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

Hydrodynamical study on the conversion of hadronic matter to quark matter 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

Shock Induced Conversion

• Phys. Rev. D 93, 043018 (2016)

Diffusion Induced Conversion

• Phys. Rev. D 93, 043019 (2016)

In Introduction: Quark Stars

Neutron Stars Strange quark Stars

u d d s u d

HM：neutrons, protons (confined quarks) QM :deconfined quarks (up, down, strange)

HM 3 quarks are confined p=uud n=udd 3QM

Pure quark stars

3QM

Hybrid stars ・Mass Radius Relations ・different cooling curves ・Quark Nova (𝟐𝟏𝟔𝟒 erg neutrinos are emitted)

Co Combu bustio ion to to S SQM

Ａ Shock induced Case HＭ ⇒ 2QM ⇒ SQM B Diffusion induced Case HM⇒SQM with small strangeness ⇒ SQM

HM 2QM

u d d u d d

SQM

s u d

Energy

C,O ⇒Ni𝟔𝟕 (Type Ia SNe） C+O2 ⇒ CO2 （Terrestrial combustion） ash P

Ａ B

Gibbs Energy

HM 2QM SQM

Fuel

Transition point

HM 2QM

u d d u d d

SQM

s u d

Fuel ash

• A. Shock induced Case

・Spin Down of (P)NS ・Accretion on (P)NS ・Merger of compact stars HM

u d d u d d

SQM

s u d

Fuel ash

• B. Diffusion induced Case

・Following Shock induced ・Capture of strangelets SQM with minimum strangeness

s d u u s d u d d

HM SQM HM

HM 2QM

u d d u d d

SQM

s u d

Fuel ash

2QM SQM HM Shock induced Case Center Surface

HM SQM HM

HM

u d d u d d

SQM

s u d

Fuel ash

SQM with minimum strangeness SQM HM Diffusion induced Case SQM with minimum strangeness

s d u u s d u d d

Center Surface

Combustion modes

P1 1/ρ1 1/ρ1 a b c d e f

Hugoniot curve

a

P0 1/ρ0

c d f

1/ρ0 P0

P1 Exothermic (terrestrial case) (Previous works) Endothermic (Our works)

a: strong detonation c: weak detonation

1 1 s

c u 

1 1 s

c u 

1 1 s

c u 

s

c u 

s

c u 

d: weak deflagration f: strong deflagration

1 1 s

c u 

1 1 s

c u 

b,e: Jouget point

Initial state

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.

p+n s

Initial State （HM） Final state （３QM）

?

u d

Pagliara ‘13

・ Endoth therm rmic case is neglec ecte ted in referen rence ce to terrest stria rial l combus ustio tion

Herzog ‘11

exo. endo.

Motivation o

• f

f Our works:

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

• n.

x Strong interaction weak interaction

p+n d u s

Time Scale

Initial State （HM） Final state （３QM） Pr Previ 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

• n.

.

QM EOS (Farhi et al. 84, Fischer et al. 10)

MIT Bag Model Larger Bag constant ⇒softer Larger Strong Coupling Constant α ⇒stiffer

2QM@P=0 ＜934MeV (HM) ←

→PNS matter(𝝇𝟏) clitical →NS matter (𝝇𝟏) critical ↑ 𝑵𝒏𝒃𝒚<２𝑵𝒕𝒗𝒐

Parameters in QM EOS 𝑪𝟐/𝟓 MeV

α

=𝜌

2 (1 − 𝑏)

↑Ｅｎｄｏｔｈｅｒｍｉｃ (Shen & 𝝇𝟏)

Model Shock Induced case

• 1D Steady flow

・Conservation Eq. of Hydrodynamics with viscos terms

• β equilibration (𝝊 = 𝟐𝟏−𝟗s)

・Mixed Phase in the front ・Volume Fraction of QM and HM QM: HM= r : （1-r） ・Global Charge Neutrality

・ＱＭ (T.Fischer 10)

Bag Model （B:Bagconstant）＋ Strong interaction(α: coupling c.)

