Stars twinkle because of turbulence in the Earth's atmosphere. You can think as the atmosphere being made up of several "layers." Each layer has a different temperature and density. As the light from a star passes through the atmosphere, it is bent by each layer, and we perceive the twinkling.

The bending of the light when it passes from one medium to another, like water to air, or one layer of air to another, is called refraction. Refraction is what makes a straw look bent when you put it in a glass of water. Refraction also makes the stars and the Sun near the horizon look higher in the sky than they really are. In fact, when the Sun is setting, we are seeing the sun's disk when the Sun is already below the horizon!

Image not to scale.

You will notice that stars closer to the horizon twinkle more; this is because there is a lot more atmosphere between you and a star near the horizon than between you and a star in the zenith (the point directly overhead) . You will also notice that planets do not twinkle. Stars are so far away that they appear as points of light, but planets are much closer and their disks can seen through telescopes. The fluctuations in the atmosphere are not large enough to affect the light coming from the planets, the Moon or the Sun.

Absolute Magnitude
When you look at the stars, the first thing you notice is that some are bright and others are faint. Without knowing the distance to a given star, you can't tell whether the star appears bright because it is close or because it is far away but intrinsically bright.

Around 150 B.C., the Greek astronomer Hipparchus assigned numbers to the stars according to how bright they looked to him. He assigned the number 1 to the brightest stars he saw, and called them first magnitude stars. He called stars in the second brightest category second magnitude stars, and so on, until the faintest he could see, which he called sixth magnitude stars. This is the limit of what the human eye can see in dark and clear skies. About 6000 stars of magnitude six and brighter can be seen in the whole sky.

In the 18th century, Herschel, the discoverer of Uranus, noticed that we receive about 100 times more light from a first magnitude star than from a sixth magnitude one. In the 19th century, astronomers took advantage of the invention of photography to quantify the amount of light that we receive from a star, using filters at a specific wavelength band. This technique is called photometry and is still used today to measure the magnitudes of stars. In 1856, Norman Pogson defined a difference of 5 magnitudes to be exactly a ratio of 100 in energy flux (amount of light energy that we receive per second). This means that a first magnitude star is 100 times brighter than a sixth magnitude star. As you can see, it was possible to quantify the magnitude scale because this scale is related to the way our eyes perceive light.

Two stars of the same magnitude put out the same amount of light. A star brighter than another one by one magnitude puts out 2.5 times more light, it doesn't matter whether one is magnitude 3 and the other magnitude 4, or whether one is magnitude 26 and the other one is magnitude 27. The important point is the difference in the two magnitudes. Of course, Pogson noticed that Hipparchus scale wasn't very accurate. For example, Hipparchus assigned Sirius and Vega a magnitude = 1. These are two very bright stars, but Sirius is in fact brighter than Vega.

Presently, all magnitudes are measured with a photometer mounted on a telescope. The magnitudes do not have to be whole numbers, and the accuracy achieved is 0.001 mag. This means that we can measure light flux differences of a tenth of a percent! Here's a table to give you an idea of what the magnitudes differences mean in terms of how more luminous is the brighter than the fainter star.

The limiting magnitude of modern telescopes with modern detectors, including the Hubble Space Telescope, is about 30. As you can see from the table, these telescopes can see objects 4 billion times fainter than the limiting magnitude of our eyes! If you like math, the last row tells you how to calculate the energy ratio of any two stars whose magnitudes differ by x amount: all you have to do is tell your calculator to raise 2.512 to the x power.

So far, we have only talked about the magnitudes of the stars as seen from Earth. These are called apparent magnitudes because they don't tell us anything about the real, or intrinsic, brightnesses of the stars (our next topic). Astronomers use the symbol mV, or simply V, to denote apparent magnitudes. The V refers to the type of filter they are using, so that they don't get confused with the magnitude measured through a different filter.

Magnitudes can have negative values: the Sun's apparent magnitude is –26.7. Sirius, the brightest star in the sky, has a magnitude of –1.5, and Vega's magnitude is 0.0. The full moon's magnitude is V = –12.6 mag.

Absolute Magnitude
The real value to astronomers is to know the intrinsic brightnesses of the stars. For this, they have to know three things: 1) how bright the stars appear here on Earth, 2) how far away they are, and 3) how much of the starlight is being absorbed by the interstellar medium, which is the "stuff" between the star and Earth (gas and dust). This process is exactly the same as if you were lost in the mountains at night and suddenly you see the light from several houses scattered in the distance. You are tired and hungry and want to get to the closest house, but there is patchy fog and you don't know the wattage of the light bulb of each house. Under these circumstances, there is no way for you to decide which is the nearest house. On the other hand, if the fog is uniform (or if there is no fog) and if you know the watts of the light bulb that each house uses, you may very well determine which is the closest one.

Astronomers have devised various methods to measure distances to the stars and absorption of light by the interstellar medium. Since they also know the apparent magnitudes of the stars, they can determine the intrinsic brightnesses by comparing the stars if they were all placed at the same distance from Earth. It's like trying to decide which light bulb is brighter by placing them all at the same distance from you.

Absolute magnitude is the apparent magnitude that a star would have at a distance of 10 parsecs from Earth. A parsec is a unit for measuring distances in the sky, it is equal to 30,860,000,000,000 km (about 19 trillion miles), or the distance to a star that subtends an angle of 1 second of arc when the baseline is the Eath-Sun distance. One parsec is equal to 3.26 light years.

The symbol for absolute magnitude is MV. Absolute magnitude is related to the luminosity of the star, which is the amount of energy that a star gives off per second. The brightest stars, which are also the hottest, have MV = –10 mag, while the faintest stars (the coolest) have MV = +17 mag. The more luminous stars are about 100 billion times brighter than the dimmest! Our Sun turns out to be an ordinary star, shinning at MV = 4.8 mag. As it turns out, Vega is intrinsically brighter than Sirius, their absolute magnitudes are, respectively, 0.6 and 1.4.

REMEMBER: the more negative the magnitude, the brighter the object. The more positive the magnitude, the dimmer the object.

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