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Home , Geology of Mars, Mars, Tharsis, Water on Mars

R ESEARCH A RTICLES (COM) (12). The global of is now known to greater accuracy than The Global Topography of Mars ’s in a root mean square (rms) sense. and Implications for Surface Global shape. The difference of ϳ20 km between the polar and equatorial radii indi- Evolution cates that the largest contribution to shape is the planetary (Table 1), which is David E. ,1* Maria T. Zuber,1,2 Sean C. Solomon,3 due mostly to the rotation of Mars with a Roger J. Phillips,4 James W. Head,5 James B. Garvin,1 small contribution (ϳ5%) (13) from the vast W. Bruce Banerdt,6 Duane O. Muhleman,7 Gordon H. Pettengill,2 -tectonic province (Fig. 2), situated near the . Subtraction of the Gregory A. Neumann,1,2 Frank G. Lemoine,1 James B. Abshire,1 2 4 4 gravitational potential or (14) from Oded Aharonson, C. David Brown, Steven A. Hauck, radii measurements represents in 7 3 1 Anton B. Ivanov, Patrick J. McGovern, H. Jay Zwally, terms of topography and eliminates the con- Thomas C. Duxbury6 tribution due to rotation, thus clarifying other long-wavelength components of the shape. Elevations measured by the Mars Orbiter Altimeter have yielded a high- Figure 2 illustrates that topography on Mars accuracy global map of the topography of Mars. Dominant features include the has a 30-km dynamic range, the largest of the low northern hemisphere, the Tharsis province, and the Hellas impact basin. The terrestrial . The large topographic ex- northern hemisphere depression is primarily a long-wavelength effect that has cursions are due to ancient impact basins, been shaped by an internal mechanism. The topography of Tharsis consists of large shield volcanoes, and the ability of the two broad rises. Material excavated from Hellas contributes to the high ele- ’s rigid outer shell () to sup- vation of the southern hemisphere and to the scarp along the hemispheric port significant stresses associated with sur- boundary. The present topography has three major drainage centers, with the face and subsurface loads (15). northern lowlands being the largest. The two polar cap volumes yield an A useful representation of the planetary upper limit of the present surface inventory of 3.2 to 4.7 million cubic shape is the triaxial , for which the kilometers. axes and orientation with respect to a coor- dinate system with origin at the COM of Long-wavelength topography (changes in to- 9 and Viking imagery (8), and the 9 Mars are given in Table 1. The best fit ellip- pography over scales of hundreds to thou- and spectrometers (9). soid (16) is dominated by a displacement sands of kilometers) reflects processes that Disparate measurement types were combined from the COM by Ϫ2986 m along the z axis, have shaped Mars on a global scale and thus into digital terrain models (10) that were of which represents an offset between the COM is of particular interest in the context of the variable spatial resolution and typically char- and the planet’s geometric center or center of planet’s evolution. The Mars Orbiter Laser acterized by vertical errors of ϳ1to3km. figure (COF) along the polar axis. The sign of Altimeter (MOLA) (1), an instrument on The model from MOLA (Fig. 2) (11) has a the offset indicates that the pole has a the (MGS) space- spatial resolution of ϳ1° (or ϳ59 km sepa- higher than the north pole by ϳ6 craft (2), recently acquired the first globally ration at the equator) and an absolute accu- km, which corresponds to a systematic south- distributed, high-resolution measurements racy of 13 m with respect to Mars’ center of to-north downward slope of 0.036°. The tri- of the topography of Mars (3). A geodeti- cally controlled topographic model derived Fig. 1. Global profile of N 15 km from circum-Mars (Fig. 1) and northern Mars from MOLA crossing 60û hemisphere (4, 5) profiles has enabled 52°E and 60û quantitative characterization of global- 247°E. The north and south polar caps are at scale processes that have shaped the mar- the top and bottom. The tian surface. and Alba 30û Before the MGS mission, models of mar- Patera volcanic shields, 30û tian topography were derived from Earth- both located within the Alba based ranging (6), and Vi- Tharsis province, appear -15 km king 1 and 2 radio (7), stereo and at the upper left, and the Hellas impact basin is at photoclinometric observations from Mariner the lower right. The con- 0û 0û trast in elevation and re- Pavonis 1Earth Sciences Directorate, NASA/Goddard Space gional topographic rough- Flight Center, Greenbelt, MD 20771, USA. 2Depart- ness between the north- ment of Earth, Atmospheric, and Planetary Sciences, ern and southern hemi- Massachusetts Institute of Technology, Cambridge, spheres is also apparent. MA 02139, USA. 3Department of Terrestrial Magne- The dichotomy boundary tism, Carnegie Institution of Washington, Washing- scarp can be seen at ϳ50° -30û Hellas ton, DC 20015, USA. 4Department of Earth and Plan- east of north. Distributed -30û etary Sciences, Washington University, St. Louis, MO points above the surface 63130, USA. 5Department of Geological Sciences, correspond to false re- Brown University, Providence, RI 02912, USA. 6Jet turns caused by solar Propulsion Laboratory, Pasadena, CA 91109, USA. 7Di- background at the laser -60û -60û vision of Geological and Planetary Sciences, California wavelength and represent Institute of Technology, Pasadena, CA 91125, USA. Ͻ0.5% of the transmitted S *To whom correspondence should be addressed. E- pulses. Clustered returns mail: [email protected]..gov above the surface near the south pole are from . The vertical exaggeration is 100:1.

