  We have discovered seven type Ia cluster supernovae (SNe) in the course of
the Wise Observatory Optical Transients Search in the fields of galaxy clusters
with redshifts between z=0.06 and z=0.2. Two of these events, SN 1998fc in
Abell 403 (z=0.10) and SN 2001al in Abell 2122/4 (z = 0.066), have no obvious
hosts. Both events appear projected on the halos of the central cD galaxies,
but have velocity offsets of 750-2000 km/s relative to those galaxies,
suggesting they are not bound to them. We use deep Keck imaging of the
locations of the two SNe to put upper limits on the luminosities of possible
dwarf hosts, M_R > -14 mag for SN 1998fc and M_R > -11.8 mag for SN 2001al. The
fractions of the cluster luminosities in dwarf galaxies fainter than our limits
are less than 3 x 10^-3 and 3 x 10^-4, respectively. Thus, 2/7 of the SNe would
be associated with less than 3 x 10^-3 of the luminosity attributed to
galaxies. We argue, instead, that the progenitors of both events were probably
members of a diffuse population of intergalactic stars, recently detected in
local clusters via planetary nebulae and red giants. Considering the higher
detectability of hostless SNe compared to normal SNe, we estimate that
20^{+12}_{-15} percent of the SN Ia parent stellar population in clusters is
intergalactic. This fraction is consistent with other measurements of the
intergalactic stellar population, and implies that the process that produces
intergalactic stars (e.g., tidal disruption of cluster dwarfs) does not disrupt
or enhance significantly the SN Ia formation mechanism. Hostless SNe are
potentially powerful tracers of the formation of the intergalactic stellar
population out to high redshift.
