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arxiv: 2605.16498 · v1 · pith:K6JASXGVnew · submitted 2026-05-15 · 🌌 astro-ph.SR · astro-ph.HE

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

Pranav Nagarajan , Kareem El-Badry , Aniket Sanghi This is my paper

Pith reviewed 2026-05-19 21:52 UTC · model grok-4.3

classification 🌌 astro-ph.SR astro-ph.HE
keywords high-contrast imagingblack hole binariesneutron star binariestertiary companionshierarchical triplesGaia compact objectsLMXBsadaptive optics
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The pith

Deep imaging rules out main-sequence and hot white-dwarf tertiaries to black hole and neutron star binaries at large separations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper searches for third stars orbiting black hole and neutron star binaries with low-mass companions using high-contrast near-infrared imaging. Hierarchical triple systems offer one way these binaries could form, so detecting or ruling out tertiaries tests that idea. No bound companions are found, allowing the authors to exclude main sequence stars and young hot white dwarfs beyond about 500 astronomical units for nearby Gaia systems and 2000 au for more distant ones. This implies such tertiaries are uncommon, though older cooler white dwarfs could still exist and require deeper observations to detect.

Core claim

Using adaptive optics-assisted near-infrared imaging and reference star differential imaging with the Karhunen-Loève Image Processing algorithm, the authors detect no robustly bound tertiary candidates around five quiescent BH LMXBs, Gaia BH1, and twelve Gaia NSs. They convert non-detections into 5-sigma limits that rule out plausible main sequence tertiaries and young, hot white dwarf tertiaries at projected separations greater than or equal to 500 au for the Gaia compact object binaries and greater than or equal to 2000 au for the more distant BH LMXBs.

What carries the argument

High-contrast imaging with adaptive optics and reference star differential imaging processed by the Karhunen-Loève Image Processing algorithm to achieve sensitivity at close separations and derive mass and temperature limits on undetected tertiaries.

If this is right

  • The ruled-out tertiaries are not present at the probed separations around these compact object binaries.
  • Triple formation channels may be less common than isolated binary evolution for these systems.
  • Observations are still consistent with evolved intermediate-mass tertiaries that are now cool white dwarfs.
  • Follow-up proper motion measurements are needed to confirm or reject physical association of any faint stars detected.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Deeper imaging with JWST could test for the presence of cooler white dwarf tertiaries that current observations cannot reach.
  • If tertiaries are rare, this would favor formation models without hierarchical triples for most black hole and neutron star binaries with low-mass companions.

Load-bearing premise

The injection-recovery tests and contrast curves accurately reflect the true sensitivity to bound companions instead of being limited by residual speckles or other unaccounted systematics.

What would settle it

A measurement of common proper motion between one of the detected faint stars and the target binary that confirms physical binding at the separations where limits were set would falsify the non-detection claim.

Figures

Figures reproduced from arXiv: 2605.16498 by Aniket Sanghi, Kareem El-Badry, Pranav Nagarajan.