www.sciencemag.org VOL 284 28 MAY 1999 1495 R ESEARCH A RTICLES axial ellipsoid is also displaced by Ϫ1428 m rian-aged ridged dominate in some approximately the same band as the along the y axis, in the general direction of regions. All are characterized by a rougher southern rise, but extends to ϳ60°N. The the Tharsis topographic rise (Fig. 2). topography than the northern plains. The northern rise is dominated by the massive Major features of topography. The boundary between the smooth northern hemi- volcanic construct of Alba Patera (compare dominant feature of the topography is the sphere and the rough southern hemisphere is Fig. 1). -aged volcanic fans ema- striking difference (ϳ5 km) in elevation be- characterized by , knobs, and interven- nate radially from this shield into the northern tween the low northern hemisphere and high ing plains (22), as well as regional elevation lowlands for distances of more than 1000 km. southern hemisphere that represents one of changes of up to 4 km over distances of 300 The new data emphasize the distinctive na- the outstanding issues of evolution. to 1300 km (23). Where the regional eleva- ture of the Alba Patera structure as well as its This hemispheric dichotomy also has a dis- tion change is relatively steep, it is referred to connection to the region. In tinctive expression in the surface of as the dichotomy boundary scarp (compare contrast, the massive volcano Mars. The surface of the in the southern Fig. 1). appears to sit off the western edge of the hemisphere is old and heavily cratered, The Tharsis province is a vast region of Tharsis rise rather than on the flank, as pre- whereas that in the north is younger and more and deformation that appears to viously mapped (10). By its spatial associa- lightly cratered and was probably volcanical- interrupt the global dichotomy boundary be- tion, Olympus Mons is nonetheless likely to ly resurfaced early in Mars’ history (17). The tween the southern cratered highlands and have had a genetic to volcanism in Thar- hemispheric difference is also manifest in northern lowland plains (24). In previous sis proper. surface roughness (Fig. 3) calculated from work the province was displayed as a broad The new topographic data illuminate a the MOLA topographic profile data (18). topographic rise (10). However, Fig. 2 (see long-standing debate over the dominant con- Most of the northern lowlands is composed of also Fig. 6) shows that topographically Thar- tributors to the high elevations of the Tharsis the Late Hesperian–aged (19) Vastitas Borea- sis actually consists of two broad rises. The region. A prominent ridge (containing Clari- lis Formation, which is flat and smooth (Fig. larger southern rise is superposed on the tas Fossae; Fig. 2) extends southward from 2), even at a scale as short as 300 m (Fig. 3). highlands as a quasi-circular feature that ex- the region of the Tharsis Montes, and then The -aged (19) Arcadia Forma- tends from ϳ220°E to ϳ300°E and from curves northeastward in a “scorpion tail” pat- tion, which overlies the ϳ50°S to ϳ20°N and spans about 107 km2 in tern. This arcuate ridge bounds Solis Planum, Formation, is also smooth at large and small area. The highest portion of the southern rise a plateau within the southern rise. The ridge scales, consistent with either a sedimentary contains the Tharsis Montes (Ascraeus, Pavo- contains an abundance of heavily cratered (4, 20) or volcanic (21) origin for these nis, and Arsia). Eastward of the highest ter- material that has presumably es- plains. In the southern hemisphere Noachian- rain but still elevated are the ridged plains of caped resurfacing by younger Tharsis volca- aged (19) ridged plains form locally flat in- Lunae Planum (Fig. 2). The smaller northern nic flows because of its high elevation. It has tercrater deposits, whereas younger Hespe- rise is superposed on the lowlands and covers been suggested (25) that the termination of

Fig. 2. Maps of the global topography of Mars. The projections are Mercator to 70° and stereographic at the poles with the south pole at left and north pole at right. Note the elevation difference between the northern and southern hemispheres. The Tharsis vol- cano-tectonic province is centered near the equator in the longitude range 220°E to 300°E and contains the vast east-west trending system and several major vol- canic shields including Olympus Mons (18°N, 225°E), Alba Patera (42°N, 252°E), (12°N, 248°E), Pavonis Mons (0°, 247°E), and (9°S, 239°E). Regions and struc- tures discussed in the text include Solis Planum (25°S, 270°E), Lunae Planum (10°N, 290°E), and (30°S, 255°E). Major impact basins in- clude Hellas (45°S, 70°E), Argyre (50°S, 320°E), Isidis (12°N, 88°E), and Utopia (45°N, 110°E). This analysis uses an areocentric coordinate convention with east longitude positive. Note that color scale saturates at elevations above 8 km.

1496 28 MAY 1999 VOL 284 SCIENCE www.sciencemag.org R ESEARCH A RTICLES the ridge structure could have formed by (29)]. An alternative explanation for the to- contributes to the topographic expression lithospheric buckling, as could, by analogy, pography is that this outermost ring might along part of the dichotomy boundary. other ridge structures in the south Tharsis represent the highly degraded basin rim, Implications for evolution. The hemi- region. The southern rise (southward of with additional ring structures lying lower spheric dichotomy represents both an eleva- ϳ35°S) also contains exposures of heavily within the basin. Figure 4 also shows that tion difference and a difference in surface cratered Noachian units. These elevated an- material from Hellas’ topographic annulus geology, and although these two defining cient terrains are consistent with the view that the broad expanse of the southern rise (ele- Table 1. Mars geodetic parameters from MOLA. vations Ͼϳ3 km; see Fig. 2) formed at least in part by structural uplift (26). Such a hy- Parameter Value Uncertainty pothesis is supported by the orientation of fractures and in Claritas Fossae (24), Mean radius* (m) 3,389,508 Ϯ 3 although it is also possible that there has been Mean equatorial radius† (m) 3,396,200 Ϯ 160 Ϯ a contribution from lateral tectonic forces North polar radius* (m) 3,376,189 50 South polar radius* (m) 3,382,580 Ϯ 50 (25). The high elevations of the Tharsis Mon- tes region as well as of the northern rise Triaxial ellipsoid a (m) 3,398,627 display major contributions from volcanic b (m) 3,393,760 construction (27), although some structural c (m) 3,376,200 uplift may have subsequently been masked 1/flattening 169.8 Ϯ 1.0 by volcanism (28). Directions of principal ellipsoid axes The Hellas impact basin has the deepest a 1.0°N, 72.4°E topography on Mars and is characterized by a b 0°N, 342.4°E total relief of more than 9 km (Fig. 4). Moun- c 89.0°N, 252.4°E tains and massifs previously identified as con- Ellipsoid offset of COF from COM ⌬ (m) Ϫ233 stituting the main basin ring of Hellas have a ⌬y (m) Ϫ1,428 diameter of ϳ2300 km (29) and are situated on ⌬z (m) Ϫ2,986 the inner slopes of the topographic basin (Fig. Volume of north polar cap (106 km3)‡ 1.2 to 1.7 4). Basin material surrounding Hellas has Volume of south polar cap (106 km3) 2 to 3 not been mapped at the global scale; units that Elevation comparison with landers surround the basin are dominated by Noachian- (m) 45 aged heavily cratered plains (19). MOLA data (m) 0 reveal, however, a peak in the distinctive topo- Pathfinder (m) 94 graphic annulus that surrounds Hellas at a di- *See (65). †See (66). ‡See (51). ameter of ϳ4000 km, lying ϳ2 km above the main ring. In terms of and morphology, Hellas 0û 180û has striking similarities to the South Pole– Aitken basin on the farside of the . 120û These two impact structures have similar di- 60û ameters and volumes (30), as well as distri- 300û 240û butions of surrounding excavated material, though the material encircling South Pole– Aitken is more asymmetric. Hellas represents a major topographic excursion that dominates 240û 300û much of Mars’ southern hemisphere topogra- 120û 60û phy (compare Fig. 1). Previous researchers have noted the great depression, but no pre- vious topographic model has resolved the 180û 0û expanse of Hellas’ exterior topographic an- (m) nulus, which is likely due to ejecta, but pos- 1000 60û sibly includes contributions from impact 500 melt, structural uplift, and admixed local ma- 400 terial. This material represents a major redis- 30û 300 tribution of Mars’ early crust. Figure 4 was 200 used to determine that the volume of the 100 0û I topographic annulus, if “refilled” into the 80 Q basin, would cause the basin and surround- 60 S -30û ings to have an elevation of ϳ600 m with 40 respect to the global reference. Material re- 20 moved from Hellas thus accounts for a sig- 10 -60û nificant amount of the high-standing topog- 5 raphy of Mars’ southern hemisphere. The 0 observed topographic annulus around Hellas 180û 240û 300û 0û 60û 120û 180û is close to the position of the outermost Fig. 3. Interquartile scale (IQS) surface roughness (18) of Mars calculated from MOLA profiles on mapped basin ring [diameter ϳ4200 km a 330-m baseline in a 100-km running window. The projections are the same as in Fig. 2.

