24 June 1983, Volume 220, Number 4604 SCIENCE

the carries the stars toward the observer, spectral lines are shifted to- ward the blue region of the spectrum with respect to the central velocity. On the opposite side, where rotation carries The Rotation of Spiral Gala3Kies the stars away from the observer, lines are shifted toward the red spectral re-

Vera C. ]Rubin gion.Several years later, Pease (8) convinc- ingly illustrated that rotation was respon- sible for the inclined lines. Using the 60- inch telescope on Mount Wilson during Historians of astronomy may some um, Scheiner correctly concluded that the months of August, September, and day call the mid-20th century the era of the nucleus of M31 w;as a stellar system October 1917, he patiently acquited a 79- Downloaded from . During those years, astrono- composed of stars li1 ce the sun, rather hour exposure. of the spectrum of the mers made significant progress in under- than a gaseous object. nuclear region of M3 1 with the slit standing the structure, formation, and Even earlier, LordIand Lady Huggins aligned along the apparent major axis of evolution of galaxies. In this article, I (4) had attempted at tlheir private obser- the galaxy. Inclined lines appeared. A will discuss a few selected early steps in vatory to obtain a spectrum of M3 1, but second exposure made during these 3 determining the internal dynamics of gal- their labors were frauight with disaster. months in 1918, with the slit placed per- http://science.sciencemag.org/ axies, as well as current research con- Exposure times were so long that each pendicular- to the major axis along the cerning the rotation and mass distribu- fall when M31 was overhead they would apparent minor axis, showed no inclina- tion within galaxies. These studies con- expose consecutively on one plate dur- tion of the lines. Along the minor axis, stars move at right angles to the line-of- sight of the observer, so no Doppler shift Summary. There is accumulating evidence that as much as 90 percent of the mass appears. The rotation of galaxies was of the universe is nonluminous and is clumped, halo-like, around irndividual galaxies. established even before astronomers un- The gravitational force of this dark matter is presumed to be responsible for the high derstood what a galaxy was. rotational velocities of stars and gas in the disks of spiral galaxie:s. At present, the By the mid-1920's, astronomers knew form of the dark matter is unknown. Possible candidates span a range in mass of that we lived in a Galaxy composed of on March 24, 2021 1070, from non-zero-mass neutrinos to massive black holes. billions of stars distributed principally in a disk, all rotating about a distant center. Each spiral viewed in a telescope, locat- tribute to the present view that much of ing the early evening hours, until they ed at an enormous distance beyond our the mass of the universe is dark. could build up the requisite exposure Galaxy, is itself a gigantic gravitationally In 1845, Lord Rosse (1) constructed a (perhaps 100 hours). They would then bound system of billions of stars all mammoth 72-inch reflecting telescope, superpose a solar spe:ctrum adjacent to orbiting in concert about a common cen- which remained the largest telescope in the galaxy spectrum to calibrate the ter. This knowledge came from a variety the world until the construction of the wavelength scale. Yea?r after year, their of observational discoveries: Henrietta "modern" 100-inch telescope on Mount single exposure was a failure, sometimes Leavitt's (9) discovery of Cepheid varia- Wilson in 1917. Unfortunately, the showing no galaxy spe,ctrum, sometimes bles, stars whose periods of light fluctua- Rosse telescope did not automatically contaminated by the solar spectrum; tion reveal their true brightnesses and compensate for the rotation of the earth, once the plate was a(ccidentally placed hence distances; Shapley's (10) demon- so an object set in the field of the tele- emulsion side down, wrhere it dried stuck stration that the globular clusters sur- scope would race across the field. Nev- to the laboratory tabl4e. A copy of their round our own Galaxy like a halo, with a ertheless, Lord Rosse made the major 1888 failure is publishced along with their geometric center located not at the sun discovery that some nebulous objects remarkable stellar spectra (4). but at a great distance in the dense star show a spiral structure (2). Slipher (5), workinjg with the 24-inch clouds of Sagittarius; and Hubble's (11) Insight into the nature of these enig- reflector at Lowell Otbservatory, initiat- discovery