Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.3 4.3bsd-beta 6/6/85; site ucbvax.BERKELEY.EDU Path: utzoo!watmath!clyde!burl!ulysses!bellcore!decvax!ittatc!dcdwest!sdcsvax!ucbvax!space From: JOSH@IBM-SJ.ARPA Newsgroups: net.space Subject: (none) Message-ID: <8603081251.AA14819@s1-b.arpa> Date: Fri, 7-Mar-86 11:41:26 EST Article-I.D.: s1-b.8603081251.AA14819 Posted: Fri Mar 7 11:41:26 1986 Date-Received: Sun, 9-Mar-86 08:27:44 EST Sender: daemon@ucbvax.BERKELEY.EDU Organization: The ARPA Internet Lines: 95 Subject: Clusters, Clusters, Clusters >Date: Thu, 6 Mar 86 22:37:45 EST >From: "Keith F. Lynch" >Subject: Size of the Galaxy > > As an aside, it is interesting to note that in the early part of this > > century, an incorrect accounting for interstellar absorption caused many > > astronomers to believe our galaxy was a small elliptical one, rather > > than the large spiral it really is. > > Actually, I think it was the other way around. For a while it was >thought that this galaxy was unusually large. The determination of the distance to and the distribution of the globular clusters (I've apparently got lots of cluster problems ;-) by Harlow Shapley established that the center of the Milky Way star system was about 10Kpc (kilo parsec) from the solar system. This substantially changed the ideas of the location of center of the galaxy from before Shapely's work. The exact history of the errors in calibration of the distance measures is complex and not well known to me. It may be that the ideas of the size of the Milky Way were also wrong in the direction of being too large earlier, but I believe the proximate effect the discovery of the distribution of globular clusters was to increase the best idea of the size of the galaxy at that time. In any event, Shapley's calibration of the period luminosity relationship of "cluster variables" was off by some factor (like two? see references in Weinberg's (see below) sections on "the cosmic distance ladder"). I've received several comments to the effect that indeed clusters can make a difference in Olbers paradox. I remain unconvinced, perhaps I also remain incorrect. The contention that small scale clustering of the sort cited by R.E. Mass (a la Cantor ternay set) I think is inappropriate in this context. A common example in the context of fractal dimension is the length of the coast line of Britain. On many scales, the "jaggedness" of the coast line appears the same. Thus the length of the coast line depends on the length of the "ruler" used to measure it. This property (the statistical characteristics of the coast line appear the same on multiple scales) of self similarity breaks down at both large and small scales in the case of the coast line of Britain. On size scales smaller than a grain of sand, the self similarity breaks down (or certainly by the size scale of an individual atom) and on size scales larger than the British Isles the self similarity breaks down (or at least by the size scale of the whole earth). For Olbers paradox, we are considering the case of the PHYSICAL universe. In this case, the size of stars imposes a lower limit on the clustering on small scales. This means that, for example, the filling factor of a given volume is bounded below by having all the stars in the volume closely packed in the center of the volume element. Thus above some size scale, probably something of order a parsec for the universe we live in, the clustering of stars BELOW that size scale can be neglected and each (for example) cubic parsec replaced with a volume with some expected (non-zero) filling factor. Therefore, I think clustering on a small scale is not relevant to the problem in Olbers paradox. Basically, the same point is ignored when arriving at the (erroneous) conclusion that the sky is infinitely bright in the usual Olbers paradox: neglecting the finite size of stars. It is NOT something peculiar to the clustering argument. One reasonable reference is the section on Olbers Paradox in Steven Weinberg's book "Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity" (John Wiley 1972) pp. 611-613. In particular, he mentions the apparent divergence in the "classical" Olbers paradox and why it does not occur. Weinberg also gives the condition for which a steady state universe (with expansion) can avoid Olbers paradox, but it already violates another assumption, of Olbers, namely that the universe is static. I am less certain about the question of clustering on large scales. It is true that if the self similarity of clustering continues to larger and larger scales, it may not be possible to define a universal average density. However, at any particular size scale, there is a definable average density (for the Universe inside that size scale). For larger and larger scales, the average density may fluctuate around and never converge to anything, but above some size scale, for example whatever size it would take to have every line of sight end on a star for a homogeneous (unclustered) distribution of stars times some suitable large factor, further clustering is irrelevant since all lines of sight have already terminated (with high probability). Obviously Olbers model is not a good one (it is in Weinberg's section on "naive" cosmologies) but it's the one the paradox goes with. But I still don't think clustering fixes it, at least if we leave in stars. Sorry I can't easily post this to net.astro, where it would probably be more appropriate. Josh Knight IBM T.J. Watson Research Center josh.yktvmh@ibm-sj.arpa, josh@yktvmh.BITNET