Pulsar Timing Arrays and Gravity Tests in the Radiative Regime

In this paper, we focus on testing gravity theories in the radiative regime using pulsar timing array observations. After reviewing current techniques to measure the dispersion and alternative polarization of gravitational waves, we extend the framework to the most general situations, where the combinations of a massive graviton and alternative polarization modes are considered. The atlas of the Hellings-Downs functions is completed by the new calculations for these dispersive alternative polarization modes. We find that each mode and corresponding graviton mass introduce characteristic features in the Hellings-Downs function. Thus, in principal, we can not only detect each polarization mode, measure the corresponding graviton mass, but also discriminate the different scenarios. In this way, we can test gravity theories in the radiative regime in a generalized fashion, and such method is a direct experiment, where one can address the gauge symmetry of the gravity theories in their linearised limits. Although current pulsar timing still lacks enough stable pulsars and sensitivity for such practices, we expect that future telescopes with larger collecting area could make such experiments be feasible.

Model-based asymptotically optimal dispersion measure correction for pulsar timing

In order to reach the sensitivity required to detect gravitational waves, pulsar timing array experiments need to mitigate as much noise as possible in timing data. A dominant amount of noise is likely due to variations in the dispersion measure. To correct for such variations, we develop a statistical method inspired by the maximum likelihood estimator and optimal filtering. Our method consists of two major steps. First, the spectral index and amplitude of dispersion measure variations are measured via a time-domain spectral analysis. Second, the linear optimal filter is constructed based on the model parameters found in the first step, and is used to extract the dispersion measure variation waveforms. Compared to current existing methods, this method has better time resolution for the study of short timescale dispersion variations, and generally produces smaller errors in waveform estimations. This method can process irregularly sampled data without any interpolation because of its time-domain nature. Furthermore, it offers the possibility to interpolate or extrapolate the waveform estimation to regions where no data is available. Examples using simulated data sets are included for demonstration.

Testing Gravity Theories In The Radiative Regime Using Pulsar Timing Arrays

General relativity has predicted the existence of gravitational waves (GW), which are waves of the distortions of space-time with two degrees of polarization and the propagation speed of light. Alternative theories predict more polarizations, up to a maximum of six, and possible deviation of propagation speed from the light speed. The present paper reviews recent proposals to test the gravity theories in the radiation regime by observing GWs using pulsar timing arrays.

Lower bounds of altitudes for pulsar $gamma$-ray radiation

Determining radiation location observationally plays a very important role in testing the pulsar radiation models. One-photon pair production in the strong magnetic field, $gamma-e^{+}e^{1}$, is one of the important physical processes in pulsar radiation mechanisms. Photons near pulsar surface with sufficient energy will be absorbed in the magnetosphere and the absorption optical depth for these GeV $gamma$-ray photons is usually large. In this paper, we include the aberrational, rotational and general relativistic effects and calculate the $gamma$-B optical depth for $gamma$-ray photons. Then we use the derived optical depth to determine the radiation altitude lower bounds for photons with given energies. As a case study, we calculate the lower bounds of radiation altitudes of Crab pulsar for photons with energy from 5 GeV to 1 TeV.