TIC 278825952: a triply eclipsing hierarchical triple system with the most intrinsically circular outer orbit Free

ABSTRACT

We report the discovery of a compact triply eclipsing triple star system in the southern continuous viewing zone of the TESS space telescope. TIC 278825952 is a previously known, but unstudied circular eclipsing binary with a period of 4.781 d with a tertiary component in a wider, circular orbit of 235.55-d period that was found from three sets of third-body eclipses and from light travel-time effect dominated eclipse timing variations. We performed a joint photodynamical analysis of the eclipse timing variation curves, photometric data, and the spectral energy distribution, coupled with the use of PARSEC stellar isochrones. We find that the inner binary consists of slightly evolved, near twin stars of masses of 1.12 and 1.09 M_⊙ and radii of 1.40 and 1.31 R_⊙. The third, less massive star has a mass of 0.75 M_⊙ and radius of 0.70 R_⊙. The low mutual inclination and eccentricities of the orbits show that the system is highly coplanar and surprisingly circular.

1 INTRODUCTION

Triply eclipsing hierarchical triple systems are not easy to spot. The reason for this is that their discoveries need not only a lucky orbital configuration of the stars, but also long-term, continuous, and precise photometric observations are essential to detect them. Thanks to the rapidly growing number of available light curves with such advantages produced by space-based photometric surveys (e.g. CoRoT, Kepler, K2, TESS), their numbers are slowly, but steadily increasing.

These systems are very important in the field of stellar parameter determination because they allow us to derive the orbital and physical parameters of all of the constituent stars (e.g. their individual masses) with a high precision. Moreover, with the appropriate data set, e.g. containing both light and radial velocity curves, this can be accomplished in a completely model-independent way. Almost all theoretical fields of stellar astronomy benefit from these precise parameters derived from observations. They can be used, e.g. to fine-tune star formation and stellar evolution theories or to analyse short- and long-term dynamical evolution of stellar systems (see, e.g. Tauris & van den Heuvel 2014; de Vries, Portegies Zwart & Figueira 2014; Moe & Kratter 2018).

Until now, less than two dozen triply eclipsing hierarchical triple stellar systems are known in the literature (see an informative collection of them in Borkovits et al. 2020b). While, in order to observe both inner and outer eclipses in a hierarchical triple system, it is necessary to view both the inner and outer orbits almost edge-on, there are no restrictions (at least in theory) on the mutual inclination of the inner and outer orbital planes¹ (see Conroy et al. 2014). It is, of course, another question as to how the orbital plane precession, which necessarily occurs for non-coplanar systems, affects the visibility intervals of third-body eclipses, or even inner binary events, thereby providing a chance to detect such systems. This problem, in the context of transiting circumbinary planets, was discussed in the papers of Martin & Triaud (2015) and Martin (2017).

Regarding the above-mentioned relative, or mutual, inclination of the inner and outer orbits, it is one of the most relevant parameters of a triple, or multiple stellar system from the point of view of its formation, and past and future evolutionary history (see, e.g. Toonen, Hamers & Portegies Zwart 2016; Toonen et al. 2020, for recent reviews). In this context, flat (coplanar) systems might have extraordinary importance. The reason is that for most of the hierarchical triple stars, the mutual inclination is subject to substantial variations (including even flip-flops from prograde to retrograde configurations and vice versa) due to various dynamical effects. A partial list of such effects includes the (eccentric) Lidov–Kozai effect (see Naoz 2016, for a review), its interplay with tidal friction (see, e.g. Kiseleva, Eggleton & Mikkola 1998; Naoz & Fabrycky 2014) (which may freeze the mutual inclination), and resonant interactions with stellar spins (Correia, Boué & Laskar 2016). In the case of a flat system, however, especially, as far as none of its components have undergone a Roche lobe filling stage, one can expect that the alignment of the orbital planes is a certain relic of the formation process of the given triple star (in this regard see, e.g. Tokovinin & Moe 2020, and references therein).

