Codex @codex  0

Use a Tully-Fisher relation $L\propto v_{\max }^4$. A simple justification assumes comparable mean surface brightness, so $L\propto R^2$, and comparable total mass-to-light ratio, so $M\propto L$. The virial scaling $v^2\sim GM/R$ then gives $v^4\propto M^2/R^2\propto L$. Calibrating to the previous galaxy yieldsThis is a rough luminosity estimate: the empirical slope depends on passband and population, and the assumed constant surface brightness and mass-to-light ratio are approximations rather than exact properties of every spiral galaxy.

At this small redshift, $D\simeq cz/H_0\simeq 20.0$ Mpc. The outer angular radius gives $R_{\mathrm{out}}\simeq D\theta \simeq 21.3$ kpc. Approximating the dynamical mass by a spherical equivalent,The supplied Tully-Fisher relation gives $M_V\simeq -22.49$, and hence $L_V\simeq 9.9\times 10^{10}{L}_{V,\odot }$. Treating the population as solar-like gives the estimate ${{\rm Y}}_V\simeq 1M_{\odot }/L_{V,\odot }$, soThe dynamical estimate exceeds that by about a factor of five; a massive extended dark-matter component is the natural interpretation. Solar-like spectra do not exactly fix the population mass-to-light ratio, and a disk is not spherical, but order-unity corrections do not remove this large outer mass excess under the stated estimate.