Phys 1830: Lecture 28

1. Phys 1830: Lecture 28 Shapely 1, Malin Registrars Office: Exam locations available at the end of November. • Previous Classes: • Stars: Luminosity, Temperature, Radii • Hertzsprung-Russell Diagram • This class: • Radii, Mass, Lifetime on Main Sequence • Stellar evolution: star birth and death of a star with 1 solar mass. • Next Classes: • Stellar Evolution: 1 solar mass and more massive stars. • black holes

2. Stars: Hertzsprung-Russell Diagram How do we get the radius of a star? Can we do it with imaging? • Given the temperature we need to know the radius to get the luminosity. • Similarly if we know the luminosity we need the radius to get the temperature.

3. Red Giant “Toby Jug” HST Proxima Centauri ~ 4 ly – our nearest neighbour Can’t see surface features Resolve material around a star • Very Large Telescope, Chile

4. Stars: Radii – Speckle Interferometry Michael Richmond • Atmospheric seeing means that the image of the star dances around on our detector.

5. Stars: Radii – Speckle Interferometry • Take short exposures to freeze the motion (left). • Process each frame to reconstruct image without atmospheric seeing (right). • Done for a few dozen nearby, large stars.

6. Stars: Radii – Adaptive Optics European Southern Observatory/Very Large Telescope. Yuri Beletsky • Uses a very bright star to assess the turbulence in the atmosphere. • The star can be artificially created using a laser. • Knowing how the atmosphere is behaving, the mirror is deformed to compensate.

7. Stars: Radii – Adaptive Optics Gemini Observatory Mirror used by the Institute of Astronomy. • A deformable mirror can be placed within the optical system. • The mirror backing is made of a material that moves when an electrical voltage is applied. • The voltage is applied with actuators. There are 85 actuators on this mirror.

8. Stars: Radii – Adaptive Optics UBC Liquid Mirror Telescope • Researchers at Laval University are now testing ferromagnetic liquids for liquid mirror telescopes. • The primary mirror can be distorted by magnets.

9. Stars: Radii – Adaptive Optics - Example • Adaptive optics applied to the globular cluster M 13. • Note that these stars are still points of light – we are not seeing the surface of each star.

10. Stars: Radii – Adaptive Optics - Example ESO/VLT Adaptive Optics Betelgeuse (Not on same scales.) • Left: Constellation Orion with Betelgeuse • Middle: Betelgeuse with regular optics. The point of light is spread out forming a disk that is unrelated to the size of the star. • Right: 37 milliarcsec resolution with adaptive optics • roughly the size of a tennis ball on the International Space Station (ISS) as seen from the ground. • 0.0037 arcsec c.f. 0.04 arcsec on HST  Adaptive optics in the IR is an order of magnitude better!

11. Stars: Radii – Interferometry • Can use optical/IR telescopes as interferometers. • Synthesize a larger mirror size.

12. Stars: Radii – Interferometry - Example AMBER Consortium VLTI/ESO Wide Field Imaging Adaptive Optics Interferometry • Can resolve an apparent star into a star and a companion star.

13. Stars: Radii – Interferometry - Example Artist’s Illustration of Betelgeuse • detect indirectly details four times finer still than the adaptive optics images had already allowed (in other words, the size of a marble on the ISS, as seen from the ground). • “The AMBER observations revealed that the gas in Betelgeuse's atmosphere is moving vigorously up and down, and that these bubbles are as large as the supergiant star itself. Their unrivalled observations have led the astronomers to propose that these large-scale gas motions roiling under Betelgeuse’s red surface are behind the ejection of the massive plume into space.”

14. Dusty Arcs in environment of Betelgeuse • ESA’s Hershel Space Observatory • FIR and submm • Arcs moving at 30 km/s will collide with ISM filament on left in 5000 yrs

15. Stars: Radii – Interferometry - Example T Leporis VLTI/ESO • One of the sharpest colour images ever made. • The central disc is the surface of the star, which is surrounded by a spherical shell of molecular material expelled from the star • Resolution is about 4 milli-arcsec (as small as a two-storey house on the Moon). • obtained by combining hundreds of interferometric measurements • the blue channel includes infrared light from 1.4 to 1.6 micrometres, the green, from 1.6 to 1.75 micrometres, and the red, from 1.75 to 1.9 micrometres. • In the green channel, the molecular envelope is thinner, and appears as a thin ring around the star.

