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Semi-analytical Light Curve Model for Transients Preceding Binary Mergers. I: Supernova Precursor Emission from Compact Object Companions

This paper presents a semi-analytical light curve model and associated inference framework for accretion-powered emission from binary systems undergoing unstable mass transfer, which successfully constrains the progenitor systems of long-rising supernova precursors like SN 2023zkd, 2023fyq, and 2021qqp.

Original authors: Daichi Tsuna, Morgan Macleod, V. Ashley Villar

Published 2026-07-24✓ Author reviewed ⓘ

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CC BY 4.0

Original authors: Daichi Tsuna, Morgan Macleod, V. Ashley Villar

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 by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a cosmic dance floor where stars are the dancers. Most of the time, these dancers spin alone, but often they pair up in binary systems, holding hands so tightly that they influence each other's entire lives. Sometimes, this dance goes wrong. One star might grow too big, spilling its outer layers onto its partner. If the partner is a tiny, dense "compact object" like a black hole or a neutron star, this spill-over can trigger a runaway reaction. Instead of a gentle waltz, the orbit shrinks rapidly, and the two stars spiral toward a violent crash. But before they smash together, there's often a long, slow buildup—a "pre-show" of glowing gas and energy that lasts for years. Astronomers are fascinated by these pre-shows because they are like a time machine, letting us see the history of the stars before the final explosion. Understanding this buildup helps us figure out what kind of stars were dancing and how they were moving, which is crucial for understanding how the universe creates the heavy elements that make up everything around us.

This paper builds a new "recipe book" to understand that pre-show. The authors, Daichi Tsuna, Morgan Macleod, and V. Ashley Villar, created a semi-analytical model—a mix of math and physics—to predict what the light curve (the brightness over time) of these events should look like. They focused on a specific scenario: a massive star donating its mass to a compact companion just before they merge. Think of it like a leaky faucet (the donor star) dripping water onto a spinning turbine (the compact object). The water hits the turbine, gets heated up, and shoots out as a super-fast wind. This wind glows brightly, creating the "precursor" light we see years before the final crash.

The team tested their recipe book on three real-life cosmic events: SN 2023zkd, SN 2023fyq, and SN 2021qqp. These were supernovae that showed a slow, years-long rise in brightness before exploding. By feeding the observed light and temperature data from these events into their model, the authors were able to "rewind the tape" and infer the history of the mass transfer. They found that the model works well, suggesting that these events were indeed caused by unstable mass transfer in binary systems. For example, in the case of SN 2023zkd, the model suggests a massive star was shedding about 0.1 to a few times the mass of our Sun every year in the years leading up to the explosion.

One of the most exciting findings is that the model helps solve a mystery: why do some of these light curves have two peaks? The authors suggest that the first peak might be the result of the stars spiraling in and the wind glowing, while the second peak is the actual explosion happening after the compact object finally crashes into the donor's core. This "delayed explosion" idea could explain the strange double-hump shape seen in these events. The paper also highlights that while we have found a few of these events, there are likely many more "dimmer" versions that our current telescopes can't see yet. When the Vera C. Rubin Observatory starts its massive survey of the sky, it is expected to find tens or even hundreds of these pre-shows, giving astronomers a treasure trove of data to test this model further.

The authors are careful to note that while their model fits the data well, it is a simplification. They suggest that the physics of the wind and the exact nature of the compact object (whether it's a black hole or a neutron star) still have some uncertainties. For instance, the model suggests that for the massive star events, the companion is likely a heavy black hole, while for the helium-rich event (SN 2023fyq), it's likely a neutron star. However, they emphasize that these are inferences based on their current model, and future observations will be needed to confirm the details. The paper doesn't claim to have solved the entire puzzle of stellar mergers, but it provides a powerful new tool to decode the light curves of these dramatic cosmic finales, turning a blurry picture of a dying star into a clear story of its final moments.

Technical Summary: Semi-Analytical Light Curve Model for Transients Preceding Binary Mergers

Problem Statement
Recent archival data has revealed a class of interacting supernovae (SNe) exhibiting long-rising precursors lasting years with luminosities of $10^{40}–10^{42}$ erg s $^{-1}$ (e.g., SN 2023zkd, SN 2023fyq, SN 2021qqp). Interpreting these as single mass ejection events requires unphysically large ejecta masses ( $>100 M_\odot$ ) to explain the diffusion timescales. Instead, these events are hypothesized to result from dynamically unstable mass transfer in binary systems containing a compact object (neutron star or black hole) and a massive donor star, leading to a merger-driven explosion. However, a quantitative framework to model the precursor emission and infer the binary's mass-transfer history from observed light curves has been lacking.

