A star's power output across all wavelengths is called its bolometric luminosity. Astronomers in practice also measure an object's luminosity in specific wavebands so that we can discuss an object's X-ray or visible luminosities for example. This is also used to measure a star's colour as described on the next page. Our Sun has a luminosity of 3. This approach is convenient as the luminosity of stars varies over a huge range from less than 10 -4 to about 10 6 times that of the Sun so an order of magnitude ratio is often sufficient.
As we have seen in the section on spectroscopy, we can approximate the behaviour of stars as black body radiators. Fundamentally there are just two key properties - the effective temperature, T eff and the size of the star, its radius, R. Let us look briefly at each of these:. Temperature : A black body radiates power at a rate related to its temperature - the hotter the black body, the greater its power output per unit surface area. An incandescent or filament light bulb is an everyday example.
As it gets hotter it gets brighter and emits more energy from its surface. The relationship between power and temperature is not a simple linear one though. The power radiated by a black body per unit surface area is given varies with the fourth power of the black body's effective temperature, T eff. As a star is not a perfect black body we can approximate this relationship as:.
This relationship helps account for the huge range of stellar luminosities. A small increase in effective temperature can significantly increase the energy emitted per second from each square metre of a star's surface. Size radius : If two stars have the same effective temperature but one is larger than the other it has more surface area.
The power output per unit surface area is fixed by equation 4. This becomes apparent when we plot stars on an HR diagram. Using equation 4. Large differences in brightness actually appear much smaller using this scale, Rothstein said. Light-sensitive charged-coupled devices CCDs inside digital cameras measure the amount of light coming from stars, and can provide a more precise definition of brightness. Using this scale, astronomers now define five magnitudes' difference as having a brightness ratio of Vega was used as the reference star for the scale.
Initially it had a magnitude of 0, but more precise instrumentation changed that to 0. When taking Earth as a reference point, however, the scale of magnitude fails to account for the true differences in brightness between stars. The apparent brightness, or apparent magnitude, depends on the location of the observer. Different observers will come up with a different measurement, depending on their locations and distance from the star.
Stars that are closer to Earth, but fainter, could appear brighter than far more luminous ones that are far away. The solution was to implement an absolute magnitude scale to provide a reference between stars. To do so, astronomers calculate the brightness of stars as they would appear if it were Another measure of brightness is luminosity, which is the power of a star — the amount of energy light that a star emits from its surface.
It is usually expressed in watts and measured in terms of the luminosity of the sun. For example, the sun's luminosity is trillion trillion watts. One of the closest stars to Earth, Alpha Centauri A , is about 1. To figure out luminosity from absolute magnitude, one must calculate that a difference of five on the absolute magnitude scale is equivalent to a factor of on the luminosity scale — for instance, a star with an absolute magnitude of 1 is times as luminous as a star with an absolute magnitude of 6.
While the absolute magnitude scale is astronomers' best effort to compare the brightness of stars, there are a couple of main limitations that have to do with the instruments that are used to measure it. See Technical Requirements in the Orientation for a list of compatible browsers. How bright will the same light source appear to observers fixed to a spherical shell with a radius twice as large as the first shell?
Since the radius of the first sphere is d, and the radius of the second sphere would be 2 x d This equation is not rendering properly due to an incompatible browser. Since the same total amount of light is illuminating each spherical shell, the light has to spread out to cover 4 times as much area for a shell twice as large in radius. The light has to spread out to cover 9 times as much area for a shell three times as large in radius. So, a light source will appear four times fainter if you are twice as far away from it as someone else, and it will appear nine times fainter if you are three times as far away from it as someone else.
Thus, the equation for the apparent brightness of a light source is given by the luminosity divided by the surface area of a sphere with radius equal to your distance from the light source, or. The apparent brightness is often referred to more generally as the flux, and is abbreviated F as I did above.
In practical terms, flux is given in units of energy per unit time per unit area e. Since luminosity is defined as the amount of energy emitted by the object, it is given in units of energy per unit time [e. The distance between the observer and the light source is d, and should be in distance units, such as meters. You are probably familiar with the luminosity of light bulbs given in Watts e. This value is usually referred to as the solar constant. Skip to main content.
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