Multiply Lensed Transients Overview

• Multiply lensed transients are explosive astrophysical events whose light or gravitational wave signals are deflected by massive structures to produce multiple images with distinct magnifications and time delays.
• They are analyzed using techniques like the thin-lens approximation and standard-candle calibration to measure lens mass profiles, time delays, and cosmological parameters.
• Observational strategies with surveys like LSST and JWST optimize detection and modeling, advancing studies in dark matter substructure and stellar demographics while reducing systematic biases.

Multiply lensed transients are explosive astrophysical events (supernovae, tidal disruption events, gravitational waves, fast radio bursts, etc.) whose photon or GW paths are strongly deflected by intervening mass distributions—typically galaxies or galaxy clusters—such that multiple distinct images arrive at Earth with different magnifications, positions, and arrival times. Their rapidly evolving light curves, compact emission regions, and geometric properties make them exceptionally valuable for precision measurements of lens mass profiles, time delays, cosmological parameters, small-scale dark-matter substructure, and stellar or black-hole demographics.

1. Physical Principles and Lensing Formalism

Multiply lensed transient phenomena arise when a compact, time-varying astrophysical source is closely aligned with a massive foreground deflector that can create multiple images. Mathematically, in the thin-lens approximation, the system is described by the lens equation:

$$\boldsymbol{\beta} = \boldsymbol{\theta} - \nabla\psi(\boldsymbol{\theta})$$

where $\boldsymbol{\theta}$ is the image position, $\boldsymbol{\beta}$ is the source position, and $\psi$ is the projected lensing potential. The Jacobian determinant $$|\partial\boldsymbol{\beta}/\partial\boldsymbol{\theta}|$$ gives the signed magnification factor:

$$\mu(\boldsymbol{\theta}) = \frac{1}{\det\left[\mathbb{I} - \nabla\nabla\psi(\boldsymbol{\theta})\right]}$$

Multiple images arise when the mapping possesses stationary points in the Fermat potential—each corresponds to a distinct path with unique arrival time $$t_d(\boldsymbol{\theta},\boldsymbol{\beta}) = \frac{1}{2}|\boldsymbol{\theta}-\boldsymbol{\beta}|^2 - \psi(\boldsymbol{\theta})$$. The observed time delays between images $i$ and $j$ are

$$\Delta t_{ij} = (1+z_l)/c \, (D_l D_s/D_{ls}) [ t_d(\boldsymbol{\theta}_i,\boldsymbol{\beta}) - t_d(\boldsymbol{\theta}_j,\boldsymbol{\beta}) ]$$

Image multiplicities, separations, and delays are controlled by the mass, profile, and substructure of the lens. For nearly isothermal galaxy lenses, double and quadruple image configurations are common; cluster lenses can produce higher multiplicities and longer delays (Vujeva et al., 3 Jan 2025, Wojtak et al., 2019).

2. Astrophysical Sources and Observational Signatures

Multiply lensed transient classes include:

• Supernovae (SNe Ia, core-collapse, SLSN): Exquisitely standardizable light curves (especially Ia) enable measurement of absolute magnification, robust time delays, and cosmological inference (Goobar et al., 2022, Pierel et al., 2022, Sharon et al., 2014). Characteristic timescales are tens to hundreds of days, with typical image delays from days to weeks.
• Tidal Disruption Events (TDEs): Flares from stellar disruption by supermassive BHs, with predicted multiply imaged rates of $\sim${0.4–15} yr${}^{-1}$ for LSST, predominantly at $z_{s}\sim1.5$–2.0; image delays are $\sim${days–months} (Mamuzic et al., 26 Feb 2025, Szekerczes et al., 5 Feb 2024).
• Fast Transients in Lensed Galaxies: Recurrent LBV eruptions, fast novae, or microcaustic crossings (lensed SG stars) in cluster arcs have been detected. Spectral and light-curve diagnostics distinguish these origin scenarios (Rodney et al., 2017, Diego et al., 2023).
• Gravitational Waves and FRBs: Binary mergers and millisecond radio bursts can be multiply imaged, with rate predictions dependent on lens population and detailed geometry (Vujeva et al., 3 Jan 2025, Oguri, 2019).
• Lensed Stellar Transients: JWST can resolve multiple images of individual massive stars undergoing microcaustic crossings near galaxy/cluster critical curves, enabling both dark matter and stellar population studies (Li et al., 19 Sep 2025).

