Dynamically hot stellar systems , whether star clusters or early-type galaxies , follow well-defined scaling relations over many orders of magnitudes in mass .
These fundamental plane relations have been subject of several studies , which have been mostly confined to certain types of galaxies and/or star clusters so far .
Here , we present a complete picture of hot stellar systems ranging from faint galaxies and star clusters of only a few hundred solar masses up to giant ellipticals ( gEs ) with 10 ^ { 12 } M _ { \sun } , in particular including – for the first time – large samples of compact ellipticals ( cEs ) , ultra-compact dwarf galaxies ( UCDs ) , dwarf ellipticals ( dEs ) of nearby galaxy clusters and Local Group ultra-faint dwarf spheroidals ( dSphs ) .
For all those stellar systems we show the effective radius–luminosity , effective radius–stellar mass , and effective mass surface density–stellar mass plane .
Two clear families of hot stellar systems can be differentiated : the ’ galaxian ’ family , ranging from gEs over Es and dEs to dSphs , and the ’ star cluster ’ family , comprising globular clusters ( GCs ) , UCDs and nuclear star clusters ( NCs ) .
Interestingly , massive ellipticals have a similar size–mass relation as cEs , UCDs and NCs , with a clear common boundary towards minimum sizes , which can be approximated by R _ { \mathrm { eff } } \geq 2.24 \cdot 10 ^ { -6 } \cdot M _ { \star } ^ { 4 / 5 } pc .
No object of either family is located in the ’ zone of avoidance ’ beyond this limit .
Even the majority of early-type galaxies at high redshift obeys this relation .
The sizes of dEs and dSphs ( R _ { \mathrm { eff } } \sim 1.0 kpc ) as well as GCs ( R _ { \mathrm { eff } } \sim 3 pc ) barely vary with mass over several orders of magnitude .
We use the constant galaxy sizes to derive the distances of several local galaxy clusters .
The size gap between star clusters and dwarf galaxies gets filled in by low mass , resolving star clusters and the faintest dSphs at the low mass end , and by GCs/UCDs , NCs and cEs in the mass range 10 ^ { 6 } < M _ { \star } < 10 ^ { 9 } M _ { \sun } .
In the surface density–mass plane the sequences of star clusters and galaxies show the same slope , but are displaced with respect to each other by 10 ^ { 3 } in mass and 10 ^ { 2 } in surface density .
Objects that fall in between both sequences include cEs , UCDs , NCs and ultra-faint dSphs .
Both , galaxies and star clusters , do not exceed a surface density of \Sigma _ { \mathrm { eff } } = 3.17 \cdot 10 ^ { 10 } \cdot M _ { \star } ^ { -3 / 5 } M _ { \sun } pc ^ { -2 } , causing an orthogonal kink in the galaxy sequence for ellipticals more massive than 10 ^ { 11 } M _ { \sun } .
The densest stellar systems ( within their effective radius ) are nuclear star clusters .