www.sciencemag.org SCIENCE VOL 284 28 MAY 1999 1497 R ESEARCH A RTICLES aspects may be related, they do not necessar- elevation difference, causing a large part of the masked by processes that occurred subse- ily share the same mechanism of formation. southern hemisphere, away from Tharsis and quent to formation. Hypotheses to explain the hemispheric di- Hellas, to display elevations as low as those MGS gravity data (40) provide additional chotomy have included thinning of the north- over a significant fraction of the northern hemi- perspective on crustal structure beneath the ern hemisphere crust by convection sphere. Together, Figs. 5 and 6 demonstrate that resurfaced northern hemisphere. Large (31, 32), an early period of tectonic plate the COM-COF offset accounts for most of the (though smaller than hemispheric-scale) im- recycling (33), and one or more large impacts elevation difference between the northern and pacts such as Utopia and Hellas are marked in the northern hemisphere (34–36). southern hemispheres and indicate that the by distinctive positive gravitational anoma- A key issue is to determine how much of hemispheric elevation difference is primarily a lies (40). However, no other anomalies of the hemispheric elevation difference is due to long-wavelength effect. comparable spatial scale occur in association the long-wavelength planetary shape rather A projection of the northern hemisphere with regional topographic lows in the north- than the boundary scarp (23, 37); this issue topography from the pole to the equator (Fig. ern hemisphere, except for the previously can be explored from the global distribution 7) further illustrates the of the northern known Isidis impact structure that sits on the of elevations and slopes (Fig. 5). As shown in hemisphere depression. Note the distinctive dichotomy boundary. We thus suggest that Fig. 5, which plots histograms of elevations circular signature of the buried Utopia basin, the long-wavelength topographic expression before and after removing the offset between originally proposed as an impact feature on of the northern hemisphere depression was the COM and COF along the polar axis, the z the basis of geological evidence (35), but not shaped by an internal process or processes. component of the COM-COF difference is observed in earlier topographic studies. The largely equivalent to the hemispheric eleva- circular expression of Utopia is apparent de- tion difference. A histogram of the distribu- spite its location within the area of northern tion of 100-km baseline slopes (38) calculat- hemisphere resurfacing (5, 39). However, ed from the global topographic grid (Fig. 5C) even after accounting for the formation of the peaks at ϳ0.3° and is long-tailed, the latter Tharsis rise, presumably subsequent to the feature a result of topographic excursions process that produced the hemispheric eleva- associated with volcanoes, impact basins, and tion difference, the boundary of the northern tectonic features. The slope corresponding to hemisphere depression is clearly noncircular, the peak in the distribution is close to the and we see no compelling topographic evi- average longitudinal slope associated with dence for a hemispheric-scale single impact the COM-COF offset along the z axis and is such as previously proposed (34). Formation partly a result of the offset. But the peak slope of the elevation difference by multiple small- also contains contributions due to Tharsis and er impacts has also been suggested (36). Be- regional-scale features. yond Utopia, however, no circular structures Subtracting the COM-COF offset along the of comparable scale are apparent in the to- polar axis from the global topography model pography of the northern plains, although (Fig. 6) eliminates most of the hemispheric arguably such structures could have been

Fig. 4. Regional topo- graphic model of the Hel- 0 las basin. (Top) Azimuth- ally averaged radial to- pography used in the cal- -5

culation of infilling the elevation (km) basin with surrounding -3000 0 3000 60 material postulated to distance (km) ° ° have been excavated 90

from it. (Bottom) Color- 30 coded topography plotted ° in an equal-area projec- tion with the same scale as that in Fig. 2. The ° lines correspond to zero- 0 °

elevation contours. 120

Fig. 5. Histograms of (A) topography, (B) heights with respect to an ellipsoid shifted by Ϫ ° -30 2.986 km along the z axis, and (C) 100-km ° -30 baseline slopes. The histogram in (A) shows ° the distinct bimodal signature that repre- 150 sents the elevation difference between the northern and southern hemispheres. That in (B) shows elevations plotted with respect to 330 ° an ellipsoid whose center is shifted so as to remove the effect of the COM-COF offset along the polar axis. The effect of the shift is to produce a unimodal distribution of eleva- -60 ° tions; that is, the hemispheric difference in ° -60 elevation largely disappears.

