Astronomy & Celestial Mechanics
the sky, computed
Concept

Binary fraction — where it appears

The fraction of stars in a population that have a companion. It is between a third and a half for solar-type stars, it has to be measured in the system being studied rather than assumed, and it sets how much of a measured velocity dispersion is orbital motion.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

A collapse that stops 29 astronomical units short. Equatorial rotation speed against radius for a collapsing cloud core of 1 solar mass, turning at 10⁻¹⁴ radians a second at a radius of 0.05 parsecs, compared with the Keplerian speed at the same radius. Both axes are logarithmic; both curves are computed from the same specific angular momentum, 2.4·10¹⁶ square metres a second, held fixed. The rotation speed rises as the reciprocal of the radius and the orbital speed only as its inverse square root, so they must cross, and the crossing is measured off the drawn curves at 4.27·10¹² metres — 29 astronomical units, or 6135 solar radii. Inside that radius the material is orbiting rather than falling, and no further collapse happens along the equator at all. To arrive at a star turning once in 25.38 days the core must dispose of a factor of 1.7·10⁴ in specific angular momentum, and nothing in the collapse itself removes any: it has to be handed to a magnetic field, to a disc, or to a companion. The figure assumes uniform rotation and a spherical core, both of which are simplifications a real core violates in the direction that makes the problem worse.

A cloud that cannot become a star

A molecular cloud core turning once every twenty million years sounds like a body at rest. Conserve its angular momentum through a collapse by a factor of ten thousand and it stops at the orbit of Neptune, spinning, having failed to make anything at all.

galaxies · Star formation A virial mass inflated 23.2-fold by orbits nobody resolved. The factor by which a virial mass is overestimated when the velocity dispersion is measured from single-epoch spectra, against the system's true dispersion, for four numbers of observing epochs. Every star in a binary carries its own orbital velocity, which adds in quadrature to the system's own, and the orbital velocities of ordinary binaries are of order a kilometre a second. A system whose real dispersion is 0.3 km/s therefore measures 1.45, and since a virial mass goes as the square of the dispersion the mass comes out 23.2 times too large. Repeat epochs fix it: the orbital velocities are uncorrelated between visits while the system's own are not, so the binary variance falls as one over the number of epochs and the correction is measured rather than modelled.

A dispersion inflated by orbits nobody resolved

A velocity dispersion measured from single spectra is not the dispersion of the system's centres of mass. Every star in a binary carries its own orbital velocity of a kilometre or so, and for a dwarf galaxy whose real dispersion is smaller than that, the measured value — and the dark-matter content computed from its square — is mostly binaries.

galaxies · Velocity dispersion

Named alongside it

The objects these essays reach for when they reach for this one.

Ambipolar diffusionAngular momentum problemAngular momentum transportCentrifugal barrierDark matterDisc windDwarf spheroidalFlux problemFragmentationFree-fall timeMagnetic brakingMass-to-flux ratio

All concepts