The subset of compact, extremely flat systems with very accurately known mutual inclinations is very small, and listed in table 5 of Borkovits et al. (2020b). More than half of these systems (four of seven) come from the triply eclipsing triples, emphasizing the extremely fortuitous role of such systems in determining accurate mutual inclinations. Among these objects, only one (HD 181068; Derekas et al. 2011; Borkovits et al. 2013) has a highly circular outer orbit which is an unusual configuration for such a system.

In this paper, we report the discovery and the first study of TIC 278825952 as a triply eclipsing compact, hierarchical triple stellar system that joins the company of HD 181068 with a surprisingly circular outer orbit. The system is located in the southern continuous viewing zone (SCVZ) of the TESS spacecraft and, therefore, was observed nearly continuously during Year 1 of the ongoing TESS mission. This high-precision and almost uninterrupted data set was essential in order to discover the triply eclipsing nature of the object and to determine its astrophysical and orbital parameters precisely. In Section 2, we describe all the available observational data and their preparation for the complex, joint photodynamical analysis, which is discussed in Section 3. Then, the results are discussed and, finally, summarized in Sections 4 and 5.

2 OBSERVATIONAL DATA

2.1 Catalogue data

In Table 1, we collected photometric passband magnitudes of the system from different surveys, e.g. APASS (AAVSO Photometric All Sky Survey; Munari et al. 2014), 2MASS (Two Micron All-Sky Survey; Skrutskie et al. 2006), AllWISE (Wide-field Infrared Survey Explorer: All-Sky Data Release; Cutri et al. 2013), and Gaia in order to construct the spectral energy distribution (‘SED’) of the system. The SED along with theoretical isochrones and the photodynamical model of the system provides an opportunity to determine the masses of the components in a model-dependent way (see Section 3 for details).

We found only two dedicated spectroscopic surveys containing data about TIC 278825952 (RAVE DR5; Radial Velocity Experiment, Kunder et al. 2017; TESS-HERMES DR1, Sharma et al. 2018), despite the fact that this is a relatively bright system. These catalogues list spectroscopically determined effective temperature, log g, and metallicity values assuming that the two stars in the binary dominate the light and are near twins. We can use these values to compare with our results from photometry, and thus we have included these quantities in Table 1 as well. We also note that the Gaia DR2 catalogue lists a large rms scatter for its radial velocity measurements (from 11 spectra), directly indicating the binary, or multiple, nature of the source.

2.2 TESS photometry

The TESS space telescope (Ricker et al. 2015) is monitoring a significant fraction of the sky, spending about a month on each 22^○ × 96^○ sector of the sky. Nearly a whole hemisphere is thereby covered in a year. Regions close to the ecliptic poles are observed almost continuously, resulting in a year long data set for objects located in these regions. TIC 278825952 has been observed during the first 13 sectors of TESS with a 30-min cadence on the full-frame images (FFIs). However, data from Sector 7 are missing because our target fell between two CCDs due to its unfortunate positioning. Nevertheless, we still have a 1-yr-long continuous photometric data with a one-month-long gap in the middle, which is more than suitable for further analysis of the system.

After downloading the FFI data from the MAST portal,² the light curve from each sector was obtained by a convolution-based differential photometric pipeline based on the fitsh package (Pál 2012) – see also Borkovits et al. (2020a) for more details about the practical implementation. For a final step, we converted the magnitudes to normalized fluxes and applied a careful detrending method using the wōtan package (Hippke et al. 2019), which filters out any instrumental trends and preserves all other features in the light curves. Sections of the detrended light curve of TIC 278825952 based on all available TESS observations can be seen in Fig. 1. It shows primary and secondary eclipses of the inner binary stars with an orbital period of 4.78 d. The light curve also reveals three pairs of extra eclipses (in Sectors 3, 8, and 12) caused by the third star on a wider (‘outer’) orbit passing in front of and behind the inner binary components. This immediately shows that the target is at least a hierarchical triple star with an outer orbital period of 235.5 d.