1498 28 MAY 1999 VOL 284 SCIENCE www.sciencemag.org R ESEARCH A RTICLES The MOLA topography does not permit us to tic lithosphere thickness to that inferred from hemispheric elevation contrast also has rule out the possibility of a focusing of inter- Hellas, but more detailed modeling of gravi- played a role in the present distribution of nal activity in the vicinity of an early impact ty, topography, and magnetics will ultimately surface volatiles, which can be quantified by (36, 41). However, if this focusing occurred, be required to distinguish whether there ex- the MOLA topographic model. subsequent reworking of the northern crust isted any resolvable difference in lithospheric The largest present reservoirs of surface by internal processes must have obliterated thermal structure between the time of Hellas volatiles on Mars are the north and south the record of basin circularity. basin formation and earlier. polar caps (Fig. 2). Visually, the southern Distinguishing between internal mecha- The proposal that the hemispheric bound- cap is smaller in extent than the northern, nisms, mantle flow versus plate recycling, ary scarp represents a primary structure asso- although the southern polar layered deposits will require further study. ciated with one or more major impacts (34– extend farther from the ice cap and exhibit a calculations show that a deep-mantle phase 36) in the northern hemisphere does not re- more asymmetric distribution than their north- transition would enable the development of ceive strong support from the MOLA data, at ern counterparts (19). Residual ice, which per- hemispheric-scale (harmonic degree 1) con- least along those portions of the boundary not sists throughout the seasonal cycle, is much vective instabilities on Mars (42), but addi- strongly affected by (22). But the new more limited in extent (an area with about tional analysis is required to understand how topographic data do suggest that an impact in one-third the diameter of the north polar cap) such a mantle flow scenario, coupled with its the southern hemisphere (Hellas) contributes and is offset from the present rotational pole lithospheric response, could produce the ob- to the boundary topography in its vicinity. toward 35° to 40°E such that the pole does served long-wavelength topography. Recent The dichotomy boundary as manifest in sur- not fall within the residual ice deposit. The observations by the MGS magnetometer ex- face geology and regional topography ap- topography is highest in the south polar re- periment show magnetic anomalies of high pears to contain three dominant contribu- gion within the residual ice deposits (87°S, that have been interpreted as evi- tions: (i) volcanic construction associated ϳ10°E), where a broad dome is present with dence of an early, vigorous hydrodynamic with Tharsis, (ii) major excavated deposits more than 3 km of relief at one end of the cap dynamo in core (43). The largest approximately circumferential to Hellas, with (Fig. 8). The relief of the southern polar cap magnetic anomalies are confined to the additional contributions from Isidis and prob- is comparable to that of the northern cap. southern highland crust, and because anoma- ably Utopia ejecta, and (iii) modification of The area of probable ice-rich material lies are generally absent near large southern the intervening region by greatly exceeds the region of residual ice that hemisphere impact basins, a rapid decay in associated with the that is apparent from images. Support for this the strength of the dynamo and the global empty into . In addition, pre- interpretation comes from the existence of in the first ϳ500 million viously documented [for example, (35)] con- distinctive plateau regions that correlate with of martian history is inferred (43). Either an tributions from fracturing and resurfacing layered terrain units (19), as would be expect- early Noachian era of plate recycling (33, 43) dictate that the boundary formed in response ed if the layers were deposited on cratered or vigorous mantle convection would be con- to multiple, complex mechanisms. terrain. In addition, impact craters within the sistent with an early core dynamo. Polar caps and present surface volatile plateaus share unusual geometric properties Important new constraints on the litho- budget. The process that produced the low with counterparts in the north polar region spheric thermal structure and heat flow in the northern hemisphere occurred early in mar- (46) that are observed to have formed in an southern hemisphere of Mars come from the tian history. The resulting elevation differ- ice-rich substrate. This similarity suggests high relief (Fig. 4) and gravity signature (40) ence must have dominated the transport of that significant portions of the south polar ice of the Hellas basin and the amplitudes of the throughout its history. The cap may be buried beneath mantling largest crustal magnetic anomalies (43). The 9 km of present relief displayed by Hel- las implies that the mechanical lithosphere of Mars at the time of basin formation was at -10 -2 -1 -0.5 0 0.5 1 2 10km least locally of substantial thickness and long-term strength. The implied differ- 90°N ences supported by martian lithospheric strength exceed those for the South Pole– 60°N Aitken basin on the moon (30) with its lower gravitational attraction, and would be larger ° still if the proposed ϳ2 to 3 km thickness of 30 N Late Noachian to Amazonian units that blan- ket the floor of Hellas (44) were removed. If 0° the basin is ϳ90% isostatically compensated, as suggested from gravity data (40), then a ° basin relaxation model (45) indicates that the 30 S elastic lithosphere thickness at the time of Hellas’ formation was ϳ30 km. The thick- 60°S nesses of coherently magnetized crustal blocks required to account for the observed 90°S magnetic anomalies with magnetizations no 180° 240° 300° 0° 60° 120° 180° greater than for common terrestrial rocks also demand that were below the Fig. 6. Map of Mars’ shape with zonal spherical harmonic degree 1 (COM-COF offset along the of the dominant magnetic polar z axis) removed. The projection is rectangular to show topography from pole to pole. Note the general similarity in elevation between the northern and southern hemispheres. The figure to significant depths before the Hel- highlights the two other significant components of martian topography: the Tharsis province and las (43). The amplitudes of the the Hellas impact basin. Here we have not removed shorter wavelength topographic features, magnetic anomalies yield a comparable elas- including those composing the dichotomy boundary scarp.

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-8 -4 0 4 8 km -8 -4 0 4 8km 180û 0°

150û 210û

120û 60 ° ° 240û 300

300û 240Eû ° 60û

120

330û 30û

0û 180° Fig. 7 (left). equal-area projection of pole-to-equator topography in the northern hemisphere. The Utopia basin is the circulardepression (in light blue) in the upper right. Fig. 8 (right). Polar stereographic projection of topography from latitude 55°S to the pole.

deposits. Third, profiles across the northern cause the amount of dust mixed with the ice Much future work will be needed to reconcile and southern caps (Fig. 9) show a striking cannot be distinguished from ice flow models the present surface volatile inventory with pri- correspondence in shape that argues for a unless the temperature of the ice is known well mordial estimates and with models of climatic similarity in composition and suggests that (55), the volatile content implied by the south cycling of water and mechanisms of volatile the southern cap may have a significant polar volume must be considered only an upper loss. water ice component. The surface exposure limit. The correspondingly greater range of pos- Implications for hydrological trans- of the residual south polar cap has been sible for the southern layered unit port. The low northern hemisphere has been

observed to display a CO2 composition yields potentially larger deflections and flexural hypothesized as the site of an early martian (47), which led to the idea that CO2 is the infill volumes than the northern cap models (51, ocean (58). One of the proposed “shorelines” dominant volatile in the southern cap. 52), thus producing a larger uncertainty in the corresponds approximately to an equipoten- However, recent experiments on the rheol- volume estimation (53). Combined with our tial surface, consistent with that hypothesis

ogy of solid CO2 (48) combined with rela- previous volume estimate for the northern ice (20), as is a correlation of low elevation with tive elevation measurements from stereo cap (51) (Table 1), we determine a total surface high topographic smoothness. Application of ϫ 6 ϫ imaging (49) suggest that H2O is the more volatile inventory of up to 3.2 10 to 4.7 smoothness data to assess the possible hydro- likely dominant volatile constituent of the 106 km3, which is equivalent to a global layer logical origin of individual small occurrences southern cap (50), although the dust content of 22 to 33 m thickness. Even if it is assumed of units elsewhere on Mars, however, must be

in the deposits remains uncertain. that both caps have a pure H2O composition, done with caution and in combination with By accounting for the possible contribution this range is at the low end of previous esti- other data [see, for example, (20)]. Smooth- of flexure of the basal surface due to the layered mates of the amount of water believed to have ness alone can be due to several sources, such deposit load (51, 52), we estimate that the south been present early in Mars’ history (56). How- as volcanism, as seen in the Amazonian polar cap has a volume of 2 ϫ 106 to 3 ϫ 106 ever, the may represent only a flows on the southwestern flanks of Tharsis km3, and that it extends over an area of 1.44 ϫ fraction of the water believed to be stored cur- (Fig. 3). 106 km2 (53). The average relief above the rently beneath the surface in the (57). The MOLA data reveal that there are at surroundings is ϳ815 m. The uncertainty in the volume includes contributions from errors in Fig. 9. Comparison of top- 5 the mapped surface and the interpolated polar -2 ographic profiles of the 4 gap, as well as in the depth of the estimated southern (solid line) and -3 northern (dotted line) re- 3

basal surface. The volume of the south polar S, km -4 N, km 2 cap load (ice plus layered deposits) is greater sidual ice caps across lon- -5 than that calculated for the northern cap (51). gitudes 0°E to 180°E. The 1 gaps in the middle of the 75 80 85 90 85 80 75 But because the thickness of dust that overlies southern cap profile are Latitude, degrees much of the plateau cannot be determined from due to lack of coverage poleward of 87°S. The northern profile is shifted 6.7 km upward and 1° in imaging or thermal inertia data (54), and be- latitude, which makes the shapes of the two caps nearly coincident. The vertical exaggeration is 100:1.

