Metallicity

because there's actually only a few dozen Cepheids in the Milky Way, so it's going to be difficult to precisely measure these new dependencies from such a small sample to begin with, as well as of course challenging to measure those same properties for other galaxies down the road.

Metallicity is a particularly challenging topic because for Cepheids, you can't even often measure their metallicity directly.

Instead, we rely on the surrounding environment's oxygen abundance as a proxy.

The dependency of luminosity upon metallicity is characterized by this coefficient in the Leavitt law equation.