2.3 WASP photometry

TIC 278825952 was also observed in the images of the WASP-South project (Collier Cameron et al. 2006; Pollacco et al. 2006) during four seasons between 2008 September and 2012 March. The WASP instruments each consists of an array of eight cameras with Canon 200-mm f/1.8 lenses and 2k×2k e2V CCD detectors providing images with a field of view of 7|${_{.}^{\circ}}$|8 × 7|${_{.}^{\circ}}$|8 at an image scale of 13.7 arcsec pixel⁻¹. Images are obtained through a broad-band filter covering 400–700 nm. Fluxes are measured in an aperture with a radius of 48 arcsec for the WASP data. The data are processed with the SYSRem algorithm (Tamuz, Mazeh & Zucker 2005) to remove instrumental effects.

While archival WASP data have lower quality than the high-accuracy TESS observations, and are also subjected to diurnal and seasonal data gaps, their use was essential for, and therefore they were included in, our analyses (see Section 3). Sections of WASP data are plotted in Fig. 2.

2.4 ASAS-SN photometry

ASAS-SN³ (All-Sky Automated Survey for Supernovae) currently has 24 telescopes around the Earth covering the entire sky. TIC 278825952 was included in a targeted, supplementary survey towards the SCVZ of TESS conducted by the ASAS-SN network (Jayasinghe et al. 2019). As a result, it was catalogued as an eclipsing binary with the identifier of ASASSN-V J064152.94-554741.9. For these observations, the units named ‘Brutus’ (Haleakala, Hawaii) and ‘Cassius’ (CTIO, Chile) were used, which comprise of four 14-cm telescopes each with a field of view of 4.5 deg² and a pixel size of 8 arcsec. The images were processed using image subtraction combined with aperture photometry, and the resultant light curves are publicly available in the ASAS-SN light-curve server⁴ (Shappee et al. 2014; Kochanek et al. 2017). According to the back-projected photodynamical model (see Section 3), two ASAS-SN photometry points belong to ‘extra’ third-body eclipsing events. One of them is shown in that 50-d-long section of the ASAS-SN observations, which is plotted in Fig. 3.

2.5 ETV data

The overall ETV curve for TIC 278825952 is plotted in Fig. 4 along with the best-fitting model that is described in the next section. The points determined both from the regular primary and secondary eclipses of the TESS data (lower right-hand panel of Fig. 4) both exhibit the same closely sinusoidal shape curve, with P₂ = 235.5 d, revealing that both the inner and outer orbits are nearly circular. As one can see in the lower right-hand panel of Fig. 4, the outer eclipsing events closely correspond to the extrema of the ETV curve. Since in the present case the ETV curve is clearly light-travel-time-effect (LTTE)-dominated (see Section 4 for a discussion), this fact evidently shows that in the case of the deeper extra eclipses (in Sectors 3 and 12), the third star passes in front of the binary members, while in the case of the more shallow third-body events (in Sector 8), the situation is the opposite.

Turning to the older ETV points determined from the archival WASP data (lower left-hand panel of Fig. 4), they have significantly larger uncertainties. However, they show that no other periodic variations can be detected in the system, at least on the time-scale of a decade.

3 JOINT ANALYSIS OF THE AVAILABLE DATA

We used the software package lightcurvefactory (see Borkovits et al. 2019, 2020a,b, and further references therein) to carry out a complex photodynamical modeling of the system based on the data collected in Section 2. The analysis has followed exactly the same steps that were discussed in Borkovits et al. (2020a,b) in detail; therefore, there is no need to repeat it here. Instead, we note only some specific points.

For the photodynamical analysis, we fitted simultaneously (i) the 30-min cadence Year 1 TESS light curve, (ii) the WASP light curve, (iii) the ETV curves of the primary and secondary eclipses and, finally, (iv) the observed stellar SED in the form of catalogued passband magnitudes. As in our previous works, the SEDs were fitted to theoretical passband magnitudes⁵ calculated with interpolation from the grids of tabulated theoretical PARSEC isochrones (Bressan et al. 2012).

