-stable quark 56 Fe matter is more bound than 56 Fe.” .” matter is more bound than Consider three massless quarks: up, down Consider three massless quarks: up, down strange. From beta stability the chemical strange. From beta stability the chemical µ d = µ s potentials µ µ potentials d = implying that the density of s implying that the density of strange = density of down. From charge strange = density of down. From charge Weber 2004 Weber 2004 neutrality then the number of up must be = to neutrality then the number of up must be = to the number of down. The EoS: the number of down. The EoS: Starting with a mixture of up and Starting with a mixture of up and down quarks, the weak process down quarks, the weak process u+d->u+s allows to decrease E/A u+d->u+s allows to decrease E/A (a new Fermi sphere opens up) to (a new Fermi sphere opens up) to values smaller than 930 MeV values smaller than 930 MeV ν f =6 (color * spin degeneracy) Where ν (depending on the values of the (depending on the values of the Where f =6 (color * spin degeneracy) parameters) B is the bag constant of the MIT bag model parameters) B is the bag constant of the MIT bag model

Birth of quark stars Birth of quark stars 1) Nucleation of strange quark matter 1) Nucleation of strange quark matter (not in this talk, see e.g. Iida & Sato 98) (not in this talk, see e.g. Iida & Sato 98) 2) Expansion and merging of strange quark 2) Expansion and merging of strange quark matter droplets, formation of a strange quark matter droplets, formation of a strange quark matter core matter core (not in this talk, see e.g. Horvath et al. 92) (not in this talk, see e.g. Horvath et al. 92) 3) Macroscopic conversion of a hadronic star 3) Macroscopic conversion of a hadronic star (here!!) (here!!)

Modeling the conversion Modeling the conversion The conversion starts from strange hadronic The conversion starts from strange hadronic matter & involves strong interaction matter & involves strong interaction (deconfinement) + flavor changing weak (deconfinement) + flavor changing weak interactions u+d->u+s. interactions u+d->u+s. nucleons hyperons Very complicated to model: deconfinement Very complicated to model: deconfinement is a non-perturbative phenomenon. is a non-perturbative phenomenon. Olinto 87: let us ignore : let us ignore Olinto 87 Ouyed et al 2013 Ouyed et al 2013 deconfinement and treat the deconfinement and treat the process as a chemical reaction and process as a chemical reaction and borrow the formalism of borrow the formalism of advection-diffusion-reaction PDE advection-diffusion-reaction PDE

Combustion process Combustion process Kinetic theory approach: diffusion of Kinetic theory approach: diffusion of quarks between the two fluids (which quarks between the two fluids (which Ouyed et al 2013 Ouyed et al 2013 are in mechanical equilibrium) and are in mechanical equilibrium) and weak interactions weak interactions Microphysics: “a” strangeness fraction (n.down- Microphysics: “a” strangeness fraction (n.down- n.strange)/n.baryons n.strange)/n.baryons 1) Typical burning velocity: 1) Typical burning velocity: Diffusion coefficient: Diffusion coefficient: ∼ sqrt(D / τ ) v ∼ sqrt(D / τ ) ~ ~ 10 10 4 cm/s and v 4 cm/s and scales as T -5/6 scales as T -5/6 Dimensional Dimensional Typical time scale for u+d->u+s: analysis: Typical time scale for u+d->u+s: analysis: 2)Typical width of the combustion 2)Typical width of the combustion δ∼ sqrt(D τ ) zone: δ∼ sqrt(D τ ) ~ ~ 10 10 - cm thus zone: -5 5 cm thus very small in comparison with very small in comparison with the size of a star the size of a star This approach does not take into account macroscopic flows driven by This approach does not take into account macroscopic flows driven by pressure/density gradients pressure/density gradients

Coupling with hydrodynamics Coupling with hydrodynamics Such a calculation would be impossible in 2 Such a calculation would be impossible in 2 Ouyed 2010: 1D – no gravity – no star! Ouyed 2010: 1D – no gravity – no star! or 3D which are needed to study the possible or 3D which are needed to study the possible occurrence of hydrodynamical instabilities. occurrence of hydrodynamical instabilities. A similar problem when simulating type Ia A similar problem when simulating type Ia SN. SN. Two possible strategies: Two possible strategies: 1) Khokhlv 1993: 1) Khokhlv 1993: K and R are rescaled to enlarge the width of K and R are rescaled to enlarge the width of the combustion zone over several the combustion zone over several computational cells. It underestimates computational cells. It underestimates hydro-instabilities. hydro-instabilities.

2) Calculate the burning velocities profiles 2) Calculate the burning velocities profiles from the microscopic kinetic theory model, from the microscopic kinetic theory model, assume an infinitely thin combustion layer infinitely thin combustion layer. . assume an Hillebrandt 1999 for type Ia SN Hillebrandt 1999 for type Ia SN Books: Landau, Fluid dynamics. Books: Landau, Fluid dynamics.

Ideal-hydro modeling Ideal-hydro modeling 2 n2 p: pressure, e: energy density, n: baryon density, w=e+p: enthalpy density, X: (e+p)/n p: pressure, e: energy density, n: baryon density, w=e+p: enthalpy density, X: (e+p)/ γ: Lorentz factor, fluid four velocity, γ: dynamical volume, T T : energy momentum tensor, : energy momentum tensor, u u fluid four velocity, Lorentz factor, dynamical volume, j: number of baryons converted per unit of surface and time. j: number of baryons converted per unit of surface and time. Simplifying: let us Simplifying: let us consider a stationary and consider a stationary and 1D physical situation (we 1D physical situation (we consider only the “x” consider only the “x” dependence of the fluid dependence of the fluid variables) variables) Eqs. of ideal hydrodynamics Eqs. of ideal hydrodynamics Ex: from hydrod. (continuity Ex: from hydrod. (continuity Surface of discontinuity: flame front Surface of discontinuity: flame front Eqs.): Eqs.): p e e 1 p 1 n 1 n e e 2 p 2 n 2 2 p n 1 1 1 2 2 fuel ashes fuel ashes

The first two equations can be The first two equations can be rewritten as: rewritten as: This equation defines the so-called This equation defines the so-called “detonation adiabat” “detonation adiabat” which is formally identical to a shock adiabat but for the fact which is formally identical to a shock adiabat but for the fact that there are two different fluids and thus two different EoSs. that there are two different fluids and thus two different EoSs. Detonation adiabat Detonation adiabat Given the initial state 1, Given the initial state 1, and for a fixed value of j and for a fixed value of j (computed from the (computed from the microphysics model), the microphysics model), the state of fluid 2 is state of fluid 2 is determined. determined. j j X

Qualitatively we can distinguish Qualitatively we can distinguish two different combustion modes: two different combustion modes: -) detonation detonation (the combustion is (the combustion is -) driven by a shock wave which driven by a shock wave which heats up the fuel thus catalysing heats up the fuel thus catalysing the conversion) the conversion) -) deflagration deflagration (the combustion is (the combustion is -) driven by the microscopic driven by the microscopic properties: transport of properties: transport of heat/chemical species and rate of heat/chemical species and rate of reactions) reactions) By introducing the By introducing the sound velocities in the sound velocities in the two fluids c ci two fluids i Several calculations (see Drago 2007) have shown that in the case of burning of hadronic stars, Several calculations (see Drago 2007) have shown that in the case of burning of hadronic stars, detonations are quite unlikely. The combustion proceeds as a deflagration. detonations are quite unlikely. The combustion proceeds as a deflagration.