Standard Candles
Imagine an "on" light-bulb. Now imagine a sphere around the bulb. The sphere completely contains the bulb, so all of the light output by the bulb is received by the sphere. Regardless of the size of the sphere, it receives the same amount of energy. This energy is called the bulb's luminosity, measured in Watts, and equal (if including heat) to the Watt rating of the bulb.
But now imagine that you were an ant of the inside of the sphere. If the
sphere expanded, you would see the bulb become fainter. This is because, while
the surface area of the sphere is increasing the area of your pupil is not, so
the fraction of the total light you receive is the ratio of the area of your
pupil to the area of the sphere. One can express this situation
mathematically.
| Light hitting pupil | Area of Pupil | Area of Pupil | ||
| ------------- | = | ------------- | = | ------------- |
| Total Light | Area of sphere | 4*pi*radius^2 |
If we divide the light we see by the area of the pupil, we have the
flux, which is simply luminosity / (4*pi*radius^2). Of course, the
radius of the sphere is simply our distance from the bulb, so we can right the
distance as a function of flux and luminosity
distance = sqrt[luminosity/(4*pi*flux)]
There are a handful of astronomical objects which behave much like light bulbs. We can estimate their "Watt rating" via other physical properties, and measure their flux to determine their distance. Such objects are called Standard Candles.
- Cepheids: The historical import of Cepheid variables cannot be overstated.
In the early part of this century, Henrietta Leavitt, at Harvard College
Observatory noticed a very interesting trend in particular variable stars which
were similar in property to Delta Cephei, the fourth brightest star in the
constellation Cepheus. She noticed that there was a correlation between the
period of the brightness variation, and the brightness itself: the brighter the
star, the longer its period. This is called the Period-Luminosity
Relation. Using parallax distances to nearby Cepheids, and their fluxes,
we can determine their absolute luminosity of those stars. Using these local
stars as calibrators, we can use the P-L relation to determine the absolute
luminosity of any Cepheid. By measuring its flux and period, we can determine
its distance, using the method above.
Perhaps the most important astronomical work of the century before World War II
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