The luminosity must be obtained by some means. The sequence starts with parallax and distances to nearby star clusters. From stellar theory we know that there are only certain types of stars with certain intrinsic luminosities (e.g. main sequence stars, for which luminosity is a well defined function of mass and chemical composition). We calibrate the luminosities using nearby clusters for which we know the distances by direct measurement. From our knowledge of these nearby stars we can move out to more distant clusters, using the known luminosities to learn about the intrinsic luminosities of more objects. So the whole distance ladder is built in stages, in which more secure knowledge is the foundation for extrapolation to more uncertain realms.
You have to determine the period-luminosity relationship by independent means, which entails measuring distances to Cepheids using other techniques. This isn't as hard as you might think since Cepheids occur in clusters, and we can use our knowledge of stellar intrinsic luminosities to compute the distance to the cluster. The distinction between Type I and type II was realized when more and better data for cluster distances were obtained, showing that Type I was inherently much more luminous than Type II. Finally, modern stellar structure theory is able to compute models of Cepheid stars so that we understand the physics that makes them pulsate, which in turn leads to a theoretical relationship between period and luminosity.
Redshift refers to the lengthing of the wavelength of light at observation compared with its length at emission. Redshifts can be produced by several processes. One is simply due to relative motion in the sources (the simple Doppler shift). Another is relativistic time dilation. Still another process is the result of a photon losing energy as it climbs out of a gravitational field. This latter effect is a gravitational redshift and it is mathematically expressed in the spacetime metric produced by the gravitating body. The term cosmological redshift is reserved for the redshifts produced by the overall expansion of space (mathematically expressed in the Robertson-Walker metric for expanding space). It is important to keep the various causes of redshift distinct.
In general relativity space isn't exactly "nothing" - it is curved by mass and it tells mass how to move. It is physical and can have properties, e.g., intrinsic geometric curvature. This can be defined in a real, measurable and reproducable way. Expansion can be defined phenomenologically: the worldlines of freefalling observers in the cosmos will diverge with time. But this is significant only over large distances and after large times. Further, all particles in the cosmos are not freefalling with respect to the cosmos as a whole. For example if I was floating in space between galaxies the atoms of my body might like to participate in the Hubble flow, but the intermolecular forces would hold me together - I don't expand any more than I am stretched out by the tidal force difference between my head to my feet on the Earth. Galaxies, clusters, solar systems are held together by their own gravity.
Think of spacetime as a great block of gelatin; what we call an instant of time is a spacelike slice through that block. We are allowed a certain amount of freedom in how we do this, so long as our slices are spacelike. In the Robertson-Walker metric we have chosen to slice up spacetime in terms of something called "cosmic time," which is the same for all observers and corresponds to the rest frame with respect to the uniform background of density in the completely homogeneous and isotropic universe. In this slicing, there is a Hubble law and galaxies recede from on another according to this law. There are other possible ways of slicing up spacetime, but doing it in terms of cosmic time seems to be the most natural.
Think of the tendency to expand as an expansion force. Free particles will respond to this expansion force. However, the expansion force is very weak - it only becomes significant over megaparsec scales. Galaxies, stars, etc. can easily hold themselves together against this force through their own self-gravity.
The scale at which gravitationally bound structures end and expansion takes over is an interesting question. For example, as clusters of galaxies become bigger, they are more loosely held together by self-gravity, so it may be that at some stage, these huge apparent clusters are in fact not bound together and will spread out over time.
It isn't expanding into anything. The expansion can be experienced purely locally: two test particles set down in space will gradually drift apart. An analogy is a rubber sheet being stretched: if you observe two points on the sheet locally they will move apart.
Not all Messier objects are clouds of gas; some are other objects such as globular clusters and nearby galaxies. Even the relatively close gas nebulae are so far away that they exhibit no parallax, and although some of them are expanding or shifting, their great distance and extremely slow motions (on human timescales) means that their apparent size changes too slowly for us to readily detect without the aid of photographs. Many gaseous nebulae do emit colored light due to the presence of specific ionized gases, but even through a telescope the light falling upon the observer's eye is very faint. The color response of the human eyes is extremely poor in faint light. How much color can you distinguish in dim light at night? Color photography of astronomical objects generally requires long exposures.
The broadening of the 21 cm emission line of a galaxy gives a rough estimate of the rotation rate of the galaxy. The rotation rate depends upon the total mass of the galaxy, whereas the luminosity comes only from luminous mass. The Tully-Fisher relationship between these two quantities depends upon a calibration against nearby galaxies; the relationship is empirical rather than a theoretical. In order to make use of this relationship, it is necessary to assume that the mass to light ratio is more or less the same within a given class of galaxies. Thus as long as all galaxies of a given type contain approximately the same density of neutron stars, black holes, etc., the relationship will take such dark matter properly into account.
By Hubble's law, matter outside our Hubble sphere is moving away from us at faster than the speed of light. But that is expansion relative to us, not a physical velocity. Light beyond the Hubble sphere behaves normally as determined locally. The Hubble sphere isn't an edge in the physical sense, any more than a lightcone from an event represents some sort of hard plastic cone separating space into different regions.
The radius at which the universe is expanding at the speed of light relative to us is the Hubble sphere, and it constitutes a kind of horizon (recall the black hole horizon of chapter 9). Light rays emitted toward us from outside the Hubble sphere actually recede from us (like light trying to get outside of a black hole) and we can never receive them. But it is different from the black hole horizon because the Hubble sphere can change with time (as H changes) and that which is now outside of our sphere can come inside later. Moreover, each point in the universe has its own Hubble sphere. There is nothing special about our being outside the Hubble sphere of some distant galaxy, for instance.
Three spatial dimensions, yes. But Flat refers to the curvature (zero) of the three space dimensions, not the number of dimensions. Curvature is an intrinsic property of a geometry whatever its dimensions.
There seem to be two possible questions here. First, is the apparent expansion of the universe really because we (and other galaxies) are shrinking? Believe it or not, that has been suggested. But it is contrived, there is no physical principle to account for it, and its most straightforward application wouldn't agree with observations. Second, could the universe already be contracting (e.g. as occurs in the closed model) and we are just not yet aware of it because distant light hasn't reached us yet? If the universe begins contracting we would begin to see blueshifts in the nearest galaxies first and more distant galaxies later. Remember that the universe would begin to contract at the same point in cosmic time everywhere, by the cosmological principle. So if contraction began we would soon know of it and have plenty of time to say our prayers.
Expansion does not imply expansion into something. Expansion manifests itself locally. The Cosmological Principle does not permit the universe to have an edge; that would be a special location. If the universe has an edge (which would require that the CP be correct only approximately) we know nothing of the edge or what its properties would be.
No. The solar system's self-gravity is far stronger than the expansion effect. The Milky Way stopped expanding when its mass was locally great enough to pull itself together despite expansion.
As the universe decelerates, the Hubble sphere becomes larger and larger. So, in principle, as time goes to infinity (assuming an open model) all of the universe comes into the Hubble sphere. However, if there is a cosmological constant and the universe accelerates, the Hubble constant gets bigger and the size of the Hubble sphere shrinks. In that case there would be parts of the universe we would never be able to observe.
Cosmological redshifts occur because light is traveling through an overall expanding space as it moves from its source to us. Gravitational redshifts occur when light comes to us from a source located in stronger gravity than where we receive it (the light climbs out of the gravitational field and loses energy).
Copyright © 2003 John F. Hawley