Modern Rate-of-Decline Relations for Novae

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: $t_2 \simeq 0.5~t_3$.

Figures (1)

• Figure 1: Top panel: The linear least-squares fit of $\log t_3$ as a function of $\log t_2$ for 244 novae included in the Schaefer2025 nova sample. The best fitting linear relation is shown by the solid red line. Bottom Panel: The least-squares fit of $\log t_2$ as a function of $\log t_3$ for the same sample of novae. Again, the best fitting linear relation is shown by the red line. In both panels, the dotted red lines show the $\pm1\sigma$ error bands to the fit, while the position of the unusual system, V2362 Cyg, is shown in blue.