 
These notes will supplement the text and the discussion in class. In class, I shall describe the "distance pyramid" with the following building blocks:
These methods are basically dependent on the earlier ones the pyramid. For example, distances obtained using Cepheid Variables exploit the Period-Luminosity relation . The P-L relation is established using a dozen or so Cepheids located in open clusters. Distances to such a cluster is found using the brightness of its main sequence stars and assumed luminosities of these stars (i.e., spectroscopic parallax). The latter are obtained from similar stars whose distances are measured using their trigonometric parallaxes. Finally, the method of trigonomical parallax is based on the AU which is determined by radar ranging. We should expect the building blocks of the pyramid to change with time, as our understanding evolves, and to be in part a personal choice. A recent change is the use of the trigonometric parallax to determine distances to a few of the nearest galactic Cepheids. This is now possible -- just -- thanks to the Hipparcos satellite that measured trigonometric parallaxes from above the Earth's atmosphere. Our list of distance indicators is not complete. Several other methods are in use. Here, I describe three:
The Tully-Fisher relation An important alternative to standard candles
was discovered in the 1970s, when astronomers found a clear correlation
between the rotational speeds and the luminosities of spiral
galaxies within a few tens of megaparsecs of the Milky Way. Because
rotation speed is a measure of a galaxy's total mass, we should
perhaps not be surprised that it related to luminosity -- the
more mass a spiral galaxy has, the faster its disk rotates and
the brighter it is. What is surprising is how tight the correlation
is. The Tully-Fisher relation, as it is now known (after
its discoverers), allows us to obtain a remarkably accurate estimate
of a spiral galaxy's luminosity simply by observing how fast
it rotates. Comparing the galaxy's inferred luminosity
brightness with its observed brightness then yields the distance. To see how this method is used in practice,
imagine we are looking edge-on at a distant spiral galaxy (the
Milky Way, say, seen from far outside). Let's suppose we are
observing one particular emission line. Radiation from the side
of the galaxy where matter is generally approaching was blueshifted
by the Doppler effect. Radiation from the other side (which is
receding from us) is redshifted by a similar amount. The overall
effect is that line radiation is "smeared out" or "broadened,"
by the galaxy's rotation. The faster the rotation, the greater
the amount of broadening. Conversely, by measuring the amount
of broadening, we can determine the galaxy's rotation speed.
Once we know that, the Tully-Fisher relation tells us the galaxy's
luminosity. As before, comparing the known absolute brightness
(that is, the luminosity) with the measured apparent brightness
allows us to determine the distance to the galaxy. The particular line normally used in these
studies actually lies in the radio part of the spectrum. It is
the 21-m line of cold, neutral hydrogen in the galactic disk.
It is used in preference to optical lines because (1) optical
radiation is strongly absorbed by dust in the disk under study
and (2) the 21-cm line is normally very narrow, making the broadening
easier to observe. In addition, astronomers often use infrared,
rather than optical, luminosities in the Tully-Fisher relation
to avoid absorption problems caused by dust, both in our Galaxy
and in others. The Tully-Fisher relation is found using galaxies whose distances are known from Cepheid variables. Then, the relation may be used to get distances to more distant galaxies.
Planetary Nebulae The central stars of planetary nebulae
are very bright in the ultraviolet part of the spectrum. The
most luminous ones have total luminosities, including ultraviolet
radiation, of 104 - 105 L Planetary nebulae are easy to find in other
galaxies. All one has to do is photograph the light of one of
the emission lines. Ordinary stars will not emit strongly at
this wavelength, and the planetary nebulae will therefore stand
out from the background light of other stars. Observations how that the number of planetaries
in a galaxy depends on their intrinsic luminosity. Suppose you
were to count all the planetaries in a galaxy whose distance
you already know from a study of the Cepheids in it. If you then
plot the number of planetaries that fall within each interval
of luminosity, you will find that there will be relatively few
very bright planetaries. You will also discover that the number
of planetaries increases with decreasing brightness. What you
have done is determined what is called a luminosity function
for planetary nebulae. Furthermore, if you study planetaries
in many galaxies, you will find that this luminosity function
is the same for every galaxy. All you have to do to determine a distance to a galaxy whose distance is not already known is to count the number of planetary nebulae as a function of apparent brightness. Since the luminosity function is the same in every galaxy, you can then determine the intrinsic luminosity of those planetaries by comparing your results with the known luminosity function. Since the apparent (brightness) and intrinsic luminosities are known, the distance can be calculated from the inverse square law for the propagation of light.
Surface Brightness Fluctuations As Boy Scouts, we had to be able to estimate distances to an accuracy of 10% or better up to a distance of a mile or so. Our technique was based on the visual appearance of people. Up to a certain (small) distance, facial features are distinguishable. Beyond a certain (large) distance, it is difficult to separate persons in a crowd. Astronomers have developed a method of measuring distances along similar lines. (The following is edited from Morrison et al.) There is a particular type of galaxy called
an elliptical galaxy, which contains mostly very old stars and
very little gas or dust. A picture of an elliptical galaxy taken
with perfect resolution would look much like that of a globular
cluster, with many individual stars appearing as discrete points
of light. Even with the blurring of the image caused by the Earth's
atmosphere, the image of an elliptical galaxy does not appear
to be perfectly smooth. Rather it is mottled or bumpy because
of the lumpy distribution of the light emitted by the individual
stars that belong to this galaxy. Furthermore, the amount of
the bumpiness depends on the distance of the galaxy. For a nearby
galaxy, the stars are more nearly well resolved, and the image
has more bumps of varying brightness. For a very distant galaxy,
the stars cannot be resolved at all, and the image will be smooth. In order to estimate the distance of an elliptical galaxy, it is therefore necessary only to measure the degree of bumpiness in the distribution of light. This technique will not work for spiral galaxies, which contain large amounts of dust that also cause fluctuations in surface brightness.
Summary
|
. The
ultraviolet light emitted by the central star is absorbed in
the surrounding nebula, and such of it is re-emitted in the form
of emission lines in the optically visible part of the spectrum,
where it can be easily observed.