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Stars: brightness, distance, luminosity. Two factors determine how bright a star appears to be. First is the amount of energy the star radiates, its luminosity. Second is its distance. The “brightness” measured by a detector is determined by the rate that energy enters the detector.
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Two factors determine how bright a star appears to be. • First is the amount of energy the star radiates, its luminosity. • Second is its distance.
The “brightness” measured by a detector is determined by the rate that energy enters the detector.
Adetector 4 dis2 L 4 dis2 fraction of L that enters the detector L Adetector 4 dis2 measured brightness L = Adetector energy flux measured brightness fraction of L that enters the detector
Effect of Distance and on Observed Samples In general when we survey the universe for some kind of object we work to the limit of some detector. Let’s use the human eye as an example. Basically if a star isn't bright enough you can’t see it. Astronomers often measure brightness in magnitudes. The brightest naked eye stars are 1st magnitude; the faintest are 6th under the best of conditions. In Charlottesville you normally cannot see fainter than 5th magnitude. So from Charlottesville you can survey the sky to a limit of 5th mag with the naked eye. Magnitudes are difficult to work with and we will normally not use them. All you need know is that magnitudes (or more specifically apparent magnitudes) are a measure of brightness and that bigger magnitudes refer to fainter objects. In reading you may also encounter absolute magnitudes---this is another way of describing luminosity.
L 4(10pc)2 L 400pc2 It turns out that if we viewed the Sun from a distance of 10 it would be 5th mag --- just visible to the naked eye. The energy flux would be: flux-at-10pc = If some other star had the same flux it would also have the same brightness.
100L 4(100pc)2 L 400pc2 For example, the first magnitude stars Aldebaran, visible in the winter/spring, and Arcturus, visible in the fall, both have luminosities 100 L . fluxAldebaran-at-100pc = = flux-at-10pc If either were viewed from a distance of 100 they would be as bright as the Sun at 10. Hence in both cases we observe 5th mag stars, near the limit of the naked eye.
Surveying the sky with the naked eye we can see all Suns within a sphere of radius 10, and all Arcturuses and Aldebarans within a sphere of 100 pc. How many of each class can we find? The density of suns is about 1 solar-type-star/10pc3. Suppose 100 L stars occurred with the same frequency in the Galaxy.
dis3 4 3 4 3 4 3 4 105 (100pc)3 The number we can find is number found = (number density) (volume surveyed) = (number density) 400 number of suns = 0.1/pc3 (10pc)3 number of 100 L stars = 0.1/pc3 This is 1000 times the number of suns and more than 100 times the number of naked eye stars. Obviously, 100 L stars must be less common than solar-type stars.
Conclusion: What we see is dominated by the luminous objects unless they are intrinsically rare.
Of the 30 brightest stars, all except 2 are more luminous than the Sun. Almost half are more luminous than 1000 L .
In an unbiased sample of all stars closer than 10, the vast majority are less luminous than the Sun. The typical star is a dinky little thing with L < L /100.
