Astronomy 340 Fall 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 H 2 O 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 & T b  B = 2kT/λ 2  T b = c 2 B ν /2kν 2 Jupiter’s emission  T = 130 K  W m -2 Hz -1  Real emission is W m -2 Hz -1  K!!!

Jupiter’s Magnetic Field Planck Function & T b  B = 2kT/λ 2  T b = c 2 B ν /2kν 2 Jupiter’s emission  T = 130 K  W m -2 Hz -1  Real emission is W m -2 Hz -1  K!!!  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 B 2 /8π = n e mv 2 / 2R J 2 V = 400 km/s, n = 10 cm -3 V = velocity of solar wind, n = density of solar wind R J = 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  L p /L * = p(λ,α)(R p /a) 2 α  angle between star and observer as seen from planet p  geometric albedo Ratio ~ 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 M p sin i, not M p 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 = (M p /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 1 st “planet” detected was around a pulsar  hard to believe! Planet causes a tiny wobble which would affect timing of pular  Τ p = 1.2 (M pulsar /M planet )(P/1 year) 2/3 ms Discovery of few Earth mass sized objects around pulsar PSR 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 ~ (R p /R * ) 2  Tiny fractions for terrestrial planets  Timing – transits are short!  Τ = (P/π)(R * cosδ + R p )/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?