Astronomy & Celestial Mechanics
the sky, computed
Concept

Convective turnover time — where it appears

The time a convective cell takes to carry gas once round, roughly the size of the largest eddies divided by their speed. Dividing a star's rotation period by it gives the Rossby number, and it is usually calibrated empirically rather than computed.

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

A period, a colour, and an age. Rotation period against colour for stars of 125, 625, 1000, 2500, 4570 million years, under the empirical relation P = t^0.5189 × 0.7725(B−V − 0.4)^0.601. The isochrones do not cross and are separated at every colour by exactly the age ratio raised to 0.5189, which is what allows a single measured period to be inverted for an age once the colour is known. The Sun, at B−V = 0.653 and 4570 million years, is placed by the relation at 26.8 days against the 25.4 days it is observed to have. Three clusters are marked at a common colour to show the spacing directly. The dashed boundary at the left is where the Rossby number — the period divided by the convective turnover time — passes 2 on the oldest isochrone, at B−V = 1.35: past that point the braking weakens and the relation is known to over-predict the age, which is the one place a rotation period stops being a clock. What the figure cannot show is the scatter, which is a few days at fixed colour and age and is the real error bar on any single star.

The clock that starts by forgetting

An ordinary star tells nothing about its age. It sits on the main sequence for billions of years at almost fixed brightness and colour, and the one property that changes monotonically is how fast it turns — but only because the braking law destroys the initial condition first, and only until it stops.

stars · Magnetic braking X-ray activity against Rossby number, with and without a tachocline. The X-ray luminosity of a star as a fraction of its total, against its Rossby number — the rotation period divided by the convective turnover time — for a synthetic sample of 600 stars of 0.4 to 1.2 solar masses, which have a radiative core and a tachocline below their convection zones, and 220 of 0.1 to 0.35 solar masses, which are convective to the centre and have neither. Both are drawn from one relation: saturated at a ratio of 10⁻³·¹³ below a Rossby number of 0.13 and falling as its −2.7th power above, with 0.25 dex of scatter. The saturated stars of the two kinds average −3.09 and −3.16 in the logarithm; 56 of the fully convective stars rotate slowly enough to lie on the unsaturated branch. This is the shape the measured relation has: the stars with no tachocline lie on the same line as those with one, saturated at the same level and falling along the same slope.

A dynamo that did not need the shear layer

The Sun's magnetic cycle has long been placed in the thin layer of shear beneath its convection zone, where a rigidly rotating interior meets a differentially rotating envelope. Stars below about a third of a solar mass have no such layer — they are convective to the centre — and they are as magnetically active as the Sun, saturate at the same level, and fade with slowing rotation along the same line. The saturation is the cleaner half of that evidence, because the slope depends on a turnover time that was itself calibrated from activity.

stars · Internal rotation

Named alongside it

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

Rossby numberActivity saturationAsteroseismologyCalibrationConvective envelopeDifferential rotationFully convective starGyrochronologyIsochroneM dwarfMagnetic brakingMain-sequence turn-off

All concepts