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4.2. Measuring the Hubble Constant

As stated previously, the expansion of the universe follows the Hubble law given by Eq. (6). Observationally, we measure the recession velocity as a redshift, z, in the light from the supernova (vr = cz). Since every type Ia supernovae has about the same absolute magnitude, Eq. (26), the apparent magnitude provides an indirect measure of its distance. Therefore, for nearby supernovae (z leq 0.3) the Hubble Law is equivalent to a relationship between the redshift and the magnitude. Inserting (26) into (24), using (6), and applying to the current epoch, yields the redshift-magnitude relation

Equation 27 (27)

Defining the z = 0 intercept as

Equation 28 (28)

we can write equation (27) as

Equation 29 (29)

As shown in Fig. 1, low-redshift data can be used to find M tilde and Eq. (28) to solve for the Hubble constant. Studies on type Ia supernova [12] consistently suggest a value for the Hubble constant of about 63 km s-1 Mpc-1.

Figure 1

Figure 1. Using low-redshift supernovae to determine the Hubble constant. The data points are from Ref. 12. The inset graph shows a close-up view of the data and the best-fit line. The best-fit line determines the intercept M tilde which can be used in Eq. (28) to determine the Hubble constant.

The result for H0, found from low-redshift supernovae, tends to set the lower bound when compared with other methods for obtaining H0. For example, if the distances to enough galaxies can be accurately found, then the Hubble law can be used directly to obtain a value of H0. This has partly been the goal of the Hubble Space Telescope Key Project. [13] This project has shown that a careful consideration of the type Ia supernova results in combination with the other methods for obtaining H0 produces what has become a widely accepted value for the Hubble constant

Equation 30 (30)

The value given in Eq. (30) is the one that we shall adopt in this paper.

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