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The curious case of
Mercury’s internal structure
Steven A. Hauck II et al.
Journal of Geophysical Research: Planets
2013
Why studying planetary interiors?
Why studying planetary interiors?
•
Tells us about their history
Why studying planetary interiors?
•
Tells us about their history
•
Explains internal phenomena that manifest externally
Why studying planetary interiors?
•
Tells us about their history
•
Explains internal phenomena that manifest externally
•
Link between internal and external processes
Why studying planetary interiors?
•
Tells us about their history
•
Explains internal phenomena that manifest externally
•
Link between internal and external processes
•
Testing ground for fundamental physics
Mercury
•
•
•
1st planet of the Solar system
Smallest terrestrial planet (0.38 Earth
radii)
Orbital period: 88 days
•
3:2 spin-orbit resonance
•
Self-sustained magnetic field
Outline
Outline
1.
State of the art
How do we probe planetary interiors, and what does it tells us about Mercury?
Outline
1.
State of the art
How do we probe planetary interiors, and what does it tells us about Mercury?
2.
Monte-Carlo approach of the modeling of Mercury
What is the most probable set of parameters describing Mercury?
Outline
1.
State of the art
How do we probe planetary interiors, and what does it tells us about Mercury?
2.
Monte-Carlo approach of the modeling of Mercury
What is the most probable set of parameters describing Mercury?
3.
New insights and implications
A complex picture of Mercury’s interior concordant with other observations
State of the art
Observations of Mercury
XIVth century BC: First mention in Assyria
Vth century AD: diameter estimated within 1% of its current value by Indian astronomers
XVIIth century: first telescopic observations by Galileo
1962: first Earth-based radar observations
1974-1975: Mariner 10 discovers a magnetic field
2008: MESSENGER reaches Mercury
2011: MESSENGER in orbit
2019: BepiColombo?
Moment of inertia (1)
Moment of inertia (1)
•
Measure of an object’s resistance to being spun up/down
Moment of inertia (1)
•
Measure of an object’s resistance to being spun up/down
•
Governed by mass distribution
2M
I=
5

5
Router
3
Router
<
5
Rinner
3
Rinner
Moment of inertia (1)
•
Measure of an object’s resistance to being spun up/down
•
Governed by mass distribution
2M
I=
5

5
Router
3
Router
5
Rinner
3
Rinner
<
Assumes axisymmetric mass distribution
Moment of inertia (2)
Moment of inertia (2)
•
C
= 0.4 for a homogeneous sphere
Normalized polar moment of inertia
2
MR
Moment of inertia (2)
•
C
= 0.4 for a homogeneous sphere
Normalized polar moment of inertia
2
MR
•
If lower, indicates a concentration of denser material toward the center
Moment of inertia (2)
•
C
= 0.4 for a homogeneous sphere
Normalized polar moment of inertia
2
MR
•
If lower, indicates a concentration of denser material toward the center
•
Cm
Cc
Separate contributions
+
=1
C
C
How do we measure it?
How do we measure it?
•
The gravity potential is decomposed into spherical harmonics (assume no external sources
of mass)
1
1 X X̀ h a i`+1
V =
(C`m cos m' + S`m sin m')P`m (cos ✓)
a
r
m=0
`=0
How do we measure it?
•
The gravity potential is decomposed into spherical harmonics (assume no external sources
of mass)
1
1 X X̀ h a i`+1
V =
(C`m cos m' + S`m sin m')P`m (cos ✓)
a
r
m=0
`=0
•
C20 and C22 together with obliquity give
C
M R2
How do we measure it?
•
The gravity potential is decomposed into spherical harmonics (assume no external sources
of mass)
1
1 X X̀ h a i`+1
V =
(C`m cos m' + S`m sin m')P`m (cos ✓)
a
r
m=0
`=0
C
M R2
•
C20 and C22 together with obliquity give
•
Cm
The amplitude of longitudinal librations give
B A
How do we measure it?
