Star Light ... Star Bright ...

Until recently, even with the best of telescopes, stars showed up as a single point of light instead of a disk.  This is because stars are so incredibly far away.  However, even a youngster notices a vast range in the brightness of stars.  Some stars are bright, many are dim.  The Greek, Hipparchus, was the first to assign a number to a star's brightness.  He said the brightest stars were 1 in magnitude and dimmest stars were designated 6 in magnitude.  This system was later revised so that a difference in 5 magnitudes would correspond to a factor of 100 in brightness.  In keeping with the original scale, a magnitude of 6 is considered the eye limit (under best viewing conditions).  As a result of this adjustment, some stars then had magnitudes even brighter than 1 ... so what do you do?  Go to zero!  Even brighter objects become negative.  This explains why the modern magnitude scale seems so bizarre.

Apparent Magnitude - m_v

The brightness of a star (or anything in the sky) as seen from earth is known as the apparent visual magnitude and is given the symbol m_v.  It should be obvious that the sun should top the list.  Using the scale as defined above, the sun has an apparent magnitude of -26.7.  The full moon is about -11, the planet Venus (at its brightest) is about -5.  The brightest star is Sirius (actually Sirius A because it has a companion, Sirius B) is listed at -1.46.  The very best telescopes are able to observe visually to about +30 to +36 on this scale.  Please do not worry (yet) about the last column ... that will come very soon.

The Brightest Stars

Suppose two stars had apparent magnitudes of 2 and 7, respectively.  The first one would be about as bright as Polaris and the second one would not be visible to the naked eye.  In addition, you would know that the first star appears 100 times brighter to us than the second star (since the difference in magnitudes is 5).  If a planet is listed in the newspaper as having a magnitude of -3, it will be 100 times brighter than the first star (5 magnitudes again) and 10,000 times brighter than the second star (100x100).

There is a difference of about 25 magnitudes when comparing the apparent magnitudes of the sun with Sirius.  This means the sun appears 10,000,000,000 (100x100x100x100x100x100) times brighter to us than Sirius.

Why does a star appear bright?

The observed brightness of a star really depends mainly on two variables:

• the light output of the star (luminosity)

• the distance to that star

• and if there is anything in between (like a nebula) which might obscure the light ... but we will ignore that factor here.

To illustrate the point, you know that light bulbs come in different wattages.  The higher the wattage, the more light it emits intrinsically.   We say that a 100 watt light bulb is more luminous than a 25 watt light bulb.  However, the brightness you observe also depends on how far away the light bulb is from you.  In fact, you can make a 25 watt light bulb appear much brighter than a 100 watt light bulb by placing the 25 watt bulb very close to you, and the 100 watt bulb very far away.  The same thing can happen with stars.  For that reason, the apparent magnitude is generally a useless number.  It is, however, a very easy number to obtain.  Just aim a light meter on the star and get a digital readout.

So how do astronomers sort this out?  Fortunately, the laws governing light intensity are well understood.  It acts very much like gravity, ... following an inverse square law.  If you double your distance from a light source, the brightness decreases by a factor of 4.  With this understanding, it is possible to predict a star's brightness at any distance provided you know its brightness at one known distance.  Astronomers can't pick up stars and move them, but they can do it on paper.  They have developed another quantity known as the absolute (visual) magnitude which is given the symbol M_v.

The absolute magnitude is the calculated magnitude of a star if seen from a distance of 10 parsecs.  If all stars are lined up at the same distance (on paper), then any numeric differences would have to come from luminosity differences (light output) of the stars.  It is as if we could take all the light bulbs (of various wattages) and move them all 100 yards away.  Now if a light appears bright, it is because it has a higher wattage.

