hovik grigorian, - Объединенный институт ядерных...

CONSTRAINTS FOR PROPARTIES OF NUCEAR MATTER

FROM NEUTRON STAR COOLING

Hovik Grigorian,Rostock University & Yerevan State University

•General schem for cooling simula-tions

•Compact object

•Temperature-Age diagram

•Observational Constraints

HOVIK GRIGORIAN

DUBNA , JULY-AUGUST 2005

QCD PHASE DIAGRAM & COMPACT STARS

Quark Matter

Novae

AGS Brookhaven

SIS Darmstadt

CERN-SPS

Super-

Quark-Gluon-PlasmaC

ON

FIN

EM

EN

T

1 3

[T =

140 M

eV]

H

[n =0.16 fm ]ο

1.5

0.1

-3

DECONFINEMENT

FAIR (Project)

RHIC, LHC (construction)

Hadron gas

Nuclear matter

QC

D -

Lat

tice

Gau

ge

Th

eory

Neutron / Quark Stars

Baryon Density

Tem

per

ature

Big Bang

Heavy Io

n Collis

ions

COLOR SUPERCONDUCTIVITY

Transport Properties,

Dense QCD / Nuclear Matter

EoS and NS constraints

Cooling Code Obs. Data

NS configurations

Microscopic Approach to

Pairing Gaps

Neutrino Emissivities,

HOVIK GRIGORIAN


COOLING OF A NEUTRON STAR

0 1 2 3 4 5 6 7

log(t[yr])

5.6

5.8

6

6.2

6.4

log

(Ts [K

])

RX

J0

82

2-4

3

1E

12

07

-52

RX

J0

00

2+

62

PS

R 0

65

6+

14

PS

R 1

05

5-5

2R

X J

18

65

-37

54

Vela

Gem

ing

a

PS

R J

02

05

+6

4 i

n 3

C5

8

Cra

b

0.5011.0001.4001.4801.8391.8401.8411.930

Normal Cooling for HJ EoSour crust, without medium effects

Evolution of the surface temperature Ts of ahadronic star

dU

dt=

∑i

CidT

dt= −εγ −

∑j

εjν

Data taken from:Yakovlev et al.,A & A 389 (2002) L24;

Calculation:D. Blaschke, H. Grigorian and D. N. Voskre-sensky, Astron. Astrophys. 424 (2004) 979.

HOVIK GRIGORIAN


BOLTZMANN EQUATION IN CURVED SPACE - TIME

The Boltzmann equation for massless particlesLindquist, R.W. 1966, Ann. Phys., 37, 478

pβ

(∂f

∂xβ− Γα

βγpγ ∂f

∂pα

)=

(df

dτ

)coll

(1)

• f is the invariant neutrino distribution function

• pα is the neutrino 4-momentum

• Γαβγ are the Christoffel symbols for the metric

ds2 = −e2φdt2 + e2Λdr2 + r2dθ2 + r2 sin2 θ dΦ2 (2)

The BE in the comoving basis

pb

(eβb

∂f

∂xβ− Γa

bcpc ∂f

∂pa

)=

(df

dτ

)coll

(3)

The non-zero Ricci coefficients are

Γ100 = Γ0

01 = e−φe−Λ

(∂(γeφ)

∂r+

∂(γveΛ)

∂t

), Γ0

11 = Γ110 = e−φe−Λ

(∂(γeΛ)

∂t+

∂(γveφ)

∂r

),

Γ220 = Γ0

22 = Γ330 = Γ0

33 = −vΓ122 = vΓ2

21 = −vΓ133 = vΓ3

31 =γve−Λ

r, Γ2

33 = −Γ332 = −cot θ

r. (4)

HOVIK GRIGORIAN


HEAT TRANSPORT AND NEUTRINO DIFFUSION

The neutrino 4-momentum is

pa =(ω, ωµ, ω(1− µ2)

1/2cos Φ, ω(1− µ2)

1/2sin Φ

)

•µ is the cosine of the angle between the neutrino momentum and the radial direction

