summary Phys 1830 Lecture 28 Recall column Shapely

summary Phys 1830: Lecture 28 Recall column 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

Stars: Hertzsprung-Russell Diagram summary Recall column 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.

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

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

Stars: Radii – Speckle Interferometry summary Recall column • 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.

Stars: Radii – Adaptive Optics summary European Southern Observatory/Very Large Telescope. Yuri Beletsky Recall column • 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.

Stars: Radii – Adaptive Optics summary Recall column 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.

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

Stars: Radii – Adaptive Optics - Example summary Recall column • 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.

Stars: Radii – Adaptive Optics - Example summary Recall column 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!

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

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

Stars: Radii – Interferometry - Example Recall column summary 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. ”

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

Stars: Radii – Interferometry - Example summary T Leporis VLTI/ESO Recall column • • • 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 twostorey 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.

Stars: Radii summary Recall column 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?

Review summary Recall column • 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. a) True b) False

Stars: Radii summary Recall column • If we know the surface temperature (T) and the luminosity (L) of a star then we can determine the radius (r). • T from 1. Spectral Class, or 2. Photometry

Stars: Radii summary Recall column • L from 1. Inverse square brightness law. 1. Distance from parallax (e. g. Hipparcos data). 2. Measure apparent brightness. 2. Periodically varying stars like Cepheid variables have a known luminosity. 3. Measuring the width of the spectral lines in a star’s atmosphere. 1. Line width depends on density. 2. Density is well-correlated with luminosity, generating luminosity classes. Distinguish supergiants, main sequence stars and white dwarfs.

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

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

Stars: Red Giants summary Recall column • E. g. Antares by David Malin. • Dust grains floating away very tenuous surface. • Low T, high L R very large (e. g. 100 s 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.

Stars: White Dwarf summary Recall column 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.

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

Stars: Luminosity, Temperature and Radius on H-R diagram summary Recall column • 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.

Stars: Mass Recall column summary • The majority of stars are in pairs – binary systems. (Do this derivation as homework. ) 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).

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

Stars: Mass summary Recall column • 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.

Review: Recall column summary • Masses of stars can only be determined for stars on the main sequence. a) True b) False

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

Stars: MS Lifetimes Depend on Mass Recall column summary • 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?

Stars: MS Lifetimes Depend on Mass Recall column summary • 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.

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

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

Stars: MS Lifetimes Depend on Mass summary Recall column • 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. Substitute in mass of P and life time of Q Re-arrange the equation. The MS life time of star P is only 10 million years!

Stars: Stellar Populations summary Recall column • 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.

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