Torres i Cuadrat, A

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29th International Cosmic Ray Conference Pune (2005) 4, 251254Compact Star Properties revised with Color Superconducting Phases ofQuark Matter: Implications on Rotation and EmissionA. Torres i Cuadrat and F. Weber(a) Physics Department, Universitat Autonoma de Barcelona, Cerdanyola del Valles E-08193, Spain(b) Physics Department, San Diego State University, San Diego CA 92226, U.S.A.Presenter: A. Torres i Cuadrat (andreu.torres@uab.es), spa-torres-A-abs1-og22-posterThere has been much recent progress in our understanding of quark matter, culminating in the discovery thatif such matter exists in the cores of neutron stars it ought to be in a Color Superconducting state. This paperpresents a detailed study of the consequences of superconducting quark matter on the properties of CompactStars such as Masses, Radii, Surface gravity and Photon Emission patterns. Special emphasis is put on theRotational properties of such stars and their temporal evolution.1. IntroductionUnderstanding the composition of matter inside compact stars is one of the toughest theoretical challengesof relativistic astrophysics [1, 2]. Despite some progress that has been made over the years, the physics ofthe ultra-dense core of such objects is still only vaguely known. Recently it has been theorized that the coremay be made of color superconducting quark matter [3, 4], rather than just ordinary nucleons. If true, thiswould change our traditional understanding of neutron stars dramatically. This paper studies the implicationsof color superconducting quark matter on the global properties of neutron stars. The study is based on threedifferent models for the Equation Of State (EoS). The first model is the Hartree V EoS [5] which treats thecore matter as made of conventional hadronic particles (nucleons and hyperons) in chemical equilibrium withleptons (electrons and muons). The second EoS is known as 			[2] and describes the matter in the starin two phases, one being regular hadronic matter (in the outer layers of the star), the other being deconfinedquark matter described by the MIT Bag Model (with a nuclear compressibility of 300 MeV and a value for thebag constant of 180 MeV). The third model for the EoS treats quark matter in the color flavor locked (CFL)superconducting phase [4]. Figure 1 shows the Pressure-Energy relations for the three EoS used in the paper.2. Results and ConclusionsIn this section we present various plots which illustrate the differences between conventional neutron stars(Hartree V), and neutron stars with color superconducting quark matter cores (CFL) and non-superconductingquark matter cores ( 			). In figure 2 we present the calculations for the Mass-Radius relations of differentstars according to the EoS that rule their interior composition. Because of the extreme softness of the CFLEoS, these stars are much more compressed than the other two stars of our collection. The mass peak of theCFL sequence is at around 1.36  and the corresponding radius of 9 km. In contrast to this, the conventionalneutron stars (Hartree V) can have masses up to around 2  and radii of  km. This differences in sizeand mass can also be seen in figure 3 where we also plot the evolutionary (constant stellar baryon number,  )paths that isolated rotating neutron stars would follow during their stellar spin-down caused by the emissionof magnetic dipole radiation and a wind on  – ﬀ pairs. Figure 3 reveals that CFL stars may spend consid-erably more time in the spin-down phase than their competitors of the same mass. Figure 4 shows the generalrelativistic effect of frame dragging [1] which is tremendously pronounced for the CFL stars, from the centerof the star ( ﬁﬂﬃ =0.48) all the way up to about two times the size of the star. This may be of great importance252 A. Torres i Cuadrat and F. Weber500 1000 1500 2000 2500 3000ε [MeV/fm3]2004006008001000P [MeV/fm3 ]Hartree HVG300B180CFL mixedp, n, e- , µ−quarks, Κ, etc.CFL, 2SC, (?)Figure 1. Equations of State used in this study. The shaded areas indicate competing stellar compositions in the P ! plane.8 10 12 14 16 18Req [km]0.20.40.60.81.01.21.41.61.82.02.22.4M/MsunHartree VG300B180CFL8 10 12 14 16 18Req [km]0.20.40.60.81.01.21.41.61.82.02.22.4M/MsunHartree VG300B180CFLFigure 2. MassRadius Relations of static (left panel: "#%$ ) and rotating (right panel: "&#%"' ) neutron stars computedfor the EoS of this work. "(' denotes the general relativistic Kepler (mass shedding) frequency.for binary millisecond neutron stars