The Stellar Magnitude Scale
One of the most common terms that you will encounter in astronomy is stellar magnitude. It is the scale astronomers use to measure the brightness of all astronomical objects from stars and planets to distant galaxies and quasars.
It is something that every keen astronomer should get to grips with, and this post will help you do just that.
Stellar Magnitude Definition
Stellar magnitude is the scale used by astronomers to measure an astronomical object’s brightness.
Unlike many other measurement scales where larger numbers imply something is bigger or better, the stellar magnitude scale is the opposite. The lower the number, the brighter the object; extending into negative numbers for the most brilliant of objects.
For every 5 steps along the magnitude scale, the brightness will change by exactly 100 times. This means that for each step along the magnitude scale, the brightness of the object changes by a factor of approximately 2.512.
For example, a magnitude 1 star is exactly 100 times brighter than a magnitude 6 star.
Origin of the Stellar Magnitude Scale
The origins of the stellar magnitude scale date back to ancient Greece. You can find the first use of the term ‘magnitude’ to describe the brightness of stars in Ptolemy’s Almagest, dated circa 150 AD.
The use of the magnitude scale almost certainly precedes Ptolemy, however, its exact origin cannot be pinpointed and is often attributed, perhaps incorrectly, to another ancient Greek astronomer Hipparchus (circa 190 to 120 BC).
Hipparchus (left) and Ptolemy (right) developed and used the earliest known stellar magnitude scale. Public domain
The original scale divided the stars up into six magnitudes, or brightnesses, from 1 to 6. The brightest stars were classed as 1st magnitude, stars not quite as bright 2nd magnitude, then 3rd, and so on, up to 6th magnitude stars at the limit of human vision.
Star brightness in ancient Greece could only be measured with the naked eye, making this early magnitude scale subjective and not at all precise.
It wasn’t until the middle of the 19th century that English astronomer Norman Robert Pogson provided a more rigorous definition.
Pogson standardised the scale so that every five steps in magnitude changed the brightness by exactly 100 times. This modification meant that each increment along the scale changed the brightness by a factor of approximately 2.512.
For example, a magnitude 2 star is 2.512 times brighter than a magnitude 3 star and a magnitude 1 star is 2.512 times brighter than a magnitude 2 star, and so on.
This number became known as Pogson’s ratio and is still in use today.
Norman Robert Pogson (1829-1891) is best known for developing the stellar magnitude system. Public domain
Pogson’s revised stellar magnitude scale needed a set point to calibrate the rest of the scale. Initially, the North Star, Polaris, was chosen to represent magnitude +2.0.
However, the discovery that Polaris was a variable star meant that a more stable set-point was needed.
This time the bright star Vega was selected to represent magnitude 0.0 and the rest of the scale now extended from this point.
With this new definition, new set-point, and more accurate methods of measuring star brightness, the stellar magnitude system was now more robust and reliable.
Reclassification of the stars using this new system resulted in the need to assign some of the brightest stars with zero or even negative magnitude values.
It was also necessary to extend the scale beyond the 6th magnitude to include fainter objects only visible through binoculars or telescopes.
The stellar magnitude scale is now open-ended in both directions.
The Sun shines with a brightness of magnitude -26.7, whereas the faintest objects detected by the Hubble Space Telescope have a magnitude of +31.0, which is incredibly faint.
Hubble Space Telescope is capable of imaging the faintest astronomical objects, by Juan Carlos. Public Domain Mark 1.0
Apparent Magnitude
The brightness of an astronomical object, when viewed from the Earth, is known as its apparent magnitude.
It is the magnitude value that will be the most useful to you when viewing the night sky as it represents the brightness of objects as they appear to you.
Knowing an astronomical object’s apparent magnitude will help you understand if the object is bright, barely visible to the naked eye, or if you will need binoculars or a telescope to see it.
Limiting Stellar Magnitude
The apparent magnitude of the faintest object you can see in the night sky with your naked eye or with a telescope is known as the limiting magnitude.
