Galaxy Distances

Distance is obviously a key property, but one that becomes increasingly difficult to evaluate as we leave our own neighborhood. Within a few thousand light-years, we can use parallax angles, shifts in stars' positions as seen from opposite sides of the Earth's orbit, for trigonometric ranging to nearby stars, to provide the most foolproof rung on the cosmic ladder of distance indicators. Beyond this, we must take more subtle cues, most of them depending on our knowledge of how light propagates through space. Until we span cosmological distances, the traditional inverse-square law is an accurate description of how light disperses through three-dimensional space. Light from a source of luminosity L will spread out so that the intensity I measured at some large distance D from the source is given by

This may be further modified by such factors as absorption of light by intervening dust grains, which we can often measure by the changes it produces in the source's color. To estimate the distance of a star or galaxy, we need to measure some property which is invariant to its distance from us. Examples include the pulsation period of variable stars, orbital velocity of stars within a galaxy, separation of images by a gravitational lens, or fraction of microwave background radiation absorbed by hot gas in a cluster of galaxies.

Stepping outward from the nearby stars whose distances we can measure with parallax across the Earth's orbit, we can broaden the demographics of stars with known distances by using star clusters. Stellar evolution gives distinct patterns in the temperatures and luminosities of stars of a certain age, which we can use by taking the stars of kinds we understand well from nearby examples and use the fact that other members of the same cluster are at the same distance. We need this to get large calibrated sets of the brightest stars, which we can then use to larger distances— bridging the gulf to other galaxies. This is particularly important in getting us to the next rung on the distance ladder—Cepheids.

Traditionally, the most reliable measures of the distances to nearby galaxies have relied on the use of Cepheid variable stars. Cepheids are a class of supergiant star whose combination of temperature and luminosity does not allow a stable structure, oscillating regularly in size and temperature about their averages. This class is named after the first discovered example, S Cephei, but the brightest example is well known for another reason unrelated to its mild variability—Polaris. The utility of Cepheids in distance measurements stems from a strong relation between the pulsation period, easily measured from the associated light variations, and the stars' luminosity. This was initially discovered by Henrietta Leavitt, analyzing photographic data on the Large Magellanic Cloud. This nearby galaxy is an excellent laboratory for the study of stellar populations, being close enough to resolve many kinds of stars individually and offering a large sample of stars all at practically the same distance, so that patterns can be discerned without the laborious star-by-star distance measurements often needed within the Milky Way.

One of the goals of the Hubble Space Telescope was using Cepheid variables to measure distances to a useful number of galaxies at the 10% level, tightening up this technique's contribution to the overall extragalactic distance scale. This was done largely through a so-called "Key Project'', involving an international team of dozens of astronomers. It proved possible to locate and measure Cepheids in galaxies beyond the prominent Virgo Cluster (Figure 4.1), so that the remaining issues in going from these distances to the expansion rate of the Universe—the Hubble constant—now hinge on how fast we are moving relative to the Virgo Cluster and how accurately the local Cepheid calibration is known.

In recent years, several less traditional, but effective, distance indicators have come into use, allowing even ground-based telescopes to measure distances to galaxies as distant as the Virgo Cluster. These rely on the statistical properties of the stellar populations in various ways. For galaxies with large numbers of globular clusters, we use the fact that their distribution in luminosity—the luminosity function—is remarkably constant from galaxy to galaxy (in groups and clusters, where we can compare them directly). These are the brightest subsystems in elliptical and S0 galaxies, making them attractive in these galaxies that contain no young stars and hence no

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Period (days)

Figure 4.1. The period-luminosity relation for Cepheid variables, as seen in the Hubble Key Project data for the spiral galaxy NGC 3198. Near-infrared I magnitudes are shown, time-averaged over the pulsation periods, to reduce scatter produced by dust extinction. The central line indicates the mean relation, with the upper and lower ones showing the width of the band expected from stellar evolution (through the finite width of the instability region in the Hertzsprung-Russell diagram). Distance is measured from the brightness ratio (that is, vertical offset) with respect to some system of well-known distance, often the Large Magellanic Cloud. (These data were published by D. Kelson et al., Astrophysical Journal, 514, 614, 1999.)

