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THE INHABITANCE PARADOX: HOW HABITABILITY AND INHABITANCYARE
INSEPARABLE.
Colin Goldblatt, University of Victoria, Victoria, B.C., Canada
([email protected]).
Introduction
The dominant paradigm in assigning “habitability” toterrestrial
planets is to define a circumstellar habitablezone: the locus of
orbital radii in which the planet isneither too hot nor too cold
for life as we know it. Onedimensional climate models have
identified theoreticallyimpressive boundaries for this zone: a
runaway green-house or water loss at the inner edge (Venus), and
low-latitude glaciation followed by formation of CO2 cloudsat the
outer edge. A cottage industry now exists to “re-fine” the
definition of these boundaries each year to thethird decimal place
of an AU. Using the same class ofclimate model, I show that the
different climate statescan overlap very substantially and that
“snowball Earth”,moist temperate climate, hot moist climate and a
post-runaway dry climate can all be stable under the samesolar
flux. The radial extent of the temperate climateband is very narrow
for pure water atmospheres, but canbe widened with di-nitrogen and
carbon dioxide. Thewidth of the habitable zone is thus determined
by the at-mospheric inventories of these gases. Yet Earth teachesus
that these abundances are very heavily influenced(perhaps even
controlled) by biology. This is paradox-ical: the habitable zone
seeks to define the region aplanet should be capable of harbouring
life; yet whetherthe planet is inhabited will determine whether the
cli-mate may be habitable at any given distance from thestar. This
matters, because future life detection missionsmay use habitable
zone boundaries in mission design.
The habitable zone and physical climate
A typical description of the “habitable zone” is the re-gion of
circumstellar space in which a planet might behabitable. Rather by
convention, the practical definitionhas become the existence of
liquid water, for life as weknow it (that is: Earth) relies on
this.
As our conceptualization relies on the existence ofon a certain
phase of a certain chemical, our problembecomes finding the
conditions of the physical climate ofa planet which would put the
surface and atmosphere ina desirable region of the
pressure–temperature space ofthe phase diagram. Necessarily, we
need to consider allthree phases (all exist on Earth). This becomes
a ratherrich problem, for the different phases interact
differentlywith electromagnetic radiation. There are,
therefore,various climate feedbacks which express through
water.
Ou
tgoin
g t
herm
al fl
ux (
F, W
m-2
)
300
350
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Surface temperature (T, K)
2000
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Surface temperature (T, K)
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Coalb
ed
o (
1-α
)
1.0
0.5
0.6
0.7
0.8
0.9
0.5
0.4
Flu
x (
F, W
m-2
)
300
350
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Surface temperature (T, K)
2000
1500
250
300
500
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Compare absorbed solar radiation with thermal emission to find
steady states ( = stable, = unstable)
250
300
350
450
500
1500
2000
400
Su
rface t
em
pera
ture
(T,
K)
200
1.0
1.5
0.5
Solar Constant (S/S0)0.
60.
70.
80.
91.
11.
21.
31.
4
Figure 1: Graphical derivation of steady states of climate
withvarying background gas inventories: none / pure water
(blue)with orange through brown representing increasing pN2.
(a)Planetary co-albedo (b) Outgoing thermal flux (c) Examplecase of
finding steady states by balancing outgoing thermalflux with the
product of incident solar flux and co-albedo (d)Consequent
bifurcation diagram, with steady states as a func-tion of distance
from the Sun, stable in solid lines and unstabledotted. These
figures are schematics, sketched from my pre-vious numerical
results[1, 2]
The framework of dynamical systems theory be-comes fundamental,
as climate state depends on history;our task is to look for stable
steady states of climate. Tomake progress, we can separately
consider the fate ofsolar photons incident on Earth which may
transfer en-ergy to us, and the escape of thermally emitted
photonswhich transfer energy away. Where energy fluxes areequal,
there exists a steady state. Steady states whichare stable to a
small perturbation are habitable zone can-didates. Thus, in Figures
1 and 2, we derive bifurcationdiagrams for Earth’s climate, mapping
climate states asa function of circumstellar distance. There exist
ice-covered, temperate moist, hot moist and hot dry climatestates.
