Type Ia supernovae (SNe Ia) have been used as cosmological distance indicators for more than two decades, providing early evidence of the accelerating expansion of the Universe. Today, SN Ia distances are used at low red shift (z ≤ 0.15) for distance ladder measurements of the Hubble constant (H0), currently the subject of a 4 − 6σ tension, as well as measurements of the dark energy equation-of-state parameter, w which incorporate SNe at z ≤ 2.2 (currently consistent with w = −1). Recent measurements of H0, as well as most large studies of SNe across the observed redshift range for the last decade, have relied upon the SALT2 light-curve model for the brightness standardization of SNe Ia in their analysis.
SN Ia distances are typically estimated by fitting their light curves with a model to determine an overall flux, a color, and one (or more) light-curve shape parameters. The apparent magnitude (as computed from the flux) is standardized with a linear combination of color and light-curve parameters (referred to as the Tripp estimator) to produce a standardized apparent magnitude relative to a fiducial SN Ia. The SALT2 (Spectral Adaptive Light-curve Template) model describes SN Ia light curves as a combination of component spectral energy distributions (flux surfaces defined in wavelength and time), multiplied by a color-dependent term described by a color law that is similar to that of the Milky Way.
Now, Kenworthy and colleagues presented an improved model framework, SALTshaker (also called SALT3), which has several advantages over current models including the leading SALT2 model (SALT2.4). While SALT3 has a similar philosophy, it differs from SALT2 by having improved estimation of uncertainties, better separation of color and light-curve stretch, and a publicly available training code.
The SALT3.K21 model itself includes updated calibration with Supercal, a training sample with 1083 SNe − 2.5 times larger than the SALT2 training sample and has greatly reduced calibration uncertainties.
The resulting trained SALT3.K21 model has an extended wavelength range 2000-11000 Å (1800 Å redder) and reduced uncertainties compared to SALT2, enabling accurate use of low-z I and iz photometric bands. Including these previously discarded bands, SALT3.K21 reduces the Hubble scatter of the low-z Foundation and CfA3 samples by 15% and 10%, respectively.
To check for potential systematic uncertainties authors compared distances of low (0.01 < z < 0.2) and high (0.4 < z < 0.6) redshift SNe in the training compilation, finding an insignificant 2±14 mmag shift between SALT2.4 and SALT3.K21. While the SALT3.K21 model was trained on optical data, their method can be used to build a model for rest-frame NIR samples from the Roman Space Telescope.
Several light-curve models have been developed for cosmological supernovae, including MLCS, MLCS2k2, SiFTO, SNooPy, SNEMO, SUGAR, and BayesSN. In this context, SALT3 offers an approach to model design and training process that prioritizes the use of heterogeneous spectral and photometric data to provide extensive phase and wavelength coverage and native k-corrections through cosmology independent training.
“Over the coming years, we expect SALTshaker will continue to be developed and improved as additional SN data becomes available and additional SN standardization parameters (e.g., host mass) are discovered and explored. Further development work could focus on the error model, which is currently based on central filter wavelengths rather than integrated quantities. This is a potential source of systematic uncertainty because observer-frame filter functions are contracted in the rest frame. Additionally, SALTshaker enables a more rigorous evaluation of systematic uncertainties such as those arising from limited training data, photometric calibration uncertainties, or treatment of SN spectra. These can be evaluated in a straightforward and rigorous way by re-training the SALT3 model surfaces on simulated data. Although we have demonstrated that SALTshaker can faithfully recover a truth model at the ∼1% level, future work will also be able to fully validate the model training process using an entire analysis chain that includes training, bias corrections, and cosmology fitting.”— told Kenworthy, first author of the study
Their open-source training code, public training data, model, and documentation are available at https://saltshaker.readthedocs.io/en/latest/, and the model is integrated into the sncosmo and SNANA software packages.
Featured image: Scatterplot of the x1 and c light-curve parameters measured with SALT2.JLA and SALT3.K21. They observed a linear transformation of the parameters, as expected from changes in the demographics of the training sample and their procedure for separating stretch and color. Best fit c-x1 lines and correlation coefficients r are shown to illustrate the rotation of the distribution as SALT3 forces the independence of x1 and c. © Kenworthy et al.
Reference: W. D. Kenworthy, D. O. Jones, M. Dai, R. Kessler, D. Scolnic, D. Brout, M. R. Siebert, J. D. R. Pierel, K. G. Dettman, G. Dimitriadis, R. J. Foley, S. W. Jha, Y.-C. Pan, A. Riess, S. Rodney, C. Rojas-Bravo, “SALT3: An Improved Type Ia Supernova Model for Measuring Cosmic Distances”, ArXiv, pp. 1-25, 2021. https://arxiv.org/abs/2104.07795
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