🔭 astrophysics

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

This paper evaluates the detectability of self-lensing signals in white dwarf–neutron star and white dwarf–black hole binary systems using TESS and Roman telescope data, concluding that while Roman is unlikely to detect such events, TESS could potentially observe at least one signal if a small fraction of white dwarfs possess these compact companions.

Original authors: Sedighe Sajadian, Man Ho Chan

Published 2026-04-15

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Sedighe Sajadian, Man Ho Chan

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Cosmic Magic Trick: When Stars Play "Hide and Seek"

Imagine you are watching a magic show. A magician (a tiny, dense star called a White Dwarf) is walking behind a giant, invisible trampoline (a Neutron Star or a Black Hole). As the magician passes behind the trampoline, the trampoline's gravity bends the light coming from the magician, making them look slightly brighter for a split second. Then, the magician walks back out, and the light returns to normal.

This is called Self-Lensing. It's a cosmic game of "Hide and Seek" where gravity acts as a magnifying glass.

The paper you asked about is a study by two scientists, Sedighe Sajadian and Man Ho Chan, who asked a big question: "Can our space telescopes actually see this magic trick happening?"

They focused on two specific teams of stars:

The White Dwarf + Neutron Star Team: A small, dense star paired with an even denser, city-sized star.
The White Dwarf + Black Hole Team: A small star paired with a monster that eats light.

The Two Detectives: TESS and Roman

To catch these fleeting moments, the scientists simulated what two different space telescopes would see:

TESS (The Speedster): This telescope is like a fast runner taking quick snapshots every 2 minutes. It watches a specific patch of sky for about a month. It's great at catching fast events.
Roman (The Deep Diver): This is a future telescope that will take very high-quality photos but only once every 15 minutes. It looks very deep into the crowded center of our galaxy.

The Simulation: Running a Cosmic Casino

Since we can't wait around for years to see if these events happen, the scientists built a virtual universe on their computers.

The Setup: They created millions of fake binary star systems, mixing and matching different masses, distances, and speeds.
The Rules: They programmed the physics of gravity to see how much the light would bend (magnify) when the stars lined up perfectly edge-on (like looking at a coin from the side, rather than from the top).
The Test: They ran these fake systems through the "cameras" of TESS and Roman to see if the telescopes would spot the tiny brightening.

The Big Findings

Here is what they discovered, broken down simply:

1. The "Edge-On" Problem

For this magic trick to work, the two stars must be lined up perfectly from our point of view. If they are tilted even a tiny bit, the light doesn't bend enough to be seen.

Analogy: Imagine trying to see a coin flip. If you are looking from the side, you see the whole coin. If you are looking from the top, you just see a flat circle. These stars need to be perfectly "side-on" for us to see the lensing effect.
Result: The stars have to be aligned almost perfectly (within a fraction of a degree). This is very rare.

2. The Speed vs. Quality Trade-off

TESS (The Speedster): Because TESS takes photos every 2 minutes, it can catch these events. The "flash" of light usually lasts about 6 to 16 minutes. TESS is fast enough to catch a few data points during the flash.
Roman (The Deep Diver): Roman takes a photo only every 15 minutes. The problem? The flash often happens between the photos.
Analogy: Imagine a firework that explodes for 10 seconds. If you take a photo every 2 seconds, you'll catch it. If you take a photo every 15 seconds, you'll likely miss it entirely.
Result: The study concludes that Roman will likely miss these signals completely because its "shutter speed" is too slow for how fast these events happen.

3. The "Crowded Room" Issue

When looking at the center of our galaxy (where Roman looks), there are billions of stars packed together, like a crowded concert.

Analogy: If you are trying to spot a single person holding a small flashlight in a packed stadium, it's hard because the light from thousands of other people blurs together.
Result: Even if Roman did take a photo at the right time, the "noise" from nearby stars makes it nearly impossible to tell if the White Dwarf got brighter or if it was just a neighbor star.

The Final Verdict: Will We See It?

