Ten new, ultracompact triply eclipsing triple star systems

TL;DR

We identify ten ultracompact triply eclipsing triple-star systems from TESS data in the northern ecliptic hemisphere and perform a comprehensive photodynamical analysis that jointly fits light curves, eclipse timing variations, and spectral energy distributions. Using Lightcurvefactory with PARSEC isochrones and an MCMC search over 25–27 parameters, we derive precise orbital elements, masses, radii, temperatures, and distances for all ten systems, finding predominantly flat configurations with mutual inclinations $i_{ m mut}\lesssim 5^{\circ}$. Outer periods lie in $P_{ m out}\\in\{46.8,101.4\}$ days, with four systems showing rapid apsidal motion and TIC 403916758 as a double-twin triple (inner and outer mass ratios near unity). The results, combined with over 30 previously studied compact triples, reveal systematic patterns in mass ratios, eccentricities, and dynamical effects, demonstrating the power of photodynamical modeling to extract physical parameters without RV data and highlighting these systems as stringent tests of hierarchical dynamics and formation scenarios.

Abstract

We have identified more than a hundred close triply eclipsing hierarchical triple star systems from data taken with the space telescope TESS. Many of them have outer periods less than or, close to 100 days, hence, we call them `ultracompact hierarchical triples'. These systems are noteworthy in that we can potentially determine their dynamical and astrophysical parameters with a high precision, in many cases even without radial velocity data. In the present paper we report the comprehensive study of ten new ultracompact triply eclipsing triple star systems, located in the northern ecliptic hemisphere, taken from this larger sample: TICs 198581208, 265274458, 283846096, 337993842, 351404069, 378270875, 403792414, 403916758, 405789362, 461500036. Most of the data for this study come from TESS observations, but we obtained supplemental ground-based photometric measurements for two of the systems. The eclipse timing variation curves extracted from the TESS and the ground-based follow up data, the photometric light curves, and the spectral energy distribution are combined in a complex photodynamical analysis to yield the stellar and orbital parameters of all ten systems. The outer periods are in the range of 46.8-101.4 days. We found third-body forced, rapid apsidal motion in four systems. Moreover, TIC 403916758 was found to be a double twin triple (i.e. both the inner and the outer mass ratios are close to unity). All of the systems are substantially flat, with mutual inclination angles of $<5^o$. Finally, we have taken the results for the ten systems in the present paper, and combined them with the system parameters for more than 30 other compact triples that we have reported on in previous work, in order to examine some of the global properties of these systems on a statistical basis.

Figures (12)

• Figure 1: Light curves (blue points) and model fits (smooth red curves) near three illustrative third-body eclipses of TIC 283846096. Dark/pale blue points are for those light curve sections which were used/not-used for the photodynamical solution. The sector numbers are indicated in the lower left corner of each panel. Letters 'i' or 's' after the sector numbers refer to the inferior or superior conjunction of the third star, respectively.
• Figure 2: Primary and secondary ETV curves (red and blue circles, respectively) formed from the TESS observations with the best-fit photodynamical solution for TIC 351404069 (see Sect. \ref{['sec:photodynamics']}). The dynamically forced, rapid apsidal motion of the inner, eccentric EB is nicely visible. (Be aware of the huge amplitude of the ETV!) The horizontally centred black curve represents the pure LTTE contribution. Vertical lines mark the times of the observed outer eclipses (green -- the binary occulting the tertiary star and, brown -- vica versa).
• Figure 3: Schematic flow chart of the entire photodynamical fitting process. Parameters marked in red font give those input parameters that are allowed to adjust during each MCMC trial step. Green symbols stand for the constrained quantities, while the black symbols denote quantities derived directly from the (adjustable, red) input parameters just at the beginning of each trial step and used during the subsequent part of the given step. The other quantities, not shown in the chart, but listed in the result tables below are computed a posteriori, at the end of the entire photodynamical analysis process. Note also, the only parameter with fixed input value ($\Omega_\mathrm{in}=0$) is given in blue font. (For the meaning of each symbol, see Table \ref{['tbl:definitions']}.)
• Figure 4: Statistical plots for properties of 44 triply eclipsing triples uniformly analysed (see text for references). Top-row panels:$M_{\rm Ab}$ vs. $M_{\rm Aa}$, $M_{\rm B}$ vs. $M_{\rm Aa}$, and $P_{\rm in}$ vs. $P_{\rm out}$. Middle-row panels:$e_{\rm out}$ vs. $P_{\rm out}$, $i_{\rm out}$ vs. $i_{\rm mut}$, and $q_{\rm in}$ vs. $q_{\rm out}$. Bottom-row panels:$R_{\rm B}$ vs. $M_{\rm B}$, $e_{\rm in}$ vs. $e_{\rm out}$, and the age of the systems vs. the masses of the tertiary (blue), primary (dark grey) and secondary (light grey) EB stars. In this latter panel as well as the first two panels, the masses of TIC 290061484 are $\sim$7 M$_\odot$ and are off the plots. The red curve in the middle right panel shows how nearly all the systems are confined to $0.2 < q_{\rm out} < 1.0$ and $q_{\rm in} > 0.2$. In the central panel the vertical lines denote the transition to the Von Zeipel-Lidov-Kozai (ZLK) cycles naoz16, and to retrograde orbits, respectively. The sloped dashed lines in the lower left panel are for $R_{\rm B}$ =1 M$_{\rm B}$ and = 5 M$_{\rm B}$ (both expressed in solar units), as rough guides of unevolved and quite evolved stars, respectively.
• Figure 5: Eccentricity of the outer orbit of compact triply eclipsing triples vs. the ratio of the tertiary's radius to the outer semimajor axis. With three exceptions (lower left corner), it seems reasonable to infer that tidal circularization of the outer orbit by evolved (i.e., large) tertiaries is responsible for the decaying outer eccentricity with increasing $R_{\rm B}/a_{\rm out}$.