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20ûN on Mars was once ubiquitous, much of it, even at high southern [such as would be liberated by basal melting (57) of an earlier and significantly thicker south polar cap], would have flowed to the northern plains. If the ex- 10ûN tended period of formation of the Tharsis prov- ince did not significantly modify regional slopes in the southern hemisphere, then Hellas and Argyre would each have collected water from about one-eighth of the planet. Hellas, 0ûN with its great volume, would have been better able to absorb an influx, whereas Argyre may have breached and drained into the northern basin. Of course, water sources bear closely on the drainage. Recent images (60) indicate that 10ûS many networks formed in response to subsurface sources rather than . The distribution of subsurface or surface sourc- es would clearly control the water that would have been available to drain into any given area. 20ûS Some of the Valles Marineris 270ûE 280ûE 290ûE 300ûE 310ûE 320ûE have been considered as source areas for outflow channels (61). Previous topography elevation (km) (62) was characterized by inconsistent gradi- ents along the canyon floor, but these maps Ð5.5 Ð5.2 Ð4.9 Ð4.6 Ð4.3 Ð4.0 Ð3.7 Ð3.4 Ð3.1 Ð2.8 Ð2.5 Ð2.2 lacked geodetic control. MOLA topography Fig. 10. Elevations within the floor of the Valles Marineris canyon system and the adjacent Chryse (Fig. 10) now enables accurate calculation of outflow channels. All areas not color contoured have elevations above Ϫ1.9 km. floor slopes and their relation to the adjacent Chryse outflow channels. The canyon system is deepest (ϳ11 km) in Coprates at present, and probably for much of Mars’ nature of the basin floor can be consistent ϳ300°E where the floor elevation is also history, only three major closed basins that with fluvial, lacustrine, or aeolian deposition, lowest in an absolute sense (about Ϫ5 km). can act as sinks for the surficial flow of water all of which have been proposed on the basis The increasing trough depths from the head or ice (Table 2); the low-lying northern plains of geological characterization of the deposits of the canyon to Coprates superimposed on are by far the largest of these. Its watershed, that fill central Hellas (44). the flank of Tharsis result in a net eastward the basin along with the remaining area of the Argyre has a relatively small volume com- canyon-floor downward gradient of ϳ0.3°. planet that would drain into it, constitutes pared with Hellas but has a watershed that is East of Coprates, however, the trough floors three-quarters of Mars’ surface area. The oth- just as large. The watershed breaches into slope gently uphill by ϳ0.03°, a gradient that er basins are Hellas and Argyre/Solis Pla- Chryse Planitia through a well-developed set of is consistent over at least 1500 km. This num, both in the southern hemisphere. flood-carved channels. The Solis Planum part uphill slope would present a barrier to surface Hellas is much smaller in area than the of this watershed is unique in comparison with water flow from Valles Marineris to the cha- northern plains, but its great depth gives it a other southern hemisphere drainage centers in otic terrain and outflow channels to the north- volume that approaches that of the much that it is apparently a tectonic structure rather east unless the water depth was sufficient to shallower northern basin. Its floor has the than the result of a major impact. The Solis overcome the relief difference of ϳ1 km. lowest elevation on Mars. The highest closed Planum drainage area is shallow; the mean Local or regional (for example, contour is at 1250 m, at which level it breach- depth is only ϳ500 m. deepening or large-scale tilting) as well as es into the Isidis basin. However, Hellas’ The COM-COF offset along the polar axis infilling could explain the east-west drainage area is relatively small. Two out- is responsible for the global-scale south-to- floor gradients, and at least some of these flow channels empty into the basin from the north transport of volatiles indicated by flow processes could have postdated the outflow east. These likely formed as a result of the directions of outflow channels and valley net- channels. However, the downhill floor gradi- interaction of or ground ice with works (59), an observation supported by the ent going westward from ϳ330°E suggests several ancient southern hemisphere volcanic global distribution of topographic gradients that certain localized depressions could have shields (19). The flat though rough (Fig. 3) (Fig. 5C). Thus, if surface or near-surface water served as source areas for water infilling of Valles Marineris.

Table 2. Mars global drainage basins. References and Notes 1. M. T. Zuber et al., J. Geophys. Res. 97, 7781 (1992). Highest closed Area Volume Watershed 2. A. A. Albee, F. D. Palluconi, R. E. Arvidson, Science Region 6 2 6 3 6 2 279, 1671 (1998). contour (m) (10 km ) (10 km ) (10 km ) 3. The data set includes topographic profiles of the Ϫ northern hemisphere collected during the capture Northern plains* 2000 50 100 110 , hiatus orbit, and Science Phasing Hellas 1250 9 60 20 Orbit phases of the Mars Global Surveyor mission Argyre during the period 15 September 1997 to 31 July Basin 0 1.5 4 20 1998, and circum-Mars profiles spanning the latitude Solis Planum 3250 1.1 0.55 2 range 87°N to 87°S for the period 1 March to 15 April 1999. *The dichotomy boundary was chosen for purposes of computing area and volume. 4. D. E. Smith et al., Science 279, 1686 (1998).

