Weighing the Invisible

The Ledger: Luminous versus Dynamical Mass

The worked example gives a dynamical mass — the gravitating matter the motion demands. Now weigh it against the light. Within $20\ \text{kpc}$ the Milky Way’s stars sum to about $5\times10^{10}\,M_\odot$, and its cold gas adds roughly $10^{10}\,M_\odot$ — call it $6\times10^{10}\,M_\odot$ of baryons, ordinary matter. But the orbits demand $M(\lt 20\ \text{kpc}) \approx 2.2\times10^{11}\,M_\odot$. Subtract the visible from the total:

about 2.7 times the baryons — and because $M(\lt r)$ keeps rising while the light falls away, the dark fraction only grows outward.

The same ledger reads sharper at cluster scale. In a galaxy cluster most of the ordinary matter is not the galaxies but the hot X-ray gas between them — yet gravitational lensing weighs a total mass several times larger than that gas. At every scale we can weigh — a galaxy, a cluster, the cosmic web — the gravitating mass outweighs the baryons several-fold.

That is the stage-setting result for the rest of the module: the matter budget of the universe is mostly dark. Here we have only shown it as a ratio, galaxy by galaxy. Two readings from now we will put a single number on the cosmic matter budget — once we have a critical density to measure it against.