# How do we know that the intrinsic brightness of Cepheid variables corresponds to their period?

As I understand it, beyond parallax the next way of estimating the distance to astronomical objects is by using a relationship between the period and intrinsic luminosity of Cepheid variables. How do we know that relationship? Are there some close enough that we used parallax to validate it, or is there a theoretical reason, or something else?

• Sorry in advance, it was a late night... An additional reason we know the brightness is that there is a specific time it takes light to travel to our eyes/sensors, and therefore we can measure the time it takes the star to go from its dimmest to it's brightest. This time gives us a $\Delta x$ distance that can be used to determine the min and max radius (of variation) which is then added to the base radius given from the spectral class and dimmest brightness of the star. Know the radius+luminosity=know brightness. – LaserYeti Jan 1 '17 at 21:25