In order to reduce computational costs we dropped out from the analysis the out-of-eclipse sections of both the TESS and WASP light curves, i.e. in other words, only the |$\phi =\pm 0{_{.}^{\circ}}05$| phase sections of the regular eclipses were kept, with the exception of the outer eclipses, where longer, 6–8-d-long sections of the light curves were also retained. Note that, in case of the WASP light curve, our treatment slightly departed from that which was followed in Borkovits et al. (2020b), where the full WASP light curve was considered in the photodynamical analysis. The reason is that, in the present situation, the TESS light curve by itself made it possible to determine accurately the outer period and, therefore, we were able to pre-compute the expected locations of the outer eclipses in the intervals of the WASP observations. For further reduction in computational costs, we formed 1-h average points from the WASP observations, and these data were used for the analysis (naturally, with the appropriate cadence corrections).

Without radial velocity measurements, the masses of the components cannot be determined directly; nevertheless, using theoretical PARSEC isochrones can help us to construct model-dependent masses for the components (see Borkovits et al. 2020a). This allowed us to constrain a physically and dynamically consistent model of the system and determine its orbital and physical properties.

In the majority of the MCMC (Markov chain Monte Carlo) runs, the following parameters were adjusted:

• Of the 12 orbital element related parameters, 9 describing the two perturbed, osculating Keplerian orbits at epoch t₀ = 2458 320.0, as follows: e₁cos ω₁, e₁sin ω₁, and i₁ giving the eccentricity, argument of periastron, and the inclination of the inner orbit; furthermore, the parameters of the wide, outer orbit, namely P₂, e₂cos ω₂, e₂sin ω₂, i₂, the time of the inferior conjunction of the third component, |$\mathcal {T}_2^{\mathrm{inf}}$|⁠, and the ascending node of the outer orbit, Ω₂.⁶

• Three parameters connected to the stellar masses: primary star’s mass, m_A, and the mass ratios of the inner and outer subsystems q_{1, 2}.

• The passband-dependent extra lights ℓ_TESS, ℓ_WASP account for two additional parameters.

• Finally, three parameters for the PARSEC isochrone and SED fitting: the logarithm of the age of the three stars, log τ, the metallicity [M/H], and the extinction coefficient E(B − V).

Furthermore, 21 additional parameters were internally constrained, as follows:

• The inner binary’s orbital period, P₁, and the time of an inferior conjunction |$\mathcal {T}_1^{\mathrm{inf}}$| of the secondary star of the inner pair at epoch t₀ were constrained via the ETV curves (see appendix A of Borkovits et al. 2019).

• The effective temperatures, T_{A, B, C}, and radii, R_{A, B, C}, of the three stars were calculated from interpolation at each trial step with the use of the PARSEC tables (see Borkovits et al. 2020a).

• The distance of the system was constrained a posteriori by minimizing the value of |$\chi ^2_\mathrm{SED}$|⁠.

• Finally, note that similar to our previous modelling efforts, we applied a logarithmic limb-darkening law of which the coefficients for each stars in both bands were interpolated from passband-dependent tables downloaded from the Phoebe 1.0 Legacy page.⁷ These tables are based on the Castelli & Kurucz (2003) atmospheric models and were originally implemented in former versions of the phoebe software (Prša & Zwitter 2005).

4 RESULTS AND DISCUSSION

The median values of the orbital and physical parameters of the system derived from the MCMC posteriors and their 1σ statistical uncertainties are summarized in Table 3. Furthermore, the synthetic model light curves derived from the best-fit joint solution are displayed in Figs 1 and 2, while the corresponding ETV curves are presented in Fig. 4. Finally, in the two panels of Fig. 5, we illustrate the goodness of the SED-fitting part of the combined solution both in the flux and the passband magnitude domain.

