Detection of dark companions via the combination of eclipse timing variation, Hipparcos and/or Gaia astrometry: the cases of V Puppis and CY Ari

TL;DR

The paper introduces a joint framework that combines eclipse timing variation (ETV) LTTE signals with Hipparcos and Gaia astrometry to detect and characterize dark companions around eclipsing binaries, thereby breaking the $M\sin I$ degeneracy and yielding true mass $M_C$ and inclination $I_C$. The method models LTTE (plus optional dynamical/apsidal terms) and simulates Gaia DR2/DR3/DR4 as well as Hipparcos epoch data, using a likelihood-based Bayesian approach with robust MCMC sampling. Validation on Gaia BH3 shows consistent outer-body masses with literature, while applications to V Pup and CY Ari reveal a 14.0-year stellar-mass black-hole candidate around V Pup and a 5.41-year white-dwarf companion around CY Ari, both with nearly edge-on orbits indicative of coplanarity. The results demonstrate that combined ETV–astrometry enables precise orbit and mass determinations for dark companions, with significant implications for the demographics and formation of hierarchical triple systems across a broad mass spectrum.

Abstract

The third body is expected to shape the formation and evolution of close binary systems. In this work, we develop a method to detect and characterize the tertiary companion around eclipsing binaries through the combined analysis of eclipse timing variation, Hipparcos and/or Gaia astrometry. This method allows us to determine both the true mass and the inclination of the tertiary body that inferred from light-travel time effect. For the massive B-type binary V Pup, we do not confirm the previously reported 5.47-yr signal; instead, we identify a longer period of 14 yr. The orbital semi-major axis and mass of the outer body are revised to $a_C={17.88}_{-0.15}^{+0.15}$\,au and $M_C={7.73}_{-0.14}^{+0.14}\,M_\odot$, confirming it as a promising stellar-mass black-hole candidate for further follow-up study. For the tertiary of the contact binary CY Ari, we obtain $P_C=5.406_{-0.016}^{+0.017}$ yr, $e_C=0.526_{-0.027}^{+0.032}$, $I_C={85.6}_{-6.5}^{+7.8}$$^\circ$, and a true mass of $M_C=0.640_{-0.029}^{+0.029}\,M_\odot$, supporting the white dwarf hypothesis proposed in previous study. The orbits of both systems are nearly edge-on ($I=90^{\circ}$), implying that they may form in a coplanar environment. We highlight the advantages of our method for detecting dark companions in binary and triple systems.

Figures (9)

• Figure 1: Gaia PMa SNR map across the $m-a$ space for Gaia BH3 systems. The blue, white and black contour lines respectively correspond to SNR$=$1, 3 and 6. The cyan stars denote the currently observed values of Gaia BH3 in $m-a$ space. It is evident that the theoretical PMa of the system induced by the unseen companion is significant. Because the orbital elements are sampled uniformly, the SNR map reflects only the average behaviour and may differ for any one specific orbital configuration.
• Figure 2: Gaia PMa significance map across the $m-a$ space for CY Ari and V Pup systems. Symbols are similar to Figure \ref{['fig:pms_bh']}. Compared with the CY Ari system, the PMa induced by V Pup C is weak, owing to the large uncertainties in the Gaia astrometry.
• Figure 3: Comparison of RV+GDR23 and RV+GDR4 model for Gaia BH3. Panel (a): the best-fit orbit to RVs from RV+GDR4 model. Because the RV part of these two model is nearly identical, we only show one result to avoid repetition. Panel (b): RV residuals between best-fit solution and observations. Panel (c): the best-fit astrometric orbit of the star (or photocentre) in the sky-projected plane from RV+GDR23 model. The central plus symbol marks the barycenter and the gray line connects it with the position of the periastron. The thich dotted line shows the line of nodes, and the arrow indicates the direction of the motion along the orbit. Gaia epoch data simulated with GOST are indicated by colored solid dots. The small panel in the lower right corner is an enlargement of the region of the fitting to GDR23, depicting the best fit to Gaia GOST data and the comparison between the best-fit and catalog astrometry (positions and proper motions) at GDR2 and GDR3 reference epochs. The shaded regions represent the uncertainty of catalog positions and proper motions after removing the motion of the BOS. The two segments and their center dots (green and blue) represent the best-fit proper motion and position offsets induced by the black hole at GDR2 and GDR3, respectively. Panel (d): the residuals of the along-scan (AL) astrometric measurements for RV+GDR4 solution. The gray dots denote the original data, while the colored dots with error bars show the binned data for each transit. Panel (e): the best-fit astrometric orbit from RV+GDR4 model. The post-fit residuals are projected into the R.A. and decl. axes (gray dots). For panel (c), (d) and (e), the dots of the same color share identical orbital phase.
• Figure 4: Generalized Lomb-Scargle (GLS) periodograms for V Pup ETV. Upper panel: the periodogram for O-C data with the parabolic trend removed. A periodic signal at 5255 day is significant. Middle panel: the periodogram for O-C residuals. A signal near the sample window emerges (365 day). The horizontal grey lines, top to bottom, indicate the 0.001, 0.01, 0.1 False Alarm Probability (FAP) levels, respectively. Bottom panel: window function.
• Figure 5: Best-fit orbit to ETVs and Hip-Gaia astrometry of V Pup from our joint fitting. Top-left panel: the thick black line is the best-fit curve to ETVs, and the red dashed line is the quadratic term. Middle-left panel: the ETV curve (pure LTTE) after correcting the quadratic term. Bottom-left panel: the final residuals. Right panel: the absolute astrometric acceleration in right ascension and declination. The horizontal error bar of each data point denotes the temporal baseline of each catalog.