Paper Title: Variational inference for acceleration of SN Ia photometric distance estimation with BayeSN
Authors: Ana Sofía M. Uzsoy, Stephen Thorp, Matthew Grayling, and Kaisey S. Mandel
First Author Institute: Center for Astrophysics | Smithsonian & Harvard
Status: Published in Monthly Notices of Royal Astronomical Society, open access
Supernova Cosmology
Of the many types of astrophysical transients, Type Ia supernovae are the ones that are most immediately applicable to cosmology, the study of the universe on the largest scale. This is because their light curves can be used as standard candles. The peak brightness of a type 1a supernova’s light curve is directly related to how quickly the light curve evolves. Brighter light curves evolve slower than dimmer light curves, which must be corrected for in observations. After applying this correction, all type 1a supernovae have the same “corrected” light curve, which always peaks at the same brightness (see figure 1). Because corrected light curve of any Type Ia supernova always has the same intrinsic luminosity (how much light it actually emits), the observed luminosity (how much light reaches us) can be used to infer the distance to the supernova, making it a standard candle!
Therefore, we can do a lot of cosmology using Type Ia supernovae! However, this means it is super important to get the original light curve of the supernova as it was emitted by the progenitor system. As light from distant objects travels through the universe, the light becomes dimmer and redder as obscuring material in the way absorbs, re-emits, and reddens the originally emitted light. As such, to measure the peak brightness of any supernova, it is extremely crucial to account for reddening along the line of sight to the supernova. This is measured using a parameter called AV, which can be used to calculate the number of magnitudes that have been extinguished by reddening in any filter when multiplied by a number specific to that filter.
BayeSN and Fitting Algorithms
BayeSN is a software package that models the light curve of Type Ia supernovae, accounts for reddening, and implements the brightness-duration correction mentioned earlier to measure the cosmological distance to a given Type Ia supernova. This model has 5 free parameters, including the distance modulus μ (the distance to the supernova) and AV, the reddening. The goal of BayeSN is to find a distribution of possible values for the distance modulus μ (the distance to the supernova) and AV (the reddening along the line of sight to the supernova) that could feasibly describe the light curve of a given Type 1a supernova.
BayeSN traditionally does this fitting using Markov Chain Monte Carlo (MCMC), a very widely used and versatile fitting algorithm. However, MCMC is slow compared to other fitting algorithms, meaning BayeSN would not be fast enough to keep up with the expected deluge of Type Ia supernovae discoveries when the Rubin Observatory comes online. Realizing something faster was needed in short order, the authors of today’s paper built an implementation of the Variational Inference (VI) fitting algorithm into BayeSN, which should work quickly enough to keep up with future discoveries made by the Rubin Observatory. VI works by attempting to find an analytical function that describes the distribution of possible μ and AV values. VI initially takes a function as a guess for the distribution of each parameter of the fit (this is called the prior distribution) and attempts to find a final function that describes the true distribution of the parameter (this is called the posterior distribution).
Rebuilding the Prior
Traditionally, most implementations of VI take a Gaussian distribution as the initial guess for each parameter. However, because the amount of reddening can only be a positive value or zero, a Gaussian prior, which includes both negative and positive numbers, would not be correct for AV. Thus the authors implement VI in BayeSN with a “truncated Gaussian”, which is a Gaussian distribution that truncates at AV = 0. The authors of this work refer to this as a multivariate zero lower truncated normal (MVZLTN, which the first author pronounces “M.V. Zoltan”!) distribution. With this newly implemented prior, it became possible to allow for AV = 0, while disallowing negative values. In figure 2, the authors show the posterior distributions for three of the fit parameters for the light curve of a real Type Ia supernova—SN 2017cjv. This supernova is known to have a small AV, and the MVZLTN prior recovers this better than the other fitting algorithms tested, and faster than MCMC.
Conclusion
In all, the authors of this paper did a lot of work to make sure BayeSN will work accurately and quickly enough to keep up with the Rubin Observatory. Today’s paper is another example of using machine learning to speed up statistical inference in preparation for Rubin. The authors took great efforts to ensure the statistical background and assumptions baked into an inference package better accurately represent the astrophysics studied. It will be super exciting to process Type Ia light curves in real time as they are detected by Rubin in the very near future! With Rubin and tools like BayeSN, we will be able to map out much much more of the universe!
Astrobite edited by Diana Solano-Oropeza
Featured image credit: Type Ia Explosion from NASA/CXC/U. Texas, Rubin Obs./NSF/AURA, Edited by Author of Bite
