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Abstract:

We report observations of the optical counterpart of the long gamma-ray burst (LGRB) GRB 221009A. Due to the extreme rarity of being both nearby ($z = 0.151$) and highly energetic ($E_{\gamma,\mathrm{iso}} \geq 10^{54}$ erg), GRB 221009A offers a unique opportunity to probe the connection between massive star core collapse and relativistic jet formation across a very broad range of $\gamma$-ray properties. Adopting a phenomenological power-law model for the afterglow and host galaxy estimates from high-resolution Hubble Space Telescope imaging, we use Bayesian model comparison techniques to determine the likelihood of an associated SN contributing excess flux to the optical light curve. Though not conclusive, we find moderate evidence ($K_{\rm{Bayes}}=10^{1.2}$) for the presence of an additional component arising from an associated supernova, SN 2022xiw, and find that it must be substantially fainter ($<$ 67% as bright at the 99% confidence interval) than SN 1998bw. Given the large and uncertain line-of-sight extinction, we attempt to constrain the supernova parameters ($M_{\mathrm{Ni}}$, $M_{\mathrm{ej}}$, and $E_{\mathrm{KE}}$) under several different assumptions with respect to the host galaxy's extinction. We find properties that are broadly consistent with previous GRB-associated SNe: $M_{\rm{Ni}}=0.05$ - $0.25 \, \rm{M_\odot}$, $M_{\rm{ej}}=3.5$ - $11.1 \, \rm{M_\odot}$, and $E_{\rm{KE}} = (1.6$ - $5.2) \times 10^{52} \, \rm{erg}$. We note that these properties are weakly constrained due to the faintness of the supernova with respect to the afterglow and host emission, but we do find a robust upper limit on the $M_{\rm{Ni}}$ of $M_{\rm{Ni}}<0.36\, \rm{M_\odot}$. Given the tremendous range in isotropic gamma-ray energy release exhibited by GRBs (7 orders of magnitude), the SN emission appears to be decoupled from the central engine in these systems.Comment: 18 pages, accepted to ApJL, 4 tables, 5 figures. Updated abstract in Previe

Abstract:

Symbolic Regression (SR) algorithms attempt to learn analytic expressions which fit data accurately and in a highly interpretable manner. Conventional SR suffers from two fundamental issues which we address here. First, these methods search the space stochastically (typically using genetic programming) and hence do not necessarily find the best function. Second, the criteria used to select the equation optimally balancing accuracy with simplicity have been variable and subjective. To address these issues we introduce Exhaustive Symbolic Regression (ESR), which systematically and efficiently considers all possible equations&#x2014;made with a given basis set of operators and up to a specified maximum complexity&#x2014; and is therefore guaranteed to find the true optimum (if parameters are perfectly optimised) and a complete function ranking subject to these constraints. We implement the minimum description length principle as a rigorous method for combining these preferences into a single objective. To illustrate the power of ESR we apply it to a catalogue of cosmic chronometers and the Pantheon+ sample of supernovae to learn the Hubble rate as a function of redshift, finding 40 functions (out of 5.2 million trial functions) that fit the data more economically than the Friedmann equation. These low-redshift data therefore do not uniquely prefer the expansion history of the standard model of cosmology. We make our code and full equation sets publicly available.