Calibration-Induced Systematics in SALT3 Training and Their Impact on Dark Energy Constraints from Stage IV Supernova Surveys

The gist The calibration-induced systematics in SALT3 training and their impact on dark energy constraints from Stage IV supernova surveys are analyzed by perturbing photometric zero-points and filter mean wavelengths to quantify their effect on spectral model recovery, estimated distances, and dark energy figure of merit (FoM) based on the w0waCDM model.

Introduction and Motivation

Type Ia supernovae (SNe Ia) are critical for discovering the accelerating expansion of the universe and improving measurements of dark energy properties. While results have been largely consistent with a cosmological constant, recent analyses hint that the dark energy equation of state parameter may evolve with cosmic time. SNe Ia are standardizable distance indicators, and this standardization is implemented using spectral time-series models such as SALT (Guy et al. 2005, 2007). Uncertainties in the spectrophotometric model for SNe Ia time series data, which depend on the photometric calibration of the surveys, are one of the largest systematic uncertainties in cosmological analyses.

Methodology and Simulation

The analysis involves simulating realistic light-curve samples for Rubin-LSST and Roman using the optical+NIR SALT model, SALT3.NIREXT, as the true input SED model. The simulation framework uses the SuperNova ANAlysis software package (SNANA; Kessler et al. 2009b) to generate catalogue-level simulations reflecting predicted survey conditions, including observational effects such as depth per filter and cadence. The training process involves several steps:

1. Simulation: Simulate realistic light-curve samples for Rubin-LSST and Roman using the filter transmission curves for both surveys, along with Roman prism spectra to use in the SALT3 training.

2. Training: Train the SED model on a high-quality SN Ia subset to obtain a nominal model as well as “biased” models that are produced using shifted zero-points and filter transmissions.

3. Light-curve fitting: Fit the light curves from the full sample in step (1) with all of the SED models from step (2).

4. Classification: Run the SCONE classifier (Qu et al. 2021) to weight each event during the distance modulus measurement stage.

Systematic Accounting and Inference

The systematic accounting procedure compares recovered, biased distance modulus values to those recovered when light curves are fit with the nominal model, propagating differences into a systematic covariance matrix. The total uncertainty covariance matrix is defined as Ctot = Cstat + Csyst, where Csyst is computed using the formula X NS S=1 ⟨∆µiS⟩ ⟨∆µjS⟩ W2 S. Cosmological parameter inference is performed by minimizing a chi-squared function χ2 = ∆µT C−1 tot∆µ + χ2 prior, where ∆µ = µBBC − µtheory(z; omegaM, w0, wa). The constraining power is quantified by the Dark Energy Task Force figure of merit (FoM) defined as FoM = h σw0 σwa p 1 − ρ2 i−1.

Impact of Calibration Uncertainties

The study investigates three sets of analysis variants: Survey (LSST WFD+DDF, Roman WIDE+DEEP), Systematics (Train, Fit, Train+Fit), and Perturbation (Fixed or Random shift). The key findings regarding the impact on FoM are:

: Zero-point shifts of 5 mmag and filter mean wavelength shifts of 5˚A lead to a ∼ 50% decrease in the FoM relative to a statistical-only case when calibration uncertainties are propagated only through light-curve fitting.

: The same calibration shifts applied only during model training produce a smaller ∼ 13% degradation.

Contrary to previous analyses, calibration uncertainties in light-curve fitting dominate over those from model training. The FoM dependence on the size of the calibration uncertainties (in the range of expected sizes) is roughly linear."

Conclusion

The results show that introducing calibration systematics during fitting stages (Fit and Train+Fit) leads to a much greater impact, dropping the FoM to roughly 50% of the baseline value. The most severe loss of constraining power occurs if all SNe from the Rubin-LSST Deep Drilling Fields (DDF) are excluded. The paper concludes that calibration errors—5 mmag in zero-points and 5˚A in filter mean wavelengths—reduce the dark energy FoM by ∼50% relative to the baseline statistical-only analysis. The results underscore that statistical gains will only translate into improved cosmological constraints if photometric calibration is controlled at the sub-percent level.

