Revisiting the relation between the number of globular clusters and galaxy mass for low mass galaxies
Using a new method to estimate total galaxy mass (M$_{\rm T}$) and two samples of low luminosity galaxies containing measurements of the number of globular clusters (GCs) per galaxy (N$_{\rm GC}$), we revisit the N$_{\rm GC}-$M$_{\rm T}$ relation using a total of 203 galaxies, 157 of which have M$_{\rm T}$ $\ \le 10^{10}$ M$_\odot$. We find that the relation is nearly linear, N$_{\rm GC} \propto$ M$_{\rm T}^{0.92\pm0.08}$ down to at least M$_{\rm T} \sim 10^{8.75}$ M$_\odot$. Because the relationship extends to galaxies that average less than one GC per galaxy and to a mass range in which mergers are relatively rare, the relationship cannot be solely an emergent property of hierarchical galaxy formation. The character of the radial GC distribution in low mass galaxies, and the lack of mergers at these galaxy masses, also appears to challenge models in which the GCs form in central, dissipatively concentrated high-density, high-pressure regions and are then scattered to large radius. The slight difference between the fitted power-law exponent and a value of one, leaves room for a shallow M$_{\rm T}$-dependent variation in the mean mass per GC that would allow the relation between total mass in GCs and M$_{\rm T}$ to be linear.