The moist states both enjoy liquid water sur-faces, but the
sea-level temperature conditions are onlyfavourable for
life-as-we-know-it in the temperate moiststate.
For the fundamentals of how energy fluxes changeas a response to
water inventory (controlled by surface
arX
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The Inhabitance Paradox
Ou
tgoin
g t
herm
al fl
ux (
F, W
m-2
)
300
350
250
200
150
100
Surface temperature (T, K)
2000
1500
250
300
500
350
400
450
200
Surface temperature (T, K)
2000
1500
250
300
500
350
400
450
200
Coalb
ed
o (
1-α
)1.0
0.5
0.6
0.7
0.8
0.9
0.5
0.4
Flu
x (
F, W
m-2
)
300
350
250
200
150
100
Surface temperature (T, K)
2000
1500
250
300
500
350
400
450
200
Compare absorbed solar radiation with thermal emission to find
steady states ( = stable, = unstable)
250
300
350
450
500
1500
2000
400
Su
rface t
em
pera
ture
(T,
K)
200
1.0
1.5
0.5
Solar Constant (S/S0)0.
60.
70.
80.
91.
11.
21.
31.
4
Figure 2: Graphical derivation of steady states of climate
withvarying greenhouse gas inventories: red with some N2 butno CO2,
pink through purple representing increasing pCO2.Other description
as Figure 1.
temperature via the Clausius-Claperon equation), I deferto
descriptions in my previous papers[3, 1, 2]. Herein,the focus is on
how variation in atmospheric compositionmodifies these.
Gases may be separated into radiatively active andbackground
gases. The former absorb photons directly,and the most important
subset of these, greenhouse gases,does so in the infrared; carbon
dioxide is the prototypefor Earth. The latter absorb little
radiation directly butwill broaden the absorption of the radiative
gases andscatter solar photons; di-nitrogen is the prototype
forEarth.
More background gas means less energy absorbedfrom the Sun
because of higher albedo, and less or morethermal energy emitted
depending on temperature (lessat low temperatures where
pressure-broadening is dom-inant, more at intermediate temperature
where dilutionof water aloft lowers the emission level). Consequent
isthe wet temperate climate state moving to higher solarconstants
and broadening: the habitable zone is widerand further from the
Sun.
More greenhouse gas simply reduces outgoing ther-mal radiation,
and only does so significantly at lowertemperatures. Thus the wet
temperate climate state ismoved to lower solar constants and is
broader: the hab-itable zone is wider and nearer to the Sun.
Controls on atmospheric composition
Is there an atmosphere?There are two kinds of planets, those
with atmo-
spheres and those without. The planets with atmo-spheres are
simply those which have not lost them. Thiscan be seen clearly on
the “Zahnle diagram”: with axis ofescape velocity (planet mass) and
solar heating, a simplepower law empirically separates the two
classes[4, 5].
Carbon DioxideThere are two end member cases of how a planet
may store a carbon dioxide reservoir, represented in oursolar
system by Earth and Venus. On Earth, there is asmall atmospheric
reservoir and a larger ocean reservoir,but the vast majority of
oxidized carbon is stored incarbonate rocks. On Venus, the
atmospheric carbondioxide inventory is roughly equivalent to the
contentsof Earth’s carbonate rocks, but there is neither an
oceaninventory (as there is no ocean) nor any evidence ofcarbonate
rocks.
Let us consider how oxidized carbon is partitionedbetween
reservoirs on an Earth-like planet. The par-tial pressure of
atmospheric CO2 and the dissolved con-centration in the ocean are
in direct proportion, de-scribed by Henry’s Law. But dissolved CO2
is notthe major reservoir; in aqueous solution, the dissolu-tion
products of carbonic acid, bicarbonate ion and car-bonate ion, will
often be larger reservoirs. Conserva-tion of mass is described via
Dissolved Inorganic Car-bon (DIC = [CO2] + [HCO–3] + [CO2–3 ]).