According to our model, the inner binary of TIC 278825952 consists of two almost identical, slightly evolved main-sequence stars with masses of |$m_\mathrm{A}=1.12_{-0.08}^{+0.07}$|  M_⊙, |$m_\mathrm{B}=1.09_{-0.07}^{+0.08}$| M_⊙, and effective temperatures of |$T_\mathrm{eff,\, A}=6261_{-69}^{+97}$|  and |$T_\mathrm{eff,\, B}=6229_{-71}^{+95}$|  K. The outer tertiary component has a lower mass of |$m_\mathrm{C}=0.75_{-0.03}^{+0.03}$|  M_⊙ and effective temperature of T|$_\mathrm{eff,\, C}=4894_{-88}^{+115}$| K. According to the SED and PARSEC isochrone-fitting part of the combined analysis, this |$\tau =4.81_{-0.72}^{+0.94}$| Gyr-old system most probably has a solar like metallicity of |$[M/H]=-0.09_{-0.21}^{+0.13}$|⁠. The corresponding distance, obtained after taking into account the reddening of |$E(B-V)=0.08_{-0.02}^{+0.03}$|⁠, is found to be |$d=590_{-15}^{+11}$| pc, which is slightly higher than, but within 2σ of, the trigonometric distance of d_DR2 = 561 ± 8 pc derived from the Gaia DR2 parallax by Bailer-Jones et al. (2018).

Regarding this slight discrepancy, we show correlation plots of the a posteriori distributions of m_A and metallicity [M/H] versus photometric distance in the first row of Fig. 6. Use of the Gaia DR2 distance would lead to a primary mass of about |$m_\mathrm{A}\sim 1\, \mathrm{M}_\odot$| and also a metallicity of [M/H] ∼ −0.3 to − 0.4. Note that both spectroscopic studies cited previously in Section 2 and listed in Table 1 have resulted in a metallicity in this latter range, while our photodynamical analyses evidently prefer somewhat different results. These findings show that some caution is needed in regard to those parameters of our solution that primarily depends on the evolutionary tracks (especially m_A, [M/H], and log τ). Therefore, dynamical mass determinations based on future radial velocity measurements are highly desirable for confirming our results or, helping to refine the PARSEC evolutionary tracks close to the terminal age main-sequence stage of our stars.

Turning to the astrophysical-model independent dynamical properties, both the inner and outer orbits are very close to circular and, as the low value of mutual inclination indicates, the system is also very flat. This should make the orbital parameters of the system stable on the nuclear timescale of the stars. While the circular inner orbit for such an old and close binary is quite natural, one cannot state the same for the outer orbit. Oppositely, it is quite rare that the third, distant component of a hierarchical triple star system (even for quite compact outer orbits) would have an almost circular orbit. For example, Borkovits et al. (2016) have reported 22 triple star candidates with outer period P₂ ≤ 240 d among the eclipsing binaries in the original Kepler field, and only for 5 of them was an outer eccentricity of e₂ ≤ 0.1 found. More specifically, considering only the flat, compact hierarchical triple systems with accurately known parameters tabulated in table 5 of Borkovits et al. (2020b), only one of them has outer orbit less eccentric than e₂ ∼ 0.2. This only exception, HD 181068 is similar to the present system not only in its flatness, but it also has two circular orbits (Borkovits et al. 2013). On the other hand, however, in the case of HD 181068, the distant component is a red giant revolving on a much closer outer orbit (P₂ ∼ 45.5 d), and in such a manner, the circular outer orbit might be explained by either (i) the much stronger tidal effects during the red giant phase, or (ii) the effects of mass-loss and mass transfer in the system. In the case of TIC 278825952, we cannot find any physical reasons for circularization of the outer orbit, and therefore we suppose that it is of primordial origin. Formation scenarios for wide multiple star systems such as this one are quite uncertain, but a number of interesting idea have been put forth by e.g. Kratter, Murray-Clay & Youdin (2010), Antognini & Thompson (2016), and Tokovinin (2017).

Turning to the flatness of the system, we checked the possibility of a flat, but retrograde configuration, but all the MCMC chains initiated with Ω₂ ∼ 180° resulted in significantly higher χ² values, i.e. we found that |$(\chi ^2_\mathrm{min})_\mathrm{retrograde}\sim 1.25\times (\chi ^2_\mathrm{min})_\mathrm{prograde}$|⁠. Therefore, we conclude that the system most probably has a flat, prograde configuration.

