For a point source, it is more natural to express the signal, and thus the
sensitivity, in unit of flux. The flux (
) of a point source is
linked to its brightness temperature
through
with |
(4) |
where
is the Boltzman constant, and
is the effective area
of the antenna (eq. 3-113 in Kraus , 1982), and
the conversion
factor for a typical interferometer antenna. The effective area depends on
the observing wavelength when the surface rms accuracy becomes a
significant fraction of the wavelength. For NOEMA, the effective area is
close to the antenna geometrical surface at 3 mm but significantly lower
than it at 1 mm. Using the same conversion factor for the sensitivity, we
yield
 |
(5) |
We have the same subtlety for
as for
, ie,
here
characterizes one baseline between, eg., antennas
and
. Instead of
just
, we should write in all generality
with
 |
(6) |
where
and
are the single dish conversion
factors for antenna
and
. For simplicity, we will also keep the
notation
hereafter.