The scientists crunched the numbers to see how many of these systems exist in our galaxy and how many we might catch.

The Good News: If about 8% of White Dwarfs have Black Hole neighbors, and 3% have Neutron Star neighbors, the TESS telescope might actually catch at least one of these events in the next few years. It's a long shot, but it's possible!
The Bad News: The Roman telescope will almost certainly not see any of these specific events. The signals are too short, and the view is too crowded.

Summary in a Nutshell

The universe is full of invisible giants bending light around tiny stars. While this is a beautiful phenomenon, it is incredibly hard to catch.

TESS is fast enough to maybe catch a glimpse, provided the stars are lined up perfectly and the "magic trick" happens often enough.
Roman is too slow and looking at too crowded a scene to catch these specific, fleeting flashes.

The paper is essentially a "feasibility study" telling astronomers: "Keep an eye on TESS data for these tiny blips, but don't hold your breath for Roman to find them."

1. Problem Statement

The paper investigates the detectability of self-lensing and eclipsing signals in binary systems composed of a White Dwarf (WD) and a compact companion, specifically a Neutron Star (NS) or a Stellar-mass Black Hole (BH). While binary systems with compact objects are known sources of gravitational waves and multi-messenger events, their photometric signatures (specifically self-lensing) in edge-on configurations remain under-explored for large-scale surveys.

The authors aim to determine:

The physical properties (Einstein radius, finite-source effects) of self-lensing signals in WD+NS and WD+BH systems.
The probability of detecting these signals using current and future space-based telescopes: the Transiting Exoplanet Survey Satellite (TESS) and the Nancy Grace Roman Space Telescope (Roman).
The expected number of detectable events given realistic population distributions.

2. Methodology

Analytical Framework

The authors developed an analytical formalism to model the lensing geometry:

Parameters: Defined by component masses ( $M_{WD}, M_{lens}$ ), orbital period ( $T$ ), eccentricity ( $\epsilon$ ), inclination ( $i$ ), and projection angles.
Key Metrics:
- Einstein Radius ( $R_E$ ): Calculated based on the lens mass and orbital separation.
- Normalized Source Radius ( $\rho_\star$ ): Defined as $R_{WD}/R_E$ . This is crucial for determining finite-source effects.
- Magnification ( $A$ ): Calculated using the lens equation and inverse-ray shooting methods (utilizing the VBMicrolensing package).
Finite-Source vs. Finite-Lens: The study notes that while WD+NS systems often suffer from significant finite-source effects ( $\rho_\star \sim 1$ ), WD+BH systems generally have smaller $\rho_\star$ (down to $\sim 0.01$ for massive BHs), leading to higher magnification. Finite-lens effects (occultation by the lens) are negligible for NS/BH lenses due to their small radii compared to $R_E$ .

Monte Carlo Simulations

To move beyond analytical approximations, the authors performed extensive Monte Carlo simulations:

Population Generation:
- WDs: Based on the Kilic et al. (2020) catalog of confirmed WDs within 100 pc, scaled to Galactic distributions (Besançon model).
- Companions: NS masses drawn from a Gaussian distribution ( $1.28 \pm 0.24 M_\odot$ ); BH masses uniformly distributed ( $3.3 - 50 M_\odot$ ).
- Orbits: Semi-major axes and eccentricities derived from Öpik's law and period-eccentricity relations.
Light Curve Synthesis:
- Generated light curves for edge-on systems ( $i \approx 0$ ).
- Applied observing protocols for TESS (27.4-day continuous window, 2-min cadence) and Roman (62-day window, 15-min cadence).
- Included photometric errors based on apparent magnitude and blending effects (critical for Roman's Galactic bulge observations).
Detection Criteria: A signal was deemed detectable if:
1. Orbital period $1 \le T \le T_{obs}$ .
2. Signal-to-Noise Ratio (SNR) $\ge 3$ (conservative) or $6$ (strict).
3. Signal depth $\Delta F > 2\sigma_A$ (twice the photometric error).
4. Signal duration $\Delta t \ge$ observing cadence ( $\tau$ ).
5. Covered by at least one data point.

