An Astrophysical Application of Crystalline Color Superconductivity Roberto Anglani Physics...
-
Upload
lydia-garrick -
Category
Documents
-
view
217 -
download
2
Transcript of An Astrophysical Application of Crystalline Color Superconductivity Roberto Anglani Physics...
An Astrophysical Application of An Astrophysical Application of Crystalline Color Crystalline Color
SuperconductivitySuperconductivity
Roberto AnglaniRoberto AnglaniPhysics DepartmentPhysics Department - U- U BariBari
Istituto Nazionale di Fisica Nucleare, ItalyIstituto Nazionale di Fisica Nucleare, Italy
SM&FT 2006XIII workshop on Statistical Mechanics and non
perturbative Field Theory
Bari, SMFT 20.IX.06 Anglani (U Bari) 2/12
Direct and Modified Direct and Modified URCA processesURCA 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)
[2] Iwamoto, Ann. Phys. 141 1 (1982)
Bari, SMFT 20.IX.06 Anglani (U Bari) 3/12
Color Superconductivity in the CS coreColor Superconductivity in the CS core
Aged compact stars T < 100 KeVTCS is of order of 10-20 MeV:.
Asymptotical densities: Color-Flavor-Locked phase is favored. But direct URCA processes are strongly suppressed in CFL phase because thermally excited quasiquarks are exponentially rare.
Relevant density for compact stars: not
asymptotic!
Matter in the core could be in one of the possible Color Superconductive phases
effects due to the strange quark mass ms
must be included.
β – equilibrium
Color neutrality
Electrical neutralitya mismatch between Fermi
momenta of different quarks depending on the in-medium
value of ms.GROUND
STATE ??????????????
Bari, SMFT 20.IX.06 Anglani (U Bari) 4/12
The Great Below of gapless phasesThe Great Below of gapless phases
μAsymtptotia Temple
Great below of GAPLESS phases
CHROMOMAGNETC INSTABILITY DANGERHuang 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 WAYCiminale, et al., PL B636 317 (2006)
T=0
Bari, SMFT 20.IX.06 Anglani (U Bari) 5/12
Simplified models of toy starsSimplified models of toy stars
5 km
10 km 10 km
5 km
Normal quark matter n ~ 9 n0
LOFF matter n ~ 9 n0
Noninteracting nuclear matter
12 km - n ~ 1.5 n0
Noninteracting nuclear matter
n ~ 1.5 n0
Alford and Reddy nucl-th/0211046
1
3 2
n0 = 0.16 fm-
1
M = 1.4 MO.
Bari, SMFT 20.IX.06 Anglani (U Bari) 6/12
Dispersion laws forDispersion laws for ( (rrd –d – ggu) andu) and ( (rrs s – – bbu) u)
1. LOFF phase is gapless
2. Dispersion laws around gapless modes could be considered as linear
Bari, SMFT 20.IX.06 Anglani (U Bari) 7/12
““The importance of being gapless”The importance of being gapless”
The contribution of gapped modes are exponentially suppressed since we work in the regime
T<<<<
Each gapless mode contributes to specific heat by
a factor ~ T
Bari, SMFT 20.IX.06 Anglani (U Bari) 8/12
Neutrino EmissivityNeutrino EmissivityWe consider the following – decay process
for color = r, g, b.
Neutrino emissivity = the energy loss by -neutrino emission per volume unit per time unit.
Electron capture process Thermal distributions Bogoliubov coefficients
Transition rate
Neutrino Energy
(1)
(2)
Bari, SMFT 20.IX.06 Anglani (U Bari) 9/12
Cooling lawsCooling laws
NUCLEARNUCLEAR mattermatter[Shapiro][Shapiro]
LOFFLOFF mattermatter
UNPAIREDUNPAIRED Q. Q. mattermatter
[Iwamoto][Iwamoto]
--LuminosityLuminosity ~ T~ T88 ~ T~ T66 ~ T~ T66
Specific HeatSpecific Heat ~ ~ TT ~ ~ TT ~ ~ TT
--LuminosityLuminosity ~ T~ T2.22.2 ~ T~ T2.22.2 ~ T~ T2.22.2
(1)
t < t < ~~11 MMyryrmain mechanism is neutrino
emission
t > t > ~~1M1Myr yr main mechanism is photon
emission
Bari, SMFT 20.IX.06 Anglani (U Bari) 10/12
ResultsResults
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 cV ~T. Normal quark matter curve: only for comparison between different models.