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Period (days)

Figure 4.1. The period-luminosity relation for Cepheid variables, as seen in the Hubble Key Project data for the spiral galaxy NGC 3198. Near-infrared I magnitudes are shown, time-averaged over the pulsation periods, to reduce scatter produced by dust extinction. The central line indicates the mean relation, with the upper and lower ones showing the width of the band expected from stellar evolution (through the finite width of the instability region in the Hertzsprung-Russell diagram). Distance is measured from the brightness ratio (that is, vertical offset) with respect to some system of well-known distance, often the Large Magellanic Cloud. (These data were published by D. Kelson et al., Astrophysical Journal, 514, 614, 1999.)

supergiant stars to be Cepheid variables. Another possibility for these early-type galaxies is the use of surface-brightness fluctuations. These arise because each piece of a galaxy's image contains the light from a finite number of stars, and for a fixed surface brightness that number of stars depends on the galaxy's distance (Figure 4.2). In the ideal case of identical stars, the fluctuations between adjacent regions would reflect Poisson statistics, having a standard deviation relative to the mean of 1/^/n when an average of n stars contribute in each part of the image ("part" being defined as a region which can be separately resolved). If we know the luminosity function of the giant stars contributing much of the light in elliptical galaxies (or in principle the bulges of spiral galaxies), a measurement of the statistical fluctuations between neighboring points in the image can give a distance estimate. Finally, as for globular clusters, the luminosity functions of planetary nebulae in galaxies are almost constant from one galaxy to the next. Images through filters that transmit only a very narrow band including the intense emission line of 0++ at 5007 A are very effective at detecting planetary nebulae and, together with images at other wavelengths, can distinguish them from other emission-line sources such as star-forming regions and supernova remnants. Ground-based imaging had ranged as far as Virgo for these detections, including a population of planetary nebulae in the space between the individual galaxies.

All three of these techniques furnish an interesting contrast to the use of Cepheids, because they can be applied to kinds of galaxies that do not host Cepheids.

Figure 4.2. Measuring distances using surface-brightness fluctuations. This shows a small region of the Local Group elliptical galaxy M32 {top). The brightest individual red-giant stars are visible. Successive panels show the effect of observing it at distances greater by factors of 2, so that the amplitude of observed fluctuations for a given surface-brightness level changes. This occurs as the mean number of stars per resolution element changes. (Images made with data retrieved from the NASA Hubble Space Telescope archive; R.M. Rich was the original principal investigator.)

Figure 4.2. Measuring distances using surface-brightness fluctuations. This shows a small region of the Local Group elliptical galaxy M32 {top). The brightest individual red-giant stars are visible. Successive panels show the effect of observing it at distances greater by factors of 2, so that the amplitude of observed fluctuations for a given surface-brightness level changes. This occurs as the mean number of stars per resolution element changes. (Images made with data retrieved from the NASA Hubble Space Telescope archive; R.M. Rich was the original principal investigator.)

They can, of course, be extended by the use of space observations to higher resolution and sensitivity, and such work is in progress.

Among stellar standard candles (more accurately "standard bombs") the brightest are supernova explosions (Figure 4.3). These come in a bestiary of types, some of which are much more standard and better understood than others. The distinctions among various kinds of supernovae—denoted types Ia, Ib, Ic, II, and perhaps others—can be made from their spectra and pattern of fading after the outburst. Type II supernovae, which have the confusing property of being associated

IC 4830 SN 2001bt"(Ia)

NGC 1637 SN 1999em (It)

NGC 1699 SN 2001ep (Ia)j

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NGC3368 SN 1998bu (la)

Figure 4.3. A gallery of supernovae. These images, made close to maximum light, demonstrate how bright supernovae can become, which is one of the factors making them important distance indicators. Three of these are type la explosions, which have sufficiently consistent peak luminosity to make them useful in probing cosmology. (Images courtesy of Nicholas Suntzeff, Cerro Tololo Inter-American Observatory.)

