Peremennye Zvezdy (Variable Stars) 43, No. 10, 2023 Received 1 November; accepted 24 November.	Article in PDF
	DOI: 10.24412/2221-0474-2023-43-115-120

Period Changes in the Ultracompact Binary ZTF J213056.71+442046.5

Sergey V. Antipin¹, Leonid N. Berdnikov¹, Konstantin A. Postnov¹, Alexandra M. Zubareva^2,1, Alexandre A. Belinski¹, Marina A. Burlak¹, Natalia P. Ikonnikova¹

1. Sternberg Astronomical Institute, M.V. Lomonosov University of Moscow, 13, University Ave., Moscow 119992, Russia [serge_ant@inbox.ru]

2. Institute of Astronomy, Russian Academy of Sciences, 48, Pyatnitskaya Str., Moscow 119017, Russia

1. Introduction

In the light of the planned space projects aimed to observe mHz gravitational waves, e.g. LISA and TianQin, careful studies of potential sources producing measurable gravitational signal are topical. Such sources include Galactic binary systems with ultrashort periods. Ren et al. (2023) published a list of ultracompact binary stars that are potential sources of gravitational waves detectable by LISA (Amaro-Seoane et al., 2017) and TianQin (Luo et al., 2016) space laser interferometers. Galactic binaries with precisely known orbital parameters (orbital period, masses of the components, binary inclination, etc.) and distance (also known as "verification binaries") are primary sources for calibration of the space laser interferometers. Most of several dozen currently known verification binaries include, in particular, AM CVn stars, detached double white dwarfs, and subdwarf binaries that resulted from evolution of low-mass binaries. One of the binaries in the list with orbital periods shorter than one hour is ZTF J213056.71+442046.5 (hereafter ZTF J2130+44).

ZTF J2130+44 was found independently by G. Murawski (Rivera Sandoval et al., 2019) and Kupfer et al. (2020) in the public data release of the Zwicky Transient Facility (ZTF) survey as a very short period ( ) eclipsing variable star. Kupfer et al. (2020) proposed a model of the binary system consisting of a typical white dwarf and a helium low-mass hot subdwarf star filling its Roche lobe. For the derived binary system parameters, Kupfer et al. (2020) predict the orbital decay of the system due to gravitational-wave emission with a period decrease rate of s s.

Although ZTF J2130+44 is not the brightest verification binary, we tried to measure the expected orbital decay rate due to emission of gravitational waves. This is an important task because the data analysis of gravitational wave sources requires as precise as possible knowledge of the orbital period and its change rate to dig out the signal against the expected Galactic and extragalactic stochastic noise in the mHz frequency band for space interferometers like LISA or TianQin (Staelens & Nelemans, 2023). To study the period variations of a potentially detectable gravitational-wave source and to compare these variations with predictions, we started photometric monitoring of ZTF J2130+44.

2. Observations and Reduction

Our photometric observations of ZTF J2130+44 were carried out in April-October, 2023 with the automated ASA RC600 60-cm reflector of the Caucasus Mountain Observatory (CMO) of the Sternberg Astronomical Institute, Lomonosov Moscow University, equipped with an Andor iKon-L (DZ936N-BV) CCD camera (Berdnikov et al., 2020). A total of 1912 CCD frames in the band with exposure times of 30 seconds were collected. The log of observations is presented in Table 1. The corresponding light curves are shown in Fig. 1. The VaST¹ software (Sokolovsky & Lebedev, 2018) was used to perform the aperture photometry and magnitude calibration. magnitudes of an ensemble of comparison stars within the field of view were derived from the APASS catalog.

3. O-C analysis

For the most accurate determination of the times of primary brightness minima, we apply the method by Hertzsprung (1919) algorithmized by Berdnikov (1992). To expand the time span of observations, we employed the SNAD ZTF object viewer² (Malanchev et al., 2023). ZTF - and -band data are very similar to our dataset in exposures (30 s) and photometric errors (about 001). The resulting time interval of ZTF J2130+44 brightness measurements suitable for our O-C analysis has thus increased to 5.5 years. The times of minima along with their O-C values are listed in Table 2. The O-C residuals were calculated using the linear light elements:

The corresponding phased light curve of ZTF J2130+44 folded with the elements (1) is presented in Fig. 2. The linear light elements (1) match the current O-C residuals with very small uncertainties in deriving the period and the time of primary minimum. However, in the anticipation of the binary's orbital evolution, we have also fitted them with quadratic light elements. It resulted in the following ephemeris:

Both linear and quadratic approximations are shown in Fig. 3. The solid and dashed curves in the figure correspond to formulas (1) and (2), respectively.

The quadratic light elements (2) imply a linear decrease of the period with the rate s s, which is consistent with the theoretical value published by Kupfer et al. (2020), i.e. s s. Note, however, that the accuracy of our quadratic elements is low. Further observations would be very helpful to improve the quality of the expected quadratic fit and confirm the binary orbital decay in this source.

4. Conclusions

To study the period variations of the potential LISA verification source ZTF J213056.71 +442046.5, we have obtained 1912 -band CCD frames with the 60-cm reflector RC600 of the Caucasus Mountain Observatory in 2023. To expand the time span of observations, we have used available ZTF data, enabling us to increase the resulting interval of ZTF J2130+44 brightness measurements suitable for our O-C analysis to 5.5 years.

We have derived 28 times of the primary minima of the close binary suitable for further O-C analysis. The constructed O-C diagram is in a good agreement with the linear light elements ( ).

The attempt to fit the O-C residuals with quadratic light elements results in determination of the linear period changes at a rate of s s that is very similar to the theoretical value assuming the orbital decay of the binary system solely due to gravitational wave emission. We stress the need for additional high-precision photometry of the source to definitely determine the orbital decay rate reported in this paper.

Acknowledgements. The work of SVA and KAP is supported by the Russian Science Foundation through grant 23-42-00055. This work was supported in part by M.V. Lomonosov Moscow State University Program of Development. This research was made possible through the use of the AAVSO Photometric All-Sky Survey (APASS), funded by the Robert Martin Ayers Sciences Fund and NSF AST-1412587.

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