Surface Heat Flow of Venus

Surface Heat Flow of Venus

Author: J. J. Leitner

Surface Heat Flow as an Indicator for:

The sun provides about 99.98 % of the thermal energy at the surface, geothermal energy contributes only 0.02 %. The geothermal heat flow defines the surface and the interior of the planet.

origin and evolution of the surface structure-elements

planetary interior heat production

distribution of radioactive elements (K, U, Th)

planetary interior heat transport mechanisms (cooling)

geothermal gradient

etc.

Mean Global Surface Heat Flow on Earth:

well determined in-situ in thousands of different locations:

Location Amount [mW m-2]1

oceanic crust 101 ± 2.2continental crust 65 ± 1.6mid-ocean-ridges up to 400oceanic basins ~ 60subduction zones ~ 35

Global mean surface heat flow on Earth: 4.43 × 1013 W or 87 mW/m2

1Turcotte D. L. and Schubert G., 2002

AEarth = 5.1 x 108 km2

Ac = 2 x 108 km2

Ao = 3.1 x 108 km2

geothermal gradient: ~ 20-30 K km-1

Measurement of the Surface Heat Flow on Earth:

Measurement Procedure:

Determination of (1) the thermal gradient in deep drill holes, because climatic variations in the Earth’s surface temperature influence the temperature in the near-surface rocks

for example: daily variations (~ 30 cm)yearly variations (~ 5 m)ice-ages (~ 1000 m)

and (2) the thermal conductivity of the rocks.

For continental crust at least 100 m are necessary to avoid convective ground-water heat transfer.

Mean Global Surface Heat Flow on Venus:

no measurements up to now

Estimations derived from:(1) global scalings according to Earth(2) catastrophic/episodic resurfacing model(3) parameterized convection models(4) capacities of the heat transport mechanisms

(1) Global Scalings According to Earth:

(a) Solomon S. C. and Head J. W., 1982:

(b) Turcotte D. L., 1995: same model, but due to a different value for qEarth

EarthVenus qq 815.0

mass ratio between Venus and Earth

results in: 63 mW m-2

results in: 78 mW m-2

(1) Global Scalings According to Earth:

(c) Leitner J. J., 2005:

Assumption: 2 different kinds of crust

Venus surface:low- and uplands (± 1.5 km of planetary datum, 92 %) ~ oceanic crusthighlands (~8 %) ~ continental crust

Scaling:mean heat flow of continental crust on Venus: ~ 53 mW m-2

mean heat flow of oceanic crust on Venus: ~ 82 mW m-2

mean global heat flow results in: ~ 80 mW m-2

(2) Catastrophic/Episodic Resurfacing Model:

Turcotte D. L., 1992, 1993 and 1999

‘standard’ model for Venusian resurfacing

Main topics:

strong time-dependent (episodic?) heat loss an active period characterized by extensive plate-tectonics

(especially subduction) or extensive hot-spot-volcanism and a high surface heat loss with a duration of ~ 150 million years resulted in a too cold lithosphere, which could not support active

plate-tectonics anymore (since ~ 500 million years) since the last resurfacing period only thermal conduction active continuous heat production in the planet’s interior, which

reheats the upper mantle increasing temperature results in an unstable lithosphere and

initiates a new (global) resurfacing event

(2) Catastrophic/Episodic Resurfacing Model:

2-m mW 11~ in results 2/1)()(

tTTkq sm

Venus

1Turcotte D. L., 1993

Tm mean mantle temperatureTs surface temperaturek thermal conductivityκ thermal diffusivityt time, since the lithosphere has

stabilized (mean surface age)YL thickness of the lithosphereρM mean mantle densityα thermal expansion coefficientή viscosityg gravitational acceleration

1

)(])([ 3

tYTtTgRa LSMM

critical RaNumber:

(3) Parameterized Convection Models:

Phillips R. J. and Malin M. C., 1983: no core heat component: results in ~ 50 mW m-2

Arkani-Hamed J. et al., 1983: assumptions: 90 % of the heat-producing elements are concentrated in the outer 120 km, constant density regime, without mantle phase transitions, surface temperature has not undergone any changes up to the present: results in: 42 and 80 mW m-2, resp.

Solomatov V. N. and Moresi L. N., 1996: constant viscosity conditions (no stagnant lid): results also in ~ 50 mW m-2

Solomatov V. N. and Moresi L. N., 1996: constant viscosity regime is switched to a stagnant-lid regime 0.6 Gyr ago (after the switch the heat flux and lithospheric thickening are purely controlled by a diffusion cooling lithosphere): results in ~ 15 mW m-2

(4) Capacities of the Heat Transport Mechanisms:

Which mechanisms contribute how much to the totalsurface heat loss?

on Earth1! on Venus1?

