🔭 astrophysics

Self-lensing binaries as probes of Supernova physics

Using population synthesis simulations, this study demonstrates that self-lensing binaries serve as powerful probes for constraining supernova physics and the mass gap, with specific models predicting distinct observable populations that future surveys like ZTF and LSST can detect to characterize compact object formation.

Original authors: Grzegorz Wiktorowicz, Matthew Middleton, Aleksandra Olejak, Cordelia Dashwood-Brown, Madeleine-Mai Ward, Adam Ingram

Published 2026-02-18

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CC BY 4.0

Original authors: Grzegorz Wiktorowicz, Matthew Middleton, Aleksandra Olejak, Cordelia Dashwood-Brown, Madeleine-Mai Ward, Adam Ingram

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

Imagine the Milky Way galaxy as a giant, bustling city. Most of the "residents" in this city are stars, but hidden among them are the "ghosts": invisible, ultra-dense remnants of dead stars called Neutron Stars and Black Holes. These ghosts are hard to find because they don't emit light. Usually, we only spot them if they are actively eating a companion star (like a vampire feeding), which makes them glow brightly. But what about the ghosts that are just sitting there, quiet and invisible?

This paper is like a detective's guide on how to find these "quiet ghosts" using a cosmic trick called Self-Lensing.

The Magic Trick: The Invisible Magnifying Glass

Imagine you are walking down a street at night. You see a streetlamp (a normal, bright star). Suddenly, a tiny, invisible person (a black hole or neutron star) walks directly in front of the lamp.

Because that invisible person is so heavy, their gravity acts like a magnifying glass. It bends the light from the streetlamp around them, making the lamp briefly look brighter to you. This is Self-Lensing.

The paper asks: How many of these "invisible magnifying glasses" are out there, and what can they tell us about how stars die?

The Big Mystery: The "Missing Middle"

Astronomers have a puzzle called the "Mass Gap."

Small ghosts: Neutron stars are usually light (about 1.5 times the mass of our Sun).
Big ghosts: Black holes are usually heavy (more than 5 times the mass of our Sun).
The Gap: There seems to be a "missing middle" between 2 and 5 solar masses. Are there ghosts in this size range, or is the gap real?

The answer depends on how stars explode (Supernovae). Think of a supernova like a firework.

The "Rapid" Firework: Explodes quickly and violently. This theory suggests the "Mass Gap" is real and empty.
The "Delayed" Firework: Takes a long time to build up pressure before exploding. This theory suggests the gap is full of ghosts that are just waiting to be found.

The Experiment: Simulating the Galaxy

The authors used two super-computer programs (named StarTrack and COSMIC) to simulate the entire history of the Milky Way. They acted like cosmic architects, building billions of binary star systems (pairs of stars) and watching them evolve over billions of years.

They tested three different "firework recipes" (Supernova models) to see which one creates the most "quiet ghosts" that we could actually see.

The Findings: Who is Watching?

The team looked at three major telescopes that act like different pairs of eyes:

TESS: A fast-acting camera that watches small patches of sky very closely.
ZTF: A wide-angle camera that scans the whole sky frequently.
LSST: A massive, future camera that will take incredibly detailed photos of the whole sky for 10 years.

The Results:

ZTF is the Champion: It's predicted to find the most of these events (dozens to hundreds). It's like having a security guard who checks every corner of the city every night.
The "Mass Gap" Clue: If the "Delayed" firework model is correct, ZTF could find 10 times more of those mysterious "middle-sized" ghosts than if the "Rapid" model is correct. This could finally solve the mystery of the Mass Gap!
The "Slow and Steady" Rule: The ghosts they find will mostly be moving very slowly. Why? Because if a star explodes violently (giving the ghost a huge kick), the pair often flies apart, and the ghost escapes into the dark. Only the calm, slow-moving pairs stay together long enough to be caught by our telescopes.

