10.2 Measuring
151
The basic reduction formula in magnitudes is
M f = m f − k
f X + T f (CI ) + ZP f ,
(10.4)
where M f is the standard catalogue magnitude of the reference air massstar in band
f , m f is the instrumental magnitude of the reference star in band f , k
f is the extinction
coefficient in band f , X is the air mass, T f is the colour correction for band f , CI is
the colour index, and ZP f is the current band f zero point.
The zero point is an offset between the instrumental magnitude and the standard
magnitude. In broad terms, it is a measure of the sensitivity of your optical system
to light. Hence, space-based telescopes also have a zero point. A zero point can be
either a flux or a magnitude. In the case of a flux, it is applied by dividing the time
and gain as a normalised count by the zero point. If it is expressed as a magnitude,
it is just added to the instrumental magnitude, as shown in (10.4).
The extinction coefficient reflects the proportion of light that is lost as it travels
through the atmosphere for a given air mass and hence is both wavelength and
filter dependent, as well as being altitude specific. The colour index is the ratio of
flux received from a star over two bands, or more understandably, the difference in
magnitude between two bands for that star. So, for example, the star HIP 2027 has
an R magnitude of 7.574 and a V magnitude of 7.640 and hence a V-R colour index
of 0.065.
Different wavelengths are subjected to differing amounts of extinction as they
pass through the atmosphere, with more blue light being scattered than red (hence
the sky appearing blue). A blue star will therefore be affected by the atmosphere
more than a red one, whence the need to apply an extinction coefficient that is air
mass and filter specific. Note that the air mass is a function of the altitude at which
the object is observed, and applying
X = 1/ cos(z),
(10.5)
where z = 90 deg −altitude gives the air mass X . Note that this is the altitude angle
of the object, not the altitude of the observer.
The colour transformation T f (CI ) is effectively stable and can be used on successive nights unless there have been significant changes in the optical system, and
likewise for the extinction coefficient. The zero point is related to the entire optical
pathway and will change between individual nights of observing, so it should be
recalculated for every session. The air mass X is a function of the actual observation.
You may have heard the terms first- and second-order extinctions in the context
of photometric reductions. The first order applies to the air mass coefficient, whilst
second order applies to the colour transform. In some cases, the first-order extinction
can be ignored if you are using calibration stars at the same air mass. However, as this
might not be the case and given that they are largely immutable, it is worth having
their values at hand.
151
The basic reduction formula in magnitudes is
M f = m f − k
f X + T f (CI ) + ZP f ,
(10.4)
where M f is the standard catalogue magnitude of the reference air massstar in band
f , m f is the instrumental magnitude of the reference star in band f , k
f is the extinction
coefficient in band f , X is the air mass, T f is the colour correction for band f , CI is
the colour index, and ZP f is the current band f zero point.
The zero point is an offset between the instrumental magnitude and the standard
magnitude. In broad terms, it is a measure of the sensitivity of your optical system
to light. Hence, space-based telescopes also have a zero point. A zero point can be
either a flux or a magnitude. In the case of a flux, it is applied by dividing the time
and gain as a normalised count by the zero point. If it is expressed as a magnitude,
it is just added to the instrumental magnitude, as shown in (10.4).
The extinction coefficient reflects the proportion of light that is lost as it travels
through the atmosphere for a given air mass and hence is both wavelength and
filter dependent, as well as being altitude specific. The colour index is the ratio of
flux received from a star over two bands, or more understandably, the difference in
magnitude between two bands for that star. So, for example, the star HIP 2027 has
an R magnitude of 7.574 and a V magnitude of 7.640 and hence a V-R colour index
of 0.065.
Different wavelengths are subjected to differing amounts of extinction as they
pass through the atmosphere, with more blue light being scattered than red (hence
the sky appearing blue). A blue star will therefore be affected by the atmosphere
more than a red one, whence the need to apply an extinction coefficient that is air
mass and filter specific. Note that the air mass is a function of the altitude at which
the object is observed, and applying
X = 1/ cos(z),
(10.5)
where z = 90 deg −altitude gives the air mass X . Note that this is the altitude angle
of the object, not the altitude of the observer.
The colour transformation T f (CI ) is effectively stable and can be used on successive nights unless there have been significant changes in the optical system, and
likewise for the extinction coefficient. The zero point is related to the entire optical
pathway and will change between individual nights of observing, so it should be
recalculated for every session. The air mass X is a function of the actual observation.
You may have heard the terms first- and second-order extinctions in the context
of photometric reductions. The first order applies to the air mass coefficient, whilst
second order applies to the colour transform. In some cases, the first-order extinction
can be ignored if you are using calibration stars at the same air mass. However, as this
might not be the case and given that they are largely immutable, it is worth having
their values at hand.