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3Peremennye Zvezdy (Variable Stars) 43, No. 10, 2023 Received 1 November; accepted 24 November.
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. Zubareva2'1, 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 [[email protected]]
2 Institute of Astronomy, Russian Academy of Sciences, 48, Pyatnitskaya Str., Moscow 119017, Russia
We performed the O-C analysis of period variations of the ultracompact binary system ZTF J213056.71+442046.5, a potentially detectable source of mHz gravitational waves for planned space laser interferometers. We combined our photometric observations carried out at the RC600 telescope of the Caucasus Mountain Observatory with publicly available ZTF survey data, thus increasing to 5.5 years the time interval covered with measurements. The O-C diagram is well fitted with linear light elements (P = 0d0273195154) but can be also described with quadratic light elements corresponding to a period decrease rate of dP/dt = (-2.00±0.60) x 10-12 s s-1. This finding is in a good agreement with the predicted value of the orbital period decay of this binary system due to gravitational wave emission.
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 (P = 0d0273195) 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 dP/dt = (-1.68±0.42) x 10-12 s s 1.
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
Table 1: Log of observations, RC600 telescope, V band
HJD range Date, 2023 Number of frames
2460051.49951 - .55136 April 16/17 86
2460120.36373 - .41047 June 24 104
2460121.34266 - .47812 June 25 299
2460140.39830 - .52204 July 14/15 268
2460159.48402 - .51429 August 2/3 286
2460183.41566 - .55114 August 26/27 262
2460208.40522 - .54511 September 20/21 308
2460230.31552 - .45160 October 12 299
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) 2048 x 2048 CCD camera (Berdnikov et al., 2020). A total of 1912 CCD frames in the V 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. V 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 g- and r-band data are very similar to our dataset in exposures (30 s) and photometric errors (about 0m01). 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:
HJD Min = 2,459,247.796853(±0.000004) + 0d0273195154(±0.0000000002) ■ E. (1)
1 https://scan.sai.msu.ru/vast
2 https://ztf.snad.space/
Figure 1. Individual light curves of ZTF J213056.71+442046.5, CMO V band observations.
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:
HJD Min
2,459,247.796871 (±0.000007) + 0d02731951548(±0.00000000014) ■ E -2.7271(±0.8178) x 10-14 ■ E2. (2)
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 dP/dt = (-2.00 ± 0.60) x 10-12 s s-1, which is consistent with the theoretical value published by Kupfer et al. (2020), i.e. dP/dt = (-1.68 ± 0.42) x 10-12 s s-1. 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 V-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.
Table 2: Times of minima for ZTF J213056.71+442046.5
min HJD err, d Source, band N O-C, d Epoch
2458265.27775 0.00002 ZTF, g 51 -0.00005062 -35964
2458340.84358 0.00002 ZTF, r 154 -0.00000025 -33198
2458368.32699 0.00002 ZTF, g 87 -0.00002276 -32192
2458465.83036 0.00001 ZTF, r 461 -0.00000328 -28623
2458695.17770 0.00002 ZTF, r 122 0.00000482 -20228
2458701.40655 0.00002 ZTF, g 111 0.00000530 -20000
2458766.61823 0.00002 ZTF, g 72 0.00000200 -17613
2458768.50330 0.00002 ZTF, r 75 0.00002544 -17544
2459007.38514 0.00002 ZTF, g 63 0.00002265 -8800
2459015.38976 0.00001 ZTF, r 307 0.00002464 -8507
2459117.20959 0.00002 ZTF, g 125 0.00002068 -4780
2459121.85393 0.00002 ZTF, r 109 0.00004306 -4610
2459377.20940 0.00003 ZTF, r 53 0.00000248 4737
2459419.71856 0.00002 ZTF, g 82 -0.00000351 6293
2459491.86939 0.00004 ZTF, r 30 -0.00001372 8934
2459754.13674 0.00003 ZTF, r 56 -0.00001170 18534
2459757.63364 0.00002 ZTF, g 47 -0.00000968 18662
2459882.92102 0.00003 ZTF, g 38 0.00007263 23248
2459888.98590 0.00004 ZTF, r 33 0.00002021 23470
2460092.32503 0.00005 ZTF, g 22 -0.00000302 30913
2460092.32505 0.00005 ZTF, r 21 0.00001698 30913
2460051.50964 0.00004 CMO, V 85 -0.00003699 29419
2460121.14711 0.00002 CMO, V 403 -0.00001179 31968
2460140.46203 0.00001 CMO, V 266 0.00001082 32675
2460159.44908 0.00002 CMO, V 286 -0.00000240 33370
2460183.49024 0.00002 CMO, V 262 -0.00001596 34250
2460208.48759 0.00001 CMO, V 308 -0.00002257 35165
2460230.37053 0.00001 CMO, V 294 -0.00001442 35966
Figure 2. Phased light curve of ZTF J213056.71+442046.5.
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 (P = 0d0273195154).
The attempt to fit the O-C residuals with quadratic light elements results in determination of the linear period changes at a rate of dP/dt = (-2.00 ± 0.60) x 10—12 s s—1 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.
References:
Amaro-Seoane, P., Audley, H., Babak, S., et al. 2017, arXiv:1702.00786 Berdnikov, L. N., 1992, Soviet Astron. Letters, 18, 207
Berdnikov, L. N., Belinskii, A. A., Shatskii, N. I., et al., 2020, Astron. Rep., 64, 310 Hertzsprung, E., 1919, Astron. Nachr., 210, 17
Kupfer, T., Bauer, E.B., Marsh, T.R., et al. 2020, Astrophys. J, 891, id45 Luo, J., Chen, L.-S., Duan, H.-Z., et al. 2016, Classical and Quantum Gravity, 33, id. 035010
Malanchev, K., Kornilov, M. V., Pruzhinskaya, M. V. et al., 2023, Publ. Astron. Soc. Pacific, 135, id. 024503
Figure 3. O-C diagram for ZTF J213056.71+442046.5 relative to the linear light elements (1). The solid line corresponds to the elements (1), the dashed curve corresponds to the elements (2). Open squares mark the ZTF g band, open circles are for ZTF r band, and the filled circles, for our V-band observations.
Ren, L., Li, C., Ma, B., et al., 2023, Astrophys. J. Suppl., 264, 39 Rivera Sandoval, L. E., Maccarone, T., & Murawski, G. 2019, Astron. Tel., 12847, 1 Sokolovsky, K. V. & Lebedev, A. A., 2018, Astron. and Computing, 22, 28 Staelens, S. & Nelemans, G., 2023, Astron. & Astrophys., in press, arXiv:2310.19448
