Infrared Mass-to-Light Profile Throughout the Infall Region of the Coma Cluster

Using a redshift survey of 1779 galaxies and photometry from the 2-Micron All-Sky Survey (2MASS) covering 200 square degrees, we calculate independent mass and light profiles for the infall region of the Coma cluster of galaxies. The redshift survey is complete to $K_s=12.2$ (622 galaxies), 1.2 magnitudes fainter than $M^*_{K_s}$ at the distance of Coma. We confirm the mass profile obtained by Geller, Diaferio, & Kurtz. The enclosed mass-to-light ratio measured in the $K_s$ band is approximately constant to a radius of $10 \Mpc$, where $M/L_{K_s}= 75\pm 23\mlsun$, in agreement with weak lensing results on similar scales. Within $2.5\Mpc$, X-ray estimates yield similar mass-to-light ratios (67$\pm32h$). The constant enclosed mass-to-light ratio with radius suggests that K-band light from bright galaxies in clusters traces the total mass on scales $\lesssim10 \Mpc$. Uncertainties in the mass profile imply that the mass-to-light ratio inside $r_{200}$ may be as much as a factor of 2.5 larger than that outside $r_{200}$. These data demonstrate that K-band light is not positively biased with respect to the mass; we cannot rule out antibias. These results imply $\Omega_m = 0.17 \pm 0.05$. Estimates of possible variations in $M/L_{K_s}$ with radius suggest that the density parameter is no smaller than $\Omega_m \approx 0.08$.