For a rotating galaxy , the inner circular-velocity gradient d _ { R } V ( 0 ) provides a direct estimate of the central dynamical mass density , including gas , stars , and dark matter .
We consider 60 low-mass galaxies with high-quality H I and/or stellar rotation curves ( including starbursting dwarfs , irregulars , and spheroidals ) , and estimate d _ { R } V ( 0 ) as V _ { R _ { d } } / R _ { d } , where R _ { d } is the galaxy scale-length .
For gas-rich dwarfs , we find that V _ { R _ { d } } / R _ { d } correlates with the central surface brightness \mu _ { 0 } , the mean atomic gas surface density \Sigma _ { gas } , and the star formation rate surface density \Sigma _ { SFR } .
Starbursting galaxies , such as blue compact dwarfs ( BCDs ) , generally have higher values of V _ { R _ { d } } / R _ { d } than dwarf irregulars , suggesting that the starburst is closely related to the inner shape of the potential well .
There are , however , some “ compact ” irregulars with values of V _ { R _ { d } } / R _ { d } similar to BCDs .
Unless a redistribution of mass takes place , BCDs must evolve into compact irregulars .
Rotating spheroidals in the Virgo cluster follow the same correlation between V _ { R _ { d } } / R _ { d } and \mu _ { 0 } as gas-rich dwarfs .
They have values of V _ { R _ { d } } / R _ { d } comparable to those of BCDs and compact irregulars , pointing at evolutionary links between these types of dwarfs .
Finally , we find that , similarly to spiral galaxies and massive starbursts , the star-formation activity in dwarfs can be parametrized as \Sigma _ { SFR } = \epsilon \Sigma _ { gas } / \tau _ { orb } , where \tau _ { orb } is the orbital time and \epsilon \simeq 0.02 .