Galaxies are the building blocks that trace large scale structure in the universe. Contained within these building blocks is most of the small scale structure in the universe. Clustered in groups, the groups spread along filaments, galaxies concentrate a majority of all matter, leaving the space between galaxies mostly empty. The concentration of matter in galaxies allows many intricate processes to occur, such as the formation of stars and planets. While we lack detailed knowledge of galactic evolution and there is no consensus on such fundamental parameters as the age of the universe, qualitatively we understand the universe's evolution. A timeline appears in Table 1. (For a general overview of cosmology, see, for example, Silk 1989).
Table 1. The History of the Universe
| Time (Gyr) | Redshift | Event |
| -15 | Inf. | The Big Bang. |
| -14.9997 | 1000 | Matter and radiation decouple. Recombination begins. |
| -13 | 5 | Gas settles into clouds and fragments. Galaxies begin to form. |
| -11.9 | 4.5 | Gas fragments compress sufficiently to form the first stars. |
| -11 | 3 | Bulges and Population II stars form. Quasar activity. |
| -8 | 1 | Stellar disks and Population I stars form. |
| -5 | The Sun is born from the solar nebula. | |
| -4 | 0.25 | The Earth forms and cools. |
| -0.002 | Homo Sapiens appears. |
For roughly 300,000 years following the Big Bang, there were no large scale structures in the universe, only a slightly anisotropic distribution of gas and energy (Silk 1989). The temperature and density in the early universe prevented the formation of atoms. Individual photons possessed sufficient energy to ionize any nearby hydrogen atoms, breaking them into protons and electrons as quickly as the atoms would form. But as the universe expanded, it cooled, and at roughly 300,000 years the energy of the photons became too low to ionize hydrogen atoms. Thus began the Decoupling Era. Recombination, the formation of hydrogen atoms, ensued. Lacking the opposing radiation pressure, gravity began compressing the matter.
Over the next few billion years, the overdense regions increased their mass, gravitationally attracting material from regions of lower density and slowly accumulating a majority of the matter in the universe. As they grew, these vast clouds became unstable, fragmented and continued to collapse on smaller scales, forming the seeds of today's galaxies. It is thought that these primordial overdense regions formed the super-clusters and large-scale structure in our present universe (Silk 1989).
The fragmentation of these clouds created many differently sized objects. The larger objects formed the cores and bulges of the galaxies observed today. Smaller objects rained in upon these cores, concentrating gas in what would eventually form the disk. Not all of the smaller clumps vanished into these proto-galaxies; some persisted to the present day, becoming satellite galaxies (cf. Searle & Zinn 1978).
In their younger years, during the four billion years following the Big Bang, the proto-galaxies interacted gravitationally, large ones consuming small, those of equal-size disrupting one another and merging. Some interactions prompted a dramatic period of stellar formation that converted most of the proto-galaxies' free gas into stars. Others forced gas into the central core, possibly powering the high-energy objects known as quasi-stellar objects, or quasars. Most proto-galaxies converted their gas into stars slowly, forming the bulges observed in spiral galaxies today. The disks of gas surrounding the bulges slowly flattened and cooled, forming stars roughly 7 billion years after the Big Bang. Our sun formed 10 billion years after the Big Bang.
Spiral galaxies like the Milky Way are now 12 billion years old. Within their embrace, countless stars are born, grow to old age, and die, circling the galactic core. Loose gases and the shed atmospheres from stars gone supernova blow through the disk, sometimes coalescing to form new stars. Fresh gases, pulled in from extragalactic space, mingle with these remnants of stars. Massive pressure waves, an outwards transfer of angular momentum (cf. Shu 1982, pp. 281), spiral the galaxy, compressing dust and gas, providing the instability and compression required to form more stars. Outside large galaxies orbit small satellite companions. Farther away, galaxies cluster in small groups and large associations of groups, forming a filamentary structure of matter against the voids which fill the universe.
Spiral galaxies consist of three basic components: a central spheroid, or bulge; a disk of stars, dust, and gas; and an enormous halo, which envelops the galaxy (see Figure 2). Properties such as the extent of the disk and size of the bulge vary from galaxy to galaxy. Some galaxies possess tightly wound spiral arms while others are loosely wound. Some of the latter also possess a bulge-centered, symmetric bar of luminous material in lieu of inner spiral arms. The galactic properties enumerated below are generally those of the Milky Way, but bear similarity to most spiral galaxies.
