Astronomy & Celestial Mechanics
the sky, computed
Concept

Macroturbulence — where it appears

A broadening of stellar lines attributed to motions on scales larger than the region where the line forms, so that flux is redistributed without being absorbed. It is a fitted parameter rather than a measured motion, and it is degenerate with rotation in a single line.

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

Three profiles of equal equivalent width, 28.6 mÅ. Three absorption profiles with the same equivalent width — 28.6 milliångström, 1.72 km/s at 500 nm, matched to better than 0.1% by root-finding over the quadrature — differing in nothing but shape. Left: the cores, on a common velocity axis. Right: the same three normalised to their own half widths, on a logarithmic depth scale. The thermal profile is a Gaussian set by Fe's mass at 6000 K, 1.34 km/s; the collisional one a Lorentzian of γ = 2.28e-3 nm; the rotational one the classical kernel of a disc turning at v sin i = 1.73 km/s, which is exactly zero beyond 1.28 half widths and is the only one of the three with an edge. Matching the areas does not match the widths: the half widths are 1.11 km/s (thermal), 1.35 km/s (rotational), 0.68 km/s (collisional), a factor of 1.98 between the widest and the narrowest. At three half widths the collisional wing is 49 times the thermal one and at five it is 1.27·10⁶ times — six decades, which is why a line's shape stays diagnostic long after its width has stopped being so. 11% of the Lorentzian's own equivalent width lies beyond the right-hand panel's edge and is not drawn anywhere.

The same width for three different reasons

Thermal motion, rotation and collisions each widen an absorption line, and they can be tuned to areas that agree to a part in a thousand. What separates them is the shape, and the shape carries a rotation speed from one profile and a surface gravity from another.

starlight · Line formation A bump that crosses the line from -41 to 25 km/s. The residual of a rotationally broadened line profile during a transit, drawn at five epochs and offset vertically. The planet covers a strip of the stellar disc whose radial velocity is the projected rotation at that position, so it removes light from one velocity and leaves a bump in the residual there. As the planet crosses, the bump travels across the profile — and where it starts and ends is set by the geometry of the chord. An orbit aligned with the star's equator gives a track symmetric about the line centre; this one, tilted by 30 degrees, runs from -41 to 25 kilometres a second and is not. The measurement is of a path rather than of a centroid, which is why it works on rapidly rotating stars where the velocity anomaly is swamped by the line's own width.

A shadow crossing a rotating line

A transiting planet hides a strip of a rotating star, and that strip has a definite velocity. So the planet removes light from one place in the line profile and leaves a bump there — a bump that travels across the line as the transit proceeds, tracing the path the planet took across the disc.

exoplanets · Spin–orbit alignment

Named alongside it

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

Damping wingsDegeneracyDoppler broadeningDoppler tomographyEquivalent widthImpact parameterLimb darkeningLine-broadeningLine profileMigrationPressure broadeningProjected obliquity

All concepts