We have discovered seven cluster supernovae (SNe) of Type Ia in the course of the Wise Observatory Optical Transients Search in the fields of 0.06 -14 mag for SN 1998fc and MR > -11.8 mag for SN 2001al. The fractions of the cluster luminosities in dwarf galaxies fainter than our limits are less than 3 × 10-3 and less than 3 × 10-4, respectively. Thus, 2/7 of the SNe would be associated with ≤3 × 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 with normal SNe, we estimate that 20 (20) percent at the 68% (95%) confidence level 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.
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