hadronic matter to quark matter Shock Induced Conversion Diffusion - PowerPoint PPT Presentation

Hydrodynamical study on the conversion of hadronic matter to quark matter Shock Induced Conversion Diffusion Induced Conversion Phys. Rev. D 93, 043018 (2016) Phys. Rev. D 93, 043019 (2016) Shun Furusawa (National Astrophysical Observatory of Japan ⇒ ＦＩＡＳ ) collaborator : Shoichi Yamada (Waseda University) The other work: Core Collapse Supernovae (5/30 FIGSS seminar) 05/10 2016 Astro Coffee

In Introduction: Quark Stars Strange quark Stars Neutron Stars Hybrid stars Pure quark stars HM 3QM 3QM HM ： neutrons, protons QM :deconfined quarks (confined quarks) (up, down, strange) d 3 quarks are confined d p=uud u d n=udd u s ・ Mass Radius Relations ・ different cooling curves ・ Quark Nova ( 𝟐𝟏 𝟔𝟒 erg neutrinos are emitted)

Co Combu bustio ion to to S SQM Energy 2QM Gibbs Energy d HM HM Ａ 2QM d u d SQM u d d SQM B u s Fuel ash C,O ⇒ Ni 𝟔𝟕 (Type Ia SNe ） C+ O2 ⇒ CO2 （ Terrestrial combustion ） P Transition point Ａ Shock induced Case H Ｍ ⇒ 2QM ⇒ SQM B Diffusion induced Case HM ⇒ SQM with small strangeness ⇒ SQM

HM 2QM d d u d u d SQM A. Shock induced Case d ・ Spin Down of (P)NS u s ・ Accretion on (P)NS ・ Merger of compact stars Fuel ash HM SQM with minimum strangeness d u d d d B. Diffusion induced Case s ・ Following Shock induced ・ Capture of strangelets SQM u d d d d s u u u u s d Fuel ash

Shock induced Case HM 2QM d d u d u d SQM SQM d HM HM u s Fuel ash HM 2QM SQM Surface Center

HM Diffusion induced Case SQM with minimum strangeness d u d d d s SQM u SQM d d d d HM s u u u HM u s d Fuel ash HM SQM SQM with minimum strangeness Surface Center

Combustion modes P 1 Hugoniot P 1 a curve a Endothermic Exothermic (Our works) (terrestrial case) (Previous works) d b c Initial state P 0 d P 0 f f c e 1/ρ 0 1/ρ 1 1/ρ 1 1/ρ 0 u  u  c c 0 s 0 0 s 0 u  c u  a: strong detonation d: weak deflagration c 1 s 1 1 s 1 u  c c: weak detonation u  1 s 1 c f: strong deflagration 1 s 1 u  c b,e: Jouget point 1 s 1

Previous works (Olint nt ’87, Benvenuto’89 Mishu hustin stin ’14, Drago ’15) ・ St Structu tures res inside de the front t are not solved ed. d p+n ? u Initial State Final state （ HM ） （３ QM ） s ・ Endoth therm rmic case is neglec ecte ted in referen rence ce to terrest stria rial l combus ustio tion Herzog ‘11 Pagliara ‘13 endo. exo.

Previ Pr vious works ・ St Structu tures res inside de the front t are not solved ed. ・ Endoth thermi rmic case is neglec ecte ted due to a strain ined ed interpret retat ation on. . f Our works: Motivation o of １ , What happens inside combustion front when QS is formed? 2, Which combustion modes are realized for the two scenarios. 3, List up all possibl ible e structu tures res inside de the front t for wide ranges es of parame meter er s in EOS S of QM and initia ial l conditi tion on. p+n d Initial State Final state （ HM ） （３ QM ） s u 0 x Strong interaction Time Scale weak interaction

QM EOS (Farhi et al. 84, Fischer et al. 10) MIT Bag Model Larger Bag constant ⇒ softer Larger Strong Coupling Constant α ⇒ stiffer

Parameters in QM EOS ↑ 𝑵 𝒏𝒃𝒚 < ２ 𝑵 𝒕𝒗𝒐 → NS matter (𝝇 𝟏 ) critical 𝑪 𝟐/𝟓 MeV ↑ Ｅｎｄｏｔｈｅｒｍｉｃ (Shen & 𝝇 𝟏 ) 2QM@P=0 ＜ 934MeV → PNS matter (𝝇 𝟏 ) clitical (HM) ← α = 𝜌 2 (1 − 𝑏)

