## 3. Model results1. By design, the model is in qualitative agreement with data
showing photometric and polarimetric fluctuations about some mean
values (see Robert 1992). Fig. 2 shows how typical polarisation,
position angle, and scattered light fraction change with the total
number of blobs emitted from the start - i.e with time, starting from
ejection of the first blob, for the model with the indicated
parameters. The observables all rise to steady mean values within the
first few flow times, because thereafter the number of blobs near the
star, which dominate the scattered light, becomes steady on average.
Polarisation changes are also shown as a locus in the Q - U plane (see
Fig. 2) which, as expected, shows no preferred direction, since the
mean structure is spherical. In Fig. 3 we show "observational"
time-smoothed results for the variations in mean polarisation and
scattered light. We applied "boxcar" smoothing with a width of about
one flow time (i.e., about 1 hour for the chosen star parameters).
Standard deviations, , of these
quantities are also plotted in Fig. 3. Fig. 4 is the ratio
versus total number of blobs
2. To confirm the dominance of inner blobs explicitly, we show the
cumulative contributions of blobs to the polarisation and scattered
light after a long time in Fig. 5.
We find that only the blobs which are close to the star give
significant contributions. That is, once enough blobs have entered the
flow so that the inner few stellar radii contain a mean steady state
number of blobs, then steady mean values for
3. In the Richardson et al. (1996) analysis,
, ,
and were taken as randomly
distributed so that in effect it was assumed that
was constant. The total number of
blobs
4. Results for "observables" as a function of
from our time-dependent
model are shown in Table 1 with
occultation effects included, for the values of
, ,
, ,
etc., indicated. In each case we ran our code for 5000 blobs in total
and for the same value of
(equivalent to a cone semi-angle of roughly
). In Fig. 7 we show that results
are relatively insensitve to (unless
we go to extreme values like 0 or
which yield zero polarisation by spherical symmetry). The same is also
true of which is the blob width.
Fig. 8 shows the effects of varying .
As expected, all absolute values of scattered light parameters
From Table 1, we can see that in the first three rows, the polarisation and scattered light exceed unity due to the high blob density and optical depth for small , so that our model violates its single scattering basis for very low blob ejection and high mass loss rates but is otherwise self-consistent. 5. Fig. 9 shows that for different
, we get different
versus
curves with
going to near constant values for
large . The larger the
we have, the lower that
becomes. The reason is that large
implies more blobs near the star
where
© European Southern Observatory (ESO) 2000 Online publication: May 3, 2000 |