Hubble diagram

The cosmological parameters and a can be determined from the Hubble diagram, provided that we have some well-calibrated cosmological standard candle that can be observed across a wide range of redshifts. This is precisely the approach adopted by Riess et al. (1998) and Perhnutter et al. (1999) when they used the type la supernovas. Pilar Ruiz-Lapuente at the University of Barcelona and Renald Pain at the University of Paris both made contributions to this exemplary cosmological programme. 

The simplest method is to assume that all supernovae are identical. This is, of course, not true (see previous paper) but it turns out that the subclass of the Type la supernovae is indeed rather homogeneous. The first to plot a Hubble diagram of Type la Supernovae was Kowal Kowal 1968. There are essentially three quantities that can be derived from such a Hubble diagram in the nearby universe the slope of the expansion line, the scatter around the expansion line and the value of the local Hubble constant from the intercept at zero redshift (e.g. Tammann Leibundgut 1990 Leibundgut. Pinto 1992). The slope gives an indication of the local expansion and for a linear expansion in an isotropic universe it has a fixed value. The scatter around the expansion line provides a measure of the accuracy of the standard candle and the measurement errors. The intercept of the line, finally, together with an estimate of the... 

Figure 12.1. Hubble diagram of nearby Type la supernovae. The distances are derived from light curve shape corrected luminosities (data from Tonry et al. 2003). The solid line is for an empty universe (Qa = Ojh = 0), the dotted line for an Einstein-de Sitter model (Qa = 0, Hm = 1) and the dashed line for a model with no matter and all cosmological constant (Qa = 1,0 1 = 0). The concordance model (Qa = 0.7, Qaj = 0.3) is shown as the line fitting the data best. The bottom panel shows all distances relative to the empty universe model.

The K-band Hubble diagram shows increased scatter above a redshift of 2, but remains remarkably ti t overall. The curves show the predictions for a constant-mass, passivdy evolving stellar population, qo = 0.1, and a range of z/ the modd/data correspondence looks oicouraging. The same modds with qo = 0.5 do not fit the data at aU, a result that agrees with, but is independent of the age-redshift argument above. A more detailed discussion is given by McCarthy (1993). 

Fig. 1. The Hubble-Toomre diagram, relating the present morphologies of (large) galaxies and their (major) merger histories. Quantification of at least one merger and assembly history, for the Milky Way, is required to test the generality of these evolutionary paths.

M. Schwarzschild, A. Sandage and others pioneer theory of stellar evolution without extensive mixing and apply it to HR diagrams of globular clusters getting ages of several Gyr, comparable to the new inverse Hubble constant. 

Hubble redshift-magnitude diagram an important cosmological tool expressing the rate of expansion of the Universe in the past... 

Systematic research using wide-held images taken at intervals of three to four weeks have allowed two independent groups, the Supernova Cosmology Project and the High-z Supernova Search Team, to identify more than 50 SNIa events at intermediate redshifts. The Hubble redshift-magnitude diagram has been extended out to z = 1. 

Fig. 5.46. <4 large twin in a poly diacetylene single crystal, (a) Scanning electron micrograph of twin (b) schematic diagram of twin on a molecular level. (Young, Bloor, Batchelder and Hubble, J. Mater, Sci., 13 (1978) 62, reproduced with permission.)... 

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