Figure
8.1 shows that the derived circumstellar excess is negative. For the free-free,
free-bound interactions which occur in the disc to cause the photons to be re-emitted at a
shorter wavelength would require
Tdisc > T*, (
i.e., a non radiative method of heating
the disc). It is also expected therefore that this effect would occur, on average,
across all wavelengths, since it has already been shown, see Chapter
7, that this is
not the case and no literature reports such an effect, a different solution must be
sought.
In an effort to dissolve this effect the spectral type of each star was lowered by
one spectral type, making the object bluer than it would normally be and hence
making any excess more positive. This was done to see whether the spectral type had
been systematically wrongly identified, this made no significant difference to the
excess.
However in deriving the constituent parts of the observed flux in Chapter 7 two types of error
were calculated, the random error, and a systematic error which will move the fitted line in
Figure 8.1 up or down. Therefore the circumstellar excess was recalculated including the
systematic error.
The result of adding this systematic offset can be seen in Figure 8.2, where on average
E(b - y)cs > 0. The difference in the Spearman rank (rs) level, between the plots with and
without the systematic offset, is minimal with the confidence level between the plots
remaining identical, the results may be examined in Table 8.1.
It should be noted that the method used to produce Figures 8.1 & 8.2 does not differentiate
between spectral types, as does the method derived by Fabregat and Torrejon (1998). In an
effort to compare like-to-like Figure 8.2 is re-plotted with only those objects whose
spectral types are below B5, see Figure 8.3, which can be directly compared to
Figure 6.5. Although it should be noted that the objects used in each method are not
identical as not all the Be stars had associated (H - K) data produced in Chapter 7.
The errors on the fits increase when the data sample is reduced in size but the confidence
levels remain constant. Two anomalies are evident. (i) The fractional error on the plot
(Figure 8.3) showing E(b - y)cs vs H
, inclusive of the systematic offset and showing only
those
B5, has increased dramatically, although the fitted gradient is identical to Figure 6.5,
the direct counter-part derived using the method of Fabregat and Torrejon (1998). The
fractional errors evident in Figure 6.5 are still much larger than the fractional errors seen in
Figure 8.3 - the plot derived here. (ii) The confidence level of the plot (Figure 8.3) showing
E(b - y)cs vs H
has decreased slightly from 3
to 2.5
, no explanation is evident for
this.
| Plot | rs | dof | Sig. level | Conf. level | Stan. dev. | Gradient | Intercept |
E(b-y)cs vs H | 0.27 | 23 | 0.10 | 3.0 | ±0.19 | 0.0012±0.0007 | -0.109±0.016 |
E(b-y)cs vs H | 0.30 | 23 | 0.10 | 3.0 | ±0.20 | 0.0206±0.0047 | -0.172±0.021 |
E(b-y)cs inc. systematic vs H | 0.28 | 23 | 0.10 | 3.0 | ±0.19 | 0.0014±0.0007 | +0.046±0.016 |
E(b-y)cs inc. systematic vs H | 0.31 | 23 | 0.10 | 3.0 | ±0.20 | 0.0220±0.0047 | -0.019±0.021 |
| E(b-y)cs vs E(H ¡ K)cs | 0.55 | 23 | 0.005 | 3.5 | ±0.18 | 0.4081±0.0944 | +0.041±0.012 |
| Including only values earlier than B5 |
E(b-y)cs inc. systematic vs H | 0.30 | 18 | 0.10 | 3.0 | ±0.21 | 0.0009±0.0008 | +0.054±0.022 |
E(b-y)cs inc. systematic vs H | 0.25 | 18 | 0.25 | 2.5 | ±0.20 | 0.0129±0.0052 | +0.020±0.026 |
| E(b-y)cs vs E(H ¡ K)cs | 0.53 | 18 | 0.10 | 3.0 | ±0.19 | 0.2513±0.1371 | +0.043±0.022 |
Table 8.1: Full Table of Reduced Results for the Representative Sample (uvby
). Col. 1 indicates the plot and whence it has been derived,
the Spearman rank correlation coefficient is listed in Col. 2 and the number of degrees of freedom of the test in Col. 3. Col. 4 shows the
significance levels obtained from the lookup tables of Wall (1996) and Col. 5 the confidence levels extracted from Wall (1979). The standard
deviation about the weighted least squares fit is given in Col. 6 and Cols. 7 & 8 give the weighted gradient and intercept of each fit.