Spectral Cosmology
Type Ia Supernovae · PCA · Standardisation
Spectral Cosmology
Principal Component Analysis of Type Ia Supernova Spectra: Improving Standardisation and Twinning
A unified framework for compressing supernova spectra into a low-dimensional representation and using that information for both global and local standardisation.
Can spectral information improve the way Type Ia supernovae are standardised?
Type Ia supernovae are powerful cosmological distance probes, but they are not intrinsically identical. Conventional standardisation methods such as SALT2 correct their observed luminosities using light-curve parameters, yet residual scatter remains.
Spectra provide a richer description of each event. Their continuum and absorption features encode information related to composition, temperature, ejecta velocity and the physical diversity of the explosion.
This project asks whether principal component analysis can compress that high-dimensional information into a practical representation and then use it to improve both population-wide and pairwise standardisation.
One spectral coordinate system, two complementary standardisation strategies.
After preprocessing, each spectrum is projected into PCA space. The resulting coefficients provide a compact description of spectral diversity that can be used either as additional standardisation terms or as coordinates for spectral matching.
Supernova spectra
Near-peak spectra are shifted to the rest frame, interpolated onto a common wavelength grid and normalised.
PCA coefficients
High-dimensional spectra become a compact set of ordered coefficients describing the dominant modes of variation.
SALT2 + PCA
Principal-component coefficients are added to the standard SALT2 relation as extra correction terms, allowing spectral diversity to influence the inferred distance modulus across the wider sample.
Spectral twins
Euclidean distance between PCA coefficients is used to find spectroscopically similar supernovae for local pairwise comparison and efficient twin candidate screening.
The reduced spectral space preserves useful structure for both reconstruction and standardisation.
Almost 90% of the dataset's spectral variation is retained using roughly ten components.
The PCA-extended standardisation reduced average Hubble scatter while retaining a large sample.
PCA distance closely follows the corresponding full-spectrum similarity measure.
The closest matched spectral twins reached very low pairwise residual scatter.
Most spectral structure lives in relatively few dimensions.
The first principal components capture the broad continuum and dominant spectral variation, while later components add increasingly fine structure. Reconstructions show that a small number of coefficients can preserve much of the information required for comparison.
The same representation supports both scalable and local correction.
The SALT2 extension provides a modest sample-wide correction, while spectral twinning targets much rarer but exceptionally similar pairs. The central result is therefore the shared PCA framework rather than either method in isolation.
Lancaster University Physics Department
27 April 2026
The dissertation is the primary record of the research.
It develops the full project from cosmological motivation and spectral preprocessing through PCA decomposition, reconstruction, SALT2 extension, spectral distance, twin candidate screening, robustness testing and future methodological development.
The individual catalogue studies isolate particular parts of that work for easier exploration. This summary page keeps the dissertation itself at the centre.
From an MPhys framework to a broader spectral standardisation programme.
The current analysis shows that PCA provides a useful common representation, but it also exposes the assumptions that now need to be tested more rigorously.
The next stage is therefore not simply to repeat the same analysis on more data. It is to make the representation more physical, extend it across redshift and phase, and determine whether global and local standardisation can be combined within one mature methodology.
Spectral time series
Move beyond a single near-peak spectrum and represent how each supernova evolves spectroscopically through time.
High-redshift twinning
Project higher-redshift spectra into a low-redshift PCA basis and test whether reliable low-to-high-redshift spectral matching can be retained under increasing observational noise.
Non-linear representations
Test kernel PCA, autoencoders and related methods to determine whether useful structure is being missed by a linear, variance-driven representation.
Spectral sub-populations
Use clustering or nested PCA to identify more homogeneous supernova populations, then evaluate whether local standardisation within those groups can reduce scatter further.
Physically weighted distance
Replace equal weighting in PCA distance with a metric informed by how strongly individual spectral modes relate to intrinsic luminosity.
Unified standardisation
Combine the scalable global PCA–SALT2 correction with local spectral twinning so both approaches operate within one common low-dimensional framework.
A common spectral representation that can move between population-wide correction and physically motivated local comparison.
That is the longer-term research question established by the dissertation: whether reduced spectral information can become a practical bridge between supernova diversity and higher-precision cosmological distance measurements.
Individual studies develop the components of the wider research framework.
PCA Reconstruction
Testing how accurately a reduced PCA representation reproduces the structure and spectral features of Type Ia supernovae.
Optimal Components
Examining how reconstruction quality changes as further principal components are added.
Sigma Clipping
Investigating how outlying spectra influence the PCA basis and the representation of the wider sample.
PCA Distance
Using distance in PCA coefficient space as a compact measure of spectral similarity.
Spectral Twins
Identifying unusually similar supernova pairs and evaluating their potential for local standardisation.
SALT2 Extension
Adding PCA-derived spectral information to conventional light-curve standardisation.
Hubble Analysis
Evaluating the cosmological impact of improved supernova standardisation through Hubble residuals.
Project information
- Researcher
- Reis Tyson
- Degree
- MPhys Physics, Astrophysics & Cosmology
- Institution
- Lancaster University
- Supervisor
- Dr Mathew Smith
- Submitted
- 27 April 2026
- Dataset
- ZTF Type Ia Supernova DR2
- Methods
- PCA · SALT2 extension · spectral distance · twinning
Research scope
The work is an exploratory standardisation framework rather than a final cosmological prescription. Its results depend on preprocessing choices, component selection and the assumptions of a linear PCA representation.
Spectral twinning also assumes that sufficiently similar spectra correspond to sufficiently similar intrinsic luminosities. The report tests the method empirically, while identifying stronger physical validation as an important next step.
The central contribution is the shared representation: spectra are reduced into a coordinate system that can support reconstruction, similarity measurement, candidate screening and standardisation within the same methodology.