Template banks based on Zn and An∗ lattices

Abstract

Matched filtering is a traditional method used to search a data stream for signals. If the source (and hence its n parameters) are unknown, many filters must be employed. These form a grid in the n-dimensional parameter space, known as a template bank. It is often convenient to construct these grids as lattices. The simplest of these, Zn, is used in both continuous gravitational-wave and gamma-ray pulsar searches; we wanted to investigate how much might be gained by replacing it with the more elaborate An∗ lattice. To determine this, we calculate the distribution of the mismatch function, both in the traditional quadratic approximation and with the recently proposed spherical ansatz. The fraction of signals which are lost is determined by the even moments of this distribution, which we find. Many of these quantities have a simple and well-defined n→∞ limit, which often gives an accurate estimate even for small n. Our main conclusions are the following: (i) a fairly effective template-based search can be constructed at mismatch values that are shockingly high in the quadratic approximation; (ii) the minor advantage offered by an An∗ template bank (compared to Zn) at small template separation becomes even less significant for large template spacings. In most cases, the gain from employing an An∗ lattice is not enough to justify the increase in complexity.