A close-in substellar object orbiting the sdOB-type eclipsing-binary system NSVS 14256825

HW Virginis (HW Vir) binaries are a group of detached eclipsing-binary systems that consist of a very hot subdwarf B or OB type primary and a fully convective Mtype secondary with periods usually shorter than 4 h. They are believed to be formed through a common envelope ejection (Heber 2009, 2016). The hot sdB-type components in this group of binaries are on the extreme horizontal branch (EHB) of the Hertzsprung-Russell diagram, burning helium in their cores and having very thin hydrogen envelopes. They have very high temperature and similar size compared to their M-type companions, which cause the eclipse profiles of this type of binary to be very sharp and deep. Benefiting from this characteristic, the light arrival time of the binary can be measured to a high precision (e.g., Kilkenny 2011, 2014). Therefore, small wobbles caused by the orbits of other substellar companions can be discovered. To date, this timing method is the most successful one to be applied to the detection of substellar objects orbiting evolved stars, such as giant planets orbiting around the eclipsing white dwarf CVn (Han et al. 2018) and RR Cae (Qian et al. 2012a), around eclipsing polars DP Leo (Qian et al. 2010a; Beuermann et al. 2011) and HU Aqr (Qian et al. 2011; Goździewski et al. 2015), around eclipsing dwarf nova V2051Oph (Qian et al. 2015), etc. Up till now, the reported HW Vir-type binaries have been rare, numbering not more than 20. Some of them have been found to be the hosts of substellar objects using the timing method, i.e., HW Vir (Qian et al. 2008; Lee et al. 2009; Beuermann et al. 2012a), HS 0705+6700 (Qian et al. 2008, 2013; Beuermann et al. 2012b), NY Vir (Qian et al. 2012b), HS 2231+2441 (Almeida et al. 2014, 2017), OGLE-GDECL-11388 (Hong et al. 2017), 2M1938+4603 (Baran et al. 2015), etc.

With an orbital period of 2.65 h, NSVS 14256825 ( = V1828 Aql = 2MASS J20200045+0437564 = UCAC2 33483055 = USNO-B1.0 0946-0525128) (hereafter NSVS 1425) is an HW Vir-like eclipsing binary possibly containing hierarchical substellar companions. Its light variability was found in the public data release from the Northern Sky Variability Survey (NSVS, Wo´zniak et al. 2004). Wils et al. (2007) carried out multi-band CCD observations and obtained the first group times of light minimum for NSVS 1425 with a high precision (with uncertainties of less than 0.0002 d). Almeida et al. (2012) analyzed their UBVR_cI_cJH light curves and radial velocity curve simultaneously using the Wilson-Devinney code, and provided reliable fundamental parameters of NSVS 1425 as M₁ = 0.419 ± 0.070 M_⊙, M₂ = 0.109 ± 0.023 M_⊙, R₁ = 0.188 ± 0.010 R_⊙, R₂ = 0.162 ± 0.008 R_⊙ and i = 82.5° ± 0.3°. They pointed out that NSVS 1425 is an sdOB+dM eclipsing binary. Qian et al. (2010b) and Zhu et al. (2011) found a hint about cyclic period change in this system. Kilkenny & Koen (2012) suggested that the period of NSVS 1425 is rapidly increasing at a rate of about 12 × 10⁻¹² d orbit⁻¹. Beuermann et al. (2012b) reported that there may be a giant planet with a mass of roughly 12 M_Jup in NSVS 1425. Almeida et al. (2013) revisited its O − C curve and explained the changes in the O − C diagram by the presence of two circumbinary bodies with masses of 2.9 M_Jup and 8.1 M_Jup. Wittenmyer et al. (2013) presented a dynamical analysis of the orbital stability of the model suggested by Almeida et al. (2013). They found that a two-planet model of NSVS 1425 is unstable on timescales of less than a thousand years. Later, Hinse et al. (2014) concluded that insufficient coverage of the timing data prevents reliable constraints of the associated parameters. Recently, Nasiroglu et al. (2017) published their new times of light minimum, which extended the time span to November 2016. Their best-fitting model ruled out the two-planet model and reported a cyclic change that was explained as the presence of a brown dwarf. However, their data still do not cover a full cycle.

It has been shown that the chemical compositions and evolutionary statuses of sdOB- and sdB-binary stars are quite different (e.g., Heber 2016). On the T-log g diagram given by Almeida et al. (2012), the position of the primary component of NSVS 1425 is close to that of the primary of the first sdOB-type binary AA Dor, but is far away from those of other sdB-type binaries. The investigations by Kilkenny (2011, 2014) demonstrated that the O − C curve of AA Dor is constant indicating that no substellar objects are orbiting around it. Therefore, whether there are any substellar objects orbiting NSVS 1425 is a very interesting question. In this paper, we present our 84 newly determined high precision timings for NSVS 1425 obtained from observations between Dec. 2008 and Dec. 2018, which effectively extend the baseline of the timing data and cover more than a full cycle of the cyclic variation in the O − C diagram. Combined with high precision timings collected from the literature, we perform a new orbital period investigation of this HW Vir-type binary.