The Catch: It's Harder Than It Looks

The paper also puts on the "realist" hat. While the computers say there are thousands of potential events, reality is messy.

Noise: Stars twinkle, and telescopes have static (noise).
Timing: If the telescope isn't looking at the right spot at the exact moment the "magnifying glass" effect happens, we miss it.

When the authors added these realistic "noise" filters, the number of guaranteed detections dropped by about 100 times. However, they still predict that ZTF and LSST will find a few dozen solid candidates.

The Bottom Line

This paper is an optimistic roadmap for the future of astronomy. It tells us that by watching stars get slightly brighter for a few hours, we can:

Find the "invisible" black holes and neutron stars that are currently hiding.
Figure out exactly how stars explode (the "firework" recipe).
Finally fill in the "Mass Gap" and understand why some dead stars are small, some are huge, and some might be the missing middle.

It's like using a magnifying glass to find the invisible, proving that even the quietest ghosts in the galaxy have a story to tell.

1. Problem Statement

The Galactic population of compact objects (neutron stars and black holes) remains poorly constrained, particularly regarding the "mass gap" (2–5 $M_\odot$ ), a region where few compact objects have been observed. The existence and population of objects in this gap are critical for understanding supernova (SN) explosion mechanisms.

Current Limitations: Traditional methods (X-ray binaries, gravitational waves) suffer from selection biases, often favoring high-mass objects or specific evolutionary paths.
The Opportunity: Self-lensing (SL) occurs when a compact object in a binary system transits its non-compact companion, causing a temporary brightening. This method is unbiased regarding the mass of the lens and can detect quiescent (non-accreting) compact objects, offering a unique window into the "pristine" properties of compact object formation.
The Question: How do different supernova engine physics (specifically convective growth timescales) affect the observable population of SL systems, and can SL observations constrain the existence of the mass gap?

2. Methodology

The authors utilized two independent binary population synthesis codes, startrack and COSMIC, to simulate the Galactic population of binary systems containing compact objects.

Galactic Model: Simulations covered the Galactic disk and bulge, incorporating realistic star formation histories, metallicity distributions, and Initial Mass Functions (IMF).
Supernova Models: The study tested three variants of SN remnant formation based on the convective growth timescale ( $f_{mix}$ $f_{mi x}$ ):
1. $f_{mix} = 0.5$ (Delayed Model): Corresponds to a long growth timescale for Rayleigh-Taylor instabilities, predicting a "soft" mass gap with many objects in the 2–5 $M_\odot$ range.
2. $f_{mix} = 1.0$ (Intermediate): A transitional case.
3. $f_{mix} = 4.0$ (Rapid Model): Corresponds to a short growth timescale, predicting a "hard" mass gap (few objects between 2–5 $M_\odot$ ).
- Note: The COSMIC code used equivalent "Delayed" and "Rapid" models from Fryer et al. (2012).
Observational Simulations: The synthetic populations were folded through the instrumental characteristics of three major surveys:
- TESS: High cadence, short duration.
- ZTF: Wide-field, moderate cadence.
- LSST: Deep, wide-field, long duration.
Detection Criteria:
- Raw Detection: Defined as systems where at least one observation occurs during the SL event.
- Conservative Detection: Applied filters for apparent magnitude limits and Signal-to-Noise Ratio (SNR) thresholds ( $2\sigma$ and $3\sigma$ ) to account for photometric noise.
- Metrics: Analyzed lens mass ( $M_{lens}$ ), Einstein crossing time ( $\tau_{eff}$ ), center-of-mass velocity ( $v_{cm}$ ), and recurrence rates.