1Leitner J. J. and Firneis M. G., 2005

(4) Capacities of the Heat Transport Mechanisms:

(a) Thermal Conduction:

for old crust:

t

ak

akT

akTqC 2

2

exp2

a … thicknessT … temperature difference between top and bottomk … thermal conductivityt … age of the crust

important differences between Earth and Venus in T, t and a

1 after Sclater J. G. et al., 1980

1

(4) Capacities of the Heat Transport Mechanisms:

for 500 Myr old crust on Venus: qcond ~ 33.5 mW m-2

in a good agreement with Turcotte D. L., 1995 (37.7 mW m-2)

(a) Thermal Conduction:

Leitner J. J. and Firneis M. G., 2005 Leitner J. J. and Firneis M. G., 2005

(4) Capacities of the Heat Transport Mechanisms:

(b) Hot-Spot/Corona Volcanism:

Coronae are volcano-tectonic structures of circular or elliptical shape(diameters between 60 and 2600 km)

raised up to 1.5 km above the surrounding terrain and possessa raised rim

(4) Capacities of the Heat Transport Mechanisms:

(b) Hot-Spot/Corona Volcanism:

two evolution stages:

Nova Arachnoid

(4) Capacities of the Heat Transport Mechanisms:

(b) Hot-Spot/Corona Volcanism:

Are Coronae the Venusian equivalents to terrestrial hot-spots?

known numbers of Coronae, Arachnoids and Novae vary from catalogue to catalogue: USGS catalogue: 328 Coronae Stofan E. R. et al., 2001: 515 Coronae Brown University database: 206 Coronae, 265 Arachnoids and

63 Novae

2-m mW 6.0 in results 4.1)( dtdVHTcnq fPWcor

1Leitner J. J. and Firneis M. G., 2006

ρ and cP density and the specific heat of the volc. mat.Hf fusion heat of the magma dV/dt volumetric flux of magma with time∆T temp. difference between the eruption

temp. of the magma and the surface temp.

nW as a weight-factor for all presumably active plume-induced structures

at present

1

(4) Capacities of the Heat Transport Mechanisms:

(b) Hot-Spot/Corona Volcanism:

Assumption: each Venusian Corona/Arachnoid/Nova (= hot-spot)is caused by a separate mantle plume

neglecting: multiple Coronae and Corona-chains

(4) Capacities of the Heat Transport Mechanisms:

(c) Plate-Tectonics: MAGELLAN revealed that on Venus nowadays plate-recycling is not operative!!!

Model calculations: van Thienen P. et al., 2004: considerations only based on buoyancy

arguments resulted in no explanation for the present lack of plate-tectonics Leitner J. J. and Firneis M. G. 2005: plate-recycling driving forces model

at present on Earth: 13:1 (trench pull to ridge push)

at present on Venus: 0.7:1

no present contribution to the total heat loss

(4) Capacities of the Heat Transport Mechanisms:

(c) Plate-Tectonics:

plate-recycling driving forces model: 2D model for a convection cell in afluid heated from below

(1) tTTTTgFm

vmvmR

)(

21 0101

(2) 2/1

0001 2

2

uTTbgF CvT

(3) 2/1

00

02 2

2

uTTF osC

T

FT1 gravitational body force due to its temperature deficit relative to the adjacent mantle

FT2 downward grav. body force due to the phase boundary elevation ρm mantle densityρω density of the Venusian atmosphere at the surface of the planetρ0 mean densityγ slope of the Clapeytron curvet age of the crustκ thermal diffusivityT1 base temperature of the convection cell T0 surface temperatureTc temperature in the nearly isothermal core of the convection cellλ dimension parameter of the convection cellu0 horizontal fluid velocity∆ρos positive density difference between the Olivin/Spinel Phasesb depth of the convection cellg equatorial surface accelerationαv volumetric coefficient of thermal expansion

(4) Capacities of the Heat Transport Mechanisms:

(c) Plate-Tectonics:

Leitner J. J. and Firneis M. G., 2005

(4) Capacities of the Heat Transport Mechanisms:

Thermal conductivity: 33.5 mW m-2

Corona/hot-spot volcanism: 6 ± 1.4 mW m-2

Plate-recycling: no contribution at presentMean surface heat flow

on Venus at present: ~ 39.5 ± 1.4 mW m-2

on Earth1 on Venus1

1Leitner J. J. and Firneis M. G., 2005

Summary of the Models:

model type present-day heat flow [mW m-2]

global scalings according toEarth

~ 63 and ~ 78

catastrophic/episodic resurfacing model

~ 11

parameterized convection models

~ 15 – 50~ 42 – 80

capacities of the heat transport mechanisms

39.5 ± 1.4

In-Situ Determination on Venus :

… the extrem surface conditions on Venus make it very improbable todrill an adequate borehole for determining the vertical thermal gradient …

an alternative:

heat flow sensor in direct contact with the surface

possible on Venus due to:

the lack of surface- and groundwater and the stable surface temperature