While there are two general kinds of galaxies, spiral and elliptical, HI disks are observed only in the former and I limit discussion to them. In this paper, the term "galaxy" refers only to spiral galaxies. Similarly, though many different molecular gases appear in galaxies, the term "gas" refers to the most common gas, HI.
At the center of a galaxy is the bulge, a slightly flattened spheroid roughly 4 kpc in radius, containing roughly 30% of the galaxy's visible mass. The bulge consists mostly of old, red, metal-poor stars; bulges formed prior to disks. The bulge stars are supported by dispersion and lack coherent rotation. The kinematics and luminosity distribution of bulges are similar to those of elliptical galaxies though it is unknown if there is a direct relationship.
Encircling the bulge is the disk, a large, very flat distribution of young and old stars, gas, and dust. The disk contains much of the galaxy's visible mass, and provides most of its luminosity. The disk itself contains three distinct components: a stellar disk of mixed-age stars, dust, and gas in a spiral structure; a thick disk of older metal-poor stars; and a very thin disk of neutral hydrogen gas. Table 2 summarizes the properties of the Milky Way's stellar disk.
Table 2. Properties of the Galactic Stellar Disk (Binney & Tremaine 1987)
| Mass | R | R0 | Rd | Rz |
| 6 x 1010 Mu | 15 kpc | 8.5 kpc | 3.5 0.5 kpc | ~600 pc |
R: stellar disk radius. R0: Solar radius. Rd: scale length. Rz: scale height.
Stellar disks are very thin. While the radius of the Milky Way's stellar disk is about 15 kpc, it is only 600 pc thick. Roughly 25 times wider than it is thick, the disk has a shape like that of a phonograph record. Stars in the disk orbit the Galaxy's center of mass in epicycle motion, where the radial period differs from the longitudinal period. If the periods were identical, an orbit would exactly close, returning to its starting point. To a stationary observer above the galactic pole, stars trace rosettes about the galactic core. The vertical frequencies of disk stars are much greater than the orbital frequencies; during one orbit, a star passes through the disk plane many times. The orbits of stars, once oscillating vertically, do not easily damp. Collisionless stellar interactions are unable to remove vertical energy, so once thickened, stellar disks remain thick. Due to the fragile nature of thin disks, dynamicists use the thinness, the 600 pc scale height, to constrain the perturbations suffered by the Galaxy.
The thick disk was discovered only recently (For a review, see Gilmore et al. 1989). Observations of the Galaxy's luminosity profile are poorly fitted by a two component bulge-disk model. The thick disk is a population of older stars with a larger vertical amplitude than those in the stellar disk. The thick disk's scale height is ~1 kpc. These stars have apparently received kinetic energy oriented perpendicularly to the disk. The thick disk is possibly a remnant of a perturbed young disk, or an artifact of infalling material accreted by the galaxy on non-planar orbits.
The gaseous disk is even thinner than the stellar disk, roughly 100 pc thick and ~30 kpc in radius. Of the 109 Mu of HI in the Milky Way, 81% lies in this disk, beyond R = 11 kpc (Audouze & Israël 1985). The gaseous disk is thin because gas easily settles into the Galaxy's equatorial plane. Unlike collisionless stellar interactions, gaseous collisions are dissipative; cloud-cloud interactions swiftly remove energy.
Together, the bulge and the stellar disk comprise the optically visible galaxy. Density waves within the stellar disk compress regions of gas and dust, providing the initial instabilities which cause star formation. Star formation along these curved density waves produces the dramatic spiraling arms, which give spiral galaxies their name. The gaseous disk is visible only in the light of HI radio emissions.
The third component of a galaxy is the halo, or corona, a vast spheroid enclosing the disk and bulge. Optically, the halo contains only very few old red stars and globular clusters. However, in addition to the optical material, there is overwhelming evidence for an enormous quantity of non-luminous matter, or "dark matter". For spiral galaxies, estimates for the amount of dark matter vary between 10 and 30 times the total mass of the luminous matter (Silk 1989). For a galaxy like the Milky Way, this is roughly 1012 Mu.
