8.3 Results and Discussion


Initial plot of E(b-y) versus H-alpha Initial plot of E(b-y) versus and H-Beta
Figure 8.1: An initial plot of E(b-y)cs versus Ha EW/Å(left panel) and Hb EW/Å for the representative sample, derived using the Howells et al. (2001) method.

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.


Graph pf E(b-y)cs versus H-Alpha Graph pf E(b-y)cs versus H-Beta
Figure 8.2: A plot of E(b-y)cs versus Ha EW/Å(left panel) and E(b-y)cs versus Hb EW/Å(right panel) for the representative sample, derived using the Howells et al. (2001) method and incorporating the systematic errors.

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.


An initial plot of E(b-y)cs versus H-Alpha An initial plot of E(b-y)cs versus H-Beta
Figure 8.3: An initial plot of E(b-y)cs versus Ha EW/Å (left panel) and E(b-y)cs versus Hb EW/Å (right panel) for the representative sample, derived using the Howells et al. (2001) method and incorporating the systematic errors. Including only those objects classified as being below B5.

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 Ha, 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 Hb has decreased slightly from 3s to 2.5s, no explanation is evident for this.


Plot rs dof Sig. level Conf. level Stan. dev. Gradient Intercept
E(b-y)cs vs Ha 0.27 23 0.10 3.0s ±0.19 0.0012±0.0007 -0.109±0.016
E(b-y)cs vs Hb 0.30 23 0.10 3.0s ±0.20 0.0206±0.0047 -0.172±0.021
E(b-y)cs inc. systematic vs Ha 0.28 23 0.10 3.0s ±0.19 0.0014±0.0007 +0.046±0.016
E(b-y)cs inc. systematic vs Hb 0.31 23 0.10 3.0s ±0.20 0.0220±0.0047 -0.019±0.021
E(b-y)cs vs E(H ¡ K)cs 0.55 23 0.005 3.5s ±0.18 0.4081±0.0944 +0.041±0.012
Including only values earlier than B5
E(b-y)cs inc. systematic vs Ha 0.30 18 0.10 3.0s ±0.21 0.0009±0.0008 +0.054±0.022
E(b-y)cs inc. systematic vs Hb 0.25 18 0.25 2.5s ±0.20 0.0129±0.0052 +0.020±0.026
E(b-y)cs vs E(H ¡ K)cs 0.53 18 0.10 3.0s ±0.19 0.2513±0.1371 +0.043±0.022
Table 8.1: Full Table of Reduced Results for the Representative Sample (uvbyb). 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.