Light Curve Models for the Supernova in the Optical Counterpart of X-Ray Flash 030723

XRF 030723 is the first X-ray flash (XRF) to show in its optical light curve (LC) a bump that has been interpreted as the signature of a supernova (SN). After subtracting the afterglow component from the observed optical LC of the XRF counterpart, the properties of the SN are constrained by means of synthetic LCs of core-collapse SNe. For the range of redshift suggested for XRF 030723 ($z \sim 0.3$ -- 1), all possible models require a rather small mass of synthesized \Nifs, i.e. $M$(\Nifs) $\sim$ 0.01 -- 0.3 $\Msun$. The models used to describe the hypernovae (HNe) associated with gamma-ray bursts (SNe 1998bw and 2003dh) are too massive for the observed LC. If the relation between ejected \Nifs mass and total ejecta mass established from models of various Type Ic SNe/HNe also holds for the SN in XRF 030723, the ejecta mass is constrained to be $\sim$ 1 -- 3 $\Msun$ and the kinetic energy $\lsim 1\times 10^{52}$ erg. This corresponds to a progenitor with $15\Msun \lesssim M_{\rm MS}\lesssim 25\Msun$. The SN therefore appears to have properties intermediate between a normal SN Ic like SN 1994I and an object at the low-energy and low-mass end of the HN sequence, like SN 2002ap.