It's total output is therefore the 'brightness' you see.
Red giants are large, and the total output is high.How can a star be so bright yet have such a low surface temperature?
Generally, the lower the wavelength of the light emitted by a star, the cooler it is (there are other factors that effect wavelength too) . The brightness of a star can also be effected by your distance from it and many other factors and does not necessarily give any implication of temperature.How can a star be so bright yet have such a low surface temperature?The really quick answer - apparent brightness of a star has to do with its proximity to Earth. The temperature of a star can still be low, even though it appears to be a very bright and presumably hot star. Low temperature, high luminosity stars are giants and supergiants. The reason they are so luminous while being relatively cool is because they're so damn big (50 times more massive than our Sun - or more).
The detailed answer -
Stellar brightness is measured on a logarithmic scale. If the *apparent magnitude* of star A is 5 less than that of star B, that means that star A is 100 times brighter. But, if a star is further away from Earth, it will appear to be dimmer (headlights are dimmer the farther away they are on the road). The intensity of the star light that reaches us on Earth is inversely proportional to the square of the distance between the star and the observer. Just read that a few times to drill it in, because it's important. If the distance between the star and we humans is doubled, we will see only 25% of the original intensity. This is the inverse square law, and you can throw some numbers around with it to prove how things work.
All of these big words mean that the *apparent* magnitude of a star isn't actually an intrinsic property of the star. So a star can look dim just because it's farther away. To get a real measure of how bright a star actually is, we have to calculate its *absolute* magnitude. This is the apparent magnitude of an object at some standard distance from us. This standard distance has been chosen to be about 32 light years (10 parsecs - Han Solo and the Kessel Run!). With this in mind, the apparent magnitude of our Sun is -26.8, but its absolute magnitude is just 4.8. The absolute magnitude describes the luminosity, which is the amount of energy radiated per second, of the star.
Different stars have different colors. To precisely describe the color of a star, it's necessary to specify the spectrum of the star. The spectrum is a graph that plots the relative intensity at each wavelength of radiation. Usually, the spectrum doesn't tell us the total energy the star radiates out. In general, if the peak of a spectrum is at the red light region, the star will appear to be red. If the spectrum is flat, the star is white in color.
For a warm and dense object (such as a star or a piece of metal), it will radiate light (electromagnetic radiation) and the spectrum follows black body radiation. The spectrum only depends on the temperature of the object. If the temperature is low, the peak of the spectrum is at red region. For higher temperature, the peak shifts towards the yellow, blue, finally in the ultraviolet region. Hotter objects also radiate more energy per unit area than cooler objects. Therefore, the color of a star is mainly determined by its surface temperature, but its luminosity is determined both by its surface temperature and the surface area.
Not all spectra are black body spectra. Gas in low pressure and low density will alter the light that passes through it. The gas will absorb light at some particular wavelengths and re-radiate it in random directions (much like our sky). So, after passing through the low pressure gas, the spectrum of the original white light will have dark lines, called absorption lines. In the other direction, you'll see the emission lines of the gas. Since different gas has different set of lines, we on Earth can tell which kind of gas it is by analyzing the line spectrum.
The Hertzsprung-Russel diagram, or H-R diagram, is the most important diagram in discussing stellar evolution. It is a plot of the surface temperature versus the brightness or luminosity of stars. We know the luminosity is directly related to the absolute magnitude. So, in practice, we usually use absolute magnitudes instead.How can a star be so bright yet have such a low surface temperature?
Low surface temperature = smaller number of watts per square metre (and reddish color). flux
However, big star (like a red giant) means lots of square metres, therefore lots of watts = high luminosity (flux * area)
If you are talking about apparent brightness, then its distance from us will also have an impact.
Half the distance = 4 times brighter.
One third the distance = 9 times brighter.
And so on.How can a star be so bright yet have such a low surface temperature?The luminosity of a star depends on two things: its surface temperature, and its size. (Also, a little bit on its composition.) If it's cool and bright, it has to be big.How can a star be so bright yet have such a low surface temperature?
The total light a given star emits is decided by several things, among them being the star's physical size. A red-giant star may be cool but still be extremely large; there's more area to emit light.How can a star be so bright yet have such a low surface temperature?
It has air conditioning.
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