m=A+k*C-2.5*log(f) (1)
where m is the magnitude in the Landolt system, A is the calibration
zero
point, f is the flux in CCD counts and k*C is a color term(more than
one are used sometimes),
which takes into account the differences between the total transmission
of the system employed by the
observer (filter+CCD+optics+atmosphere) and the one used by Landolt.
It should be kept
in mind therefore, that this expression gives the magnitude that the
object will have
if observed with the Landolt transmission function.
Therefore, if we want to generate synthetic colors of the objects we
will also need to use the
Landolt transmission function to convolve the corresponding templates.
However,
the exact shape of this function is not known, and it may differ considerably
from our filter
system, what could lead to big photometric errors for objects with
rather extreme
colors, since the linear color term transformation is only an approximation.
Thus it is usually
more reasonable to use the transmission functions from our own system,
for which the expression (1)
is not valid.
One solution is to follow the approach of Oke
et al.1998, observing a set of spectrophotometric
standards and obtaining the absolute zeropoints of our filters in the
AB system. This is a quite a
complex procedure, but luckily there is an approximate way of doing
this which yields similar results.
As Oke et al. 1998 proposed we can define a 'natural' system based
on our filter set. If we make
this system Vega-based, it will be defined for each filter as
m_n=2.5*log(f_Vega)-2.5*log(f)
Where f_Vega is the counts we will measure from Vega on our CCD through
each filter.
Since by definition the magnitude and colors of Vega in the Landolt
system is approx 0
(actually the magnitude of Vega on BVRI is approx 0.02), comparing
the magnitude of Vega
in our natural system with its magnitude in Landolt system (equation
1) we have
that 2.5*log(f_Vega)=A.
There our natural Vega system is defined as
m_n \approx A-2.5*log(f)
That is, it has the same zero point that the Landolt transformation
but no color terms.
If we want to make our magnitudes
AB calibrated, we have to add to them the magnitude of Vega on the
AB system for that particular filter.
AB_n=A-2.5*log(f)+Vega_AB
Approximate expressions for Vega_AB can be found in Fukugita
et al. 1995
or can be calculated using the function flux_sed in the bpz_tools package.
In this way it is straightforward to compute the adequate model colors
by convolving the
templates with our filter set and then applying to them the adequate
normalization, Vega or AB.