In table 1 of Borkovits et al. (2020b), we listed the inner and outer periods of all the 17 triply eclipsing triple stars having precisely known inner and outer orbital periods. TIC 278825952 now joins this small group of triple stars. Its outer period (P₂) places it in the 10th position (in increasing order). From a dynamical point of view, it is one of the most relaxed systems, especially considering (i) the relatively high period ratio of P₂/P₁ = 49.3 and low outer mass ratio of q₂ = 0.34, the two parameters that basically set the amplitude of the dynamical perturbations, and also (ii) the doubly circular, coplanar configuration of the inner and outer orbits. These two effects render the lowest order (quadruple) perturbative terms to be nearly zero (see, e.g. Soderhjelm 1982; Borkovits et al. 2003, for the ‘apse-node’ and the P₂-time-scale perturbations, respectively). Furthermore, the nearly equal masses of the inner binary stars (q₁ = 0.98) also substantially reduce the amplitudes of the next, octuple-order perturbations, which disappear when the inner mass ratio tends toward unity (see again Soderhjelm 1982; Borkovits et al. 2015, for the two above classes of third-body perturbations).

5 SUMMARY

In this paper, we have reported the discovery and first comprehensive analysis of the triply eclipsing hierarchical triple star TIC 278825952 observed by the TESS spacecraft almost continuously for ∼11 months in its SCVZ. The space-borne observations cover more than one outer orbital cycle, including third-body eclipsing events around two consecutive inferior and one superior conjunctions of the distant third star, allowing the accurate determination of the dynamical and astrophysical parameters of the system. In order to obtain these parameters with the highest available accuracy, we carried out a joint photodynamical analysis that included not only the above mentioned TESS light curve, but also earlier archival ground-based WASP photometry, the ETVs extracted from these observations and, furthermore, the SED and theoretical PARSEC isochrones. Note, however, that due to the lack of radial velocity observations, we were unable to carry out a fully model-independent, purely dynamical study of the stellar masses.

Our comprehensive analysis revealed that TIC 278825952 consists of a near-twin pair of slightly evolved main-sequence stars on a circular orbit with a lower mass outer companion that is also on a circular orbit. The system is one of the few members of the currently known class of hierarchical triple star systems exhibiting outer third-body eclipses in a highly coplanar configuration. Nevertheless, it is unique in that it has the most inherently circular outer orbit among them, raising a question about the origin of the low eccentricity of its wide orbit. For a system with such age and constituent stars, this is unexpected and we could not find any physical reasons that explain the highly circular nature of the outer orbit, so we propose that it most probably represents its primordial configuration.

Because of its fortuitous location in the SCVZ, TIC 278825952 is also scheduled to be observed in all the 13 sectors of the first year of the TESS extended mission. According to our model, the forthcoming outer eclipsing events are expected to be observed during Sectors 29, 33, and 38 (and hopefully will be), leading to a more refined photodynamical model.

ACKNOWLEDGEMENTS

T M and T B acknowledge the financial support of the Hungarian National Research, Development and Innovation Office – NKFIH Grant KH-130372.

This paper includes data collected by the TESS mission. Funding for the TESS mission is provided by the NASA Science Mission directorate. Some of the data presented in this paper were obtained from the Mikulski Archive for Space Telescopes (MAST). STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant NNX09AF08G and by other grants and contracts.

This work has made use of data from the European Space Agency (ESA) mission Gaia,⁸ processed by the Gaia Data Processing and Analysis Consortium (DPAC).⁹ Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.

This publication makes use of data products from the Wide-field Infrared Survey Explorer, which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration.

This publication makes use of data products from the Two Micron All-Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation.

We used the Simbad service operated by the Centre des Données Stellaires (Strasbourg, France) and the ESO Science Archive Facility services (data obtained under request number 396301).

DATA AVAILABILITY

The TESS data underlying this paper were accessed from MAST (Barbara A. Mikulski Archive for Space Telescopes) Portal (https://mast.stsci.edu/portal/Mashup/Clients/Mast/Portal.html), including the data products found in the bulk download website (http://archive.stsci.edu/tess/bulk_downloads/bulk_downloads_ffi-tp-lc-dv.html). Part of the data were derived from sources in public domain as given in the respective footnotes. The derived data generated in this research and the code used for the photodynamical analysis will be shared on reasonable request to the corresponding author.

Footnotes

REFERENCES