Lunar and Planetary Science XLVIII (2017)
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Comparitive evolution of Earth and Mars with volatile cycling. J. Seales1 and A. Lenardic2, 1 Department of Earth
Science, Rice University, Houston, TX 77005, USA ([email protected]).
Introduction: Conventional wisdom suggests that a smaller
planet will cool more quickly than a large one. This argument follows the logic that as the radius of a planet decreases, the ratio of surface area to volume also decreases. An
implication of this is that heat is transfered from the interior
through the surface more rapidly. Data gathered in this solar
system suggest that planetary cooling may not be as simple
as this scaling argument would like to suggest. There is evidence that the Martian mantle may have began cooling only
recently. A paleo-heatflow study found that for some periods
of Mars history, heatflows were less than radiogenic heat
prodcution suggesting that rather than cooling, Mars interior
was heating for over a significant portion of its thermal history [1]. Another line of evidence highlighting the possibility
of a nearer present cooling of the Mars interior result from an
estimate of the mantle potential temperature of different aged
meteorites [2]. There is some disagreement however amongst
the studies where orbiatal measurements provide a lesser
temperature [2,3]. A suggested hypothesis for how this delay
in the onset of cooling may occur is the inclusion of volatile
cycling into the thermal history models [1,4]. Here we perform numerical experiments to investigate the feasibility of a
volatile cycling to affect the thermal evolution a smaller,
stagnant lid Mars like planet as compared to a larger Earth
like planet thermally evolving in the plaet tectonics regime.
Model: To perfrom these numerical experiments, we use a 1D parameterized convection code that calculates the spherically averaged mantle temperature over the history of each
planet [5]. This temperature is computed by tracking the
balance between the heat produced within the planetary mantle by radiogenic decay (H) and that leaving through the surface by convective heat transfer (Q). The ratio of H/Q is
known as the Urey ratio (Ur). While Ur is greater than one,
the interior of the planet is heating. It is only when Ur falls
below unity that the planet begins cooling.
To quantify the value of Q, a Nusselt-Rayleigh parameterization is employed where the Nusselt number is the nondimensional ratio of convective to conductive heat flow and the
Rayleigh number (Ra) describes the vigor of convection. The
value of Ra is proportional to the mantle temperature and
inversely proportional ot the mantle viscosity. In this model,
the viscosity is both temperature and volatile dependent [6].
As the mantle temperature increases, convective vigor increases resulting in a larger heat flow through the mantle
surface. As the mass of water the mantle decreases, the mantle stiffens, thereby inhibiting effective transfer of heat from
the interior to the surface. It is this competition between the
thermal and volatile state of the mantle that controls the dynamic evolution of the planetary interior [7]. A heating mantle will cause more volatiles to be degassed, and a degassing
mantle will allow for less efficient heat transfer.
Essential to this model is the cycling of water between the
mantle and surface reservoirs [8,9,10]. For the plate tectonic
regime, water is degassed from the mantle at the midocean
ridge. As hot mantle upwells beneath the ridge and crosses
the solidus, melting ensues [11]. The melt fraction and
amount of water within this melt is calculated. A specified
fraction of water is allowed to transition from the mantle to
the surface reservoir. In these models this is the degassing
efficiency (Xd). The mantle is regassed at subduction zones.
This process is controlled by the thickness of the serpentinized layer [12,13]. Much of the water is degassed from the
hydrated layer and released back to the surface, but a fraction
of the water is carried into the deep mantle. This is defined to
be the regassing efficiency factor (Xr). In the case of a stagnant lid planet, it is assumed that only degassing occurs.
Melting is taken to occur over only a fraction of the mantle
surface area. Of the melt produced, only a some reaches the
surface. This fraction is Xd for the stagnant lid case.
To explore the effects of water cycling, different values of
Xd and Xr are prescribed for model evolution. This paired
with a wide range of initial water fractions in the mantle
allow a wide transect of the parameter space to evaluate possible outcomes for the thermal evolution.
Water effects on thermal evolution: The results of our
numerical experiments are presented in figure 1 which shows
the mantle temperature, Ur and age of cooling -- the time
when Ur drops below one. The parameter space was explored
systematically. First planetary radius was varied for a nonvolatile dependent mantle viscosity. Planets falling in the
stagnant lid regime end up warmer but with a lower Urey
ratio. Next we explored the endmember cases of only degassing and only regassing for Earth like planets. Of the two, the
regassing endmember suite tends towards a lower present
day Urey ratio since water is being taken from the surface
and continually added to the mantle thereby decreasing mantle viscosity and increasing convective vigor. The next suite
of models combined different values of Xd and Xr to map
out the range of potential solutions for an Earth like planet.