•ω is the neutrino energy in a comoving frame

The BE in the spherically symmetric case

ω(et0 + µet

1)∂f

∂t+ ω(er

0 + µer1)

∂f

∂r− ω2

(µΓ1

00 + µ2Γ110 + (1− µ2)Γ2

20

)∂f

∂ω

− ω(1− µ2)(Γ1

00 + Γ122 + µΓ1

10 − µΓ220

)∂f

∂µ=

(df

dτ

)coll

. (5)

Applying the operator to equation (5) and defining the ith momentThorne, K. S. 1981, MNRAS 194, 439

1

2

∫ +1

−1

dµ µi , i = 0, 1, 2, · · · , Mi =1

2

∫ +1

−1

dµ µif, Qi =1

2

∫ +1

−1

dµ µi

(df

dτ

)coll

.

HOVIK GRIGORIAN



Let us introduce Nν, Fν, and SN are the number density, number flux and number source term,respectively, while Jν, Hν, Pν, and SE are the neutrino energy density, energy flux, pressure,and the energy source term:

Nν =

∫ ∞

0

dω

2π2M0ω

2 , Fν =

∫ ∞

0

dω

2π2M1ω

2 , SN =

∫ ∞

0

dω

2π2Q0ω (6)

Jν =

∫ ∞

0

dω

2π2M0ω

3 , Hν =

∫ ∞

0

dω

2π2M1ω

3 , Pν =

∫ ∞

0

dω

2π2M2ω

3 , SE =

∫ ∞

0

dω

2π2Q0ω

2 . (7)

• integrating over the neutrino energy

• utilizing the continuity equation

• assumption of a quasi-static evolution

The neutrino transport equation Burrows, A., & Lattimer, J. M. 1986, ApJ, 307, 178

∂(Nν/nB)

∂t+

∂(eφ4πr2Fν)

∂a= eφSN

nB

∂(Jν/nB)

∂t+ Pν

∂(1/nB)

∂t+ e−φ∂(e2φ4πr2Hν)

∂a= eφSE

nB

HOVIK GRIGORIAN



The distribution function in the diffusion approximation:

f(ω, µ) = f0(ω) + µf1(ω) , f0 = [1 + e(ω−µν

kT )]−1 (8)

• f0 is the distribution function at equilibrium (T = Tmat, µν = µeqν )

•ω and µν are the neutrino energy and chemical potential

The moments Mi of f are

M0 = f0 , M1 =1

3f1 , M2 =

1

3f0 , and M3 =

1

5f1 . (9)

The equation (??) is now

e−Λ

(∂f0

∂r− ω

∂φ

∂r

∂f0

∂ω

)= 3

Q1

ω. (10)

The collision term Q1 can be represented as(df

dτ

)coll

= ω

(ja(1− f)− f

λa+ js(1− f)− f

λs

)(11)

• ja is the emissivity

• λa is the absorptivity

• js and λs are the scattering contributions

HOVIK GRIGORIAN



The explicit form of the diffusion coefficient D

D(ω) =

(j +

1

λa+ κs

1

)−1

. (12)

Using the relation (ην = µν/T is the neutrino degeneracy parameter)

∂f0

∂r= −

(T

∂ην

∂r+

ω

T

∂T

∂r

)∂f0

∂ω, (13)

we obtain

f1 = −D(ω)e−Λ

[T

∂η

∂r+

ω

Teφ

∂(Teφ)

∂r

](− ∂f0

∂ω

). (14)

Now the energy-integrated lepton and energy fluxes are

Fν = − e−Λe−φT 2

6π2

[D3

∂(Teφ)

∂r+ (Teφ)D2

∂η

∂r

]

Hν = − e−Λe−φT 3

6π2

[D4

∂(Teφ)

∂r+ (Teφ)D3

∂η

∂r

]. (15)

HOVIK GRIGORIAN



The coefficients D2, D3, and D4 are defined through (x = ω/T )

