The Universe Revealed

Stellar Luminosity

Stellar Luminosity

The reason I'm bringing this up is because it's important to an understanding of astronomy.

Of all of the things in astronomy, luminosity is one of the most important characteristics of any object in space. The reason this is so important is because it allows astronomers to calculate the distance to a star using the concept of magnitude.

But, first we must define what luminosity is.
The definition of luminosity is the amount of electromagnetic energy that a celestial body radiates over a given period or unit of time. There are two forms: visual and bolometric. Visual is what its name indicates: visual light only. Bolometric means the total radiant energy, including infrared, which is essentially heat. Most star luminosities are given in comparison to our Sun's.

What's really neat is that a star's luminosity can be determined by measuring its size and temperature. This is because stars fit into categories based on these two parameters. A star can be considered to behave in the same manner as a black body radiator in which temperature determines how much energy it radiates. By measuring a star's temperature one can determine the star's apparent brightness and distance.

What exactly is a black body radiator? This is an idealized object that is completely opaque and non-reflective and held at a uniform temperature and in thermodynamic equilibrium with its surroundings. A black body at room temperature is black, hence the name. When a black body is heated and begins to radiate electromagnetic energy, it does so across the spectrum. However, as it heats up, the visible spectrum output moves from red through blue emission. In other words, its color is dependent on its temperature. This means that by measuring the color of a black body radiator one can determine its temperature. This concept is the kingpin of determining a star's luminosity.

When you look up at the sky at night, you'll notice that stars have different colors. This is because stars come in different sizes and spectral types. Astronomers took notice of this and created a family category for the different colored stars. This allowed them to come up with a method to determine the distance to nearby stars just by measuring their spectra and brightness.

Luminosity is proportional to temperature to the fourth power. This is due to Boltzmann's equation where  L=σAT (to the 4th power). Luminosity of a black body object equals the Stefan-Boltzmann constant (5.67 x 10 -8 power watts per meter squared per Kelvin degrees the - 4th power) times Area of the body times the temperature to the 4th power. This is important because light from a star changes its brightness due to two factors: distance and surface area. The larger a star is the less bright it will appear at a given luminosity because its radiating energy that's distributed over a larger surface.

To make this calculation make more sense astronomers came up with the idea of magnitude, which is a logarithmic scale of observed visible brightness. There are two magnitudes: apparent and absolute. Absolute magnitude is equal to the apparent magnitude at 10 parsecs distance.

The apparent magnitude is found by calculating the brightness (Fx) for the star of a particular spectral class, and then using the following formula: m = -5 log (Fx / Fx0). Basically, you're comparing the brightness as seen from Earth with the brightness it would have at the reference point of 10 parsecs.
The apparent magnitude m minus absolute magnitude M is equal to 5 times (Log d -1) where d is the distance to the star in parsecs. (m - M = 5 (Log d - 1))

The Sun's apparent magnitude is -27, and the full moon is -13. Venus is -5 and Sirius is -1.5.
Magnitude is a logarithmic value of an object like a star measured in the visible and near infrared spectrum. The apparent magnitude is the brightness as it appears in the night sky from Earth. Absolute magnitude is the intrinsic brightness of a star at 10 parsecs away. It's like a standard candle. The brighter an object appears the lower the value of its magnitude, where a negative magnitude indicates a very bright object like the full moon, which has a magnitude of -13. The more positive the magnitude the less bright it appears. Why is this scale backwards? It's because it's logarithmic.

So, this is how astronomers figured out how to determine how far away some stars are. First, they found the distance to nearby stars by using triangulation. As the Earth moves around the sun, a nearby star changes position compared to its background stars that are much further away. Then, by noting the spectral class of the star, they knew what its apparent luminosity should be. This allowed them to know how the luminosity decreases with distance according to the equations. Once they had the basic chart of star spectral classes, they could measure a star's brightness and then use the equations to determine its distance. Think of it this way. If you had a candle and used a light meter to measure its brightness, then you could move away and measure the brightness fall off. This would show you how the brightness falls off with distance. With this in hand, one could put the candle at any distance within reason, measure its brightness and calculate how far away it was.

Stars are not candles, but once you know from the spectra what the star's brightness should be, you can use your calculation to determine its distance. That's essentially how they do it.

Thanks for reading.