The Milky Way, The Local Galaxies \& the IR Tully-Fisher Relation

Using the near infrared fluxes of local galaxies derived from COBE/DIRBE J(1.25 $\mu$m) K (2.2 $\mu$m) & L (3.5 $\mu$m) band maps and published Cepheid distances, we construct Tully-Fisher (TF) diagrams for the nearby galaxies. The measured dispersions in these luminosity-linewidth diagrams are remarkably small: ${\sigma }_J=0.09$ magnitudes, ${\sigma }_K=0.13$ magnitudes, and ${\sigma }_L=0.20$ magnitudes. For the J and K bands, Monte Carlo simulations give a 95% confidence interval upper limit on the true scatter in the T-F diagram of ${\sigma }_J\le 0.35$ and ${\sigma }_K\le 0.45$. We determine Milky Way’s luminosity and place it in the T-F diagram by fitting a bar plus ``standard’’ values of its size and circular speed (Sun-Galactic center distance $R_0=8.5\text{kpc}$ and ${\mathrm{\Theta }}_0=220\text{kms}$), the Milky Way lies within $1.5\sigma$ of the TF relations. We can use the TF relation and the Cepheid distances to nearby bright galaxies to constrain $R_0$ and ${\mathrm{\Theta }}_0$. Alternatively, we can fix the parameters of the Galaxy to their standard values, ignore the Cepheid zero-point, and use the Tully-Fisher relation to determine the Hubble Constant directly: $H_0=66\pm 12$ km/s/Mpc.