SALT3-UV: Advancing SN Ia UV Standardization

• SALT3-UV is a robust, empirically trained optical–UV spectral energy distribution model for Type Ia supernovae that achieves precise calibration with reduced uncertainties.
• It employs a principal-component expansion with smooth cubic spline interpolation and an enhanced color law, significantly lowering uncertainty factors in the critical UV range.
• The model’s improved UV performance and assessment of redshift evolution mitigate systematic biases in estimating dark-energy parameters for future cosmological surveys.

The SALT3-UV model is a robust, empirically trained, optical–ultraviolet (UV) spectral energy distribution (SED) model for Type Ia supernovae (SNe Ia), explicitly constructed to enable precise and accurate photometric and spectroscopic standardization for upcoming cosmological surveys that probe the rest-frame UV. SALT3-UV was developed as an extension and refinement to the SALT3 model, addressing the challenge of high model uncertainties and calibration limitations in the UV seen in earlier releases, most notably the SALT3-K21 model (Wang et al., 31 Dec 2025, Kenworthy et al., 2021).

1. Formal Framework of the SALT3-UV SED Model

SALT3-UV models the rest-frame flux $F(p,\lambda)$ of an SN Ia at phase $p$ (days from $B$-band maximum) and rest-frame wavelength $\lambda$ as a principal-component expansion supplemented by a wavelength-dependent color law,

$$F(p,\lambda)=x_0\left[M_0(p,\lambda)+x_1 M_1(p,\lambda)\right] \exp[c\, CL(\lambda)],$$

where:

• $M_0(p,\lambda)$: mean spectral surface,
• $M_1(p,\lambda)$: first-order principal component representing light-curve “stretch” or shape,
• $x_0$: global flux amplitude (distance indicator),
• $x_1$: stretch parameter,
• $c$: color parameter (intrinsic plus host-dust),
• $p$0: color law, normalized as $p$1, $p$2.

The $p$3 and $p$4 surfaces are implemented as cubic splines in phase and wavelength with knots $p$5, $p$6, and color-law coefficients $p$7, respectively. To avoid degeneracies, $p$8 is defined with zero mean and unit variance in the training sample, and $p$9 at $B$0. The color law is required to be smooth (piecewise cubic polynomial from $B$1–$B$2 Å with linear tails). Regularization (gradient and dyadic) is applied in poorly constrained regions via the SALTshaker training likelihood (Wang et al., 31 Dec 2025, Kenworthy et al., 2021).

2. Training Procedure and UV Data Integration

SALT3-UV was trained using SALTshaker with two major modifications to accommodate the expanded UV regime:

• Extension of the wavelength domain to $B$3 Å (with model application valid for filters from $B$4 to $B$5 Å),
• Suppression of the standard “spectral mangle” correction for HST/STIS data, leveraging their inherent $B$6 absolute and $B$7 relative flux calibration.

The training sample unifies:

• The 1083 SNe Ia and 1207 spectra of the K21 core “Supercal/Fragilistic” sample,
• New high-quality HST/STIS ($B$8) spectra: 67 spectra from 18 SNe Ia, spanning $B$9–$\lambda$0 Å,
• Auxiliary photometric data from ZTF ($\lambda$1, $\lambda$2–$\lambda$3 uncertainties), ATLAS (“orange” and “cyan” bands, $\lambda$4 mmag nominal), Swift UBV (restricted to $\lambda$5), and established SN surveys (Pan-STARRS1, DES, SNLS, Foundation, CSP, CfA).

The HST/STIS spectra obviate the need for spectral warping for calibration—unlike previous K21 or earlier datasets. Table 1 summarizes the improvement in UV coverage:

Survey	# SNe	# UV Spectra
HST/STIS	18	67
K21 low-$\lambda$6	12	22
K21 high-$\lambda$7	36	42
Total UV	65	129

Before SALT3-UV, only 13 K21 spectra probed $\lambda$8 Å, necessitating heavy regularization and inflating uncertainties below $\lambda$9 Å (Wang et al., 31 Dec 2025).

3. Ultraviolet Performance: Comparison to SALT3-K21

Retraining with the new UV dataset and relaxed UV-regularization resulted in significant improvements for $$F(p,\lambda)=x_0\left[M_0(p,\lambda)+x_1 M_1(p,\lambda)\right] \exp[c\, CL(\lambda)],$$0 Å:

• In the $$F(p,\lambda)=x_0\left[M_0(p,\lambda)+x_1 M_1(p,\lambda)\right] \exp[c\, CL(\lambda)],$$1–$$F(p,\lambda)=x_0\left[M_0(p,\lambda)+x_1 M_1(p,\lambda)\right] \exp[c\, CL(\lambda)],$$2 Å regime, the $$F(p,\lambda)=x_0\left[M_0(p,\lambda)+x_1 M_1(p,\lambda)\right] \exp[c\, CL(\lambda)],$$3 uncertainties in $$F(p,\lambda)=x_0\left[M_0(p,\lambda)+x_1 M_1(p,\lambda)\right] \exp[c\, CL(\lambda)],$$4 decreased by factors $$F(p,\lambda)=x_0\left[M_0(p,\lambda)+x_1 M_1(p,\lambda)\right] \exp[c\, CL(\lambda)],$$5 versus SALT3-K21.
• The model color-scatter at $$F(p,\lambda)=x_0\left[M_0(p,\lambda)+x_1 M_1(p,\lambda)\right] \exp[c\, CL(\lambda)],$$6 Å is $$F(p,\lambda)=x_0\left[M_0(p,\lambda)+x_1 M_1(p,\lambda)\right] \exp[c\, CL(\lambda)],$$7 mag (previously $$F(p,\lambda)=x_0\left[M_0(p,\lambda)+x_1 M_1(p,\lambda)\right] \exp[c\, CL(\lambda)],$$8 mag in K21), a $$F(p,\lambda)=x_0\left[M_0(p,\lambda)+x_1 M_1(p,\lambda)\right] \exp[c\, CL(\lambda)],$$9–$M_0(p,\lambda)$0 improvement.
• The continuum in SALT3-UV falls smoothly to zero at $M_0(p,\lambda)$1 Å, correcting K21’s artificially flat behavior at these wavelengths.
• Essential iron-group line blends (Fe II, Co II, Mg II at $M_0(p,\lambda)$2 Å and $M_0(p,\lambda)$3 Å) are now reproduced with physically consistent amplitude and position.