The effect of strong plates were simulated by varying a scaling parameter in the Nu-Ra relationship [14] which resulted
in shifting Ur towards a lower value. An Earth sized planet
evolving in the stagnant lid regime was explored next to
provide a reference case for the stagnant lid regime. The
models resulted in a higher present day temperature, lower
Urey ratio due to the more efficient convection and a delay in
the onset of cooling. Finally, a Mars like planet was investigated with a result of a delayed onset of cooling to near, at or
beyond the present day. An important trend present in this
figure is that the Mars like models result in a higher Ur at
present day than the Earth like models. According to these
models, it is even possible that some that the present day
value of Ur is greater than unity. This would indicate that
Mars would still be heating. This trend is also highlighted by
the age of cooling panel. In the case of Mars like behavior,
many of the models suggest that the onset of cooling only
occurs within the last 1 Byr whereas the Earth like cases
have the onset of cooling earlier.
To gain a better understanding of the results, the suites of
Earth and Mars like data can be evaluated from a different
perspective. Figure 2 shows a probability plot for the present
day Ur of Earth like models in blue and Mars like models in
orange. The peak for the Earth like models occurs around 0.6
whereas the peak for Mars like models occurs around 0.9.
Besides the peaks, it can be seen that the distribution of Ur
for Mars is higher as a whole. These results indicate it is
indeed likely that the smaller Mars may have began cooling
more recently than Earth if it behaved as a one plate planet
Lunar and Planetary Science XLVIII (2017)
with volatile cycling throughout its history. To have a better
idea of when this occurred, constraints on the amount of
water present within the Mars system through time should be
investigated. Also, a better understanding of how the Martian
mantle is degassing needs to be understand.
To understand how such a result may be achieved for the
Mars like case, we must understand the intertwined effects
volatile content and temperature have on the viscous mantle.
The stagnant lid is inefficient at transferring the heat generatred within to mantle through its surface. A result of this is
that the temperature of the mantle increases. As the mantle
temperature increases, convection should occur more viogorously. However, in the case investigated here, there is also
degassing of the mantle by water to the surface reservoir.
This process is continuously stiffening the mantle. Therefore,
these two effects are competing with one another. As more
water is degassed from the mantle, the mantle viscosity increases, decreasing the amount of heat that leaves and causing the mantle to warm. As the mantle warms, the viscosity
would like to decrease. In the scenario we have investigated,
the degassing effect is winning out over the temperature
effect. This means that as long as the mantle is degassed
efficiently, it will continue to heat up. It is only when temperature effects overtake those of mantle degassing that the
planet begins to cool. If all the water becomes degassed from
the interior, this returns to a classical thermal history problem
with only temperature affecting the mantle viscosity. The
important effect to remember here is that if the mantle can be
degassed efficiently in a planet evolving in the stagnant lid
regime, there will be a delay in the onset of cooling and
higher present day Urey ratio.
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This model has deomonstrated that a recently cooling
Mars is at least feasible working under the assumptions presented within this model, however, there is room for improvement. For instance, only the degassing endmember was
investigated for the Mars case. It is indeed possible that some
sort of volatile recycling process may be occurring and needs
to be accounted for. Also, this model only includes interactions between the mantle itself and the planetary interior. It
assumes that the amount of water within the system is constant over the duration of the model. This could be improved
upon by adding an atmosphere module to the water cycling
code. This would potentially allow a better understanding of
the interactions between surface and interior processes.
References: [1] Ruiz et al. (2011) Icarus, 215, 508-517.
[2] Filiberto and Dasgupta (2015) Geophys. Res. Planets,
120, 109-122. [3] Baratoux et al. (2011) Nature, 472, 338341. [4] Stevenson (2003), C. R. Geoscience, 335, 99-111.
[5] Schubert et al. (1979), Icarus, 198, 192-211. [6] Li et al.
(2008) J. Geophys. Res., 113. [7] Crowley et al. (2011) Earth
and Planetary Science Letters, 310, 380-388. [8] McGovern
and Schubert (1989), Earth Planet. Sci. Lett., 96, 27-37. [9]
Sandu et al. (2011) J. Geophs. Res., 116. [10] Sandu and
Kiefer (2012) Geophys. Res. Lett., 39. [11] Katz et al (2003),
Geochem., Geophys., Geosyst., 4(9), 1073. [12] Rupke et al.
(2004), Earth Planet Sci. Lett., 223, 17-34. [13] Ulmer and
Trommsdorf (1995), Science, 268, 858-861. [14] Conrad and
Hager (1999) Geophys. Res. Lett., 26, 3041-3044.
Figure 2: Probability plot of the present day Urey ratio for
Earth (blue) and Mars (Orange).
Figure 1: Temperature, Ur and Age of cooling for differnt
model setups: D-degassing allowed, R-regassing allowed, DR – both degassing and regassing allowed. ML and SL represent plate tectonics and stagnant lid regimes, respectively.