Dn =

∫ ∞

0

dx xnD(ω)f0(ω)(1− f0(ω)) ,

The explicit expression for the absorption mean free path

1

λa=

G2F

π2

∫ ∞

0

dEe E2e [1− feq(Ee)]

∫ +1

−1

d cos θ(cos θ − 1)

1− e−z[AR1 + R2 + BR3] (16)

Routs = 4G2

F

(cos θ − 1)

1− e−z[AR1 + R2 + BR3] (17)

The polarization functions

R1 = (V2 +A2) [Im ΠRL(q0, q) + Im ΠR

T (q0, q)] (18)

R2 = (V2 +A2) Im ΠRT (q0, q)−A2 Im ΠR

A(q0, q) R3 = 2VA Im ΠRV A(q0, q) . (19)

• V = CgV and A = CgA for the absorption, C is the Cabibbo factor

• V = gV /2 and A = gA/2 for the scattering

To include all six neutrino types, one can redefine the diffusion coefficients

D2 = Dνe2 + Dνe

2 , D3 = Dνe3 −Dνe

3 , D3 = Dνe4 + Dνe

4 + 4Dνµ

4 . (20)

HOVIK GRIGORIAN


HOT NEUTRON AND QUARK STAR EVOLUTION

Using the equation for the electron fraction and the matter energy equation

∂Ye

∂t= −eφSN

nB, YL =

Nν

nB+ Ye (21)

d(E/NB)

dt+ P

d(V/NB)

dt= −eφSN

nB(22)

Teφ∂s

∂t+ µνe

φ∂YL

∂t+

∂(e2φ4πr2Hν)

∂a= 0 (23)

we obtain

∂Nν/nB

∂t+

∂Ye

∂t+

∂(eφ4πr2Fν)

∂a= 0 (24)

∂YL

∂t+

∂(eφ4πr2Fν)

∂a= 0 (25)

(26)

Fν = − e−Λe−φT 2

6π2

[D3

∂(Teφ)

∂r+ (Teφ)D2

∂η

∂r

]

Hν = − e−Λe−φT 3

6π2

[D4

∂(Teφ)

∂r+ (Teφ)D3

∂η

∂r

]. (27)

HOVIK GRIGORIAN


QUASI-EQUILIBRATE EVOLUTION OF COMPACT OBJECT

The structure equations are

∂r

∂a=

1

4πr2nBeΛ,

∂m

∂a=

ρ

nBeΛ(28)

∂φ

∂a=

eΛ

4πr4nB

(m + 4πr3P

), (29)

∂P

∂a= −(ρ + P )

eΛ

4πr4nB

(m + 4πr3P

)(30)

with the boundary conditions

r(a = 0) = 0; m(a = 0) = 0,

φ(a = as) =1

2log

[1− 2m(a = as)

r(a = as)

]; P (a = as) = Ps (31)

HOVIK GRIGORIAN


COOLING EVOLUTION WITHOUT NEUTRINO TRAPPING

• The flux energy per unit time l(r) through a spherical slice at distance r from the center is:

l(r) = −4πr2k(r)∂(T(r)eΦ)

∂re−Φ

√1− 2M

r.

The factor e−Φ√

1− 2Mr corresponds to the relativistic correction of the time scale and the

unit of thickness.

• The equations for energy balance and thermal energy transport are:

∂

∂NB(le2Φ) = −1

n(ενe

2Φ + cV∂

∂t(TeΦ))

∂

∂NB(TeΦ) = − 1

k

leΦ

16π2r4n

where n = n(r) is the baryon number density, NB = NB(r) is the total baryon number inthe sphere with radius r and

∂NB

∂r= 4πr2n

(1− 2M

r

)−1/2

D. Blaschke, H. Grigorian and D. N. Voskresensky, Astronomy and Astrophysics 368, 561 (2001).HOVIK GRIGORIAN


STELLAR MATTER UNDER COMPACT STAR CONDITIONSThe stellar matter including the quark core of compact stars consists of neutrons protons,up, down quarks, electrons and neutrinos in beta equilibrium and with the charge neutralitycondition.

