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10 Photometry
Error Analysis
You will now have to look at the uncertainties in your magnitude calibration system. Because the steps involved are complex, the easiest way of determining the
uncertainty is by comparison with known magnitudes.
Using the instrumental magnitude for each of your calibration stars in your uncertainty field, calculate the instrumental colour index for each calibration star using
CI i = (((v − k
v × X v ) − (r − k
r × X r )) × T vr ) + ZP vr ,
(10.9)
where X is the air mass for that image and filter. Use the mean value for each star
observed for the star’s instrumental colour index, CI i .
You can now transform the instrumental magnitudes to standard magnitudes using
the mean instrumental magnitudes for each calibration star and applying
M v = =v − (k
v × X ) + (T v × CI i ) + ZP v .
(10.10)
By looking at M v − V you will be able to determine the level of uncertainty in
your photometry and see whether there are any systemic errors.
10.3.6 Analysis
As usual, you should write your analysis in a standard format including all the
data, plots, and calculations. Give special attention to discussing the level of your
uncertainties given that a typical survey has photometric uncertainty errors of 0.1
mags. Where do you think your errors are and how do you think you could improve
them?
In your discussion, include how you would be able to determine just the zero
point if you were observing on another night. Observers of exoplanet transits might
need photometric uncertainties of 0.001 mags. How do you think they can achieve
this given the levels of uncertainty in your results?
10.4 Differential Photometry
One of the questions asked in Practical 8 is how exoplanet transits can be detected if
millimagnitude precision is needed to give the level of uncertainty in our photometry
as determined in the practical. The answer lies in the second-order extinction coefficient determination. When we image the reference stars in the same field as the object
of interest, we can ignore the first-order coefficients. For most observations, we are
not interested in the change of colour of an object over time, although that itself is
interesting and contains a considerable amount of physics. Rather, we are interested
10 Photometry
Error Analysis
You will now have to look at the uncertainties in your magnitude calibration system. Because the steps involved are complex, the easiest way of determining the
uncertainty is by comparison with known magnitudes.
Using the instrumental magnitude for each of your calibration stars in your uncertainty field, calculate the instrumental colour index for each calibration star using
CI i = (((v − k
v × X v ) − (r − k
r × X r )) × T vr ) + ZP vr ,
(10.9)
where X is the air mass for that image and filter. Use the mean value for each star
observed for the star’s instrumental colour index, CI i .
You can now transform the instrumental magnitudes to standard magnitudes using
the mean instrumental magnitudes for each calibration star and applying
M v = =v − (k
v × X ) + (T v × CI i ) + ZP v .
(10.10)
By looking at M v − V you will be able to determine the level of uncertainty in
your photometry and see whether there are any systemic errors.
10.3.6 Analysis
As usual, you should write your analysis in a standard format including all the
data, plots, and calculations. Give special attention to discussing the level of your
uncertainties given that a typical survey has photometric uncertainty errors of 0.1
mags. Where do you think your errors are and how do you think you could improve
them?
In your discussion, include how you would be able to determine just the zero
point if you were observing on another night. Observers of exoplanet transits might
need photometric uncertainties of 0.001 mags. How do you think they can achieve
this given the levels of uncertainty in your results?
10.4 Differential Photometry
One of the questions asked in Practical 8 is how exoplanet transits can be detected if
millimagnitude precision is needed to give the level of uncertainty in our photometry
as determined in the practical. The answer lies in the second-order extinction coefficient determination. When we image the reference stars in the same field as the object
of interest, we can ignore the first-order coefficients. For most observations, we are
not interested in the change of colour of an object over time, although that itself is
interesting and contains a considerable amount of physics. Rather, we are interested