Effect of timing noise on targeted and narrow-band coherent searches for continuous gravitational waves from pulsars

Most searches for continuous gravitational waves from pulsars use Taylor expansions in the phase to model the spin-down of neutron stars. Studies of pulsars demonstrate that their electromagnetic (EM) emissions suffer from timing noise, small deviations in the phase from Taylor expansion models. How the mechanism producing EM emission is related to any continuous gravitational-wave (CW) emission is unknown; if they either interact or are locked in phase, then the CW will also experience timing noise. Any disparity between the signal and the search template used in matched filtering methods will result in a loss of signal-to-noise ratio, referred to as “mismatch.” In this work we assume the CW suffers a level of timing noise similar to its EM counterpart. We inject and recover fake CW signals, which include timing noise generated from observational data on the Crab pulsar. Measuring the mismatch over durations of order $\sim 10$ months, the effect is, for the most part, found to be small. This suggests recent so-called “narrow-band” searches which placed upper limits on the signals from the Crab and Vela pulsars will not be significantly affected. At a fixed observation time, we find the mismatch depends upon the observation epoch. Considering the averaged mismatch as a function of observation time, we find that it increases as a power law with time, and so may become relevant in long baseline searches.

Figure 1

Illustration of the jumps between “local” per-month templates in frequency space, defining the frequency jump $\mathrm{\Delta }f$. This depiction amplifies the order of magnitude of $\mathrm{\Delta }f$ in order to highlight the timing noise: for the jumps in the ephemeris, $\mathrm{\Delta }f$ is several orders of magnitude smaller than the change in frequency due to spin-down alone.

Figure 2

In (a) we show the mismatch as a function of parameter space for a signal without timing noise. The injected signal has parameters $[f_0,{\dot{f}}_0,{\ddot{f}}_0]$, as a result the mismatch has a minimum at this point. This can be compared with (b) which shows the mismatch from a signal including timing noise. The signal is generated from the Crab ephemeris between MJD 45150 and 45668.

Figure 3

Measured best mismatch ${\mu }_{\min }$ as a function of grid spacing parameter $m$ (see eqn. (2), for the Crab pulsar over the S5 period. This demonstrates that ${\mu }_{\min }$ plateaus at a nonzero mismatch suggesting we are resolving a mismatch due to timing noise instead of the effect of finite grid resolution.

Figure 4

Minimum mismatch ${\mu }_{\min }$ found in six-month sliding window searches as a function of epoch at the center of window. Vertical dashed lines indicate glitch events as described by Espinoza et al. [23]. The solid vertical line indicates the date MJD 55362, a period of anomalously large mismatch.

Figure 5

Averaging the mismatch for sliding window searches and varying the observation times. The points give the mean while the bars correspond to one standard deviation.