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Self-Lensing Signals in Binary Systems Containing White Dwarfs with Neutron star or Stellar-mass Black hole Companions

T0 review · 2 major / 2 minor · reviewed 2026-05-10 · grok-4.3

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Pith's one-line read White dwarf binaries with neutron star or black hole companions produce self-lensing signals with probabilities of 10^{-3} to 10^{-2} that TESS could detect under stated assumptions.

desk verdict The paper supplies new occurrence probabilities and TESS/Roman detection efficiencies for self-lensing in WD+NS and WD+BH binaries, but the headline TESS detection forecast depends on externally assumed companion fractions. read the letter →

arxiv 2604.12705 v1 submitted 2026-04-14 astro-ph.SR astro-ph.HE

Sedighe Sajadian , Man Ho Chan This is my paper · ORCID
classification astro-ph.SRastro-ph.HE
keywords self-lensingwhitedwarfsneutronstarsblackholesbinarysystemsTESSdetectabilitylightcurves
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper calculates the probabilities of self-lensing signals in white dwarf plus neutron star and white dwarf plus black hole binaries as roughly 0.001 and 0.01 respectively, with the highest rates occurring for low-mass white dwarfs orbiting the most massive companions. It then models the resulting light curves, incorporates finite-source effects, and applies the actual observing windows, cadences, and noise properties of the TESS and Roman telescopes to determine detection efficiencies. A reader would care because these signals offer a purely photometric route to identifying otherwise elusive stellar-mass black holes and neutron stars paired with white dwarfs.

What carries the argument

Finite-source self-lensing in edge-on WD+NS and WD+BH binaries, quantified via the normalized source radius ρ_star and used to generate occurrence probabilities together with synthetic light curves matched to telescope cadences.

What would settle it

A search of TESS light curves for thousands of white dwarfs that returns zero events matching the predicted short-duration, high-inclination self-lensing signatures would falsify the expected detection rate under the assumed companion fractions.

Watch

Extended reading notes

Core claim

Analytical calculations show the probabilities of self-lensing signals in WD+NS and WD+BH systems are ∼10^{-3} and ∼10^{-2}, maximized for low-mass white dwarfs revolving around massive neutron stars or black holes. Simulations of light curves under TESS and Roman observing protocols demonstrate that detectable events satisfy 1 ≤ orbital period ≤ observation window, SNR thresholds of 3 or 6, depth greater than twice the photometric error, and coverage by at least one datum. Such systems exhibit inclinations ≲0.2°, periods near 6–19 days, and event durations of 6–30 minutes, yielding detection efficiencies of ∼2–6×10^{-4} for TESS and ∼2–12×10^{-10} for Roman. TESS could therefore register at

Load-bearing premise

The conclusion that TESS might detect at least one signal rests on the external premise that 8% of white dwarfs have neutron-star companions and 3% have black-hole companions.

Editorial extensions

If this is right

  • WD+NS systems with periods ≲25 days show large finite-source sizes with ρ_star ≳1.
  • WD+BH systems with periods ≳3 days exhibit small source sizes, reaching ρ_star ∼0.01 for black holes of several tens of solar masses.
  • Detectable signals require orbital inclinations ≲0.2° and last 6–30 minutes.
  • TESS detection efficiency lies between 2×10^{-4} and 6×10^{-4} while Roman efficiency is orders of magnitude lower.
  • At least one event is expected in TESS data if the companion fractions reach the stated 8% and 3% levels.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A confirmed detection would provide an independent photometric confirmation of compact-object companions to white dwarfs that does not require X-ray emission or radial-velocity monitoring.
  • The observed rate of such events could be compared with binary population synthesis models to test the assumed fractions of white dwarfs paired with neutron stars or black holes.
  • Similar calculations applied to ground-based surveys with different cadences might identify longer-period systems missed by space-based continuous monitoring.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 2 minor

Summary. The manuscript analytically derives the occurrence probabilities of self-lensing signals in WD+NS (~10^{-3}) and WD+BH (~10^{-2}) binaries, showing maximization for low-mass WDs with massive companions, and computes normalized source radii indicating finite-source effects for short-period WD+NS systems. It simulates light curves under TESS (T_obs=27.4 days) and Roman (T_obs=62 days) protocols, applies detectability cuts (1 ≤ T ≤ T_obs, SNR ≥ 3 or 6, depth > 2×photometric error, coverage by ≥1 datum), and reports average detectable systems with i ≲ 0.2°, periods ~6-19 days, and durations 6-30 minutes. Detection efficiencies are ~2-6×10^{-4} (TESS) and ~2-12×10^{-10} (Roman), leading to the conclusion that Roman detection is impossible while TESS could detect at least one signal if 8% of WDs have NS companions and 3% have BH companions.

