Starspots in three minutes

A starspot is a cool, dark patch on a star's surface — the same physics as a sunspot, but on a star we cannot resolve. We see the star as a single point of light. As it rotates, a spot swings into view and out again, and the total brightness dips and recovers. That periodic dimming is the entire signal.

The one idea to take away. We never see the map. We see one number per observation — the disk-integrated flux. Everything below is about how much of a surface survives being squashed into that one number.

Play with it

the star, as you would see it
the surface map (grey band = never visible at this inclination)
light curve current phase
modulation depth
spot covers
visible at some phase?

What you should notice

Latitude hides in inclination

A spot near the equator sweeps fully in and out of view and gives a deep dip. Push it to high latitude on an inclined star and it stays partly visible all the time, so the dip shrinks — without the spot getting any smaller. Spot latitude and stellar inclination are famously entangled for exactly this reason.

Two spots look like half the period

Put two similar spots on opposite sides and the curve dips twice per rotation. Fold it at P/2 and the two dips land on top of each other and look like one — a perfectly good fit to the wrong period. This is the harmonic ambiguity, and it is the bridge to the next page.

Some of the star is simply gone

At inclination i, everything beyond colatitude i + 90° never rotates into view. Drag a spot in there and the light curve goes flat: the data contains no information at all about that cap. Any map you publish showing structure there is showing you your prior.

Where this is going. The hidden cap is the most obvious piece of what a light curve cannot see, but it is far from the largest. On a real survey cadence the data pins down about 19 numbers out of thousands of map pixels. The paint-a-star explorer lets you add an arbitrary invisible component and watch the light curve refuse to move.