Solar System

Evidence of interior convection in the Sun

Surface granulation (light and dark spots on the photosphere)

Helioseismology

• study of standing pressure waves visible at surface

• carry information about temp profile, pressure profile, density profile, rotation

• informs numerical models about sun’s interior e.g. boundary between convective and radiative regions

Sunspots

• cooler regions of enhanced magnetic fields

• revealed by Zeeman splitting of absorption lines

• formed from differential rotation of the sun warping magnetic fields, preventing convection in some areas, leading to cooler regions

What causes magnetic flux loops in the Sun?

• magnetic dynamo

• requires bulk shearing

• shearing comes from differential rotation (equator rotates faster than poles) and tachocline (core rotates as a solid body)

Seeing the solar atmosphere

• extended atmosphere, Corona, visible during eclipse

• light scatters from electrons

• can see photosphere in optical where sun goes from optically thick to thin

• in extreme UV, gamma and X-ray, can see emission from hot plasma. Shows temperature inversion.

How is the emitted plasma confined?

• confined in mag. field loops

• Lorentz force

How can coronal plasma escape?

travels along ‘open field lines’ via solar winds

Temperature of Sun’s corona

10⁷ K

Mass loss of the sun consequences

• ~ 3×10^-14M☉ per year

• significant for ang. mom. loss and spin down as wind co-rotates with sun

• leads to significant magnetic braking

• explains slow rotation of sun

Heliosphere

Bubble blown in interstellar medium by solar wind ~ 120 au

Solar flares

• sudden releases of magnetic energy and X-ray emission

• driven by magnetic reconnection in coronal flux loops

Coronal Mass Ejections

• space weather at Earth and causes aurora

• erosion of planetary atmospheres

3 classes of planets

• terrestrial

• gas giants

• ice giants

Where are dwarf planets, asteroids and comets found?

• asteroid belt

• Kuiper belt

• Oort cloud

Nebular Hypothesis

• sun and planets formed together from gravitational collapse of gas with shared ang. mom.

• comes from planets being in mostly circular orbits in ecliptic plane, well aligned with sun

Definition of a planet

• in orbit around the sun

• in hydrostatic equilibrium (spherical)

• has cleared its neighbourhood orbit

Equilibrium temperature of a planet

Geocentric model of Solar System

• Earth centred

• occasional retrograde motion explained with epicycles (circular motion around an average circular motion)

Heliocentric model of the Solar System

• Copernicus

• retrograde motion explained as Earth overtakes planets

• but still required epicycles as orbits assumed circular

Kepler’s Laws

• planet orbits the sun in an ellipse with the Sun at a focus of the ellipse

• a line connecting a planet to the Sun sweeps out equal areas in equal time

• P² = ka³ (k found from Newton’s laws of gravity)

Eccentricity values corresponding to allowed orbits

• e = 0 => circular

• 0<e<1 => elipse

• e = 1 => parabola

• e > 1 hyperbola

One body problem

• mass of one object dominates

Two body problem

• both masses significant

General version of Kepler’s third law

Three body problem

• generally no analytical solutions

• consider instead restricted 3 body problem

Restricted 3 body problem

• 3rd mass negligible

• stable orbits in Roche Potentials at Lagrangian points

Lagrangian points

areas where gravitational potential is locally flat

Hill Sphere

Approximate sphere of influence around a body where orbits can be stable

Alternative 3 body case

• one mass dominates, other bodies treated as perturbations

• leads to secular resonance in eccentricity and inclination

• e.g. Milankovitch cycles

What happens if periods between bodies have integer ratios

• perturbations grow in mean motions resonances

• often drives systems unstable

Tidal interactions

• come from differential gravity across an object

• lead to tidal bulges

• bulges offset by rotation

• grav. force acts to synchronise rotation with the orbit

• tidal locking

Tidal forces and eccentricity

• eccentric orbits misalign tidal bulges after synchronisation

• dissipation of energy and heating of moon through internal friction

• orbit loses energy at constant ang. mom.

• circularisation of orbit

Roche Limit

When tidal forces on a body are greater than the self gravity holding it together, leading to the breaking apart of the body.

