Astronomy & Celestial Mechanics
the sky, computed
Series

Stellar streams — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. A stream that is not the orbit it came from. 456 stars released in pairs from the two saddles of a 10⁵ solar-mass cluster over 4.0 billion years, integrated in a halo whose circular speed is 220 kilometres a second, drawn with the progenitor's own orbit. The cluster runs between 10 and 25 kiloparsecs and the orbit is the thin closed-looking curve; the stars are everything else. The point of the figure is the discrepancy. Stars leaving through the inner saddle are on slightly smaller orbits, turning round at a median of 24.77 kiloparsecs rather than the progenitor's 25.00, and therefore running ahead; stars leaving through the outer saddle reach 25.22 and fall behind. The whole spread is 1.8 per cent of the apocentre, which is the number worth carrying: an offset far too small to see in this drawing builds the entire stream, because it acts for four billion years. The two arms are therefore not merely displaced along the orbit, they are on different orbits, and the track a survey measures is a family of them rather than any single one. Fitting a Galactic potential by demanding that a stream lie along an orbit is wrong by exactly this much, and the size of the error grows with the mass of the progenitor, because the mass is what sets the distance between the two doors.

    A stream is not the orbit it came from

    A cluster torn apart by a galaxy leaves a thin trail of stars across the sky, and the obvious thing to do with it is fit an orbit. That is wrong by a knowable amount, because stars leave through two doors with a small energy offset and end up on a family of orbits rather than on one.

    part 1 · galaxies
  2. A gap's depth is one number: 2GmT ÷ v b². The central density of the gap against impact parameter, 4 billion years after the encounter, for subhaloes of 10⁶, 10⁷, 10⁸ solar masses. Points are read off the drawn density profiles; the curves are 1/(1 + 2GmT/v b²), the stretch the map applies at the encounter point, and the two agree to 3.0 per cent wherever the histogram has enough stars left in the gap to measure a depth at all. Everything about the encounter enters the depth through that one combination. The consequence is the horizontal reading: a gap of a given depth is produced by every point along a locus on which the mass rises as the square of the impact parameter — half depth at 0.42, 1.33, 4.19 kiloparsecs for the three masses drawn, an exponent of 0.500 against the half the algebra requires. What breaks that particular degeneracy is the gap's width, which scales as the impact parameter itself while the depth does not: rescale s by b and the map is identical, so the profile is one shape stretched. Depth and width together give the impact parameter and the product mT. They do not give the mass.

    A hole that says mass times time

    A gap in a stellar stream is the strongest evidence available that dark subhaloes exist, and its depth depends on the perturber's mass, the impact parameter and the elapsed time only through one combination. Two of those three are unobservable, so a gap is a measurement of a product.

    part 2 · galaxies

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