•
The gravity potential is decomposed into spherical harmonics (assume no external sources
of mass)
1
1 X X̀ h a i`+1
V =
(C`m cos m' + S`m sin m')P`m (cos ✓)
a
r
m=0
`=0
C
M R2
•
C20 and C22 together with obliquity give
•
Cm
The amplitude of longitudinal librations give
B A
Cm
= 4C22
C
✓
MR
C
2
◆✓
Cm
B A
◆
The giant core of Mercury
The giant core of Mercury
•
Margot et al., 2012:
•
C
=0.346±0.014 (sphere: 0.4, the Earth: 0.331)
2
MR
There is a concentration of denser materials around the center of Mercury
The giant core of Mercury
•
Margot et al., 2012:
•
•
C
=0.346±0.014 (sphere: 0.4, the Earth: 0.331)
2
MR
There is a concentration of denser materials around the center of Mercury
Cm
=0.431±0.025 → the outer shell is thin, ~400km
C
The giant core of Mercury
•
Margot et al., 2012:
•
•
C
=0.346±0.014 (sphere: 0.4, the Earth: 0.331)
2
MR
There is a concentration of denser materials around the center of Mercury
Cm
=0.431±0.025 → the outer shell is thin, ~400km
C
Composition of the core
Composition of the core
•
Large bulk density → large iron-dominated core
Composition of the core
•
Large bulk density → large iron-dominated core
•
Pure iron core would be solid
Composition of the core
•
Large bulk density → large iron-dominated core
•
Pure iron core would be solid
•
Moment of inertia
Composition of the core
•
Large bulk density → large iron-dominated core
•
Pure iron core would be solid
•
Moment of inertia
•
Magnetic field
Composition of the core
•
Large bulk density → large iron-dominated core
•
Pure iron core would be solid
•
Moment of inertia
•
Magnetic field
Composition of the core
•
Large bulk density → large iron-dominated core
•
Pure iron core would be solid
•
•
Moment of inertia
•
Magnetic field
Iron alloyed with light elements to lower its melting point
Composition of the core
Composition of the core
•
Low surface Fe content (~1-2 wt %)
Composition of the core
•
Low surface Fe content (~1-2 wt %)
•
High surface S content
Composition of the core
•
Low surface Fe content (~1-2 wt %)
•
High surface S content
Reducing conditions
Composition of the core
•
Low surface Fe content (~1-2 wt %)
•
High surface S content
Reducing conditions
Liquid metal core
Composition of the core
•
Low surface Fe content (~1-2 wt %)
•
High surface S content
Liquid metal core
Reducing conditions
Fe-S-Si liquid core
Composition of the core
Composition of the core
•
Fe-S-Si core
Composition of the core
•
Fe-S-Si core
•
In the shallow region of Mercury’s core, FeS
and FeSi might not be miscible
Composition of the core
•
Fe-S-Si core
•
In the shallow region of Mercury’s core, FeS
and FeSi might not be miscible
•
FeS would precipitate at the CMB
Composition of the core
•
Fe-S-Si core
•
In the shallow region of Mercury’s core, FeS
and FeSi might not be miscible
•
FeS would precipitate at the CMB
Take away
Take away
•
(Partially) Liquid metal core
(MoI, Dynamo) ~2000km
Take away
•
(Partially) Liquid metal core
(MoI, Dynamo) ~2000km
•
Solid shell ~400km
Take away
•
(Partially) Liquid metal core
(MoI, Dynamo) ~2000km
•
Solid shell ~400km
•
Inner core?
Take away
•
(Partially) Liquid metal core
(MoI, Dynamo) ~2000km
•
Solid shell ~400km
•
Inner core?
•
FeS layer at CMB?
Take away
•
(Partially) Liquid metal core
(MoI, Dynamo) ~2000km
•
Solid shell ~400km
•
Inner core?
•
FeS layer at CMB?
•
New Earth-based estimates of
the moments of inertia
Take away
•
(Partially) Liquid metal core
(MoI, Dynamo) ~2000km
•
Solid shell ~400km
•
Inner core?
•
FeS layer at CMB?
•
New Earth-based estimates of
the moments of inertia
•
Recent determination of the
gravity field by MESSENGER
Monte Carlo approach of
the modeling of Mercury
Monte-Carlo methods
Monte-Carlo methods
•
Generate a large number of models constrained only by Mercury’s radius and mass
Monte-Carlo methods
•
Generate a large number of models constrained only by Mercury’s radius and mass
•
Use significance test to keep only the models satisfying the known values of C/MR2 and
Cm/C
Do I get the good C and Cm because my model is good, or by luck?
Monte-Carlo methods
•
Generate a large number of models constrained only by Mercury’s radius and mass
•
Use significance test to keep only the models satisfying the known values of C/MR2 and
Cm/C
Do I get the good C and Cm because my model is good, or by luck?