The image properties—separations, delays, magnifications, multiplicity—encode the integrated lens mass and its substructure. For SNe Ia, standard-candle fluxes break the mass-sheet degeneracy and allow direct calibration of lens model magnifications (Goobar et al., 2022, Agrawal et al., 9 Oct 2025).

3. Lens Modeling, Image Multiplicity, and Magnification Bias

Lens modeling for multiply lensed transients employs parametric (SIE, NFW, PIEMD) or free-form mass reconstructions, constrained by observed image positions, flux ratios, arrival times, and host-galaxy arcs.

• Galaxy-scale lenses: Singular isothermal ellipsoid (SIE) models parameterize Einstein radius $\theta_E$, axis ratio $q$, and central velocity dispersion $\sigma$. The strong-lensing optical depth and cross-section are given by $\tau(z_s)$ and $\sigma_{\mathrm{lens}}=f(q)\pi\theta_E^2$ (Murieta et al., 4 Jul 2024).
• Cluster-scale lenses: Multi-component mass models (PIEMD, dPIE subhalos) yield strongly structured Fermat surfaces with complex caustics and higher-order image multiplicities—e.g., up to 8 images per event (Vujeva et al., 3 Jan 2025, Sharon et al., 2014).

Magnification estimates from lens models must be cross-checked with standard-candle measurements. Recent work reveals systemic $\sim$1 mag overprediction of cluster-lens $\mu$ relative to photometric measurements for SNe Ia, highlighting the mass-sheet degeneracy and slope uncertainty (Agrawal et al., 9 Oct 2025). Multiple modeling approaches (parametric, free-form, hybrid) are integrated with ensemble host and lens constraints to mitigate bias.

Time delays are predominantly set by the lens geometry and mass normalization, and, together with measured magnifications, yield cosmographic inferences such as $H_0$ and dark energy constraints (Pierel et al., 2019).

4. Event Rates, Survey Yields, and Search Strategies

Survey predictions for multiply lensed transients depend on lens and source populations, volumetric rates, and survey depth:

• LSST/WFD: For SNe, yields range from $\sim${300–600} yr${}^{-1}$, with $\sim$88 glSNe per year (39 Ia, 41 II, 6 Ibc) (Murieta et al., 4 Jul 2024, Wojtak et al., 2019).
• TDEs: $\sim$10 total multiply lensed TDEs over LSST's decade survey at $z_{s}\mlt 2$ (Mamuzic et al., 26 Feb 2025, Szekerczes et al., 5 Feb 2024).
• ZTF: $\sim$2 Ia and 4 core-collapse SNe per year as multiply imaged events, primarily identified via magnification in the restricted r-band depth (Wojtak et al., 2019).
• JWST: For galaxy-galaxy lenses such as the Cosmic Horseshoe, $\sim$60 lensed stellar transients per pointing at $m_{AB}=29$ (Li et al., 19 Sep 2025).

Detection methods utilize both magnification-based (standard-candle outliers) and image-multiplicity-based algorithms, with a hybrid strategy at LSST depth yielding $\sim$30–50% boost in discovery rates (Wojtak et al., 2019). Hostless transient rates are significant, particularly in shallow surveys where a majority of lensed hosts fall below the magnitude threshold (Ryczanowski et al., 2020).

Efficient identification relies on cross-matching real-time transient streams with dynamically maintained lens-plane and source-plane watch-lists, leveraging both confirmed arcs and massive-cluster catalogs (Ryczanowski et al., 2020).

5. Applications: Cosmology, Small-Scale Structure, and Host Properties

Multiply lensed transients serve as cosmographic tools, probes of dark matter microstructure, and diagnostics of stellar and black-hole populations at high redshift.