• β-equilibrium n←→ p + e− + νe;–in nuclear matter

d←→ u + e− + νe–in quark matter

µn = µp + µe + µνe

µd = µu + µe + µνe

where µe, µνe are the electrons and the neutrino chemical potentials.

• Charge neutrality np − ne = 0: –in nuclear matter23nu − 1

3nd − ne = 0 –in quark matter

The contribution from the leptons should be added to the thermodynamical potential Ω q:

Ω(φ, ∆; µq, µI, µe, T ) = Ωq(φ, ∆; µq, µI, T ) + Ωe(µe, T ) + Ωνe(µνe, T )

HOVIK GRIGORIAN


PHASE TRANSITION:NUCLEAR MATTER −→ QUARK MATTER

• Walecka model (p,n,e)+(σ,ω) −→ Bag model (u,d,e)

• Maxwell construction: PHad = PQuark µHadB = µQuark

B

1000

ε[ MeV / fm3 ]

1

10

100

1000

P[

MeV

/ f

m3 ]

Nuclear MatterB

1/4= 220

B1/4

=200B

1/4 =190

B1/4

=180

EoS at T = 0 B1/4

[MeV]

1000 1250 1500 1750 2000µ

B[ MeV]

600

1200

1800

ε[ M

eV /

fm

3 ]

Walecka ModelBag Model, B

1/4=190 MeV

µ = 1472.5 MeV

HOVIK GRIGORIAN


EOS FOR QUARK STAR WITH SHELLPHASE TRANSITIONS

• In order to consider then quarkstars with a possible hadronicshell we made the phase tran-sition between the quark mat-ter EoS and a hadron EoS: lin-ear (LW) and nonlinear Waleckamodel (NLW).

• The phase transition is calculatedvia the Maxwell construction (Pconstant for equal µq)

HOVIK GRIGORIAN


CONFIGURATION OF COMPACT STARS WITHOUT SHELLCONDENSATE AND TEMPERATURE EFFECT

3 6 9n

B [n

0]

0

0.5

1

1.5

2

M [

Msu

n]

6 8 10R [km]

T = 0, ∆ = 0T = 0T = 40 MeVT = 60 MeV

Gaussian

The star configuration could be defined fromthe Tolman-Oppenheimer-Volkoff equations

dP

dr= −[ε(r) + P (r)][m(r) + 4πr3P (r)]

r[r − 2m(r)]

m = 4π

∫ r

0

r2ε(r)dr

The equations are solved for the set of cen-tral densities nq(0) for which the stars are sta-ble. The total mass M = m(r) of the star isdefined on the radius r so that P (r) = 0.The integral parameters M and R feel the ex-istence of the diquark condensation: the EoSbecames softer. Also are sensitive on tem-perature variations. Both are decresing thevalues of the Mmax and Rmax of the core ap-proximately 10% from their values of the T = 0

and ∆ = 0 cases.

HOVIK GRIGORIAN


STABILITY OF HADRONIC AND HYBRID STARS

•Mass - Radius relationGaussian model

• Lorentzian model

HOVIK GRIGORIAN


MASS DEFECT - ESTIMATION OF ENERGY

0.8

1

1.2

1.4

1.6

1.8

M [

Msu

n]

∆Μ(Α) = 0.06 Μsun ∆Μ(Β) = 0.09 Μ

sun

Mi(A) = 1.51 M

sun

Mi(B) = 1.51 M

sun

Mf(B) = 1.44 M

sun

Mf(B) = 1.42 M

sun

0 1 2 3 4 5n

B [n

0]

0.8

1

1.2

1.4

1.6

1.8

2

NB[N

sun]

Conserved NB(A) = 1.68 N

sun, N

B(B) = 1.57 N

sun

Gaussian

T = 0T = 0 , ∆ = 0T = 40 MeV, ∆ = 0T = 40 MeV

• During the cooling evolution thestar must loose an amount of en-ergy: the energy release will havean equivalent in a mass defect.We estimated this from the di-quark condensation as about 0.1

