StellarMagnitudes

A basic observable quantity for a star is its brightness. Because stars can have a very broad range of brightness, as we have discussed, astronomers commonly introduce a logarithmic scale called a magnitude scale to classify the brightness. Here we take another look at this.

### The Magnitude Scale

The magnitudes m1 and m2 for two stars are related to the corresponding brightnesses b1 and b2 through the equation

where "log" means the (base-10) logarithm of the corresponding number; that is, the power to which 10 must be raised to give the number. Because this relation is logarithmic, a very large range in brightnesses corresponds to a much smaller range of magnitudes; this is a major utility of the magnitude scale.

### Apparent Magnitude

Apparent Visual Magnitudes

Object Apparent Visual
Magnitude

Sirius (brightest star) -1.5
Venus (at brightest) -4.4
Full Moon -12.6
The Sun -26.8
Faintest naked eye stars 6-7
Faintest star visible from
Earth telescopes
~25
Faintest star visible from
Hubble Space Telescope
~?
The preceding equation gives us a way to relate the magnitudes and brightnesses of two object, but there are several ways in which we could specify the brightness and this leads to several different magnitudes that astromers define. One important distinction is between whether we are talking about the apparent brightness of an object, or its "true" brightness. The former is a convolution of the true brightness and the effect of distance on the observed brightness, because the intensity of light from a source decreases as the square of the distance (the inverse square law).

The apparent magnitude of an object is the "what you see is what you get" magnitude. It is determined using the apparent brightness as observed, with no consideration given to how distance is influencing the observation. Obviously the apparent magnitude is easy to determine because we only need measure the apparent brightness and convert it to a magnitude with no further thought given to the matter. However, the apparent magnitude is not so useful because it mixes up the intrinsic brightness of the star (which is related to its internal energy production) and the effect of distance (which has nothing to do with the intrinsic structure of the star).

The apparent magnitude of various objects determined using light from the visible part of the spectrum is given in the adjacent table.

### Absolute Magnitude

Clearly, a star that is very bright in our sky could be bright primarily because it is very close to us (the Sun, for example), or because it is rather distant but is intrinsically very bright (Betelgeuse, for example). It is the "true" brightness, with the distance dependence factored out, that is of most interest to us as astronomers. Therefore, it is useful to establish a convention whereby we can compare two stars on the same footing, without variations in brightness due to differing distances complicating the issue.

Astronomers define the absolute magnitude to be the apparent magnitude that a star would have if it were (in our imagination) placed at a distance of 10 parsecs (which is 32.6 light years) from the Earth. I can do this if I know the true distance to the star because I can then use the inverse square law to determine how its apparent brightness would change if I moved it from its true position to a standard distance of 10 parsecs. There is nothing magic about the standard distance of 10 parsecs. We could as well use any other distance as a standard, but 10 parsecs is the distance astronomers have chosen for this standard. A common convention, and one that we will mostly follow, is to use a lower-case "m" to denote an apparent magnitude and an upper-case "M" to denote an absolute magnitude.

Notice the very important point that I can determine the apparent magnitude m of a star simply by measuring how bright it appears to be, but to determine the absolute magnitude M the distance to the star must also be known. As we shall see, determining distances to stars is a quite non-trivial matter in the general case.

### The Influence of Wavelength

You might think that introducing the apparent and absolute magnitudes would resolve ambiguities about what we mean when we refer to the brightness of a star, but there is a further complication. The brightness of an object (whether apparent or absolute) depends on the wavelength at which we observe it, as we saw clearly in the discussion of radiation laws.

Generally, astronomical observations are made with an instrument that is sensitive to a particular range of wavelengths. For example, if we observe with the naked eye, we are sensitive only to the visible part of the spectrum, with the most sensitivity coming in the yellow-green portion of that. On the other hand, if we use normal photographic film to record our observation, it is more sensitive to blue light than to yellow-green light.

Thus, to be precise in discussing brightness or the associated magnitude, we must specify which region of the electromagnetic spectrum our instrument is most sensitive to.

### The Brightest Stars

Here is a list of the 20 brightest stars in the sky:

The 20 Brightest Stars in the Sky

Common
Name
Luminosity
Solar Units
Distance
LY
Spectral
Type
Proper Motion
arcsec / year
R. A.
hours min
Declination
deg min

Sirius 40 9 A1V 1.33 06 45.1 -16 43
Canopus 1500 98 F01 0.02 06 24.0 -52 42
Alpha Centauri 2 4 G2V 3.68 14 39.6 -60 50
Arcturus 100 36 K2III 2.28 14 15.7 +19 11
Vega 50 26 A0V 0.34 18 36.9 +38 47
Capella 200 46 G5III 0.44 05 16.7 +46 00
Rigel 80,000 815 B8Ia 0.00 05 12.1 -08 12
Procyon 9 11 F5IV-V 1.25 07 39.3 +05 13
Betelgeuse 100,000 500 M2Iab 0.03 05 55.2 +07 24
Achernar 500 65 B3V 0.10 01 37.7 -57 14
Beta Centauri 9300 300 B1III 0.04 14 03.8 -60 22
Altair 10 17 A7IV-V 0.66 19 50.8 +08 52
Aldeberan 200 20 K5III 0.20 04 35.9 +16 31
Spica 6000 260 B1V 0.05 13 25.2 -11 10
Antares 10,000 390 M1Ib 0.03 16 29.4 -26 26
Pollux 60 39 K0III 0.62 07 45.3 +28 02
Fomalhaut 50 23 A3V 0.37 22 57.6 -29 37
Deneb 80,000 1400 A2Ia 0.00 20 41.4 +45 17
Beta Crucis 10,000 490 B0.5IV 0.05 12 47.7 -59 41
Regulus 150 85 B7V 0.25 10 08.3 +11 58

Source: Fraknoi, Morrison, and Wolff, Appendix 11

Here is a list of the 314 stars brighter than apparent magnitude 3.55 in both hemispheres.