Models (physics)
Models (physics)
For 1 model:
Models (physics)
For 1 model:
•
Choose crust and mantle densities, core composition and inner core size
Models (physics)
For 1 model:
•
Choose crust and mantle densities, core composition and inner core size
•
Compute pressure, density and temperature profiles that match Mercury’s radius and bulk
density
Models (physics)
For 1 model:
•
Choose crust and mantle densities, core composition and inner core size
•
Compute pressure, density and temperature profiles that match Mercury’s radius and bulk
density
3K0
P =
2
"✓
⇢
⇢0
◆7/3
Birch-Murnaghan
(✓ ◆
✓ ◆5/3 # "
2/3
⇢
3 0
⇢
· 1 + (K0 4)
⇢0
4
⇢0
1
)#
+ ↵0 K0 (T
T0 )
Models (physics)
For 1 model:
•
Choose crust and mantle densities, core composition and inner core size
•
Compute pressure, density and temperature profiles that match Mercury’s radius and bulk
density
3K0
P =
2
"✓
⇢
⇢0
◆7/3
Birch-Murnaghan
(✓ ◆
✓ ◆5/3 # "
2/3
⇢
3 0
⇢
· 1 + (K0 4)
⇢0
4
⇢0
1
)#
+ ↵0 K0 (T
Hydrostatic equilibrium
P (r) =
Z
r
⇢(x)g(x)dx
R
4⇡G
g(r) = 2
r
Z
r
⇢(x)x2 dx
0
T0 )
Models (physics)
For 1 model:
•
Choose crust and mantle densities, core composition and inner core size
•
Compute pressure, density and temperature profiles that match Mercury’s radius and bulk
density
3K0
P =
2
"✓
⇢
⇢0
◆7/3
Birch-Murnaghan
(✓ ◆
✓ ◆5/3 # "
2/3
⇢
3 0
⇢
· 1 + (K0 4)
⇢0
4
⇢0
1
)#
+ ↵0 K0 (T
Hydrostatic equilibrium
P (r) =
Z
r
4⇡G
g(r) = 2
r
⇢(x)g(x)dx
R
Z
r
⇢(x)x2 dx
0
Temperature profile
dT
↵T
=
dP
⇢Cp
↵0 K0 = ↵K
dP
K=⇢
d⇢
T0 )
New insights and
implications
Mantle reservoir
Mantle reservoir
•
Mercury is Fe-rich, but observations show low surface content
Mantle reservoir
•
Mercury is Fe-rich, but observations show low surface content
•
Mercury’s surface is of magmatic origin
Mantle reservoir
•
Mercury is Fe-rich, but observations show low surface content
•
Mercury’s surface is of magmatic origin
→ Iron-rich deep layer in the mantle?
Mantle reservoir
•
Mercury is Fe-rich, but observations show low surface content
•
Mercury’s surface is of magmatic origin
→ Iron-rich deep layer in the mantle?
•
Can be modeled by S-rich core composition
Mantle reservoir
•
Mercury is Fe-rich, but observations show low surface content
•
Mercury’s surface is of magmatic origin
→ Iron-rich deep layer in the mantle?
•
Can be modeled by S-rich core composition
•
Possible (fits within ±1σ)
Mantle reservoir
•
Mercury is Fe-rich, but observations show low surface content
•
Mercury’s surface is of magmatic origin
→ Iron-rich deep layer in the mantle?
