Lecture 38 - Large Scale Structure (4/19/96)

Seeds: Chapter 13,14,15

1. Clustering in the Universe
   • Galaxies don't like to be alone, they seem to come in groups.
   • The Local Group of which we are a member contains around 20 galaxies (mostly dwarf ellipticals) with 3 main spirals (Milky Way, M31 Andromeda, and M33 Triangulum) all within a diameter of around 1 Mpc.
   • The nearest large cluster is the Virgo Cluster at a distance of 17 Mpc. It contains more than 2500 galaxies (again mostly dwarfs), and has a total mass of around 10^14 Msun within a radius of 1 Mpc or so.
   • The Virgo cluster exerts a strong gravitational force - the Local Group is moving toward Virgo at around 300 km/s.
   • Like most larger clusters, there is a massive giant elliptical galaxy (M87) at the center of the Virgo cluster. It may have grown large by "cannibalizing" numerous dwarf galaxies that happened to fall into the center of the cluster.
   • M87 is also a strong radio source (Virgo A) and has an active nucleus. It probably contains a supermassive (10^8 Msun) black hole.
   • The Coma cluster at a distance of 100 Mpc has a mass of 10^15 Msun within a radius of over 1.5 Mpc. It contains a giant elliptical and a large S0 at the center. It is made up of mostly E's and S0's with few spirals.
   • Large clusters are mostly devoid of spirals, probably due the the high frequency of close encounters with other galaxies.
   • Our local group and the Virgo cluster seem to be part of a cluster of clusters in the shape of a roughly flattened pancake called the Local Supercluster.
   • Surveys of galaxy redshifts out to 200 Mpc show a network of filaments and walls of galaxies surrounding empty regions called voids. The scale of these structures is approximately 100 Mpc.
   • There may be larger structures still (supervoids? superwalls?) but current redshift survey are not "deep" enough to see more than about 200 Mpc. There are some indications that 100 Mpc is the scale of the largest structures, but we will not really know until we look!
   • The Sloan Digital Sky Survey will give us a look on larger scales, measuring redshifts for 100 million galaxies!
   • There appears to be a hierarchy of clustering: galaxies -> groups -> clusters -> superclusters -> walls? filaments? voids? -> ?????
   • Current popular theories predict a large-scale structure formation scheme from the smallest to the largest scales, or bottom up. The smallest scales collapse first, then organize themselves through gravity into larger clusters and superclusters.
   • Alternative models predict that the largest scale structures form first, then fragment into smaller subunits (like star formation in molecular clouds), or a top down scheme. This is out of favor now.
2. Introduction to Cosmology
   • The distribution of galaxies, on scales greater than 200 Mpc, appears to be the same everywhere in space. Thus, we believe the Universe is homogeneous on large scales.
   • Furthermore, it appears the same in every direction we look, or isotropic.
   • These two statements are called the cosmological principle: the Universe is homogeneous and isotropic on large scales.
   • This means the all "observers" anywhere in the Universe at the same time will see the same general properties. There is no special place in the Universe (the ultimate Copernicanism)!
   • The laws of physics are universal, they apply the same everywhere in the Universe and at all times.
   • The laws of physics we discover based on experiments on the Earth can be applied to the Universe at large!
   • It turns out, using universal laws of physics (Einstein's theory of Relativity in particular), the assumption of homogeneity and isotropy of the Universe restricts the possible cosmologies to a particular set. Requiring the solution to be expanding (as we observe) narrows the choices down further to the Freidmann - Robertson - Walker (FRW) solutions.
   • These solutions of the Einstein equations for the Universe results in an unbounded Universe (no edges), either finite in volume (like the surface of a sphere) or infinite (like an infinite plane).
   • Since the Universe is expanding, any length scale, like the average distance between galaxies, must have been smaller in the past. Extrapolation back in time of the equations gets us to a point where the distance is zero - the Universe is infinitely dense. This point is called the Big Bang, but should not be thought of as an explosion thought it was indeed very hot then.
3. Is the Sky Dark at Night?
   • Does the Universe extend forever?
   • The finite speed of light c: distance = time. When you look out into the Universe, you look back in time.
   • The expansion of the Universe: distance = redshift. The wavelength of light emitted at large distances (and early times) is increased on the way to us.
   • Because the Universe is unbounded, and thus paths can be essentially infinite in length, you would expect if it were filled uniformly with galaxies like we see, that the sky would be bright as a star at night, because every line of sight would end at the surface of a star in the infinite distance somewhere.
   • This like being in an infinite forest, you could never see anywhere that you didnt see a tree!
   • This is called Olber's Paradox, because the sky appears to be pretty darn dark at night to us!
   • So why is the sky dark at night if we think the Univese is unbounded?
   • Well, though if we look in a particular direction, we look back in time. If the Universe had a beginning, it would be unbounded in space but bounded in time by its beginning!
   • Thus, the sky is dark at night mostly because galaxies were formed about 15 billion years ago (about a billion years after the "beginning" of the Universe). Thus, the edge of the "forest" of galaxies is at 15 billion light-years distance!
   • There is another effect due to the Hubble redshift from the expansion.
   • Light emitted at great distances will be redshifted to longer wavelengths. The peak of the stellar blackbody in the visible will be redshifted to the IR or radio waves, and thus the sky could appear dark in the visible, but bright in the infrared or radio.
   • This is a part of the solution to Olber's paradox, and as we will discover the sky is indeed bright in the microwaves!
4. The Expansion of the Universe
   • In 1929, Edwin Hubble at Mount Wilson Observatory near Los Angeles discovered the Universe was expanding uniformly.
   • He found that every galaxy had a Doppler redshift that implied a velocity proportional to the distance: v = H d
   • This is true at small distances where the Doppler formula holds: wavelength obs/true = 1 + v/c
   • The redshift z is defined: wavelength obs/true = 1 + z
   • Thus, for small distances: d = c z / H
   • This expansion of the Universe, with velocity proportional to distance, is characteristic of a universe with uniform expansion, where the distance between any two points is increasing at the same fractional rate.
   • This fractional rate is the Hubble constant H, in units of distance / distance per unit time (and thus velocity / distance). The customary unit is km/s per Mpc (or km/s/Mpc).
   • The solutions to Einsteins equations give this uniform expansion due to the creation of new space between all points in the Universe!
   • There is no necessary real velocity, it is space that is expanding. There is no explosion hurling galaxies outward from a center (there is no center from the cosmological principle).
   • Furthermore, General Relativity stated that space-time is curved in the presence of mass (like a black hole). Thus, the space-time of the Universe is curved due to the presence of mass (like us) in it!

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