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The star that is hotter will have a higher luminosity.
Generally speaking, the apparent luminosity would be an inverse square relationship, which is to say, if the same star was at twice the distance, a quarter of the light would be reaching the observer. But absolute luminosity can of course vary without regard to distance from Earth - dim stars can be close, or bright stars distant, or vice-versa.
Luminosity depends directly on mass because more massive main-sequence stars do not need to graviationally contract as far to reach fusion temperatures, and so they have a larger volume and contain a much larger amount of light energy, which diffuses out and generates a higher luminosity, very roughly in proportion to the higher volume.
Main sequence stars
Cepheids have a certain relationship between their period, and their absolute luminosity. Thus, their absolute luminosity can be determined. Comparing this with their apparent luminosity allows us to calculate their distance.Cepheids have a certain relationship between their period, and their absolute luminosity. Thus, their absolute luminosity can be determined. Comparing this with their apparent luminosity allows us to calculate their distance.Cepheids have a certain relationship between their period, and their absolute luminosity. Thus, their absolute luminosity can be determined. Comparing this with their apparent luminosity allows us to calculate their distance.Cepheids have a certain relationship between their period, and their absolute luminosity. Thus, their absolute luminosity can be determined. Comparing this with their apparent luminosity allows us to calculate their distance.
On a logarithmic scale for luminosity, it is quite close to a negative linear relationship.
as surface temperature increases, luminosity increases
No. Main sequence stars are simply stars that are fusing hydrogen into helium and have a specific relationship between color and luminosity. They range from red dwarfs to large O-type main sequence stars.
The star that is hotter will have a higher luminosity.
The star that is hotter will have a higher luminosity.
The basic luminosity classes are: I for supergiants, III for giants, and V for main-sequence stars.
On such a diagram, those stars lie on a curve called the "main sequence". It is not a simple relationship - for example, it isn't a straight line on the diagram. Therefore, it isn't easy to describe in words. It's best if you look up "Main sequence", for example on the Wikipedia, and look at the corresponding diagram.
The scatter plot of the relationship between a star's temperature and luminosity is represented by the Hertzsprung-Russell diagram. In a standard H-R diagram the horizontal axis shows the [surface] temperature, increasing from right to left, while the vertical axis shows luminosity increasing from bottom to top. When both axis are on a logarithmic scale, the main sequence stars from a diagonal belt stretching from top right (very hot and very luminous) to bottom left (not so hot and not so luminous).
It shows the relationship between stars luminosity versus their classifications and effective temperatures
There is no simple relation. The color does not depend only on the mass. The same star can change color, without a significant change in mass. For example, our Sun is currently yellow; in a few billion years, it is expected to get much larger, becoming a red giant. However, if we limit the sample of stars to those on the "main sequence" of the "HR diagram", there is something of a relation between mass and color. The most massive stars are blue or white. They are also hottest and most luminous. The least massive are the red dwarf stars, which are relatively cool and dim. Our Sun, which is a "main sequence" star at present, is somewhere in between those extremes. (There is a strong relationship between mass and luminosity for main sequence stars. The HR diagram, of course, shows there is a relationship between luminosity and color for the main sequence stars.)
Generally speaking, the apparent luminosity would be an inverse square relationship, which is to say, if the same star was at twice the distance, a quarter of the light would be reaching the observer. But absolute luminosity can of course vary without regard to distance from Earth - dim stars can be close, or bright stars distant, or vice-versa.
Luminosity depends directly on mass because more massive main-sequence stars do not need to graviationally contract as far to reach fusion temperatures, and so they have a larger volume and contain a much larger amount of light energy, which diffuses out and generates a higher luminosity, very roughly in proportion to the higher volume.