3. Key Contributions

Analytical Characterization: Provided detailed maps of $R_E$ , $\rho_\star$ , and magnification factors across the mass-period parameter space for WD+NS and WD+BH systems.
Quantification of Detection Efficiencies: Calculated the total detection efficiency ( $\epsilon_{tot}$ ) for both TESS and Roman, breaking it down into geometric probability ( $\epsilon_1$ ) and photometric detectability ( $\epsilon_L$ ).
Synthetic Data Generation: Produced synthetic light curves and data points mimicking real survey conditions, including the specific cadence and noise characteristics of TESS and Roman.
Blending Analysis: Specifically addressed the "blending effect" in the Roman Galactic Exoplanet Survey (RGES), demonstrating how crowding in the Galactic bulge severely hinders the detection of faint WDs.

4. Key Results

Physical Properties of Signals

WD+NS Systems:
- For short periods ( $T \lesssim 25$ days), $\rho_\star \gtrsim 1$ (finite-source effects dominate).
- For longer periods ( $T \gtrsim 25$ days), $\rho_\star \lesssim 1$ .
- Signals are short, lasting $\sim 6$ minutes on average.
- Detection requires extremely tight alignment: inclination $i \lesssim 0.2^\circ$ .
WD+BH Systems:
- Generally have smaller $\rho_\star$ (down to $0.01$ for massive BHs), resulting in higher magnification.
- Signals last longer ( $\sim 16-34$ minutes) due to larger Einstein radii.
- Slightly more forgiving alignment requirements ( $i \lesssim 0.9^\circ$ for TESS).
Eclipsing: Pure eclipsing signals (blocking light) are virtually undetectable in these systems because the lens (NS/BH) is too small to block significant flux, and the NS/BH flux itself is negligible compared to the WD ( $F \ll 1$ ).

Detection Efficiencies and Counts

TESS:
- Total detection efficiency: $\epsilon_{tot} \sim 2 - 6 \times 10^{-4}$ .
- Predicted Yield: If $\sim 8\%$ of WDs have NS companions and $\sim 3\%$ have BH companions, TESS is expected to detect at least one self-lensing signal over its survey duration.
- Detectable systems typically have $T \sim 6$ days and $i \lesssim 0.2^\circ$ .
Roman (RGES):
- Total detection efficiency: $\epsilon_{tot} \sim 2 - 12 \times 10^{-10}$ .
- Predicted Yield: Detecting self-lensing signals with Roman is effectively impossible.
- Reasons for Failure:
  1. Cadence Mismatch: The 15-minute cadence is too sparse to capture signals lasting only 6–34 minutes (often resulting in only 1–2 data points per event).
  2. Blending: The high stellar density in the Galactic bulge makes it difficult to resolve faint WDs, and the blending factor reduces the effective signal depth below detection thresholds.

5. Significance

Multi-Messenger Astronomy: This work identifies a new photometric channel for detecting compact binary systems, complementing gravitational wave and radio/X-ray observations.
Survey Strategy Validation: It provides a critical reality check for the Roman Space Telescope's ability to detect short-duration microlensing events in crowded fields, suggesting that its 15-minute cadence is insufficient for self-lensing in compact binaries.
TESS Potential: It highlights TESS as a viable instrument for discovering the first self-lensing WD+NS or WD+BH systems, provided the binary fraction of WDs is not negligible.
Parameter Constraints: The study demonstrates that detecting these signals offers a unique way to constrain the mass of the compact companion and the orbital inclination, breaking degeneracies present in other observational methods.

In conclusion, while self-lensing in WD+NS and WD+BH systems is a theoretically robust phenomenon, its detection is highly constrained by geometric alignment and observational cadence. TESS offers a realistic chance of discovery, whereas Roman's current survey design is ill-suited for this specific class of transient events.