of Cepheids in M31 and M33. matic objects was slow in coming, but by ed in 1912 systematic spectral observa- In a brilliant study, Opik (12) used the 1899 the combination of good tracking tions of the bright in ner regions of the rotational velocities in M31 to estimate telescopes and photographic recording nearest galaxies. FoIr NGC 4594, the its distance. His result, 450,000 made it possible for Scheiner (3) to ob- , he detected inclined he correct- tain at the Potsdam Observatory a spec- lines [(6); see also (7)],, which Vera C. Rubin is a staff member of the Depart- trum of the nucleus of the giant spiral in ly attributed to stars c(ollectively orbiting ment of Terrestrial Magnetism, Carnegie Institution of Washington, Washington, D.C. 20015, and an Andromeda, M3 1. From the prominence' about the center of tbiat galaxy. On the adjunct staff member of the Mount Wilson and Las of the H and K absorption lines of calci- side of the nucleus whLere the rotation of Campanas Observatories. 24 JUNE 1983 1339 (1 pc = 3 x 10i3 km), comes closer to measurements may be made from stellar tory (near La Serena, Chile). A few the distance in use today, 750,000 pc, absorption lines. One way around this spectra come from the 2.5-m du Pont than the distance of 230,000 pc which difficulty is to measure velocities from Telescope of the Carnegie Institution of Hubble derived from the Cepheids and the emission lines arising in the ionized Washington at Las Campanas (also near which he was still using in 1950 (13). gas clouds surrounding the hot young La Serena). Optical observations are Opik's distance was based on the proce- blue stars which delineate the spiral made with spectrographs which incorpo-' dure used currently to determine the structure. Because the light from these rate an RCA C33063 image tube (20). masses ofgalaxies, and I will discuss it in clouds is emitted principally in a few The image is photographed from the final some detail. For a particle of mass m lines of abundant elements (hydrogen, phosphor of this tube. Use of this elec- moving in a circular orbit with velocity V ionized oxygen, ionized nitrogen, and tronic enhancement device makes it pos- about a spherical distribution of mass M ionized sulfur), a measurable exposure is sible to obtain spectra at a high spatial at distance r from the center, the equality obtained in a fraction of the time re- scale and of high velocity accuracy with of gravitational and centrifugal forces quired for the stellar exposure. This is exposure times of about 3 hours, on gives the method we employ in our optical Kodak IIIa-J plates which have been (1) observations. A third procedure is to baked in forming gas and preflashed to GM(r)m = mV2(r) observe in the radio spectral region, at enhance their speed. r2 r the wavelength of 21 cm emitted by the We choose galaxies that are relatively where G is the constant of gravitation hydrogen atom. Hydrogen gas, a major isolated, that are not strongly barred, and M(r) is the total mass contained out constituent of the prominent dust lanes that subtend an angular size at the tele- to a distance r from the center. It follows seen in spiral galaxies and hence opaque scope which approximately matches the that the mass interior to r is given by for an optical astronomer, becomes the length of the spectrograph slit, and that object of observation for the radio as- are viewed at relatively high inclination = M(r) rV2(r)/G (2) tronomer. to minimize uncertainties in transform- Downloaded from or Following the pioneering work dis- ing line-of-sight velocities to orbital ve- in the Distances are cal- = (3) cussed above, observations of the rota- locities galaxy. V(r) [GM(r)lr]"2 tion of galaxies proceeded very slowly. culated from velocities arising from the Today we adopt a distance to a galaxy A major addition to our knowledge came cosmological expansion, adopting a (generally from its Hubble velocity), de- frotn the extensive work of Margaret and Hubble constant of 50 km sec- Mpc . termine the rotational velocity V at each Geoffrey Burbidge (14). Due to the long A sample of Sc program galaxies and http://science.sciencemag.org/ r, and then calculate the variation of M observing times, velocities were ob- spectra is shown in Fig. 1; the spectra with r. Opik assumed that the ratio of tained only for the brightest inner re- were taken with the spectrograph slit mass to luminosity was the same for M3 1 gions. Only for a few of the nearest aligned along the galaxy major axis. The as for our Galaxy, and used M and V to galaxies was it possible to observe indi- galaxies are arranged by increasing lumi- determine r. Both the dynamics and the vidual regions and map the rotation to nosity. Velocities are determined by astrophysics were sound, and the result large'nuclear distance (15). Until recent- measuring the displacement of the emis- convinced many astronomers that spiral ly, radio observations had limited spatial sion lines with respect to the night sky galaxies were external to our own Milky resolution and hence poor velocity accu- lines to an accuracy of 1 ,um. We mea- Way system. racy. Astronomets attempting to exam- sure with a microscope which moves in