・PNS HＭ

(Shen ＥＯＳ ’11)

3 14

/ 10 3 cm g

i

   MeV 10 

i

T

𝑍

𝑚𝑓𝑞 = 0.3



s eq s s

f f dx df u  

Const. Const. Const.



s eq s s

f f dx df u  

P Ｔ T[MeV]

①shock compression HM(x<6) ②deconfinement starts @x~6 HM& 2QM ③deconfinement finishes @x~9 2QM ④3QM toward β eq. (9<x<20) 3QM

Complete- De Deconfinement Case ase

𝑪𝟐/𝟓 = 𝟐𝟓𝟏 MeV 𝜷𝒕 = 𝟏. 𝟓 𝑵𝒋 = 𝟒. 𝟏

nb

X (typical length of weak interaction)

s e u 𝝃 p d n Mixed phase⇒

①shock compression HM(x<7.5) ②deconfinement starts @x~7.5 HM& 2QM ③shock compression stop and s quarks appear @（x~12） ③deconfinement finishes @x~12 3QM ④3QM toward β eq. (18<x<30) 3QM

In Incomplete- De Deconfinement Case ase

𝑪𝟐/𝟓 = 𝟐𝟓𝟏 MeV 𝜷𝒕 = 𝟏. 𝟕 𝑵𝒋 = 𝟒. 𝟏

s e u p d n ν P Ｔ nb

2, Model diffusion induced case

• 1D Steady flow（local analysis）
• Conservation Eq. of Hydrodynamics
• Diffusion Equation of Strange quarks

・Mixed Phase in the front ・Volume Fraction of QM and HM QM: HM= r : （1-r） ・Global Charge Neutrality

・ＱＭ (T.Fischer 10)

Bag Model （B:Bagconstant）＋ Strong interaction(α: coupling c.)

・PNS HＭ

(Shen ＥＯＳ ’11)

3 14

/ 10 3 cm g   

MeV T 10

0 

𝑍

𝑚𝑓𝑞 = 0.3



s eq s s

f f dx df u  

Const. Const. Const.

s e u 𝝃 p d n Result lt

(𝑪𝟐/𝟓 = 𝟐𝟓𝟏 MeV 𝜷𝒕 = 𝟏. 𝟓 )

ｘ=0 start of deconfinemet x~0.5 end of deconfinement x>0.5 equilibration to 3QM

𝑣𝑗 = 2.3 ∗ 104 cm/s X (typical length of weak decay)

Result lt :E :Evolu lution of

• f component in

in th the fr front (𝑪𝟐/𝟓 = 𝟐𝟓𝟏 MeV 𝜷𝒕 = 𝟏. 𝟓 ) Endothermic 𝑪𝟐/𝟓 = 𝟐𝟓𝟏 MeV 𝜷𝒕 = 𝟏. 𝟓 Exothermic 𝑪𝟐/𝟓 = 𝟐𝟑𝟔 MeV 𝜷𝒕 = 𝟏. 𝟗

Both cases show weak deflagrations

initial final final Normalized Volume Normalized Pressure

STABILITY OF THE COMBUSTION FRONT

𝝇ash 𝝇fuel 𝜷 = 𝝇ash/𝝇fuel <1 exothermic

>1 endothermic combustion front x

α<1 exothermic ⇒ ω real part>0 (σ=0) ⇒unstable (previous works) α>1 endothermic ⇒ω real part<0 (any σ) ⇒stable （our work） gravity surface effect 3D simulation in Exothermic regime (Pagliara ’13) ⇒spherical propagation in endothermic?

g

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.

Stiff Soft medium

EOS dependence

転位点

Deconfinement Starts Initial

Dif iffusion Constant Dependence

Ｔ u

𝒗𝒋 ∝ 𝑬 ∝ 𝝂/𝑼 Front velocities are highly dependent on T & ρ

stiff soft

ＥＯＳ dependence

𝒗𝒋~𝟓. 𝟒 × 𝟐𝟏𝟓 cm/s for fs=0.1 𝒗𝒋~𝟐𝟐. 𝟕 × 𝟐𝟏𝟓 cm/s for fs=0.2

.Combustion velocity depends on Fraction of Strangeness at x=0.

fs0=0.2 fs0=0.1

Relativistic scheme 𝑪𝟐/𝟓 = 𝟐𝟓𝟏 MeV , 𝜷𝒕 = 𝟏. 𝟕 𝐛𝐨𝐞 𝑵𝒋 = 𝟑. 𝟔

Rela Non- rela