Semicoherent search strategy for known continuous wave sources in binary systems

C. Messenger

Phys. Rev. D 84, 083003 – Published 10 October 2011

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.

Received 11 November 2010

DOI:https://doi.org/10.1103/PhysRevD.84.083003

Authors & Affiliations

C. Messenger^*

Albert-Einstein-Institut, Hannover, Callinstraße 38, D-30167, Germany, and School of Physics and Astronomy, Cardiff University, Queens Buildings, The Parade, Cardiff CF24 3AA, United Kingdom

^*chris.messenger@astro.cf.ac.uk

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Vol. 84, Iss. 8 — 15 October 2011

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Images

Figure 1
Shown here are the results of a simulation in which the mismatch $μ (u)$ has been computed over a region in the three-dimensional parameter around the location of a simulated signal. The simulation models a single segment of 200 seconds length with signal parameters $ν = 200 Hz$ , $a = 1 second$ , $Ω = 10^{- 4} rads s^{- 1}$ , $e = 0.02$ , and $ω = 1 rad$ ( $t_{asc}$ chosen randomly from the range $[- P / 2, P / 2]$ ). Each panel shows the mismatch as a function of each pair of parameters where the mismatch has been maximized over all other parameters. The solid black and grey contours indicate the measured mismatch ranging from $μ = 0.1$ (black) in steps of 0.1. The dashed red ellipses are those calculated using the metric given in Eq. (21) on the approximate phase given by Eq. (20).Reuse & Permissions
Figure 2
The results of a simulation in which the mismatch $μ (θ, Δ θ)$ has been computed over a region in the six-dimensional parameter space around the location of a simulated signal. The simulation modeled 500 individual coherently analyzed segments each of 200 seconds length spread over a period of $τ = 10^{8} seconds$ . The signal parameters were $ν = 200$ , $a = 1$ , $Ω = 10^{- 4} rads s^{- 1}$ , $e = 0.02$ , and $ω = 1$ ( $t_{asc}$ chosen randomly from the range $[- P / 2, P / 2]$ ). Each panel shows the mismatch as a function of each pair of parameters where the mismatch has been maximized over all other parameters. The solid black and grey contours indicate the measured mismatch ranging from $μ = 0.1$ (black) in steps of 0.1. The dashed red ellipses are those calculated using the approximate metric given in Eq. (27).Reuse & Permissions
Figure 3
An orbital parameter subspace represented as the eccentricity versus the product of the signal frequency and projected semimajor axis. The dashed lines correspond to the semicoherent metric’s requirement for templates in the eccentricity parameters $κ$ and $η$ . Each line represents a different coherent observation length measured in units of $Ω Δ T$ . Above each dashed curve a semicoherent analysis would require templates in the eccentricity parameters for a mismatch $μ = 0.1$ . Correspondingly, as the coherent integration time increases (relative to the orbital period) a limit is achieved at the boundary of the shaded region. Below this limit, one need not include eccentricity in the signal model.Reuse & Permissions
Figure 4
The results of a simulation in which the mismatch $μ (λ)$ has been computed over a region in the six-dimensional parameter around the location of a simulated signal. The simulation modeled a single coherently analyzed segment of $10^{6} seconds$ length containing a signal with parameters $ν = 200 Hz$ , $a = 1$ sea, $Ω = 10^{- 4} rads \sec^{- 1}$ , sea, $e = 0.005$ , and $ω = 1 rad$ ( $t_{asc}$ chosen randomly from the range $[- P / 2, P / 2]$ ). Each panel shows the mismatch as a function of each pair of parameters where the mismatch has been maximized over all other parameters (these are not slices). The solid black and grey contours indicate the measured mismatch ranging from $μ = 0.1$ (black) in steps of 0.1. The dashed red ellipses are those calculated using the approximate metric given in Eq. (30).Reuse & Permissions

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