An algorithm for solving the pulsar equation

We present an algorithm of finding numerical solutions of pulsar equation. The problem of finding the solutions was reduced to finding expansion coefficients of the source term of the equation in a base of orthogo- nal functions defined on the unit interval by minimizing a multi-variable mismatch function defined on the light cylinder. We applied the algorithm to Scharlemann & Wagoner boundary conditions by which a smooth solu- tion is reconstructed that by construction passes success- fully the Gruzinov's test of the source function exponent.Comment: 4 pages, 4 figures, accepted for publication in ApSS (a shortened version of the previous one

Electric field representation of pulsar intensity spectra

Pulsar dynamic spectra exhibit high visibility fringes arising from interference between scattered radio waves. These fringes may be random or highly ordered patterns, depending on the nature of the scattering or refraction. Here we consider the possibility of decomposing pulsar dynamic spectra -- which are intensity measurements -- into their constituent scattered waves, i.e. electric field components. We describe an iterative method of achieving this decomposition and show how the algorithm performs on data from the pulsar B0834+06. The match between model and observations is good, although not formally acceptable as a representation of the data. Scattered wave components derived in this way are immediately useful for qualitative insights into the scattering geometry. With some further development this approach can be put to a variety of uses, including: imaging the scattering and refracting structures in the interstellar medium; interstellar interferometric imaging of pulsars at very high angular resolution; and mitigating pulse arrival time fluctuations due to interstellar scattering.Comment: 7 Pages, 2 Figures, revised version, accepted by MNRA

Coherent network analysis for continuous gravitational wave signals in a pulsar timing array: Pulsar phases as extrinsic parameters

Supermassive black hole binaries are one of the primary targets for gravitational wave searches using pulsar timing arrays. Gravitational wave signals from such systems are well represented by parametrized models, allowing the standard Generalized Likelihood Ratio Test (GLRT) to be used for their detection and estimation. However, there is a dichotomy in how the GLRT can be implemented for pulsar timing arrays: there are two possible ways in which one can split the set of signal parameters for semi-analytical and numerical extremization. The straightforward extension of the method used for continuous signals in ground-based gravitational wave searches, where the so-called pulsar phase parameters are maximized numerically, was addressed in an earlier paper (Wang et al. 2014). In this paper, we report the first study of the performance of the second approach where the pulsar phases are maximized semi-analytically. This approach is scalable since the number of parameters left over for numerical optimization does not depend on the size of the pulsar timing array. Our results show that, for the same array size (9 pulsars), the new method performs somewhat worse in parameter estimation, but not in detection, than the previous method where the pulsar phases were maximized numerically. The origin of the performance discrepancy is likely to be in the ill-posedness that is intrinsic to any network analysis method. However, scalability of the new method allows the ill-posedness to be mitigated by simply adding more pulsars to the array. This is shown explicitly by taking a larger array of pulsars.Comment: 30 pages, 11 figures, revised version, published in Ap

The optimal schedule for pulsar timing array observations

In order to maximize the sensitivity of pulsar timing arrays to a stochastic gravitational wave background, we present computational techniques to optimize observing schedules. The techniques are applicable to both single and multi-telescope experiments. The observing schedule is optimized for each telescope by adjusting the observing time allocated to each pulsar while keeping the total amount of observing time constant. The optimized schedule depends on the timing noise characteristics of each individual pulsar as well as the performance of instrumentation. Several examples are given to illustrate the effects of different types of noise. A method to select the most suitable pulsars to be included in a pulsar timing array project is also presented.Comment: 16 pages, 6 figures, accepted by MNRA

Growth rates of the Weibel and tearing mode instabilities in a relativistic pair plasma

We present an algorithm for solving the linear dispersion relation in an inhomogeneous, magnetised, relativistic plasma. The method is a generalisation of a previously reported algorithm that was limited to the homogeneous case. The extension involves projecting the spatial dependence of the perturbations onto a set of basis functions that satisfy the boundary conditions (spectral Galerkin method). To test this algorithm in the homogeneous case, we derive an analytical expression for the growth rate of the Weibel instability for a relativistic Maxwellian distribution and compare it with the numerical results. In the inhomogeneous case, we present solutions of the dispersion relation for the relativistic tearing mode, making no assumption about the thickness of the current sheet, and check the numerical method against the analytical expression.Comment: Accepted by PPC