Cosmic distance scale

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 apparent motion between the cosmos and the stationary Minkowski frame is entirely virtual. To establish a cosmic distance scale, stationary states at two different points, r apart, are compared, choosing unit radius for unispace leading to... 

The current understanding of interaction between stellar objects is clouded by biased estimates of the cosmic distance scale and may improve after reassessment of cosmological redshifts. 

The expansion of the Universe in encoded into the time dependence of the scale factor ad ). The quantity t corresponds to the cosmic time. One can easily show that observers situated at xl = Const follow geodesics, therefore cosmic time corresponds to the proper time of such observers. It is assumed that any matter element is at rest or almost at rest with respect to the spatial part of the coordinate system. For this reason, the xl are called comoving coordinates, and any distance measured using line element ijdx dx3 is called comoving distance. 

The ionisation provided by cosmic-rays and UV photons drives an ion-molecule chemistry in CSEs which leads to a rich variety of molecular species. In order to be important, chemical processes must occur on a time-scale faster than that of the expansion. Figure 1 from Nejad (1986) shows a number of such time-scales for the case of lRC+10216. One sees that a number of fast processes such as reaction with Hj and dissociative recombination can occur faster than the expansion time but that grain surface processes will be unimportant in the outer envelope as discussed in 2.2. An important point to note in this figure is that fast reaction of a molecular ion with H2 can dominate even dissociative recombination out to a radial distance of - 10 cm. 

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