Colloquium: Measuring the neutron star equation of state using x-ray timing

Abstract

One of the primary science goals of the next generation of hard X-ray timing instruments is to determine the equation of state of the matter at supranuclear densities inside neutron stars, by measuring the radius of neutron stars with different masses to accuracies of a few percent. Three main techniques can be used to achieve this goal. The first involves waveform modelling. The flux we observe from a hotspot on the neutron star surface offset from the rotational pole will be modulated by the star's rotation, and this periodic modulation at the spin frequency is called a pulsation. As the photons propagate through the curved space-time of the star, information about mass and radius is encoded into the shape of the waveform (pulse profile) via special and general relativistic effects. Using pulsations from known sources (which have hotspots that develop either during thermonuclear bursts or due to channelled accretion) it is possible to obtain tight constraints on mass and radius. The second technique involves characterising the spin distribution of accreting neutron stars. A large collecting area enables highly sensitive searches for weak or intermittent pulsations (which yield spin) from the many accreting neutron stars whose spin rates are not yet known. The most rapidly rotating stars provide a very clean constraint, since the limiting spin rate where the equatorial surface velocity is comparable to the local orbital velocity, at which mass-shedding occurs, is a function of mass and radius. However the overall spin distribution also provides a guide to the torque mechanisms in operation and the moment of inertia, both of which can depend sensitively on dense matter physics. The third technique is to search for quasiperiodic oscillations in X-ray flux associated with global seismic vibrations of magnetars (the most highly magnetized neutron stars), triggered by magnetic explosions. The vibrational frequencies depend on stellar parameters including the dense matter equation of state, and large area X-ray timing instruments would provide much improved detection capability. We illustrate how these complementary X-ray timing techniques can be used to constrain the dense matter equation of state, and discuss the results that might be expected from a 10m 2 instrument. We also discuss how the results from such a facility would compare to other astronomical investigations of neutron star properties.

Equation of State for Nucleonic and Hyperonic Neutron Stars With Mass and Radius Constraints

“…It is expected that robust observational upper bounds on stellar radii will be within reach in the near future. With space missions such as NICER (Neutron star Interior Composition ExploreR; Arzoumanian et al 2014), high-precision X-ray astronomy will be able to offer precise measurements of masses and radii (Watts et al 2016), while gravitational-wave signals from neutron star mergers hold promise to determine neutron star radii with a precision of 1 km (Bauswein & Janka 2012;Lackey & Wade 2015).…”

Gravitational Waves from F-modes Excited by the Inspiral of Highly Eccentric Neutron Star Binaries

“…For example, X-ray measurements from the upcoming NICER mission (Gendreau et al 2012; the launch is scheduled for 2017) and from the planned LOFT mission (Feroci et al 2012;Watts et al 2016) will constrain neutron star masses and radii.…”

Dispersion and decay of collective modes in neutron star cores

“…One model of quasi-periodic oscillations observed in the tails of magnetar giant flares in- vokes a coupling between internal modes of the neutron star crust and the global magnetic field to provide a mechanism by which surface emission can be modulated at characteristic frequencies [29]. It would be interesting to explore if a similar coupling between the magnetic field and core p-modes can lead to observable effects.…”