GEOPHYSICALRESEARCH
LETTERS, VOL. 8, NO. 4, PAGES313-316,

MAGMATRANSPORT OF HEAT ON IO'APRIL 1981

A MECHANISM ALLOWING A THICK LITHOSPHERE

Thomas C. O'Reilly

and Geoffrey

F. Davies

Department of Earth and Planetary Sciences and McDonnell Center for Space
Sciences Washington University,
St. Louis, Missouri 63130

Abstract. Models indicate that the highheat flow from Io would result in a very thinmelting caused by tidal flexing from Jupiterand Europa. Assuming tidal flexing is the only
heat source, and that heating occurs only in anouter solid silicate
lithosphere,
Peale et al.

(approximately5 kin) silicate lithosphere

overlying a molten interior,
if all heat wastransported through the lithosphere via
conduction. However, the presence of mountains

calculatea totalsurface heat flow of 0.4 W/m2
and a conduction-limited
lithosphericthicknesswith relief in excess of 10 km would seem
demanda thick lithosphere, at least locally.
A significant fraction of Io's heat flow maybe

of 18 km.
The heat flow valueof Matson
would lead to an even smaller(4.5
km)
conduction-limited
thickness.

transported via advection through volcanoes.
Advective heat transfer permits a thicker

Rugged mountains having

lithosphere than does pure conduction, possibly

1979].

topography.

Infrared(IR)observations,observations

silicate

plumes andflows, and the prediction of large tidal energy

thick.

estimate

topography?
of 6 kbar

lithospherewould be only on the order of 10 km

Calculationof theforthecase of a 5 km-thicksupporting a mountain 10 km highand 10 km wide.
This is much greater thanestimates of the strength of the Earth's
lithosphere at low pressure (maximum is 1-2

On the other hand, the Voyager images

show relief

This observation poses an interesting

maximumbending stress in a floating elastic
lithosphere (see McNutt, 1980) yields andissipationin Io all indicatethat Io has alarge surface heat flux,
such that a conductive

lithospherein excess ofquestion; how can the thin lithosphere implied
by Io's high heat flow support 10 km of

the Voyagerof volcanical.

10 km, and apparently of silicatecomposition,
have been observed by Voyager [Carr et al.,reconciling Io's high heat flow with the rugged

spacecraft

reliefetof the order of 10 km in polar

regions, which seems to demand a thicklithosphere.
Here we present a model thatkbar).
Thus it seems unlikely that a 5 km
lithosphere could support such a load without

allows both high heat flow and theoretically

failure,causing the mountains to "founder."There are at least three possibilities;

unlimitedlithosphere

In addition
spacecraft

thickness.

to active plumes, the Voyager

observed

over

100 calderasa)on Io'ssurface, many of them surrounded by radiating
flow patterns hundreds of kilometers long
[Smith, et al., 1979, Cart, et al., 1979].
Analysis of Voyager IR spectrometer data hasrevealed a hot spot within a caldera at atemperature of approximately 300 K, and anotherin the vicinityof an active plume at 650-700 K[Hanel, 1979, Sinton, 1980].
Earthbased IR
observationsofare consistenta transientwith

5 micronb)Dynamic support, i.e. convection within
Io is holding up the mountains.
Thelocalized nature of the topography would
seem to demand some special pleading tomaintain this hypothesis.
The mountains are compensated by a thicklower density root.
Conductive warming
would probably

limitthat both mountain and root are dynamic
features.
Perhaps analogy can be madewith terrestrial
plate tectonics,
but nooutburst

a blackbody at 600 K andcovering 2x10-4 of the total surface

evidence[Witteborn,
et al.,
1979].
Based onanomalously high IR fluxes emitted by Io whilein eclipse by Jupiter, Matson et al. [1981]
constructeda thermal model consistingof
hotspots laterally
distributed
within a cooler
regolith.
Their data are consistent withhotspots comprising 2 +__1% of the Ionian

recognized.
The lithospheresurfaceand a total

average

heat

flow

c)

for

possibilityof 2 + 1

times

alternativevalue!

[1981]

deriveda valueof

1.5 + 0.3 W/m2.
In a report published a week before the
Voyager 1 encounter, Peale et al. 1979
predicted a largely melted interior andconsequent surface volcanism due to "runaway"by

Copyright 1981 by the AmericanGeophysicalUnion
Paper number1L0010.
0094-8276/81/001L-0010501.00

been

A

it

is not claimedthatmodels can be definitely
at thisstage.

