Discovery of a New Possible Quadruple Star Consisting of Two Eclipsing Binaries with Periods Close to a 3:2 Ratio

CzeV1640³ is a new candidate for a quadruple star system, consisting of two close eclipsing detached binary stars (EA + EA), further referred as CzeV1640A and CzeV1640B. CzeV1640 was discovered in the course of long-term photometric study of a field in the Auriga constellation. The study was performed at a private observatory⁴ near Zlín, Czechia, using 0.3 m custom-build telescope optimized for wide field of view and Moravian Instruments G4-16000 CCD camera.

The field in Auriga was observed for 12 nights from 2018 November to 2019 April. The variability of CzeV1640 was discovered the first observing night. The star was then registered in the CzeV catalog (Skarka et al. 2017). The shape of the CzeV1640 light curve suggests detached eclipsing binary system (Algol-type).

Observations are performed without filter to maximize throughput of the imaging system. A comparison star⁵ with similar B–V index⁶ 0.57 is chosen (CzeV1649 B–V index is 0.56) to suppress the effect of atmospheric extinction on light curve shape. Its non-variability is checked using other comparison stars within the field of view—there are 11 selected comparison stars with increasing color index used for 144 total variable stars observed in this particular field. The comparison star for CzeV1640 is also used with 26 other variable stars with similar color indexes.

Photometry of all stars within the field of view is processed using the SIPS software package and resulting light curves from all nights are handled with the SILICUPS software package. Five instances of primary minima and two instances of secondary minima allow determination of basic epoch and period of CzeV1640A:

$$\begin{eqnarray*}\begin{array}{rcl}{T}_{0A} & = & 2458521.336200\,[\mathrm{HJD}]\\ {P}_{A} & = & 0.554234\,[\mathrm{days}].\end{array}\end{eqnarray*}$$

The light curve from the first night shows signatures of possible additional eclipses, overlapping the regular primary and secondary eclipses of CzeV1640. Deformations of light curve, resembling overlapped eclipses, were also detected during subsequent nights (see the top panel of Figure 1), suggesting that the observed light curve anomalies were not caused only by artifacts induced by instrument, observing conditions, or data processing.

Phenomenological model of eclipses (Mikulášek 2015) was fitted to the observed data using scipy⁷ Python package. The phase of secondary minimum is fixed to 0.5.

$$\begin{eqnarray}\begin{array}{rcl}f(P) & = & {A}_{1}\left(1+{C}_{1}\displaystyle \frac{{P}^{2}}{{D}_{1}^{2}}\right)\left\{1-{\left[1-\exp \left(1-\cosh \displaystyle \frac{P}{{D}_{1}}\right)\right]}^{{{\rm{\Gamma }}}_{1}}\right\}\\ & & +\ {A}_{2}\left(1+{C}_{2}\displaystyle \frac{{P}_{2}^{2}}{{D}_{2}^{2}}\right)\left\{1-{\left[1-\exp \left(1-\cosh \displaystyle \frac{{P}_{2}}{{D}_{2}}\right)\right]}^{{{\rm{\Gamma }}}_{2}}\right\}\\ & & +\ a\cos (4\pi P)+b\end{array}\end{eqnarray} \tag{ 1 }$$

where

$$\begin{eqnarray}&&{P}_{2}=P-0.5-\mathrm{round}(P-0.5).\end{eqnarray} \tag{ 2 }$$

A new set of photometric data, created as original data with subtracted phenomenological model, corresponds very well to another eclipsing variable star (see the bottom right panel of Figure 1). Data are again processed using the SILICUPS software and four minima instances, identified within the new set, allowed us to find orbital elements for CzeV1640B:

$$\begin{eqnarray*}\begin{array}{rcl}{T}_{0B} & = & 2458439.502871[\mathrm{HJD}]\\ {P}_{B} & = & 0.842581[\mathrm{days}].\end{array}\end{eqnarray*}$$

Despite the amplitude of brightness changes out of the transits being approximately as high as the depth of primary transits (approx. 0.03 mag), CzeV1640B light curve contains distinct transits. This hints to detached binary star (Algol-type).

The relatively low angular resolution 134 pixel⁻¹ of the used photometry telescope does not allow us to decide whether the stars are physically connected or just projected to the same photometric aperture. Ruling out the second possibility is a complicated task.

Gaia DR2 catalog (Gaia Collaboration et al. 2018) contains 5 stars within 16'' radius around CzeV1640 coordinates (angular radius of the used photometry aperture). The brightest star (presumably the CzeV1640 itself) brightness⁸ is 14.50 mag, while the second brightest star brightness is 18.57 mag. The flux ratio of these two brightest stars is 42.44, which results to 0.026 mag maximum contribution of the brightest nearby star to the brightness of CzeV1640. However, the measured brightness amplitude of the CzeV1640B exceeds 0.060 mag. This rules out the possibility the overlapped light curve originates in any nearby star within photometry aperture, contained in the Gaia DR2 catalog.

The orbital periods of CzeV1640A and CzeV1640B are close to 3:2 ratio,

$$\begin{eqnarray*}&&\displaystyle \frac{3\cdot {P}_{A}}{2\cdot {P}_{B}}=0.987,\end{eqnarray*}$$

which may suggest mutual physical interaction between both binary stars (Cagaš & Pejcha 2012).

CzeV1640 may be another member of growing family of known hierarchical multiple star systems (Lee et al. 2008; Lehmann et al. 2012; Zasche & Uhlař 2016) whose close binary star members exhibit eclipses. This system deserves continued monitoring to fully cover light curves of both systems and to determine orbital elements more precisely. A careful study of possible changes in orbital periods and/or times of minima could prove or disprove physical connection between CzeV1640A and CzeV1640B. Reliable data about such systems can contribute to understanding of evolution of close binary stars (Fabrycky & Tremaine 2007).

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I thank Ondřej Pejcha and Petr Cagaš for valuable inputs and comments.

This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC,  https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.