ine the dynamical properties of galaxies two dimensions, a rather old-fashioned on March 24, 2021 (16) had few measured velocities well but still very accurate technique. Many Modern Optical Observations of beyond the bright nuclear regions. astronomers now trace plates with a mi- Spiral Galaxy Rotation For the past several years, W. K. crodensitometer or obtain digital data Ford, Jr., N. Thonnard, D. Burstein, B. directly at the telescope. From the mea- Several observational procedures are Whitmore, and I (17-19) have been using sured velocities on each side of the nu- available today to study the rotation modern detectors to study the dynamical cleus a mean curve is formed. It de- (that is, orbiting) of stars and gas in a properties of isolat'ed spiral galaxies. We scribes the circular velocity in the plane spiral galaxy. A spectrograph with a long attempt to measure the rotational veloci- of the galaxy as a function of distance slit will record the light arising from all of ties across the entire optical galaxy. We from the nucleus, as shown on the right the stars in the galaxy along each line-of- have observed galaxies of Hubble types in Fig. 1. sight. The resulting spectrum will be Sa (disk galaxies with large central Within a Hubble type, rotation curves composite, the sum of individual stellar bulges, and tightly wound weak arms vary systematically with luminosity. For spectra. A stellar motion toward the ob- with few emission regions), Sb, and Sc a low-luminosity galaxy (NGC 2742), ve- server will displace each spectral line (disk galaxies with small central bulges, locities rise gradually from the nucleus toward the blue region ofthe spectrum; a and open arms with prominent emission and reach a low maximum velocity only motion away from the observer will dis- regions), emphasizing galaxies of high in the outer regions. For a high-luminos- place each line toward the red. Measure- and low luminosity within each class. ity galaxy (UGC 2885), rotational veloci- ment of the successive displacements Our aim is to learn how rotational prop- ties rise steeply from the nucleus and along a spectral line will give the mean erties vary along the Hubble sequence of reach a "nearly flat" portion in a small velocity of the stars corresponding to galaxies, and within a Hubble class, and fraction of the galaxy radius. An Sc of that location in the galaxy. The shape to relate the dynamical properties to low luminosity (6 x 109 solar luminos- and width of the line contain information other galaxy parameters. ities) has a maximum rotational velocity concerning the random motions along For 60 Sa, Sb, and Sc program galax- Vmax near 100 km sec1, compared with the line-of-sight. ies, we have obtained spectra with the 4- Vmax near 225 km sec'l for an Sc of high Starlight from external galaxies is gen- m telescopes at Kitt Peak National Ob- luminosity (2 x 1011 solar luminosities). erally too faint to permit a dense spectral servatory (near Tucson, Arizona) and ]Dynamical variations from one Hubble exposure on which accurate positional Cerro Tololo Inter-American Observa- class to another are equally systematic. 1340 SCIENCE, VOL. 220 What differentiates Sa and Sc galaxies of Mass Distribution Within Spiral Galaxies an integral equation is solved for the equal luminosity are the amplitudes of density distribution as a function of r their rotational velocities. At equal lumi- What do these flat rotation curves tell (21). nosity, an Sa has a higher rotational us about the mass distribution within a In several cases of special interest, the velocity than an Sb, which in turn has a disk galaxy? Unfortunately, we cannot velocity or mass distribution follows di- higher velocity than that of an Sc. A low determine a unique mass distribution rectly from Eq. 2 or Eq. 3, for a simple luminosity Sa has Vmax = 175 km sec'-, from an observed rotation curve; only spheroidal model. These cases are now a high-luminosity Sa has Vmax = 375 km the mass distribution for an assumed briefly discussed. sec-1. Each value is higher than that of model can be deduced. In practice, a 1) Central mass. In the solar system, the corresponding Sc galaxy. spheroidal or disk model is adopted, and where essentially all of the mass is in the

