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Quark matter in compact stars?

Nature volume 445, pages E7E8 (18 January 2007) | Download Citation



Arising from: F. Özel. Nature 441, 1115–1117 (2006)10.1038/nature04858; Özel replies

In a theoretical interpretation of observational data from the neutron star EXO 0748–676, Özel concludes that quark matter probably does not exist in the centre of neutron stars1. However, this conclusion is based on a limited set of possible equations of state for quark matter. Here we compare Özel's observational limits with predictions based on a more comprehensive set of proposed quark-matter equations of state from the literature, and conclude that the presence of quark matter in EXO 0748–676 is not ruled out.


Özel's stated lower limits on the mass and radius are M ≥ 2.1 ± 0.28 M and R ≥ 13.8 ± 1.8 km. She correctly points out that these values exclude a soft equation of state, but then infers that there is no quark matter in this compact star. However, this conclusion is not justified because quark matter can be as stiff as nuclear matter, because effects from strong interactions (quantum chromodynamics, QCD) can harden the equations of state substantially. The corresponding hybrid or quark stars can indeed reach a mass of 2M, as demonstrated in calculations using the MIT bag model2, perturbative corrections to QCD3, and the Nambu–Jona–Lasinio model4. The mass–radius relations for compact stars using various quark-matter and nuclear-matter equations of state, together with the lower limits derived by Özel, are shown in Fig. 1.

Figure 1: Lower limit of mass, M, and radius, R, from Özel's analysis of EXO 0748–676 (1σ and 2σ error bars are shown), and the calculated MR curve for various quark- and nuclear-matter equations of state.
Figure 1

These include pure nuclear matter described by the DBHF (relativistic Dirac–Brueckner–Hartree–Fock) equation of state6(black line); a hybrid star with a core of 2SC quark matter (a two-flavour colour-superconducting phase, in which only the up and down quarks form Cooper pairs) and a mantle of DBHF nuclear matter8 (red line); a hybrid star with a core of 2SC quark matter and mantle of HHJ nuclear matter (APR with high-density causality corrections)7 (blue line); a hybrid star whose core is a mixed phase of APR nuclear matter (based on the Argonne υ18 two-nucleon interaction with variational chain summation) and CFL quark matter (the 'colour–flavour-locked' colour-superconducting phase in which all three colours and flavours undergo Cooper pairing)2 (brown line); and a pure quark-matter star using an equation of state with order αs2 QCD corrections3(green line). The presence of quark matter is therefore not excluded by the EXO 0748–676 results.

In addition to the mass and radius, there are potential constraints on (or signatures of) the presence of quark matter from observations of the cooling, spin-down and precession of neutron stars, and from transient phenomena such as glitches, magnetar fiares and superbursts.

Cooling observations of firmly identified neutron stars are mostly consistent with a 'minimal' model of nuclear-matter cooling. However, there is evidence of faster cooling in limits obtained from supernova remnants, and the presence of exotic forms of matter is not ruled out5. A detailed analysis of cooling data, including information from elliptical fiow in heavy-ion collisions, was unable to find any purely nuclear equation of state that was compatible with all the data6. Models involving some quark matter in the cores of neutron stars were more successful7,8.

Measurements of the spin-down rate of neutron stars can be used to constrain the shear and bulk viscosity of the interior, because sufficiently low viscosity would lead to very fast spin-down by gravitational radiation from unstable r-modes. Preliminary calculations rule out a strange star made of 'colour–flavour-locked' (CFL) matter9, but hybrid stars are not ruled out. More controversially, it has also been argued that the measured precession of some stars is inconsistent with the standard understanding of nuclear matter10.

Glitches (temporary speeding-up in the rotation of a neutron star that is gradually spinning down) are only partially understood, but are believed to provide evidence for a substantial crust overlapping with a superfiuid region inside the star11. This does not exclude the presence of a quark-matter core, and may not even exclude strange stars, as there are superfiuid and crystalline phases of quark matter12,13.

Observations of quasi-periodic oscillations in soft gamma repeaters have been used to obtain the frequencies of toroidal shear modes of their crusts. The results are not consistent with these objects being purely strange stars, but they put no limits on the presence of a quark-matter core inside them14.

Observations of superbursts in low-mass X-ray binaries yield ignition depths much smaller than those predicted for standard neutron stars, and are more compatible with these objects being hybrid stars with a relatively thin baryonic crust15.

We conclude that Özel's analysis, assuming that it is indeed correct, can be used to put constraints on the parameters of the quark-matter equations of state, but that neither Özel's analysis nor the other available observational data have yet ruled out the presence of deconfined quarks in compact stars.


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Author information


  1. *Department of Physics, Washington University, St Louis, Missouri 63130, USA

    • M. Alford
  2. †Instytut Fizyki Teoretycznej, Uniwersytet Wroclawski, 50-204 Wroclaw, Poland

    • D. Blaschke
  3. ‡Institut für Physik, Universität Rostock, 18051 Rostock, Germany

    • D. Blaschke
    •  & T. Klähn
  4. §Dipartimento di Fisica, Universitä di Ferrara, 44100 Ferrara, Italy

    • A. Drago
    •  & G. Pagliara
  5. INFN, Sezione di Ferrara, 44100 Ferrara, Italy

    • A. Drago
    •  & G. Pagliara
  6. ¶GSI, 64291 Darmstadt, Germany

    • T. Klähn
  7. Institut für Theoretische Physik, Goethe Universität, 60438 Frankfurt am Main, Germany

    • J. Schaffner-Bielich


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