HOLISMOKES

VII. Time-delay measurement of strongly lensed Type Ia supernovae using machine learning^⋆

¹ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild Str. 1, 85741 Garching, Germany
e-mail: shuber@MPA-Garching.MPG.DE
² Technische Universität München, Physik-Department, James-Franck-Straße 1, 85748 Garching, Germany
³ Institute of Astronomy and Astrophysics, Academia Sinica, 11F of ASMAB, No. 1, Section 4, Roosevelt Road, Taipei 10617, Taiwan
⁴ Informatik-Department, Technische Universität München, Boltzmannstr. 3, 85748 Garching, Germany
⁵ Institute of Physics, Laboratory of Astrophysics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland
⁶ Heidelberger Institut für Theoretische Studien, Schloss-Wolfsbrunnenweg 35, 69118 Heidelberg, Germany
⁷ Munich Re, IT1.6.1.1, Königinstraße 107, 80802 München, Germany
⁸ Astrophysics Research Centre, School of Mathematics and Physics, Queen’s University Belfast, Belfast BT7 1NN, UK

Received: 5 August 2021
Accepted: 29 November 2021

Abstract

The Hubble constant (H₀) is one of the fundamental parameters in cosmology, but there is a heated debate around the > 4σ tension between the local Cepheid distance ladder and the early Universe measurements. Strongly lensed Type Ia supernovae (LSNe Ia) are an independent and direct way to measure H₀, where a time-delay measurement between the multiple supernova (SN) images is required. In this work, we present two machine learning approaches for measuring time delays in LSNe Ia, namely, a fully connected neural network (FCNN) and a random forest (RF). For the training of the FCNN and the RF, we simulate mock LSNe Ia from theoretical SN Ia models that include observational noise and microlensing. We test the generalizability of the machine learning models by using a final test set based on empirical LSN Ia light curves not used in the training process, and we find that only the RF provides a low enough bias to achieve precision cosmology; as such, RF is therefore preferred over our FCNN approach for applications to real systems. For the RF with single-band photometry in the i band, we obtain an accuracy better than 1% in all investigated cases for time delays longer than 15 days, assuming follow-up observations with a 5σ point-source depth of 24.7, a two day cadence with a few random gaps, and a detection of the LSNe Ia 8 to 10 days before peak in the observer frame. In terms of precision, we can achieve an approximately 1.5-day uncertainty for a typical source redshift of ∼0.8 on the i band under the same assumptions. To improve the measurement, we find that using three bands, where we train a RF for each band separately and combine them afterward, helps to reduce the uncertainty to ∼1.0 day. The dominant source of uncertainty is the observational noise, and therefore the depth is an especially important factor when follow-up observations are triggered. We have publicly released the microlensed spectra and light curves used in this work.