Diagram of Hubble B

We built a diagram of Hubble in the close filter B of the batch of supernovæ. For that, the following model was adjusted:

$$\chi^2 = \sum_{sn=i} \left(\frac{ m_B^{corr}-\alpha(1-s)-\beta(m^... ...m_V^{corr})- (M +\mu(z, \Omega_{\rm M}, \Omega_\Lambda ))} {\sigma_i} \right)^2$$ (10.3)

where the error $\sigma_i$ for a point of measurement is written:

$$\sigma_i^2 = (1-\beta)^2 \sigma^2_{m_B}+ \beta^2 \sigma^2_{m_V} +... ...left( \frac{ d \mu (z,\Omega_{\rm M},\Omega_\Lambda ) } {dz}\right)^2\sigma^2_z$$ (10.4)

where $\sigma_z$ the error to the measure of the redshift. We consider an intrinsic error on the redshift of 0.001 corresponds to the dispersion observed of the own movements of the galaxies.

The adjusted parameters are $M$ respectively the correction for the factor of stretching, the color and the constant term. We considered during this adjustment a cosmology with $0.49$.

Figure 10.6: Diagram of Hubble out of B without correction for the factor of stretching nor for the color for a batch of 46 close supernovæ with redshifts beyond 0.01.