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Fig. 1. Spectra and rotation curves for five Sc galaxies, arranged according to increasing luminosity. Photographs for NGC 2742, 1421, and 2998 are copies of the television screen which displays the image reflected off the spectrograph slit jaws. The dark line crossing the galaxy is the spectrograph slit. NGC 801 and UGC 2885 are reproduced from plates taken at the prime focus of the 4-m telescope at Kitt Peak National Observatory by B. Carney. The corresponding spectra are arranged with wavelength increasing from the bottom to the top. The strongest step- shaped line in each spectrum is from hydrogen in the galaxy, and is flanked by weaker lines offorbidden ionized nitrogen. The strong vertical line in each spectrum is the continuum emission from stars in the nucleus. The undistorted horizontal lines are emission from the earth's atmosphere, principally OH. The curves at the right show the rotational velocities as a function of nuclear distance, measured from the emission lines in the spectra. 24 JUNE 1983 + w0q<-i~~~100 1341 sun, M(r) is constant for all distances 7.0 the average density of the nonluminous beyond the sun. Velocities of all planets matter is several orders of magnitude decrease as r 1/2, that is, a Keplerian _6.0 / _ greater than the mean density of mass in decrease, with increasing distance from the universe. Hence it is clumped around the sun (Eq. 3). Mercury (solar dis- E50 galaxies and is not just an extension of tance = 0.39 of the earth's distance) or- the overall background density. bits with a velocity of 47.9 km sec-'. 0 During the past decade, there has been 0 0 the idea that per- Pluto, 100 times farther (39 earth dis- 0~~~~~~~~~~~~. growing acceptance of tances), moves with a velocity one-tenth 030 haps 90 percent of the mass in the uni- that of Mercury, V = 4.7 km sec'-. For verse is nonluminous (22). The require- galaxies, the lack of a Keplerian falloff in ments for such mass come from a variety velocities indicates that most ofthe mass of observations on a variety of distance is not located in the nuclear regions. scales. In our own Galaxy, we can calcu- 2) Solid body. For a body of uniform late the disk mass at the position of the density, M(r) a r3. Thus V(r) increases sun by observing the attraction of the linearly with r; the object will exhibit a disk on stars high out of the plane, and constant angular velocity which pro- comparing this mass with that which we duces solid body rotation. Some galaxies 4.10 20 30 40 50 can enumerate in stars and gas. Oort (23) show linear velocity curves near the nu- r (distance from nucleus, kpc) first showed that the counted density at cleus, although the spatial resolution is Fig. 2. Integral mass interior to r, as a func- the sun is less by about one-third than generally poor. Solid body rotation is tion of r, for Sc and Sa galaxies of high (IC that implied by the dynamics, 0.15 solar rare in the outer regions of disk galaxies. 724, NGC 801) and intermediate (NGC 4698, mass per cubed. But self-gravitat- 1421) luminosity. Mass is increasing approxi- stars unstable Downloaded from 3) Constant velocity. For V(r) con- mately linearly with r and is not converging to ing disks of are against stant, M(r) increases with r. This varia- a limiting mass at the edge of the optical formation of barlike distortions. Hence it tion describes the velocities we observe galaxy. is appealing to place the unseen matter in in galaxies. Density, M(r)lr3, decreases a halo, rather than a disk, and solve both with increasing r as h1r2 for spherical the problem of the Oort limit and that of models. Although the density is decreas- quently, the average mass per unit (blue) the stability of spiral disks. Moreover, a ing outward, the mass in every concen- luminosity in a galaxy, a measure of the halo of low density at the solar position http://science.sciencemag.org/ tric shell r is the same for all r. Hence a stellar population in the galaxy, is a good is consistent both with the Oort limit and rotation curve which is flat (or slightly indicator of Hubble type. with a halo which becomes dominant rising) out to the final measurable point These observational resuilts are sum- beyond the optical galaxy. indicates that the mass is not converging marized in Fig. 3 and as