•
Can be modeled by S-rich core composition
•
Possible (fits within ±1σ)
•
Improbable because S/Fe content of
chondrites too low
Core composition
Fe-S models
Fe-Si models
Fe-S-Si
Core composition
Fe-S models
Fe-Si models
Fe-S-Si
•
All models catch the actual C/MR2 and
Cm/C
Core composition
Fe-S models
Fe-Si models
Fe-S-Si
•
All models catch the actual C/MR2 and
Cm/C
•
Fe-S-Si does at least as well as the binary
models
Core composition
Fe-S models
Fe-Si models
Fe-S-Si
•
All models catch the actual C/MR2 and
Cm/C
•
Fe-S-Si does at least as well as the binary
models
•
Fe-S-Si models:
Core composition
Fe-S models
Fe-Si models
Fe-S-Si
•
All models catch the actual C/MR2 and
Cm/C
•
Fe-S-Si models:
•
•
Fe-S-Si does at least as well as the binary
models
deep core Fe-Si rich (solid+liquid)
Core composition
Fe-S models
Fe-Si models
Fe-S-Si
•
•
All models catch the actual C/MR2 and
Cm/C
Fe-S-Si does at least as well as the binary
models
•
Fe-S-Si models:
•
deep core Fe-Si rich (solid+liquid)
•
shallow part FeS rich (solid)
Evolution of C, Cm in the parameter space
Core radius
Shell density
Core density
Evolution of C, Cm in the parameter space
Core radius
•
Shell density
Core density
An increase in core radius leads to an
increase in C/MR2 and Cc/C
Evolution of C, Cm in the parameter space
Core radius
Shell density
Core density
•
An increase in core radius leads to an
increase in C/MR2 and Cc/C
•
An increase in shell density yields an
increase in C/MR2 and Cm/C
Evolution of C, Cm in the parameter space
Core radius
•
An increase in core radius leads to an
increase in C/MR2 and Cc/C
•
An increase in shell density yields an
increase in C/MR2 and Cm/C
•
An increase in core density results in a
decrease in C/MR2 and Cc/C
Shell density
Core density
Parameters recovery
Fe-S models
Fe-Si models
Fe-S-Si
Parameters recovery
Fe-S models
Fe-Si models
Fe-S-Si
•
105-106 models per set (i.e. per color)
Parameters recovery
Fe-S models
Fe-Si models
Fe-S-Si
•
105-106 models per set (i.e. per color)
•
Error RMS against observed C/MR2 and Cm/C (noted x and y)
"
✓
◆2 ✓
◆2 !#1/2
1
xmodel xobs
ymodel yobs
RM S =
+
2
xobs
yobs
Outer radius of liquid core
Outer radius of liquid core
Fe-S models (low)
2034km (2007±31)
Outer radius of liquid core
Fe-S models (low)
2034km (2007±31)
Fe-Si models
2022km (2001±30)
Outer radius of liquid core
Fe-S models (low)
2034km (2007±31)
Fe-Si models
2022km (2001±30)
Fe-S models (high)
2042km (2066±25)
Outer radius of liquid core
Fe-S models (low)
2034km (2007±31)
Fe-Si models
2022km (2001±30)
Fe-S models (high)
2042km (2066±25)
Fe-S-Si
2023km (2017±29)
Outer radius of liquid core
Fe-S models (low)
2034km (2007±31)
Fe-Si models
2022km (2001±30)
Fe-S models (high)
2042km (2066±25)
Fe-S-Si
2023km (2017±29)
Fe-Si models +
dense basal mantle
layer
2022km (2014±29)
Outer radius of liquid core
Fe-S models (low)
2034km (2007±31)
Fe-Si models
2022km (2001±30)
Fe-S models (high)
2042km (2066±25)
Fe-S-Si
2023km (2017±29)
Fe-Si models +
dense basal mantle
layer
2022km (2014±29)
Bulk densities
Bulk densities
𝝆outer
Fe-S models (low)
3437kg/m3 (3217±192)
Fe-Si models
3390kg/m3 (3210±187)
Fe-S models (high)
3502kg/m3 (3732±183)
Fe-S-Si
3379kg/m3 (3377±201)
Fe-Si models +
dense basal mantle
layer
3364kg/m3 (3332±182)
Bulk densities
𝝆outer
Fe-S models (low)
𝝆inner
3437kg/m3 (3217±192) 6880kg/m3 (7211±308)
Fe-Si models
3390kg/m3 (3210±187) 6976kg/m3 (7250±292)
Fe-S models (high)
3502kg/m3 (3732±183) 6790kg/m3 (6538±185)
Fe-S-Si
3379kg/m3 (3377±201) 6982kg/m3 (7027±280)
Fe-Si models +
dense basal mantle
layer
3364kg/m3 (3332±182) 6997kg/m3 (7074±269)
Bulk densities
𝝆outer
Fe-S models (low)
𝝆inner
3437kg/m3 (3217±192) 6880kg/m3 (7211±308)
Fe-Si models
3390kg/m3 (3210±187) 6976kg/m3 (7250±292)
Fe-S models (high)
3502kg/m3 (3732±183) 6790kg/m3 (6538±185)
Fe-S-Si
3379kg/m3 (3377±201) 6982kg/m3 (7027±280)
Fe-Si models +
dense basal mantle
layer
3364kg/m3 (3332±182) 6997kg/m3 (7074±269)
Core composition
Core composition
•
The core composition (FeS, FeSi, Fe-S-Si) is not primordial in the
determination of Mercury’s interior structure
Core composition
•
The core composition (FeS, FeSi, Fe-S-Si) is not primordial in the
