Transcript Cooling of a Compact Star with LOFF matter core

An Astrophysical Application of
Crystalline Color Superconductivity
Roberto Anglani
Physics Department - U Bari
Istituto Nazionale di Fisica Nucleare, Italy
SM&FT 2006
XIII workshop on Statistical Mechanics and non
perturbative Field Theory
Direct and Modified URCA processes
Neutrino emission due to direct URCA process is the most efficient
cooling mechanism for a neutron star in the early stage of its lifetime.
In stars made of nuclear matter only modified URCA processes can
take place [1] because the direct processes n → p + e +  and e + p → n
+  are not kinematically allowed.
If hadronic density in the core of neutron stars is sufficiently large,
deconfined quark matter could be found. Iwamoto [2] has shown that in
quark matter direct URCA process, d → u + e +  and e + u → d +  are
kinematically allowed, consequently this enhances drammatically the
emissivity and the cooling of the star
[1] Shapiro and Teukolski,
White Dwarfs, Black Holes and
Neutron Stars. J.Wiley (New York)
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[2] Iwamoto, Ann. Phys. 141 1 (1982)
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Color Superconductivity in the CS core
Aged compact stars T < 100 KeV
TCS is of order of 10-20 MeV:.
Matter in the core could be in one of the
possible Color Superconductive phases
Relevant density for
compact stars: not
asymptotic!
effects due to the strange
quark mass ms must be
included.
Asymptotical densities: Color-FlavorLocked phase is favored. But direct
URCA
processes
are
strongly
suppressed in CFL phase because
thermally excited quasiquarks are
exponentially rare.
β – equilibrium
Color neutrality
Electrical neutrality
a mismatch between Fermi
momenta of different quarks
depending on the in-medium
value of ms.
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GROUND STATE
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??????????????
The Great Below of gapless phases
μ
Asymtptotia Temple
Great below of GAPLESS phases
T=0
CHROMOMAGNETC INSTABILITY DANGER
Huang and Shovkovy, PR D70 051501 (2004)
Casalbuoni, et al., PL B605 362 (2005)
Fukushima, PR D72 074002 (2005)
AlforD and Wang, J. Phys. G31 719 (2005)
BUT THERE IS SOMETHING THAT MAY ENLIGHT THE WAY
Ciminale, et al., PL B636 317 (2006)
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Simplified models of toy stars
Noninteracting nuclear matter
3
LOFF matter
n ~ 9 n0
Normal quark matter
n ~ 9 n0
2
n ~ 1.5 n0
5 km
10 km
n0 = 0.16 fm-1
M = 1.4 MO.
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1
5 km
10 km
Noninteracting
nuclear matter
12 km
- n(U~Bari)
1.5 n0
Anglani
Alford and Reddy
nucl-th/0211046
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Dispersion laws for (rd – gu) and (rs – bu)
1. LOFF phase is
gapless
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2. Dispersion laws
around gapless
modes could be
considered as6/12
linear
“The importance of being gapless”
The contribution of gapped modes
are exponentially suppressed
since we work in the regime
Bari, SMFT 20.IX.06 T<<D<<m
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Each gapless
mode contributes
to specific heat by
a factor ~ T 7/12
Neutrino Emissivity
We consider the following b – decay process
(1)
for color a = r, g, b.
Neutrino emissivity = the energy loss by b-neutrino emission per
volume unit per time unit.
Neutrino Energy
(2)
Electron capture
process
Thermal distributions
Bogoliubov coefficients
Transition rate
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Cooling laws
(1)
t < ~1 Myr
t > ~1Myr
main mechanism is neutrino
emission
main mechanism is photon
emission
NUCLEAR
matter
[Shapiro]
LOFF
matter
UNPAIRED Q.
matter
[Iwamoto]
-Luminosity
~ T8
~ T6
~ T6
Specific Heat
~T
~T
~T
g-Luminosity
~ T2.2
~ T2.2
~ T2.2
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Results
A star with LOFF matter core cools faster than a star
made by nuclear matter only.
REM.: Similarity between LOFF and unpaired quark matter follows from linearity of gapless dispersion laws : ε~T6
SMFT
20.IX.06
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(U Bari)
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cV ~T. Bari,
Normal
quark
matter curve: only for comparison
between
different models.
