The Baryonic Tully-Fisher Relation in the Local Group and the Equivalent Circular Velocity of Pressure Supported Dwarfs

We explore the Baryonic Tully-Fisher Relation in the Local Group. Rotationally supported Local Group galaxies adhere precisely to the relation defined by more distant galaxies. For pressure supported dwarf galaxies, we determine the scaling factor $\beta_c$ that relates their observed velocity dispersion to the equivalent circular velocity of rotationally supported galaxies of the same mass such that $V_o = \beta_c \sigma_*$. For a typical mass-to-light ratio $\Upsilon_* = 2\;\mathrm{M}_{\odot}/\mathrm{L}_{\odot}$ in the $V$-band, we find that $\beta_c = 2$. More generally, $\log \beta_c = 0.25 \log \Upsilon_* +0.226$. This provides a common kinematic scale relating pressure and rotationally supported dwarf galaxies.