The cooling phase of thermonuclear (type-I) X-ray bursts can be used to constrain neutron star (NS) compactness by comparing the observed cooling tracks of bursts to accurate theoretical atmosphere model calculations. By applying the so-called cooling tail method, where the information from the whole cooling track is used, we constrain the mass, radius, and distance for three different NSs in low-mass X-ray binaries 4U 1702-429, 4U 1724-307, and SAX J1810.8-260. Care is taken to use only the hard state bursts where it is thought that the NS surface alone is emitting. We then use a Markov chain Monte Carlo algorithm within a Bayesian framework to obtain a parameterized equation of state (EoS) of cold dense matter from our initial mass and radius constraints. This allows us to set limits on various nuclear parameters and to constrain an empirical pressure-density relationship for the dense matter. Our predicted EoS results in NS a radius between 10.5-12.8 km (95% confidence limits) for a mass of 1.4 M-circle dot, depending slightly on the assumed composition. Because of systematic errors and uncertainty in the composition, these results should be interpreted as lower limits for the radius.

A theoretical framework for emission originating from rapidly rotating oblate compact objects is described in detail. Using a Hamilton-Jacobi formalism, we show that special relativistic rotational effects such as aberration of angles, Doppler boosting, and time dilatation naturally emerge from the general relativistic treatment of rotating compact objects. We use the Butterworth-Ipser metric expanded up to the second order in rotation and hence include effects of light bending, frame-dragging, and quadrupole deviations on our geodesic calculations. We also give detailed descriptions of the numerical algorithms used and provide an open-source implementation of the numerical framework called BENDER. As an application, we study spectral line profiles (i.e., smearing kernels) from rapidly rotating oblate neutron stars. We find that in this metric description, the second-order quadrupole effects are not strong enough to produce narrow observable features in the spectral energy distribution for almost any physically realistic parameter combination, and hence, actually detecting them is unlikely. The full width at tenth-maximum and full width at half-maximum of the rotation smearing kernels are also reported for all viewing angles. These can then be used to quantitatively estimate the effects of rotational smearing on the observed spectra. We also calculate accurate pulse profiles and observer skymaps of emission from hot spots on rapidly rotating accreting millisecond pulsars. These allow us to quantify the strength of the pulse fractions one expects to observe from typical fast-spinning millisecond pulsars.

Ray tracing is a central tool for constructing mock observations of compact object emission and for comparing physical emission models with observations. We present ARCMANCER, a publicly available general ray-tracing and tensor algebra library, written in C++ and providing a Python interface. ARCMANCER supports Riemannian and semi-Riemannian spaces of any dimension and metric, and has novel features such as support for multiple simultaneous coordinate charts, embedded geometric shapes, local coordinate systems, and automatic parallel propagation. The ARCMANCER interface is extensively documented and user friendly. While these capabilities make the library well suited for a large variety of problems in numerical geometry, the main focus of this paper is in general relativistic polarized radiative transfer. The accuracy of the code is demonstrated in several code tests and in a comparison with GRTRANS, an existing ray-tracing code. We then use the library in several scenarios as a way to showcase the wide applicability of the code. We study a thin variable-geometry accretion disk model and find that polarization carries information of the inner disk opening angle. Next, we study rotating neutron stars and determine that to obtain polarized light curves at better than a similar to 1% level of accuracy, the rotation needs to be taken into account both in the spacetime metric and in the shape of the star. Finally, we investigate the observational signatures of an accreting black hole lensed by an orbiting black hole. We find that these systems exhibit a characteristic asymmetric twin-peak profile both in flux and polarization properties.

Determining neutron star (NS) radii and masses can help to understand the properties of matter at supra-nuclear densities. Thermal emission during thermonuclear X-ray bursts from NSs in low-mass X-ray binaries provides a unique opportunity to study NS parameters, because of the high fluxes, large luminosity variations and the related changes in the spectral properties. The standard cooling tail method uses hot NS atmosphere models to convert the observed spectral evolution during cooling stages of X-ray bursts to the Eddington flux F-Edd and the stellar angular size Omega. These are then translated to the constraints on the NS massMand radius R. Here we present the improved, direct cooling tail method that generalizes the standard approach. First, we adjust the cooling tail method to account for the bolometric correction to the flux. Then, we fit the observed dependence of the blackbody normalization on flux with a theoretical model directly on theM-R plane by interpolating theoretical dependences to a given gravity, hence ensuring only weakly informative priors for M and R instead of FEdd and Omega. The direct cooling method is demonstrated using a photospheric radius expansion burst from SAX J1810.8-2609, which has happened when the system was in the hard state. Comparing to the standard cooling tail method, the confidence regions are shifted by 1 sigma towards larger radii, giving R = 11.5-13.0 km at M = 1.3-1.8M(circle dot) for this NS.