We have been monitoring a group of HW Vir-like eclipsing binaries since 2006. For NSVS 1425, we began to observe it in December 2008 with several small telescopes in China and Argentina, i.e., the 2.4-m and 70-cm telescopes at the Lijiang Station of Yunnan Observatories, Chinese Academy of Sciences (YNO), 1.0-m and 60-cm telescopes at the Kunming Station ofYNO (YNO 2.4-m, YNO 70-cm, YNO 1-m and YNO 60-cm), the 2.16-m and 85-cm telescopes at the Xinglong Station of National Astronomical Observatories, Chinese Academy of Sciences (NAOC; NAOC 2.16-m and NAOC 85-cm respectively), and the 2.15-m Jorge Sahade telescope at Complejo Astronómico El Leoncito (CASLEO; CASLEO 2.15-m), San Juan, Argentina. These seven telescopes are all equipped with CCD cameras and the standard Johnson−Cousin−Bessel BVR_cI_c filters. Using these telescopes, we obtained observations covering ten years from December 2008 to December 2018. All image reductions were done by applying the IRAF package. Seventy-two primary eclipsing profiles and 12 secondary eclipsing profiles were obtained. They all display symmetric light variations. To derive the times of light minimum, we modeled these eclipsing profiles using the amplitude of a Gaussian peak function

$$\begin{eqnarray}&&G(t)={m}_{0}+A{e}^{-\frac{{(t-{t}_{c})}^{2}}{2w}}.\end{eqnarray} \tag{ 1 }$$

In this function, m₀ is the offset; A is the amplitude; t_c is the timing and w is the width with $2w={\rm{FWHM}}/\sqrt{{\rm{ln}}(4)}$. Figure 1 depicts some examples of the observed eclipsing light curves (open circles) and the corresponding fits (solid lines). All the derived times of light minimum are listed in Table 1.

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Based on the times of light minimum, several authors have studied the O − C diagram of NSVS 1425. Among them, Nasiroglu et al. (2017) collected the most comprehensive timings up to the end of 2016. By adding our new eclipse times, we calculated the cycle number E and the O − C values according to the following ephemeris from Beuermann et al. (2012b)

$$\begin{eqnarray}\begin{array}{ll}{\rm{Min}}.I({\rm{BJD}})= & 2454274.208923(4)\\ & +0.1103741324{(3)}^{{\rm{d}}}\times E.\end{array}\end{eqnarray} \tag{ 2 }$$

The newly constructed O − C curve extends the coverage baseline for another two years, which is plotted in Figure 2. Our O − C values calculated from new timings are signified with green dots, while others are displayed with blue dots. From this figure, one can see that another minimum in the O − C curve has been caught, enabling analysis based on one full cycle of the periodical variation. As the light-travel time effect (LTT) signals caused by the low mass or/and long period objects are small, low precision timings may lead to this signal being submerged in scattered points, such as in the case of EG Cep (Zhu et al. 2009). Therefore, we just use the timings with errors smaller than 0.0002 to reconstruct the O − C curve and display it in the upper panel of Figure 3. The cyclic variation is obvious in this figure. To describe the O − C curve, the following equation was used

$$\begin{eqnarray}&&O-C=\Delta {T}_{0}+\Delta {P}_{0}\times E+\tau,\end{eqnarray} \tag{ 3 }$$

where ΔT₀ and ΔP₀ are, respectively, the revised epoch and period with respect to the ephemeris values in Equation (2). τ is described by Irwin (1952) as the cyclic change term due to the LTT caused by a third body

$$\begin{eqnarray}\begin{array}{ll}\tau & =K[(1-{e}^{2})\frac{\sin (\nu +\omega )}{1+e\cos \nu }+e\sin \omega ]\\ & =K[\sqrt{1-{e}^{2}}\sin {E}^{* }\cos \omega +\cos {E}^{* }\sin \omega ].\end{array}\end{eqnarray} \tag{ 4 }$$

In this equation, e is the eccentricity, ν is the true anomaly, ω is the longitude of the periastron passage in the plane of the orbit and E^* is the eccentric anomaly. K = asini^'/c is the projected semi-major axis given in days, where a is the semi-major axis of the elliptic orbit. By means of the Levenberg-Marquardt method, the results of the nonlinear fit for the O − C diagram are obtained. The solid line in the top panel of Figure 3 represents a combination of a revised linear ephemeris and a periodic variation. All derived parameters are listed in Table 2. The revised period is 0.1103741030(5) d.

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Our final result indicates that the O − C curve shows a cyclic change with a period of 8.83(6) yr and an amplitude of 0.000536(5) d that can be seen more clearly in the middle panel of Figure 3. The residuals are depicted in the bottom panel and its standard deviation is 0.00005. The results demonstrate that the third body in NSVS 1425 has a minimal mass of 14.15 M_Jup, which orbits the central HW Vir-type binary in an eccentric orbit with e ∼ 0.12(2).

