The interiors of neutron stars contain matter at very high densities, in a state that differs greatly from those found in the early Universe or achieved in terrestrial experiments. Matter in these conditions can only be probed through astrophysical observations that measure the mass and radius of neutron stars with sufficient precision. Here I report a determination of the mass and radius of the neutron star EXO 0748 - 676 that appears to rule out all the soft equations of state of neutron-star matter. If this object is typical, then condensates and unconfined quarks do not exist in the centres of neutron stars.
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