In our model, illustrated
in Figure 1, partof the heat is removed by advection, i.e.,magma from depth rises to the surface throughisolated vents, spreads out, and cools.
Thesolid lithosphere subsides under the weight offlows and is heated by conduction.
Solidmaterial at the base of the lithosphere melts,
beginning the cycle again.

obtained a value of 1.8 + 0.6 W/m2, andand Telesco

hasthat is addressed by our

althoughexcludedThis high value has recently
beencorroborated by two independent heat flow
determinations
from eclipse data; Sinton [1981]
Morrisonon Io

subsidence of lithosphericmaterial.
thicker lithosphere
could support
uncompensated topography.
It is thismodel,

terrestrial

thisis thick under themountains, and perhaps globally,
andconductive warming is suppressed by

2
watts per squaremeter (W/m),or nearly 30--

thethe age of a static

root to 106-107 years, which implies

The heat flow qa due to advection is given

qa= v0 [AHf+ Cp(Tm- To)]
313

(1)

O'Reillyand Davies'

Magma Transportof Heat on Io

where qt is the total heat flow (advected plusoconducted), and, as a consequence of all heatbeing produced in a layer of thickness d, theadditional condition A=qt/d is applied.

[For

detailsof solutions of equations of this type,see, e.g., Oxburgh and Turcotte, 1971].
If all other parameters are fixed, a given
value of subsidence velocity
v uniquely

constrains advected heat flow qa (equation 1)
Partialand lithospheremelt

thicknessd.

In Figure

2 weshowd as a function of v and qa/qt for

z

•ig.

1.

Model of •onian

temperature Tm rises
acrossTo.

surface,lithosphere.

Magma atthrough vents and spreads

cooling

to surface

temperature

Weight of flows depresses lithosphere at

subsidence velocityv, which equals resurfacing

internal

assuming a total

As the measured heat flow

values have large uncertainties
attached tothem, our values should be regarded as very
preliminary
and mainly illustrative.
It can be
seen

rate.

and bottom heating,heat flow of 1 W/m2.

thatd increases

without

limit

in

both

cases as v and qa increase, but that dincreases
fasterin the internallyheated case.
In both cases, as v approaches zero, qa becomes

where v is the subsidence rate (equal to theresurfacing rate in our model), 0 is the magma

negligible

density, AHf is the heat of fusion, Cp is the

For large v, conducted heat flow qcs becomes

specific heat, Tm is the melting temperature,
and To is the surface temperature. Heat will

negligible
and heat is transported mostly by
advection.
If the magma can find its way
efficiently
through the lithosphere,
it cancarry most of the heat and the lithospherecan.be arbitrarily
thick.
Thus the high heat flow
and rugged topography of Io may be reconciled.
The rate of resurfacing
necessary totransport most of the heat by advection can bealso be conducted through the subsiding solidmaterial.
For sufficiently
wide spacing of thevents, conduction will be vertical,
and theequation of interestis (forz positive

downwards);•2T= v •z
•T

• •z

A

and simple conduction predominates.

(2)

pC
p

V (mm/ r)•T

where • is thermal diffusivity,•--•
verticalheating

is the0temperature gradient,and A is therate per unit volume in the solid

30'

layer.
We canconsidertwo

extremecases.

-

One

extreme case is "bottom heating;"
all heat is
supplied from below and none is produced in thesolid layer (A--O). If Io's heat is indeed
produced by tidal flexing,
bottom heating may
be a valid approximation,
as some studies
suggest that strain heating is greatest in
regions of partial
melt [Mavko and Nur, 1975,
O'Connell and Budiansky, 1975].
The other
extreme case is "internal
heating,"
in which
all heat production is confined to anduniformly distributed
within the solid layer.
The expressions for temperature andcorresponding upwards conductive heat flow qcs
that satisfy
equation 2 are, for the bottom
heating case (A--O);z/œ
T = AT(e- l) + To
d/œ1
KAT

(3a)

qcs = •(•Z/Oz)z•0 • •( e•/Z-1)

(3•)

ß

1

2

3

4

5

,

,

,

,

' 135

bottomintepnal-

2o10 -/-90// / /
4,5

-

/

L__

0ll'--I-7--••li! I I I !1.0IO
0
0,.5
qa/qt
Fig.

whereAT=Tm-To,
œ--e/v,d is the solid2.

