It has been proposed that a galaxys nova rate might be enhanced by the production of nova progenitor binaries in the dense cores of its globular clusters (GCs). To explore this idea, relative nova rates in three Virgo elliptical galaxies, M87, M49 and M84, which have significantly different GC specific frequencies ($S_{N}$) of 14, 3.6, and 1.6, respectively, were measured over the course of 4 epochs spanning a period of 14 months. To simplify the analysis, observations of the nearly equidistant galaxies were made on the same nights, with the same integration times, and through the same filter (H$alpha$), so that the relative numbers of novae discovered would reflect the relative nova rates. At the conclusion of our survey we found a total of 27 novae associated with M87, 37 with M49, and 19 with M84. After correcting for survey completeness, we found annual nova rates of $154^{+23}_{-19}$, $189^{+26}_{-22}$, and $95^{+15}_{-14}$, for M87, M49, and M84, respectively, corresponding to $K$-band luminosity-specific nova rates of $3.8pm1.0$, $3.4pm0.6$, and $3.0pm0.6$ novae per year per $10^{10}~L_{K,odot}$. The overall results of our study suggest that a galaxys nova rate simply scales with its luminosity, and is insensitive to its GC specific frequency. Two novae, one in M87 and one in M84, were found to be spatially coincident with known GCs. After correcting for the mass fraction in GCs, we estimate that novae are likely enhanced relative to the field by at least an order of magnitude in the GC systems of luminous Virgo ellipticals.
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