Astronomy & Celestial Mechanics
the sky, computed
Series

Galactic structure — the series

4 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. the Milky Way measured from inside it — the tangent-point construction. Left: the disc in plan, with the Sun at 8.2 kpc from the centre and four lines of sight at galactic longitudes 20°, 40°, 60°, 80°. Each one grazes a circle of radius R₀ sin l, and at that tangent point the whole circular velocity lies along the line of sight, so the largest velocity in the spectrum belongs to a radius the geometry fixes and no distance has to be measured. Right: the four radii and speeds that yields, on the model curve they are read against. The construction reaches only radii inside the Sun's, which is why the outer curve — the half of it that carries the argument — needs distances after all.

    A galaxy measured from inside it

    The Milky Way is the one galaxy nobody can photograph, and the only one whose rotation can be measured without knowing a single distance. A line of sight at a chosen longitude grazes a circle of known radius, and the fastest gas along it is orbiting there.

    part 1 · galaxies
  2. Two geometries, one bit of data, and the bit decides. Rotation measure against galactic longitude for two field geometries that look identical in every image ever taken. An axisymmetric field runs the same way round the disc at every azimuth, so the component along the line of sight changes sign exactly 2 times as the longitude goes round — once where the field turns toward the observer and once where it turns away. A bisymmetric field reverses its own direction from one side of the galaxy to the other, and that doubles the count to 4. Nothing about the brightness, the arms or the colour distinguishes the two; the sign of a rotation measure does, and a sign is one bit. The measurement is made against several hundred background sources, each contributing one rotation measure through the whole disc — the sources are not the object of study, they are the illumination. The Milky Way's own answer is untidy: broadly axisymmetric with at least one reversal inside the solar circle, which is neither clean case, and is why the field's origin is still argued about.

    Two geometries and one bit to choose between them

    A galaxy's large-scale magnetic field either runs the same way round the disc everywhere or reverses from one side to the other. No image distinguishes the two. The sign of a rotation measure does — two reversals around the sky for one geometry and four for the other — and a sign is one bit of information.

    part 2 · galaxies
  3. One velocity, two distances — 4.7 and 9.5 kiloparsecs. The radial velocity of gas along a line of sight at galactic longitude 30 degrees, against distance from the Sun, for a flat rotation curve. The velocity rises to a maximum at the tangent point — where the line of sight is tangent to a circle of radius R₀ sin l — and falls again beyond it, so every velocity below the maximum corresponds to two distances. A cloud observed at 84 kilometres a second is at either 4.7 or 9.5 kiloparsecs, and nothing about its velocity says which. The two possibilities differ by a factor in distance and by its square in luminosity and mass, so the ambiguity is not a refinement — it decides whether a star-forming region is an ordinary one nearby or a monster on the far side of the Galaxy.

    One velocity and two distances

    Inside the Sun's orbit a line of sight crosses each galactocentric radius twice, and the two crossings have identical radial velocities. So a cloud's velocity gives two candidate distances, near and far, differing by a factor — and nothing about the velocity says which, though the choice decides whether the object is ordinary or extraordinary.

    part 3 · galaxies
  4. Arms drawn into a disc that has none. Left: 1400 gas clouds spread uniformly over a disc between 3 and 13 kpc from the Galactic centre (cross), seen from above with the Sun (ring) 8.2 kpc out; the two thin curves mark where a two-armed spiral density wave of pitch 12° has its arms. The clouds have no arms in their positions, only in their motions: each streams by 10 km/s in a pattern locked to the arms. Right: the same clouds placed at their kinematic distances, read from their velocities with a circular rotation curve and on the correct side of every tangent point. The streaming has moved them by up to a few kiloparsecs, along lines of sight, and into bands. Lines of sight within 12° of the Galactic centre and 18° of the anticentre, where the velocities carry no distance, are left out. Counted in square kiloparsecs between 4 and 12 kpc, the densest fifth of the map holds 30 per cent of the clouds in reality and 45 per cent in the kinematic map.

    A spiral drawn by velocities alone

    A map of the Milky Way's gas is built by turning each cloud's velocity into a distance with a circular rotation curve. Gas in a spiral arm does not move on circles: it streams by ten or fifteen kilometres a second in a pattern locked to the arms, so the distance errors are locked to the arms too. Read that way, a disc with no arms in it at all comes out of the calculation with arms.

    part 4 · galaxies

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