While it had long been suspected that galactic clusters contained dark matter, J. Ostriker and Peebles (1973) hypothesized the existence of massive halos around isolated galaxies. They argued that spiral galaxies, possessing a rapidly rotating thin disk, could not be stable unless they were supported gravitationally by an extensive massive halo. Observational support for the existence of a massive halo came from the motion of the Milky Way's satellites relative to the sun. These satellites moved faster than expected; their high speed was interpreted as an effect of a large galactic mass.
In the early 1980s, further evidence supporting massive halos appeared. Using spectroscopic measurements of the Doppler shift, Rubin et al. (1980) measured the rotational velocities of many spiral galaxy disks. Their observations showed that disks do not rotate as they would if the disks were moving under the influence of a central concentration of mass. The rotational velocity, instead of decreasing monotonically as radius increases, becomes constant outside of the bulge and continues roughly constant to the limit of detection.
This is a surprising result, as the distribution of luminosity in a spiral galaxy leads to the inference that the mass is concentrated towards the center and becomes sparse with increasing radius. A system of orbits about a prominent central mass is known as a Keplerian system, and follows the laws of planetary orbits derived by Kepler. Kepler's third law states that t2 ~ r3, the square of the period is proportional to the cube of the distance (semi-major axis), or equivalently v ~ r-1/2. Thus, the tangential velocity of matter orbiting the center of mass is expected to fall rapidly with increasing radius. The discovery that galaxies possess flat rotation curves implies that v is roughly constant. Galaxies are therefore non-Keplerian, containing a large amount of matter beyond the optical galactic radius.
The true mass, extent, and distribution of galactic halos is unknown. Zaritsky and White (1994) use a satellite galaxy ensemble to statistically estimate the typical mass of isolated spirals as 1.5 - 2.6 x 1012 Mu within 200 kpc. Dubinski et al. (1996a) employ a novel method of setting an upper limit on halo mass and extent by examining the length of tails created by spiral-spiral mergers. To form lengthy tails, such as those observed in NGC 4038/39 (the Antennae), the halo mass cannot be much more than 6 x 1011 Mu. The orbital dynamics of the LMC lead Lin et al. (1995) to predict a halo of ~5.5 ± 1 x 1011 Mu, but one in which 50% of the mass exists between ~50 and 100 kpc. In general, cold dark matter (CDM) cosmologies predict total galactic masses in excess of 1012 Mu (Silk 1989).
While many dynamicists assume a spherical or oblate halo for simplicity, there is some evidence that halos may be triaxial (e.g. Larsen & Humphreys 1996). The composition of galactic halos is also unknown: theories propose several different forms of matter, including exotic non-baryonic particles, black holes, burned-out stars, and other non-luminous remnants of galactic construction.
Large spiral galaxies generally possess satellite galaxies. The Milky Way has two large satellites, the Large and Small Magellanic Clouds (properly known as Magellanic Irregulars), and eight known dwarf spheroidals (dSph), five of which lie within a Galactocentric radius of about 100 kpc. Table 3 summarizes the general properties of the Galaxy's satellites. Most of the satellites travel in near-circular orbits, narrowly confined to within 70° of the polar plane (Lynden-Bell 1976).
Our closest neighbor, the Andromeda Galaxy (~700 kpc distant), has four small elliptical satellites and several smaller dwarf spheroidals. Little is known about the orbits of the Andromeda satellites, except that they lie within ~100 kpc of Andromeda. One satellite, M32, is thought to lie close to Andromeda, presently interacting with the disk (Byrd & Valtonen 1987). Another, NGC 205, is suspected as a progenitor of the Andromeda warp (Sato & Sawa 1986). The low luminosity of dwarf galaxies makes them difficult to detect at distances farther than the Andromeda Galaxy; we can only speculate that they exist around other spirals. Satellites are not uncommon, Zaritsky and White's (1994) satellite ensemble suggests that bright spirals like the Milky Way have, on average, one large satellite (and presumably several dim ones). In general, galaxies occur with increasing frequency as luminosity decreases, predicting a large population of dim satellites.