Normalized

silicatelithospherelithosphere thickness, K=pCp_is the thermal

thickness d/d o as a function of advected heatflow fraction qa/qt and subsidence velocity

T=To at(=resurfacing(solid curve)

conductivity,internallyand the boundary conditions

z=O and T=Tm at

z=d.

For

heated case the solutions

are;

(ez/œ
-1)
+-•-•
z +TO
[•eT
-qt/vpCp]•qt
KFAT-qt/v0Cpt
qcs=• /eaZZ_']+ va

T= d/•_
1

are

the

curve).
(4a)(4b)rate) v, for bottom heating
and internal
heating (dashedThickness normalization

factor do is

4.5km (the thickness of a purely conductive
bottom-heated lithosphere),
and total heat flow

qt is assumed
to be 1 W/m
2. Silicate magma
parametersare K=3W/mK,
0=3000kg/m3, Cp--1000J/kgK,AHf=4.5x105j/kg, AT=1500K.

19448007, 1981, 4, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/GL008i004p00313 by Ryan Ogliore - Universite Cote D'azur , Wiley Online Library on [15/08/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License314

and Davies' MagmaTransport of Heat on Io

TABLE

315

1

RESURFACINGRATES
NEEDEDTOADVECT
0.5 W/m
2 HEAT
FLUX

Sulfur1
2

SilicateO(kg/m3)

AHf(J/kg) Cp(J/kgøK)AT(øK)

v(mm/yr)

1810

3.7x104

730

290

35

3000

4.5x105

1000

1500

3

1.

Physico-chemical data for sulfur

2.

Order-of-magnitudeis from the International

Tables.

values from various sources, e.g. Yoder, 1976.

obtained from equation 1. For silicate
magma,a resurfacing rate of 3 mm/yr transports 50% of
the heat by advection; for sulfur magma thenecessary rate is 35 mm/yr (Table 1).

The ratefor sulfur is an order of magnitude higher thanthat for silicate
mainly because of the lower
melting point and heat of fusion of sulfur.
Both resurfacing rates are compatible with theminimum resurfacing rate of 0.1 to 10 mm/yr as

infer'--'---re--dfrom the lack of impact craters in the
Voyager images [Johnson, et al., 1979].
Most of Io's surface may be covered bysulfuror a mixture of sulfur
and S02 ice,

both the sulfur/S02

Criticaland underlying

andsilicates

The high heat flow first
et

al.

has

been

measurements

reported

substantiated.

of the heightby Matson

Moreaccurateand extent

of thetopography, together with the relevant
calculations,
may yield a minimum value for thelithosphericthickness.
Also needed are moreaccurate (if possible) determinations of theresurfacing rate, which could help constrain
the nature and properties of Ionian eruptive
materials.

If

the resultsof this

paper

are

sustained, then one more characteristicof Io
may be added to its list of unique features; a
new kind of lithospheretransport mechanism.

withan unusual heat

may be resurfaced and recycled [Smith, et al.,Acknowledgments. We thank R.E. Arvidson,
Goettel,E. Strickland,and N. Sturchio of
Wash. U., and T. Johnson, D. Matson, and G.

1979].
In that case, both the silicate
andsulfur/S0 2 would have to transport the total
heat

flux,

and both the above rates

would

apply, except that the observed resurfacing

Ransford

would be identified

advice.
This research was supported
NSF grant EAR78-23675.

layer.

with

Of course, if

thatof thesulfur/S02

S02 plays a significantrole,
the values of the physical parameters
used in calculatingthe "sulfur" rate will not
be accurate, but will still
be indicativeofthebehaviorofvolatiles

relativetosilicates.