Significance. If the derivations hold, the work supplies useful analytical expressions for self-lensing probabilities and ρ_★ in compact-object binaries, together with simulated light curves that quantify the stringent requirements (small inclinations, specific periods) for detection. The forward calculation from standard binary assumptions to efficiencies under realistic satellite protocols, without circularity in the central quantities, provides a concrete basis for assessing the rarity of these events and prioritizing follow-up strategies in white-dwarf population studies.

major comments (2)
  1. [Abstract] Abstract and final results paragraph: the claim that TESS 'potentially manifests at least one' self-lensing signal is reached only after multiplying the derived p_selflens (~10^{-3}, 10^{-2}) and eff_detect (~2-6×10^{-4}) by externally assumed fractions f_NS=0.08 and f_BH=0.03. No population-synthesis derivation, citation, or sensitivity analysis for these fractions appears; the expected count N_WD × f_comp × p × eff therefore scales directly with them, and the headline statement is not robust if the true fractions differ by even a factor of a few.
  2. [Results on detectability] Simulation and detectability section: while the criteria (SNR thresholds, depth >2×error, coverage) are stated, the manuscript does not provide the exact mass-period distributions used to generate the synthetic population, the full error-propagation procedure, or the numerical values of photometric errors and sampling rates applied in the TESS/Roman mocks. This prevents independent verification of the reported efficiencies 2-6×10^{-4} and 2-12×10^{-10}.
minor comments (2)
  1. [Abstract] Notation for orbital period is introduced as T but later appears as T_obs; a single consistent symbol or explicit definition would improve clarity.
  2. [Detectable systems paragraph] The range of signal durations [6,30] minutes is given without specifying whether it is the 16-84 percentile or full range of the detectable subsample; adding this detail would aid interpretation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments, which have helped us improve the clarity and robustness of the manuscript. We address each major comment point by point below.

read point-by-point responses

  1. Referee: [Abstract] Abstract and final results paragraph: the claim that TESS 'potentially manifests at least one' self-lensing signal is reached only after multiplying the derived p_selflens (~10^{-3}, 10^{-2}) and eff_detect (~2-6×10^{-4}) by externally assumed fractions f_NS=0.08 and f_BH=0.03. No population-synthesis derivation, citation, or sensitivity analysis for these fractions appears; the expected count N_WD × f_comp × p × eff therefore scales directly with them, and the headline statement is not robust if the true fractions differ by even a factor of a few.

    Authors: We agree that the detection statement in the abstract is conditional on the adopted companion fractions and that the manuscript would benefit from greater transparency on this point. These fractions are drawn from observational estimates in the white-dwarf binary population literature rather than derived via new population synthesis within the present work. In the revised version we have (i) rephrased the abstract to make the conditional nature explicit, (ii) added a short sensitivity discussion in the final section showing how the expected TESS yield scales when f_NS and f_BH are varied by factors of 2–3, and (iii) inserted the relevant citations that motivated the original 8 % and 3 % values. These changes preserve the original numerical results while rendering the headline claim more robust. revision: partial

  2. Referee: [Results on detectability] Simulation and detectability section: while the criteria (SNR thresholds, depth >2×error, coverage) are stated, the manuscript does not provide the exact mass-period distributions used to generate the synthetic population, the full error-propagation procedure, or the numerical values of photometric errors and sampling rates applied in the TESS/Roman mocks. This prevents independent verification of the reported efficiencies 2-6×10^{-4} and 2-12×10^{-10}.

    Authors: We acknowledge that the simulation section lacked sufficient detail for full reproducibility. In the revised manuscript we have expanded the relevant section and added an appendix that now specifies: (1) the exact mass–period distributions adopted for the synthetic WD+NS and WD+BH populations (drawn from standard binary-evolution prescriptions with explicit parameter ranges), (2) the complete error-propagation formulae, including how photometric uncertainties are computed from the published TESS and Roman noise models, and (3) the numerical values of photometric errors and sampling cadences used in the mock light-curve generation. With these additions the quoted detection efficiencies can be independently verified. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity; probabilities and efficiencies derived independently from external assumptions

full rationale

The paper performs analytical calculations for self-lensing occurrence probabilities (~10^{-3} for WD+NS, ~10^{-2} for WD+BH) based on orbital parameters, finite-source sizes, and inclination distributions. It then simulates light curves and applies external TESS/Roman observing protocols (SNR thresholds, photometric error criteria, coverage) to obtain detection efficiencies (~2-6e-4 for TESS). The final conditional statement multiplies by assumed companion fractions (8% NS, 3% BH) but does not derive or fit those fractions inside the work, nor does any central quantity reduce by the paper's equations to a self-defined input. No self-citations, ansatzes, or uniqueness theorems are invoked as load-bearing steps. The derivation chain is self-contained against external benchmarks.

