The goal of a sensitivity estimator is to find the rms noise obtained when
observing during the elapsed telescope time,
. The total
integration time spent on-source
is shorter than the elapsed
telescope time due to several factors. The actual on source time is then
computed taking into account the following points:
- Instrumental setup time: At the beginning of an observing track
a significant time (
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
. The setup time is computed as
 |
(23) |
where
is the minimum setup time when only one frequency is
observed (40 minutes),
is the additional setup time per
additional frequency, and
is the number of frequency
observed in frequency cycling mode.
is for the moment
also set to 40 minutes.
- Number of tracks per science goal: Also, for long projects
observed in several (
) tracks the time spent for tuning and
calibration is
. We thus define the time spent
for observations (i.e. without instrumental setup)
as:
 |
(24) |
The number of tracks is computed as
 |
(25) |
where
is the typical time when the source is visible from
Bure, which depends on the source declination:
- Sources above
are observed 8 hours at most (for
instrumental management),
- 8.2 hours for a declination of
(truncated to 8 hours),
- 6.5 hours for a declination of
,
- 3.9 hours for a declination of
,
- 0.0 hours for a declination of
.
- Sources below
can not be observed.
A linear interpolation with the declination is performed in the
appropriate range between
and
.
For short projects (
), the number of tracks
is set to 1. Otherwise, the floating value of
is
used in the computation of
. Since
is constant whatever
the length of a track the use of a floating value for
is
somehow unnatural but it ensures that the conversion from
to
is a monotonic function, without regular threshold effects.
- 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
is defined
as
 |
(26) |
where
is the observing efficiency. The exact computation of
depends on the observing mode. The observing mode can be split
into two categories that can be combined:
- Detection vs Imaging projects: From the sensitivity
estimation viewpoint, the main difference between these observing modes
is the number of gain calibrators regularly observed:
for detection, and 2 for mapping projects.
- Frequency cycling mode: In this case, the gain calibrators have to
be observed at each frequency of the cycle.
These results in a computation of the observing efficiency as
 |
(27) |
Note that the exact value of
and
actually depend on several parameters such as the distance between the
source and the calibrator(s). In “standard” mode, we obtain the usual
and 1.9, for detection and mapping projects,
respectively. In frequency cycling mode with 2 frequencies, we
yield
and 2.5 for detection and mapping projects,
respectively.
- From
to on-source time: Finally, the distribution of
observing time into the time spent on-source,
, actually used to
estimate the sensitivity depends on three main observation kinds that are
assumed exclusive from each other.
- 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
, where
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.
- Overall efficiency Finally, the overall observing
efficiency,
, is evaluated by computing the sum of the on-source
time over the total telescope time
 |
(28) |
The sum of the on-source time allows us to take into account the fact
that 1) the telescope time may be shared between sources or frequencies,
and 2) dual band observations are more efficient than single band ones;.
We also stress that when frequency cycling is combined with dual band
observations, both receiver bands are affected by the efficiency loss of
the frequency cycling even though one of the two bands could not require
frequency cycling at all! A warning is raised when
.