An ideal phase test has 16 percent power for 163 CM Draconis flares under an aligned polar model

We test how much orbital flare phase can tell us about flare latitude in CM Draconis. We use public TESS observation times from 15 sectors and published binary dimensions. We compare a uniform surface population with two caps at absolute latitude of 60 degrees or more. The caps follow the orbital axis. Both stars have equal flare rates outside eclipse. Flares are independent points on the surface. The detected rate per unit surface area has weight mu^1.28, where mu is the viewing cosine. Selection is known and constant in the main test. Power is the probability that the test selects the caps when the caps are true. We condition on the count in each sector. At a 5 percent false-positive rate, the most powerful phase test has 15.7 percent power for 163 detected flares. About 2800 flares give 80 percent power. The cap model still loses 8.3 percent of its rate during eclipse, averaged over valid TESS exposure. A second published set of binary dimensions gives 17.0 percent power at 163 flares. A specified photon-noise model reduces the mean uniform-surface deficit from 21.1 to 9.0 percent. This is a conditional forecast for peak times. It is not a measurement of actual flare latitude or detector completeness. The package includes the original data, source hashes, code, numerical checks, and figures.

CM Draconis · stellar flares · eclipsing binaries · flare latitude · TESS · statistical power · selection effects