Table 3. Properties of Some Milky Way Satellites (Audouze & Israël 1985)
| Name | Mstellar | Mgas | R |
| LMC | 0.6 - 1.5 x 1010 Mu | ~109 Mu | 50 kpc |
| SMC | 1-2 x 109 Mu | ~108 Mu | 58 kpc |
| Typical dSph | 0.1 - 1 x 108 Mu | ~0 Mu | 70-100 kpc |
Mstellar: mass in stars; Mgas: mass in gas; R: galactocentric distance.
The Milky Way's satellites are a subject of scrutiny in part because the orbital motion of a galaxy's satellites (and globular clusters) allows a calculation of the mass enclosed by their orbits, roughly using the relationship M RV2. Unfortunately, exact orbits are difficult to measure, and in the case of the Milky Way, it is not clear that all of the satellites are gravitationally bound (Lynden-Bell 1983; Binney & Tremaine 1987; see also Zaritsky & White 1994).
The Magellanic Clouds receive specific attention because of their large size and close proximity (see Table 3), and because of an associated feature called the Magellanic Stream (MS). The Clouds are gas-rich satellites; the gas content of the LMC is ~109 Mu, equivalent to that of the entire Milky Way (Audouze & Israël 1985). The MS consists of a long chain of HI (~107 Mu) extending more than 100° from the Clouds in a polar orbit. The radial distance and velocity of the MS varies smoothly from its tip to the distant end associated with the Clouds: Lynden-Bell (1976) whimsically likened its appearance to the extended proboscis of a nectar sipping hawk-moth. Three-body calculations indicate that the MS is comprised of gas from the SMC tidally-liberated by the LMC when the Clouds passed within a few kpc of one another ~5 x 108 years ago. This gas was then stripped by the Galaxy during perigalacticon ~2 x 108 years ago (Murai & Fujimoto 1983). The conclusion that the Clouds are near perigalacticon and closely interacted ~108 years ago are supported by recent work (Gardiner et al. 1994; Lin et al. 1995). Many of these simulations predict close interactions between the Clouds in the past, possibly ejecting previous streams > 2 Gyr ago.
The closest satellite, a dSph in the constellation Sagittarius, lies at galactocentric radius ~16 kpc (Ibata et al. 1994). This satellite spans an area of sky about 200 times larger than the full moon (essentially the size of one's hand held at arms length). It is axially elongated ~3:1 from tidally stripped stars along the orbital path. The satellite possesses a mass on order ~108 Mu. Its orbit is still uncertain; it will pass through the disk in a few hundred million years, or passed a few hundred million years ago.
Over the last few decades, observational and computational astronomers have well refuted the notion that galaxies are isolated "island universes". The peculiar, irregular galaxies that perplexed astronomers of the 1940s we now known to be the settling remnants of merging galaxies. Toomre and Toomre (1972) performed much of the seminal work in this area. Their computer simulations recreated the tails and other structures observed in these remnants. A. Toomre later suggested that the merger of similar-massed spiral galaxies, once settled, would form objects with characteristics similar to those of elliptical galaxies, a suggestion which seems to be correct (e.g. Hernquist 1992). Using rough numbers for the settling time and frequency of interaction, Toomre (1977) made the shocking proposition that nearly all elliptical galaxies (~10% of all galaxies) could be formed via mergers. Much of the research into mergers has consequently focused on spiral-spiral mergers.
While Toomre's infamous "merger hypothesis" has not been proven either way, major mergers certainly produce some fraction of the observed ellipticals and many irregular galaxies. Only recently, with a degree of consensus regarding major mergers, have minor mergers drawn attention. Minor mergers, where the smaller galaxy contains only a few percent of the total mass, are thought to be more common than major mergers (Tremaine 1980; Binney & Tremaine 1987). While small quantities of stellar material influence the disk only slightly, the dissipative effect of gas drives starbursts and other dramatic, albeit short-lived, phenomena (Hernquist & Mihos 1995).
The regular disk of the Milky Way precludes any catastrophic mergers, but has the Milky Way suffered minor mergers? The Milky Way satellites travel in near-circular retrograde polar orbits (Lynden-Bell 1976). These orbits may have endured because both high-inclination and retrograde orbits couple weakly with the galactic disk (Quinn & Goodman 1986). While dynamical friction provides a constant orbital erosion, resonant coupling quickly removes orbital energy.
