which type of binary can have their sizes measured directly by photometry
The type of binary system that can have their sizes measured directly by photometry is known as an "eclipsing binary."
Eclipsing binaries are binary star systems in which the two stars periodically eclipse each other as seen from Earth. By analyzing the light curves, which represent the changes in brightness over time, astronomers can obtain valuable information about the properties of the stars, including their sizes.
To measure the sizes of the stars in an eclipsing binary using photometry, astronomers typically observe the system over multiple complete orbits. They measure the depths and durations of the primary and secondary eclipses, which correspond to when one star passes in front of the other. By comparing these measurements with models and calculations, scientists can determine the relative sizes of the stars through a process known as light curve analysis.