Model Shock Induced case  eq df f f  eq  df f f s s s u  s s s u   dx • 1D Steady flow dx Const. ・ Conservation Eq. of Const. Hydrodynamics with viscos terms Const. • β equilibration ( 𝝊 = 𝟐𝟏 −𝟗 s ) ・ PNS H Ｍ ・ＱＭ (T.Fischer 10) (Shen ＥＯＳ ’11) 𝑍 𝑚𝑓𝑞 = 0.3 Bag Model （ B:Bagconstant ）＋     14 3 T 10 MeV 3 10 g / cm Strong interaction(α: coupling c.) i i ・ Mixed Phase in the front ・ Volume Fraction of QM and HM QM: HM= r : （ 1-r ） ・ Global Charge Neutrality

d u Complete- n Deconfinement Case De ase e p s 𝑪 𝟐/𝟓 = 𝟐𝟓𝟏 MeV 𝝃 𝜷 𝒕 = 𝟏. 𝟓 𝑵 𝒋 = 𝟒. 𝟏 ① shock compression Mixed phase ⇒ HM(x<6) ② deconfinement starts @x~6 HM& 2QM P ③ deconfinement n b finishes @x~9 2QM Ｔ T[MeV] ④ 3QM toward β eq. (9<x<20) 3QM X (typical length of weak interaction)

In Incomplete- n p Deconfinement Case De ase 𝑪 𝟐/𝟓 = 𝟐𝟓𝟏 MeV e d 𝜷 𝒕 = 𝟏. 𝟕 𝑵 𝒋 = 𝟒. 𝟏 ν u ① shock compression s HM(x<7.5) ② deconfinement starts @x~7.5 HM& 2QM ③ shock compression stop and s quarks P appear @ （ x~12 ） n b ③ deconfinement finishes Ｔ @x~12 3QM ④ 3QM toward β eq. (18<x<30) 3QM

2, Model diffusion induced case  eq df f f  s s s u  • 1D Steady flow （ local analysis ） dx Const. • Conservation Eq. of Hydrodynamics Const. • Diffusion Equation of Strange quarks Const. ・ PNS H Ｍ ・ＱＭ (T.Fischer 10) (Shen ＥＯＳ ’11) 𝑍 𝑚𝑓𝑞 = 0.3 Bag Model （ B:Bagconstant ）＋ 0     14 3 T 10 MeV 3 10 g / cm Strong interaction(α: coupling c.) 0 ・ Mixed Phase in the front ・ Volume Fraction of QM and HM QM: HM= r : （ 1-r ） ・ Global Charge Neutrality

Result lt ( 𝑪 𝟐/𝟓 = 𝟐𝟓𝟏 MeV 𝜷 𝒕 = 𝟏. 𝟓 ) ｘ =0 start of deconfinemet x~0.5 end of deconfinement x>0.5 equilibration to 3QM d p n 𝑣 𝑗 = 2.3 ∗ 10 4 cm/s u e s 𝝃 X (typical length of weak decay)

Result lt :E :Evolu lution of of component in in th the fr front ( 𝑪 𝟐/𝟓 = 𝟐𝟓𝟏 MeV 𝜷 𝒕 = 𝟏. 𝟓 ) Endothermic Exothermic 𝑪 𝟐/𝟓 = 𝟐𝟓𝟏 MeV 𝜷 𝒕 = 𝟏. 𝟓 𝑪 𝟐/𝟓 = 𝟐𝟑𝟔 MeV 𝜷 𝒕 = 𝟏. 𝟗 Normalized Pressure final initial final Normalized Volume Both cases show weak deflagrations

STABILITY OF THE COMBUSTION FRONT 𝜷 = 𝝇ash/𝝇fuel <1 exothermic 𝝇fuel >1 endothermic g 𝝇ash combustion front x gravity surface effect α<1 exothermic ⇒ ω real part>0 (σ=0) ⇒ unstable (previous works) α >1 endothermic ⇒ ω real part<0 (any σ) ⇒ stable （ our work ） 3D simulation in Exothermic regime (Pagliara ’13) ⇒ spherical propagation in endothermic?

Summary We have cleared the structure of combustion front. ● The type of combustion ・ diffusion induced case: weak deflagration ・ shock induced case: strong detonation ● Even in Endothermic Case, Combustion can take place !! ・ Conversion front of deflagration is stable in Endothermic Case ● There are some conversion patterns ・ Complete- or Incomplete- deconfinement Future Works ・ dependence of Surface tension, EoS of HM （ underway ） ・ Conversion from Hyperonic to 3QM and 3QM to HM ・ Dynamical Simulation from NS to QS.

EOS dependence Stiff medium 転位点 Soft Deconfinement Starts Initial

Dif iffusion Constant Dependence Ｔ u 𝒗 𝒋 ∝ 𝑬 ∝ 𝝂/𝑼 Front velocities are highly dependent on T & ρ

ＥＯＳ dependence soft fs0=0.1 fs0=0.2 stiff 𝒗 𝒋 ~𝟓. 𝟒 × 𝟐𝟏 𝟓 cm/s for fs=0.1 𝒗 𝒋 ~𝟐𝟐. 𝟕 × 𝟐𝟏 𝟓 cm/s for fs=0.2 .Combustion velocity depends on Fraction of Strangeness at x=0.

Relativistic scheme 𝑪 𝟐/𝟓 = 𝟐𝟓𝟏 MeV , 𝜷 𝒕 = 𝟏. 𝟕 𝐛𝐨𝐞 𝑵 𝒋 = 𝟑. 𝟔 Non- rela Rela