Look at the table above and examine the column marked Absolute Magnitude.  You will see that our sun drops to a puny +4.85.  This means if you place our sun 10 parsecs away, it is not very impressive (just barely visible).  Now compare the light output of our sun with the star, Arcturus.  The sun is +4.85 (can we call this +5 ?) and Arcturus is -.3 (can we call this zero ?).  Arcturus would appear pretty bright if seen from 10 parsecs.  Arcturus has an absolute magnitude 5 greater than our sun (remember, the more negative, the brighter).  By definition (see above), this means Arcturus would appear 100 times brighter if both stars were 10 parsecs away.  This can only happen if Arcturus is 100 times more luminous than our sun.  Wow!  That star is putting out a lot of light!  Now compare the light output of Arcturus and Antares.  You can see that Antares is 5 magnitudes higher than Arcturus (Arcturus is about 0 and Antares is about -5).  Antares is 100 times more luminous than Arcturus ... making it 100x100 = 10,000 times more luminous than our sun.  Double Wow!! If you look at the chart, you will see that there are stars that put out even more light than Antares.  No wonder why these stars made the list.  These are cosmic lighthouses which can be seen from far away.  In fact, when you look at this chart, you might get the impression that our sun is totally outmatched by all the stars in the sky, ... after all, it has the lowest luminosity of all the stars on the chart.  Stay tuned ...

Calculating Absolute Magnitude

Astronomers use the following formula to calculate the absolute magnitude of a star:

You can see that all you need is two quantities: apparent magnitude (m_v) which is easy to get, and the distance (in parsecs).  You will not be required to do any calculations with this formula on any tests.

Once the absolute magnitude of a star is known, astronomers usually convert this to a number which compares the light output to our sun.  That is, we treat our sun as if it were the standard (with a luminosity of 1).  For example, consider a star with an absolute magnitude of 0 (like Arcturus).  Since this star is 5 magnitudes greater, it also means it gives off 100 times more light than the sun.  Therefore, Arcturus is often listed in books as having a luminosity of 100 x Sol  (or 100 Sol or 100 ʘ).  In contrast, any star with an absolute magnitude of +10 is listed with a luminosity of .01 Sol (1/100 Sol).

Want to get technical? (I don't!) To convert any magnitude difference to a brightness difference, take 2.512 and raise it to that power.  That is, if the difference in magnitudes is only 3, the brightness difference is 2.512³ ≈ 16.  For example, if a star is listed as having an absolute magnitude of 2.85, you would know that has a luminosity of 6.3 Sol.  How?  The absolute magnitude difference is 2 (4.85-2.85), ... therefore 2.512² ≈ 6.3.  Another example: look at the chart below and compare the stars Alpha Cen A with Groombridge 34 B.  You will see that their absolute magnitudes differ by exactly 9 (13.37 - 4.37).  This means that Alpha Cen A is about 3,980 as luminous as Groombridge 34 B (2.512⁹).  Don't worry, I won't be asking questions like this on the test.  The point is, if you know a star's absolute magnitude, you can compare its light output to our sun.

What you see is NOT what you get ...

Now we examine another chart, ... a list of the closest stars to us (see below).  Examine the absolute magnitudes and compare them with the sun.  I'll save you the leg work.  The sun is +4.85 (OK ... +5) and the average of the list is about +10.  From this chart you can see that the sun is about 5 magnitudes higher than our close neighbors (or they are 5 magnitudes dimmer).  That is to say, ... our sun puts out about 100 times more light than the stars around us.  When we looked at the first chart, our sun looked like a loser ... now it appears one of the big winners (in terms of luminosity).  This is because most stars in the sky (by far) are low luminosity stars.  Even though they are very close to us, their light output is so low that most are not even visible to the naked eye (see m_v).  The stars that made the first list are actually quite rare, but they draw attention to themselves because of their incredible luminosities.  It is as if you stood in a huge crowd of people and you were 6' 8".  You would certainly peer over most people but you would also be able to make out the very few 7' 5" people in the crowd (even if they were very far away).

The Closest Stars

                                                                                                                                     Average = +10.2
©Jim Mihal 2004, 2014- all rights reserved