Review of Noack et al., “Volcanism and outgassing of stagnant-lid planets:
Implications for the habitable zone,” submitted to PEPI
Review by Edwin Kite ([email protected])
In this paper, Noack et al. use a 2D mantle convection model to calculate melt
production on stagnant lid planets, varying (a) planet mass, (b) planet core mass
fraction (c) initial temperature of the mantle. They find that the rate of melting (and
thus volcanism) is lower for planets that are massive, or that have a high core-mass
fraction. They infer that the rate of volcanic outgassing (e.g. of CO2) will be lower on
planets with a lower rate of volcanism, and link this to habitability.
This paper may be publishable following clarifications, and perhaps also some
modifications of the statements about habitable-zone implications. This manuscript
falls within the scope of PEPI. I have three major queries, and some other
corrections and suggestions. My main worry is about the habitable zone
implications (query 3).
Major queries:
Query 1: size-dependence of volcanism.
On stagnant-lid planets, the size-dependence of the rate of volcanism is affected by
at least 3 factors:



Thinning the decompression-melting zone by the increase in gravity.
Approximating R = M^(1/4), where R is radius in Earth units and M is mass
in Earth units, g = M^(1/2) where g is gravity in Earth units.
Reduction of the lithospheric thickness due to increased heat flow Q
(increased volume/area ratio). Let’s choose units so that Q = 1 for 1 Earth
mass, and assume that heat production per unit (mantle) mass is constant.
Then, for a Urey ratio that does not vary strongly with planet mass
(reasonable assumption), and for constant core mass fraction, Q = M/R^2 =
M^(1/2).
Increase in convective velocity associated with higher heat flow ( higher
temperature). This will scale roughly as the Nusselt number. As flow speed
goes up, melt rate will go up because more mantle parcels are advected
through the melt zone.
The manuscript says, “For larger masses, the larger surface gravitational acceleration
(which approximately scales with the mass to power 0.5, see values in Tables 2-4))
leads to a steep pressure gradient, and the solidus melting temperature below the
lithosphere is larger compared to the smaller planets, whereas the adiabatic
temperature increases less strongly with pressure. For the 2 and 3 Earth masses
simulations, the temperature of hot, uprising plumes exceeds the melting temperature
therefore only in a very thin region […]”
This is OK as far as it goes, but does not discuss the third bullet point (increase in
convective velocity) and does not mention the second bullet point (decrease in
lithospheric thickness). The second bullet point is briefly mentioned later on page
19. I suggest the authors explain each of the following, when setting out their massdependence result:
(1) what is the trend in lithospheric thickness (after 4.5 Gyr) with planet mass in
the model? (if it is constant at 100 km, that would be a serious concern);
(2) what is the trend in convective velocity (after 4.5 Gyr) with planet mass in
the model?
(3) Are the results similar to, or different than, the results of Kite et al. (2009;
Figure 16) and those of O’Rourke & Koreanaga (2012, Figure 7c)? Using the
Katz et al. 2003 melting prescription and a simple parameterized convection
code, Kite et al.’s plot shows the instantaneous rate of volcanism – not the
time-integrated volcanism as plotted here. However, one can see that the
“5x” and “10x” contours show the same behavior as in the manuscript under
review – i.e., volcanism rate for stagnant-lid planets is maximized for
intermediate planet mass. If the basic result is the same, that is OK, because
CHIC is a much more sophisticated model, however a discussion might be
interesting.
Query 2: partition coefficient of CO2.
The melt model assumes a partition coefficient of 1 for CO2 going into the melt. This
is unrealistic – there is strong evidence that CO2 is highly incompatible (e.g. Saal et
al. Nature 2002). I suggest the authors do either:
(A) say in the conclusions and the introduction (and preferably also in the
abstract) that the model assumes that CO2 has a partition coefficient of 1.
(B) do the degassing calculation for a partition coefficient of ∞ (all CO2
partitions into even a small percentage of melt). Then, if the conclusions are
unaffected, then the partition coefficient does not matter.
This assumption could change the results qualitatively. For example, in Fig. 4,
if the CO2 is highly incompatible, then the dark green region in the “4 Earth mass”
planet after 4.5 Gyr is really fully degassed. So this planet would be almost as
habitable as the 0.1 Earth mass case.
Query 3: implications for habitability.
The authors correctly say that O(10) bars of CO2 are needed to maintain habitability
at the outer edge of the habitable zone. They relate this to a calculation of total
outgassing. The CHIC outgassing model starts below the solidus (by design, no melt
is allowed to be produced at the first timestep). However, a lot of CO2 (secondary
atmosphere, not primordial atmosphere) is thought to be outgassed during the
magma ocean stage – magma oceans are more likely for planets much larger than
Earth. E.g. Zahnle et al. Space Science Reviews, (2007)
http://adsabs.harvard.edu/abs/2007SSRv..129...35Z . I suggest the authors either:
(A) Accept that many bars of CO2 can be degassed during the magma ocean
stage and remain in the atmosphere, and reword habitability statements
accordingly.
(B) Argue that hydrodynamic escape will strip any volatiles released during
the magma ocean stage. This may be difficult however, because of the
high gravity of the large planets being considered, and their location
relatively far from the star. A calculation of the energy-limited CO2 lost
(assuming UV-driven escape) might be helpful.
A second (less important) problem is that on a habitable planet, some CO2 will
always be lost by weathering. Thus 10 bars might not be enough. The authors might
point out that without tectonic recycling, the amount of CO2 consumed could stay
small, because fresh surface area for weathering will not be produced sufficiently
quickly.
Other suggestions:
-
-
-
-
The authors may wish to look through recent papers by Abbott
(http://adsabs.harvard.edu/abs/2016arXiv160603030A) and Menou
(http://adsabs.harvard.edu/abs/2015E%26PSL.429...20M) - this might
allow them to be more quantitative about the implications for habitability of
reduced rate of volcanism (not merely reduced total volcanism).
Radioactive enrichment in the crust is briefly mentioned. However, I did not
find an explicit statement that radioactive elements are not extracted during
melting. It would be helpful to include an explicit statement if there is not one
already.
Discussion of Kite et al. 2009: the manuscript says that Kite et al.
speculatively linked the pressure-dependence of the viscosity and the
compressibility effect on melt to the decoupling of melting and degassing.
That is not correct. Kite et al. 2009 speculatively linked the compressibility
effect on melt to the decoupling of melting and degassing (no role for
pressure dependence of viscosity).
Page 17, numbered point 3: the model applies a zero-flux boundary condition
at the CMB, so isn’t the effect of mantle thickness on Rayleigh number of
order 4 (for internal heating, column heat production is linear in depth?)
Figs. 11-12 – These attractive cartoons show the “default” HZ, which the
manuscript is modifying with the results shown in Fig. 10. The authors might
add a “cartoon” version of Fig. 10, drawn in the same format as the attractive
Figs. 11-12, to qualitatively summarize their key result for busy readers.
English usage suggestions:
Overall, this paper is well-written, clear and concise. There are a few places where
the authors might benefit from having the manuscript checked by someone whose
first language is English:
-
“the effectiveness of the latter to preserve surface water” – ambiguous
whether “the latter” is “outgassing” or “the formation of a secondary
atmosphere through outgassing” or “secondary atmosphere”
Last sentence of section 1 – this sentence is not clear as written.
Last sentence of conclusions – this sentence uses “inhabitable” when in
context “Uninhabitable” is meant.
Edwin Kite
University of Chicago
17 August 2016