Acknowledgments

K.A and D.S acknowledge support from NASA under contract 80NSSC24M0023 through the Roman Supernova Project Infrastructure Team, and from the University of Chicago’s Research Computing Center for computing resources. D.O.J. acknowledges support from NSF grants AST-2407632, AST-2429450, and AST-2510993, NASA grant 80NSSC24M0023, and HST/JWST grants HST-GO-17128.028 and JWST-GO05324.031, awarded by the Space Telescope Science Institute (STScI), which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555. JP thanks the LSSTDA Data Science Fellowship Program, which is funded by LSST-DA, the Brinson Foundation, the WoodNext Foundation, and the Research Corporation for Science Advancement Foundation. The work is also funded in part by the Gordon and Betty Moore Foundation through Grant GBMF13900 to D.O.J.

References

The paper references numerous prior works, including those by Riess et al. 1998, Schmidt et al. 1998, Perlmutter et al. 1999, and various papers related to SALT3 model training and systematic uncertainty quantification. The paper cites works by Brout et al. 2022a, Vincenzi et al. 2024a, Rubin et al. 2025, and others to support its methodology and results. The references include those by Kessler et al. 1998, Guy et al. 2005, Popovic et al. 2023, and others related to the surveys and modeling techniques. The paper also cites foundational works such as Albrecht et al. 2006 and Tripp 1998. The list of references is extensive, including those by Anderson et al. 2025, Adame et al. 2025, Alam et al. 2021, and many others covering cosmology and supernova research. The references cover various aspects of the analysis, from photometric calibration to cosmological parameter estimation<ref:2604.

1. Improve photometric calibration control by implementing a rigorous uncertainty propagation framework that explicitly models uncertainties during both model training and light-curve fitting, as demonstrated by how "Brout et al. (2022b) showed that propagating these uncertainties both at the SALT model training and at light-curve fitting simultaneously produces roughly twice the change in the recovered cosmology compared to modifying either component on its own."

2. Develop a robust systematic uncertainty budget for future surveys that accounts for the effect during light-curve fitting [varies] smoothly with redshift and is nearly degenerate with cosmology, preventing mitigation through self-calibration, suggesting that systematic mitigation strategies must be tailored to the specific survey and redshift regimes.

3. Implement a convergence criterion for calibration uncertainty modeling, utilizing the finding that the FoM is effectively converged by ∼60 realizations to optimize computational resources while maintaining high accuracy in cosmological parameter estimation.

4. Enhance SN Ia classification reliability by incorporating Bayesian Estimation Applied to Multiple Species (BEAMS) formalism, as it addresses this by modeling mixed samples and incorporating photometric classification probabilities, ensuring that non-Ia contaminants do not bias distance measurements.

5. Develop a strategy for maximizing scientific return from Stage IV surveys by achieving calibration control at the sub-percent level, as the paper concludes that statistical gains will only translate into improved cosmological constraints if calibration is controlled at this level, noting that current systematic errors cause a ∼50% decrease in the FoM relative to a statistical-only case.

In the coming years, the Vera Rubin Observatory's Legacy Survey of Space and Time (Rubin-LSST) and the Nancy Grace Roman Space Telescope's (Roman) High Latitude Time Domain Survey (HLTDS) are expected to discover more than a million Type Ia supernovae (SNe Ia), several orders of magnitude more than current samples and with a tighter control on systematic uncertainties. One of the largest systematic uncertainties in cosmological analyses with SNe Ia is the accuracy of the spectro-photometric model for SNe Ia time series data, which depends on the photometric calibration of the surveys. To quantify the impact of this uncertainty, we analyze simulated Rubin-LSST and HLTDS data, perturb the photometric zero-points and filter mean wavelengths, and propagate these systematics to spectral model recovery, estimated distances, and dark energy figure of merit (FoM) based on the w 0 w a CDM model. Zero-point shifts of 5 mmag and filter mean wavelength shifts of 5 angstrom lead to a about 50% decrease in the FoM relative to a statistical-only case when calibration uncertainties are propagated only through light-curve fitting. The same calibration shifts applied only during model training produce a smaller about 13% degradation. Contrary to previous analyses, calibration uncertainties in light-curve fitting dominate over those from model training. Their effect during light-curve fitting varies smoothly with redshift and is nearly degenerate with cosmology, preventing mitigation through self-calibration. Finally, we show that the FoM dependence on the size of the calibration uncertainties (in the range of expected sizes) is roughly linear.