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In order to test the third hypothesis we need an independent set of galaxy or group distances. We have made the comparison between SBF and 8 other sets of distance: planetary luminosity function (PNLF), Tully-Fisher (TF) from TuRy's forthcoming catalog, Dn - sigma from the Seven Samurai, TF distances from Burstein's Mark II catalog, Cepheid distances, type II supernovae, and type Ia supernovae both as standard candles, and corrected for rate of light curve decline.

These comparisons are shown in Figures 11 and 12, and summarized in Table 1. In each case the population corrected <m
barI0> for each group is plotted against the other distance estimator. Note that in some cases, such as Cepheids, the other distance is based on Mpc, and is therefore shown as a true distance modulus (m - M). In other cases, such as Dn - sigma the zero point is founded on the distant Hubble flow, so the estimator is "5 log d", where d is the distance in terms of the Hubble flow, in km s-1.

Figure 11

Figure 11. Distance comparison between SBF and PNLF, TF, and Dn - sigma.

Figure 12

Figure 12. Distance comparison between SBF and Cepheid, SNII, and SNIa.

Each of the eight plots shows the two variables plotted against each other for the groups in common, and above lies a histogram of the difference of ordinate minus abcissa. The weighted mean of this distribution is listed along with the rms scatter about the mean. Except for SNIa the scatter is consistent with the expected errors in the two estimators. In view of the extraordinary claims made recently about the accuracy of SNIa as distance estimators, it was disappointing to find that the scatter is about 20% in distance.

We prefer the Cepheid zero point so here's our new (and final) calibration.

Equation 4.5 (4.5)

The other values for the zero point which we derive from PNLF and TF are not independent since they are also fundamentally based on the same Cepheid distances.

Table 1. Distance Comparisons.

Estimator N m
barI0 - (m - M) N mbarI0 - 5 log d
Cepheid 7 -1.74 ± 0.16    
PNLF 10 -1.69 ± 0.20    
SNII 4 -1.76 ± 0.22    
TF 26 -1.69 ± 0.41 29 13.55 ± 0.59
Dn - sigma     28 13.64 ± 0.44
SNIa (Mmax)     6 13.92 ± 0.38
SNIa (Deltam15)     6 14.01 ± 0.40
Theory -1.81 ± 0.11    

However, the SNII and theoretical zero points are largely independent of the Cepheid distance scale, so they confirm the validity of this zero point.

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