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5. M. T. Zuber et al., Geophys. Res. Lett. 25, 4393 18. Because the topographic distribution function has a 46. J. B. Garvin, S. E. H. Sakimoto, J. J. Frawley, C. Schnet- (1998). long tail as a result of cratering, faulting, and other zler, in preparation. 6. L. E. Roth, G. S. Downs, R. S. Saunders, G. Schubert, localized processes, we define regional roughness 47. H. H. Kieffer, J. Geophys. Res. 84, 8263 (1979); D. A. 42, 287 (1980); G. S. Downs, P. J. Mouginis- using the interquartile scale (IQS) variation of topog- Paige et al., ibid. 95, 1319 (1990). Mark, S. H. Zisk, T. W. Thompson, J. Geophys. Res. 87, raphy in a window of width 100 km along individual 48. W. B. Durham, S. H. Kirby, L. A. Stern, Lunar Planet. 9747 (1982). profile tracks. The IQS, defined by the estimator (64) Sci. 30, 2017 (1999). 7. A. J. Kliore, D. L. Cain, G. Fjeldbo, B. L. Seidel, M. J. N 49. P. M. Schenk and J. M. Moore, in preparation. ϭ ͑ Ϫ ͒ Sykes, Icarus 17, 484 (1972); G. F. Lindal et al., J. Rq Ϫ Q3 Q1 50. J. F. Nye, W. B. Durham, P. M. Schenk, J. M. Moore, in Geophys. Res. 84, 8443 (1979). 2N 1 preparation. 8. L. A. Soderblom and D. B. Wenner, Icarus 34, 622 where Qi is the elevation of the ith quartile point and 51. M. T. Zuber et al., Science 282, 2053 (1998). (1978); S. S. C. Wu, P. A. Garcia, R. , F. J. N is the number of points, measures the width of a 52. C. L. Johnson et al., in preparation. Schafer, Nature 309, 432 (1984). histogram of the most significant 50% of the eleva- 53. We developed a high-resolution digital terrain model 9. C. W. Hord, Icarus 17, 443 (1972); B. Conrath et al., tions. The parameter Rq, which is commonly divided for the region from 70°S to 90°S, with the surface J. Geophys. Res. 78, 4267 (1973). by 0.673 (the IQS of a normal distribution), is a elevation interpolated in the polar gap between 86° and 10. S. S. C. Wu, U.S. Geol. Surv. Map I-2160 (1991). robust estimator in the sense that it is not sensitive 90°S. For an estimate of the volume of polar cap 11. In the current topographic model, which combines el- to outliers in as much as half of the population or as material if lithospheric flexure is first ignored, we used liptical and mapping orbit observations, ground shots little as a quarter. the 1750-m surface contour, which approximates the with valid -attitude knowledge, with pointing 19. D. H. Scott and K. L. Tanaka, U.S. Geol. Surv. Misc. edge of the polar layered deposits [unit Apl of (19)]. We angle Ͻ6° except where off-nadir ranging was per- Inv. Series Map I-1802-A (1986); R. and J. E. then removed a trend surface, with a mean elevation of formed to cover the north pole, numbered 26.6 million. Guest, U.S. Geol. Surv. Misc. Inv. Series Map I-1802-B 1408 m, fit to the area outside this contour. The derived All ground shots were projected sinusoidally and binned (1987); K. L. Tanaka and D. H. Scott, U.S. Geol. Surv. volume of cap material is 1.5 ϫ 106 km3. Given its on a 1° by 1° equal-area global grid, and the median Misc. Inv. Series Map I-1802-C (1987). Mars is divided thickness and spatial extent, the southern layered ter- topography and location coordinates were obtained. into three primary stratigraphic units. The Noachian rain may constitute a significant lithospheric load, and Planetary radii were projected and similarly binned. A system is the oldest and consists of ancient cratered thus assessment of the contribution due to lithospheric 36th degree-and-order harmonic model was fit to the terrain. The Hesperian overlies the Noachian and flexure of the layered deposits is required. We modeled data by least squares. This harmonic model was used in consists principally of ridged plains materials. The the polar deposit load by a spherical harmonic expan- the determination of the best-fit ellipsoid. Amazonian system has the youngest relative age and sion, to degree and order 90, of the south polar topog- 12. The MOLA instrument measures the round trip time is represented mainly by smooth plains. raphy within the 1750-m contour. We considered elas- of flight of individual laser pulses between the MGS 20. J. W. Head et al., Geophys. Res. Lett. 25, 4401 (1998). tic shell thickness values from 40 to 200 km. Because of spacecraft and the . Each measure- 21. A. McEwen et al., Lunar Planet. Sci. 30, 1829 (1999). the uncertainty in the of the polar layered unit, Ϫ3 ment is tagged at the transmit time; the receive time 22. R. P. Sharp et al., J. Geophys. Res. 76, 331 (1971). we used load densities of 1000 kg m (pure H2O ice) of the pulse is derived from the time of flight and the R. P. Sharp, ibid. 78, 4073 (1973). and 2000 kg mϪ3 (ice plus dust). Forward models of transmit time. The spacecraft inertial positions are 23. H. Frey, S. E. Sakimoto, J. Roark, Geophys. Res. Lett. loading of a spherical elastic shell (51, 52) by a load derived for both transmit and receive times, and the 25, 4409 (1998). approximating the southern polar deposits indicate that light path is traced from the transmit position to the 24. W. B. Banerdt, M. P. Golombek, K. L. Tanaka, in Mars, the of these deposits could extend from 300 to surface (accounting for spacecraft attitude) and back H. H. Kieffer, B. M. Jakosky, C. W. Snyder, M. S. 2500 m beneath the cap edge, yielding additional con- to the spacecraft at the receive position and time. Matthews, Eds. (Univ. of Press, Tucson, tributions to the volume from 4.0 ϫ 105 to 1.5 ϫ 106 The martian radius is obtained for the coordinates of 1992), pp. 249–297; P. B. Esposito et al., ibid., pp. km3. The total volume of cap material is thus 2 to 3 ϫ the “bounce point” of the laser pulse on the surface 209–248. 