1. Somak Raychaudhury www.sr.bham.ac.uk/~somak/Y2SiU/  Two-body problem  Binary stars  Visual  Eclipsing  Spectroscopic  How to find extrasolar planets Lecture 7 Guest Lecturer: Dr W. J. Chaplin

2. 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.

3. Two-body problem: centre of mass But

4. Types of binary stars

5. Visual Binary Stars Orbit of Star 1 Orbit of Star 2 Centre of Mass

6. 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

7. Eclipsing binaries In these stars, inclination is close to 90 deg

8. 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

9. 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

10. Spectroscopic binaries The absorption lines are redshifted or blueshifted as the star moves in its orbit

11. Radial Velocity Curve HDE 226868

12. 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 where i is the angle of inclination

13. Measuring masses in a binary Kepler 3: Observed speeds We know the value of i only if the binary has eclipses

14. Methods of finding exoplanets 2004 (2M1207) Direct obs. 2002 ? (Gl 876 b) Astro- metry 2003 (O235/M53) 1995 (51 Peg b) Micro- lensing Doppler shift Transit 2000 and 2004 (HD209458b) Pulsar timing 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.

15. Extrasolar planet searches As of last Friday, 429 planets have been detected outside our solar system (http://exoplanets.org/)http://exoplanets.org/ Most of these have a M Jupiter

16. Direct Detection: very hard The albedo of the Earth is about A V =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.

17. Doppler Shifts: the #1 method This technique directly measures the velocity imparted to a star by having planets going around it:

18. 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!

19. 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

20. Measuring masses in a binary Kepler 3: Observed speeds We know the value of i only if the binary has eclipses

21. 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?

22. 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.

23. 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.

24. Transit method

27. Space Interferometry mission NASA: Would have searched for terrestrial planets around the nearest ~250 stars, with astrometry accurate to 1  as. Cancelled in 2010

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

29. Cygnus-Lyra regions along the Orion arm Field of view

33. 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

34. 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

35. Kepler Results Chaplin et al. (2010)