Star luminosity depends upon both radius and temperature because luminosity is a measure of energy output. A larger star puts out more energy than a similar, but smaller star, just as a hotter star puts out more energy than a similar, but cooler star.
Stars are large, thermonuclear reactions that release incredible amounts of energy. Scientists that study stars measure this energy and call it luminosity. Luminosity is typically measured in the amount of energy produced in a given unit of time, such as joules per second. As an example, the sun produces about 500 million million million mega joules of energy per second.
Given that the two stars are similar, one that is twice the size of the other has four times the amount of surface area. Accordingly, the larger star produces four times the energy of the smaller star. Temperature causes changes that are even more drastic in terms of luminosity. Every time the temperature of a star doubles, the luminosity becomes sixteen times greater.
Luminosity helps scientists to determine how far away stars are. To do so, scientists compare the luminosity of a star with its apparent size. Stars that have high luminosity, but are very far away, may appear very small. Conversely, low luminosity stars may be very close, but relatively cool in temperature.