Figure 1
Figure 1. Figure 1: Comparison of Pan-STARRS (K. C. Chambers et al. 2016) optical survey images and NIRC2-LGS images (this work) for Gaia BH1 and Swift J1727. The targets are identified with purple cross-hairs in the Pan-STARRS images. Artifacts due to persistence have been masked (see Section 2.2.1). Due to improved depth and spatial resolution, we detect numerous neighboring sources that were unknown to previous survey imag… view at source ↗
Figure 2
Figure 2. Figure 2: Reduced and stacked NIRC2-LGS images taken with the narrow (10′′ × 10′′) camera. The location of each target is marked with a red circle. We resolve numerous sources previously undetected in survey imaging, especially for dense fields at low Galactic latitudes. Detected SNR > 5 point sources with low (i.e., < 0.05) chance alignment probabilities, which we consider to be tertiary candidates ( [PITH_FULL_IM… view at source ↗
Figure 3
Figure 3. Figure 3: Same as [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: High contrast narrow camera images of BH and NS binaries with low-mass companions, following post-processing with principal component analysis to model and subtract the target PSFs. Specifically, we perform reference star differential imaging with 16 principal components. We mask the central 0.12′′, where residuals are strongest. Detected 5σ candidates with chance alignment probability < 0.05 are marked wi… view at source ↗
Figure 5
Figure 5. Figure 5: Same as [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6 [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Same as [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Upper limits on main sequence (MS) companions as a function of projected physical separation. We use Ks-band absolute magnitude-mass relations (A. W. Mann et al. 2019; J. Choi et al. 2016) and our 5σ contrast curves to derive limits on the maximum mass of MS tertiaries that are consistent with a non-detection. In general, we can rule out most MS companions above the hydrogen burning limit at separations of… view at source ↗
Figure 9
Figure 9. Figure 9 [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Constraints on main sequence tertiaries to Gaia BH1 from NIRC2-LGS AO imaging (blue, this work), precision radial velocities (RVs, orange) (P. Nagarajan et al. 2024), and spectral disentangling (red) (K. El-Badry et al. 2023a). We also show regions of parameter space that are excluded by dynamical constraints (gray) (R. A. Mardling & S. J. Aarseth 2001) and Gaia observations (green). Given these constrain… view at source ↗
Figure 11
Figure 11. Figure 11: ). Specifically, we do not detect any SNR > 5 sources in our post-processed image obtained using ADI (lower left panel of [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Injection-and-recovery tests for close tertiary candidates identified via RDI ( [PITH_FULL_IMAGE:figures/full_fig_p017_12.png] view at source ↗
read the original abstract

Hierarchical triple evolution provides a promising alternative to isolated binary formation models for black holes (BHs) and neutron stars (NSs) with low-mass stellar companions. To search for tertiaries, we perform deep, adaptive optics-assisted, near-infrared imaging of five quiescent BH low-mass X-ray binaries (LMXBs), Gaia BH1, and twelve Gaia NSs. We detect several faint stars previously unresolved in survey imaging, but none are close enough to robustly rule out a chance alignment. To achieve high contrast sensitivity at close separations, we use the reference star differential imaging strategy with the Karhunen-Lo\'eve Image Processing algorithm to model and subtract the point-spread function of each target. We identify tertiary candidates in the speckle-dominated regime, but injection-recovery tests suggest most 5$\sigma$ detections are likely artifacts. We derive $5\sigma$ contrast curves and convert these to limits on the mass of main sequence (MS) tertiaries and the effective temperature of white dwarf (WD) tertiaries consistent with a non-detection. We rule out plausible MS tertiaries and young, hot WD tertiaries at projected separations $\gtrsim 500$ au for the Gaia compact object binaries and $\gtrsim 2000$ au for the more distant BH LMXBs. While the recent discovery of a $1.2\,M_{\odot}$ tertiary to V404 Cygni supports triple formation scenarios for BH LMXBs, our results suggest such companions are relatively rare. Our observations remain consistent with intermediate-mass tertiaries that have since evolved into cool WDs, detectable with deeper JWST imaging. Follow-up observations are required to measure proper motions and confirm or rule out physical association of tertiary candidates.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. This manuscript reports high-contrast adaptive optics-assisted near-infrared imaging of five quiescent BH LMXBs, Gaia BH1, and twelve Gaia NSs to search for tertiary companions. The authors employ reference-star differential imaging with the KLIP algorithm to subtract the PSF, identify faint stellar candidates at close separations, and use injection-recovery tests to classify most 5σ detections as likely artifacts. They derive 5σ contrast curves, convert these to limits on MS tertiary masses and WD effective temperatures, and conclude that plausible MS tertiaries and young hot WDs are ruled out at projected separations ≳500 au for Gaia compact-object binaries and ≳2000 au for the more distant BH LMXBs, implying such companions are relatively rare while remaining consistent with evolved cool WDs.