Table 2 (summarized):

Wavelength	Unc.~$M_0(p,\lambda)$4 K21	Unc.~$M_0(p,\lambda)$5 UV	Improvement
$M_0(p,\lambda)$6 Å	$M_0(p,\lambda)$7	$M_0(p,\lambda)$8	$M_0(p,\lambda)$9
$M_1(p,\lambda)$0 Å	$M_1(p,\lambda)$1	$M_1(p,\lambda)$2	$M_1(p,\lambda)$3

RMS color-scatter at $M_1(p,\lambda)$4 Å improves from $M_1(p,\lambda)$5 mag (K21) to $M_1(p,\lambda)$6 mag (UV), and at $M_1(p,\lambda)$7 Å from $M_1(p,\lambda)$8 to $M_1(p,\lambda)$9 mag (Wang et al., 31 Dec 2025).

4. Probing Redshift Evolution in the UV Template

SALT3-UV models were retrained on redshift-stratified subsamples to probe possible SNe Ia UV evolution:

• Low-$x_0$0 model: $x_0$1 SNe (351 SNe, 87 UV spectra; dominated by HST/STIS coverage),
• High-$x_0$2 model: Excludes rest-frame $x_0$3 Å data for $x_0$4 SNe and observer-frame $x_0$5 (36 SNe, 42 UV spectra; mean $x_0$6).

Key findings:

• The high-$x_0$7 $x_0$8 surface exhibits a $x_0$9 brighter continuum below $x_1$0 Å; line-blend depths near $x_1$1 Å are $x_1$2 deeper.
• The color law difference, $x_1$3–$x_1$4 between $x_1$5–$x_1$6 Å, translates to $x_1$7 mag for characteristic color scatter.
• Synthetic average light curves show magnitude offsets of $x_1$8 mag in LSST $x_1$9 at $c$0 and LSST $c$1 at $c$2; $c$3 mag at $c$4 for Roman F062.

These effects are statistically significant ($c$5) at the highest redshifts and, if confirmed, indicate non-negligible redshift evolution in SN Ia rest-frame UV SEDs (Wang et al., 31 Dec 2025).

5. Cosmological Impact of UV SED Evolution

Cosmological simulations (using SNANA) quantified how ignoring UV SED evolution affects measurement of the dark-energy equation-of-state parameter $c$6. Two sets of cosmological fits were compared:

• riz-only (no rest-frame UV at high-$c$7): $c$8,
• griz (includes high-$c$9 $p$00 band = rest-frame UV): $p$01.

Thus, even under idealized assumptions, unaccounted UV evolution induces a $p$02 bias in $p$03, directly impacting precision cosmology goals of LSST, Roman, and similar future surveys. If rest-frame UV photometry is included without allowances for SED evolution, the inferred $p$04 may be systematically biased at the few-percent level (Wang et al., 31 Dec 2025).

6. Practical Application and Model Recommendations

For application, SALT3-UV is encoded as a publicly available model with templates and variance surfaces suitable for use in sncosmo and SNANA pipelines. Key guidelines include:

• Valid phase range: $p$05 (recommended: $p$06 to $p$07 d).
• Wavelength validity: $p$08; for UV filters, pivot wavelengths should reside within the trained range.
• K-corrections: No new k-corrections required; observer-frame filters are correctly integrated against the SED.
• Model covariances (both diagonal and color) must be included in cosmological fits to propagate the full model uncertainty budget.
• Caution is advised for data at $p$09 Å (sparse training) and Swift UVOT uvm2/uvw2 at $p$10 (could probe $p$11 Å), which should be flagged or downweighted.

Best practices include routine validation on SNe with well-calibrated UV spectroscopy, and careful monitoring for systematic color residuals (Kenworthy et al., 2021, Wang et al., 31 Dec 2025).

7. Outlook and Future Directions

SALT3-UV provides a significant advance in UV standardization of SNe Ia, substantiating a $p$12 decrease in model uncertainties, accurate reproduction of physical line features, and the framework for robust UV-based cosmology. However, preliminary evidence of SED evolution between low- and high-$p$13 SN subsamples, at a level ($p$14–$p$15 mag) commensurate with current systematic floors in cosmological experiments, indicates that continued UV spectroscopic campaigns (HST, JWST) and wide-field surveys (ULTRASAT) are critical for confirming, modeling, and correcting such effects. Addressing UV SED evolution is pivotal to ensuring that rest-frame UV data augment, rather than limit, next-generation cosmological measurements (Wang et al., 31 Dec 2025).