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Register a new userModel-Based Cross-Correlation Search for Gravitational Waves from Scorpius X-1
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We consider the cross-correlation search for periodic GWs and its potential application to the LMXB Sco X-1. This method coherently combines data from different detectors at the same time, as well as different times from the same or different detectors. By adjusting the maximum time offset between a pair of data segments to be coherently combined, one can tune the method to trade off sensitivity and computing costs. In particular, the detectable signal amplitude scales as the inverse fourth root of this coherence time. The improvement in amplitude sensitivity for a search with a coherence time of 1hr, compared with a directed stochastic background search with 0.25Hz wide bins is about a factor of 5.4. We show that a search of 1yr of data from Advanced LIGO and Advanced Virgo with a coherence time of 1hr would be able to detect GWs from Sco X-1 at the level predicted by torque balance over a range of signal frequencies from 30-300Hz; if the coherence time could be increased to 10hr, the range would be 20-500Hz. In addition, we consider several technical aspects of the cross-correlation method: We quantify the effects of spectral leakage and show that nearly rectangular windows still lead to the most sensitive search. We produce an explicit parameter-space metric for the cross-correlation search in general and as applied to a neutron star in a circular binary system. We consider the effects of using a signal template averaged over unknown amplitude parameters: the search is sensitive to a combination of the intrinsic signal amplitude and the inclination of the neutron star rotation axis, and the peak of the expected detection statistic is systematically offset from the true signal parameters. Finally, we describe the potential loss of SNR due to unmodelled effects such as signal phase acceleration within the Fourier transform timescale and gradual evolution of the spin frequency.
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We describe the application of the lattice covering problem to the placement of templates in a search for continuous gravitational waves from the low-mass X-Ray binary Scorpius X-1. Efficient placement of templates to cover the parameter space at a given maximum mismatch is an application of the sphere covering problem, for which an implementation is available in the LatticeTiling software library. In the case of Sco X-1, potential correlations, in both the prior uncertainty and the mismatch metric, between the orbital period and orbital phase, lead to complications in the efficient construction of the lattice. We define a shearing coordinate transformation which simultaneously minimizes both of these sources of correlation, and allows us to take advantage of the small prior orbital period uncertainty. The resulting lattices have a factor of about 3 fewer templates than the corresponding parameter space grids constructed by the prior straightforward method, allowing a more sensitive search at the same computing cost and maximum mismatch.
We present results of a search for continuously-emitted gravitational radiation, directed at the brightest low-mass X-ray binary, Scorpius X-1. Our semi-coherent analysis covers 10 days of LIGO S5 data ranging from 50-550 Hz, and performs an incoherent sum of coherent $mathcal{F}$-statistic power distributed amongst frequency-modulated orbital sidebands. All candidates not removed at the veto stage were found to be consistent with noise at a 1% false alarm rate. We present Bayesian 95% confidence upper limits on gravitational-wave strain amplitude using two different prior distributions: a standard one, with no a priori assumptions about the orientation of Scorpius X-1; and an angle-restricted one, using a prior derived from electromagnetic observations. Median strain upper limits of 1.3e-24 and 8e-25 are reported at 150 Hz for the standard and angle-restricted searches respectively. This proof of principle analysis was limited to a short observation time by unknown effects of accretion on the intrinsic spin frequency of the neutron star, but improves upon previous upper limits by factors of ~1.4 for the standard, and 2.3 for the angle-restricted search at the sensitive region of the detector.
The cross-correlation search has been previously applied to map the gravitational wave (GW) stochastic background in the sky and also to target GW from rotating neutron stars/pulsars. Here we investigate how the cross-correlation method can be used to target a small region in the sky spanning at most a few pixels, where a pixel in the sky is determined by the diffraction limit which depends on the (i) baseline joining a pair of detectors and (ii) detector bandwidth. Here as one of the promising targets, we consider the Virgo cluster - a hot spot spanning few pixels - which could contain, as estimates suggest $sim 10^{11}$ neutron stars, of which a small fraction would continuously emit GW in the bandwidth of the detectors. For the detector baselines, we consider advanced detector pairs among LCGT, LIGO, Virgo, ET etc. Our results show that sufficient signal to noise can be accumulated with integration times of the order of a year. The results improve for the multibaseline search. This analysis could as well be applied to other likely hot spots in the sky and other possible pairs of detectors.
We present the results of a semicoherent search for continuous gravitational waves from the low-mass X-ray binary Scorpius X-1, using data from the first Advanced LIGO observing run. The search method uses details of the modelled, parametrized continuous signal to combine coherently data separated by less than a specified coherence time, which can be adjusted to trade off sensitivity against computational cost. A search was conducted over the frequency range from 25 Hz to 2000 Hz, spanning the current observationally-constrained range of the binary orbital parameters. No significant detection candidates were found, and frequency-dependent upper limits were set using a combination of sensitivity estimates and simulated signal injections. The most stringent upper limit was set at 175 Hz, with comparable limits set across the most sensitive frequency range from 100 Hz to 200 Hz. At this frequency, the 95 pct upper limit on signal amplitude h0 is 2.3e-25 marginalized over the unknown inclination angle of the neutron stars spin, and 8.03e-26 assuming the best orientation (which results in circularly polarized gravitational waves). These limits are a factor of 3-4 stronger than those set by other analyses of the same data, and a factor of about 7 stronger than the best upper limits set using initial LIGO data. In the vicinity of 100 Hz, the limits are a factor of between 1.2 and 3.5 above the predictions of the torque balance model, depending on inclination angle, if the most likely inclination angle of 44 degrees is assumed, they are within a factor of 1.7.
Scorpius X-1 (Sco X-1) and X-ray transient (XTE) J1751-305 are Low-Mass X-ray Binaries (LMXBs) that may emit continuous gravitational waves detectable in the band of ground-based interferometric observatories. Neutron stars in LMXBs could reach a torque-balance steady-state equilibrium in which angular momentum addition from infalling matter from the binary companion is balanced by angular momentum loss, conceivably due to gravitational-wave emission. Torque-balance predicts a scale for detectable gravitational-wave strain based on observed X-ray flux. This paper describes a search for Sco X-1 and XTE J1751-305 in LIGO Science Run 6 data using the TwoSpect algorithm, based on searching for orbital modulations in the frequency domain. While no detections are claimed, upper limits on continuous gravitational-wave emission from Sco X-1 are obtained, spanning gravitational-wave frequencies from 40 to 2040 Hz and projected semi-major axes from 0.90 to 1.98 light-seconds. These upper limits are injection validated, equal any previous set in initial LIGO data, and extend over a broader parameter range. At optimal strain sensitivity, achieved at 165 Hz, the 95% confidence level random-polarization upper limit on dimensionless strain $h_0$ is approximately $1.8 times 10^{-24}$. Closest approach to the torque-balance limit, within a factor of 27, is also at 165 Hz. These are the first upper limits known to date on $r$-mode emission from this XTE source. Upper limits are set in particular narrow frequency bands of interest for J1751-305. The TwoSpect method will be used in upcoming searches of Advanced LIGO and Virgo data.
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