6.6 Results

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MPhys Thesis

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6.6 Results

Object	(b -y)_st	Err(b -y)_st	m_1st	Errm_1st	c_1st	Errc_1st	H_st	ErrH_st








BD -00 03543	-0.023	0.011	1.707	0.170	0.299	0.151	3.467	0.324






BD -12 05132	-2.594	0.078	0.314	0.360	2.467	0.825	4.372	0.840






BD -19 05036	0.242	0.013	0.336	0.080	0.011	0.056	2.826	0.080






BD -20 05381	0.029	0.012	0.377	0.074	0.112	0.052	2.728	0.050






BD +02 03815	0.099	0.011	0.577	0.084	0.105	0.056	2.753	0.057






BD +23 1448	0.461	0.021	-0.147	0.112	0.197	0.133	2.473	0.118






BD +27 797	0.285	0.014	-0.447	0.086	0.216	0.112	2.477	0.095






BD +27 850	0.098	0.013	-0.003	0.067	0.176	0.076	2.571	0.068






BD +36 03946	0.349	0.014	-0.149	0.079	-0.039	0.066	2.582	0.063






BD +37 03856	0.289	0.014	0.027	0.076	-0.016	0.060	2.629	0.051






BD +37 675	-0.002	0.010	0.526	0.079	0.123	0.052	2.738	0.052






BD +40 1213	0.020	0.011	0.232	0.067	0.117	0.052	2.699	0.045






BD +42 1376	0.073	0.011	0.145	0.066	0.098	0.052	2.672	0.044






BD +46 275	-0.031	0.010	0.592	0.082	0.164	0.061	2.744	0.055






BD +47 03985	-0.025	0.010	0.257	0.067	0.145	0.056	2.700	0.045






BD +49 614	-0.018	0.011	0.585	0.083	0.133	0.054	2.770	0.061






BD +55 552	0.166	0.015	0.366	0.079	-0.012	0.052	2.703	0.048






BD +55 605	0.241	0.013	0.084	0.073	-0.050	0.059	2.668	0.044






BD +56 473	0.275	0.013	-0.075	0.074	0.010	0.060	2.613	0.055






BD +56 478	0.255	0.014	-0.001	0.074	-0.021	0.058	2.628	0.051






BD +56 511	0.397	0.015	0.232	0.089	-0.132	0.081	3.438	0.202






BD +56 573	0.309	0.015	-0.235	0.082	0.088	0.078	2.597	0.057






BD +20 4449	0.030	0.008	0.037	0.052	0.029	0.017	2.622	0.051






BD +29 3842	0.342	0.013	0.166	0.081	-0.075	0.033	2.689	0.044






BD +29 4453	0.077	0.008	-0.004	0.053	-0.019	0.016	2.660	0.043






BD +31 4018	0.194	0.009	-0.108	0.061	-0.027	0.021	2.617	0.052






BD +42 4538	0.107	0.008	0.321	0.060	-0.013	0.017	2.705	0.044






BD +50 825	0.065	0.007	0.629	0.072	0.105	0.018	2.763	0.059






BD +58 554	0.279	0.011	0.635	0.089	-0.040	0.027	2.806	0.072






CD -22 13183	0.144	0.012	0.405	0.078	0.092	0.057	2.709	0.047

Table 6.2:

The full Strömgren data set for the representative sample.

The fits to the plotted graphs may be compared in Table 6.3. The data in both graphs of Figure 6.5 are found to correlate at the 3

level, although the form of that correlation is not returned. Regarding this a cautionary note is sounded by Anscombe’s quartet (Anscombe, 1973, see also Wall 1996), which shows four simple eleven point x,y scatter plots each of which contain the same mean x and y value, the same correlation coefficient, the same linear fits and error on the fits, but very different scatters. Two of the plots would not normally be associated with linear fits; whilst the data maybe correlated the form of that correlation is far from clear and not necessarily a simple linear. To be noted also is that the correlation test does not take into account errors on the data; “No quantity is of the slightest use unless it has an error of measurement associated, the uncertainties must be known” (Wall, 1996). To ascertain the form of the association a linear relationship is fitted as a first attempt.

The results of both fits are in agreement with those of Fabregat and Torrejon (1998), however the errors on those fits are too large to regard the data to be linearly related on the basis of these data alone, the source of the errors on the fits come from the observations. The _reduced²=1.047 which gives more substance to the linear fit being correct. Fabregat and Torrejon (1998) supply 1 error values ( = 0.043), although this value appears to be the scatter about the fitted line and not an error on the fits, as a comparison the standard deviation on the representative sample is 0.07. It is therefore not clear whether the fits presented by Fabregat and Torrejon (1998) can be regarded with more significance than those derived for the representative sample.

In an attempt to ascertain how significant the effect of including objects above B5 is, the full representative data sample is plotted, see Figure 6.6. Whilst r_s is smaller for those plots containing the full data sample (see Table 6.3) the confidence levels are the same, indicating that there is no significant difference between the two data sets and that the change in correlation between data sets is minimal.

circumstellar emission versus H-alpha, full sample

circumstellar emission versus H-beta, full sample

Figure 6.6:

A plot of E(b-y)_cs versus H

EW/Å(left panel) and E(b-y)_cs versus H

EW/Å(right panel) using the full-sample of the representative sample, derived using the Fabregat and Torrejon (1998) method.

Plot rs dof Sig. level Conf. level Stan. dev. Gradient Intercept _____ E(b - y)cs vs H

0.34 26 0.05 3.0

±0.06 0.0008±0.0011 +0.017±0.027 E(b - y)cs vs H

0.28 26 0.10 3.0

±0.07 0.0030±0.0068 +0.021±0.029 Mv (Stromgren) vs Mv (Schmidt-Kaler) 0.77 24 <0.0005 4.0

±1.44 0.4788±0.1240 +0.710±0.344 Including only values earlier than B5 E(b - y)cs vs H

0.43 21 0.025 3.0

±0.07 0.0008±0.0011 +0.022±0.028 E(b - y)cs vs H

0.40 21 0.05 3.0

±0.07 0.0050±0.0067 +0.020±0.028 Mv (Stromgren) vs Mv (Schmidt-Kaler) 0.72 21 <0.0005 4.0

±1.27 0.2954±0.065 +0.077±0.072__ Table 6.3: 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.

Using zero age main sequence fits, derived by Balona and Shobbrook (1984), it is possible to derive the magnitude (M_v) of the underlying Be star. The generated magnitudes are plotted against magnitudes tabulated by Schmidt-Kaler (1982). The results are plotted in Figure 6.7.

Derived magnitude against externally derived magnitudes

Derived magnitude against tabulated magnitude

Figure 6.7:

Plot of M_v derived using Balona and Shobbrook (1984) against tabulated M_v values (Schmidt-Kaler, 1982) for the full represenatative sample (left panel) and those stars earlier than B5 (right panel).

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