M4 Galactic Dynamics

Topic

The central element of this model is the galaxy, understood as a rotating system sustained by a mass that is, for the most part, invisible.

The rotation curve of the galaxy's disk remains virtually flat at large radii, rather than declining as it would if only the disk's visible mass were sustaining that rotation. The fact that the curve remains flat instead of dropping makes this flatness the most direct kinematic evidence that a dark matter halo envelops the entire galaxy.

For its part, the galaxy's stellar disk follows a density profile that decays exponentially with radius, whereas the density profile of the dark halo itself—as predicted by N-body simulations—decays much more gradually near the galactic center than at greater distances, where the drop-off becomes much steeper: two clearly distinct regimes within a single halo.

The virial theorem, applied here to elliptical galaxies and globular clusters rather than a single disk, allows for the estimation of the total mass of each of these systems based on the velocity dispersion observed among their member stars.

On the scale of the entire universe, this dark matter accounts for nearly one-quarter of the total energy content, and it dominates the mass of galaxies and galaxy clusters, making up well over eighty percent of the total. The evidence pointing to its existence is manifold and mutually independent: the flat rotation curves of galaxies like the one introduced at the beginning of this text; velocity dispersion within clusters; light deflection via gravitational lensing—which reveals all present mass, including the invisible component; the observed separation between gas and total mass following the collision of two galaxy clusters; and the fluctuations of the cosmic microwave background itself. The most widely discussed particle candidate to explain this dark matter—a weakly interacting massive particle—has an annihilation cross-section that strikingly matches the value that naturally reproduces the dark matter abundance observed today; this coincidence is often referred to as the "WIMP miracle." Weak gravitational lensing is currently the primary tool for mapping the distribution of dark matter on a cosmological scale. Thus, from the galaxy with which this document begins to the cosmological-scale mapping with which it concludes—and taking in the flat rotation curve, the dark halo, and the virial theorem along the way—galactic dynamics reveal how a single invisible mass, governed by the same logic, sustains both the rotation of an individual galaxy and the structure of the entire universe.

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