Abstract. We study the structure of neutron stars in perturbative f (R) gravity models with realistic equations of state. We obtain mass-radius relations in a gravity model of the form f (R) = R+αR 2 . We find that deviations from the results of general relativity, comparable to the variations due to using different equations of state (EoS'), are induced for |α| ∼ 10 9 cm 2 . Some of the soft EoS' that are excluded within the framework of general relativity can be reconciled with the 2 solar mass neutron star recently observed for certain values of α within this range. For some of the EoS' we find that a new solution branch, which allows highly massive neutron stars, exists for values of α greater than a few 10 9 cm 2 . We find constraints on α for a variety of EoS' using the recent observational constraints on the mass-radius relation. These are all 5 orders of magnitude smaller than the recent constraint obtained via Gravity Probe B for this gravity model. The associated length scale √ α ∼ 10 5 cm is only an order of magnitude smaller than the typical radius of a neutron star, the probe used in this test. This implies that real deviations from general relativity can be even smaller.

We show that the period clustering of anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs), their X-ray luminosities, ages and statistics can be explained with fallback disks with large initial specific angular momentum.The disk evolution models are developed by comparison to self-similar analytical models. The initial disk mass and angular momentum set the viscous timescale.An efficient torque, with (1 − ω 2 * ) dependence on the fastness parameter ω * leads to period clustering in the observed AXP-SGR period range under a wide range of initial conditions. The timescale t 0 for the early evolution of the fallback disk, and the final stages of fallback disk evolution, when the disk becomes passive, are the crucial determinants of the evolution. The disk becomes passive at temperatures around 100 K, which provides a natural cutoff for the X-ray luminosity and defines the end of evolution in the observable AXP and SGR phase. This low value for the minimum temperature for active disk turbulence indicates that the fallback disks are active up to a large radius, > ∼ 10 12 cm. We find that transient AXPs and

The recent detection of pulsations from the ultra luminous X-ray source (ULX) NuSTAR J095551+6940.8 in M82 by Bachetti et al. indicates that the object is an accreting neutron star in a high mass X-ray binary (HMXB) system. The superEddington luminosity of the object implies that the magnetic field is sufficiently strong to suppress the scattering cross-section unless its beam is viewed at a favourable angle. We show that the torque equilibrium condition for the pulsar indicates the dipole magnetic field of the neutron star is 6.7 × 10 13 G, two orders of magnitude higher than that estimated by Bachetti et al., and further point to the possibility that even stronger magnetic fields could well be in the higher multipoles. This supports the recent view that magnetars descent from HMXBs if the magnetic field decays an order of magnitude during the process of transition.

Neutron stars 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 two observables of neutron stars-mass and radius (M-R)-both depend on the choice of EoS and relativistic gravity, meaning that neutron stars cannot be simultaneously good laboratories for both of these questions. A measurement of mass and/or radius would constrain the less well known physics input. The most common assumption-namely, 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 neutron star 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 the neutron stars is a rather remarkable extrapolation from the regime of tested validity, as opposed to that of EoS models. Our larger ignorance of gravity within neutron stars suggests that a measurement of mass and/or radius constrains gravity rather than the EoS, and given that the 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 the EoS in this region is fairly well known. This renders the crust as the best site to look for deviations from GR.

Deviations from the predictions of general relativity due to energy-momentum squared gravity (EMSG) are expected to become pronounced in the high density cores of neutron stars. We derive the hydrostatic equilibrium equations in EMSG and solve them numerically to obtain the neutron star mass-radius relations for four different realistic equations of state. We use the existing observational measurements of the masses and radii of neutron stars to constrain the free parameter, α, that characterizes the coupling between matter and spacetime in EMSG. We show that −10 −38 cm 3 /erg < α < +10 −37 cm 3 /erg. Under this constraint, we discuss what contributions EMSG can provide to the physics of neutron stars, in particular, their relevance to the so called hyperon puzzle in neutron stars. We also discuss how EMSG alters the dynamics of the early universe from the predictions of the standard cosmological model. We show that EMSG leaves the standard cosmology safely unaltered back to t ∼ 10 −4 seconds at which the energy density of the universe is ∼ 10 34 erg cm −3 .

Fallback disks are expected to form around new-born neutron stars following a supernova explosion. In almost all cases, the disk will pass through a propeller stage. If the neutron star is spinning rapidly (initial period ∼ 10 ms) and has an ordinary magnetic moment (∼ 10 30 G cm 3 ), the rotational power transferred to the disk by the magnetic field of the neutron star will exceed the Eddington limit by many orders of magnitude, and the disk will be rapidly disrupted. Fallback disks can thus survive only around slow-born neutron stars and around black holes, assuming the latter do not torque their surrounding disks as strongly as do neutron stars. This might explain the apparent rarity of fallback disks around young compact objects.

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Abstract. We study the structure of neutron stars in R + βR µν R µν gravity model with perturbative method. We obtain mass-radius relations for six representative equations of state (EoSs). We find that, for |β| ∼ 10 11 cm 2 , the results differ substantially from the results of general relativity. Some of the soft EoSs that are excluded within the framework of general relativity can be reconciled for certain values of β of this order with the 2 solar mass neutron star recently observed. For values of β greater than a few 10 11 cm 2 we find a new solution branch allowing highly massive neutron stars. By referring some recent observational constraints on the mass-radius relation we try to constrain the value of β for each EoS. The associated length scale √ β ∼ 10 6 cm is of the order of the the typical radius of neutron stars implying that this is the smallest value we could find by using neutron stars as a probe. We thus conclude that the true value of β is most likely much smaller than 10 11 cm 2 .