3. Key Contributions

First Systematic Comparison of SN Engines via SL: The paper is the first to explicitly link specific supernova engine physics (convective growth timescales) to the observable statistics of self-lensing binaries.
Mass Gap Probing: It demonstrates that SL surveys can statistically distinguish between SN models based on the number of detected objects in the 2–5 $M_\odot$ mass gap.
Dual-Code Robustness: By using both startrack and COSMIC, the authors quantify inter-code systematic uncertainties, confirming that qualitative trends are robust despite quantitative differences in event rates.
Velocity Selection Effects: The study highlights a strong selection bias where detectable SL systems are dominated by low-velocity binaries ( $v_{cm} \lesssim 20$ km/s) due to the survival probability of binaries against natal kicks.

4. Key Results

A. Population Statistics and Survey Yields

Survey Ranking: ZTF consistently predicts the highest number of detectable SL events, followed by LSST, and then TESS.
- Example (Disk, $f_{mix}=0.5$ ): ZTF predicts ~6,300 raw events; LSST ~3,200; TESS ~590.
Galactic Component: The Galactic disk produces significantly more detectable events (order of magnitude higher) than the bulge across all models and surveys.
Impact of SN Models:
- The Delayed model ( $f_{mix}=0.5$ ) predicts significantly higher event rates for disk populations compared to the Rapid model ( $f_{mix}=4.0$ ), particularly for low-mass lenses.
- For the mass gap (2–5 $M_\odot$ ), the $f_{mix}=0.5$ model predicts up to 10 times more detections in the disk for ZTF compared to the $f_{mix}=1.0$ model.

B. Mass Gap Discrimination

The $f_{mix}=0.5$ (Delayed) model efficiently populates the 2–5 $M_\odot$ region with massive neutron stars and low-mass black holes.
The $f_{mix}=4.0$ (Rapid) model creates a distinct gap with very few objects in this range.
Conclusion: If future SL surveys detect a significant population of 2–5 $M_\odot$ lenses, it strongly favors the "Delayed" SN mechanism.

C. System Clustering and Properties

The authors identified three distinct populations based on lens mass and crossing time:

GNS (Gravitational Neutron Stars): $M_{lens} \le 2 M_\odot$ . Characterized by high magnifications and low velocities (often formed via electron-capture SNe with no natal kick).
GBH,short: $M_{lens} > 2 M_\odot$ , $\tau_{eff} < 1$ day. Short-period, high-mass systems.
GBH,long: $M_{lens} > 2 M_\odot$ , $\tau_{eff} \ge 1$ day. Long-period, high-mass systems.

D. Velocity Distributions

A strong preference for low center-of-mass velocities ( $v_{cm} \lesssim 20$ km/s) was found across all models.
Systems with large natal kicks are less likely to remain bound, reducing their detectability.
Massive black holes (formed via direct collapse/fallback) and electron-capture neutron stars dominate the low-velocity tail.

E. Conservative Detection Limits

Applying realistic SNR constraints ( $3\sigma$ ) reduces predicted detection rates by two orders of magnitude compared to raw estimates.
LSST remains the most robust under conservative constraints, with only a 30–40% reduction from filter-only rates.
TESS suffers the most severe reduction due to noise and cadence limitations.
Despite the reduction, ZTF and LSST are still predicted to yield tens of well-covered, high-SNR detections in the disk, sufficient for statistical characterization.

5. Significance

This paper establishes Self-Lensing as a powerful, independent probe of Supernova physics.

Resolving the Mass Gap: It provides a concrete observational pathway to determine if the 2–5 $M_\odot$ mass gap is real or an artifact of current detection biases. A high yield of mass-gap objects would validate "Delayed" SN explosion models.
Compact Object Demographics: It offers a method to census the population of quiescent, non-accreting compact objects, which are invisible to X-ray surveys.
Survey Strategy: The results guide future observational strategies, suggesting that long-duration, high-cadence surveys (like ZTF and LSST) are essential for characterizing the physics of stellar collapse, while emphasizing the need for follow-up radial velocity measurements to confirm candidates.

In summary, the study demonstrates that upcoming photometric surveys will not only detect hundreds of self-lensing binaries but will also provide the statistical power necessary to distinguish between competing theories of core-collapse supernovae.