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which are the oldest exposed part of the   Figure 3. (A) Obliquity of Mars at 2–6 Ma as cal-  50°
          martian crust, contain abundant evidence   culated by Touma and Wisdom (1993). Note that           A
          of erosion by water. Mars is freezing cold   obliquity exceeded 40° at 5–6 Ma. (B) Probability
                                             of reaching high obliquities during the chaotic
          now and, with similar surface and atmo-  obliquity evolution of Mars over a range of time   40°
          spheric conditions, should have been even   periods, with initial 25° obliquity (from Laskar et
                                             al., 2004). (C) Total annual insolation versus lati-
          colder at 3–4 Ga. Some drainages are   tude for obliquity variation of 0°–90°. Insolation   Obliquity
          thousands of kilometers long and were   units are relative to the solar constant at 1.52 AU   30°
                                             (from Ward, 1974). (D) Normalized density func-
          fed by numerous tributaries that reached   tion for chaotic eccentricity variation for Mars
          drainage divides in headwater regions   (from Figure 18d of Laskar et al., 2004). At pres-  20°
          (Howard et al., 2005; Hynek et al., 2010).   ent  eccentricity,  solar  insolation  at  perihelion
                                             (orbital point closest to the Sun) is 45% greater
          Many rivers flowed into or through crater   than at aphelion.
          lakes, and some left delta deposits (Irwin                               10° 6    5     4      3      2
          et al., 2005; Fassett and Head, 2008b;                                               Age (Ma)
          Goudge et al., 2016). Calculations based   obliquity is currently 23°, but because of
          on canyon width and depth indicate that   stabilizing tidal forces associated with the   100
          canyons reflect ~10 –10  years of erosion   Moon, obliquity varies over geologic time              B
                         3
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          and were not incised by catastrophic out-  by <± 2° (Laskar et al., 1993). Mars, with   80
          flows (Barnhart et al., 2009; Hoke et al.,   current obliquity of 25°, does not have a
          2011; Rosenberg and Head, 2015).   massive moon, and its obliquity is not   60
          Precipitation, drainage incision, and    similarly stabilized. Because of tidal   Probability (percent)
          crater-lake filling are inferred at ca.    forces exerted on Mars by the Sun and   40  50 Ma
          3.3–3.9 Ga based on crater density in   planets, obliquity varied chaotically over   25 Ma  100 Ma
          affected terrains (Fassett and Head,   millions of years to >60° (Figs. 3A and   20  10 Ma       250 Ma
          2008a; Hoke and Hynek, 2009) (Fig. 2E).  3B) (Touma and Wisdom, 1993; Laskar
            Several factors would have supported   et al., 2004). At obliquities >~45°, polar   0  5 Ma
          warmer Noachian environmental condi-  regions receive more sunlight than equa-  40°    50°     60°
          tions, although maybe not enough for pre-  torial regions, potentially resulting in sea-  Maximum obliquity (degrees)
          cipitation and flowing water. The pressure   sonal sublimation and evaporation at high
          of the modern martian atmosphere, at 6–10   latitudes and snow at low latitudes at   0.5
          millibars, is ~1% that of Earth, but the   times near summer solstices (Fig. 3C)                   C
          ancient atmosphere was much thicker. The   (Ward, 1974; Jakosky and Carr, 1985;   0.4
          size and abundance of the smallest martian   Wordsworth, 2016). High-latitude evapo-  75° 90°
          impact craters can be used to determine   ration would be especially effective if the   0.3
                                                                                         60°
          atmospheric pressure because the smallest   summer solstice coincided with greater   Annual insolation  60°
                                                                                        45°
          meteorites are slowed or destroyed during   proximity to the Sun during a period of   0.2  45°
                                                                                        30°
          passage through the atmosphere and so do   high orbital eccentricity, which also    30°
          not create impact craters. Size-frequency   varies chaotically (Fig. 3D).  0.1
                                                                                       15°
          distributions for craters in fluvial deposits   Favorable obliquity and eccentricity,   15°
          near Gale crater indicate that Noachian   and a thick CO  atmosphere, may have   0.0  0° 0°
                                                         2
          atmospheric pressure was in the range of   been adequate for evaporation and subli-  90°  75°  60°  45°  30°  15°  0°
          ~1–2 bars during heavy Noachian bom-  mation of ice at low elevations and accu-      Latitude
          bardment (Kite et al., 2014). Atmospheric   mulation of snow and ice at high eleva-
          pressure greater than a few hundred mil-  tions, but warmer conditions are needed                   D
          libars results in a vertical temperature pro-  to melt snow and ice at high elevations   10  present
          file that approximates an adiabatic gradi-  and produce runoff to carve river valleys   Probability
          ent (Wordsworth, 2016). Under such   and fill lakes in the Noachian highlands   5
          conditions, surface temperatures are lower   (Forget et al., 2012). Global climate mod-
          at higher elevation, with potential accumu-  els indicate that 1%–10% hydrogen and   0 0.0  0.05  0.10  0.15
          lation of snow and ice at high elevations.   methane in a thick CO  atmosphere could   Eccentricity
                                                              2
          Even if the atmosphere was pure CO ,   have elevated temperatures sufficiently to
                                      2
          however, this would not be adequate to   melt ice at high elevations (Wordsworth
          warm early Mars to the point of supporting   et al., 2017). These reduced gases are
          running water, especially in highland   highly effective at absorbing infrared   produce a weak bond in which the two
          regions (Kasting, 1991; Forget et al., 2012).  radiation that would otherwise leave the   gas molecules can absorb infrared radia-
            Orbital factors relevant to early Mars   planet because of a process called “colli-  tion that would not be absorbed by the
          climate are the variable tilt of its spin axis   sion-induced absorption.” In this process,   individual gas molecules. Collision-
          relative to the normal to the orbital plane   extremely brief (~10  s) electrostatic   induced absorption with these gases can
                                                             –13
          (the obliquity) and the variable eccentric-  interactions between colliding gas mol-  potentially produce an early Mars atmo-
          ity (ellipticity) of the orbit. Earth’s   ecules (CO -H  and CO -CH  in this case)   sphere warm enough to cause melting and
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