The recent detection of pulsations from the ultraluminous 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 super-Eddington 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 that the dipole magnetic field of the neutron star is 6.7 × 10¹³ 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.

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, $\alpha$, that characterizes the coupling between matter and spacetime in EMSG. We show that $-{10}^{-38}{\mathrm{cm}}^3/\mathrm{erg}<\alpha <+{10}^{-37}{\mathrm{cm}}^3/\mathrm{erg}$. 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 $t\sim {10}^{-4}$ seconds at which the energy density of the universe is $\sim {10}^{34}\mathrm{erg}{\mathrm{cm}}^{-3}$.

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\char22{}mass and radius (M-R)\char22{}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\char22{}namely, that M-R measurements can be used to constrain the EoS\char22{}presumes that 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 $r>10\text{ }\text{ }\mathrm{m}$, 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 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.

The recently discovered rotationally powered pulsar PSR J1640–4631 is the first to have a braking index measured, with high enough precision, that is greater than 3. An inclined magnetic rotator in vacuum or plasma would be subject not only to spin-down but also to an alignment torque. The vacuum model can address the braking index only for an almost orthogonal rotator, which is incompatible with the single-peaked pulse profile. The magnetic dipole model with the corotating plasma predicts braking indices between 3 and 3.25. We find that the braking index of 3.15 is consistent with two different inclination angles, 18.°5 ± 3° and 56° ± 4°. The smaller angle is preferred given that the pulse profile has a single peak and the radio output of the source is weak. We infer the change in the inclination angle to be at the rate −0.°23 per century, three times smaller in absolute value than the rate recently observed for the Crab pulsar.

We study the structure of neutron stars in R+βR^μνR_μν gravity model with perturbative method. We obtain mass-radius relations for six representative equations of state (EoSs). We find that, for |β| ~ 10¹¹ cm², 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 10¹¹ cm² 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)^1/2 ~ 10⁶ cm is of the order of the the typical radius of neutron stars, the probe used in this test. This implies that the true value of β is most likely much smaller than 10¹¹ cm².

The discovery of pulsating ultraluminous X-ray sources (PULX) suggests that neutron stars are presumably common within the ultraluminous X-ray source (ULX) population though the majority of the population members currently lack pulsations. These systems are likely to host neutron stars accreting mass at super-Eddington (supercritical) rates from their massive companion in high-mass X-ray binaries. Taking into account the spherization of the accretion flow in the supercritical regime, the beaming of X-ray emission, and the reduction of the scattering cross section in a strong magnetic field, we infer the ranges for the neutron-star surface magnetic dipole field strengths, beaming fractions, and fastness parameters in the PULX M82 X-2, ULX NGC 5907, ULX NGC 7793 P13, NGC 300 ULX1, M51 ULX-7, NGC 1313 X-2, and Swift J0243.6+6124 from a set of conditions based on a variety of combinations of different spin and luminosity states. Using the observed spin-up rates under the critical luminosity condition, we estimate the surface-field strengths in the ∼10¹¹–10¹³ G range for all PULX. In general, the results of our analysis under the subcritical luminosity condition indicate surface-field strengths in the ∼10¹¹–10¹⁵ G range. We argue that PULX do not require magnetar-strength surface dipole fields if beaming is taken into account, yet the fields are strong enough for the neutron stars in ULX to magnetically channel the accretion flow in supercritical accretion disks.