Modern Rate-of-Decline Relations for Novae

TL;DR

This paper analyzes the relationship between nova decline times $t_2$ and $t_3$, deriving empirical relations that suggest $t_2$ is approximately half of $t_3$, refining understanding of nova light curve behavior.

Contribution

The study provides new empirical relations between $t_2$ and $t_3$ times for novae, accounting for regression asymmetry, and simplifies the relation to a proportionality.

Findings

Derived best-fit relations between $ ext{log } t_2$ and $ ext{log } t_3$

Established that $t_2$ is approximately 0.5 times $t_3$ within uncertainties

Performed regression analysis considering asymmetry in data fitting

Abstract

A large sample of $t_2$ and $t_3$ times from the recent compilation of nova properties given in Schaefer (2025) have been analyzed to determine relationships between these two parameters. Fits were performed in both directions (from $\log t_2$ to $\log t_3$ and vice-versa) to account for the asymmetry inherent in ordinary least-squares regression, which minimizes residuals only in the dependent variable. The following best-fit relations were found: $\log t_3 = (0.877\pm0.019) \log t_2 + (0.444\pm0.027)$, and $\log t_2 = (1.018\pm0.023) \log t_3 - (0.316\pm0.037)$, corresponding to $t_3 = (2.78\pm0.17)~t_2^{(0.877\pm0.019)}$ and $t_2 = (0.483\pm0.041)~t_3^{(1.018\pm0.023)}$, respectively. Within the uncertainties, the latter relation reduces to a simple proportionality: $t_2 \simeq 0.5~t_3$.