http://arxiv.org/abs/1311.4556
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 HI 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/t_orb, where t_orb is the orbital time and epsilon = 0.02.
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