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Physics LibreTexts

12.14 Stellar Luminosity

One fundamental property of a star is the total amount of energy it radiates each second. This energy output is called the luminosity or absolute brightness. Unlike apparent brightness, which depends on how far from us the star is, luminosity is intrinsic to a star, similar to the way that wattage is intrinsic to a light bulb. The most useful concept of luminosity is bolometric luminosity — the total amount of energy radiated each second in all forms at all wavelengths. Since many stars radiate mostly visible light, visual luminosity and bolometric luminosity are often roughly the same. Note, however, that objects much hotter than the Sun radiate primarily at ultraviolet wavelengths, and objects much cooler than the Sun radiate primarily at infrared wavelengths. In these cases, visual luminosity represents only a small part of the bolometric luminosity. Luminosity generally means bolometric luminosity, abbreviated L.

The most basic method of estimating luminosity derives from the measurement of distance. A faint light in the night may be a candle a hundred meters away, a streetlight a few kilometers away, or a brilliant lighthouse beacon 100 kilometers away. Once we know the distance to an object, we can determine its absolute brightness. This method becomes less accurate for very distant stars. For one thing, parallax distance measures become unreliable beyond about 1000 parsecs. More important, the space between stars contains a thin haze of dust that dims starlight over larger distances. Just as smog might make it difficult to estimate the distance to a distant mountain range, an unknown amount of interstellar material complicates estimates of stellar luminosity. Since interstellar dust reduces the apparent brightness of a star, it results in an underestimate of the luminosity.
 

Astropedia Image
Hertzsprung-Russell diagram showing color and size of stars. Click here for original source URL.

The luminosity, the distance, and the apparent brightness of an object are all interrelated. If we know any two of these quantities, we can estimate the third — they are related by the inverse square law. If F is the apparent brightness, or flux, of the star, d is the distance, and L is the luminosity, then a star of a known luminosity and distance will have a flux, F = L / 4 π d2. Rearranging this equation, knowing the flux from a star and its distance, the luminosity can be calculated, L = 4 π F d2. These calculations are basic to stellar astronomy.
 

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Schematic for calculating the parallax of a star. Click here for original source URL.

Here are some examples. If two stars have the same apparent brightness but one is three times more distant than the other (as determined by a parallax measurement of the two stars), then the more distant star has nine times the luminosity of the nearer star. Alternatively, if two stars have equal luminosity and one appears to be four times fainter than the other (this is the case where we might have evidence that both stars are like the Sun), then the fainter star is twice as distant as the brighter one. Or, if two stars have equal distance (this might be a case of binary stars or stars in a cluster), then the star that appears five times brighter is five times more luminous. The situation where stars are at roughly equal distances (compared to their distance from the Earth) gives astronomers a rare opportunity. For stars in pairs, multiples or clusters, their relative apparent brightness is a good guide to their relative luminosities.