Somak Raychaudhurywww.sr.bham.ac.uk/~somak/Y2SiU/

Two-body problem Binary stars

VisualEclipsingSpectroscopic

How to find extrasolar planets

Lecture 7Guest Lecturer: Dr W. J. Chaplin

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

Orbit of Star 2

Centre of Mass

Astrometric binariesAstrometric 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

What do these spectra tell us about the system?

Spectrum of stars- Obs 2

Spectrum of stars- Obs 3

Spectrum of stars- Obs 4

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

ivv

ivv

r

r

sin

sin

2max2

1max1

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

2004(2M1207)

Direct obs.

2002 ?(Gl 876 b)

Astro-metry

2003(O235/M53)

1995(51 Peg b)

Micro-lensing

Dopplershift

Transit

2000 and 2004

(HD209458b)

Pulsartiming

1992(PSR 1257+12)

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.

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 hardThe 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!

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.=

Sun’s wobble due to Jupiter

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 1as. Cancelled in 2010

Kepler

• NASA mission launched in 2009• Searching for large numbers of stars for Earth-sized terrestrial planets using the transit method.

Cygnus-Lyra regions along the Orion arm

Field of view

• 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

NASA Kepler Mission

Kepler ResultsChaplin et al. (2010)