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

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 $(\dot M_{\rm acc},M_{\rm WD})$.