M. It corresponds to the esti-mated energy (∆/µ)2 1052 ergof the diquark condensate, seeRef. [*].

*D. K. Hong, S. D. Hsu and F. Sannino, Phys. Lett. B516,362 (2001).HOVIK GRIGORIAN


PNS EVOLUTION WITH NEUTRINO TRAPPING

νeν

T = 40 MeV

e

νe

νeνe

νe

νe

νe

νe

νe

νe

νeνe

νe

µ = 72 MeV

γ

γ

QM

γ

γ

γ

γγ

νe

νe

QM

νe

νe

νe

µ

νe

νe

νeνe

νeνe

νe

νe

νe

T > 1 MeV

γ

γ

γ

γ

γ

γγ

= 72 MeV

2SC νe

νe

νe

νe

µ

νe

νe

T = 0

νe

γ

γ

= 0

γ

γ

γ

γγ2SC

1.3

1.4

1.5

1.6

1.7

1.8

M [

Msu

n]

final state0.07 M

sun

µνe = 0

µνe = 72 MeV

µνe = 150 MeV

10 10.5 11 11.5 12 12.5 13n

q[n

0]

1.2

1.3

1.4

1.5

1.6

NB

[N

Bsu

n]

initial state A

initial state B

0.32 Msun

•Mass defect ∆M ∼ 0.05÷ 0.4 M ⇒ 1053 ÷ 1054

erg

•Effect due to Un-Trapping of (Anti-)Neutrinos

•Explosion possible: Phase transition 1st Order

•GRB with time delay⇒ Cannon Ball Model

D. N. Aguilera, D. Blaschke, H. Grigorian, arXiv:astro-ph/0212237HOVIK GRIGORIAN


NEUTRINO PROCESSES IN QUARK MATTER: EMISSIVITIES

• Quark direct Urca (QDU) the most efficient processesd→ u + e + ν and u + e→ d + ν

εQDUν 9.4× 1026αsuY

1/3e ζQDU T 6

9 erg cm−3 s−1,

Compression u = n/n0 2 , strong coupling αs ≈ 1

• Quark Modified Urca (QMU) and Quark Bremsstrahlung (QB)d + q → u + q + e + ν and q1 + q2 → q1 + q2 + ν + ν

εQMUν ∼ εQB

ν 9.0× 1019ζQMU T 89 erg cm−3 s−1.

• Suppression due to the pairingQDU : ζQDU ∼ exp(−∆q/T )

QMU and QB : ζQMU ∼ exp(−2∆q/T ) for T < Tcrit,q 0.4 ∆q

• e+ e→ e+ e+ ν+ ν

εeeν = 2.8× 1012 Y

1/3e u1/3T 8

9 erg cm−3 s−1,

becomes important for ∆q/T >> 1

-

u

e-

ν

d

u

u

e-

ν

d

-

u

D. BLASCHKE, H. GRIGORIAN, D.N. VOSKRESENSKY , ASTRON. & ASTROPHYS. 368 (2001) 561

FLOWERS, ITOH, APJ 250 (1981) 750; SCHAAB, VOSKRESENSKY, SEDRAKIAN, WEBER, WEIGEL, A & A 321 (1997)591

YAKOVLEV, LEVENFISH, SHIBANOV, PHYS. USP. 169 (1999) 825; BAIKO, HAENSEL, ACTA PHYS. POLON. B 30 (1999) 1097HOVIK GRIGORIAN


HADRON MATTER: PAIRING GAPS AND CRUST OF STARS

•Neutron and Proton pairing gaps

0.01 0.1 1

n / n0

0

0.5

1

1.5

2

∆ [

MeV

]

n 1S0

n 3P2

p 1S0

0.5 1 2 4n / n

0

0

0.03

0.06

∆3

P2 [

MeV

]

•Crust model

5.6 5.8 6 6.2 6.4 6.6 6.8 7 7.2

log10

(Ts[K])

7

7.5

8

8.5

9

9.5

log

10(T

in[K

])

