We compare nuclear globular clusters ( nGCs ) in dwarf galaxies and Galactic GCs with extended ( hot ) horizontal branches ( EHBs-GCs ) in order to test the suggested external origin of the latter and the conditions at which GC self-enrichment can operate .
Using luminosities and structural parameters of nGCs in low-mass ( mainly late-type ) dwarf galaxies from HST/ACS imaging we derive the present-day escape velocities ( \upsilon _ { esc } ) of stellar ejecta to reach the cluster tidal radius and compare them with those of EHB-GCs .
We show that nGCs in dwarf galaxies are very similar in their photometric and structural properties ( colour \langle V - I \rangle = 0.9 , magnitudes \langle M _ { V } \rangle < -9 mag , ellipticities \langle \epsilon \rangle = 0.11 ) to EHB-GCs .
The nGCs populate the same M _ { V } vs . r _ { h } region as EHB-GCs , although they do not reach the sizes of the largest EHB-GCs like \omega Cen and NGC 2419 .
We argue that during accretion the r _ { h } of an nGC could increase due to significant mass loss in the cluster vicinity and the resulting drop in the external potential in the core once the dwarf galaxy dissolves .
For EHB-GCs , we find a correlation between the present-day \upsilon _ { esc } and their metallicity as well as ( V - I ) _ { 0 } colour .
The similar \upsilon _ { esc } , ( V - I ) _ { 0 } distribution of nGCs and EHB-GCs implies that nGCs could also have complex stellar populations .
The \upsilon _ { esc } – [ Fe/H ] relation could reflect the known relation of increasing stellar wind velocity with metallicity , which in turn could explain why more metal-poor clusters typically show more peculiarities in their stellar population than more metal-rich clusters of the same mass do .
Thus the cluster \upsilon _ { esc } can be used as parameter to describe the degree of self-enrichment .
All our findings support the scenario in which Galactic EHB-GCs have originated in the centres of pre-Galactic building blocks or dwarf galaxies that were later accreted by the Milky Way .