A semi-coherent search for optical pulsations from Scorpius X-1

TL;DR

This work targets continuous gravitational-wave emission from rapidly spinning neutron stars in binaries, focusing on Sco X-1 as the brightest accreting source. It develops and applies a semi-coherent optical pulsation search using SiFAP2/TNG data, dividing observations into short coherent segments and incoherently summing their detection statistics to account for orbital motion. Validating the method on PSR J1023+0038 shows the approach can recover known optical pulsations in binaries using data alone, while applying it to Sco X-1 yields no detections but sets the tightest optical pulsed-amplitude upper limit to date, A_ul ≈ 9.23×10^{-5}, improving prior X-ray limits by ~4×. The results underscore the promise of high-time-resolution optical observations for deep searches of fast pulsars and inform future improvements in long-baseline, multi-epoch analyses.

Abstract

The emission of continuous gravitational waves (CWs) possibly explains why pulsars spinning with a period shorter than a millisecond have not been observed so far. Neutron stars accreting mass at the highest rates are the most promising targets for a search for CWs, because a strong emission of gravitational waves is required to balance the torque exerted by mass accretion onto the neutron star. Detecting coherent pulsations in the electromagnetic emission maximizes the search sensitivity, but has so far not been successful for most of the brightest accreting neutron stars. Here, we present the first search for pulsations in the optical band from the brightest accreting neutron star known, Sco X-1. To this end, we tailored semi-coherent search strategies to data obtained over four years, for a total of $\sim$$56$ ks, by the SiFAP2 fast photometer mounted at the Telescopio Nazionale Galileo (TNG). These searches are especially suited to analysing long observations of systems for which only limited knowledge on the orbital parameters is available, and involve joining coherent analyses on shorter segments without connecting the spin phase between them. The large count rates afforded by an optical telescope and the efficiency of the search strategy employed allowed us to set an upper limit of $9 \times 10^{-5}$ to the pulsed amplitude, which is lower by a factor of four with respect to previous searches in the X-ray band. We also show that the application of semi-coherent searches to SiFAP2 observations of the first detected optical millisecond pulsar, PSR J1023+0038, could have preceded its detection in the radio band. These results highlight the role played by high-time-resolution optical observations in performing deep searches of quickly rotating pulsars.

Figures (4)

• Figure 1: Maximum values of the summed power $\Sigma$, regardless of the corresponding orbital parameter combination, in the ${50 - 1550}$ Hz frequency range, on a SiFAP2 observation of PSR J1023+0038. The dashed black line represents the $1\%$ false-alarm threshold, which instead is calculated for all the combinations explored.
• Figure 2: Counts distribution from a 128-s SiFAP2 lightcurve binned at $2.5\times10^{-4}$ s (histogram), with binomial uncertainties (light blue area, 95% c.l.), compared with the expected distributions from pure Poissonian noise (orange dashed line), and GP noise arising from 1-, 4-, and 8-pixel crosstalk (solid lines).
• Figure 3: Upper panel - Power distribution of the PDS from the same data in Fig. \ref{['fig:noisecountdist']} (histogram), with binomial uncertainties (light blue area, 95% c.l.), compared with a $\chi^2$ distribution with two d.o.f. (burgundy points, normalized to the total number of powers). Lower panel - Same as upper panel, but after rescaling every power in the PDS by the dispersion index of the data. The $\chi^2$ distribution in the two panels is the same.
• Figure 4: Upper panel - Power distribution of all of the $\Sigma$ values obtained in the analysis of the $1349-1450$ Hz interval for dataset D2 (see Sect. \ref{['sec:SCOX1']}). The histogram was renormalized to the number of $\Sigma$ values considered, i.e., the $51712 \times695\times 45$ templates (over the $f$, $a_\perp$, and $T_{\mathrm{asc}}$ dimensions). The dashed line is the expected $\chi^2_{2M}$ probability density function in the case of noise alone. Lower panel - Distributions of the maximum values of $\Sigma$ over subsets of our parameter space. The blue histogram was obtained by taking non-overlapping blocks of close templates, with block sizes equal to 128, 3, and 5 points in the $f$, $a_\perp$, and $T_{\mathrm{asc}}$ dimensions, respectively; the orange histogram was obtained in the same way, but after randomly shuffling the position of all points in our space. Both histograms were renormalized to the number of subsets, $842\,340$. The dashed line is the expected $n$-trials-corrected $\chi^2_{2M}$ probability density function (Eq. \ref{['eq:multipdf']}).