A starspot tells the time at its own latitude

A dark patch comes around the limb

Watch a spot cross the bright face of a rotating star. Near the centre it covers a large apparent area; near the edge it is foreshortened. The edge is also dimmer than the centre. When the patch turns behind the star, its missing light disappears from our view and the total brightness recovers.

A distant telescope usually cannot resolve that patch. It records the total light of the whole disk. A repeatable dip can still carry the rhythm of the moving surface. The Lab adds the light from visible surface cells, then exposes that same star at saved observing times. The moving patch and the light curve have a common physical cause.

Choose the lasting-clock preset. Its equator turns in ten days. The single prescribed patch returns with a ten-day pattern, and a second dip appears after another ten days. A small amount of measurement noise roughens the points without changing the underlying surface.

Reading: Curtis et al. (2020), When Do Stalled Stars Resume Spinning Down? Advancing Gyrochronology with Ruprecht147, arXiv2010.02272v1

The same star can carry different clocks

The Sun rotates at different rates at different latitudes. A simple solar-like rule lets an equatorial belt turn faster than a high-latitude belt. Imagine two marks painted on those belts: after a few rotations they no longer line up.

For a ten-day equator, latitude sixty degrees and a shear of one fifth, our illustrative law gives a local period of about 11.8 days. That is the time the patch takes to return. The light curve alone has not measured its latitude. Correcting the measured period with the latitude we secretly used to make the picture would give the estimator information that an unresolved observation never supplied.

Now imagine two nearly identical patches on opposite sides. A dip arrives whenever either one faces us. A ten-day star can produce a five-day repeating light pattern. The Lab therefore retains declared one-pattern and two-pattern clock hypotheses. Their equal prior weights express an explicit modelling choice. The number and geometry of real spots remain unresolved by the repeated brightness alone.

A turning star can lose its photometric rhythm

If a patch fades before it completes a circuit, the record follows one episode of activity growth and decay. A persistent mark would instead give repeated views. A period search still has to return peaks somewhere. In a separate short-life synthetic test, a ten-day star produced an apparent 27-day peak. The large leftover residuals reveal that a stable repeating pattern describes the data poorly.

Looking straight down the rotation axis creates a different failure. A fixed patch circles at essentially the same projected angle. In this axisymmetric brightness model, its disk-integrated light stays constant. Noise can supply the tallest period-search peak even though the rotating surface supplies no changing signal. The constant-model comparison then withholds an age.

These examples explain why a peak alone is an incomplete answer. We need a visible modulation, enough repeated cycles, and a model that describes the saved points within their stated errors.

A population gives the clock an age scale

A magnetized stellar wind carries angular momentum away from a star. For many cool main-sequence stars, slower rotation accompanies greater age. Star clusters help establish the comparison: their members share a roughly common formation age, and stars of similar temperature can be compared across clusters.

The relation changes with temperature. In the fixed sample used by our tutorial, many cool stars in the one-billion-year-old NGC 6811 cluster rotate at nearly the same rate as younger Praesepe stars. A clock can pause over part of its life. A universal square-root slowing law then makes the older cool stars look too young.

The age panel uses a temperature-dependent empirical sequence and the full set of supported periods. Its output is a distribution conditional on three fixed cluster ages, their adopted temperatures and a stated prior. A broad or split distribution is useful information: the light and the calibration have left more than one age plausible. The following chapters derive how that information enters the calculation.

Reading: Curtis et al. (2019), A Temporary Epoch of Stalled Spin-Down for Low-Mass Stars: Insights from NGC6811 with Gaia and Kepler arXiv1905.06869v3 · Curtis et al. (2020), When Do Stalled Stars Resume Spinning Down? Advancing Gyrochronology with Ruprecht147, arXiv2010.02272v1 · Bouma, Palumbo & Hillenbrand (2023), The Empirical Limits of Gyrochronology, arXiv2303.08830v1