# PhotoRed Reductions Routines - Target Standard Magnitudes
Using data created in
PhotoRed
Using data imported from Canopus
This routine is similar to the one for comparison stars save that the results are
handled a bit differently. For one, the values are not stored in the Transforms form.
Another is that in addition to the plots you see above, if the data was imported from a
Canopus session, it can be exported out to files that can be used in Canopus for analysis
or merging with other Canopus data.
As with the comparisons routine, you need to have observations in only one filter but
you must know the standard color index of the target before you run this routine. If the
asteroid is a target, you should shoot three images in each filter in as short a time as
possible. It’s best not to group images by filter when shooting but in sequence,
e.g., VRVRVR and not VVVRRR. The reason is so that when you measure the images, you put
the first V and R in group 1, the next V and R in group 2, and so on. This keeps the two
different filter images close together in time. PhotoRed then finds the average for the
three readings to provide the single color index value. Were you to shoot in VVVRRR
fashion and the asteroid is changing magnitude quickly (as in the second plot above), then
the color index value is affected. For example, if the asteroid is fading, then the
average of the three R images will be dimmer more than it should be and so the result V-R
greater than the real value.
Why the two plots for the same routine? It depends on the data you provide. The first
plot (partly covered with only one data point) was the result of measuring a target field
in PhotoRed in order to get a single V reading for the target, i.e., there was no
time-series involved. This might be the case if you’re working a set of variables and
getting only one or very small number of readings per night. The second plot is the result
of working with data that was imported from Canopus where a protracted time-series session
was created to monitor an asteroid (an eclipsing variable star might have a similar
curve). As an aside, note the vertical axis is divided into 0.05m steps. This was high
quality data with errors generally <0.01m.
The process for this routine follows these steps
- For each group, PhotoRed finds the average value of the instrumental magnitudes for each
comparison and the target.
- Using the transforms and standard color indices for the target and each comparison,
PhotoRed uses the differential formula to find the reduced standard
*differential*
magnitude of the target based on one comparison at a time.
Mathematically
DM_{f} = (TI_{avg} – CI_{xavg}) + T_{f} * (CI_{T} – CI_{xc})
Where DM_{f} differential standard magnitude in filter f
TI_{avg} average of target instrumental magnitudes
CI_{xavg} average of comparison X instrumental magnitudes
T_{f} transform for filter f
CI_{t} standard color index of target
CI_{xc} standard color index of the comparison X
- The average of the reduced
*differential* values is then applied to the average of
the reduced average standard magnitudes of the comparisons to find the final standard
magnitude of the target for the group.
Mathematically
SMf = Avg(M_{Cf}) + Avg(DM_{f1-n})
Where SMf standard magnitude of target in filter f
Avg(M_{cf}) average of reduced standard magnitudes of the comparisons
Avg(DM_{f1-n}) average of standard differentials 1 through N
It’s important to appreciate what’s going on in step 2. Say five comparisons
are used. One way to find the target’s standard magnitude might be to find the
average of the reduced standard magnitudes of the comparisons and simply subtract that
from the reduced standard magnitude of the target. That would work *if all the
comparisons and target were exactly the same color*. Since they most likely are not,
the standard color index for each comparison and the target comes into play to get the
best possible standard magnitude for the target. To do that without the differential
approach would require having observations in two standard filters. Instead, using the
transforms based on one-color observations and known standard color indices, a reduced *differential*
standard magnitude of the target versus a comparison is found for each comparison, giving
five differential values.
Step 3 takes the average of those differential values and applies them to the average
of the standard magnitudes of the comparisons to get the final standard magnitude of the
target. |