106 km3. The south polar volume has recently been in a COM reference frame. In the MGS mapping orbit 25. R. A. Schultz and K. L. Tanaka, J. Geophys. Res. 99, estimated from stereo imaging to be 1.6 ϫ 106 to 2.3 ϫ the instrument’s 10-Hz sampling rate combined with 8371 (1994); J. Dohm and K. Tanaka, Planet. Space 106 km3 (49). The MOLA topographic surface is about the laser beam divergence of 400 ␮rad results in a Sci. 47, 411 (1999). two orders of magnitude more precise than that from surface spot size of ϳ160 m and shot-to-shot spac- 26. W. B. Banerdt, R. J. Phillips, N. H. Sleep, R. S. Saunders, the images, and in addition, individual elevations from ings of ϳ330 m. The precision of MOLA range mea- J. Geophys. Res. 87, 9723 (1982). MOLA are geodetically referenced and permit the to- surements approaches the limiting resolution of 37.5 27. S. C. Solomon and J. W. Head, ibid. 82, 9755 (1982). pography of the cap to be related accurately to the cm on smooth level surfaces and may increase up to 28. R. J. Phillips, N. H. Sleep, W. B. Banerdt, ibid. 95, 5089 surroundings. The stereo-based estimate did not con- ϳ10 m on 30° slopes. The accuracy of the spot (1990). sider the effect of flexure of the basal surface, which is location in latitude and longitude is limited by the 29. R. A. Schultz and H. V. Frey, ibid., p. 14175. responsible for the bulk of the uncertainty in our esti- knowledge of the spacecraft pointing at 1 to 3 mrads 30. M. T. Zuber, D. E. Smith, G. A. Neumann, F. G. mate of the south polar volume, and which may con- (400 to 2000 m on the surface, depending on the Lemoine, Science 266, 1839 (1994). tribute as much as half of the volume. Error due to the spacecraft altitude) and spacecraft position uncer- 31. R. E. Lingenfelter and G. Schubert, Moon 7, 172 presence of the Prometheus under part of the tainties of a few hundred meters. The estimate of (1973); D. U. Wise, M. P. Golombek, G. E. McGill, layered terrain is small in comparison to the uncertainty global topographic accuracy includes contributions Icarus 35, 456 (1979); J. Geophys. Res. 84, 7934 associated with flexure. from radial orbit error (7 m rms) (63), instrument (1979). 54. D. A. Paige and K. D. Keegan, J. Geophys. Res. 99, error (3 m rms), and geoid error (Ϯ10 m rms) (40). 32. G. E. McGill and A. M. Dimitriou, J. Geophys. Res. 95, 25993 (1994). The accuracy estimate for the shape of the planet is 12595 (1990). 55. M. T. Zuber, L. Lim, H. J. Zwally, in First International Ϯ8 m. A comparison of the binned altimeter data set 33. N. H. Sleep, ibid. 99, 5639 (1994). Conference on Mars Polar Science and Exploration, with the locations of the Viking 1 and 2 and Path- 34. D. E. Wilhelms and S. W. Squyres, Nature 309, 138 Camp Allen, TX, 18 to 22 October 1998; S. Clifford, D. finder landing sites shows good agreement (Table 1). (1984). Fisher, J. Rice, Eds. (Lunar Planetary Institute, Hous- 13. W. M. Folkner, C. F. Yoder, D. N. Yuan, E. M. Standish, 35. G. E. McGill, J. Geophys. Res. 94, 2753 (1989). ton, 1998), pp. 45–46; W. B. Durham, ibid., pp. 8–9. R. A. Preston, Science 278, 1749 (1997); M. T. Zuber 36. H. V. Frey and R. A. Schultz, Geophys. Res. Lett. 15, 56. M. H. Carr, Water on Mars (Oxford Univ. Press, New and D. E. Smith, J. Geophys. Res. 102, 28673 (1997). 229 (1988). York, 1996). 14. This analysis uses the geoid from the MGM890i 37. D. E. Smith and M. T. Zuber, Science 271, 184 (1996). 57. S. M. Clifford, J. Geophys. Res. 92, 9135 (1987); ibid. gravitational field model of Mars, derived from MGS 38. Slopes were computed in the direction of maximum 98, 10973 (1993). gravity calibration orbit Doppler tracking, MGS ellip- gradient on 100-km baselines from a global 0.25° 58. T. J. Parker et al., Icarus 82, 111 (1989); T. J. Parker, tical orbit tracking, and historical tracking data from grid, smoothed to 100 km. The histogram uses bins of D. S. Gorsline, R. S. Saunders, D. C. Pieri, D. M. the Viking 1 and 2 and Mariner 9 orbiters (40). Zero width 0.035°. Schneeberger, J. Geophys. Res. 98, 11061 (1993); elevation is defined as the equipotential surface 39. H. V. Frey, S. E. Sakimoto, J. H. Roark, Eos Trans. Am. V. R. Baker et al., Nature 352, 589 (1991). whose average value at the equator is equal to Geophys. Union 79, P72A-03 (1998). 59. M. H. Carr and G. D. Clow, Icarus 48, 91 (1981). 3,396,00 m. 40. D. E. Smith, W. L. Sjogren, G. Balmino, G. L. Tyler, in 60. M. C. Malin and M. H. Carr, Nature 397, 589 (1999). 15. D. L. Turcotte, R. J. Willemann, W. F. Haxby, J. Norb- preparation; M. T. Zuber et al., Eos Trans. Am. Geo- 61. B. K. Luchitta et al., in (24), pp. 453–492. erry, J. Geophys. Res. 86, 3951 (1981). phys. Union, in press. 62. U.S.G.S., U.S. Geol. Surv. Misc. Inv. Series Map I-1712 16. The best-fit ellipsoid, which includes an estimation of 41. G. E. McGill and S. W. Squyres, Icarus 93, 386 (1991). (1986). the COM-COF offsets and the directions of the prin- 42. H. Harder and U. R. Christensen, Nature 380, 507 63. F. G. Lemoine et al., “Precision cipal axes, has an rms fit of 1.9 km. The new global (1996); H. Harder, J. Geophys. Res. 103, 16775 for Mars Global Surveyor during Hiatus and SPO,” shape parameters are in close agreement with values (1998); D. Breuer, D. A. Yuen, T. Spohn, S. Zhang, AIAA Space Flight Mechanics Meeting, Breckenridge, obtained in an earlier long-wavelength model based Geophys. Res. Lett. 25, 229 (1998). CO, 7 to 10 February 1999; (American Astronautics on reanalysis of Viking and Mariner mea- 43. M. H. Acun˜a et al., Science 284, 790 (1999); J. E. P. Society Publications Office, San Diego, 1999). surements (37). x,y,z are body-fixed coordinates in a Connerney et al., ibid., p. 794. 64. G. A. Neumann and D. W. Forsyth, Mar. Geophys. right-handed COM system in which the z axis is the 44. R. Wichman and P. Schultz, J. Geophys. Res. 94, Res. 17, 221 (1995). rotation axis and the x axis is the origin of longitude. 17333 (1989); J. Kargel and R. Strom, Geology 20,3 65. The mean radius was obtained from a 36th degree 17. T. A. Mutch, R. E. Arvidson, J. W. Head, K. L. , R. S. (1992); J. Moore and K. Edgett, Geophys. Res. Lett. and order spherical harmonic expansion of the binned Saunders, The (Princeton Univ. Press, 20, 1599 (1993); K. Tanaka and G. Leonard, J. Geo- data. The uncertainty is based on the rms fit of 554 m Princeton, NJ, 1976); M. H. Carr, The Surface of Mars phys. Res. 100, 5407 (1995). of the model to the data. The north and south polar (Yale Univ. Press, New Haven, CT, 1981). 45. S. Zhong and M. T. Zuber, in preparation. radii are also determined from the harmonic model.