Significance. If the contrast-curve limits and non-detection claims are robust, the work supplies useful observational constraints on hierarchical triple formation scenarios for compact-object binaries. It provides context for the known 1.2 M⊙ tertiary around V404 Cygni by suggesting such companions are uncommon, while identifying JWST follow-up as a route to detect cooler WDs. The emphasis on proper-motion confirmation for candidates is a constructive element of the analysis.

major comments (1)
  1. [Results section (contrast curves and injection-recovery tests)] The central non-detection result rests on the 5σ contrast curves accurately representing detection completeness for bound companions. The manuscript states that injection-recovery tests indicate most candidates in the speckle-dominated regime are artifacts, but without quantitative recovery fractions as a function of separation and contrast (or explicit checks for residual speckle variability, field-dependent effects, and reference-star mismatch at sub-arcsecond scales), it is difficult to confirm that the reported sensitivity fully captures real systematics rather than underestimating them. This directly affects the reliability of the exclusion zones at the smallest claimed separations.
minor comments (1)
  1. [Abstract] The abstract would be strengthened by a brief statement of the distance and age assumptions used when converting contrast to MS mass and WD temperature limits.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. The feedback on the robustness of our contrast curves and injection-recovery analysis is particularly helpful. We address the major comment in detail below and have revised the manuscript accordingly to strengthen the quantitative presentation of our results.

read point-by-point responses

  1. Referee: The central non-detection result rests on the 5σ contrast curves accurately representing detection completeness for bound companions. The manuscript states that injection-recovery tests indicate most candidates in the speckle-dominated regime are artifacts, but without quantitative recovery fractions as a function of separation and contrast (or explicit checks for residual speckle variability, field-dependent effects, and reference-star mismatch at sub-arcsecond scales), it is difficult to confirm that the reported sensitivity fully captures real systematics rather than underestimating them. This directly affects the reliability of the exclusion zones at the smallest claimed separations.

    Authors: We appreciate the referee highlighting the need for greater transparency in our injection-recovery analysis. In the original manuscript we performed these tests by injecting synthetic companions across a grid of separations and contrasts into the KLIP-processed images and measuring recovery rates with the same 5σ threshold used for candidate identification. While we summarized the outcome (most close-in 5σ detections are artifacts), we agree that explicit quantitative recovery fractions would improve clarity and directly support the claimed exclusion zones. In the revised manuscript we have added a new figure (and associated text in Section 3) that shows recovery fraction as a function of projected separation and contrast for each target class. These curves confirm >70–90% completeness at the 5σ contrast limits beyond ~0.3–0.5 arcsec, depending on the dataset. We have also expanded the methods section to discuss residual speckle variability, field-dependent PSF effects, and reference-star mismatch. Reference stars were selected to match spectral type, magnitude, and airmass as closely as possible; multiple references were used to construct the KLIP basis; and we verified that the principal components do not over-subtract at the separations of interest. These additions demonstrate that the reported sensitivities are robust and that the exclusion zones at the smallest separations remain conservative. revision: yes

Circularity Check

0 steps flagged

No significant circularity: observational upper limits derived directly from imaging data and standard models

full rationale

The paper's core derivation consists of acquiring adaptive-optics NIR images of known compact-object binaries, performing KLIP-based reference-star differential imaging to produce contrast curves, and converting those empirical curves to mass and temperature limits via standard stellar models. Non-detections at stated projected separations then yield the exclusion zones. This chain is self-contained against the measured data and external isochrones; no step reduces a claimed prediction to a fitted parameter by construction, invokes a self-citation as the sole justification for a uniqueness theorem, or renames a known result. The result is an observational constraint rather than a tautological re-expression of inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based on abstract only; the central limits rest on standard assumptions about stellar isochrones, distances to the targets, and the fidelity of PSF subtraction, none of which are quantified here.

axioms (1)
  • domain assumption Conversion of 5-sigma contrast curves to main-sequence mass and white-dwarf temperature limits assumes standard stellar evolution models and known distances
    Invoked when translating non-detections into physical constraints on tertiaries

pith-pipeline@v0.9.0 · 5873 in / 1181 out tokens · 31410 ms · 2026-05-19T21:52:50.180936+00:00 · methodology

discussion (0)

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