Although we know little about the population of protogalactic satellite orbits, we may speculate that the initial distribution contained non-polar orbits. Examining the Milky Way, we ask where are these prograde satellites now? Simulations by Walker et al. (1996) and Quinn et al. (1993) find that moderately-inclined, prograde satellite orbits quickly decay into the disk's orbital plane. Satellites orbiting near the galactic plane couple strongly to the disk and lose energy much faster than by dynamical friction alone. It is likely that orbits of moderate to low inclination have decayed and the satellites have been absorbed. Byrd and Valtonen (1987) suggest that planar satellites also lose internal energy, becoming more compact. Even the polar satellites are not eternal: dynamicists suggest that the Magellanic Clouds and Stream will merge with the Galaxy within ~5 Gyr (Gardiner et al. 1994; Tremaine 1975). Finally, the recent discovery of the Milky Way's closest satellite, the Sagittarius dSph (Ibata et al. 1994), underscores that satellite mergers continue to occur at the present epoch.
Given the thin, fragile nature of disks, can an upper limit to the mass added in recent epochs be calculated? Infalling satellites heat the disk vertically, thus the thin disk's scale height constrains the amount of post disk formation infall. Simulations limit infall to less than 10% of the disk's mass, and less than 4% within the solar radius (Tóth & J. Ostriker 1992; Quinn et al. 1993; Walker et al. 1996). The large scale height of the thick disk may be a remnant of disk heating. Tóth & J. Ostriker (1992) argue that the infall of gas and gas-rich satellites could mitigate heating effects, due to the gas settling into the equatorial plane. However, unless the satellites consist primarily of gas, they consider this effect negligible: the LMC contains only ~10% of its mass in gas. They also discount the possibility that satellites are easily stripped of their mass or disrupted, allowing a gentle accretion. Tremaine (1986) indicates that dSph sometimes contain substantial dark matter, thereby allowing them to resist disruption. Walker et al. (1996) find that ~45% of a large infalling satellite reaches the galactic core.
How much gas may have been accreted? While too faint to observe directly, an indirect probe of galactic halo chemical composition can be obtained by measuring the spectral absorption lines in quasi-stellar object (QSO) spectra. York et al. (1990) find similarities between the absorption spectra of gas-rich dwarf galaxies and those of QSOs. Wang (1993) reviews QSO observations at low z and notes that a) the absorbing gas resides in galactic halos, and b) the gas extends well past the optical extent. He finds the radial extent of the gas incompatible with the predictions of the "galactic fountain" model, proposing instead that the gas is accreted from satellites. Similarly, Schweitzer and Seitzer (1988) theorize that galactic ripples (corrugations) form due to the accretion of gas or tidally stripped stellar matter.
The Galaxy's small scale height sets a seemly strict limit on the amount of concentrated stellar material accreted post thin disk formation. It therefore seems unlikely that any satellites the size of the LMC have been absorbed in the last ~5 Gyr. However, scale height arguments cannot constrain the infall of unbound gas or small satellites. Infalling gas is thought to replenish the gas exhausted in star formation. The evolutionary consequences of satellites and infalling gas may be substantial.
The Milky Way and Andromeda each possess several satellite galaxies with masses between 1% and 10% of their visible mass. Mergers, gas infall, and tidal interactions occur in the present epoch; we believe they were more common in the past. The infall rate of satellites could be as high as ~1 per Gyr (Zaritsky & White 1994; see also discussion following Sancisi 1990).
Satellite infall affects a galaxy in three ways: a) gravitational torque from the infalling object as a whole; b) advection, kinetic energy redistribution from the object's rendered material settling within the galaxy; and c) taxation, gentle accretion of diffuse matter. As discussed in §2.4, thin disks place strict limits on advection. A warp results if through these processes, a satellite can tilt the disk's angular momentum vector. Should infalling satellites generate warps, then warps need persist only as long the period between infall.
A 10% disk mass satellite on an inclined orbit noticeably tilts the stellar disk as it merges (Quinn 1986; Hernquist 1991; Walker et al. 1996). A satellite of this mass also greatly perturbs the disk; thin disks preclude such infall. Unfortunately, there has been no work placing limits on the mass required to tilt a disk. Models of disk slewing in response to taxation are equally lacking, most existing work concentrating on the accretion of large satellites.