follows. Within Additional evidence for a massive halo to a limiting mass at the present observa- a Hubble type, high-luminosity galaxies surrounding our Galaxy comes from in- tional limit of the optical galaxy for a are larger, have higher mass and density, dividual stars and gas at greater nuclear galaxy modeled as a single spheroid. have stellar orbital velocities which are distance than the sun, whose rotational The mass interior to r is plotted against larger, but have the same value of MILB velocities continue to rise (24). The gal- r in Fig. 2 for four spirals; the mass is within the isophotal radius as do low- axy rotational velocity is high, befitting calculated from the observed velocity luminosity spirals. At equal luminosity, the enormous distances. The sun, carry- on March 24, 2021 and Eq. 2. Masses range up to several Sa, Sb, and Sc galaxies are the same ing the planets with it, orbits the galaxy times 1012 solar masses for the most size, but the Sa has a higher density, with a speed of 220 km sec'1 (500,000 luminous spirals. Because rotational ve- larger mass, higher rotational velocity, miles per hour); even so, it takes us 225 locity (at a fixed luminosity) is higher in and larger value of MILB. This interplay million years to complete one revolution. an Sa than in an Sb, and higher in an Sb of luminosity and Hubble type has con- On scale lengths of the order of galax- than in an Sc, big-bulge spirals (Sa's) vinced us that galaxies cannot be de- ies, 20 < R < 100 kpc, the flat rotation have a higher mass density (V2/r2) at scribed by a single parameter sequence, curves observed at both optical (17, 19, every r than Sb's and Sc's of the same be it Hubble type or luminosity or mass. 25) and radio (26) wavelengths and the luminosity. Moreover, the distribution of At least two parameters are necessary; consequent increase with radius of the mass with radius is similar, within a Hubble type and luminosity are one such mass-to-luminosity ratio offer support- single scale factor, for all of the Sc's, pair. ing evidence for heavy halos. Moreover, most of the Sb's, and a few of the Sa's. the dynamics ofthe globular clusters (27) In the disk of a normal spiral galaxy, and of the dwarf satellite galaxies (28) surface brightness is observed to de- Nonluminous Mass in Galaxies which orbit our Galaxy imply a mass crease exponentially with increasing ra- which increases approximately linearly dial distance, while the flat rotation Observations of rotation curves which with increasing radius, to distances as curves imply that mass density falls do not fall support the inference that great as 75 or 100 kpc. slower, as 1/r2. Hence locally the ratio of massive nonluminous halos sur-round On distance scales as great as hun- mass to luminosity MIL increases with spiral galaxies. The gravitational attrac- dreds to thousands of kiloparsecs, there increasing distance from the nucleus. If tion of this unseen mass, much of it is equally impressive evidence that the we average the mass and the luminosity located beyond the optical image, keeps gravitational mass far exceeds the lumi- across the entire visible galaxy, then the the rotational velocities from falling. The nous mass. The evidence comes from the ratio of mass to luminosity is a function increase in MILB with nuclear distance orbits ofbinary galaxies (29) (our Galaxy, of Hubble type, but is independent of indicates that this nonluminous mass is and the Andromeda galaxy form one luminosity within a type. This statement much less concentrated toward the cen- such pair), random motions ofgalaxies in holds for observed ranges of (blue) lumi- ter of the galaxy than are the visible stars clusters (30), and the distribution of hot nosity LB up to a factor of 100. Conse- and gas. Even at large nuclear distances, gas in clusters of galaxies (31) as ob- 1342 SCIENCE, VOL. 220 served by the x-ray emission. Such ob- predict whether the universe is of high Why Was It Thought That Rotational servations compose a body of evidence density, so that the expansion will ulti- Velocities Decreased? which lends support to the concept of mately be halted and the universe will heavy halos clumped around individual start to contract, or of low density, and Most present-day astronomers grew galaxies. so that the expansion will go on forever. up believing that disk galaxies had Kep- Increased interest in rotation curves Theoretical models of the formation lerian velocities at moderate distances. has led astronomers to related studies. and evolution of galaxies currently at- The reasons for this belief are