M = 1. 4 MO

R = 10 km

slow decay (C)fast decay (E)light element rich

Yakovlev, D.G., Gnedin, O.Y., Kaminker, A.D., Levenfish, K.P., Potekhin, A.Y. 2003, [arXiv:astro-ph/0306143];Yakovlev,D.G., Levenfish, K.P., Potekhin, A.Y., Gnedin, O.Y., Chabrier, G., [arXiv:astro-ph/0310259]

Takatsuka, T., Tamagaki, R. 2004, [arXiv: nucl-th/0402011].HOVIK GRIGORIAN


HADRON MATTER: DU CRITICAL DENSITIES AND CRITICALMASSES OF STARS

•DU critical densitiesnc = 2.7 n0 non linear Walecka (NLW)nc = 5.0 n0 Heiselberg, Hjorth-JensonHHJ;

0 0.2 0.4 0.6 0.8 1 1.2

n [fm-3

]

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

n p

,e,µ

[fm

-3]

p - HHJe

-- HHJ

µ - HHJp - NLWe

- - NLW

µ − NLW

Charge Particles for WNL(250) & HJ(240) EoSDensities of protons electrons and muons

•DU critical massesMc = 1.25 M - NLWMc = 1.84 M - HHJ

9 10 11 12R [km]

0.5

1

1.5

2

M [

Msu

n]

HHJ, 240 MeVNLW 250 MeV

0.3 0.6 0.9 1.2 1.5

n(0) [fm-3

]

Heiselberg, H., Hjorth-Jensen, M. 1999, [arXiv:astro-ph/9904214]HOVIK GRIGORIAN


COOLING CURVES: HADRONS (NORMAL) STARS

• our fit for crust

0 1 2 3 4 5 6 7

log(t[yr])

5.6

5.8

6

6.2

6.4

log

(Ts [K

])

RX

J0822-4

3

1E

1207-5

2R

X J

0002+

62

PS

R 0

656+

14

PS

R 1

055-5

2R

X J

1865-3

754

Vel

a

Gem

inga

PS

R J

0205+

64 i

n 3

C58

Cra

b

0.5011.0001.4001.4801.8391.8401.8411.930

Normal Cooling for HJ EoSour crust, without medium effects

• including π -condensate and mediummodification of MU

0 1 2 3 4 5 6 7

log(t[yr])

5.6

5.8

6

6.2

6.4

log

(Ts [K

])

RX

J0822-4

3

1E

1207-5

2R

X J

0002+

62

PS

R 0

656+

14

PS

R 1

055-5

2R

X J

1865-3

754

Vel

a

Gem

inga

PS

R J

0205+

64 i

n 3

C58

Cra

b

0.5011.0001.2501.3201.4001.4801.7001.8391.8401.8411.930

Normal Cooling for HJ EoS our crust, with medium effects, π cond.

D. Blaschke, H. Grigorian, and D.N. Voskresensky, (2004). arXiv:astro-ph/0403170HOVIK GRIGORIAN


COOLING CURVES: HADRONS (SUPERCONDUCTING) STARS

• with AV18 gaps, π -condensate, MMU(3P2 - suppressed)

0 1 2 3 4 5 6 7

log(t[yr])

5.6

5.8

6

6.2

6.4

log

(Ts [K

])

RX

J0822-4

3

1E

1207-5

2R

X J

0002+

62

PS

R 0

656+

14

PS

R 1

055-5

2R

X J

1865-3

754

Vel

a

Gem

inga

PS

R J

0205+

64 i

n 3

C58

Cra

b

0.5011.0001.1001.2501.3201.4001.4801.6001.7001.7501.930

Cooling for HJ EoS (AV18)Our crust , with medium effects, 3P2*0.1 π cond

•with Gaps from Yakovlev at al. 2003

0 1 2 3 4 5 6 7

log(t[yr])

5.6

5.8

6

6.2

6.4

log

(Ts [K

])

