A basic observable quantity for a star is its brightness. Because
stars can have a very broad range of brightness, astronomers commonly
introduce a logarithmic scale called a
magnitude scale to classify the
The Magnitude Scale
The magnitudes m1 and m2 for two stars are related to the
corresponding brightnesses b1 and b2 through the
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
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).
Apparent Visual Magnitudes
|Faintest naked eye
Hubble Space Telescope
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
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.
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
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
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
distances to stars is a quite non-trivial matter in the general
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
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. We address this issue in the next section.
The Brightest Stars
Here is a list of the 20 brightest stars in the sky:
The 20 Brightest Stars in the Sky
arcsec / year
Morrison, and Wolff, Appendix 11
Here is a
of the 314 stars brighter than apparent magnitude 3.55 in both hemispheres.