Astronomy 340Fall 2005

6 December 2005

Class #27

Review

What are the orbital differences between classical and resonant KBOs?

How does the distribution of particle size differ between that found in the rings of Saturn and the population of KBOs?

Generating a global magnetic field

Review

What are the orbital differences between classical and resonant KBOs?

How does the distribution of particle size differ between that found in the rings of Saturn and the population of KBOs?

Generating a global magnetic field Rotation Fluid, conducting region covection

Planetary Magnetic Field

Flavors of global magnetic field

Planetary Magnetic Field

Flavors of global magnetic field Remnant solidified rocks (e.g. magnetite) Dynamo Induced by solar wind

Terrestrial Planets

Planetary Magnetic Field

Flavors of global magnetic field Remnant solidified rocks (e.g. magnetite) Dynamo Induced by solar wind

Terrestrial Planets Moon’s B-field associated with crater basins

(youngest material) Mars residual did it once have a dynamo? Venus lacks current B-field slow rotation?

Earth’s Dynamo

Differentiation Solid inner core, liquid outer ccore Viscosity – need liqud H2O for liquid Fe at those

conditions Convective velocity ~10 km s-1

Cooling of the Core Convection still partially driven by chemical

convection conduction

Earth’s Dynamo

B-field amplified via twisting (convection + rotation) at core-mantle boundary B ~ (2ρΩ/σ)1/2

Other planets? Probably similar Note alignment what’s up with Uranus? Jupiter

Rotation yes Convection yes Conducting medium yes metallic H

Jupiter’s Magnetic Field

Planck Function & Tb

B = 2kT/λ2

Tb = c2Bν/2kν2

Jupiter’s emission T = 130 K 10-35 W m-2 Hz-1

Real emission is 10-19 W m-2 Hz-1 1018K!!!

Jupiter’s Magnetic Field

Planck Function & Tb B = 2kT/λ2

Tb = c2Bν/2kν2

Jupiter’s emission T = 130 K 10-35 W m-2 Hz-1

Real emission is 10-19 W m-2 Hz-1 1018K!!! Non-thermal emission

Relativistic particles + B-field synchrotron emission at radio frequencies accounts for most of the radio emissoin

Jupiter’s Magnetic Field

Shielding from solar wind magnetic pressure

B2/8π = nemv2/ 2RJ2

V = 400 km/s, n = 10 cm-3

V = velocity of solar wind, n = density of solar windRJ = distance to Jupiter from Sun

Pressures balance at 33 Jupiter radii

Jupiter’s Magnetic Field

Extrasolar Planets

Detection Methods

Extrasolar Planets

Detection Methods Radial velocity variation Astrometry Direct imaging transients

Imaging

Detection of “point source” image reflected stellar light Lp/L* = p(λ,α)(Rp/a)2

α angle between star and observer as seen from planet

p geometric albedo Ratio ~ 10-9 for Jupiter

Difficulties Planets are overwhelmed by starlight Separations are tiny need space

interferometry, adaptive optics

Dynamical Perturbation

Motion of planet causes reflex circular motion in star about the center of mass of star/planet system

Observables:

Dynamical Perturbation

Motion of planet causes reflex circular motion in star about the center of mass of star/planet system

Observables: Radial velocity variations Variations in position (astrometry) Variation in the time of arrival of some reference

signal (generally used for pulsars)

Radial Velocity Variations

Just use Newton and Kepler….we’ll do this on the board…

Radial Velocity Variations

Just use Newton and Kepler….we’ll do this on the board…

For Jupiter-Sun system K = 12.5 m s-1 with a period of 11.9 years

For Earth-Sun system K = 0.1 m s-1

Only measure Mpsin i, not Mp

All extrasolar planets were initially detected using radial velocity variations Resolution of 15 m s-1 are possible but keep in mind the

orbit times! Might get down to 1 m s-1

Astrometric Position

Star moves a bit as it orbits about the center of mass

Angular semi-major axis:

α = (Mp/M*) (a/d) Units: a (AU), d (pc) Jupiter-Sun system viewed from 10 pc away 500μas Earth-Sun 0.3μas

Need space interferometry impossible from the ground

Timing

1st “planet” detected was around a pulsar hard to believe!

Planet causes a tiny wobble which would affect timing of pular Τp = 1.2 (Mpulsar/Mplanet)(P/1 year)2/3 ms

Discovery of few Earth mass sized objects around pulsar PSR 1257+12

Where did they come from? Survived the SNe? Captured Formed after the formation of the neutron star

Transits/Reflections

How does planetary motion affect the apparent brightness of the star?

In suitable geometry, planet blocks out part of the star 2% for a Sun-Jupiter system ΔL/L ~ (Rp/R*)2

Tiny fractions for terrestrial planets 10-5

Timing – transits are short! Τ = (P/π)(R*cosδ + Rp)/a = 13(M*)-1/2(a)1/2(R*) h

In units of solar masses, solar radii, and AU 25 hours for jupiter 13 hours for Earth

Maybe a large survey of large numbers of possible stars?