The Hubble constant

Since no astronomical standard candle is known - all proposed objects have been shown to be essentially non-uniform in one way or another - we nowadays have to calculate and plot the distance modulus for the objects. The scatter around the linear expansion line is less than 0.2 magnitudes or 20% Tonry et al. 2003. Independent of our ignorance of the exact explosion mechanism or the radiation transport in the explosions this proves that SNe la can reliably be used as a distance indicator in the local universe. This situation is very much comparable to the Cepheid stars, where the period-luminosity relation is based on empirical data of objects in the Magellanic Clouds. 

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 

Recently, Mario Hamuy has realised that the expansion velocity and the luminosity during the plateau phase correlate and that Type II SNe may be quite good distance indicators Hamuy. Pinto. 2002. The distance accuracy achieved this way can be better than 20%. These determinations are based on the physical understanding of the plateau phase of SNe II and are linked to physics of the supernova atmosphere. This means that they are independent of the distance ladder, which is needed, e.g., for the SNe la. Typical values for the Hubble constant from SNe II are in the range of 65 to 75 km s-1 Mpc-1 Hamuy 2003. 

---

The age of the Universe is the inverse of the Hubble constant. The system of units must first be rationalised to convert all of the light-years into kilometres and then years, so that ... 

Hubble s crucial observation was that, in every direction one looks, the farther away a galaxy is, the more the light from that galaxy is red-shifted. If the red shift is a Doppler shift, this implies that the farther away the galaxy is, the faster it is moving away from us. The most reasonable explanation for this observation is that the universe is uniformly expanding everywhere. The current best estimate for the Hubble Constant, which describes the rate of expansion, is 70.8 km s-1 megaparsec-1, with an uncertainty of 5.6%. 

J. P. Vigier, G. Le Denmat, M. Moles, and J. L. Nieto, Possible local variable of the Hubble constant in VanDenBergh s calibration of Sc-type galaxies, Nature, 257, 773 (1975). 

Again, Fuli [41] established a relation between nonzero photon mass and the Hubble constant H. Using that relation, one obtains... 

Figure 9.21. Cloud of points from a Monte Carlo Markov chain sampling of the likelihood of models fit to the WMAP plus other CMB datasets. The size of the points indicates how consistent the model is with the HST Key Project on the Distance Scale value for the Hubble constant. The contours show the likelihood computed for 230 Type la supernovae (Tonry et al., 2003).

Because the matter density VLmh2 was fairly well constrained by the amplitudes, the positions of a point in Figure 9.21 served to define a value of the Hubble constant. The size of the points in Figure 9.21 indicates how well this derived Hubble constant agrees with the H0 = 72 8 from the HST Key Project (Freedman et al., 2001). Shown as contours are the Ax2 = 1, 4, 9 contours from my fits to 230 SNe la (Tonry et al., 2003). Clearly the CMB data, the HST data, and the SNe data are all consistent at a three-way crossing that is very close to the flat Universe line. Assuming the Universe actually is flat, the age of the Universe is very well determined 13.7 0.2 Gyr. 

For completeness, we present here the equations governing the evolution of an FRW Universe. First, we define the expansion rate as the value of a/a, where the overdot is a time derivative the value of the expansion rate today is the Hubble Constant,... 

The data are consistent with other cosmological observations, including the Hubble constant, Ho = 71 JJ [ km/s/Mpc, and the baryon density, QBh2 = 0.0224 0.0009. 

Re Entries [8]-[ll], Refs. [2], [8], [10], and [11]) As per Entries [8]—[11], results for the Hubble constant have improved with time, asymptotically converging onto those provided by Ref. [11]. The results for the Hubble constant as per Ref. [8] are in essential agreement with Entry [9]. The history of values of the Hubble constant also is briefly discussed in Entry [9] and Ref. [10]. Reference [10] surveys the history of values of the Hubble constant determined via work done through 2012. Reference [10] was for sale at the 27th Texas Symposium on Relativistic Astrophysics, held at the Fairmont Hotel in Dallas, Texas, December 8-13, 2013. 

In order to compare numbers across the decades, it is essential to allow for changes in the best estimate of the cosmic distance scale or the Hubble constant (H). In most cases, the L that you deduce for a galaxy (etc.) from its brightness will be proportional to the square of its distance, d, or to H 2, and the mass you calculate, from some form of M = V2R/G, will be proportional to d or H 1. Thus M/L scales as d 1 or H, and a velocity dispersion for a cluster of galaxies plus its angular size on the sky that led to M/L = 1000 for H = 500 km/sec/Mpc now, with H - 70 km/sec/Mpc, corresponds to M/L = 140. When Schwarzschild produced his table, the community was just incorporating the first of the large drops in H, from about 500 to 250 km/sec/Mpc. 

The metallicity dependence of the Cepheid period-luminosity relation, currently under debate with respect to the determination of the Hubble constant and the extragalactic distance scale. 

If the universe is expanding, the galaxies were once much closer to each other. If the rate of expansion has been unchanged, the inverse of the Hubble constant, H, would represent the age of the universe. 

Hubble. Edwin Powell (1889-1953) US astronomer, who worked at both the Yerkes Observatory and the Mount Wilson Observatory. Most of his studies involved nebulae and galaxies, which he classified in 1926. In 1929 he established the Hubble constant, which enabled him to estimate the age of the universe. The Hubble space telescope is named after him. 

Hubble constant The rate at which the velocity of recession of the galaxies increases with distance as determined by the redshift. The value is not agreed upon but current measurements indicate that it lies between 49 and 95 km s per megaparsec. The reciprocal of the Hubble constant, the Huhhle time, is a measure of the age of the universe, assuming that the expansion rate has remained constant. In fact, it is necessary to take account of the fact that the expansion of the universe is accelerating to get an accurate determination of its age. 

---