determination of Mercury’s interior structure
•
No constrain on core composition from the moments of inertia
So far, our understanding of the core composition is guided by geochemical
arguments
Core composition
•
The core composition (FeS, FeSi, Fe-S-Si) is not primordial in the
determination of Mercury’s interior structure
•
No constrain on core composition from the moments of inertia
So far, our understanding of the core composition is guided by geochemical
arguments
•
Fe-S-Si segregated core necessary for an FeS layer at the CMB:
Core composition
•
The core composition (FeS, FeSi, Fe-S-Si) is not primordial in the
determination of Mercury’s interior structure
•
No constrain on core composition from the moments of inertia
So far, our understanding of the core composition is guided by geochemical
arguments
•
Fe-S-Si segregated core necessary for an FeS layer at the CMB:
•
Need a minimum core mass fraction of ~6 wt % of S and Si
Core composition
•
Fe-S-Si segregated core necessary for an FeS layer at the CMB:
•
Need a minimum core mass fraction of ~6 wt % of S and Si
•
Also, argument on oxygen fugacity:
Fe-S-Si
Less reduced
Fe-S
Fe-Si
More reduced
Core composition
Fe-S-Si
Less reduced
Fe-S
Fe-Si
More reduced
« Anticrust »
« Anticrust »
•
Thickness of « anticrust » less than ~150km
« Anticrust »
•
Thickness of « anticrust » less than ~150km
•
Important for mantle convection: need for « cool » CMB
« Anticrust »
•
Thickness of « anticrust » less than ~150km
•
Important for mantle convection: need for « cool » CMB
Is there convection in Mercury’s mantle?
Magnetic shielding
Magnetic shielding
•
Skin effect: an electrically conductive layer tends to damp more the high frequency,
short wavelength components of the magnetic field
Magnetic shielding
•
Skin effect: an electrically conductive layer tends to damp more the high frequency,
short wavelength components of the magnetic field
•
Degree of attenuation depends on the thickness of this layer, and on its electrical
conductivity
Magnetic shielding
•
Skin effect: an electrically conductive layer tends to damp more the high frequency,
short wavelength components of the magnetic field
•
Degree of attenuation depends on the thickness of this layer, and on its electrical
conductivity
•
MESSENGER shows attenuation of harmonics >4
Magnetic shielding
•
Skin effect: an electrically conductive layer tends to damp more the high frequency,
short wavelength components of the magnetic field
•
Degree of attenuation depends on the thickness of this layer, and on its electrical
conductivity
•
MESSENGER shows attenuation of harmonics >4
Can one use this information to infer about the CMB layer’s thickness?
Constrains on the inner core
Constrains on the inner core
•
Mercury has a dipolar magnetic field → dynamo effect
Constrains on the inner core
•
Mercury has a dipolar magnetic field → dynamo effect
•
A stably stratified layer at the CMB constrains the convection to occur in the deeper
part of the core
Constrains on the inner core
•
Mercury has a dipolar magnetic field → dynamo effect
•
A stably stratified layer at the CMB constrains the convection to occur in the deeper
part of the core
•
The Si content of liquid and solid Fe-Si (i.e. inner core) is similar: weak motor for
thermosolutal convection
Constrains on the inner core
•
Mercury has a dipolar magnetic field → dynamo effect
•
A stably stratified layer at the CMB constrains the convection to occur in the deeper
part of the core
•
The Si content of liquid and solid Fe-Si (i.e. inner core) is similar: weak motor for
thermosolutal convection
•
Fe-S-Si around inner core would be an acceptable scenario, but would lead to a larger
inner core
Constrains on the inner core
•
Mercury has a dipolar magnetic field → dynamo effect
•
A stably stratified layer at the CMB constrains the convection to occur in the deeper
part of the core
•
The Si content of liquid and solid Fe-Si (i.e. inner core) is similar: weak motor for
thermosolutal convection
•
Fe-S-Si around inner core would be an acceptable scenario, but would lead to a larger
inner core
A new view on the internal structure
A new view on the internal structure
2001
A new view on the internal structure
2001
2012