Past exam of the mathematics course of the University of Cambridge 2026 iii Paper 346 1 v Solution Created 2026-09-24 Updated 2026-09-25
Near-infrared light is dominated over much of the Milky Way by old, cool, low-mass stars, with extra emission from young stars and hot dust in active regions. Because interstellar dust attenuates it much less strongly than optical light, near-infrared surface brightness and star counts are useful tracers of stellar mass and the obscured Galactic bulge and bar.
The Milky Way has a thin stellar galactic disk, radius roughly – and scale height about , containing gas, dust, young and old stars, spiral arms and most current star formation. Its stellar mass is a few . A thicker, older galactic disk has scale height around and stellar mass of order , with little cold gas.
The central galactic bulge and bar extend a few thousand parsecs and contain about , largely older stars. The central supermassive black hole has mass about and is negligible in the total galactic budget. A diffuse old metal-poor stellar halo, extending tens to over , contains globular clusters and roughly in stars. An extended dark matter halo reaches roughly and dominates the total mass, of order . These are approximate component scales; the gaseous galactic halo also extends beyond the stellar galactic disk.
Three physically distinct contributions are unseen dark matter, hot diffuse intracluster gas omitted from the summed stellar mass, and faint stars or stellar remnants missed by transferring the Milky Way mass-to-light ratio to the cluster. The first two are actual additional components; the third changes the inferred stellar budget. Departures from virial equilibrium, velocity anisotropy or extra nonthermal pressure can also bias the dynamical or X-ray estimates, although they need not remove the discrepancy.
Original schematic face-on and edge-on views of the Milky Way
. The face-on panel labels a barred centre, spiral star-forming regions, the Sun and an approximate 15 kpc bright-disk radius. The edge-on panel separates the thin dusty disk, thick disk, bulge and old halo/globular-cluster population. Halo extent is indicated schematically beyond the plotted field. Details.Schematic stellar evolutionary regions and spiral-galaxy components used in the solutions
. Details. Rainer Schödel Created 2026-10-18 Updated 2026-11-05
Rainer Schödel led a study that traced a short-period star around Sagittarius A* at the center of the Milky Way. Ten years of high-resolution astrometry captured both the nearest and farthest parts of the star's highly eccentric orbit.
The 2002 analysis found an orbital period of about 15 years and a close approach of only about 17 light-hours. Concentrating several million solar masses inside that small region excluded plausible extended clusters as the source of the central gravitational field, strengthening the supermassive black hole interpretation.[ref]
Closest Star Seen Orbiting the Supermassive Black Hole at the Centre of the Milky Way by Rainer Schödel and others. Abstract: observed orbital coverage, period, pericentre and excluded extended-mass alternatives
Reinhard Genzel Created 2026-10-18 Updated 2026-11-05
Reinhard Genzel investigates the central mass of the Milky Way using the motion of nearby stars. He coauthored the 2002 report led by Rainer Schödel that followed a close stellar orbit around Sagittarius A*.
An orbital path tests more than a high stellar speed: its curvature, timing and closest approach constrain how tightly the attracting mass is concentrated. The measured short-period orbit required several million solar masses in a compact central region, providing strong dynamical evidence for a supermassive black hole.[ref]
Closest Star Seen Orbiting the Supermassive Black Hole at the Centre of the Milky Way by Rainer Schödel and others. Author list and abstract: ten-year astrometry, Keplerian orbit and compact enclosed mass
Portrait of Reinhard Genzel
. MPE (Commons uploader HHgarching). CC BY-SA 3.0, via Wikimedia Commons. Source. Roland Diehl Created 2026-10-24 Updated 2026-11-05
Roland Diehl uses nuclear gamma rays to trace ongoing nucleosynthesis. His aluminium-26 work measures a decay line whose spatial and Doppler structure connects radioactive material with the distribution and motion of massive-star source regions in the Milky Way.[ref]
A radioactive tracer samples recent production and transport rather than the total accumulated elemental abundance. Interpreting the line therefore requires a source model and the lifetime of the isotope, in addition to the measured photon flux.
Sagittarius A* 2026-10-18
Sagittarius A* is the compact radio source at the centre of the Milky Way. Nearby infrared stars allow its central mass concentration to be studied through their orbits.[ref]
Stellar bar Created 2026-10-25 Updated 2026-11-05
An elongated nonaxisymmetric stellar structure in a galaxy, often approximated as a rotating perturbation of an axisymmetric or spherical gravitational potential. Its pattern angular velocity need not equal an individual star's orbital angular velocity. The Galactic bar is the particular example in the Milky Way.
Thick disk Created 2026-10-25 Updated 2026-11-05
A stellar galactic disk component with greater vertical extent and typically larger random velocity dispersion than a thin galactic disk. In the Milky Way it contains an important old population. Its stars are not defined simply by being in a geometrically sharp slab or by all sharing one age.


