2.4 The Magnitude Scale
15
The magnitude of an object is dependent not only on the physical characteristics
of that object but also on its distance from the observer, the amount of material
between the observer, the detector used, and the transmission characteristics of the
instrument, which is often determined by a filter. Filters are discussed at length in
Sect. 2.5, but you should be aware that magnitudes should always be quoted as being
in a particular filter band. If they are not, then it is assumed that they are unfiltered
visual magnitudes. Hence, a star or galaxy may be of magnitude 10 in the R band but
of magnitude 12 in the B band. The magnitude of extended and therefore resolved
objects is the integrated magnitude, i.e., the combined light over the whole surface
of the object, and is known as a surface brightness. You should, therefore, allow
more exposure time for extended objects than you would for stellar objects of the
same listed magnitude.
Most magnitude quotes are apparent magnitudes, the brightness as seen from
Earth. An important characteristic of a star is its absolute magnitude, the brightness
of a star at a distance of 10 pc, which hence relates directly to luminosity. Since
brightness drops off with the square of the distance, we can modify (2.5) to determine
absolute magnitude from apparent magnitude and distance:
M = m + 5 − 5 log 10 (d/ pc),
(2.6)
where M is absolute magnitude, m is apparent magnitude, and d is distance in parsecs.
A major challenge in galactic astronomy is the problem of interstellar reddening.
Gas, and in particular the dust between the object being observed and the observer,
will preferentially scatter blue light over red. Hence, an object with more scattering
appears redder. This would not be much of a problem if the material were distributed
uniformly throughout the galaxy (in fact, it would be a major advantage if it were).
However, it is not, so consequently, we need to modify (2.7) to adjust for reddening:
M = m + 5 − 5 log 10 (d/ pc) − A,
(2.7)
where A is the reddening in magnitudes.
Two photometric calibration standards are in common use, Vega and AB. The
Vega system assumes that the star Vega, α Lyra, is of magnitude zero at all wavebands,
which has the advantage that it simplified Pogson’s equation to
m 2 = −2.5 log 10 (F 1 /F 2 ),
(2.8)
so that the magnitude of a star in any filter is just the logarithm of the ratio of its flux
over that of Vega (multiplied by −2.5).
The AB system , unlike the Vega system, is based on calibrated flux measurements.
For completeness, we give the definition of AB magnitude:
m AB = −
5
8
log 10
f v
J y
+ 8.9
(2.9)
15
The magnitude of an object is dependent not only on the physical characteristics
of that object but also on its distance from the observer, the amount of material
between the observer, the detector used, and the transmission characteristics of the
instrument, which is often determined by a filter. Filters are discussed at length in
Sect. 2.5, but you should be aware that magnitudes should always be quoted as being
in a particular filter band. If they are not, then it is assumed that they are unfiltered
visual magnitudes. Hence, a star or galaxy may be of magnitude 10 in the R band but
of magnitude 12 in the B band. The magnitude of extended and therefore resolved
objects is the integrated magnitude, i.e., the combined light over the whole surface
of the object, and is known as a surface brightness. You should, therefore, allow
more exposure time for extended objects than you would for stellar objects of the
same listed magnitude.
Most magnitude quotes are apparent magnitudes, the brightness as seen from
Earth. An important characteristic of a star is its absolute magnitude, the brightness
of a star at a distance of 10 pc, which hence relates directly to luminosity. Since
brightness drops off with the square of the distance, we can modify (2.5) to determine
absolute magnitude from apparent magnitude and distance:
M = m + 5 − 5 log 10 (d/ pc),
(2.6)
where M is absolute magnitude, m is apparent magnitude, and d is distance in parsecs.
A major challenge in galactic astronomy is the problem of interstellar reddening.
Gas, and in particular the dust between the object being observed and the observer,
will preferentially scatter blue light over red. Hence, an object with more scattering
appears redder. This would not be much of a problem if the material were distributed
uniformly throughout the galaxy (in fact, it would be a major advantage if it were).
However, it is not, so consequently, we need to modify (2.7) to adjust for reddening:
M = m + 5 − 5 log 10 (d/ pc) − A,
(2.7)
where A is the reddening in magnitudes.
Two photometric calibration standards are in common use, Vega and AB. The
Vega system assumes that the star Vega, α Lyra, is of magnitude zero at all wavebands,
which has the advantage that it simplified Pogson’s equation to
m 2 = −2.5 log 10 (F 1 /F 2 ),
(2.8)
so that the magnitude of a star in any filter is just the logarithm of the ratio of its flux
over that of Vega (multiplied by −2.5).
The AB system , unlike the Vega system, is based on calibrated flux measurements.
For completeness, we give the definition of AB magnitude:
m AB = −
5
8
log 10
f v
J y
+ 8.9
(2.9)