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In this lecture we look at: 1) Neutron stars in x-ray binaries 2) Mass-radius relationship 3) Strange star candidates 4) Quark deconfinement at T=0 5) Astrophysical signals of quark matter Alfen radius RXJ 1856.5-3754 Drake et al. point out that this NS may in fact be a quark star (astro-ph/0204159) because of its small radius, which they argue is in the range between R' = 3.8 and 8.2 km!! ÄÄ Nasa press release of 10 April 2002: "Cosmic x-rays reveal evidence for new form of matter" WWW.msfc.nasa.gov/news Star's x-ray spectrum is well represented by a black body with a temperature of T'=7x105 K (X60 eV) The observed x-ray flux and temperature correspond to a stellar radius of R'= R (1-2M/R)-1/2 Y f (D/120 pc) km Drake et al.: R'=3.8 to 8.2 km Rotationally deformed, rotating neutron star Pulsar 3C58 " A 65 ms pulsar (J0205+6449) was discovered by Murray et al. (to appear in the ApJ, 2002). " This pulsar is at the center of 3C58, a young Crab-like supernova remnant (SN 1181). " Thus 3C58 is somewhat younger than Crab. " The pulsar's surface temperature is 1.12x106 K (Slane, Helfand, Murray, astro-ph/0204151, to appear in the ApJ) Nasa press release of 10 April 2002: "Cosmic x-rays reveal evidence for new form of matter" www.msfc.nasa.gov/news