Astronomers habitually classify only a few of their objects of study by shape (elliptical galaxies by degree of ellipticity, for instance), but it is my impression that most of what we see can be subsumed in about 12 categories, as follows: 1, spheres; 2, rotationally distorted spheres; 3, rotationally dominated systems with m = 2 instabilities (m in the sense of the azimuthal quantum number of the Legendre polynomials); 4, m = 3 (rare!); 5, lumpy; 6, rings and bipolar structures, not obviously dominated by magnetic effects; 7, pseudobipolarity; 8, magnetically dominated shapes; 9, rings and bipolar structures where magnetism is important; 10, distorted symmetries; 11, Rayleigh–Taylor, Kelvin–Helmholtz, Schwarzschild, and other instabilities; and 12, other (I haven’t actually put any objects in this class, but someone else will surely want to).

Cosmic Spheres Non-rotating astronomical objects and systems will be spherical when (i) they are massive enough for gravity to triumph over the other forces and (ii) enough time has elapsed for initial conditions to be wiped out. “Massive enough” in this context turns out to mean more than 10^21–22 g for things made of rocks and metals. Thus the slowly rotating planets (like Mercury, Venus, and Earth), the larger moons (like ours, Triton, and Europa), and the largest asteroids (like Ceres) are spherical, while comet nuclei (including Halley), most asteroids (including Gaspara), and the smaller moons (like Phobos and Hyperion) are triaxial ellipsoids and more complex shapes. Since gases are not good at sustaining strains, all slowly rotating stars are essentially spherical. For instance, the second moment of inertia of the sun is at most a few parts in 10⁵.

The time required for a system of n point masses to relax and erase initial conditions of the density and velocity distribution depends roughly on n⁻². Thus old rich star clusters (globular clusters) and massive non-rotating galaxies (giant ellipticals) are generally spherical, as are the most massive clusters of galaxies when they are not the products of recent mergers. Cluster shapes are most easily traced by the x-rays emitted by hot gas pervading them or by their gravitational lensing effect on the light of galaxies (etc.) behind them, rather than by looking at the positions and velocities of individual member galaxies. Curiously, many massive elliptical galaxies look exactly like ellipsoidal figures of revolution but turn out to have little or no net angular momentum.

Mass ejection from stars occurs in three contexts: planetary nebulae (the outer layers of low mass stars like the sun, shed when they die as white dwarfs), nova shells (blown off by explosive burning of hydrogen deposited on a white dwarf from a normal binary companion), and supernovae (most of the mass of a massive star whose core has collapsed to nuclear density or all of the mass of a very massive white dwarf experiencing explosive burning of carbon and oxygen). Subsets of each of these are spherical, at least approximately.

Finally, the universe itself is very nearly spherical in an extended sense. The actual geometry may be flat, that of a four-sphere, or that of a hypersphere, but both rotation and shear are exceedingly small. The rotation period of the universe is considerably larger than its present age, and the shear is at most 10⁻³ of its expansion velocity. These limits come from the extreme isotropy of the cosmic microwave background over the sky. The sky distributions of the x-ray background and of gamma ray bursters are also isotropic to within observational limits, but the limits are less tight.

The Effects of Rotation The more rapidly rotating planets, Jupiter and Saturn, are visibly flattened, as are some dwarf elliptical galaxies. More extreme flattening, in the form of disk shapes, occurs in lenticular galaxies (like spirals but without the pretty arm structures), in the old stellar populations of spiral galaxies, and in the material accreting onto newly formed stars. Residual material, like the dust (zodiacal light) of our own solar system and the dust around Beta Pictoris, is also configured in a rotating disk. The binary star CG Tauri retains a disk but with its center cleared out by tidal forces from the orbiting star pair at the center.

Accretion disks with at least approximate axial symmetry occur in a number of other contexts, including the environs of black holes in quasars and around black holes, neutron stars, and white dwarfs with close companions. When the companions fill their inner Lagrangian surfaces (Roche lobes), material streams from them and accumulates in a disk around the more compact companion star. A few rapidly rotating hot stars (called Be) are shedding material at their equators and can reasonably be described as having excretion disks.

Many stars, especially young ones, are much more rapid rotators than our sun (periods of a day or so rather than a month) and must be quite ellipsoidal in cross section. In no case do we have direct images of the shape (the few stars that are not absolute points as seen from earth have expanded as supergiants and so rotate slowly) but the effects are detectable in profiles of their spectral lines and sometimes in light variations.

Rotation with m = 2 Instabilities Most spiral galaxies, including our own, have two major arms (exhibiting varying degrees of coherence from center to outside). Both analytic and numerical calculations show that the m = 2 mode should dominate for a range of ratios of disk mass to spheroidal mass that includes the observed values for most galaxies with disks. Central bars in a subset of spirals (including again our own) are another manifestation of this instability. Virtually all spiral arms trail the direction of rotation of their parent galaxies. Leading arms and one-arms spirals do occur but seem always to be the result of a recent interaction with a nearby or companion galaxy.

Calculations indicate that the disk accretion phase of star formation is likely also to be unstable to two-arm spiral formation (but also sometimes to a single arm) and that the arms are probably relevant to the formation of binary stars and of planetary systems.

The Hubble Space Telescope has recently provided resolved images of large numbers of very distant galaxies, seen as they were when the universe was eight times or more its present density (I say it this way because ages are model-dependent, while distance scales and densities are uniquely related to observed redshift). Many of these early galaxies have clear disk structure, but well-developed spiral arms are apparently rarer than among galaxies here and now.

Threefold Symmetries Instability to m = 3 modes is apparently very rare. I can think of only two cosmic objects, the Trifid Nebula and the gas near the center of our own galaxy, that show even vague threefold symmetry. In both cases, it is probably not fundamental, but rather the result of random obscuration (in the Trifid) and gas flow (in the galactic center).

Lumpy Configurations Untidy shapes arise when the conditions for spherical symmetry mentioned above are not met. Thus meteorites, small moons and asteroids, and comet nuclei tend to be vaguely triaxial and resemble paleolithic tools. Axial ratios larger than about 3:1 are rare.

Among galaxies, the class called dwarf irregulars (including the Small Magellanic Cloud and several other members of our Local Group) have not had enough time for processes scaling like n² to have relaxed them to spheroids, disks, or ellipsoids. Other galaxies, recently affected by tidal encounters with neighbors or recently merged from two or more colliding smaller galaxies, also show conspicuous morphological relics of their wild youth. Both ground-based and Hubble Space Telescope studies indicate that irregular shapes resulting from mergers were much commoner at redshifts of one to three than they are here and now.

Bipolar Outflows, Rings, and Disks, not Obviously Magnetic Most structure of this type is probably associated with rotating or binary underlying stars. “Bipolar” outflow simply means that a combination of position of emitting gas on the sky and radial velocity data suggests that two streams (jets, cones, blobs, or less tidy components) are moving outward in roughly opposite directions at roughly equal speeds. Relatively simple shapes of this sort are associated with very young massive stars (Eta Carinae, for instance), some symbiotic stars (binaries with a white dwarf and a wind-blowing red giants, e.g., He 2–104), and many planetary nebulae.

The gas we see in planetaries is ionized by (presumably spherical) ultraviolet photons coming from a pre-white-dwarf at the center. But the distribution of the gas dense enough to be seen is a result of interaction of a fast, low-density wind emanating from the central star at the present time and a slower, denser wind left from when the star was a red giant. The resulting shape on the sky can be a simple circle, a ring (like the Ring Nebula in Lyrae), a helix (presumably because one of the winds comes from poles not aligned with rotation poles), multiple intersecting ellipses, two perpendicular bipolar outflows, on up to configurations that can only be described by analogy (e.g., with the Egyptian hieroglyph for eye for Hubble 12).

Two interesting cases in the Large Magellanic Cloud are the Tarantula nebula (whose shape has about as much mirror symmetry as the arachnid for which it is named), a region of current vigorous star formation, and Supernova 1987A (whose ejecta are currently just barely resolved and slightly elliptical, but which is surrounded by three apparently intersecting rings of illuminated pre-supernova material).

Pseudo-Bipolars The appearance of bipolar structure can result when a more-or-less spherical distribution of gas is illuminated by cones of ionizing radiation. Seyfert and radio galaxies display such behavior (and the signature is neutral gas, seen in 21-cm or CO emission, filling in between the cones or jets of ionized gas that alone are visible in optical images).

Slightly different physics is probably responsible for the bipolar optical morphology of some large distant radio galaxies with strong radio jets. Here it is thought that the outgoing relativistic plasma jets are likely to have triggered extra star formation along their axes.

Finally, spherical expansion within a dense disk will yield some sort of bipolar outflow when the edges are reached. This is expected for superbubbles within the interstellar medium, whose energy sources are supernovae and hot stellar winds (but has not precisely been seen) and has been seen for active galaxies (but is not precisely expected).

Mostly Magnetic Sunspots are the quintessential astrophysical magnetic dipoles. The commonest spot morphology is a pair of opposite polarity (powered, very crudely, by underlying toroidal flux that has popped out). Coronal loops rising from spot groups and the x-ray footprints of flares from active solar regions are similarly dipolar. A plot of sunspot latitude versus time through a number of 11-year solar cycles (called a butterfly diagram) is a manifestation of the regions of strongest magnetism migrating toward the equator as a cycle progresses. If you color code the polarities of the leading spot of each pair in the diagram, then you see a 22-year cycle, and the butterfly has alternating red and green wings.

The radiation pattern of pulsars is, to first order, a magnetic dipole, oblique to the direction of the rotation axis. Strongly magnetized neutron stars and white dwarfs in binary systems will also have dipole radiation patterns in x-rays, ultraviolet, and/or visible light because accretion can occur only along field lines, so that the poles are hotter than the rest of the star.

The radio emission pattern from Jupiter is a dipole, somewhat modified by the interaction of its moon Io with the field lines.

Bipolar Outflow with Magnetic Fields and Confining Disks or Tori My interest in giving the talk reported here originally arose from noticing how very similar maps of some very different sorts of astrophysical objects looked if one wasn’t aware of the size scales being mapped. Classes represented are young stellar objects, extragalactic radio galaxies and quasars, and the radio sources associated with some x-ray emitting binary stars within our galaxy. In all cases, one sees (at radio, infrared, or optical wavelengths, and sometimes more than one) some sort of bright compact core, with blobs of emission on either side and a jet-like emission region connecting the core with the blobs on one or both sides. Where velocity information is available from Doppler shifts or changes in structure on the plane of the sky (proper motions), it is clear that material is moving out along the jets at speeds very large for the sort of object involved—25-90% of the speed of light for the galactic binaries, more than 90% of c for many of the radio galaxies and quasars, and 10s to 100s of kilometers per second for the YSOs.

Especially among the radio galaxies, structure is aligned along the same direction (or occasionally a gently precessing direction) on scales from a fraction of a parsec to hundreds of kiloparsecs. The most obvious manifestations of relativistic velocities are associated with the smallest-scale structure (for all three kinds of objects); but lifetime considerations indicate that even the large-scale blobs of radio galaxies and of some of the Milky Way sources (like SS 433 and its associated structures W50) must be expanding at an appreciable fraction of c. Naturally all the real jet speeds are less than the speed of light, but for jets seen nearly end-on, projection effects can result in changes in structure on the plane of the sky that seem to be occurring faster. Both extragalactic and galactic radio sources that do this sort of thing are called superluminals. The detailed appearances of these various kinds of sources will be affected by Doppler boosting of the approaching jet and de-boosting of the receding one and by the amount of gas, its structure and temperature, through which the jets must make their way.

The generic model for these structures consists of a central compact object (young star, neutron star, or supermassive black hole) with a strongly magnetized gas disk around it. Differential rotation of the disk twists the field flux lines until they pop out vertically, channeling gas, angular momentum, and flux out in opposite directions perpendicular to the disk and parallel to the rotation axis of the central object. In all cases, “scenario” is probably a more accurate description of our level of understanding than “model,” let alone “theory.” There is, however, a modest amount of supporting evidence. For instance, compact radio structures tend to be polarized along the jet axis close to the central core and perpendicular further out where the jet begins to hit ambient gas and dump its energy. A Hubble Space Telescope image of the nearby active galaxy NGC 4261 shows something that looks remarkably like a torus of ionized gas perpendicular to the axis of the radio jets and blobs.

At least two supernova remnants show some evidence for similar processes. The Crab Nebula is roughly ellipsoidal on the sky with (arguably) the pulsar rotation axis along the major axis of the ellipse and a sort of belt of denser gas around the waist perpendicular to that axis. The remnant of SN 1006, imaged in x-rays, is roughly a spherical shell, but with the hottest material in two arcs on opposite sides, so that the image at highest energies looks more like a pair of parentheses than a circle. SNR 1006 is not known to have a pulsar (and is not expected to have one), so the origin of the bipolar heating must be something else.

Distorted Symmetries Objects that originally “belonged” to one of the above classes may appear more complex owing to interactions with something else. Obvious examples are planetary magnetospheres (which would be magnetic dipoles in isolation) and comets (which would be roughly spherical) being drawn out into long tails by the effects of the solar wind. Another well-known class is the head–tail radio galaxies. These would have been ordinary large doubles of the sort mentioned in the previous section, but their parent galaxies are moving rapidly relative to surrounding (intracluster) gas, so that both jet/blob sets are dragged backwards onto the same side of the compact core. Gas distribution around stars (ejected or left from star formation) can also be distorted by interactions with extraneous gas or by the presence of nearby stars and companions.

The disks of many spiral galaxies are distorted from flat planes to warped or corrugated ones (this includes the Milky Way). These warp and corrugation modes are more easily excited if the galaxy has a nearby companion. Interactions between galaxies in general are responsible for a very wide range of distorted symmetries. A small galaxy hitting a bigger one more or less face on can set ring-shaped waves moving outward. Two comparable galaxies passing close to each other can drag out oppositely-curled tails resembling insect antennae. Other combinations simply look messy, but it is expected that most mergers tend to turn disk galaxies into elliptical ones. A burst of star formation near the center of one or both galaxies is a frequent by-product of interaction. It often takes the form of a ring or partial ring.

Convection, Pulsation, and Rayleigh–Taylor Instabilities This last class is a grab-bag of morphologies on scales that are small compared with the total size of the object or system concerned. The granular pattern on the surface of the sun, with light and dark patches about 1000 km across, for instance, shows that the solar envelope transfers most of its energy outward by convection rather than radiation. Similar patches occur on other star surfaces, though the few we can resolve (from balloons, Hubble Space Telescope, etc.) are in much cooler stars with more diffuse envelopes which have many fewer patches per star.

Convection within the earth gives rise to the patterns of plate tectonics and continental drift (with the mid-Atlantic ridge, for instance, analogous to one of the bright, rising patches on the solar surface). The basic convective pattern of the earth’s atmosphere has three rolls (Hadley cells) each north and south of the equator and is driven by solar heating. The Jupiter pattern is much more complex, with more cells and long-lived tornado-like structures, driven mostly by heat released as Jupiter continues to contract.

Some images of interstellar dust and gas show semi-regular waves and stripes, reminiscent of the regular cloud patterns that sometime overlay warm ocean surfaces.

A few stars pulsate in and out as single units or in modes with only one or two radial, latitudinal, and azimuthal nodes. Larger numbers, including the sun, show only higher-order modes with many nodes in all three dimensions. The dominant period for the sun is about five minutes, but very precise records of solar brightness, radius, or radial velocity versus time deconvolve into hundreds of closely spaced modes.

Rayleigh–Taylor instabilities and convective overturn are expected whenever a light fluid attempts to support or push a heavier one. The lumpiness of the radiatively driven winds of evolved, mass-losing stars is one example. Another, only just found, because two- and three-dimensional simulations have only just become possible, occurs in type II supernovae (the ones powered by an iron core collapsing to become a neutron star). The light fluid in this case consists largely of neutrinos produced in the collapsing core; the heavy one is the ordinary material of the star’s outer layers. Understanding of this neutrino-driven overturn and convection has finally led to models of type II supernovae that actually explode, instead of having an outgoing shock stall at some intermediate point.

Finally, on the largest and truly cosmic scale, we come to the large scale structures found in the 3K microwave background radiation and in the distribution of galaxies and clusters in space discussed in the paper by M. Haynes (1). Though these bubble and cell patterns are enormous by terrestrial standards, they are small compared with the universe as a whole and presumably reflect gravitational amplification of very small fluctuations dating right back to the big bang, which would otherwise (as per “Cosmic Spheres” above) count as spherical.

I am grateful to Ernest Henley for the invitation to compile and present this material. Some of the images shown at the workshop were generously provided by Rognvald Garden (Herbig-Haro objects 1–2), Sylvie Cabrit and Claud Bertout (HL Tau), Richard Williger (SN 1006), Adam Burrows (SN II simulation), Postepy Astronomi, the Astronomical Society of the Pacific, the Space Telescope Science Institute, and a very large number of colleagues, images from whose papers and review articles were xerographed without their permission.