What a light curve can and cannot see

A star's rotational light curve is a linear measurement of its surface. Paint spots below and watch the light curve appear. Then press “randomise the invisible part”: the surface will change completely and the light curve will not move at all. That residual is the operator's null space, and on a real survey cadence it is over 99% of the map.

Drag on the left-hand map to paint. Shift-drag makes a bright feature.

real epochs
distinct nights
map pixels
modes with SNR > 1
null fraction
your map: invisible power

Your surface, split by what the data can determine

1 · the surface (paint here)

Equirectangular map. The shaded band near the bottom is the polar cap that is never visible at this inclination.

2 · what the data determines

The projection onto the operator's row space — everything a light curve can ever constrain, at any signal-to-noise.

3 · what only a prior can supply

The null-space residual. Add any amount of this and the light curve is unchanged. Every published spot map lives largely here.

The light curve

light curve of your surface after randomising the invisible part per-epoch error bar

Real posteriors: swap the prior, keep the data

These are not simulated in the browser — they are posterior means from the actual diffusion runs, under two deliberately different prior hypotheses (a smooth isotropic field vs. dark localised spots) on identical data. The data-constrained parts agree; the null-space parts do not.

casedata agreementprior divergence null corr. (generic)null corr. (spotted)