easy to Radio astronomers have determined ro- tempt to take into account the environ- identify. In the early 1900's, astronomers tational velocities beyond the optical im- mental effects of enormous quantities of were more at home with the planets than age for a few galaxies in which the neu- nonluminous matter surrounding new- with the galaxies. Slipher's early obser- tral hydrogen distribution extends far- born and evolving galaxies. Most likely, vations concerned the study of the plan- ther than the optical galaxy. Sancisi (32) the formation processes for galaxies and ets, Percival Lowell's major interest. suggests that rotation curves do fall be- for the nonluminous matter were dis- Galaxies were studied only to learn yond the optical galaxy, perhaps by 10 tinct; one attractive idea is that much of whether these nebulous disks in the sky percent in velocity over a small radial the mass of the universe was arranged in were the stuff from which planets were distance, but then level off once again. its nongaseous dark guise before the formed. Slipher used Saturn as a radial Casertano (33), Bahcall and collabora- galaxies began to form. Recent reviews velocity standard for his M31 spectra; he tors (34), and Caldwell and Ostriker (35) by Rees (36), Silk (37), and White (38) characterized the spectrum of the Som- have constructed multicomponent mass enumerate the various interesting possi- brero galaxy as "planetary." Astrono- distributions, consisting of central point bilities. An especially pleasing model by mers were predisposed to draw an analo- masses, disks (sometimes truncated), Gunn (39) suggests that disks of spirals gy between the distribution of luminosity bulges, and halos, which can reproduce form from relatively slowly infalling ma- in a galaxy and the distribution of mass the observed rotational properties of spi- terial. Regardless of which evolutionary in the solar system. Downloaded from ral galaxies. scheme ultimately explains the current Early spectral observations ofgalaxies Observations in a variety of spectral phases of galaxies and of the universe, generally did not extend beyond the ranges have been unable to detect the we have learned that galaxies are not the bright nuclear bulges. Measured veloci- dark matter. Massive halos do not ap- isolated "island universes" imagined by ties usually increased with increasing pear to radiate significantly in the ultra- Hubble (40), but that environmental ef- nuclear distances and mass distributions violet, visible, infrared, or x-ray regions; fects play a prominent role in directing were in the solid body domain. By 1950, http://science.sciencemag.org/ they are not composed of gas or of their evolution. only a handful of rotation curves had normal low-luminosity stars. Other pos- For nonbelievers in heavy halos and been determined, and astronomers were sible forms include fragments of matter invisible mass, an alternative explana- acting on their expectations when they which never became luminous (Jupiter- tion (41) modifies the hlr2 dependence "saw" a region of Keplerian falling ve- like planets, black holes, neutrinos, (Eq. 1) in Newton's law ofgravitation for locities. Mayall (42) described his newly gravitinos, or monopoles) (36). The enor- large r. Under this circumstance, the determined velocities in M33 as follows: mity of our ignorance can be measured distribution of mass follows the distribu- "As in the Andromeda , the re- by noting that there is a range in mass of tion of light, but the velocities resulting sults suggested more or less constant 1070 between non-zero-mass neutrinos from the mass distribution remain high angular velocity . .. for the main body and massive black holes. Not until we due to a modified law of gravitation. For of the spiral. Beyond the main body on March 24, 2021 learn the characteristics and the spatial the present, this possibility must remain these outer parts rotate more slow- distribution of the dark matter can we as a last resort. ly ... as in a planetary system where

1013 1 0 0 Luminosity . Luminosity 24.0 F _ 350 F 0 0O 0. a E High 50 0 12.0 F = 260 10 12 ~~~~High 0 0 p \ 4- a - 0 0U 0 I Y 0 0 0 S v a 0 0 6.0F CL C 0 zo Medium * 0 * I 0 * ~~Med?u~m1 0 4.0 150 F 0 0 S 0 £~~0 l10l F S. 01 3.0 * 1 P so E Low * * W0* * E 4 x o 0 0 10 Low Sc > 100 0 A B 1.5 - c 00