Under a very dark moonless sky and with a fully dark adapted pupil, the unaided human eye can see stars as faint as about magnitude +6.5. At this limiting magnitude, it is possible to see a few thousand stars.
With binoculars or a small telescope, the number of stars you can see increases dramatically to a few hundred thousand or more!
The larger the aperture of the telescope, the more light it can gather, and the fainter the limiting magnitude becomes, allowing you to see more stars.
The following table shows you just how many more stars you can see at each magnitude step.
| Magnitude range | Cumulative number of visible stars |
|---|---|
|
-1.50 to -0.51 |
2 |
|
-0.50 to +0.49 |
8 |
|
+0.50 to +1.49 |
22 |
|
+1.50 to +2.49 |
93 |
|
+2.50 to +3.49 |
283 |
|
+3.50 to +4.49 |
893 |
|
+4.50 to +5.49 |
2,822 |
|
+5.50 to +6.49 |
8,768 |
|
+6.50 to +7.49 |
26,533 |
|
+7.50 to +8.49 |
77,627 |
|
+8.50 to +9.49 |
217,689 |
|
+9.50 to +10.49 |
626,883 |
| Magnitude range | Cumulative number of visible stars |
|---|---|
|
-1.50 to -0.51 |
2 |
|
-0.50 to +0.49 |
8 |
|
+0.50 to +1.49 |
22 |
|
+1.50 to +2.49 |
93 |
|
+2.50 to +3.49 |
283 |
|
+3.50 to +4.49 |
893 |
|
+4.50 to +5.49 |
2,822 |
|
+5.50 to +6.49 |
8,768 |
|
+6.50 to +7.49 |
26,533 |
|
+7.50 to +8.49 |
77,627 |
|
+8.50 to +9.49 |
217,689 |
|
+9.50 to +10.49 |
626,883 |
If you live in an area that suffers from light pollution, the limiting stellar magnitude may be around +3.0 or +4.0.
This unwanted light significantly limits the number of stars you can see to just a few hundred. It is one of the main reasons why you should try to seek darker skies to improve your viewing conditions.
Apparent Magnitude Examples
Listed below are the apparent magnitudes of some important astronomical objects.
The list will give you an idea of what is visible with the naked eye, binoculars, or a 150 mm telescope aperture.
Remember, the lower the number, the brighter the object appears.
| Astronomical object | Apparent magnitude |
|---|---|
|
Sun |
-26.7 |
|
Full Moon |
-12.9 |
|
Venus |
-4.9 |
|
Jupiter |
-2.9 |
|
Mars |
-2.9 |
|
Mercury |
-2.5 |
|
Sirius (the brightest star in the night sky) |
-1.46 |
|
Saturn |
-0.55 |
|
Vega |
+0.03 |
|
Polaris – The North Star |
+1.98v |
|
Limit in a typical urban light-polluted sky |
+3.0 |
|
Andromeda galaxy |
+3.44 |
|
Orion Nebula |
+4.0 |
|
Uranus |
+5.38 |
|
M13 globular cluster in Hercules |
+5.8 |
|
Naked eye limit, under ideal dark skies |
+6.5 |
|
Ceres (dwarf planet) |
+6.6 |
|
Neptune |
+7.7 |
|
Titan (Saturn’s largest moon) |
+8.1 |
|
Limit of 10×50 binoculars, under ideal dark skies |
+9.5 |
|
Proxima Centauri (closest star to Earth) |
+11.05 |
|
Triton (Neptune’s largest moon) |
+13.4 |
|
Pluto (dwarf planet) |
+13.65 |
|
Titania (Uranus’ largest moon) |
+13.9 |
|
Approximate limit of a 150 mm (6″) telescope |
+14.0 |
| Astronomical object | Apparent magnitude |
|---|---|
|
Sun |
-26.7 |
|
Full Moon |
-12.9 |
|
Venus |
-4.9 |
|
Jupiter |
-2.9 |
|
Mars |
-2.9 |
|
Mercury |
-2.5 |
|
Sirius (the brightest star in the night sky) |
-1.46 |
|
Saturn |
-0.55 |
|
Vega |
+0.03 |
|
Polaris – The North Star |
+1.98v |
|
Limit in a typical urban light-polluted sky |
+3.0 |
|
Andromeda galaxy |
+3.44 |
|
Orion Nebula |
+4.0 |
|
Uranus |
+5.38 |
|
M13 globular cluster in Hercules |
+5.8 |
|
Naked eye limit, under ideal dark skies |
+6.5 |
|
Ceres (dwarf planet) |
+6.6 |
|
Neptune |
+7.7 |
|
Titan (Saturn’s largest moon) |
+8.1 |
|
Limit of 10×50 binoculars, under ideal dark skies |
+9.5 |
|
Proxima Centauri (closest star to Earth) |
+11.05 |
|
Triton (Neptune’s largest moon) |
+13.4 |
|
Pluto (dwarf planet) |
+13.65 |
|
Titania (Uranus’ largest moon) |
+13.9 |
|
Approximate limit of a 150 mm (6″) telescope |
+14.0 |
As you can see, many of the planets shine more brightly than any of the stars and often appear like beacons in the night sky.
