Search for gravitational waves associated with the August 2006 timing glitch of the Vela pulsar

The physical mechanisms responsible for pulsar timing glitches are thought to excite quasinormal mode oscillations in their parent neutron star that couple to gravitational-wave emission. In August 2006, a timing glitch was observed in the radio emission of PSR B0833-45, the Vela pulsar. At the time of the glitch, the two colocated Hanford gravitational-wave detectors of the Laser Interferometer Gravitational-wave observatory (LIGO) were operational and taking data as part of the fifth LIGO science run (S5). We present the first direct search for the gravitational-wave emission associated with oscillations of the fundamental quadrupole mode excited by a pulsar timing glitch. No gravitational-wave detection candidate was found. We place Bayesian 90% confidence upper limits of $6.3\times {10}^{-21}$ to $1.4\times {10}^{-20}$ on the peak intrinsic strain amplitude of gravitational-wave ring-down signals, depending on which spherical harmonic mode is excited. The corresponding range of energy upper limits is $5.0\times {10}^{44}$ to $1.3\times {10}^{45}\mathrm{erg}$.

Figure 1

A schematic view of the analysis pipeline. The odds ratio ${\mathcal{O}}_{(+,-)}$ is evaluated using on and off-source data near the pulsar timing glitch. If the odds ratio in the on-source data is greater than that expected from the distribution of odds ratios in the off-source data, we have a candidate event for follow-up investigations. If there is no significant excess in ${\mathcal{O}}_{(+,-)}$ in the on-source data, we obtain upper limits on the gravitational-wave amplitude and energy.

Figure 2

The cumulative probability distribution function (CDF) for the off-source value of $\ln {\mathcal{O}}_{(+,-)}$. $\ln {\mathcal{O}}_{(+,-)}^{*}$ indicates the observed value. The shaded region shows the 90% confidence interval on the estimate of the CDF. The vertical line (red in the online version) indicates the value of $\ln {\mathcal{O}}_{(+,-)}=-5.03$ obtained from the on-source data segment. The probability of obtaining this value or greater from background alone is 0.92, where the red line intersects the black curve. The most significant off-source trial has $\ln {\mathcal{O}}_{(+,-)}=1.07$, and the least significant has $\ln {\mathcal{O}}_{(+,-)}=-11.26$.

Figure 3

The posterior probability density distributions and upper limits on the intrinsic peak amplitude of ring-downs, assuming only a single harmonic (i.e. value of $|m|$) is excited. The upper limits for each harmonic are shown as the vertical lines in the figure. The numerical values of the 90% confidence upper limits can be found in Table 4. The $l=2$, $|m|=0$ posterior is shown as the solid (black) line, the dashed curve (blue in the online version) shows the $l=2$, $|m|=1$ posterior and the $l=2$, $|m|=2$ posterior is shown as the dotted curve (red in the online version).

Figure 4

The posterior probability density distributions and upper limits on the total gravitational-wave energy in the form of ring-downs, assuming only a single harmonic (i.e. value of $|m|$) is excited. The upper limits for each harmonic are shown as the vertical lines in the figure. The numerical values of the 90% confidence upper limits can be found in Table 4. The $l=2$, $|m|=0$ posterior is shown as the solid black line, the dashed curve (blue in the online version) shows the $l=2$, $|m|=1$ posterior, and the $l=2$, $|m|=2$ posterior is shown as the dotted curve (red in the online version).

Figure 5

Detection probabilities for software injections of ring-downs described by Eq. (10) and with parameters drawn from the prior distributions used in the search and described in Sec. 4a. Efficiencies are computed by counting the number of detections in discrete bins in amplitude. The three different curves correspond to the different harmonics (values of $|m|$). The long vertical lines indicate the 90% detection efficiencies for the different harmonics, whose numerical values are given in the text. The shorter vertical bars indicate 90% binomial confidence intervals in the estimate of the detection probability in each amplitude bin. The color-coding and line-style convention is the same as that in Figs. 3 and 4: The $l=2$, $|m|=0$ efficiency curve is shown as the solid black line, the dashed curve (blue in the online version) shows the $l=2$, $|m|=1$ efficiency curve and the $l=2$, $|m|=2$ efficiency curve is shown as the dotted curve (red in the online version).