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66. The mean equatorial radius was derived from the tics for providing the engineering foundation that such a young age by such a wide array of harmonic model (65) based on a 1° sampling of an enabled this analysis. We also thank G. Elman, P. recent independent measurements. equatorial profile. This value is 200 m larger than was Jester, and J. Schott for assistance in altimetry pro- estimated from earlier data (5) but is within the error cessing, D. Rowlands and S. Fricke for help with orbit estimate of the earlier value. The uncertainty corre- determination, S. Zhong for assistance with the Hel- Method sponds to the standard error of the mean of the 360 las relaxation calculation, and G. McGill for a con- ⍀ Any measurement of a function of h, m, and equatorial samples. structive review. The MOLA investigation is support- ⍀ 67. We acknowledge the MOLA instrument team and the ed by the NASA Mars Global Surveyor Project. ⌳ can be included in a likelihood MGS spacecraft and operation teams at the Jet Pro- N pulsion Laboratory and Lockheed-Martin Astronau- 21 April 1999; accepted 10 May 1999 ͑ ⍀ ⍀ ͒ ϭ ͹ L h, m, ⌳ Li (1) iϭ1 which I take as the product of seven of the most recent independent cosmological con- A Younger Age for the straints (Table 1 and Fig. 3). For example,

one of the Li in Eq. 1 represents the con- Charles H. Lineweaver straints on h. Recent measurements can be summarized as h៮ ϭ 0.68 Ϯ 0.10 (16). I The age of the universe in the Big Bang model can be calculated from three represent these measurements in Eq. 1 by the ⍀ likelihood parameters: Hubble’s constant, h; the mass density of the universe, m; and the ⍀ ៮ 2 cosmological constant, ⌳. Recent observations of the cosmic microwave h Ϫ h ͑ ͒ ϭ ͫϪ ͩ ͪ ͬ background and six other cosmological measurements reduce the uncertainty LHubble h exp 0.5 Ϯ 0.10 in these three parameters, yielding an age for the universe of 13.4 1.6 billion (2) years, which is a billion years younger than other recent age estimates. A different standard Big Bang model, which includes dark matter with a Another Li in Eq. 1 comes from measure- cosmological constant, provides a consistent and absolutely time-calibrated ments of the fraction of normal baryonic evolutionary sequence for the universe. matter in clusters of galaxies (14) and esti- mates of the density of normal baryonic mat- ⍀ 2 ϭ Ϯ In the Big Bang model, the age of the uni- ments with SNe and other data, I (9) have ter in the universe [ bh 0.015 0.005 ⍀ ϭ Ϯ verse, to, is a function of three parameters: h, reported ⌳ 0.62 0.16 [see (10–12) for (15, 18)]. When combined, these measure- ⍀ ⍀ ⍀ Þ ⍀ 2/3 ϭ Ϯ m, and ⌳ (1). The dimensionless Hubble similar results]. If ⌳ 0, then estimates of the ments yield mh 0.19 0.12 (19), constant, h, tells us how fast the universe is age of the universe in Big Bang models must which contributes to the likelihood through ⍀ expanding. The density of matter in the uni- include ⌳. Thus, one must use the most gen- ͑ ⍀ ͒ Lbaryons h, m verse, ⍀ , slows the expansion, and the cos- eral form: t ϭ f(⍀ , ⍀ )/h (13). m o m ⌳ ⍀ 2/3 Ϫ ⍀ 2/3 2 ⍀ mh mh mological constant, ⌳, speeds up the expan- Here, I have combined recent independent ϭ expͫϪ0.5ͩ ͪ ͬ sion (Fig. 1). measurements of CMB anisotropies (9), type Ia 0.12 Until recently, large uncertainties in the SNe (4, 5), cluster mass-to-light ratios (6), clus- (3) ⍀ ⍀ ⍀ ⍀ measurements of h, m, and ⌳ made efforts ter abundance evolution (7), cluster baryonic The ( m, ⌳)–dependencies of the remain- ⍀ ⍀ to determine to (h, m, ⌳) unreliable. The- fractions (14), -to- ratios in ing five constraints are plotted in Fig. 3 (20). oretical preferences were, and still are, often quasar spectra (15), double-lobed radio sources The 68% confidence level regions derived used to remedy these observational uncertain- (8), and the Hubble constant (16) to determine from CMB and SNe (Fig. 3, A and B) are ⍀ ϭ ties. One assumed the standard model ( m the age of the universe. The big picture from the nearly orthogonal, and the region of overlap 1, ⍀⌳ ϭ 0), dating the age of the universe to analysis done here is as follows (Figs. 1 and 2): is relatively small. Similar complementarity ϭ ϳ to 6.52/h billion years old (Ga). However, The Big Bang occurred at 13.4 Ga. About 1.2 exists between the CMB and the other data for large or even moderate h estimates billion years (Gy) later, the halo of our Galaxy sets (Fig. 3, C through E). The combination

(Ռ0.65), these simplifying assumptions re- (and presumably the halo of other galaxies) of them all (Fig. 3F) yields ⍀⌳ ϭ 0.65 Ϯ ⍀ ϭ Ϯ sulted in an age crisis in which the universe formed. About 3.5 Gy later, the disk of our 0.13 and m 0.23 0.08 (21). Ϸ Ͻ was younger than our Galaxy (to 10 Ga Galaxy (and presumably the disks of other This complementarity is even more im- Ϸ tGal 12 Ga). These assumptions also result- spiral galaxies) formed. This picture agrees portant (but more difficult to visualize) in ⍀ ed in a baryon crisis in which estimates of the with what we know about galaxy forma- three-dimensional parameter space, (h, m, amount of normal (baryonic) matter in the tion. Even the recent indications of the ⍀⌳). Although the CMB alone cannot tightly universe were in conflict (2, 3). existence of old galaxies at high redshift constrain any of these parameters, it does ⍀ Ͻ Evidence in favor of m 1 has become (17) fit into the time framework determined have a strong preference in the three-dimen- ⍀ ⍀ ⍀ more compelling (4–8), but ⌳ is still often here. In this sense, the result is not surpris- sional space (h, m, ⌳). In Eq. 1, I used ⍀ ⍀ assumed to be zero, not because it is measured ing. What is new is the support given to LCMB(h, m, ⌳), which is a generalization to be so, but because models are simpler with- out it. Recent evidence from supernovae (SNe) (4, 5) indicates that ⍀ Ͼ 0. These SNe data Table 1. Parameter estimates from non-CMB measurements. I refer to these as constraints. I use the error ⌳ bars cited here as 1␴ errors in the likelihood analysis. The first four constraints are plotted in Fig. 3, B and other data exclude the standard Einstein- through E. ⍀ ϭ ⍀ ϭ deSitter model ( m 1, ⌳ 0). The cosmic microwave background (CMB), on the other Method Reference Estimate ⍀ ⍀ ϭ hand, excludes models with low m and ⌳ ⍀ ⍀ ⍀⌳ϭ0 ϭϪ Ϯ ⍀flat ϭ Ϯ 0(3). With both high and low m excluded, ⌳ SNe (35) m 0.28 0.16, m 0.27 0.14 ⍀⌳ϭ0 ϭ Ϯ cannot be zero. Combining CMB measure- Cluster mass-to-light (6) m 0.19 0.14 ⍀⌳ϭ0 ϭ ϩ0.28 ⍀flat ϭ ϩ0.25 Cluster abundance evolution (7) m 0.17Ϫ0.10 , m 0.22Ϫ0.10 ⍀⌳ϭ0 ϭϪ ϩ0.70 ⍀flat ϭ ϩ0.50 Double radio sources (8) m 0.25Ϫ0.50 , m 0.1Ϫ0.20 ⍀ 2/3 ϭ Ϯ School of Physics, University of New South Wales, Baryons (19) mh 0.19 0.12 Sydney NSW 2052, Australia. E-mail: charley@bat. Hubble (16) h ϭ 0.68 Ϯ 0.10 phys.unsw.edu.au

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