1010 Sa Sb Sc Sa Sb Sc Sa Sb SC Fig. 3. (A) Maximum rotational velocity as a function of Hubble type for the galaxies studied. Lines show the increase in Vmax with earlier Hubble type for galaxies of low, intermediate, and high luminosity. (B) Mass (solar masses) within the optical galaxy as a function of Hubble type. Within a Hubble type, higher velocity and higher mass indicate higher luminosity. (C) Mass-to-blue luminosity ratio (solar units) as a function of Hubble type. The mean value and the lr range are indicated. Within a Hubble type, there is no correlation of the mass-to-luminosity ratio with luminosity. 24 JUNE 1983 1343 most of the mass lies inside the orbit that virtually all spiral galaxies have ro- 23. J. Oort, Bull. Astron. Inst. Neth. 15, 45 (1960); in Galaxies and the Universe, A. Sandage, M. concerned." De Vaucouleurs (43) re- tational velocities which remain high to Sandage, J. Kristian, Eds. (Univ. of Chicago Press, Chicago, 1975), p. 455. viewed the eight available rotation the limits of the optical galaxy, we can 24. S. Kulkarni, L. Blitz, C. Heiles, Astrophys. J. curves in 1959 and concluded, "In all recognize the circuitous route which Lett. 259, L63 (1982). 25. S. M. Faber and J. S. Gallagher, Annu. Rev. cases the rotation curve consists of a brought us to this knowledge. Astrono- Astron. Astrophys. 17, 135 (1979). straight inner part in the region of con- mers can approach their tasks with some 26. M. S. Roberts and A. H. Rots, Astron. As- trophys. 26, 483 (1973); A. Bosma, thesis, Rijk- stant angular velocity up to a maximum amusement, recognizing that they study suniversiteit te Groningen (1978); Astron. J. 86, at R = Rm beyond which the rotational only the 5 or 10 percent of the universe 1791 (1981); ibid., p. 1825. 27. F. D. A. Hartwick and W. L. W. Sargent, velocity decreases with increasing dis- which is luminous. Future astronomers Astrophys. J. 221, 512 (1978). 28. J. Einasto, in (22); D. Lynden-Bell, in Astro- tance to the center and tends asymptoti- will have to be clever in devising detec- physical Cosmology, H. A. Bruck, G. V. cally toward Kepler's third law (Figure tors which can map and study this ubiq- Coyne, M. S. Longair, Eds. (Pontifical Acade- my, Vatican City State, 1982), p. 85. 27)." But with the 20/20 vision of hind- uitous matter which does not reveal itself 29. S. D. Peterson, Astrophys. J. 232, 20 (1979). sight, plots of the data reveal only a to us by its light. 30. F. Zwicky, Helv. Phys. Acta 6, 110 (1933); H. J. Rood, Astrophys. J. Suppl. 49, 111 (1982); W. scatter of points, from which no certain Press and M. Davis, Astrophys. J., in press. conclusion can be drawn. References and Notes 31. D. Fabricant, M. Lecar, P. Gorenstein, As- trophys. J. 241, 552 (1980); W. Forman and C. Yet not all astronomers were blind to 1. Third Earl of Rosse, Br. Assoc. Adv. Sci. Rep. Jones, Annu. Rev. Astron. Astrophys. 20, 547 (1884), p. 79; P. Moore, The Astronomy ofBirr (1982). the contradication posed by rapidly fall- Castle (Mitchell Beazley, London, 1971). 32. R. Sancisi, private communication; and ing light distributions and nonfalling ro- 2. Third Earl of Rosse, Philos. Trans. R. Soc. R. J. Allen, Astron. Astrophys. 74, 73 (1979). London (1850), p. 110. 33. S. Casertano, Mon. Not. R. Astron. Soc., in tational velocities. In a classic paper 3. J. Scheiner, Astrophys. J. 9, 149 (1899). press. discussing the structure and dynamics of 4. Sir William Huggins and Lady Huggins, An 34. J. N. Bahcall, M. Schmidt, R. M. Soneira, Atlas of Representative Spectra (Wm. Wesley Astrophys. J. Lett. 258, L23 (1982). NGC 3115, an almost featureless disk SO and Son, London, 1899), plate II. 35. J. A. R. Caldwell and J. P. Ostriker, Astrophys. galaxy, the ever-wise Oort (44) wrote, 5. V. M. Slipher, Lowell Obs. Bull. No. 58 (1914). J. 251, 61 (1982). 6. __ , ibid. No. 62 (1914). 36. M. J. Rees, in Observational Cosmology (Gene- Downloaded from "It may be concluded that the distribu- 7. M. Wolf, Vierteljahresschr. Astron. Ges. 49, 162 va Observatory, Geneva, Switzerland, 1978), p. (1914). 259; in Astrophysical Cosmology, H. A. Bruck, tion of mass in the system must be 8. F. G. Pease, Proc. Natl. Acad. Sci. U.S.A. 4, 21 G. V. Coyne, M. S. Longair, Eds. (Pontifical considerably different from the distribu- (1918). Academy, Vatican City State, 1982), p. 3. 9. H. Leavitt, Harvard Coll. Obs. Ann. 60, 87 37. J. Silk, in Astrophysical Cosmology, H. A. tion of light." And he concluded, "The (1908); Harvard Coll. Obs. Circ. No. 179 (1912). Bruck, G. V. Coyne, M. S. Longair, Eds. (Pon- strongly condensed luminous system ap- 10. H. Shapley, Proc. Astron. Soc. Pacific 30, 42 tifical Academy, Vatican City State, 1982) p. (1918); Astrophys. J. 48, 154 (1918). 427; see also S. M. Faher, in ibid., p. 191; J. P. pears imbedded in a large and more or 11. E. Hubble, Observatory 43, 139 (1925).

