The perceived brightness of stars depends on various factors, including their temperature, size, and distance from Earth. If two stars have the same temperature but appear to have different brightness, it can be due to differences in their intrinsic luminosity or their distance from us.
Intrinsic Luminosity: Stars differ in their intrinsic brightness or luminosity, which is determined by their size and energy output. Even if two stars have the same temperature, one may be more massive or have a larger surface area, resulting in a higher intrinsic luminosity. The Stefan-Boltzmann law states that the luminosity of a star is proportional to the fourth power of its temperature and its surface area. Therefore, a larger or more massive star with the same temperature will emit more light and appear brighter.
Distance: The distance between a star and the observer affects its apparent brightness. The inverse square law of light states that the intensity of light decreases as the square of the distance from the source increases. So, if two stars have the same intrinsic luminosity but different distances from Earth, the closer star will appear brighter. Even if they have the same temperature, the farther star will appear dimmer due to its greater distance.
It's important to note that the perceived color of a star can also influence our perception of brightness. Stars emit a range of colors, and our eyes are more sensitive to certain colors. For example, blue stars may appear brighter to us than similarly luminous red stars, as our eyes are more sensitive to blue light.
In summary, the apparent brightness of two stars with the same temperature can differ due to variations in their intrinsic luminosity, differences in their distances from Earth, or differences in the perceived color of their emitted light.