Figure 4.3. A gallery of supernovae. These images, made close to maximum light, demonstrate how bright supernovae can become, which is one of the factors making them important distance indicators. Three of these are type la explosions, which have sufficiently consistent peak luminosity to make them useful in probing cosmology. (Images courtesy of Nicholas Suntzeff, Cerro Tololo Inter-American Observatory.)

with Population I stars, arise from the death of massive stars. When the stellar core can sustain no more energy-producing fusion reactions, the star's gravity collapses the core inward, yielding a neutron star (and perhaps, sometimes, a black hole immediately). This transformation drives an immense shock wave and flood of neutrinos which blows the star apart. Such an event was seen as Supernova 1987A, the self-destruction of the star Sanduleak —69° 202 in the Large Magellanic Cloud. However, type II supernovae are not very useful as distance indicators, since their progenitor stars can have a significant range of masses and evolutionary states, exemplified by the fact that SN 1987A itself was substantially less luminous than was thought typical for type II events. In contrast, type Ia supernovae have proven to be very respectably standardized. These events can be recognized by their spectra, free of hydrogen lines and dominated by strong features of such heavy elements as sulfur, calcium, silicon, magnesium, iron, and nickel. These supernovae show a consistent peak luminosity, and the consistency can be made even better by removing a correlation between peak luminosity and rate of fading, making these excellent standard sources for measuring great distances across the Universe. The evidence for an accelerating Universe—a positive cosmological constant—came from samples of high-redshift type Ia supernovae.

When suitably calibrated, there are several global relations which can be used to estimate galaxy distances. Any of the Faber-Jackson, Tully-Fisher, and Fundamental Plane relationships described below can be used in this way.

Finally, at the greatest distances and for the largest numbers of galaxies, we are forced to estimate their distances solely from the Hubble law and a value of the Hubble constant (supplemented at large redshifts by a cosmological model linking redshift and distance over such large spans that the linear redshift-distance relation will not hold. This technique has the built-in systematic error that uncertainties in H0 propagate in a systematic way across the whole sample.

The list above forms the rungs of a traditional interlinked ladder of distance indicators, in which each one helps calibrate subsequent techniques useful to greater distances. Such an approach, however carefully executed, means that the final and largest distances have error sources which have built up over all the calibrating techniques. As a check on all this, there are several more exotic distance indicators, useful in special situations, which rely more or less directly on physical principles to give galaxy distances directly from observations. Several of these provide very interesting alternate paths to extragalactic distances.

For an expanding (or alternately expanding and contracting) object, a combination of spectroscopic and brightness measurements can give its distance. In the Baade-Wesselink approach, applicable to such objects as Cepheids and the expanding envelopes of supernovae, one uses the Doppler shifts of spectral features integrated over time to ask how much, in linear units, the envelope has expanded over that time. Meanwhile, the difference in brightness and temperature, from photometric measurements, plus either blackbody physics or more detailed simulations, tells by what factor the object has expanded or contracted. The derived distance is the one at which that linear change corresponds to the right ratio and gives a consistent total brightness. This has been applied with reasonable success to both Cepheids and supernovae, giving confidence that the usual calibrations and assumptions of uniformity are sensible.

Again making use of supernovae, we can also use their light echos. The brief and intense flash of radiation from a supernova explosion illuminates the surroundings. When we include the peculiarities of seeing the illumination subject to the speed of light, what we will see is a ring of light scattered from material at a particular (increasing) distance in front of the supernova, with clouds of matter at various distances appearing as rings of different radius. As was shown in the context of light from nova outbursts by P. Couderc in 1939, these rings will expand from our vantage point at speeds well above the speed of light, purely because of the viewing geometry and the boundary condition that we see only those locations where the excess time taken for the light's detour before we see it corresponds exactly to the time since we observed the explosion. The combination of angular size and expansion speed constrains the allowed distance. This has worked most famously for SN 1987A. This approach may be extended, in principle, to older remnants in more distant galaxies by imaging in polarized light so that the scattered radiation has improved contrast.