Assumptions & free parameters 2 free parameters · 2 assumptions · 0 invented entities

The paper relies on two explicit free parameters (companion fractions) and standard domain assumptions about orbital orientations and binary demographics; no new entities are postulated.

free parameters (2)
  • Fraction of WDs with NS companions = 0.08
    Stated as 8% to conclude TESS might detect at least one signal
  • Fraction of WDs with BH companions = 0.03
    Stated as 3% to conclude TESS might detect at least one signal
assumptions (2)
  • domain assumption Orbital inclinations are isotropically distributed
    Required to compute the probability of sufficiently edge-on systems
  • domain assumption Standard mass and period distributions for WD+NS/BH binaries
    Used when averaging probabilities and detectability over the population

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Cite this review

Pith. "Pith review of Self-Lensing Signals in Binary Systems Containing White Dwarfs with Neutron star or Stellar-mass Black hole Companions." pith.science (2026). https://pith.science/paper/2604.12705

@misc{pith2026260412705,
  author       = {Pith},
  title        = {Pith review of: Self-Lensing Signals in Binary Systems Containing White Dwarfs with Neutron star or Stellar-mass Black hole Companions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2604.12705}},
  note         = {Machine review of arXiv:2604.12705}
}
abstract

Light curves from binary systems containing white dwarfs with neutron star or stellar-mass black hole companions (WD+NS and WD+BH) with edge-on orbital planes potentially show self-lensing/eclipsing signals. Here, we evaluate the properties and detectability of these signals in the NASA's Transiting Exoplanet Survey Satellite (TESS), and the Nancy Grace Roman Space Telescope (Roman) observations. WD+NS systems with orbital periods $T\lesssim25~$days mostly have considerable finite-source sizes with the normalized source radii $\rho_{\star}\gtrsim1$. WD+BH systems with $T\gtrsim3$ days have $\rho_{\star}\lesssim1$, and $\rho_{\star}\sim0.01$ for BHs with a few tens solar-mass. Our analytical calculations show the probabilities of occurring self-lensing signals in WD+NS and WD+BH systems are $\sim10^{-3},~10^{-2}$, and maximize for systems with low-mass WDs revolving massive NSs/BHs. We simulate their light curves and generate synthetic data for them by applying the observing protocols of these two satellites. We assume self-lensing signals are detectable if (i) $1\leq T\leq T_{\rm{obs}}$ (where $T_{\rm{obs}}=62~\rm{and}~27.4$ days are the Roman and TESS continuous observing windows), (ii) $\rm{SNR}\ge3,~6$, their signals are (iii) deeper than twice the photometric error, and (iv) covered by at least one datum. Systems with detectable self-lensing signals in the TESS and Roman observations on average have small inclination angles $i\lesssim0.2^{\circ}$, with the orbital periods $\sim6,~19~$days, and their signals last $\sim[6,~30]~\rm{minutes}$. The TESS and Roman efficiencies for detecting these signals are $\sim2-6\times10^{-4}$ and $\sim2-12\times10^{-10}$. Although detecting these self-lensing signals by Roman is impossible, the TESS telescope potentially manifests at least one self-lensing signal due to these binary systems, if $8\%,~\rm{and}~3\%$ of WDs have NS and BH companions.

Figures

Figures reproduced from arXiv: 2604.12705 by the authors.

Figure 1
Figure 1. Maps of RE (left panels), ρ⋆ (middle panels), and A the magnification factor for binary systems WD+NS (top row) and WD+BH (bottom row) over the 2D space made from MWD (vertical axes), and mass of NSs and BHs (horizontal axes). Here, we assume WDs are source stars, while NSs or BHs are the lens objects. Similar maps to these maps but for other values of orbital periods are also available in link1, link2, link3, link4… view at source ↗
Figure 2
Figure 2. Similar to the maps shown in [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Left panel: the normalized distributions of WDs offered by Kilic et al. (2020) versus their absolute magnitudes in the TESS T-band (solid green histogram), and the Roman W149 filter (dashed blue histogram). Right panel: the corresponding distributions of detectable WDs with the apparent magnitude in the TESS T-band ≤ 17.5 mag and in the Roman W149 ∈ [14.8, 26] mag. orbital period, the semi-major axis is a ∝ (M⋆ +Ml)… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Six examples of simulated light curves due to WD+NS binary systems. The solid black, dotted red, and dashed lime curves represent the overall normalized flux by considering both self-lensing and eclipsing effects, i.e., Atot which is given by Eq. 6, the contributions o…
Figure 5
Figure 5. Figure 5: Same as light curves shown in [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: In each map, black dots represent simulated light curves due to WD+NS binary systems over the specified 2D space, and magenta stars display events with detectable sig￾nals in the TESS observations. In right and top sides of each panel, the marginal 1D normalized distri…

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