in their final accretion stages, where the accretion disk approaches the starvery closely. As seen in Table 1, if quark matter is indeed in a color superconducting state inside the coresof neutron stars, this fact can be checked for a number of properties. In the mentioned table we show forthe static (three left columns) and the rotating (three right columns) solutions of Einstein’s field equation thecentral energy density ( )+* ), which can be up to 20 times higher than nuclear density, the Moments of Inertia,Masses and Radii which all account for the superdense form of CFL stars. We also show the surface redshifts(from the pole and from the equator with and against the direction of rotation of the star) which have a strongimpact on the observational temperature determination since ,.- ﬃ ,0/21435 ﬃ (6%7 and CFL stars can presentredshifts 50% higher than their regular hadronic matter counterparts. Finally we also show in Table 1 the sur-face gravity (in units of 98:;<>= ﬃ?@ ) which again is up to 50% higher for the CFL stars than for the other stars,the Rotational Kinetic Energy in units of the total Energy of the star (T/W) [1], the Binding Energy (BE) andCompact Star Properties revised with Color Superconducting Phases of Quark Matter 253100 10000.511.522.5M/MsunHartree V100 1000ε [Mev/fm3]      0.511.522.5G300B180100 10000.511.522.5CFLΩ=Ω KeplerΩ=0Ω=0Ω=Ω KeplerΩ=0Ω=ΩKeplerA=const.Figure 3. MassCentral Energy Relations of the three model stars of this study (for details, see text.)0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0r / Req0.40.50.60.70.80.91.0ω / ΩHartree VG300B180CFLFigure 4. Dragging of local inertial frames (Lense-Thirring effect) caused by 1.3 ACB stars rotating at a period of 2 ms.the velocity at the equator in units of D . The plots in figure 5 show the evolution of the particle populations(nucleons, hyperons, quarks) inside our three sample stars with changing stellar frequency of rotation. In eachpanel, from right to left, the two most outer-lying curves indicate the surface of the star and the end of the outercrust, followed by lines which mark the transitions to more exotic phases, as indicated in the figure. Increasingrotation rates decrease the interior stellar density drastically [1], which could constrain the existence of quarkmatter to neutron stars rotating below moderate frequencies only.3. AcknowledgementsWe would like to thank Mark Alford for providing us with an EoS that accounts for Color SuperconductingQuark Matter. We would also like to thank the NSF (USA) and the Science and Technology Department ofSpain for financial support.254 A. Torres i Cuadrat and F. WeberTable 1. Key differences between standard stars and quark matter stars of this study. (See text for more details.)Hartree V EFF			CFL Hartree V E			CFL 3G8 3H8 3I8 0J = 5360 ? K  0J = 5900 ? K  0J = 8800 ? K) * 361.0 814.3 2300.0 280.0 400.0 1100.0LNMPO=RQ0 0 0 223.6 217.1 131.8M ( S ) 1.39 1.40 1.36 1.39 1.40 1.41R (km) 14.1 12.2 9.0 17.1 16.0 12.6TEURVW/ 0.1889 0.2322 0.3356 0.2374 0.2646 0.3618TYX[Z0.1889 0.2322 0.3356 -0.1788 -0.1817 -0.2184TE\ Z0.1889 0.2322 0.3356 0.6046 0.6502 0.9190]ﬀ^`_;M<N=ﬃa?@Q1.1086 1.5447 3.0146 0.7278 0.8487 1.4493T/W 0 0 0 0.0894 0.0941 0.0787BE/ S 0.0937 0.1470 0.1534 0.0524 0.1097 0.1203b/`cﬃ< 0 0 0 0.336 0.353 0.4240 3 6 9 12 15 18r [km]02004006008001000ν [Hz]0 3 6 9 12 15 18r [km]020040060080010000 3 6 9 12 15r [km]0250500750100012501500ν = νKeplerν = νKepler ν = νKeplerp, n liquidmixed phasehadronic matterplus quarks CFLpurequarkmattercoreΛ condensateΣ condensatemixedphase crustnuclearcrustMIT baggedquark mattercoreFigure 5. Particle proles of the neutron stars of our collection, showing the various depths at which the different phasesof matter are found inside the stars. (The non-rotating stellar mass in each case is 1.4 A B .)References[1] F. Weber, Pulsars as Astrophysical Laboratories for Nuclear and Particle Physics, High Energy Physics,Cosmology and Gravitation Series, IOP Publishing, Bristol, Great Britain, (1999).[2] N. K. Glendenning, Compact Stars, Nuclear Physics, Particle Physics, and General Relativity, 2nd ed.Springer-Verlag, New York (2000).[3] K. Rajagopal and F. Wilczek, The Condensed Matter Physics of QCD, Handbook of QCD, ed. M. Shif-man, (World Scientific) (2001).”[4] M. Alford and S. Reddy, Phys. Rev. D 67, (2003)[5] N. K. Glendenning, Astrophys. J. 293, 470 (1985).

Compact Star Properties revised with Color Superconducting Phases of Quark Matter: Implications on Rotation and Emission

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