Earth interior

Differentiated into layers

• iron core

• silicate mantle

• curst of lighter minerals

Heavier materials sank when planet molten

How is Earth’s interior probed?

seismology

• p-waves (pressure: solids and liquids)

• s-waves (shear: solids only)

shadow zones of these waves allow interior to be mapped

Refractory compounds

solids at high temperatures

How can we tell Earth was formed in a warm environment?

• interior dominated by Fe, O, Si, Mg

• deficient in volatile elements e.g. H, C, N

• formed in warm environment where H₂O, CH₄, CO₂, NH₃ didn’t form solid

How does Earth’s interior remain hot?

Radioactivity

What is the origin of Earth’s strong magnetic field?

magnetic dynamo

Plate tectonics details

• fractured lithosphere moving on convecting asthenosphere

• new crust created at mid ocean ridges

• reveals polarity reversals in Earth’s magnetic field

• strong evidence for a dynamo operating in Earth

Where do volcanic Islands form?

Above mantle plumes

Lunar AND Martian Seismology results

• thick lithosphere

• molten core

• no global mag. field => no dynamo

• evidence of global mag. field in past

• marsquakes and moonquakes

Interior of Venus

• no seismology

• volcanically active but lacks plate tectonics and magnetic field

• not well understood

Mercury interior

• high density indicates oversized iron core

• iron core plus tidal heating may explain weak mag. field

• may have lost mantle in giant collision

Moon surface

• heavily cratered => ancient

• age of craters measured using radioisotope dating

• lunar surface covered with regolith - fine powder from many impacts

Radioisotope dating equation

B’ denotes isotope of B that has constant abundance in time

Surface ages of planets

• mercury - >4Gyr

• Mars - ~2Gyr

• Venus- ~1 Gyr

• Earth ~ surface <600Myr old, rocks found up to 3.8 Gyr

What causes pancake domes on Venus

• lithosphere too thin to support large volcanos

• volcanos collapse under their own weight

Earth atmosphere

• 1 Bar, ~80% N, ~20% O

• greenhouse effect raises surface temperature

• temperature inversions in stratosphere (UV heating in ozone layer) and thermosphere (X-ray heating)

Mercury and Moon atmospheres

surface gravity too low to retain significant atmospheres

Mars atmosphere

• ~1% Earths, 95% CO₂, 3% N

• T_p~ 189K, T_s ~ 130 - 308K

• surface temp range due to day/night, seasons and poor heat redistribution

Venus atmosphere

• ~100 x Earth, 96% CO₂, 4% N

• T_p ~ 230K, T_s ~735K

Greenhouse effects

• atmospheres transparent to heating from Sun in optical

• opaque to outgoing IR radiation due to molecular absorption

Surface temperature equation

Why are Earth and Venus’ atmospheres so different?

• Earth’s climate stabilised by negative feedback loop from carbon-silicate cycle

• On Venus, positive feedback loop led runaway greenhouse

• Earth not heated enough for runaway greenhouse

What happened to water on venus?

• water split by UV photolysis into H & O

• supported by excess deuterium on Venus which is less vulnerable to evaporation than H

Atmosphere mass escape rate

• lighter elements more vulnerable to escape (Jeans Escape)

• driven by solar X-ray heating of upper atmosphere

• also driven by solar wind for planets without global mag. field

• escape rate energy limited

What protects water on Earth from UV photolysis?

• Ozone layer

• trapped lower in atmosphere and condenses to clouds

Siderial day

true rotation period of Earth

Rotation of planet details

• Earth and Mars rapid rotators

• Mercury (3:2 resonance with orbit) and Venus (retrograde rotation) slow rotators due to tidal interactions with Sun

• Tides also slowing rotation of Earth, seen in sea shell fossil record

Spin obliquity

• precession of spin axis due to torque from Sun

• obliquity of Mars varies due to small torques from other planets

• obliquity of earth stabilised by moon

Gas giant

dominated by H + He

Ice Giant

• mass dominated by ices of H₂O, NH₃, CH₄

• volume dominated by H, He

Density profile for planet

Radius at which density is zero

Central density of a planet

At what state is hydrogen in in the core of Jupiter and Saturn

• rocky/ icy cores

• surrounded by layer of metallic H

• Saturn has smaller metallic layer

Oblation of Jupiter and Saturn

• flatter at poles

• caused by fast rotation

• bends spherical symmetry

How can we probe the interior of gas giants?