Bari, SMFT 20.IX.06 Anglani (U Bari) 11/12
ConclusionsConclusions
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.
Bari, SMFT 20.IX.06 Anglani (U Bari) 12/12
AcknowledgmentsAcknowledgments
In these matters the only certainty is that nothing is certain.
PLINY THE ELDERRoman scholar and scientist (23 AD - 79 AD)
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
Bari, SMFT 20.IX.06 Anglani (U Bari) 13/12
A look at the HOT BOTTLE
L ~ T2.2
cV ~ 0.5T0.5 cV ~ TL ~ T2.2
Alford et al.[astro-ph/0411560]
P1bu P2
bu
Bari, SMFT 20.IX.06 Anglani (U Bari) 14/12
LOFF3 Dispersion lawsEvery 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
Sector 45
Sector 67
Sector 89
ru g
d
bs Rd gu rs bu gs bd
det S –1 = 0 Dispersion lawsDispersion lawsRef. prof. Buballa
Bari, SMFT 20.IX.06 Anglani (U Bari) 15/12
Larkin-Ovchinnikov-Fulde-Ferrel state of artThe simplified ansatz crystal structure is
i, j = 1, 2, 3 flavor indices; , = 1, 2, 3 color indices; 2qI represents the momentum of Cooper pair and 1,2,3describe 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].
This phase results chromomagnetically stable [3]
[1] Casalbuoni, Gatto et al., PL B627 89 (2005) [2] Rajagopal et al., hep-ph/0603076
[3] Ciminale, Gatto et al., PL B636 317 (2006)
(1)Larkin and
Ovchinnikov; Fulde and Ferrell (1964)
Bari, SMFT 20.IX.06 Anglani (U Bari) 16/12
Neutral LOFF quark matter - 1
The GL approximation is reliable in a region close to the second order phase transition point where the crystal structure is characterized by
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
3. We employ a Ginzburg-Landau expansion [1]
Requiring color and electric neutrality, the energetically favored phase results in
1 = 0; 2 = 3 = < 0.30 [1]
q2=q3=q = m2s/(8 zq); zq ~ 0.83 [1]
[1] Casalbuoni et al., PL B627 89 (2005)
where 0 is the CFL gap.
Rajagopal et al., hep-ph/0605316(1)
(2)
Bari, SMFT 20.IX.06 Anglani (U Bari) 17/12
Neutral LOFF quark matter - 2
0 = 25 MeV
Finally, for our numerical estimates we use
To the leading order approximation in / one obtains
3 = 8 = 0 and e=ms
2/4[1]
= 500 MeV
The LOFF phase is energetically favored with respect to gCFL and normal phase in the range of chemical potential mismatch of
y = ms2/[130,150]
MeV
y = 140 MeV
(2)
(3)
(4)
(1)
(5)
[1] Casalbuoni, Gatto, Nardulli et al.,
hep-ph/0606242
Bari, SMFT 20.IX.06 Anglani (U Bari) 18/12
Dispersion laws forDispersion laws for ( (rruu –– ggd –d – bbs)s)
Bari, SMFT 20.IX.06 Anglani (U Bari) 19/12
Appendix A: Emissivity
Bari, SMFT 20.IX.06 Anglani (U Bari) 20/12
Appendix B: Specific Heat
μ = 500 MeV; ms = (μ 140)1/2 MeV; 1 = 0; 2 = 3 = ~ 6 MeV.
Bari, SMFT 20.IX.06 Anglani (U Bari) 21/12
Appendix C: Dispersion laws
Bari, SMFT 20.IX.06 Anglani (U Bari) 22/12
Appendix D: Dispersion laws 3X3
Bari, SMFT 20.IX.06 Anglani (U Bari) 23/12
Appendix E: Cooling laws
Bari, SMFT 20.IX.06 Anglani (U Bari) 24/12
Appendix F: Redifinition of gapless modes