We present deep Hubble Space Telescope imaging at the locations of four , potentially hostless , long-faded Type Ia supernovae ( SNe Ia ) in low-redshift , rich galaxy clusters that were identified in the Multi-Epoch Nearby Cluster Survey .
Assuming a steep faint-end slope for the galaxy cluster luminosity function ( \alpha _ { d } = -1.5 ) , our data includes all but \lesssim 0.2 \% percent of the stellar mass in cluster galaxies ( \lesssim 0.005 \% with \alpha _ { d } = -1.0 ) , a factor of 10 better than our ground-based imaging .
Two of the four SNe Ia still have no possible host galaxy associated with them ( M _ { R } > -9.2 ) , confirming that their progenitors belong to the intracluster stellar population .
The third SNe Ia appears near a faint disk galaxy ( M _ { V } = -12.2 ) which has a relatively high probability of being a chance alignment .
A faint , red , point source coincident with the fourth SN Ia ’ s explosion position ( M _ { V } = -8.4 ) may be either a globular cluster ( GC ) or faint dwarf galaxy .
We estimate the local surface densities of GCs and dwarfs to show that a GC is more likely , due to the proximity of an elliptical galaxy , but neither can be ruled out .
This faint host implies that the SN Ia rate in dwarfs or GCs may be enhanced , but remains within previous observational constraints .
We demonstrate that our results do not preclude the use of SNe Ia as bright tracers of intracluster light at higher redshifts , but that it will be necessary to first refine the constraints on their rate in dwarfs and GCs with deep imaging for a larger sample of low-redshift , apparently hostless SNe Ia .