Quark Matter In Massive Compact Stars

arXiv:1102.2869v2 [astro-ph.HE] 7 Oct 2011 Draft version October 26, 2018 Preprint typeset using LATEX style emulateapj v. 8/13/10 QUARK MATTER IN MASSIVE COMPACT STARS Simon Weissenborn1, Irina Sagert2, Giuseppe Pagliara1, Matthias Hempel3, J¨urgen Schaffner-Bielich1 1Institute for Theoretical Physics, Ruprecht-Karls University, Philosophenweg 16, 69120 Heidelberg, Germany 2Department of Physics & Astronomy, Michigan State University, East Lansing, MI 48824, USA and 3Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland Draft version October 26, 2018 ABSTRACT The recent observation of the pulsar PSR J1614-2230 with a mass of 1.97 ± 0.04 M⊙gives a strong constraint on the quark and nuclear matter equations of state (EoS). We explore the parameter ranges for a parameterized EoS for quark stars. We find that strange stars, made of absolutely stable strange quark matter, comply with the new constraint only if effects from the strong coupling constant and color-superconductivity are taken into account. Hybrid stars, compact stars with a quark matter core and an hadronic outer layer, can be as massive as 2 M⊙, but only for a significantly limited range of parameters. We demonstrate that the appearance of quark matter in massive stars depends crucially on the stiffness of the nuclear matter EoS. We show that the masses of hybrid stars stay below the ones of hadronic and pure quark stars, due to the softening of the EoS at the quark-hadron phase transition. Subject headings: stars: neutron — equation of state 1. INTRODUCTION The densities in the interior of neutron stars exceed the ground state density of atomic nuclei, n0 ∼0.16 fm−3, by far. This naturally raises the idea, that compact stars might contain a deconfined and chirally restored quark phase. Recently, Demorest et al. (2010) found a new ro- bust mass limit for compact stars by determining the mass of the millisecond pulsar PSR J1614-2230 to be M = 1.97 ± 0.04 M⊙. This value, together with the mass of pulsar J1903+0327 of M = 1.667 ± 0.021 M⊙ (Freire et al. 2010) is much larger than the Hulse-Taylor limit of M ∼1.44 M⊙(Thorsett & Chakrabarty 1999), which for a long time has been the highest precisely mea- sured pulsar mass. In this letter we want to explore the implications of this new measurement on the possible presence of quark matter in compact stars. Moreover, our aim is to map out the parameter range for the widely used quark bag model with respect to its ability to repro- duce high mass compact stars such as PSR J1614-2230. There are two classes of compact stars which contain quark matter. The first class are so-called hybrid stars, with quarks only in their interior either in form of a pure quark matter core or a quark-hadron mixed phase. The size of the core depends hereby on the critical den- sity for the quark-hadron phase transition ncrit under neutron star conditions. The second class of so-called (strange) quark stars is realized for the special scenario of absolutely stable strange quark matter (see e.g. Itoh (1970); Bodmer (1971); Witten (1984)). It is based on the idea that the presence of strange quarks can lower the energy per baryon of the mixture of up, down, and strange quarks in weak equilibrium below the one of 56Fe (∼930 MeV). As a consequence, this strange quark matter forms the true ground state of nuclear matter and occupies the entire compact star (Alcock et al. 1986; Haensel et al. 1986). The mass measurement for PSR J1614-2230 sets for the first time very strong limits for the parameters of any zero temperature equation of state (EoS), and thereby also for the one of quark matter. Usually, the appearance of strangeness in quark and hadronic matter provides an additional degree of freedom and thereby softens the nuclear EoS, that is, decreases the pressure for a given energy density. As a re- sult, quark and hybrid stars cannot reach high masses. However, many studies found that effects from the strong interaction, such as one-gluon exchange or color- superconductivity can stiffen the quark matter EoS and increase the maximum mass of quark and hybrid stars (R¨uster & Rischke 2004; Horvath & Lugones 2004; Alford et al. 2007; Fischer et al. 2010; Kurkela et al. 2010a,b). ¨Ozel et al. (2010) and Lattimer & Prakash (2010) gave first studies on the implications of the new mass limits from PSR J1614-2230 for quark and hybrid stars in the quark bag model. However, as we will show below, a systematic analysis of the whole allowed param- eter range is still missing. Lattimer & Prakash (2010) include strange quark mat- ter in form of a bag model EoS for quark stars as well as hybrid stars. The authors do not study strong ef- fects from color-superconductivity and impose the ad- ditional constraint of ncrit ≳n0. This is a reasonable (Lattimer & Prakash 2010), but not necessary condition (Witten 1984). Moreover, they exclude a priori the ex- istence of a quark-hadron mixed phase and come to the conclusion, t

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