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.
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:
