Proc. Natl. Acad. Sci. USA Vol. 93, pp. 14221–14224, December 1996 Colloquium Paper

This paper was presented at a colloquium entitled ‘‘Symmetries Throughout the Sciences,’’ organized by Ernest M. Henley, held May 11–12, 1996, at the National Academy of Sciences in Irvine, CA.

Astrophysical symmetries

VIRGINIA TRIMBLE

Physics Department, University of California, Irvine CA 92697-4575 and Astronomy Department, University of Maryland, College Park, MD 20742

ABSTRACT Astrophysical objects, ranging from meteor- spherical, while comet nuclei (including Halley), most aster- ites to the entire universe, can be classified into about a dozen oids (including Gaspara), and the smaller moons (like Phobos characteristic morphologies, at least as seen by a blurry eye. and Hyperion) are triaxial ellipsoids and more complex shapes. Some patterns exist over an enormously wide range of dis- Since gases are not good at sustaining strains, all slowly tance scales, apparently as a result of similar underlying rotating stars are essentially spherical. For instance, the second physics. Bipolar ejection from protostars, binary systems, and moment of inertia of the sun is at most a few parts in 105. active galaxies is perhaps the clearest example. The oral The time required for a system of n point masses to relax and presentation included about 130 astronomical images which erase initial conditions of the density and velocity distribution cannot be reproduced here. depends roughly on nϪ2. Thus old rich star clusters (globular clusters) and massive non-rotating galaxies (giant ellipticals) The traditional symmetries of theoretical physics are parity are generally spherical, as are the most massive clusters of reversal, charge conjugation, and time reversal. Two of these galaxies when they are not the products of recent mergers. clearly do not apply to macroscopic, astrophysical systems. Cluster shapes are most easily traced by the x-rays emitted by Time reversal would obtain only if entropy becomes a non- hot gas pervading them or by their gravitational lensing effect increasing function when (if) the universe turns around and on the light of galaxies (etc.) behind them, rather than by contracts. Informed opinion is against this. Symmetry under looking at the positions and velocities of individual member charge conservation would imply equal amounts of matter and galaxies. Curiously, many massive elliptical galaxies look ex- actly like ellipsoidal figures of revolution but turn out to have anti-matter. In fact, there are no anti-galaxies, nor, despite the little or no net angular momentum. poet, is there a Dr. Edward Anti-Teller. Something like parity Mass ejection from stars occurs in three contexts: planetary conservation does, however, appear to describe the real uni- nebulae (the outer layers of low mass stars like the sun, shed verse. A very large fraction of objects and systems are indis- when they die as white dwarfs), nova shells (blown off by tinguishable from and as common as their mirror images. The explosive burning of hydrogen deposited on a white dwarf actual patterns seen are a result of the interplay of gravitation, from a normal binary companion), and supernovae (most of angular momentum, electromagnetism (especially magnetic the mass of a massive star whose core has collapsed to nuclear forces), and concentrated energy production due to nuclear density or all of the mass of a very massive white dwarf reactions. experiencing explosive burning of carbon and oxygen). Subsets Astronomers habitually classify only a few of their objects of of each of these are spherical, at least approximately. study by shape (elliptical galaxies by degree of ellipticity, for Finally, the universe itself is very nearly spherical in an instance), but it is my impression that most of what we see can extended sense. The actual geometry may be flat, that of a be subsumed in about 12 categories, as follows: 1, spheres; 2, four-sphere, or that of a hypersphere, but both rotation and rotationally distorted spheres; 3, rotationally dominated sys- shear are exceedingly small. The rotation period of the uni- tems with m ϭ 2 instabilities (m in the sense of the azimuthal verse is considerably larger than its present age, and the shear quantum number of the Legendre polynomials); 4, m ϭ 3 is at most 10Ϫ3 of its expansion velocity. These limits come (rare!); 5, lumpy; 6, rings and bipolar structures, not obviously from the extreme isotropy of the cosmic microwave back- dominated by magnetic effects; 7, pseudobipolarity; 8, mag- ground over the sky. The sky distributions of the x-ray back- netically dominated shapes; 9, rings and bipolar structures ground and of gamma ray bursters are also isotropic to within where magnetism is important; 10, distorted symmetries; 11, observational limits, but the limits are less tight. Rayleigh–Taylor, Kelvin–Helmholtz, Schwarzschild, and other instabilities; and 12, other (I haven’t actually put any objects in The Effects of Rotation this class, but someone else will surely want to). The more rapidly rotating planets, Jupiter and Saturn, are Cosmic Spheres visibly flattened, as are some dwarf elliptical galaxies. More extreme flattening, in the form of disk shapes, occurs in Non-rotating astronomical objects and systems will be spher- lenticular galaxies (like spirals but without the pretty arm ical when (i) they are massive enough for gravity to triumph structures), in the old stellar populations of spiral galaxies, and over the other forces and (ii) enough time has elapsed for in the material accreting onto newly formed stars. Residual initial conditions to be wiped out. ‘‘Massive enough’’ in this material, like the dust (zodiacal light) of our own solar system context turns out to mean more than 1021–22 g for things made and the dust around Beta Pictoris, is also configured in a of rocks and metals. Thus the slowly rotating planets (like rotating disk. The binary star CG Tauri retains a disk but with Mercury, Venus, and Earth), the larger moons (like ours, its center cleared out by tidal forces from the orbiting star pair Triton, and Europa), and the largest asteroids (like Ceres) are at the center. Accretion disks with at least approximate axial symmetry The publication costs of this article were defrayed in part by page charge occur in a number of other contexts, including the environs of payment. This article must therefore be hereby marked ‘‘advertisement’’ in black holes in quasars and around black holes, neutron stars, accordance with 18 U.S.C. §1734 solely to indicate this fact. and white dwarfs with close companions. When the compan-

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ions fill their inner Lagrangian surfaces (Roche lobes), mate- Bipolar Outflows, Rings, and Disks, not Obviously rial streams from them and accumulates in a disk around the Magnetic more compact companion star. A few rapidly rotating hot stars (called Be) are shedding material at their equators and can Most structure of this type is probably associated with rotating reasonably be described as having excretion disks. or binary underlying stars. ‘‘Bipolar’’ outflow simply means Many stars, especially young ones, are much more rapid that a combination of position of emitting gas on the sky and rotators than our sun (periods of a day or so rather than a radial velocity data suggests that two streams (jets, cones, month) and must be quite ellipsoidal in cross section. In no blobs, or less tidy components) are moving outward in roughly case do we have direct images of the shape (the few stars that opposite directions at roughly equal speeds. Relatively simple are not absolute points as seen from earth have expanded as shapes of this sort are associated with very young massive stars supergiants and so rotate slowly) but the effects are detectable (Eta Carinae, for instance), some symbiotic stars (binaries with in profiles of their spectral lines and sometimes in light a white dwarf and a wind-blowing red giants, e.g., He 2–104), variations. and many planetary nebulae. The gas we see in planetaries is ionized by (presumably Instabilities spherical) ultraviolet photons coming from a pre-white-dwarf 2 ؍ Rotation with m at the center. But the distribution of the gas dense enough to Most spiral galaxies, including our own, have two major arms be seen is a result of interaction of a fast, low-density wind (exhibiting varying degrees of coherence from center to out- emanating from the central star at the present time and a slower, denser wind left from when the star was a red giant. side). Both analytic and numerical calculations show that the The resulting shape on the sky can be a simple circle, a ring m ϭ 2 mode should dominate for a range of ratios of disk mass (like the Ring Nebula in Lyrae), a helix (presumably because to spheroidal mass that includes the observed values for most one of the winds comes from poles not aligned with rotation galaxies with disks. Central bars in a subset of spirals (including poles), multiple intersecting ellipses, two perpendicular bipo- again our own) are another manifestation of this instability. lar outflows, on up to configurations that can only be described Virtually all spiral arms trail the direction of rotation of their by analogy (e.g., with the Egyptian hieroglyph for eye for parent galaxies. Leading arms and one-arms spirals do occur Hubble 12). but seem always to be the result of a recent interaction with a Two interesting cases in the Large Magellanic Cloud are the nearby or companion galaxy. Tarantula nebula (whose shape has about as much mirror Calculations indicate that the disk accretion phase of star symmetry as the arachnid for which it is named), a region of formation is likely also to be unstable to two-arm spiral current vigorous star formation, and Supernova 1987A (whose formation (but also sometimes to a single arm) and that the ejecta are currently just barely resolved and slightly elliptical, arms are probably relevant to the formation of binary stars and but which is surrounded by three apparently intersecting rings of planetary systems. of illuminated pre-supernova material). The Hubble Space Telescope has recently provided resolved images of large numbers of very distant galaxies, seen as they Pseudo-Bipolars were when the universe was eight times or more its present density (I say it this way because ages are model-dependent, The appearance of bipolar structure can result when a more- while distance scales and densities are uniquely related to or-less spherical distribution of gas is illuminated by cones of observed redshift). Many of these early galaxies have clear disk ionizing radiation. Seyfert and radio galaxies display such structure, but well-developed spiral arms are apparently rarer behavior (and the signature is neutral gas, seen in 21-cm or CO than among galaxies here and now. emission, filling in between the cones or jets of ionized gas that alone are visible in optical images). Threefold Symmetries Slightly different physics is probably responsible for the bipolar optical morphology of some large distant radio galaxies Instability to m ϭ 3 modes is apparently very rare. I can think with strong radio jets. Here it is thought that the outgoing of only two cosmic objects, the Trifid Nebula and the gas near relativistic plasma jets are likely to have triggered extra star the center of our own galaxy, that show even vague threefold formation along their axes. symmetry. In both cases, it is probably not fundamental, but Finally, spherical expansion within a dense disk will yield rather the result of random obscuration (in the Trifid) and gas some sort of bipolar outflow when the edges are reached. This flow (in the galactic center). is expected for superbubbles within the interstellar medium, whose energy sources are supernovae and hot stellar winds Lumpy Configurations (but has not precisely been seen) and has been seen for active galaxies (but is not precisely expected). Untidy shapes arise when the conditions for spherical symme- Mostly Magnetic try mentioned above are not met. Thus meteorites, small moons and asteroids, and comet nuclei tend to be vaguely Sunspots are the quintessential astrophysical magnetic dipoles. triaxial and resemble paleolithic tools. Axial ratios larger than The commonest spot morphology is a pair of opposite polarity about 3:1 are rare. (powered, very crudely, by underlying toroidal flux that has Among galaxies, the class called dwarf irregulars (including popped out). Coronal loops rising from spot groups and the the Small Magellanic Cloud and several other members of our x-ray footprints of flares from active solar regions are similarly Local Group) have not had enough time for processes scaling dipolar. A plot of sunspot latitude versus time through a 2 like n to have relaxed them to spheroids, disks, or ellipsoids. number of 11-year solar cycles (called a butterfly diagram) is Other galaxies, recently affected by tidal encounters with a manifestation of the regions of strongest magnetism migrat- neighbors or recently merged from two or more colliding ing toward the equator as a cycle progresses. If you color code smaller galaxies, also show conspicuous morphological relics of the polarities of the leading spot of each pair in the diagram, their wild youth. Both ground-based and Hubble Space Tele- then you see a 22-year cycle, and the butterfly has alternating scope studies indicate that irregular shapes resulting from red and green wings. mergers were much commoner at redshifts of one to three than The radiation pattern of pulsars is, to first order, a magnetic they are here and now. dipole, oblique to the direction of the rotation axis. Strongly Downloaded by guest on September 30, 2021 Colloquium Paper: Trimble Proc. Natl. Acad. Sci. USA 93 (1996) 14223

magnetized neutron stars and white dwarfs in binary systems at highest energies looks more like a pair of parentheses than will also have dipole radiation patterns in x-rays, ultraviolet, a circle. SNR 1006 is not known to have a pulsar (and is not and͞or visible light because accretion can occur only along expected to have one), so the origin of the bipolar heating must field lines, so that the poles are hotter than the rest of the star. be something else. The radio emission pattern from Jupiter is a dipole, some- what modified by the interaction of its moon Io with the field Distorted Symmetries lines. Objects that originally ‘‘belonged’’ to one of the above classes Bipolar Outflow with Magnetic Fields and Confining Disks may appear more complex owing to interactions with some- or Tori thing else. Obvious examples are planetary magnetospheres (which would be magnetic dipoles in isolation) and comets My interest in giving the talk reported here originally arose (which would be roughly spherical) being drawn out into long from noticing how very similar maps of some very different tails by the effects of the solar wind. Another well-known class sorts of astrophysical objects looked if one wasn’t aware of the is the head–tail radio galaxies. These would have been ordinary size scales being mapped. Classes represented are young stellar large doubles of the sort mentioned in the previous section, but objects, extragalactic radio galaxies and quasars, and the radio their parent galaxies are moving rapidly relative to surrounding sources associated with some x-ray emitting binary stars within (intracluster) gas, so that both jet͞blob sets are dragged our galaxy. In all cases, one sees (at radio, infrared, or optical backwards onto the same side of the compact core. Gas wavelengths, and sometimes more than one) some sort of distribution around stars (ejected or left from star formation) bright compact core, with blobs of emission on either side and can also be distorted by interactions with extraneous gas or by a jet-like emission region connecting the core with the blobs on the presence of nearby stars and companions. one or both sides. Where velocity information is available from The disks of many spiral galaxies are distorted from flat Doppler shifts or changes in structure on the plane of the sky planes to warped or corrugated ones (this includes the Milky (proper motions), it is clear that material is moving out along Way). These warp and corrugation modes are more easily the jets at speeds very large for the sort of object involved— excited if the galaxy has a nearby companion. Interactions 25-90% of the speed of light for the galactic binaries, more than between galaxies in general are responsible for a very wide 90% of c for many of the radio galaxies and quasars, and 10s range of distorted symmetries. A small galaxy hitting a bigger to 100s of kilometers per second for the YSOs. one more or less face on can set ring-shaped waves moving Especially among the radio galaxies, structure is aligned outward. Two comparable galaxies passing close to each other along the same direction (or occasionally a gently precessing can drag out oppositely-curled tails resembling insect anten- direction) on scales from a fraction of a parsec to hundreds of nae. Other combinations simply look messy, but it is expected kiloparsecs. The most obvious manifestations of relativistic that most mergers tend to turn disk galaxies into elliptical ones. velocities are associated with the smallest-scale structure (for A burst of star formation near the center of one or both all three kinds of objects); but lifetime considerations indicate galaxies is a frequent by-product of interaction. It often takes that even the large-scale blobs of radio galaxies and of some of the form of a ring or partial ring. the Milky Way sources (like SS 433 and its associated struc- tures W50) must be expanding at an appreciable fraction of c. Convection, Pulsation, and Rayleigh–Taylor Instabilities 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 This last class is a grab-bag of morphologies on scales that are changes in structure on the plane of the sky that seem to be small compared with the total size of the object or system occurring faster. Both extragalactic and galactic radio sources concerned. The granular pattern on the surface of the sun, with that do this sort of thing are called superluminals. The detailed light and dark patches about 1000 km across, for instance, appearances of these various kinds of sources will be affected shows that the solar envelope transfers most of its energy by Doppler boosting of the approaching jet and de-boosting of outward by convection rather than radiation. Similar patches the receding one and by the amount of gas, its structure and occur on other star surfaces, though the few we can resolve temperature, through which the jets must make their way. (from balloons, Hubble Space Telescope, etc.) are in much The generic model for these structures consists of a central cooler stars with more diffuse envelopes which have many compact object (young star, neutron star, or supermassive fewer patches per star. black hole) with a strongly magnetized gas disk around it. Convection within the earth gives rise to the patterns of plate Differential rotation of the disk twists the field flux lines until tectonics and continental drift (with the mid-Atlantic ridge, for they pop out vertically, channeling gas, angular momentum, instance, analogous to one of the bright, rising patches on the and flux out in opposite directions perpendicular to the disk solar surface). The basic convective pattern of the earth’s and parallel to the rotation axis of the central object. In all atmosphere has three rolls (Hadley cells) each north and south cases, ‘‘scenario’’ is probably a more accurate description of of the equator and is driven by solar heating. The Jupiter our level of understanding than ‘‘model,’’ let alone ‘‘theory.’’ pattern is much more complex, with more cells and long-lived There is, however, a modest amount of supporting evidence. tornado-like structures, driven mostly by heat released as For instance, compact radio structures tend to be polarized Jupiter continues to contract. along the jet axis close to the central core and perpendicular Some images of interstellar dust and gas show semi-regular further out where the jet begins to hit ambient gas and dump waves and stripes, reminiscent of the regular cloud patterns its energy. A Hubble Space Telescope image of the nearby that sometime overlay warm ocean surfaces. active galaxy NGC 4261 shows something that looks remark- A few stars pulsate in and out as single units or in modes with ably like a torus of ionized gas perpendicular to the axis of the only one or two radial, latitudinal, and azimuthal nodes. Larger radio jets and blobs. numbers, including the sun, show only higher-order modes At least two supernova remnants show some evidence for with many nodes in all three dimensions. The dominant period similar processes. The Crab Nebula is roughly ellipsoidal on for the sun is about five minutes, but very precise records of the sky with (arguably) the pulsar rotation axis along the major solar brightness, radius, or radial velocity versus time decon- axis of the ellipse and a sort of belt of denser gas around the volve into hundreds of closely spaced modes. waist perpendicular to that axis. The remnant of SN 1006, Rayleigh–Taylor instabilities and convective overturn are imaged in x-rays, is roughly a spherical shell, but with the expected whenever a light fluid attempts to support or push a hottest material in two arcs on opposite sides, so that the image heavier one. 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evolved, mass-losing stars is one example. Another, only just they are small compared with the universe as a whole and found, because two- and three-dimensional simulations have presumably reflect gravitational amplification of very small only just become possible, occurs in type II supernovae (the fluctuations dating right back to the big bang, which would ones powered by an iron core collapsing to become a neutron otherwise (as per “Cosmic Spheres” above) count as spherical. star). The light fluid in this case consists largely of neutrinos produced in the collapsing core; the heavy one is the ordinary I am grateful to Ernest Henley for the invitation to compile and material of the star’s outer layers. Understanding of this present this material. Some of the images shown at the workshop were neutrino-driven overturn and convection has finally led to generously provided by Rognvald Garden (Herbig-Haro objects 1–2), models of type II supernovae that actually explode, instead of Sylvie Cabrit and Claud Bertout (HL Tau), Richard Williger (SN having an outgoing shock stall at some intermediate point. 1006), Adam Burrows (SN II simulation), Postepy Astronomi, the Finally, on the largest and truly cosmic scale, we come to the Astronomical Society of the Pacific, the Space Telescope Science large scale structures found in the 3K microwave background Institute, and a very large number of colleagues, images from whose radiation and in the distribution of galaxies and clusters in papers and review articles were xerographed without their permission. space discussed in the paper by M. Haynes (1). Though these bubble and cell patterns are enormous by terrestrial standards, 1. Haynes, M. (1996) Proc. Natl. Acad. Sci. USA 93, 14216–14220. Downloaded by guest on September 30, 2021