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7.3. The results

Table 2, adapted from Freedman et al. (2001), lists the values of H0 obtained from the different methods, based on the Cepheid distances of the Key Project. Of the five calibrated methods, it is clear that the Fundamental Plane is somewhat of an outlier. Combining these results, the H0 Key Project obtained the value H0 = 72 ± 3 ± 7 km s-1 Mpc-1, where the first quoted error is random and the second is systematic. Using three different weighting schemes, all the results were found to be consistent with H0 = 72& #177; 8 km s-1 Mpc-1.

Table 2. H0 from secondary methods (the Key Project)

Error
(random, systematic)
Method H0 (%)

36 Type Ia SN, 4000 < cz < 30, 000 km s-1 71 ±2±6
21 TF clusters, 1000 < cz < 9000 km s-1 71 ±3±7
11 FP clusters, 1000 < cz < 11, 000 km s-1 82 ±6±9
SBF for 6 clusters, 3800 < cz < 5800 km s-1 70 ±5±6
4 Type II SN, 1900 < cz < 14, 200 km s-1 72 ±9±7

In an independent work, Allan Sandage, Gustav Tammann, Abijhit Saha, and collaborators used a Cepheid calibration of the peak brightness of Type Ia Supernovae (using HST), and thereby determined H0 directly from the Hubble diagram of the latter. This effort resulted to date in nine supernovae Ia with "normal" spectra (i.e., the spectra characterizing about 60% of all Type Ia supernovae) to which Cepheid distances are known (Table 3, adapted from Saha et al. 2001). After corrections based on the decline rate and colors, the weighted average of the absolute magnitudes of the calibrators was fitted to a sample of 35 more distant, "normal" Type Ia supernovae. After further correcting for some systematic errors, Saha et al. (2001) obtained H0 = 58.7 ± 6.3(internal) km s-1 Mpc-1 (for cosmological parameters OmegaM = 0.3, OmegaLambda = 0.7).

Table 3. Mean absolute B, V, and I magnitudes of nine SNe Ia with known Cepheid distances, without and with corrections for decline rate and color

SN Galaxy (m - M)o M0B MoV MoI Deltam15 (B - V)o McorrB McorrV McorrI
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)

1937C IC 4182 28.36(12) -19.56 (15) 19.54 (17) ... 0.87 (10) -0.02 -19.39 (18) -19.37 (17) ...
1960F NGC 4496A 31.03 (10) -19.56 (18) -19.62 (22) ... 1.06 (12) 0.06 -19.67 (18) -19.65 (22) ...
1972E NGC 5253 28.00 (07) -19.64 (16) -19.61 (17) -19.27 (20) 0.87 (10) -0.03 -19.44 (16) -19.42 (17) -19.12 (20)
1974G NGC 4414 31.46 (17) -19.67 (34) -19.69 (27) ... 1.11 (06) 0.02 -19.70 (34) -19.69 (27) ...
1981B NGC 4536 31.10 (12) -19.50 (18) -19.50 (16) ... 1.10 (07) 0.00 -19.48 (18) -19.46 (16) ...
1989B BGC 3627 30.22 (12) -19.47 (18) -19.42 (16) -19.21 (14) 1.31 (07) -0.05 -19.42 (18) -19.41 (16) -19.20 (14)
1990N NGC 4639 32.03 (22) -19.39 (26) -19.41 (24) -19.14 (23) 1.05 (05) 0.02 -19.39 (26) -19.38 (24) -19.02 (23)
1998bu NGC 3368 30.37 (16) -19.76 (31) -19.69 (26) -19.43 (21) 1.08 (05) -0.07 -19.56 (31) -19.55 (36) -19.31 (21)
1998aq NGC 3982 31.72 (14) -19.56 (21) -19.48 (20) ... 1.12 (03) -0.08 -19.35 (24) -19.34 (23) ...
  Straight mean -19.57 (04) -19.55 (04) -19.26 (06) -19.49 (04) -19.47 (04) -19.16 (06)
  Weighted mean -19.56 (07) -19.53 (06) -19.25 (09) -19.47 (07) -19.46 (06) -19.19 (09)

Unlike the uncertainty by a factor of two that has plagued this field for decades, therefore, the observations with HST have reduced the uncertainty in the value of the Hubble constant to about 15%.

The values obtained by both the Key Project and the Sandage-Tammann-Saha team are also consistent with other recent measurements based on combining the Sunyaev-Zeldovich effect with x-ray flux measurements of clusters, and on time delays in gravitational lensing. The systematics in these methods are still estimated to be at the 20-25% level, and the value obtained for the Hubble constant is H0 ~ 60 km s-1 Mpc-1 (e.g., Schecter 2000, Reese et al. 2002, 2000).

Analysis of Sunyaev-Zeldovich effect (Sunyaev and Zeldovich 1970) and x-ray data provides a direct method for determining distances to galaxy clusters. Clusters of galaxies are known to contain hot intracluster gas (at kT ~ 10 keV), trapped in the clusters' potential wells. Photons from the cosmic microwave background that pass through a cluster have a finite probability (optical depth tau ~ 0.01) to interact with energetic electrons in the intracluster gas. The inverse Compton scattering that ensues boosts the energy of the microwave background photon, generating a small distortion (a decrement in frequencies ltapprox 218 GHz and an increment above this value) in the spectrum of the microwave background. The Sunyaev-Zeldovich effect is proportional to the integral of the pressure along the line of sight (integ ne Te dl). Since the x-ray emission from the intracluster medium is proportional to a different power of the density, integ ne2 Lambdadl (where Lambda is the cooling function), a combination of the two measurements (given some assumptions about the cluster geometry) can be used to determine the distance to the cluster, independently of the distance scale ladder that is based on standard candles.

Finally, the Wilkinson Microwave Anisotropy Probe (WMAP) found a Hubble constant of H0 = 72±5 km s-1 Mpc-1. When the WMAP data were combined with the Key Project results, finer-scale cosmic microwave background experiments, and other large-scale structure and Lyman alpha forest data, the best-fit value of the Hubble constant was H0 = 71+4-3 km s-1 Mpc-1 (Spergel et al. 2003).

Type Ia supernovae have played a key role not only in the determination of the age of the universe (through H0), but also in the determination of the universe's geometry, and the dynamics of the cosmic expansion. This came about through a combination of ground-based and HST observations in which both careful planning and serendipity played a part.

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