Abstract
To use strongly lensed Type Ia supernovae (LSNe Ia) for cosmology, a time-delay measurement between the multiple supernova (SN) images is necessary. The sharp rise and decline of SN Ia light curves make them promising for measuring time delays, but microlensing can distort these light curves and therefore add large uncertainties to the measurements. An alternative approach is to use color curves where uncertainties due to microlensing are significantly reduced for a certain period of time known as the achromatic phase. In this work, we investigate in detail the achromatic phase, testing four different SN Ia models with various microlensing configurations. We find on average an achromatic phase of around three rest-frame weeks or longer for most color curves, but the spread in the duration of the achromatic phase (due to different microlensing maps and filter combinations) is quite large and an achromatic phase of just a few days is also possible. Furthermore, the achromatic phase is longer for smoother microlensing maps and lower macro-magnifications. From our investigations, we do not find a strong dependency on the SN model or on asymmetries in the SN ejecta. We find that six rest-frame LSST color curves exhibit features such as extreme points or turning points within the achromatic phase, which make them promising for time-delay measurements; however, only three of the color curves are independent. These curves contain combinations of rest-frame bands u, g, r, and i, and to observe them for typical LSN Ia redshifts, it would be ideal to cover (observer-frame) filters r, i, z, y, J, and H. If follow-up resources are restricted, we recommend r, i, and z as the bare minimum for using color curves and/or light curves since LSNe Ia are bright in these filters and observational uncertainties are lower than in the infrared regime. With additional resources, infrared observations in y, J, and H would be useful for obtaining color curves of SNe, especially at redshifts above ∼0.8 when they become critical.
Highlights
On the one hand, there is a tension in the Hubble constant H0 of at least 4σ (Verde et al 2019) between the early Universe measurements (Planck Collaboration I 2020) and late Universe measurements from the Cepheids distance ladder (e.g., Riess et al 2016, 2018, 2019)
We find that six rest-frame Legacy Survey of Space and Time (LSST) color curves exhibit features such as extreme points or turning points within the achromatic phase, which make them promising for time-delay measurements; only three of the color curves are independent
This was first investigated by Goldstein et al (2018), who show that microlensed color curves of LSNe Ia are “achromatic”, in other words, their color curves are independent of microlensing for up to three rest-frame weeks after explosion, and time-delay uncertainties are reduced from approximately 4% to 1% if color curves are used instead of light curves
Summary
There is a tension in the Hubble constant H0 of at least 4σ (Verde et al 2019) between the early Universe measurements (Planck Collaboration I 2020) and late Universe measurements from the Cepheids distance ladder (e.g., Riess et al 2016, 2018, 2019). While the influence of microlensing on spectra and light curves is strong in certain configurations, color curves have the following advantage: If microlensing affects light curves from different filters in a similar way, it cancels out in the color curves This was first investigated by Goldstein et al (2018), who show that microlensed color curves of LSNe Ia are “achromatic”, in other words, their color curves are independent of microlensing for up to three rest-frame weeks after explosion, and time-delay uncertainties are reduced from approximately 4% to 1% if color curves are used instead of light curves.
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