Methodology
The authors construct a semi-analytical light curve model for binary systems where a compact object accretor undergoes unstable mass transfer from a donor star. The model operates under the following physical prescriptions:

Mass Transfer Evolution: The mass transfer rate ( $\dot{M}_*$ ) is modeled to evolve from a steady phase into a dynamically unstable runaway phase as the merger approaches. The rate follows a power-law divergence, $|\dot{M}_*| \propto (t_m - t)^{-\delta}$ , where $t_m$ is the merger time and $\delta$ depends on the donor's polytropic index.
Wind Formation and Accretion Power: Due to the extreme mass transfer rates, the system is treated as highly non-conservative ( $\beta \ll 1$ ). Most mass is ejected as a quasi-steady, optically thick wind. The wind is launched from a characteristic radius ( $r_{in}$ ) carrying accretion power parameterized by an efficiency $\epsilon_{acc}$ . The model assumes equipartition between kinetic and internal energy at the launch radius.
Radiative Transfer: The model solves for the luminosity and temperature of the wind-reprocessed emission. It divides the wind into shells, accounting for adiabatic cooling (PdV work) and radiative diffusion. The emission temperature is determined by the thermalization radius ( $r_c$ ) and the trapping radius ( $r_{tr}$ ), with the latter set by the diffusion timescale.
Dust and Observables: An approximate dust correction model is included to account for extinction and reddening, calculating the dust optical depth based on the sublimation radius. The model outputs observable bolometric luminosity ( $L_{obs}$ ) and color temperature ( $T_{obs}$ ), allowing for multi-band fitting.
Parameter Inference: A Markov Chain Monte Carlo (MCMC) framework is implemented to infer binary parameters ( $\dot{M}_0, t_{MT}, t_0, t_m, \delta, r_{in}, \epsilon_{acc,0}, n_{acc}$ ) from observed light curves. The authors emphasize that incorporating temperature data is crucial to breaking degeneracies between the mass transfer rate and accretion efficiency.

Key Contributions and Results
The paper applies this model to three specific interacting supernova precursors:

SN 2023zkd (Type IIn): The model successfully reproduces the multi-year precursor emission. Inference suggests a mass transfer rate of $\sim 0.1–1 M_\odot$ yr $^{-1}$ in the years preceding the merger, with an accretion efficiency $\epsilon_{acc} \sim 10^{-4}$ . The inferred total mass lost ( $\sim 3 M_\odot$ ) aligns with the circumstellar material (CSM) mass derived from the supernova phase. The results favor a progenitor system involving a massive black hole accretor and an evolved, hydrogen-rich donor.
SN 2023fyq (Type Ibn): With tighter constraints due to more data points and pre-explosion velocity measurements, the model infers an initial mass transfer rate of $\dot{M}_0 \approx 2.7 \times 10^{-2} M_\odot$ yr $^{-1}$ and an efficiency $\epsilon_{acc,0} \approx 8.5 \times 10^{-5}$ . The reconstructed history supports a scenario of a low-mass helium star donor merging with a neutron star, consistent with independent radio observations of CSM.
SN 2021qqp (Type IIn): Using multi-band (g- and r-band) fitting due to a lack of blackbody estimates, the model reconstructs a similar mass transfer history to SN 2023zkd but with slightly lower rates. The inferred CSM velocities are consistent with spectral observations.

Significance and Claims
The authors claim that this work provides the first semi-analytical framework capable of inferring the mass-transfer history and constraining the progenitor binary systems of long-rising SN precursors. Key findings include:

Degeneracy Breaking: The study demonstrates that temperature information is essential to break the degeneracy between mass transfer rate and accretion efficiency, which cannot be resolved using bolometric luminosity alone.
Progenitor Constraints: The inferred parameters suggest that SN 2023zkd and SN 2021qqp likely involve massive black hole companions and evolved donors (Hertzsprung gap or red supergiant), while SN 2023fyq points to a neutron star companion and a low-mass helium donor.
Double-Peaked Morphology: The paper proposes a hypothesis for the double-peaked light curves observed in these events: the first peak arises from the binary merger and precursor emission, while the second peak corresponds to the final explosion occurring after a delay of several dynamical timescales as the compact object spirals into the donor's envelope.
Future Outlook: The authors assert that while current detections are rare, the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) is expected to detect tens to hundreds of such events annually. This model serves as a necessary tool to interpret this future population and distinguish merger-driven explosions from traditional core-collapse supernovae.

The paper concludes by noting that while the current model is a "one-zone" inverse problem approach, future work will require forward modeling of binary populations and numerical hydrodynamical simulations to better understand the complex phenomenology of the merger and common-envelope phases.

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