In a similar vein, SN 1987A provided an independent measure of the distance to the Large Magellanic Cloud through unintentional observations of the way its explosion illuminated material the star had earlier blown off as a ring (Figure 4.4). Ultraviolet spectra taken within the first few weeks after we observed the explosion showed a strong temporary peak in emission from diffuse gas, which faded rapidly thereafter. Imaging from the Hubble Space Telescope, launched over three years later, showed that the star had been surrounded by a ringlike nebulosity, elliptical in projection. The strong line emission was produced as the initial energetic radiation ionized this material. Thus, the peak time of emission tells us, via light travel, how far the ring is from the supernova, and the angular size now tells how far the supernova is from us.

Gravitational lenses offer a way to measure very large distances independent of assumptions about the Hubble constant. This makes them attractive since we can see gravitationally lensed objects to very large redshifts (currently to at least z = 4.7; additional candidates have multiband fluxes consistent with redshifts as large as z = 10 but are still pending spectroscopic confirmation). The relevant point in this context is that the light travel times for various images of a lensed quasar (Figure 4.5) will differ, by times from weeks to years for various cases. If the mass of the lensing galaxy is well known—for example, from a velocity dispersion measurement—the delay between the paths scales with the distance to the source (and hence inversely with the Hubble constant, if the result is expressed in that way). There have been numerous programs to seek the time delay by correlating the variability patterns of lensed images, most successfully for the "original" doubly-imaged QSO 0957+561.

Since there are many structures in galaxies that approximate disks in circular rotation, there has been discussion of combining Doppler shifts and proper motions to yield geometrically determined distances. Very small sources which can be observed with radio interferometry, such as masers in star-forming regions or the atmospheres of evolved stars, can show proper motions due to their orbital motion. If these are in a circular structure, we can use Doppler shifts of similar sources at the apparent ends of the disk to measure the characteristic orbital velocity, and derive a distance by asking how far the object must be for this to match the proper motion seen for the tracers best placed to see their transverse motion. This has actually been carried out for masers in a disk close to the nucleus of the nearby active galaxy NGC 4258, with results that gave not only a distance, but a mass estimate indicating a central black hole.

Interaction between the cosmic microwave background and the hot particles between the galaxies in clusters can also yield distance estimates. In the Sunyaev-Zeldovich effect, the microwave background photons traversing a cluster will be

Figure 4.4. The mass-loss ring around SN 1987A in the Large Magellanic Cloud, as imaged with the Hubble Space Telescope in 1994. The flash of emission as the supernova's ionizing radiation reached this ring had been observed spectroscopically shortly after the explosion was seen. Comparison of the time required for the radiation to reach the ring and the angular diameter of the ring gives a geometric distance estimate for the Large Magellanic Cloud, independent of other steps in the distance ladder. Measurement of the ring turns out to be somewhat time-critical after the explosion, since the expanding explosion ejecta are now observed reaching the ring and heating it, which will probably destroy the emission-line gas. (Image courtesy of NASA, ESA, and C. Burrows of STScl.)

Figure 4.4. The mass-loss ring around SN 1987A in the Large Magellanic Cloud, as imaged with the Hubble Space Telescope in 1994. The flash of emission as the supernova's ionizing radiation reached this ring had been observed spectroscopically shortly after the explosion was seen. Comparison of the time required for the radiation to reach the ring and the angular diameter of the ring gives a geometric distance estimate for the Large Magellanic Cloud, independent of other steps in the distance ladder. Measurement of the ring turns out to be somewhat time-critical after the explosion, since the expanding explosion ejecta are now observed reaching the ring and heating it, which will probably destroy the emission-line gas. (Image courtesy of NASA, ESA, and C. Burrows of STScl.)

boosted to slighly higher energies by scattering off the energetic electrons in the intracluster gas. This is observed as a "hole" in the microwave background, at frequencies where more energy is lost than gained. Since the intracluster gas is itself observable in X-rays, its temperature and density profile are independently known,

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