Search for continuous gravitational waves from 20 accreting millisecond x-ray pulsars in O3 LIGO data

Results are presented of searches for continuous gravitational waves from 20 accreting millisecond x-ray pulsars with accurately measured spin frequencies and orbital parameters, using data from the third observing run of the Advanced LIGO and Advanced Virgo detectors. The search algorithm uses a hidden Markov model, where the transition probabilities allow the frequency to wander according to an unbiased random walk, while the $\mathcal{J}$-statistic maximum-likelihood matched filter tracks the binary orbital phase. Three narrow subbands are searched for each target, centered on harmonics of the measured spin frequency. The search yields 16 candidates, consistent with a false alarm probability of 30% per subband and target searched. These candidates, along with one candidate from an additional target-of-opportunity search done for SAX $\mathrm{J}1808.4-3658$, which was in outburst during one month of the observing run, cannot be confidently associated with a known noise source. Additional follow-up does not provide convincing evidence that any are a true astrophysical signal. When all candidates are assumed nonastrophysical, upper limits are set on the maximum wave strain detectable at 95% confidence, $h_0^{95\%}$. The strictest constraint is $h_0^{95\%}=4.7\times {10}^{-26}$ from IGR $\mathrm{J}17062-6143$. Constraints on the detectable wave strain from each target lead to constraints on neutron star ellipticity and $r$-mode amplitude, the strictest of which are ${\epsilon }^{95\%}=3.1\times {10}^{-7}$ and ${\alpha }^{95\%}=1.8\times {10}^{-5}$ respectively. This analysis is the most comprehensive and sensitive search of continuous gravitational waves from accreting millisecond x-ray pulsars to date.

Figure 1

Summary of search results across all targets and subbands with $\mathcal{L}>{\mathcal{L}}_{\mathrm{th}}$. The different symbols correspond to candidates from different targets. The ordinate shows $p_{\text{noise}}$ for each candidate, the probability that a search of that candidate’s subband in pure noise would return at least one candidate at least as loud as the one seen. The color of each candidate indicates $\mathcal{L}$ (see color bar at right). Candidates that are eliminated by the vetoes outlined in Sec. 6 are not shown for clarity. Details on the search results are in Sec. 7 and Appendix pp2.

Figure 2

Search results for IGR $\mathrm{J}18245-2452$. Black crosses indicate the terminating frequency and $\mathcal{L}$ for the most likely path through the subband for each binary template. The vertical blue dashed (green dot-dashed) lines correspond to the threshold set via Gaussian (off-target) noise realizations, ${\mathcal{L}}_{\mathrm{th},\mathrm{G}}$ (${\mathcal{L}}_{\mathrm{th},\mathrm{OT}}$), in each subband. Solid red lines in the right panel indicate the peak frequency of known instrumental lines in the Hanford detector; the orange band indicates the width of the line in the detector frame and the yellow band indicates the increased effective width due to Doppler broadening, as described in Sec. 6a. Multiple overlapping orange bands creates the red bands. The subband around 508.8 Hz is especially noisy due to test mass suspension violin mode resonances [110]. The transparency of crosses in subbands with many templates, is adjusted relative to the maximum $\mathcal{L}$ in that subband for clarity.

Figure 3

Kernel density estimate of the PDF of the constraints on ellipticity ${\epsilon }^{95\%}$ (left panel) and dimensionless $r$-mode amplitude ${\alpha }^{95\%}$ (right panel) via Eqs. (14) and (15) respectively. Both PDFs are normalized to a height of one. The black dashes in both panels correspond to the individual estimates of ${\epsilon }^{95\%}$ or ${\alpha }^{95\%}$ from each target.

Figure 4

Search results for each target and subband, laid out as in Fig. 2. Black crosses indicate the frequency and $\mathcal{L}$ for the most likely path through the subband for each binary template. The vertical blue dashed (green dot-dashed) lines correspond to the threshold set via Gaussian (off-target) noise realizations, ${\mathcal{L}}_{\mathrm{th},\mathrm{G}}$ (${\mathcal{L}}_{\mathrm{th},\mathrm{OT}}$), in each subband. Solid red lines indicate the peak frequency of known instrumental lines in the Hanford or Livingston detectors; the red band indicates the width of the line and the yellow band indicates the increased effective width due to Doppler broadening, as described in Sec. 6a. Multiple overlapping orange bands creates the red bands. The transparency of crosses in subbands with many templates, e.g., the subbands of IGR $\mathrm{J}16597-3704$, is adjusted relative to the maximum $\mathcal{L}$ in that sub-band for clarity.

Figure 5

Top panels: frequency paths, $f(t)$, for candidates with $p_{\text{noise}}\le 0.1$. The terminating frequency bin, $f(N_T)$, is subtracted and displayed in the title of each figure for clarity. Faint horizontal grey lines demarcate frequency bins of size $\mathrm{\Delta }f=5.787037\times {10}^{-7}\mathrm{Hz}$, while faint vertical grey lines demarcate chunks of length $T_{\text{drift}}=10\mathrm{d}$. Bottom panels: the cumulative log-likelihood along the frequency path relative to the average sum log-likelihood needed to reach ${\mathcal{L}}_{\mathrm{th}}$, $C\mathcal{L}\equiv {\sum }_{i=0}^{i=t}[\mathcal{L}(i)-{\mathcal{L}}_{\mathrm{th}}/N_T]$, where ${\sum }_{i=0}^{i=t}\mathcal{L}(i)$ is $\ln P(Q^{*}|O)$ from Eq. (2) truncated after the $t$th segment. The horizontal blue dashed line corresponds to ${\sum }_{i=0}^{i=t}\mathcal{L}(i)=t{\mathcal{L}}_{\mathrm{th}}/N_T$. The grey shaded regions in both top and bottom panels correspond to the segments which have no SFTs and are therefore filled with a uniform log-likelihood, as described in Sec. 5.

Figure 6

$\mathcal{L}$, as represented by the color of each pixel, calculated at 3721 regularly spaced sky locations in a $100{\mathrm{arcmin}}^2$ patch of sky, centered on IGR $\mathrm{J}16597-3704$. See text in Appendix pp2-s1 for details.