The planet Uranus is also visible to the naked eye. It has an apparent magnitude of +5.38, so it is faint but possible for you to spot under a dark moonless sky. Binoculars will reveal it more clearly as a greenish-looking point of light.
Neptune, the Solar System’s most distant planet, is visible with binoculars at magnitude +7.7.
Neptune, the most distant planet in the Solar System, is within reach of binoculars, by Marc Van Norden. CC BY 2.0
Through binoculars, Neptune will only ever appear as a small blue point of light, but the fact that you can view the most distant planet in the Solar system with just binoculars, I think, is remarkable.
Stellar Magnitude on Star Charts
Stars on star charts are typically represented by white circles. The size of this circle will denote its brightness; with larger circles representing brighter stars and small circles fainter stars.
Your star chart will usually have a small key or legend to let you know what apparent magnitude each circle size represents.
Star charts will typically only show stars as faint as 5th or 6th magnitude, which is the limit of human vision under clear dark skies.
Absolute Magnitude
So far, I have only talked about an astronomical object’s apparent magnitude or how bright it appears to us here on Earth. This value is helpful for backyard astronomy, but it is not very useful for developing a deeper understanding of the objects you are viewing.
Astronomers are also interested in an object’s absolute magnitude, which can help astronomers understand an object’s intrinsic luminosity. The absolute magnitude is defined as the apparent brightness of an object when viewed from a fixed distance of 10 parsecs or 32.6 light-years away.
With this in mind, you might ask, what is the absolute magnitude of our Sun?
Well, it turns out the Sun is a very unremarkable star. When viewed from 32.6 light-years away,
The Sun would appear as a magnitude +4.83 star in the night sky, a rather faint star to the naked eye and not very impressive in stellar terms.
A more impressive example is the star Rigel in the constellation Orion. Despite being 860 light-years away from Earth, it still has an apparent magnitude of +0.13, making it one of the brightest stars in the night sky.
However, if Rigel were only 32.6 light-years away, then its absolute magnitude would be an astonishing -7.84 and would be easily visible during the day.
Summary
I hope that you are now able to understand some of the quirks of the stellar magnitude scale. Below are the main points that you should take away.
- The stellar magnitude scale runs backwards
- Bright objects have low or even negative magnitude values
- Faint objects have higher positive magnitude values
- Each increment along the scale changes the brightness ≈2.512 times (or 100 times every five magnitudes).
- The magnitude scale is open-ended in both directions.
- Apparent magnitude describes the brightness of an object as viewed from Earth.
- The limiting magnitude is the faintest object you can observe, either through your eyes or through a telescope.
- The naked eye can see stars as faint as about magnitude +6.5 under ideal dark sky conditions.
- Absolute magnitude is the brightness of an object when viewed from 32.6 light-years away; it indicates an object’s intrinsic brightness.
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