RX

J0822-4

3

1E

1207-5

2R

X J

0002+

62

PS

R 0

656+

14

PS

R 1

055-5

2R

X J

1865-3

754

Vel

a

Gem

inga

PS

R J

0205+

64 i

n 3

C58

Cra

b

0.5011.0001.2501.3901.4001.4201.4431.4521.4801.7001.930

Cooling for HJ EoS our crust, with medium effects, π cond. 3P

2*0.1

H. Grigorian, and D.N. Voskresensky, (2005). arXiv:astro-ph/0501678HOVIK GRIGORIAN


COOLING CURVES: HADRONS (SUPERCONDUCTING -ANOMALIES ) STARS

• with AV18 gaps, π -condensate, MMU(3P2 - is NOT suppressed)

0 1 2 3 4 5 6 7

log(t[yr])

5.6

5.8

6

6.2

6.4

log

(Ts [K

])

RX

J0822-4

3

1E

1207-5

2R

X J

0002+

62

PS

R 0

656+

14

PS

R 1

055-5

2R

X J

1865-3

754

Vel

a

Gem

inga

PS

R J

0205+

64 i

n 3

C58

Cra

b0.5011.0001.2501.3201.4001.6001.750

Cooling for HJ EoS (AV18)Our crust , with medium effects

•with Gaps from Yakovlev at al. 2003

0 1 2 3 4 5 6 7

log(t[yr])

5.6

5.8

6

6.2

6.4

log

(Ts [K

])

RX

J0822-4

3

1E

1207-5

2R

X J

0002+

62

PS

R 0

656+

14

PS

R 1

055-5

2R

X J

1865-3

754

Vel

a

Gem

inga

PS

R J

0205+

64 i

n 3

C58

Cra

b

1.0001.1001.3201.3701.3901.4001.4201.4331.452

Cooling for HJ EoS our crust, with medium effects, π cond.

D. Blaschke, H. Grigorian, and D.N. Voskresensky, (2004). arXiv:astro-ph/0403170HOVIK GRIGORIAN


HYBRID STAR MODEL WITH 2SC QUARK MATTER CORE

• Density dependent Bag Pressurefor Separable Model (SM)

1000 1200 1400 1600 1800 2000

µB [MeV]

0

50

100

150

B =

Pid

-P [

MeV

/fm

3]

Ideal gasB

0

GAUSSLORNJL

G2/G1 = 1

•Critical masses for phase transitionMc = 1.2 M HHJ - INCQM (Gaus-sian)with 2SCMc = 1.82 M - without 2SC

9 10 11 12R [km]

0.8

1

1.2

1.4

1.6

1.8

2

M [

Mo]

EXO 0748-676 (z=0.35)

HHJ - INCQM with 2SC’HHJ - INCQM without 2SCHHJ - INCQM with 2SCHHJ RX J 1856-3754

H. Grigorian , D. Blaschke , D.N. Aguilera. Phys.Rev.C 69 (2004) 065802 [arXiv:astro-ph/0303518]HOVIK GRIGORIAN


TEMPERATURE EVOLUTION IN THE INTERIOR OF THE STAR

0 5 10 15 20

Radius in km

0

0.02

0.04

0.06

0.08

0.1

0.12 ∆ = 0

∆ = 0.1 MeV

∆ = 50 MeV

0

0.02

0.04

0.06

0.08

0.1

0.120

0.02

0.04

0.06

0.08

0.1

0.12

t = 1 sect = 1 mint = 5 mint = 2 hourst = 5 hourst = 10 hourst = 1.5 dayst = 0.1 yeart = 1 yeart = 3 yearst = 4 yearst = 6 years

Temperature profiles in MeV

HOVIK GRIGORIAN


COOLING CURVES: HYBRID STARS WITH 2SC QUARKMATTER

• 2SC + X phase, ∆X = 100 keV

0 1 2 3 4 5 6 7

log(t[yr])

5.6

5.8

6

6.2

6.4

log

(Ts [K

])

