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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 ± 2.2

continental crust

65 ± 1.6

mid-ocean-ridges

up to 400

oceanic basins

~ 60

subduction zones

~ 35

AEarth = 5.1 x 108 km2 Ac = 2 x 108 km2 Ao = 3.1 x 108 km2

Global mean surface heat flow on Earth: 4.43 × 1013 W or 87 mW/m2  geothermal gradient: ~ 20-30 K km-1 1Turcotte

D. L. and Schubert G., 2002

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 groundwater 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:

results in: 78 mW

m-2

qVenus  0.815q Earth mass ratio between Venus and Earth

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

results in: 63 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 crust highlands (~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:

k (Tm  Ts ) qVenus  (t )1/ 2 critical Ra Number: 1Turcotte

results in ~ 11 mW m

 M g [TM (t )  TS ]YL Ra   (t )

D. L., 1993

-2

1T

m

Ts k κ t

3 YL ρM α ή g

mean mantle temperature surface temperature thermal conductivity thermal diffusivity time, since the lithosphere has stabilized (mean surface age) thickness of the lithosphere mean mantle density thermal expansion coefficient viscosity gravitational acceleration

(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 total surface heat loss?

on Earth1!

1Leitner

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

on Venus1?

(4) Capacities of the Heat Transport Mechanisms: (a) Thermal Conduction:

  k  kT 2kT  exp   2 t  for old crust: qC  a a  a  2

1

a … thickness T … temperature difference between top and bottom k … thermal conductivity t … age of the crust

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

1

after Sclater J. G. et al., 1980

(4) Capacities of the Heat Transport Mechanisms: (a) Thermal Conduction: Leitner J. J. and Firneis M. G., 2005

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

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)

(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 possess a 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

qcor

dV  nW  (cP T  H f ) dt nW as a weight-factor for all presumably active plume-induced structures at present

1Leitner

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

1

results in 6.0  1.4 mW m -2 ρ and cP Hf dV/dt ∆T

density and the specific heat of the volc. mat. fusion heat of the magma volumetric flux of magma with time temp. difference between the eruption temp. of the magma and the surface temp.

(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 a fluid heated from below  2   T  T   FR  g m v T1  T0 1  m v 1 0 t  (  m   )   1/ 2

    FT 1  2bg 0 v TC  T0   2u0  2TC  T0  os       0  2u0 

(2)

1/ 2

FT 2

(3)

FT1 FT2 ρm ρω ρ0 γ t κ T1 T0 Tc λ u0 ∆ρos b g αv

(1)

gravitational body force due to its temperature deficit relative to the adjacent mantle downward grav. body force due to the phase boundary elevation mantle density density of the Venusian atmosphere at the surface of the planet mean density slope of the Clapeytron curve age of the crust thermal diffusivity base temperature of the convection cell surface temperature temperature in the nearly isothermal core of the convection cell dimension parameter of the convection cell horizontal fluid velocity positive density difference between the Olivin/Spinel Phases depth of the convection cell equatorial surface acceleration 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 present

Mean surface heat flow on Venus at present: ~ 39.5 ± 1.4 mW m-2 on Earth1

1Leitner

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

on Venus1

Summary of the Models:

model type

present-day heat flow [mW m-2]

global scalings according to Earth

~ 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 to drill 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