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 $(t_3,M_{V,\max })$ for various sets of $({\dot{M}}_{\mathrm{acc}},M_{\mathrm{WD}})$, where $M_{V,\max }$ is the peak absolute $V$ magnitude, $t_3$ is the 3-mag decay time from the peak, and ${\dot{M}}_{\mathrm{acc}}$ is the mass accretion rate on to the white dwarf (WD) of mass $M_{\mathrm{WD}}$. The model light curves are uniquely characterized by $x\equiv M_{\mathrm{env}}/M_{\mathrm{sc}}$, where $M_{\mathrm{env}}$ is the hydrogen-rich envelope mass and $M_{\mathrm{sc}}$ is the scaling mass at which the wind has a certain wind mass-loss rate. For a given ignition mass $M_{\mathrm{ig}}$, we can specify the first point $x_0=M_{\mathrm{ig}}/M_{\mathrm{sc}}$ on the model light curve, and calculate the corresponding peak brightness and $t_3$ time from this first point. Our $(t_3,M_{V,\max })$ points cover well the distribution of existing novae. The lower the mass accretion rate, the brighter the peak. The maximum brightness is limited to $M_{V,\max }\gtrsim -10.4$ by the lowest mass-accretion rate of ${\dot{M}}_{\mathrm{acc}}\gtrsim 1\times 10^{-11}{M}_{\odot }$ yr${}^{-1}$. A significant part of the observational MMRD trend corresponds to the ${\dot{M}}_{\mathrm{acc}}\sim 5\times 10^{-9}{M}_{\odot }$ 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 $(t_3,M_{V,\max })$ for many sets of $({\dot{M}}_{\mathrm{acc}},M_{\mathrm{WD}})$.

23 pages, 9 figures, to appear in ApJ

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