These simulations allow us to assess the loss of signal which results
from observing extended envelopes with the dual-beam method.
As an example, Fig. 7a shows the transformation of a
input envelope model (dotted line)
after convolution with the 30 m beam (dashed-dotted line) and the
various observation/data reduction steps (solid line). For such an
extended envelope model, the beam convolution does not modify the
slope of the profile at angular radii
HPBW (i.e.,
here), in agreement with the conclusions of Adams
(1991). However, the observation/data reduction technique does change
the shape of the radial profile (see hatched region in
Fig. 7a), due to the finite size of the maps. This is
because all spatial scales larger than the azimuth extent
of the maps are filtered out. The slope of the simulated output
profile depends only weakly on the value of the wobbler throw as long
as the latter remains small compared to the map size (in azimuth).
(Note that the chop throw would be the most determinant factor in the
case of on-off/jiggle-stare maps.) The array geometry and the offset
of the source model with respect to map center have little influence
on the simulated profile providing the map is big enough that the
source is effectively imaged as a positive and a negative signal by
each bolometer. Baseline subtraction also has a negligible effect as
long as only low-order polynomials are taken out, namely a baseline of
order 0-2 applied in time on the global image, plus a simple DC level
(0-order baseline) on each map row.
In order to simulate the effect of an inner disk component, we have
added a central point source to a
power-law envelope model (see Fig. 8a). The resulting
intensity profile follows the shape of the error beam at large radii
when
.
(For a
input envelope model, the same occurs when
.) Although such large
"disk-to-envelope'' ratios could apply to T Tauri stars (e.g. HL Tau),
they are not observed in the case of bona-fide protostars which
typically have
(see,
e.g., Looney et al. 2000; Motte et al. 2001). In most cases, the disk
should thus have a negligible influence on our analysis of the
envelope radial profiles at angular radii
HPBW.
We have also embedded a
envelope model
in a Gaussian background cloud with FWHM
pc and a
cloud-to-envelope peak flux ratio of
,
corresponding to a
typical ambient column density of
.
The emission of such an extended Gaussian cloud is essentially
filtered out by the dual-beam observing technique. Thus, the apparent
power-law index
of the radial profile should
only be corrected by a small term
to yield the intrinsic index of the envelope profile, i.e.,
(see Sect. 4.2.2).
Finally, we have simulated the dual-beam observation of a finite-sized
envelope with an outer radius
similar to the values measured
from Figs. 3 and 4 (see
Table 4). Typically, our observations suggest
in Taurus and Bok
globules, and
in Perseus. According to YC91, the slopes of the
intensity profiles measured on such angular scales (i.e., HPBW
)
should be corrected by
when estimating the intrinsic slopes of the density profiles (i.e.,
), in
order to properly account for projection effects.
Figure 8b
shows that, due to dual-beam filtering, the effective correction term
is much smaller in our case:
in Taurus and Bok globules and
in Perseus.
Copyright ESO 2001