Conservation ofchange of weak acids occurs through alkalinity,
whichbalances net positive change from salts (Alk = [HCO–3]+2
[CO2–3 ]+ . . . = [Na
+]−[Cl–]+ [Mg2+]+ [Ca2+]+ . . .). Forsome DIC, alkalinity will
control the partitioning be-tween different reservoirs; low
alkalinity requires high[CO2] and low [CO2–3 ], high alkalinity the
opposite. At in-termediate alkalinity [HCO–3] dominates. Thus, for
givenDIC, alkalinity determines the atmospheric pCO2 andthus
climate (Figure 3).
Plant roots increase soil pCO2 and secrete organicacids which
will dissolve rock.
In the ocean, high alkalinity means that [CO2–3 ] willincrease
to the point where precipitation of CaCO3 isthermodynamically
favoured, and precipitation removesboth DIC and alkalinity. Thus,
the consequence of analkalinity flux from weathering is removal of
inorganiccarbon from the atmosphere-ocean system and deposi-tion in
rock. The saturation product Ω = ([Ca+][CO2–3 ])satdescribes when
precipitation is thermodynamically favoured,but this is kinetically
inhibited. Authigenic (abiological)precipitation requires Ω = 30,
but on Earth biology rulesthe roost yet again as organisms that
build calcium car-bonate shells are able to do so at Ω = 3. Just as
biologyenhances weathering, it enhances carbonate deposition,and
living Earth has lower pCO2 than her sterile equiva-lent would.
Carbonate rocks will ultimate be destroyed throughmetamorphism,
either of during subduction of oceancrust or in regional
metamorphism of carbonate rocksuplifted to the continents. This
recycled carbon con-tributes a larger part of the oft-referred to
“volcanic
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The Inhabitance Paradox
pCO2 ( µatm)
Alkilinity ( µmol kg -1)
10 2 10 3 10 4 10 5
DIC
(µ
mo
l kg
-1)
10 2
10 3
10 4
10 5
0
1
2
3
4
5
6[CO
2]/DIC
Alkilinity ( µmol kg -1)
10 2 10 3 10 4 10 5
DIC
(µ
mol kg
-1)
10 2
10 3
10 4
10 5
0
0.2
0.4
0.6
0.8
1
[HCO3
- ]/DIC
Alkilinity ( µmol kg -1)
10 2 10 3 10 4 10 5
DIC
(µ
mol kg
-1)
10 2
10 3
10 4
10 5
0
0.2
0.4
0.6
0.8
1
[CO3
2- ]/DIC
Alkilinity ( µmol kg -1)
10 2 10 3 10 4 10 5D
IC (µ
mol kg
-1)
10 2
10 3
10 4
10 5
0
0.2
0.4
0.6
0.8
1
Figure 3: Atmospheric carbon dioxide and dissolved species
concentrations as a function of DIC and Alk. There is a tendencyto
think of the total amount of carbon in the atmosphere-ocean
determining the strength of the CO2 greenhouse, but quite
clearlyalkalinity exerts equal leverage. Figures made with the
Zeebe code[6]
carbon” source than juvenile carbon. Geological pro-cesses are
thus involved in the partitioning betweenatmosphere-ocean and solid
planet reservoirs.
Now, the transition to Venus: first, the depositionof carbonates
is aqueous, so with the evaporation andloss of the oceans none can
be deposited; second, athigh temperatures, calcium carbonate will
break downCaCO3 −−→ CaO + CO2. This reaction is operated
indus-trially on Earth in lime kilns. The required temperatureof
around 1200K is quite reasonable for the surface ofVenus in a
runaway greenhouse (the hot dry state) beforewater is lost to
space.
In summary, to understand the first order controlsof atmospheric
CO2, one must understand planetary cli-mate, ocean chemistry,
surface weathering processes andthe action of life.