Although our model allows an arbitrarily
thick,
lateralcool lithosphere,
other factors,
such asconduction and the dynamics of magma

ascent may limit the thickness in reality.
Some magmas certainly
penetrate through 100 km
or more of the terrestrial
lithosphere;
theprocess may be poorly understood, but occurs
nonetheless.
Perhaps the tides raised on Io
could enhance the effectivenessof magmatransport.
Apart from the rugged topography
coexisting with high heat flow, there are atleast two independent Observations that suggest
the importance of advective heat transport on
Io.
First,
the model of Matson, et al. [1981]
indicates

that

most

of

the

heat

flow

comes

from

localized
sources covering approximately
2% ofthe surface.
Calderas,
active and dormant, areestimated to comprise about 5% of the surface[Carr, et al.,1979].
Second, the estimatedhigh resurfacing

rate[Johnson, et al.,1979]

suggests that considerable amounts of material
may be coming up from below the surface.
Reynolds and Cassen [1979] considered thepossibilityof magma heat transport,
butassumed that

becauseepisodic

could not account for more than

about

it

10% ofthetotalsuch transport
heat

flow.

must beof

JPL forvaluable

information

K.

and

in partbyReferences

Carr, M.H.,
H. Masursky,
R.G. Strom, and R.E.
Terrile,Volcanic Features of Io, Nature,
280, 729-733,
1979.
Hanel, R., Infrared
Observationsof the Jovian

System from Voyager 1, Sci___enc__•e,
2__0_4_,972-976,
1979.

Johnson,T.V.,

Soderblom,

A.F.

Volcanic

Cook II,

C. Sagan,

Resurfacing

Implications for Volatiles

and L.A.

Rates andon Io, Na__t_ur•e,

280, 246-250,
1979.
Matson, D.L.,
G.A. Ransford,

and T.V. Johnson,
Heat Flow from Io, J. Geophys. Res., inpress, 1981.
Mavko, G., and A. Nur, Melt Squirt in the
Asthenosphere, J. Geophys. Res., 80, 14441448,

1975.

McNutt,

M.,

for

State

ImplicationsofStressinof Regional

Gravity

the

Crust

Earth'sandUpper Mantle, J. Geoph•ys.Res., 85, 63776396, 1980.
Morrison,D., and C.M. Telesco,
Io'
Observational
Constraints
on Internal
Energyand Thermophysics of the Surface, Icarus,
inpress, 1981.
O'Connell,
R.J.,
and B. Budiansky, Viscoelastic
Propertiesof Fluid-Saturated
Cracked Solids,

J. Geophys. Res., 8__2_,
5719-5735, 1977.
Oxburgh, E.R., and D.L. Turcotte,
Origin of
Paired Metamorphic Belts and Crustal Dilation

19448007, 1981, 4, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/GL008i004p00313 by Ryan Ogliore - Universite Cote D'azur , Wiley Online Library on [15/08/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

O'Reilly

O'Reillyin Island

Arc Regions,1315-1327,
Peale,
S.3.,

1971.
P. Cassen,

Melting of Io by Tidal
203, 892-894,
1979.

and Davies' MagmaTransport

J. Oeophys. Res.,76,

and R.T.

Science,of Io,

in Reports

Sinton, W.M., Io'
Ground-Based Observationsof
Hot Spots, Science, 210, 1015-1017,
1980.
Sinton, W.M., The Thermal Emission Spectrum ofand

Hot Spots,

1981.

a Determination

Smith, B.A.,

The Jupiter

System ThroughE.M. Shoemaker. S.W. Kieffer,

A.F. Cook II,

of Planetary Geology Program, 1978-1979 •N•-•
Technical Memorandum
80339)', 377-379, 1979.

its

et al.,

1979.

Reynolds,

Dissipation,and the Surface

Io

Smith, B.A.,

the Eyes of Voyager 1, Science, 20__4_,
951-971,

Reynolds, R.T., and P.M. Cassen, Tidal
Dissipationof Heat on I6

of

the

Heat

J. Geophys. Res.,

Flux

Io, Nature,
280, 738-743,
1979.
Witteborn,
F.C., J.D. Bregman, and J.B.
Pollack,
Io:
An Intense Brightening
Near 5Micrometers,
Science, 203, 643-646,
1979.

Yoder,H.S., Generation_•-•_Basalti•Magm__a,National
D.C.,

Academy of Sciences,

265 p.,

WaShington

1976.

from

in press,and

The Role of S02 in Volcanism on(Received November 10, 1980;
accepted December 16, 1980.)

19448007, 1981, 4, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/GL008i004p00313 by Ryan Ogliore - Universite Cote D'azur , Wiley Online Library on [15/08/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

316