Equations. Demo sequences for some scientific cases.
Targets
There are two ways to introduce new targets in Phase 1 and Phase 2: Add target and Add several targets. Some examples are provided for each one of the two procedures.
Add target
An example is provided for each one of the accepted coordinate types:
Several scientific cases are shown when the use of Windows might be useful. These examples are purely informative and do not imply that they must be used for the scientific cases exposed below.
Supernovae
It is rather common to observe supernova only during a certain period of time, close to the maximum brightness period. For these objects, a single Window is enough to define the desired time of observation.
Start JD
End JD
Period
2456200.5
2456245.5
0
Transiting exoplanet or eclipsing binary
In transiting exoplanets and eclipsing binaries, an occultation occurs at fixed intervals. It is rather common to observe when these phenomena take place. In the following example, two Windows are used to define the eclipsing period and the need to perform the observations during a single month. In this case, all the required exposures should fit within the narrow Window of around 2.5 hours (0.105 days).
Start JD
End JD
Period
2456300.5
2456330.5
0
2456334.32335
2456334.43224
3.45323
Delays
It may seem repetitive to define Delays in both Observing constraints and Sequences. However, their value is shown in the following example.
It is rather common to observe a target a couple of times per night, during several nights with the only condition that some time should be left in between. The definition of such a observing strategy could be done with Windows. However, the Windows would impose strong constraints on the times that the two observations could be done. This is specially relevant when short TOIs want to be executed.
In the current example, a sequence like t1o1i1 & t1o1i1 can be defined, with i1 being a single one-hour exposure. The most important point in the current example is in the definition of o1. In case that o1 is defined using Windows, a possible solution would be:
Start JD
End JD
Period
2456000.55
2456000.75
1
2456000.5
2456000.55
0.08
In this case, the two Windows are used to impose a single execution per night (Window 1) and to repeat the execution every two hours (0.08 days in Window 2). A larger range between Start JD and End JD in Window one, might allow the execution of the example sequence several times per night. A larger range between Start JD and End JD in Window two, might allow the execution of both TOIs consecutively. Therefore, the first TOI of the example sequence would only be executed between 01:55:12h and 03:07:12h. In addition, the second TOI would only be executed between 03:50:24 and 05:02:24h. This is more clearly seen in the following figure.
In case that weather (or other proposals) avoid the example sequence to be executed at these exact times, the sequence would not be executed. Therefore, a better approach would be to use Delays.
The first Window in the above table can be eliminated by introducing a Delay for the whole sequence (at Step 4). Therefore, introducing a 18 hour Delay at Step 4, the example sequence could be started at 2456000.5+N*0.08, where N is an integer number. Once both TOIs were executed, the sequence would not be repeated in (at least) 18 hours. However, the observations could only start at 2456000.5+N*0.08 and would never be started at 01:00h.
In order to provide full flexibility in the time that the example sequence can be started, the second Window could be deleted and replaced by a Delay (before) equal to 1 hour at the corresponding Observing constraint (Step 2). This way, the sequence could be started at any time, and the second TOI would not be executed until (at least) one entire hour has passed. The sequence would not be repeated the same night because the a 18 hours Delay exists for the whole sequence. The final solution could be represented as shown in the following figure.
In the above figure, the Example sequence would not be repeated (at least) until 23:00 due to the 18 hour Delay (at Step 4).
In the above figure, two important aspects of Delay (before) and Delay (after) are also shown. Note that Delay (before) is always applied to TOIs. Therefore, in case that two TOIs exist, the Delay (before) or Delay (after) would be applied to each individual TOI. It is specially relevant when, for example, two filters want to be used consecutively, since they have to be defined in two different instrument configurations. Therefore, with a sequence like 2*t1o1*(i3 & i4) using the o1 Observing constraint shown above, would imply that one hour would be left between t1o1i3 and t1o1i4. In order to avoid the Delay, the second TOI should be defined using a different Observing constraint (e.g., 2*[t1o1i1>t1o2i2], where o2 would have no Delays)
Another important aspect about Delays is shown in the above figure. Note that, in the above figure, o1 also has a Delay (after) defined. However that Delay (after) is not used, since the Delay (before) of the following TOI is larger. The above example reflects the case when one TOI has a Delay (after), followed by another TOI with a Delay (before), the largest of the two Delays is applied.
Dithering
Some examples are provided showing the telescope pointing (blue crosses) with respect to the Target defined in Step 1 (green circle).
Equations
Some examples are provided with explanations to facilitate the writing of Phase 2 equations:
These two equacions are equivalent: 2 * t1o1i1 t1o1i1 > t1o1i1
But not necessary equivalent to these: [2 * t1o1i1] [t1o1i1 > t1o1i1]
The only difference between them is that both TOIs will be executed consecutively in the last two equations.
To obtain a light curve, the best option is to define the desired number of exposures in the instrument configuration. This way, instrumental overheads are largely reduced. Therefore, the equation should be: t1o1i1
However, in case that two filters have to be alternated, the equation should be: [300 * t1o1 * (i2 > i3)]
In this case, each instrument configuration has a different filter and the number of exposures is only one. Note the use of the consecutive operator ([]) to avoid having gaps in the time series.
To obtain absolute photometry with standard stars for a certain object, the following equation might be useful: o1 * (10 * (t1i1 | t2i1 | t3i1) & t4i2)
In this example t1, t2 and t3 are standard stars. Different exposure times are selected with i1 and i2. However, the above example does not ensure that standard stars will be observed at the proper airmasses. In order to ensure that the science target (t4) is observed at the lowest airmass possible and that an accurate airmass correction can be performed, the following equation would be better: o1 * ((t1i1 | t2i1 | t3i1) < t4i2 < 9 * (t1i1 | t2i1 | t3i1))
Even though, the above equation does not ensure that the same standard star is observed every time. In order to ensure that the same standard star is observed for the whole sequence, the following equation would be required: o1 * ((t1i1 < t4i2 < 9*t1i1) | (t2i1 < t4i2 < 9*t2i1) | (t3i1 < t4i2 < 9*t3i1))
