A Theory for the Maximum Magnitude versus Rate of Decline (MMRD) Relation of Classical Novae

TL;DR

This paper develops a theoretical model for the MMRD relation in classical novae using optically thick wind theory and free-free emission light curves, explaining the observed trend and its scatter.

Contribution

It introduces a new theoretical framework linking nova peak brightness and decline rate to white dwarf mass and accretion rate, explaining the observed MMRD trend and its scatter.

Findings

The MMRD relation exists but has large scatter, limiting its use as a precise distance indicator.

Peak brightness correlates with lower accretion rates, with a maximum brightness limit around -10.4 mag.

The model reproduces the distribution of observed novae in the MMRD diagram.

Abstract

We propose a theory for the MMRD relation of novae, using free-free emission model light curves built on the optically thick wind theory. We calculated $(t_3,M_{V,\rm max})$ for various sets of $(\dot M_{\rm acc}, M_{\rm WD})$, where $M_{V,\rm max}$ is the peak absolute $V$ magnitude, $t_3$ is the 3-mag decay time from the peak, and $\dot M_{\rm acc}$ is the mass accretion rate on to the white dwarf (WD) of mass $M_{\rm WD}$. The model light curves are uniquely characterized by $x\equiv M_{\rm env}/M_{\rm sc}$, where $M_{\rm env}$ is the hydrogen-rich envelope mass and $M_{\rm sc}$ is the scaling mass at which the wind has a certain wind mass-loss rate. For a given ignition mass $M_{\rm ig}$, we can specify the first point $x_0= M_{\rm ig}/M_{\rm sc}$ on the model light curve, and calculate the corresponding peak brightness and $t_3$ time from this first point. Our $(t_3, M_{V,\rm max})$ points cover well the distribution of existing novae. The lower the mass accretion rate, the brighter the peak. The maximum brightness is limited to $M_{V,\rm max} \gtrsim -10.4$ by the lowest mass-accretion rate of $\dot M_{\rm acc} \gtrsim1 \times 10^{-11}~M_\odot$ yr$^{-1}$. A significant part of the observational MMRD trend corresponds to the $\dot M_{\rm acc}\sim5\times10^{-9}~M_\odot$ yr$^{-1}$ line with different WD masses. A scatter from the trend line indicates a variation in their mass-accretion rates. Thus, the global trend of an MMRD relation does exist, but its scatter is too large for it to be a precision distance indicator of individual novae. We tabulate $(t_3, M_{V,\rm max})$ for many sets of $(\dot M_{\rm acc},M_{\rm WD})$.