What does a measurement of mass and/or radius of a neutron star constrain: Equation of state or gravity?

Neutron stars (NSs) are thought to be excellent laboratories for determining the equation of state (EoS) of cold dense matter. Their strong gravity suggests that they can also be used to constrain gravity models. The mass and radius (M-R) of a NS both depend on the choice of EoS and gravity, meaning that NSs cannot be simultaneously good laboratories for both of these questions. A measurement of M-R would constrain the less well known physics input. The assumption that M-R measurements can be used to constrain EoS-presumes general relativity (GR) is the ultimate model of gravity in the classical regime. We calculate the radial profile of compactness and curvature (square root of the full contraction of the Weyl tensor) within a NS and determine the domain not probed by the Solar System tests of GR. We find that, except for a tiny sphere of radius less than a millimeter at the center, the curvature is several orders of magnitude above the values present in Solar System tests. The compactness is beyond the solar surface value for r>10 m, and increases by 5 orders of magnitude towards the surface. With the density being only an order of magnitude higher than that probed by nuclear scattering experiments, our results suggest that the employment of GR as the theory of gravity describing the hydrostatic equilibrium of NSs is a rather remarkable extrapolation from the regime of tested validity, as opposed to that of EoS models. Our larger ignorance of gravity within NSs suggests that a measurement of M-R constrains gravity rather than EoS, and given that EoS has yet to be determined by nucleon scattering experiments, M-R measurements cannot tightly constrain the gravity models either. Near the surface the curvature and compactness attain their largest values, while EoS in this region is fairly well known. This renders the crust as the best site to look for deviations from GR.Comment: Phys.Rev. D published, typos corrected to match the published versio

The anomalous x-ray pulsar 4U 0142+61: a neutron star with a gaseous fallback disk

The recent detection of the anomalous X-ray pulsar (AXP) 4U 0142+61 in the mid infrared with the Spitzer Observatory (Wang, Chakrabarty & Kaplan 2006) constitutes the first instance for a disk around an AXP. We show, by analyzing earlier optical and near IR data together with the recent data, that the overall broad band data can be reproduced by a single irradiated and viscously heated disk model

A natural limit on the observable periods of anomalous x-ray pulsars and soft gamma-ray repeaters

We investigate the dependence of the evolution of neutron stars with fallback disks on the strength of the magnetic dipole field of the star. Using the same model as employed by Ertan et al. (2009), we obtain model curves for different dipole fields showing that the neutron stars with magnetic dipole fields greater than ∼ 1013 G on the surface of the star are not likely to become anomalous X‐ray pulsars (AXPs) and soft gamma‐ray repeaters (SGRs). Other sources with conventional dipole fields evolve into the AXP phase if their disk can penetrate the light cylinder. The upper limits to the observed periods of AXP and SGRs could be understood if the disk becomes inactive below a low temperature around 100 K. We summarize our present and earlier results indicated by the evolutionary model curves of these sources with an emphasis on the importance of the minimum disk temperature and the X‐ray irradiation in the long‐term evolution of AXPs and SGRs with fallback disks

On fallback disks and magnetars

The discovery of a disk around the anomalous X-ray pulsar 4U 0142+61, has rekindled the interest in fallback disks around magnetars. We briefly review the assumptions of fallback disk models and magnetar models. Earlier data in optical and near IR bands combined with new Spitzer data in the mid-IR range are compatible with a gas disk. Higher multipole fields with magnetar strengths together with a dipole field of 1012-1013 G on the neutron star surface are compatible with the presence of a disk around the neutron star. The possible presence and properties of a fallback disk after the supernova explosion is a likely initial condition to complement the initial rotation period and initial dipole field in determining the evolutionary paths and different types of isolated neutron stars