Searching for Extra-Solar Planets
Techniques for Detecting Exoplanets
Direct Observation - use reflected light from star or infrared from planet
Astrometry - measure change in star’s position due to planet
Doppler Spectroscopy - measure doppler induced by planet-star gravity
Transit Photometry - plot decrease in star brightness as planet passes
Microlensing - use intervening bodies to amplify planet radiation
Pulsar Timing - measure variation in pulsar timing Exoplanet Detection Techniques
Astrometry
Radial Velocity
Transit
Microlensing State of Current Technology in Direct Detection
Direct detection uses reflected star light or the planets infrared radiation - both are much weaker than the star’s light
Even the largest ground based telescopes (8-10m) require additional techniques - adaptive optics to combat atmosphere perturbation - coronagraphy to block light from star - interferometry to increase resolution
Direct detection of exoplanets remains very challenging
Visual Image of Star and Planet
100,000 times weaker Coronagraph Image of Star and Planet
1000 times weaker Detecting Exoplanets Direct Observation - use reflected light from star or infrared from planet
Astrometry - measure change in star’s position due to planet
Doppler Spectroscopy - measure motion induced by planet-star gravity
Transit Photometry - measure decrease in star brightness as star passes
Microlensing - use intervening bodies to amplify planet radiation
Pulsar Timing - measure variation in pulsar timing
A Star and Planet Orbiting Around their Common Centre of Mass
Msxas=Mpxap
as
ap Direct Measurement of A Star’s Motion
β Determining Planet Mass
Star mass determined from the mass-luminosity relationship
Planet mass determined from Kepler’s law and orbital period β is angular displacement so P is orbit period m = K βd M 2/3 d is distance from sun P k is the gravitational constant
Limited to nearby stars where angle can be measured Determining Planet Mass
Star mass determined from the mass-luminosity relationship
Motion of Sun as seen at 30 LY
Detection using Doppler Spectroscopy Doppler Shift Doppler Shifted Spectrum Doppler Shift
The recession velocity of a star is
vr = ∆λ c λ
where vr = recession velocity ∆λ = shift in wavelength λ = emitted wavelength c = speed of light Radial Velocity for 51 Pegasi
Period = 4 days Deriving Exoplanet Mass
Starting with the centripetal force on the star
2 Fs = Mv a
and a few lines of algebra, we get
v = Km (radial velocity) ( PM2 )1/3
So knowing the period (P) and the star’s mass (M), can compute the planet mass (m) Determining Planet Mass
Star mass determined from the mass-luminosity relationship
Planet mass determined from Kepler’s law and orbital period
But only determine lower limit to mass
msin(io) since orbits may not be face on
Ambiguity in Determining Radial Velocity and Mass of a Planet
Can only compute msin(io), a lower limit Detecting Planet Transit
A DIFFERENT APPROACH
• Radial velocity (Doppler spectroscopy) method unable to detect Earth-size planets • Earth-like planets are about 300 times less massive and about 100 times smaller in area than Jupiter • Need a different approach that can detect smaller planets • No method exists for detecting habitable planets from ground-based observatories • The Kepler Mission uses photometry to detect transits and can detect Earth-size planets from space • The Kepler Mission is optimized to detect habitable planets in the habitable zone of solar- like stars Exoplanet encyclopedia http://exoplanet.eu 23 DETECTING EARTH-SIZE PLANETS • The relative change in brightness (DL/L) is equal to the relative areas (Aplanet/Astar)
Jupiter: Earth or Venus 1% area of the Sun (1/100) 0.01% area of the Sun (1/10,000)
• To measure 0.01% must get above the Earth’s atmosphere • Method is robust but you must be patient: Require at least 3 transits preferably 4 with same brightness change, duration and temporal separation
24 Gravitational Lensing
One implication of Einstein’s theory of General Relativity is that space is curved by the presence of mass
It follows that light passing a massive object will follow a curved rather than straight path
This fact was demonstrated in a famous set of experiments in 1919 by Edington Gravity Bends Light Gravitational Lensing
source
apparent image Einstein Rings Gravitational Lensing Calculus*
The mass of the lensing star is
2 m = dβe 2K where βe is angular radius of the ring d is the distance to the star
The light amplification is
μ = βe β where β is angle between source and lens *see Gilmour, chapt. 6
Light Curve for Lensing Star with Planet Exoplanet Detection Techniques
Technique Planets Confirmed*
Radial velocity 632
Transit 2728
Direct imaging 44
Gravitational lensing 45
Astrometry 1 Total 3450
*As of July 2015 >5000 with >2500 confirmed