• gravitational potential gives a measurement of density profile and north south asymmetries

• see banding pattern extends to deep interior

• implies global convection

Magnetic field of gas giants

• convection, rotation, conducting interior imply magnetic dynamo

• explains strong mag fields

Consequences of strong magnetic field

• aurorae at poles

• radio emission via cyclotron/synchrotron emission

What do strong magnetic moment and lower solid wind flux at 5 Au imply about Jupiter?

Jupiter has a very large magnetosphere (about 5 times radius of the Sun!)

Radius of magnetosphere

Magnetic fields of ice giants

• strong despite lack of metallic H

• complex corkscrew magnetospheres due to high spin obliquity and dipoles misaligned with spin axis

Internal heat of Jupiter

• heat from gravitational potential energy left from formation

• ongoing differentiation from He rainout, releasing gravitational potential

Internal heat of Saturn

ongoing differentiation from He rainout, releasing gravitational potential

Internal heat of neptune

Ongoing differentiation of metals/rocky

What causes Jupiter’s banding pattern?

• bright zones from clouds of ammonia ice

• dark belts from molecules from UV photochemistry

Why is Jupiter’s banding pattern reversed in UV?

• high altitude clouds are cold and dark

• cloud free belts are brighter as seeing into high temps

Where do storms form in Jupiter’s atmosphere?

Shearing boundaries

Why is Saturn’s banding pattern muted?

• clouds form deeper in colder atmosphere

• occasional storms bring reflective NH₃ clouds at higher altidtudes

Neptune muted banding pattern

NH₃ ice clouds deeper

Where does Neptune’s blue colour come from?

• enhanced methane abundance

• methane atoms absorb in red optical

Uranus atmosphere

• almost featureless

• faint banding

• white clouds now visible, potential seasons

Trend in density for the moons of Jupiter

• decreases with increasing separation

• due to increased ice content

• due to temp gradient in disc moons formed from and tidal heating

Io

• rocky core

• volcanic

• young surface

Europa

• rocky core

• young icy surface

• resurfaced by liquid water from tidally heated sub-surface ocean

Ganymede and Callisto

• mass dominated by ice

• older cratered surfaces

• geologically active

Titan

• thick N₂ atmosphere

• liquid methane lakes

Enceladus

• tidally heated liquid water oceans below thin ice crust

Triton

• probably a dwarf planet from Kuiper belt due to retrograde orbit

• may have destabilised early Neptune

Saturn Rings

• Ice particles

• Complex structure due to orbital resonance with moons

• Thin due to collisions

• Probably formed from icy moon

Snowline

Boundary between terrestrial and giants

Planet formation by core accretion

• formation of young sun & protoplanetary disc from gravitational collapse

• Condensation of dust particles

• Growth of particles by pair-wise collisions up to planetesimals

• Planetesimal growth to protoplanets, stops at isolation mass when Hill Sphere swept out annulus of disc

• More massive cores form beyond snowline where ices form

• Massive cores accrete gas

• Terrestrials assembled via giant collisions

2 problems with planet formation by core accretion theory

• particles eroded by high velocity collisions

• Gas drag causes large particles to fall to the sun

Solutions to problems in planet formation by core accretion

• structures in disc can trap particles

• Instabilities can cause clumps of particles shielding from headwinds

Difference in formation of gas and ice giants

• Gas giant from runaway process that forms disc annulus

• Ice giant from dispersion of gas during slow gas accretion phase

Evidence for giant collisions in the early solar system

• composition of Earth’s moon same as Earth

• High density of mercury, missing mantle

• Spin obliquity of Uranus

Extremophiles

Bacteria that survive in extreme conditions e.g. around hydrothermal vents

Fundamental requirements for life

• energy source

• Carbon source

• Liquid water