NSVS 1425 is the second HWVir-type eclipsing binary consisting of a very hot subdwarf OB-type primary and a fully convective M-type secondary. Its sdOB primary lies in the EHB of the Hertzsprung-Russell diagram, having a very high temperature of about 40 000K (Almeida et al. 2013) and small size with radius 0.19 R_⊙, while its M dwarf secondary has very low temperature and small size compared to the sdOB primary. Thanks to these characteristics, the eclipsing profiles produced by them are very sharp and deep, which means that the light arrival time of the central object can be measured to a high precision and therefore its small wobbles caused by the orbiting of substellar companions can be discovered. Due to the high surface gravities and compact structures of sdB, sdOB or white dwarfs, both the radial velocity and transit methods (which have been extensively employed to search for planets around solar-type main-sequence stars) have a low efficiency in detecting substellar companions (exoplanets or brown dwarfs) of those post-red giant branch stars. Instead, this timing method, based on the LTT, is the most successful one to be applied to finding substellar objects orbiting such evolved stars, and is similar to the radio approach used to discover planets around pulsars (Wolszczan & Frail 1992; Backer et al. 1993).

We have monitored NSVS 1425 for ten years and obtained 84 new high precision times of light minimum, which effectively extended the baseline of the data and covered another minimum in the O − C curve, facilitating a full cycle constructed by the high precision data. Based on these data, we reanalyzed the O − C diagram and found a cyclic oscillation with an amplitude of 0.00053 d (or 45.8 s) and a period of 8.83 yr, which can be explained by the wobble of the binary's barycenter via the existence of a third body. Our updated parameters confirmed that there is a hierarchical substellar object orbiting around the central sdOB+dM type eclipsing binary with an orbital eccentricity of 0.12. The relationship between the mass (M₃) and distance at periastron (d₃) varying along with the inclination of the tertiary component (i^') is shown in Figure 4. The distance at periastron (d₃) of this tertiary component ranges from 3.26 AU to 3.12 AU as its inclination (i^') varies from 10 deg to 90 deg, implying that this tertiary component is a close-in object. When the orbital plane of this third body is coplanar with the orbital plane of the inner binary, its mass (M₃) should be 14.3 M_Jup, which lies in the boundary zone between planets and brown dwarfs.

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As suggested by many authors, the cyclic period oscillations of close binaries comprised of cool star components can also be explained by magnetic activity cycles (Applegate 1992). For NSVS 1425, the secondary component is a fully convective red dwarf star with a mass of 0.109 M_⊙ and an effective temperature of 2550K (Almeida et al. 2012). In order to check this possibility, we computed the energies required to cause this cyclic period change using the same method proposed by Brinkworth et al. (2006) and plotted its relationship with the assumed shell mass of the secondary in Figure 5 (solid line). The dashed line in Figure 5 represents the total energy that radiates from the fully convective red dwarf secondary in one whole period (8.83 yr). One can see that the required energies are much larger than the total energy radiated from the secondary star in one whole period. Therefore, the cyclic change cannot be explained by magnetic activity cycles of the secondary component in NSVS 1425.

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Some sdB eclipsing binaries have been reported with substellar objects orbiting around them, but not sdOB eclipsing binaries. NSVS 1425 is the first one. For single sdB- and sdO-stars, their chemical compositions and evolutionary statuses are quite different. sdB stars are mostly helium poor, while sdO stars manifest a variety of helium abundances (e.g., Heber 2016). Moreover, most sdB stars were found in binary systems, while the binary frequency of sdO stars is very low. These propertiesmay indicate that their formations are different. As for the two sdOB eclipsing binary stars, AA Dor and NSVS 1425, although they are located in the same region on the T-log g diagram (e.g., Almeida et al. 2012), the properties of their tertiary companions are quite different. A close-in substellar object is orbiting NSVS 1425, but no known substellar objects are orbiting around AA Dor (e.g., Kilkenny 2011, 2014). If the circumbinary substellar object in NSVS 1425 is formed from the remaining common-envelope material (second generation planets), why are there no substellar objects orbiting around AA Dor? Maybe AADor and NSVS 1425 have different formation channels. The detection of the close-in substellar object orbiting around NSVS 1425 will provide us with more information on the formation and evolution of sdOB-type binaries and their companions.

This work is partly supported by the National Natural Science Foundation of China (No. 11573063), the Key Science Foundation of Yunnan Province (No. 2017FA001), CAS "Light of West China" Program and CAS Interdisciplinary Innovation Team. New CCD photometric observations of NSVS 14256825 were obtained with the 2.16-m and 85-cm telescopes at Xinglong Station of NAOC, the 2.4-m, 1.0-m, 60-cm and 70-cm telescopes at the YNOs, and the 2.15-m telescope at Complejo Astronómico El Leoncito (CASLEO), San Juan, Argentina.