Di-nitrogenThe geological cycle of nitrogen, hence the
possi-
ble variation of atmospheric di-nitrogen inventory, havelong
been under-appreciated. However, modern whole-Earth nitrogen
budgets suggest that Earth’s mantle con-tains more nitrogen than
the atmosphere and that mantlenitrogen is of subduction origin. An
atmospheric massworth of nitrogen can be subducted in around a
billionyears, so variations in the atmospheric budget have to
beconsidered [1, 7].
This mantle nitrogen is biological in origin. The
only way that large amounts of di-nitrogen can be fixedis
through biological nitrogen fixation, to make ammo-nium (NH+4).
Ammonium has a similar ionic radius topotassium ion, so will
readily substitute into K-rich min-erals (particularly clays).
Stable in a geological setting,it may then be subducted. Noble gas
isotopes indicatethat the mantle nitrogen (one to a few times the
amountin the atmosphere) is indeed of subducted origin, andnot
primordial.
As with carbon dioxide, there is a prima facia casethat a mix of
biological, geochemical and geologicalprocesses control the
atmospheric inventory.
Water
Water may be somewhat unique amongst the atmo-spheric gases in
that its controls do appear to be physical,dominated by
evaporation-condensation: warmer tem-peratures leads directly to
higher partial pressure. Feed-back processes in interaction with
the radiation field giverise to the number of climate states
discussed above.
There are other considerations though. Existence ofan ocean
requires: initial delivery of water to a planetinside the snowline;
failure to lose that ocean via hy-drogen escape; failure to subduct
all water to the mantlethrough hydration and subduction of rocks
(which doeshappen to an extent on Earth).
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REFERENCES
Conclusion
Were Earth to have only water in its atmosphere, it wouldtoday
exist perilously close to both the inner and outerbounds of the
conventionally defined habitable zone.In dynamical systems terms,
there are several overlap-ping stable steady states of climate near
present solarconstant. The state with liquid water and modest
tem-perature is narrow.
Expanding the habitable zone requires other gases inthe
atmosphere: conceptually, a greenhouse gas whenthere is little
incoming sunlight and a background gas toeither scatter sunlight
when that is abundant, or broadenthe absorption of greenhouse
gasses when sunlight isscarce. The boundaries of the climate states
are deter-mined by atmospheric physics with abundances of
thesegases as a free parameter. On Earth, appeals to phys-ical
feedbacks to control carbon dioxide or di-nitrogeninventories fail:
those free parameters are controlled bygeology, geochemistry and
life itself.
Life, we see, has entered the business of controllingthe
boundaries of its own habitat in space and time,niche construction
in ecological parlance. As we viewGaia through the atmosphere, we
see that habitabilityand inhabitance are inseparable.
Acknowledgements This work was funded by an NSERCdiscovery
grant. Thanks to Ben Johnson for commentson the manuscript.
References
[1] C. Goldblatt, Tyler D. Robinson, K. J. Zahnle, andDavid
Crisp. Low simulated radiation limit forrunaway greenhouse
climates. Nature Geoscience,6(8):661–667, July 2013.
[2] C. Goldblatt. Habitability of waterworlds:
runawaygreenhouses, atmospheric expansion, and multipleclimate
States of pure water atmospheres. Astrobiol-ogy, 15(5):362–70, May
2015.
[3] C. Goldblatt and A. J. Watson. The runaway green-house:
implications for future climate change, geo-engineering and
planetary atmospheres. Phil. Trans.Roy. Soc. A,
370(1974):4197–4216, 2012.
[4] K.J. Zahnle. The Cosmic Shoreline. In AGU FallMeeting
Abstracts, 2008.
[5] K. J. Zahnle. The Cosmic Shoreline. In 44th Lunarand
Planetary Science Conference, page 2787, 2013.
[6] R. E. Zeebe and D. Wolf-Gladrow. CO2 in
seawater:equilibrium, kinetics, isotopes. Elsevier, 2001.
[7] B. Johnson and C. Goldblatt. The nitrogen budgetof Earth.
Earth-Science Reviews, 148:150–173, 2015.
