Upper bound of ejecta mass in a nova outburst

We present the maximum ejecta mass $(M_{\rm ej})_{\rm max}$ and the maximum ratio of ejecta mass and accreted mass $(M_{\rm ej}/M_{\rm acc})_{\rm max}$ of a nova for various white dwarf (WD) masses ($M_{\rm WD}=0.6$ - 1.38 $M_\odot$) and mass accretion rates ($\dot{M}_{\rm acc}=1\times 10^{-11}$ - $3\times 10^{-7} ~M_\odot$ yr$^{-1}$) based on the energy balance with nuclear burning. These maximum values serve as an upper bound of mass ejection for individual novae. Recently, B. E. Schaefer concluded that the WD masses in the recurrent novae U Sco and T CrB decreased at nova explosions, because the ejected mass is much larger than the accreted mass, i.e., $M_{\rm ej}/M_{\rm acc}= 26$ and $540$, respectively. These values are derived from the orbital period change at the nova explosions. Recurrent novae have been considered to be a progenitor system of Type Ia supernovae (SNe Ia) because their WD masses are now close to, and will possibly grow up to, 1.38 $M_\odot$ at which WDs explode as SNe Ia. From the different view point of energy generation at the thermonuclear runaway, we have obtained the much smaller value of the maximum ratio of $M_{\rm ej}/M_{\rm acc}\lesssim 2.6$ for a $1.37 ~M_\odot$ WD. This conclusion simply means that the nuclear (hydrogen) burning cannot release energy enough to expel such a large ejecta mass as B. E. Schaefer's claims. We also conclude that $(M_{\rm ej}/M_{\rm acc})_{\rm max}$ hardly increases even if we include the effect of frictional mass ejection process in the common envelope phase of a nova.