Conclusions
1. We have shown that due to existence of gapless mode in the LOFF
phase, a compact star with a quark LOFF core cools faster than a
star made by ordinary nuclear matter only.
2. These results must be considered preliminary. The simple LOFF
ansatz should be substituted by the favored more complex crystalline
structure [Rajagopal and Sharma, hep-ph/0605316].
3. In this case (2.) identification of the quasiparticle dispersion laws is a very
complicated task but probable future work. For this reason it is also
difficult to attempt a comparison with present observational data.
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Acknowledgments
Thanks to
M. Ruggieri, G. Nardulli and M. Mannarelli for the fruitful
collaboration which has yielded the work hep-ph/0607341,
whose results underlie
the present talk
In these matters the only certainty is
that nothing is certain.
PLINY THE ELDER
Roman scholar and scientist (23 AD - 79 AD)
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A look at the HOT BOTTLE
Alford et al.
[astro-ph/0411560]
Lg ~ T2.2
cV ~ D0.5T0.5
Lg ~ T2.2
cV ~ T
P1bu P2bu
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LOFF3 Dispersion laws
Every quasiquark is a mixing of coloured quarks, weighted by Bogolioubov
– Valatin coefficients. “Coloured” components of quasiparticles can be
easily found in the sectors of Gap Lagrangean in an appropriate color-flavor
basis.
Sector 123
g
ru
det S
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–1
d
=0
Sector
45
bs
Rd
gu
Sector
67
rs
Ref. prof. Buballa
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bu
Sector
89
gs
bd
Dispersion laws
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Larkin-Ovchinnikov-Fulde-Ferrel state of art
The simplified ansatz crystal structure is
Larkin and
Ovchinnikov; Fulde
and Ferrell (1964)
(1)
i, j = 1, 2, 3 flavor indices; a, b = 1, 2, 3 color indices; 2qI represents the
momentum of Cooper pair and D1, D2, D3 describe respectively d – s, u – s,
u – d pairings.
LOFF phase has been found energetically favored [1,2] with respect to
the gCFL and the unpaired phases in a certain range of values of the
mismatch between Fermi surfaces. [Ref. Ippolito’s talk and Buballa’s lecture].
[1] Casalbuoni, Gatto et al., PL B627 89 (2005)
[2] Rajagopal et al., hep-ph/0603076
This phase results chromomagnetically stable [3]
[3] Ciminale, Gatto et al., PL B636 317 (2006)
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Neutral LOFF quark matter - 1
1. Three light quarks u, d, s, in a color and electrically neutral state
2. Quark interactions are described employing a Nambu-Jona Lasinio
model in a mean field approximation
[1] Casalbuoni et al.,
PL B627 89 (2005)
3. We employ a Ginzburg-Landau expansion [1]
Requiring color and electric neutrality, the energetically favored phase
results in
(1)
D1 = 0; D2 = D3 = D < 0.3 D0 [1]
Rajagopal et al.,
hep-ph/0605316
where D0 is the CFL gap.
The GL approximation is reliable in a region close to the second order
phase transition point where the crystal structure is characterized by
(2)
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q2=q3=q = m2s/(8 m zq); zq ~ 0.83 [1]
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Neutral LOFF quark matter - 2
To the leading order approximation in dm/m one obtains
[1] Casalbuoni,
Gatto, Nardulli et al.,
m3 = m8 = 0 and me=ms2/4m
hep-ph/0606242
[1]
The LOFF phase is energetically favored with respect to gCFL and
normal phase in the range of chemical potential mismatch of
(1)
y = ms2/m  [130,150] MeV
(2)
Finally, for our numerical estimates we use
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D0 = 25 MeV
(3)
m = 500 MeV
(4)
y = 140 MeV
(5)
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Dispersion laws for (ru – gd – bs)
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Appendix A: Emissivity
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Appendix B: Specific Heat
μ = 500 MeV; ms = (μ 140)1/2 MeV;
D1 = 0; D2 = D3 = D ~ 6 MeV.
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Appendix C: Dispersion laws
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Appendix D: Dispersion laws 3X3
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Appendix E: Cooling laws
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Appendix F: Redifinition of gapless modes
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