Searching for the Third Wheel: High-Contrast Imaging Constraints on Tertiaries to Black Hole and Neutron Star Binaries

Technical Summary: Searching for the Third Wheel: High-Contrast Imaging Constraints on Tertiaries to Black Hole and Neutron Star Binaries

Problem Statement
Hierarchical triple evolution is a promising alternative to isolated binary formation models for explaining the existence of black holes (BHs) and neutron stars (NSs) with low-mass stellar companions. While isolated binary evolution struggles to account for the formation of both low-mass X-ray binaries (LMXBs) and the recently discovered population of wide, "dormant" compact object binaries (Gaia BHs and NSs), triple evolution offers mechanisms such as eccentric Kozai-Lidov oscillations to tighten inner binaries or delay common-envelope evolution. The recent discovery of a tertiary companion to V404 Cygni supports this hypothesis, yet the frequency of such tertiaries in the broader population remains unknown. This paper addresses the question of whether dormant BH and NS binaries in the Milky Way commonly host undetected tertiary companions, which would validate triple formation channels.

Methodology
The authors conducted a deep, adaptive optics (AO)-assisted near-infrared imaging campaign using the Keck II telescope's NIRC2 instrument and the Laser Guide Star (LGS) AO system.

• Sample: The study targeted 18 systems: five quiescent BH LMXBs, Gaia BH1, and twelve Gaia NSs. This represents approximately 25–57% of the dynamically confirmed populations of these objects.
• Observations: Observations were conducted in the $K'$ band (1.9–2.3 $\mu$m) to minimize thermal background. Two camera configurations were used: a narrow camera ($10'' \times 10''$) for high spatial resolution on BH LMXBs and a wide camera ($40'' \times 40''$) for Gaia NSs to facilitate photometric calibration.
• Data Processing:
  • Wide Separations ($>1''$): Sources were identified using standard photometry (SNR > 5) and compared against the TRILEGAL Galactic stellar population model to calculate chance alignment probabilities.
  • Close Separations ($\lesssim 1''$): To suppress the point-spread function (PSF) and achieve high contrast, the authors employed Reference Star Differential Imaging (RDI) using the Karhunen-Loève Image Processing (KLIP) algorithm. Libraries of reference images were constructed from dithers across the entire campaign. Principal Component Analysis (PCA) was used to model and subtract the target PSF, with the optimal number of components (16 for narrow, 12 for wide cameras) determined via injection-recovery tests.
  • Validation: Candidates were subjected to injection-recovery tests and Angular Differential Imaging (ADI) follow-up (specifically for Gaia NS1) to distinguish astrophysical sources from speckle noise and diffraction artifacts.

Key Results

• Wide Separation Candidates: The survey resolved numerous faint stars previously undetected in survey imaging. However, after calculating chance alignment probabilities and cross-matching with Gaia DR3 astrometry, only one candidate (a source $\approx 4.3''$ west of Gaia NS J1733+5808) remained viable. The other three candidates with low chance alignment probabilities were found to be unassociated based on inconsistent parallax or proper motion measurements.
• Close Separation Candidates: Several $5\sigma$ detections were identified in the PSF-subtracted images at separations $< 1''$. However, visual inspection and injection-recovery tests indicated that these detections were consistent with artifacts arising from residual speckle noise or radial diffraction spikes. No robust close tertiary companions were confirmed.
• Contrast Limits: The authors derived $5\sigma$ contrast curves for all targets. These were converted into constraints on the mass of Main Sequence (MS) tertiaries and the effective temperature of White Dwarf (WD) tertiaries consistent with non-detection:
  • Main Sequence Tertiaries: For Gaia compact object binaries, plausible MS tertiaries (above the hydrogen-burning limit, $\approx 0.08 M_\odot$) are ruled out at projected separations $\gtrsim 500$ au. For the more distant BH LMXBs, this limit extends to $\gtrsim 2000$ au.
  • White Dwarf Tertiaries: Hot, young WDs ($T_{\text{eff}} \gtrsim 10^5$ K) are ruled out at similar separations. However, cool WDs ($T_{\text{eff}} \lesssim 10^5$ K) remain undetectable with current data, as their cooling times are short ($\sim 10^6$ yr) and they fall below the detection threshold.
• Gaia BH1 Constraints: By combining these imaging limits with previous constraints from spectral disentangling and precision radial velocities, the authors constrain the parameter space for Gaia BH1. Only M-dwarf tertiaries with masses $\lesssim 0.5 M_\odot$ and orbital periods of $\sim 10^4$–$10^6$ days (or inner M-dwarfs with periods $\lesssim 5$ days) remain feasible.

Significance and Claims
The paper claims that while the discovery of a tertiary to V404 Cygni supports the viability of hierarchical triple formation for some BH LMXBs, such companions appear to be relatively rare or difficult to detect in the general population.

• The results suggest that formation channels relying on the presence of a current, bright Main Sequence tertiary are not the dominant mechanism for the observed sample of Gaia BHs, NSs, and quiescent LMXBs.
• The observations are consistent with scenarios where tertiaries have evolved into cool white dwarfs, which would require deeper imaging (e.g., with JWST) to detect.
• The study highlights the difficulty of detecting tertiaries around BH LMXBs, noting that V404 Cygni's tertiary was detectable largely due to its proximity and brightness; deeper searches using techniques like vortex coronagraphy or interferometry are necessary to fully constrain the tertiary fraction of this population.
• The authors emphasize that follow-up observations to measure proper motions are required to confirm or rule out the physical association of the few remaining candidates.