Going towards the physical world
Till now, we have “played” with our images, and with our counts to
extract the best possible instrumental magnitudes and positions.
A lot of work can be done with these measurements, but we have to
keep clear in mind that our fluxes are in some, totally arbitrary units.
A number of scientific applications need to have the stellar fluxes (or
magnitudes) in some physical units.
Therefore, we need to calibrate (*) our instrumental magnitudes into
some, properly defined photometric system.
(*) Note that the term “calibration” might generate some confusion. Someone uses the
term calibration to indicate the CCD pre-processing operations (bias, dark, flatfielding
corrections). I personally prefer to use this term to indicate the complex operations
needed to transform the instrumental magnitudes into a properly defined phot. system.
We need to match
photometries from
different
observations/data sets:
1. For comparison;
2. Variability studies;
3. Extend magnitude/color
coverage;
4. etc.
We need to compare
observations with models.
Low
metallicity
NGC 6397
Observations and models
need to be compared on the
same photometric system
(King, Anderson,
Cool, Piotto, 1999)
This implies to be able to
transform models from the
theoretical plane to some
properly defined photometric system.
Intermediate
metallicity
M4
(Bedin, Anderson,
King, Piotto, 2001)
And here the real trouble starts….
The Asiago Data Base on Photometric Systems lists 218 systems
(see http://ulisse.pd.astro.it/ADPS/enter2.html)!!!
But, even when you have chosen your photometric system, you
might still be in trouble!
The unbelivable
CMDs!
Theory predicts
that no stars can
be cooler than
the red giant
branch location!
But theory cannot
predict that
astronomers can
be so foolish to
change the
bandpasses of
their observation
without
properly
accounting
for these changes
How to operate properly
If observations are properly calibrated
and models transformed into the correct observational plane
(not necessarely a standard system), theoretical
tracks can correctly reproduce the observed CMD (apart from
intrinsic failures of the models…but this is a different story!).
A general lesson
From the previous examples we have learned a few important
things:
1. Observations must be calibrated and models must be
transformed into the same photometric system;
2. We need to use as much as possible a “standard”
photometric system;
3. If your photometric bandpasses are far from any existing
photometric system, you have the responsibility to
calibrate your system (good luck!);
4. In any case, ALWAYS trasform the models to the
observational plane, and not viceversa.
Photometric calibration of groundbased observations
Let’s suppose that we have collected a set of images of our program
objects through a set of filters properly designed to reproduce a
“standard” photometric system.
First of all, a clarification is needed:
Here, by “standard” I intend some widely used photometric system for
which a large set of standard stars, well distributed in the sky, and
which span a large color interval (at least as large as our program
objects) are available in the literature. And by standard stars I mean
stars for which accurate magnitudes and colors in the given
photometric system are available. Indeed:
the standard stars define our photometric system.
In order to calibrate the magnitudes and colors of our program objects,
we need to observe also the standard star fields, at different times
during the night, making sure that the observed standards cover a
sufficently large color interval.
Just an example (for the Johnson-Cousins system):
Landolt, 1983, AJ, 88, 439
Landolt, 1992, AJ, 104, 340
Photometric information on the standard stars in the
Landolt (1992) catalog
Position information on the
standard stars in the
Landolt (1992) catalog
Most of Landolt’s standards are too bright for modern CCDs.
Better to use Peter Stetson’s extension of Landolt’s catalog in:
http://cadcwww.hia.nrc.ca/standards
General info
Coordinates
Photometry
DSS image
It is important to realize that, even if we have collected a set of images
of our program objects through a set of filters properly designed to
reproduce a “standard” system, our observational system is always
different from the standard one.
Indeed, the collected flux depends on at least 6 different terms:
Signal=F()(1-)R()A()K()Q()
F() incoming flux
A() atmospheric absorption

fraction of the obscured mirror K() filter trasmission curve
R() mirror reflectivity
Q() detector quantum efficency
Red
leakage
Calibration steps (general):
1. Obtain aperture photometry of standard stars;
2. Fit the standard star data with equations of the type:
Where: v, b are the instrumental magnitudes;
V, B the standard magnitudes
X
the airmass
t
the time of observation (in decimal hours)
ai, bi the unknown transformation coefficents
The instrumental magnitudes must be transformed to a reference
exposure time (e.g. 1 second) and to a reference aperture (fraction of
total light of the star), or to the total light. Big problem (see later)!
