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Somak Raychaudhury
Lecture 7
www.sr.bham.ac.uk/~somak/Y2SiU/
Guest Lecturer: Dr W. J. Chaplin
 Two-body problem
 Binary stars
Visual
Eclipsing
Spectroscopic
 How to find extrasolar planets
Two-body problem: centre of mass
The two bodies must have the same
angular speed ω, otherwise one body
will catch up with another and the force
will no longer be directed towards the
common centre of the circles.
Two-body problem: centre of mass
But
Types of binary stars
Visual Binary Stars
Orbit of Star 1
Centre of Mass
Orbit of Star 2
Astrometric binaries
Astrometric binaries are unresolved visual binaries
Sirius AB was first discovered as an astrometric
binary system, but now we can resolve them, so
they are visual binaries
Sirius A & B
Eclipsing binaries
In these stars, inclination is close
to 90 deg
Eclipsing binaries
Light curve of HIP 53806, from the
Hipparcos satellite.
This star varies between about
7.58 and 7.84 magnitudes, with a
period of 4.535 days
Spectroscopic Binaries
Spectrum of Hydrogen in Lab
Spectrum of stars- Obs 1
Spectrum of stars- Obs 2
Spectrum of stars- Obs 3
Spectrum of stars- Obs 4
What do these spectra tell us about the system?
Spectroscopic binaries
The absorption lines are
redshifted or blueshifted
as the star moves in its
orbit
Radial Velocity Curve
HDE 226868
Spectroscopic binaries: circular orbits
• The radial velocities are a sinusoidal function of time. The minimum and
maximum velocities (about the centre of mass velocity) are given by
v1max
 v1 sin i
r
v2max
 v2 sin i
r
where i is the angle of inclination
Measuring masses in a binary
Kepler 3:
Observed speeds
We know the value of i only if the binary
has eclipses
Methods of finding exoplanets
Pulsar
timing
1992
(PSR 1257+12)
Doppler
shift
Astrometry
Microlensing
Direct
obs.
Transit
1995
2002 ?
2003
2004
(51 Peg b)
(Gl 876 b)
(O235/M53)
(2M1207)
2000 and
2004
Exoplanets are extreme cases of binaries, where one
member is much less massive than the other. So we
can use some of the same techniques as binaries for
detection, and mass measurement. We’ll discuss
some of these methods.
(HD209458b)
Extrasolar planet searches
• As of last Friday, 429 planets have been detected
outside our solar system (http://exoplanets.org/)
Most of these have a<1 AU and masses
>MJupiter
Direct Detection: very hard
The albedo of the Earth is about AV=0.4.
Issues to think about: How bright is it in visible (reflected)
light, relative to the Sun? How do they compare at infrared
wavelengths, where Earth emits thermal radiation?
A picture of Earth, from
the surface of Mars,
just before sunrise.
Doppler Shifts: the #1 method
• This technique directly measures the velocity
imparted to a star by having planets going around it:
All gravitationally bound
systems orbit their
Centre of Mass (CM).
Here index 1 refers to the
Sun, and 2 to the planet
C.M. outside the surface of the Sun!
Sun’s wobble due to Jupiter
Here index 1 refers to the
Sun, and 2 to the planet
Period of Jupiter’s orbit=13.86 years
Speed of Jupiter around Sun=
We expect
Speed of Sun around c.m.=
Transits
• Imagine viewing the Earth-Sun system from a distant
star. By how much will the Sun fade during a transit of
the Earth? How about during a transit of Jupiter?
Planetary transits
• This is a fairly direct technique that relies on the
correct orientation of the solar system to give rise to
the transit of a planet across the face of its star.
Transits
• Detects a planet's
shadow when it
transits in front of its
host star.
• Can be used to
measure the radius of
a planet.
Transit method
Space Interferometry mission
• NASA: Would have searched for terrestrial planets
around the nearest ~250 stars, with astrometry accurate
to 1mas. Cancelled in 2010
Kepler
• NASA mission launched in 2009
• Searching for large numbers of stars for Earth-sized
terrestrial planets using the transit method.
Field of view
Cygnus-Lyra
regions along
the Orion arm
NASA Kepler Mission
• Finding Earth-like planets
• Formal seismology component:
Kepler
Asteroseismology Investigation (KAI)
• KAI has an international consortium of ~400 scientists called the
Kepler Asteroseismology Science Consortium (KASC)
http://kepler.asteroseismology.org
NASA Kepler Mission
• Nominal mission 3.5 yr (up to 10 yr)
• Will observe Sun-like and classical pulsators:
– Survey Phase: 1-month data on ~1500 Sun-like stars!
– Long-Term Phase: data for several years on 100
Sun-like stars
Kepler Results
Chaplin et al. (2010)