• Time-delay cosmography: Measurement of $\Delta t_{ij}$ provides constraints on the time-delay distance $D_{\Delta t}$, and on $H_0$. Golden samples (Ia SNe with $\Delta t>10$ days, $\theta_{\max}>0.8''$, and resolved hosts) enable few-percent $H_0$ precision from LSST (Murieta et al., 4 Jul 2024, Pierel et al., 2019, Sharon et al., 2014, Agrawal et al., 9 Oct 2025).
• Dark matter and substructure: Flux-ratio anomalies, short-delay high-multiplicity images, and parity asymmetries constrain DM granularity, subhalo mass functions, and, via lensed star transients, fuzzy DM scenarios (axions) (Vujeva et al., 3 Jan 2025, Li et al., 19 Sep 2025, Diego et al., 2023).
• Black-hole demographics: Lensed TDEs at $z_s=1.5$–2 probe BH mass functions and accretion physics not accessible otherwise (Mamuzic et al., 26 Feb 2025, Szekerczes et al., 5 Feb 2024).
• Stellar evolution and IMF: Microlensed supergiant events and stellar caustic crossings in JWST imaging offer constraints on high-mass stellar IMF slopes at cosmic noon (Diego et al., 2023, Li et al., 19 Sep 2025).
• Systematic model biases: Multiply imaged transients directly expose magnification modeling errors, informing lens reconstruction methodologies required for high-precision cosmology (Agrawal et al., 9 Oct 2025).

6. Survey Optimization, Data Analysis, and Modeling Challenges

Advancing the science of multiply lensed transients demands tailored survey strategies and robust modeling pipelines:

• Rapid cadence ($\lesssim$2–3 days), multi-filter coverage, and low-resolution spectra for initial classification;
• Targeted high-resolution imaging (HST/JWST/ELTs) for flux ratio, image geometry, and microlensing assessment;
• Cross-survey lens-plane selection to maximize completeness, especially for hostless events and cluster lenses (Ryczanowski et al., 2020);
• Automated pipelines using standard-candle detection, PSF-fitting for image resolution, and color/microlensing treatment with techniques such as Gaussian Process Regression (Pierel et al., 2019, Pierel et al., 2022);
• Joint SL+WL+kinematic mass modeling to control mass-sheet degeneracy and achieve $<0.05$ mag accuracy in $\mu$.
• Golden-sample preselection based on wide-separation large-delay systems with resolved hosts, utilizing prior galaxy–galaxy lens catalogs (Euclid, LSST) (Murieta et al., 4 Jul 2024).

Uncertainty in lens model magnification is an active area of research; repeated use of photometric standard candles provides ongoing external calibration (Agrawal et al., 9 Oct 2025). Ensemble analyses of dozens to hundreds of events will be required to suppress residual systematics and leverage the full cosmological power of multiply lensed transients.

7. Future Prospects and Research Directions

The next decade will see orders-of-magnitude increases in the sample of multiply imaged transients as LSST, Roman, Euclid, and JWST deliver all-sky surveys with deep imaging and rapid alert streams. Anticipated advances include:

• Sub-percent determination of $H_0$ via time-delay cosmography in ensemble lensed SNe Ia (Murieta et al., 4 Jul 2024, Pierel et al., 2019, Agrawal et al., 9 Oct 2025);
• Direct constraints on dark matter properties at kpc and sub-kpc scales via flux anomalies, image sharpening, and wave-optics effects (Oguri, 2019, Li et al., 19 Sep 2025);
• Stellar population and BH demographic studies at cosmological redshifts by leveraging lensing magnification and transient detection rates (Diego et al., 2023, Mamuzic et al., 26 Feb 2025, Li et al., 19 Sep 2025);
• Refinement of lens mass models with cross-calibration against standard-candle magnifications and joint strong+weak+kinematic lensing data (Agrawal et al., 9 Oct 2025);
• Deployment of automated, robust time-delay and microlensing treatment in multi-band transient analyses using tools such as SNTD and LENSTRONOMY (Pierel et al., 2019, Pierel et al., 2022).

As multiply imaged transients become routine discoveries, they will underpin high-precision cosmological measurements, illuminate the structure of dark matter, and resolve fundamental questions in stellar and black-hole astrophysics, with continued methodological challenges focused on lens modeling fidelity and optimal survey design.