Semicoherent search strategy for known continuous wave sources in binary systems

Abstract

We present a method for detection of weak continuous signals from sources in binary systems via the incoherent combination of many short coherently analyzed segments. The main focus of the work is on the construction of a metric on the parameter space for such signals for use in matched-filter based searches. The metric is defined using a maximum likelihood detection statistic applied to a binary orbit phase model including eccentricity. We find that this metric can be accurately approximated by its diagonal form in the regime where the segment length is ( the orbital period. Hence, correlations between parameters are effectively removed by the combination of many independent observations. We find that the ability to distinguish signal parameters is independent of the total semicoherent observation span (for the semicoherent span ) the segment length) for all but the orbital angular frequency. Increased template density for this parameter scales linearly with the observation span. We also present two example search schemes. The first use a reparametrized phase model upon which we compute the metric on individual short coherently analyzed segments. The second assumes long ) the orbital period segment lengths from which we again compute the coherent metric and find it to be approximately diagonal. In this latter case we also show that the semicoherent metric is equal to the coherent metric.

Binary Millisecond Pulsar Discovery via Gamma-Ray Pulsations

“…The metric components along the search-space directions of f andḟ are constant across the entire space [see, e.g., (18,19)]. In contrast, the orbital metric components (in search-space directions of {P orb , T asc , x}) explicitly depend upon the search parameters [see, e.g., (24)]. This implies that the metric (and so the grid-point density required to not miss a signal) changes across orbital parameter space.…”

“…This f 3 max -dependency is readily seen from the fact that the amplitude of the pulsarrotational-phase modulation due to the binary motion is proportional to the spin frequency f . And, the metric components involve products of first-order derivatives of the rotational phase with respect to the parameters (17)(18)(19)24). As the number of grid points is proportional to the square root of the metric determinant, it therefore increases with f 3 (one f contribution from each of the three orbital dimensions searched).…”

“…The metric is obtained from a Taylor expansion of the fractional loss to second order around the parameter-space location of a given signal. In contrast to searching for solitary pulsars, a difficulty in the binary case is that the metric components explicitly depend on the search parameters (24). Thus, the metric (and so the grid-point density required to not miss a signal) changes across orbital parameter space.…”

“…The computing cost to coherently follow up a single semi-coherent candidate is negligible relative to the total cost of the first stage. Therefore, constructing the search grid of the semi-coherent stage as efficiently as possible is of utmost importance.The key element in constructing an optimally efficient grid for the semi-coherent search is a distance metric on the search space (17)(18)(19)24). The metric provides an analytic geometric tool measuring the expected fractional loss in signal-to-noise ratio (S/N) squared for any given pulsar-signal location at a nearby grid point.…”

Radio-quiet Gamma-ray Pulsars

“…But in a scenario where radio-quietness is due to viewing angle, astronomers also expect to observe a significant number of RQ MSPs. However, contrary to the detection of a temporal signal from a solitary pulsar, a difficulty in the binary system is that the metric components determined on the search space explicitly change across the orbital parameters (Messenger 2011), and the inefficient blind search in a high frequency domain requires large trials, which seriously reduces the significance of a possible detection. Thus far, PSR J1311-3430 is the only (Pletsch et al 2012a) recycled neutron star detected without a known contemporaneous radio ephemeris.…”