For well designed observing
systems, and for not too
extreme colors, a linear fit
may be enough.
3. The next step is to calculate
the aperture correction, i.e.
the zero point difference
between the (fitting)
instrumental magnitudes of
the program stars, and the
aperture photometry used to
obtain the calibr. coefficents.
Example of calibration eq.s to the Johnson-Cousins standard
system for rhe ESO-Dutch telescope (from Rosenberg et al. 2000)
Finally, once the calibration coefficents have been obtained, the
corresponding calibration equations can be applied to the instrumental
magnitudes of the program stars, to transform them into the beloved
magnitudes in the standard system!
Total number of photons: the growth curves
Ideally, we need to know the total number of photons received by our
observing system from a standard star. The problem here is the fact that
the shape and size of a stellar image are affected by seeing, telescope
focus, and guiding errors The easiest way to derive a consistent measure
of the total number of photons contained in a star image is simply to draw
a boundary around it, count the number of photons contained within the
boundary, and subtract off the number of photons found in an identical
region which contains no star: aperture photometry!
The problem here is that the S/N is generally very poor. Infact, at
increasing the aperture radius:
1. The photons from the stars are less and less;
2. The random noise increases with square root of the pixels,
i.e. linearly with the radius;
3. Systematic errors increase lineraly, with the area, i.e.with
the square of the radius
Solution of the problem
You choose a number of bright, isolated stars (you may think to create
them, by subtracting the neighborhoods) and perform aperture
photometry through a series of concentric apertures of increasing radius.
Then you form the magnitude differences (aperture 2 - aperture 1),
(aperture 3 - aperture 2), and so on, and determine the average value for
each of these differences from your particular sample of stars in the
frame. Then the average correction from any arbitrary aperture k to
aperture n is:
If you do this for frames with different seeing, you can also account for
the variation of the seeing during your observing run.
Examples of growth curves for different seeing conditions, from the same observing run.
In order to improve the correction, one can fit to the aperture photometry
differences a model like:
Ri is a seeing (guiding,
defocussing) related radial
scale parameter for the i-th
data frame. The model comes
from a King (1972) study of
the typical stellar seeing profile.
Non-standard photometric systems
What shall we do in case we do not have a standard photometric system,
with an appropriate set of standard stars?
It must be clearly stated that when the transmission curves of the
equipment used to collect the observations are rather different from those
of any existing standard system, the transformation of the data to a
standard system can be totally unreliable, particularly for extreme
stars (i.e., extreme colors, unusual spectral type, high reddening, etc.).
If we are dealing with groundbased obsevations…it is a long, tedious,
delicate job, and I do not have the time to enter into the problem here.
Do you want an advice? Change telescope!
Unfortunatlely, also widely desired (!) and widely used telescopes like
HST….have imagers which do not mount “standard” filters.
Do you want an advice? Do not attempt to transform your WFPC2 or
ACS instrumental magnitudes into any standard system!
So, what shall we do?
Provided that the transmission curves of the complete optical system and
detectors are known, a calibration of the zero points into physical units
is easy to obtain by using a reference star for which the spectral flux
(outside the atmosphere) as a function of the wavelength is known (e.g.
Vega). By multiplying the reference spectrum by the system transmission
curves one obtains the flux within the given pass bands, which can be
easily transformed into magnitudes. If one uses the same procedure
employing model atmospheres and theoretical fluxes, it is possible to
relate the magnitudes and colors to the physical parameters like
temperature and luminosity.
I think that Bedin et al. (2004) have written a paper which describes
in a complete and clear way the methodology, applying it to the
calibration of the HST/ACS camera.
A similar method has been applied by Holtzman et al. (1995) and
Dolphin (2000) for the calibration of the HST/WFPC2 camera.
Example (from Bedin et al., 2004):
The spectrum of Vega from
ftp://ftp.stsci.edu/cdbs/cdbs2/ grid/
k93models/standards/vega_reference.ts
has been multiplied by the (in flight) ACS
trasmission curves on the right, in order to
calculate the ACS Vega-mag flight system
zero point coefficents.
Model atmospheres and theoretical
fluxes have been multiplied by the
same transmission curves in order
to transform the models into
the same (observational) plane
above defined.
Models and observations are
compared on the left panel.