The former is typically represented in terms of solar radii, while the latter is represented in kelvins, but in most cases neither can be measured directly. Both can be measured with great accuracy in certain cases, with cool supergiants often having large angular diameters, and some cool evolved stars having masers in their atmospheres that can be used to measure the parallax using VLBI.
However for most stars the angular diameter or parallax, or both, are far below our ability to measure with any certainty. Since the effective temperature is merely a number that represents the temperature of a black body that would reproduce the luminosity, it obviously cannot be measured directly, but it can be estimated from the spectrum. Extinction can only be measured directly if the actual and observed luminosities are both known, but it can be estimated from the observed colour of a star, using models of the expected level of reddening from the interstellar medium.
In the current system of stellar classification, stars are grouped according to temperature, with the massive, very young and energetic Class O stars boasting temperatures in excess of 30,K while the less massive, typically older Class M stars exhibit temperatures less than 3,K.
Because luminosity is proportional to temperature to the fourth power, the large variation in stellar temperatures produces an even vaster variation in stellar luminosity. Because the luminosity depends on a high power of the stellar mass, high mass luminous stars have much shorter lifetimes. For example, the luminosity of Sirius is about 25 times that of the Sun.
In a later chapter, we will see that if we can measure how much energy a star emits and we also know its mass, then we can calculate how long it can continue to shine before it exhausts its nuclear energy and begins to die. Astronomers are careful to distinguish between the luminosity of the star the total energy output and the amount of energy that happens to reach our eyes or a telescope on Earth.
Stars are democratic in how they produce radiation; they emit the same amount of energy in every direction in space. Consequently, only a minuscule fraction of the energy given off by a star actually reaches an observer on Earth. If you look at the night sky, you see a wide range of apparent brightnesses among the stars.
Most stars, in fact, are so dim that you need a telescope to detect them. If all stars were the same luminosity—if they were like standard bulbs with the same light output—we could use the difference in their apparent brightnesses to tell us something we very much want to know: how far away they are. Imagine you are in a big concert hall or ballroom that is dark except for a few dozen watt bulbs placed in fixtures around the walls. Since they are all watt bulbs, their luminosity energy output is the same.
But from where you are standing in one corner, they do not have the same apparent brightness. Those close to you appear brighter more of their light reaches your eye , whereas those far away appear dimmer their light has spread out more before reaching you.
In this way, you can tell which bulbs are closest to you. In the same way, if all the stars had the same luminosity, we could immediately infer that the brightest-appearing stars were close by and the dimmest-appearing ones were far away. To pin down this idea more precisely, recall from the Radiation and Spectra chapter that we know exactly how light fades with increasing distance. The energy we receive is inversely proportional to the square of the distance.
If, for example, we have two stars of the same luminosity and one is twice as far away as the other, it will look four times dimmer than the closer one. If it is three times farther away, it will look nine three squared times dimmer, and so forth. Alas, the stars do not all have the same luminosity. Actually, we are pretty glad about that because having many different types of stars makes the universe a much more interesting place. But this means that if a star looks dim in the sky, we cannot tell whether it appears dim because it has a low luminosity but is relatively nearby, or because it has a high luminosity but is very far away.
To measure the luminosities of stars, we must first compensate for the dimming effects of distance on light, and to do that, we must know how far away they are. Distance is among the most difficult of all astronomical measurements. We will return to how it is determined after we have learned more about the stars. For now, we will describe how astronomers specify the apparent brightness of stars.
Around B. When I say apparent brightness , I mean how bright the star appears to a detector here on Earth. The luminosity of a star, on the other hand, is the amount of light it emits from its surface.
The difference between luminosity and apparent brightness depends on distance. Another way to look at these quantities is that the luminosity is an intrinsic property of the star, which means that everyone who has some means of measuring the luminosity of a star should find the same value. However, apparent brightness is not an intrinsic property of the star; it depends on your location. So, everyone will measure a different apparent brightness for the same star if they are all different distances away from that star.
For an analogy with which you are familiar, consider again the headlights of a car. When the car is far away, even if its high beams are on, the lights will not appear too bright. However, when the car passes you within 10 feet, its lights may appear blindingly bright. To think of this another way, given two light sources with the same luminosity, the closer light source will appear brighter.
However, not all light bulbs are the same luminosity. If you put an automobile headlight 10 feet away and a flashlight 10 feet away, the flashlight will appear fainter because its luminosity is smaller.
Stars have a wide range of apparent brightness measured here on Earth. The variation in their brightness is caused by both variations in their luminosity and variations in their distance.
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