As discussed in Sect. 4, internal errors for the ATESP
source parameters are well described by Condon (1997)
equations of error
propagation derived for two-dimensional elliptical Gaussian fits in presence
of Gaussian noise. In order to get the total rms error on each parameter,
a calibration term should be quadratically added.
Using Eqs. (21) and (41) in Condon (1997), total percentage
errors for flux densities (
)
and fitted axes (
,
)
can be calculated
from:
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(A3) |
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![]() |
(A4) |
![]() |
![]() |
![]() |
(A5) |
Calibration terms are in general estimated from comparison with
consistent external data of better accuracy than the one tested.
Unfortunately there are no such data available in the region of sky covered
by the ATESP survey. Nevertheless, from our typical flux and phase
calibration errors, we estimate calibration terms of about
for both
flux densities and source sizes.
As a caveat we remind (see discussion in Paper I) that the 500 m baseline
cutoff applied to our data makes the ATESP survey progressively insensitive
to sources larger than
:
assuming a Gaussian shape, only
of the flux for a
large source would appear in the ATESP images.
It is important to have this in mind when dealing with flux densities and
source sizes of the largest ATESP sources.
Right ascension and declination calibration terms have been estimated from
the astrometry results reported in Sect. 4.3.2. As already discussed,
the ATESP astrometry can be considered accurate within a small fraction of an
arcsec, even though the scarcity of (accurate) external data available in the
ATESP region makes it difficult to quantify this statement. Nevertheless
from the rms dispersion of the median offsets found between ATESP and the
external comparison samples (see Sect. 4.3.2) we can tentatively
estimate
and
.
It can be easily demonstrated that the master Eqs. (A1),
(A6) and (A7) reduce to
Eqs. (3) - (7) in Sect. 4
(where the calibration term is neglected) in the case of ATESP point sources
(
,
PA
), assuming
(or
).
For a complete and detailed discussion of the error master equations of source parameters obtained through elliptical Gaussian fits we refer to Condon (1997) and Condon et al. (1998).
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