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Observing mode and elapsed telescope time

The goal of a time estimator is to find the elapsed telescope time ( \ensuremath{\Delta t_\ensuremath{\mathrm{tel}}}) needed to obtain a given rms noise, while a sensitivity estimator aims at finding the rms noise obtained when observing during \ensuremath{\Delta t_\ensuremath{\mathrm{tel}}}. The total integration time spent on-source \ensuremath{\Delta t_\ensuremath{\mathrm{on}}} is shorter than the elapsed telescope time due to several factors. As of Gildas Jul17 release, the input time of the sensitivity estimator is telescope time. The actual on source time is then computed taking into account the following two points:

  1. Instrumental setup time: At the beginning of an observing track a significant time ( $\ensuremath{\Delta t_\ensuremath{\mathrm{tune}}}\sim 40$ minutes according to history of observations) is spent in receiver tuning and calibration observations before observing the actual astronomical target. This means that even for a very short ON source time, a project cannot be shorter than \ensuremath{\Delta t_\ensuremath{\mathrm{tune}}}. Also, for long projects observed in several ( \ensuremath{n_\ensuremath{\mathrm{track}}}) tracks the time spent for tuning and calibration is $\ensuremath{n_\ensuremath{\mathrm{track}}}\times \ensuremath{\Delta t_\ensuremath{\mathrm{tune}}}$. We thus define the time spent for observations (i.e. without instrumental setup) \ensuremath{\Delta t_\ensuremath{\mathrm{obs}}} as:
    \begin{displaymath}
\ensuremath{\Delta t_\ensuremath{\mathrm{obs}}}= \ensuremat...
...ack}}}\times \ensuremath{\Delta t_\ensuremath{\mathrm{tune}}}
\end{displaymath} (19)

    The number of tracks is computed as $\ensuremath{n_\ensuremath{\mathrm{track}}}= \frac{\ensuremath{\Delta t_\ensurem...
...ensuremath{\mathrm{track}}}}+ \ensuremath{\Delta t_\ensuremath{\mathrm{tune}}}}$ where \ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{track}}}} is the typical duration of a track, which depends on the source declination: A linear interpolation with the declination is performed in the appropriate range between $-30 \deg$ and $0 \deg$.
    For short projects ( $\ensuremath{\Delta t_\ensuremath{\mathrm{tel}}}< \ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{track}}}}+ \ensuremath{\Delta t_\ensuremath{\mathrm{tune}}}$), the number of tracks \ensuremath{n_\ensuremath{\mathrm{track}}} is set to 1. Otherwise, the floating value of \ensuremath{n_\ensuremath{\mathrm{track}}} is used in the computation of \ensuremath{\Delta t_\ensuremath{\mathrm{obs}}}. Since \ensuremath{\Delta t_\ensuremath{\mathrm{tune}}} is constant whatever the length of a track the use of a floating value for \ensuremath{n_\ensuremath{\mathrm{track}}} is somehow unnatural but it ensures that the conversion from \ensuremath{\Delta t_\ensuremath{\mathrm{tel}}} to \ensuremath{\Delta t_\ensuremath{\mathrm{obs}}} is a monotonic function.
  2. Observing efficiency: After the initial phase of instrumental setup, the observing mode does not dedicate 100% of the time to the astronomical target. Part of the time is spent for calibration (pointing, focus, atmospheric calibration,...) and to slew the telescopes between useful integrations. The time actually spent on source \ensuremath{\Delta t_\ensuremath{\mathrm{on}}} is defined as
    \begin{displaymath}
\ensuremath{\Delta t_\ensuremath{\mathrm{on}}}= \ensuremath...
...thrm{obs}}}\times \ensuremath{\eta_\ensuremath{\mathrm{tel}}}
\end{displaymath} (20)

    where \ensuremath{\eta_\ensuremath{\mathrm{tel}}} is the observing efficiency.

The exact computation depends on the observing mode. There are three main observation kinds.

Single-source, single-field observations
where the telescope tracks a single source during the full integration time. This mode is used when the signal-to-noise ratio is the limiting factor.
Track-sharing, single-field observations
where the telescope regularly cycles between a few close-by sources. This mode is used when the sources are so bright that the limiting factor is the Earth synthesis, not the signal-to-noise ratio.
Single-source mosaicking
where the telescope regularly cycles between close-by pointings that usually follows a hexagonal compact pattern whose side is $\ensuremath{\lambda}/(2\ensuremath{d_\ensuremath{\mathrm{prim}}})$, where \ensuremath{d_\ensuremath{\mathrm{prim}}} is the diameter of the interferometer antennas. This modes is used to image sources wider than the primary beam field of view.
In the following, we will work out the equations needed by the sensitivity estimator for each of these observing modes.



Subsections
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Next: Single-source, single-field observations Up: IRAM Memo 2015-2 NOEMA Previous: Actual computations   Contents
Gildas manager 2023-06-01