Ostriker, in ibid., p. 473. http://science.sciencemag.org/ less homogeneous mass of great densi- 12. E. Opik, Astrophys. J. 55, 406 (1922). 38. S. White, in Morphology and Dynamics of Gal- 13. E. Hubble, The Realm of the Nebulae (Yale axies (Geneva Observatory, Geneva, Switzer- ty." Schwarzschild (45), too, looked at Univ. Press, New Haven, Conn., 1936), p. 134; land, 1982), p. 291. E. Holmberg, Medd. Lunds Astron. Obs. Ser. 2 39. J. E. Gunn, in Astrophysical Cosmology, H. A. the rotation curve of M3 1 and noted that (No. 128) (1950). Bruck, G. V. Coyne, M. S. Longair, Eds. (Pon- "Contrary to earlier indication, the five 14. E. M. Burbidge and G. R. Burbidge, in Galaxies tifical Academy, Vatican City State, 1982), p. and the Universe, A. Sandage, M. Sandage, J. 233. normal points in Figure 1 do not suggest Kristian, Eds. (Univ. of Chicago Press, Chica- 40. E. Hubble, in The Realm of the Nebulae (Yale solid body rotation.... Rather, they go, 1975), p. 81. Univ. Press, New Haven, Conn., 1936), p. 98. 15. V. C. Rubin and W. K. Ford, Jr., Astrophys. J. 41. J. Bekenstein, Int. Astron. Union Symp., in suggest fairly constant circular velocity 159, 379 (1970). press; J. Bekenstein and M. Milgrom, preprint. over the whole interval from 25' to 115' 16. P. Brosche. Astron. Astrophys. 23, 259 (1973). 42. N. U. Mayall [Publ. Obs. Univ. Mich. No. 10 17. V. C. Rubin, W. K. Ford, Jr., N. Thonnard, (1950), p. 9] notes that the form of the rotation (5-25 kpc with the current distance)." Astrophys. J. Lett. 225, L107 (1978); V. C. curve of M3 1, compared with that of our Gal- the literature is with Rubin and W. K. Ford, Jr., Astrophys. J. 238, axy, suggests that the distance of M31 (then Indeed, replete 471 (1980). adopted as 230,000 pc) is too small. The use of on March 24, 2021 isolated comments stressing the same 18. D. Burstein, V. C. Rubin, N. Thonnard, W. K. rotational properties to establish distances is Ford, Jr., Astrophys. J. 253, 70 (1982). only now coming into wide use. point. When in 1962 Rubin et al. (46) 19. V. C. Rubin, W. K. Ford, Jr., N. Thonnard, 43. G. de Vaucouleurs, in Handbuch der Physik, S. examined the kinematics of 888 early ibid. 261, 439 (1982). Flugge, Ed. (Springer, Berlin, 1959), vol. 20, p. 20. This tube is known throughout the astronomical 311. type stars in our Galaxy, they concluded community as the "Carnegie" image tube, for 44. J. H. Oort, Astrophys. J. 91, 273 (1940). its development was the product of a coopera- 45. M. Astron. J. 59, 273 (1954). that beyond the sun "the rotation curve tive effort by RCA and a National Image Tube Schwarzschild, is approximately flat. The decrease in Committee, under the leadership of M. Tuve 46. V. C. Rubin, J. Burley, A. Kiasaipoor, B. and W. K. Ford, Jr., of the Carnegie Institution Klock, G. Pease, E. Rutscheidt, C. Smith, ibid. rotational velocity expected for Kepleri- of Washington, funded by the National Science 67, 527 (1962). an orbits is not found." Shostak (47) Foundation. 47. G. S. Shostak, Astron. Astrophys. 24, 411 21. L. Perek, Adv. Astron. Astrophys. 1, 165 (1962); (1973). noted that "the overwhelming character- A. Toomre, Astrophys. J. 138, 385 (1963). See 48. More complete references are contained in the NGC 2403 is also Burbidge and Burbidge (14). literature cited. I thank my colleagues Kent istic of the velocity field of 22. J. P. Ostriker, P. J. E. Peebles, A. Yahil, Ford and Norbert Thonnard for their continued the practically constant circular rotation Astrophys. J. Lett. 193, LI (1974); J. Einasto, A. assistance and support in all the phases of this Kaasik, E. Saar, Nature (London) 250, 309 work and Drs. Robert J. Rubin, Robert Herman, seen over much of the object." (1974). For a dissenting view, see G. R. Bur- Francois Schweizer, and W. Kent Ford, Jr., for Now that systematic studies indicate bidge, Astrophys. J. Lett. 196, L7 (1975). wise comments on the manuscript.

1344 SCIENCE, VOL. 220 The Rotation of Spiral Galaxies Vera C. Rubin

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