16. Stars: Radii Resolved Stars Unresolved Stars • Majority of images are of unresolved stars. • Note there are diffraction spikes. • The apparently “bigger” stars are brighter, not larger in actual size. • How do we get the radii of these stars?

17. Review • To get the radii of the stars in this image we measure the diameter of the star on the image in arcsec. We then find the distance using the parallax method. This allows us to convert arcseconds into linear units such as kilometres. • True • False

18. Stars: Radii • T from • Spectral Class, or • Photometry • If we know the surface temperature (T) and the luminosity (L) of a star then we can determine the radius (r).

19. Stars: Radii • L from • Inverse square brightness law. • Distance from parallax (e.g. Hipparcos data). • Measure apparent brightness. • Periodically varying stars like Cepheid variables have a known luminosity. • Measuring the width of the spectral lines in a star’s atmosphere. • Line width depends on density. • Density is well-correlated with luminosity, generating luminosity classes. •  Distinguish supergiants, giants, main sequence stars and white dwarfs.

20. Stars: Hertzsprung-Russell Diagram • Luminosity class is based on the width of the spectral line and roughly indicates the radius.

21. Review: • Can we have a low surface temperature star with a high luminosity? • Yes, if the radius is large. • No, if the star’s surface is cool it must also be dim. • No, since the temperature at the surface doesn’t tell us about the luminosity produced in the core.

22. Stars: Red Giants • E.g. Antares by David Malin. • Dust grains floating away  very tenuous surface. • Low T, high L  R very large (e.g. 100s x radius of sun). • Masses are up to 100 solar masses. • Nuclear fusion creates carbon, silicon, oxygen which are expelled into space, polluting the interstellar medium.

23. Stars: White Dwarf HST Binary system of Sirius A and Sirius B • E.g. Sirius B (Bond et al.). Dot in left corner. • High T, low L  R very small (e.g. size of Earth). • Masses ~ 1 solar mass, but a million times denser.

24. review a) b) c) • One can find the radius of a point source star using which of the following relationships: d) e) One can’t measure the radius of a point source even if it is a star.

25. Stars: Luminosity, Temperature and Radius on H-R diagram • The position of a star on the H-R diagram will depend on its mass, composition, and stage of evolution. • The lifetime of a star on the main sequence depends on its mass.

26. Stars: Mass (Do this derivation as homework.) • The majority of stars are in pairs – binary systems.  Mass of a star is determined by the velocity of the companion (squared) times the distance between the stars (r = radius of of the orbit).

27. Most stars are in binaries – a pair of stars in one system. • protostars forming as a pair • emit flashes – probably as disk material falls on them when they are close together.

28. Stars: Mass • Visual binary  r and velocity • Velocity from distance/time v = circumference of ellipse/Period of orbit. • Also can use Doppler shifts and light curves to constrain masses.

29. Review: • Masses of stars can only be determined for stars on the main sequence. • True • False

30. Stars: Masses on Main Sequence • Determined from measurements: • Mass is related to radius and luminosity (low mass, low luminosity). • Few percent are giants and supergiants.

31. Stars: MS Lifetimes Depend on Mass • Main sequence star: • H burning in the core • Energy and radiation • Hydrostatic equilibrium • When the fuel in the core is consumed then the star is no longer in hydrostatic equilibrium. It evolves off the MS, through various stages. • Most of its life is on the MS – what is its MS lifetime?

32. Stars: MS Lifetimes Depend on Mass • Lifetime = amount of fuel --------------------- rate of energy liberation • Both the fuel and rate are determined by mass. • In a more massive star the core has higher density  higher temperature • This gives more nuclear reactions so the fuel is burned faster.

33. Stars: MS Lifetimes Depend on Mass On MS only, the rate of energy liberated is the luminosity Therefore • Lifetime = amount of fuel --------------------- rate of energy liberation

34. Stars: MS Lifetimes Depend on Mass Massive stars live fast and die young! Star P is ten times as massive as star Q. Compared to star Q: • Star P has a longer life time. • Star P has a shorter life time. • They both have the same life time.

35. Stars: MS Lifetimes Depend on Mass Substitute in mass of P and life time of Q Re-arrange the equation. • Star Q has a life time of 10 billion years. What is the life time of star P that has 10 times the mass of star Q. The MS life time of star P is only 10 million years!

36. Stars: Stellar Populations • When a massive star explodes as a supernova at the end of its life, it also pollutes the interstellar medium with elements, many fused during the explosion.

37. Stars: Stellar populations • New stars form out of the polluted interstellar medium. • These stars have more elements.