RX

J0822-4

3

1E

1207-5

2R

X J

0002+

62

PS

R 0

656+

14

PS

R 1

055-5

2R

X J

1865-3

754

Vel

a

Gem

inga

PS

R J

0205+

64 i

n 3

C58

Cra

b

0.501.101.21 critical1.251.321.501.221.71.79

Cooling of Hybrid stars with 2SC Quark coreHJ (Y - 3P2*0.1) with K = 240 MeV with Med. effects, our crust, Gaussian FF

• 2SC + X phase, ∆X = 30 keV

0 1 2 3 4 5 6 7

log(t[yr])

5.6

5.8

6

6.2

6.4

log

(Ts [K

])

RX

J0822-4

3

1E

1207-5

2R

X J

0002+

62

PS

R 0

656+

14

PS

R 1

055-5

2R

X J

1865-3

754

Vel

a

Gem

inga

PS

R J

0205+

64 i

n 3

C58

Cra

b

0.501.101.21 critical1.221.231.251.421.651.71.79


Blascke, Voskresensky, Grigorian, [arXiv:astro-ph/0403171],HOVIK GRIGORIAN


COOLING CURVES: HYBRID STARS WITH 2SC QUARKMATTER

• 2SC + X phase, ∆X = 1.0Exp(−α(1− µ/µc)) MeV

1 2 3 4 5 6 7

log(t[yr])

5.6

5.8

6

6.2

6.4

log

(Ts [K

])

RX

J0822-4

3

1E

1207-5

2R

X J

0002+

62

PS

R 0

656+

14

PS

R 1

055-5

2R

X J

1865-3

754

Vel

a

Gem

inga

PS

R J

0205+

64 i

n 3

C58

Cra

b

CTA 1

1.0001.1001.214 critical1.2481.3231.4201.4961.5971.6411.7061.793


• the gaps in hadron shell by TT and Yak.

0 1 2 3 4 5 6 7

log(t[yr])

5.6

5.8

6

6.2

6.4

log

(Ts [K

])

RX

J0822-4

3

1E

1207-5

2R

X J

0002+

62

PS

R 0

656+

14

PS

R 1

055-5

2R

X J

1865-3

754

Vel

a

Gem

inga

PS

R J

0205+

64 i

n 3

C58

Cra

b

0.501.101.21 critical1.251.321.381.421.51.61.651.71.751.793


H. Grigorian, D. Blaschke, and D.N. Voskresensky, (2004) [arXiv:astro-ph//0411619];H. Grigorian (2005) [arXiv:astro-ph/0502576];

HOVIK GRIGORIAN


SELECTION OF SCENARIO WITH BRIGHTNESS CONSTRAINT

5.6

5.8

6

6.2

6.4

log(T

s [K])

5.6

5.8

6

6.2

6.4log

(Ts [K

])

0 1 2 3 4 5 6

log(t[yr])

5.6

5.8

6

6.2

6.4

log(T

s [K])

1.101.211.41

0 1 2 3 4 5 6 7

log(t[yr])

models IV & VI model IX

model III model I

model VIII

model VII

Class of model Models Models Gapswith π-condensate without π-condensate

A I IX Tsuruta law n-3P2*0.1B III IV & VIa Yakovlev et al. :2003 n-3P2*0.1B’ VII - p-1P0*0.5; n-3P2*0.1B” VIII - p-1P0*0.2; n-1P0*0.5; n-3P2*0.1

aThe model VI is the same as model IV, which was already calculated with crust (E) in Ref. D. Blaschke, H. Grigorian and D. N. Voskresensky, Astron. Astrophys. 424 (2004)979.

H. Grigorian, [arXiv:astro-ph/0507052]HOVIK GRIGORIAN

SELECTION OF SCENARIO WITH LOGN-LOGS CONSTRAINT

The mass distribution Simulation for model IX (test pass: positive)

Log N-Log S of isolated neutron stars is effective in discriminating among cooling models.S. Popov, H. Grigorian, R. Turolla and D. Blaschke arXiv:astro-ph/0411618 (2004).

HOVIK GRIGORIAN


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