Stellar Models

1. 0 Stellar Models The structure and evolution of a star is determined by the laws of • Hydrostatic equilibrium • Energy transport • Conservation of mass • Conservation of energy A star’s mass (and chemical composition) completely determines its properties. That’s why stars initially all line up along the main sequence.

2. 0 Minimum Mass of Main-Sequence Stars Mmin = 0.08 Msun At masses below 0.08 Msun, stellar progenitors do not get hot enough to ignite thermonuclear fusion. Brown Dwarfs

3. 0 Evolution off the Main Sequence: Expansion into a Red Giant When the hydrogen in the core is completely converted into He: “Hydrogen burning” (i.e. fusion of H into He)ceases in the core. H burning continues in a shell around the core. He Core + H-burning shell produce more energy than needed for pressure support Expansion and cooling of the outer layers of the star Red Giant

4. 0 Summary of Post Main-Sequence Evolution of Stars Supernova Fusion proceeds; formation of Fe core. Evolution of 4 - 8 Msun stars is still uncertain. Mass loss in stellar winds may reduce them all to < 4 Msun stars. M > 8 Msun Fusion stops at formation of C,O core. M < 4 Msun Red dwarfs: He burning never ignites M < 0.4 Msun

5. 0 Estimating the Age of a Cluster The lower on the MS the turn-off point, the older the cluster.

6. 0 Cepheid Variables: The Period-Luminosity Relation The variability period of a Cepheid variable is correlated with its luminosity. The more luminous it is, the more slowly it pulsates. => Measuring a Cepheid’s period, we can determine its absolute magnitude!

7. 0 Degenerate Matter Matter in the He core has no energy source left. Not enough thermal pressure to resist and balance gravity Matter assumes a new state, called degenerate matter: Pressure in degenerate core is due to the fact that electrons can not be packed arbitrarily close together and have small energies.

8. 0 The Remnants of Sun-Like Stars: White Dwarfs Sun-like stars build up a Carbon-Oxygen (C,O) core, which does not ignite Carbon fusion. He-burning shell keeps dumping C and O onto the core. C,O core collapses (because no further nuclear fusion) and the matter becomes degenerate. Formation of a White Dwarf

9. 0 White Dwarfs (3) The more massive a white dwarf, the smaller it is! Pressure becomes larger, until electron degeneracy pressure can no longer hold up against gravity. WDs with more than ~ 1.4 solar masses can not exist! Chandrasekhar Limit = 1.4 Msun

10. 0 Recycled Stellar Evolution Mass transfer in a binary system can significantly alter the stars’ masses and affect their stellar evolution.

11. 0 Type I and II Supernovae Core collapse of a massive star: Type II Supernova If an accreting White Dwarf exceeds the Chandrasekhar mass limit, it collapses, triggering a Type Ia Supernova. Type I: No hydrogen lines in the spectrum Type II: Hydrogen lines in the spectrum

12. 0 White Dwarfs & Neutron Stars The more massive a white dwarf, the smaller it is! neutron degeneracy pressure electron degeneracy pressure Pressure becomes larger, until electron degeneracy pressure can no longer hold up against gravity. WDs with more than ~ 1.4 solar masses can not exist! Chandrasekhar Limit = 1.4 Msun

13. 0 Formation of Neutron Stars (2)

14. 0 Lighthouse Model of Pulsars A Pulsar’s magnetic field has a dipole structure, just like Earth. Radiation is emitted mostly along the magnetic poles.

15. 0 Jocelyn Bell 1943 - “Little Green Man”

16. 0 Gravitational Radiation: General Relativity: Any rapid change in gravitational field should spread outward gravitational radiation at the speed of light. The orbital period of the binary pulsar is slowly growing shorter as the neutron stars gradually spiral toward each other – they are radiating away gravitational energy. First indirect evidence of gravitational radiation. Arecibo Observatory

17. 0 Black Holes Just like white dwarfs (Chandrasekhar limit: 1.4 Msun), there is a mass limit for neutron stars: Neutron stars can not exist with masses > 3 Msun We know of no mechanism to halt the collapse of a compact object with > 3 Msun. It will collapse into a single point – a singularity: => A Black Hole!

18. 0 Escape Velocity Velocity needed to escape Earth’s gravity from the surface: vesc≈ 11.6 km/s. vesc Now, gravitational force decreases with distance (~ 1/d2) => Starting out high above the surface => lower escape velocity. vesc vesc If you could compress Earth to a smaller radius => higher escape velocity from the surface

19. 0 The Schwarzschild Radius => There is a limiting radius where the escape velocity reaches the speed of light, c: 2GM ____ Rs = Vesc = c c2 G = Universal const. of gravity M = Mass Rs is called the Schwarzschild Radius.

20. 0 Schwarzschild Radius and Event Horizon No object can travel faster than the speed of light => nothing (not even light) can escape from inside the Schwarzschild radius • We have no way of finding out what’s happening inside the Schwarzschild radius. • “Event horizon”

21. 0 The Mass of the Milky Way If all mass were concentrated in the center, the rotation curve would follow a modified version of Kepler’s 3rd law rotation curve = orbital velocity as function of radius

22. 0 The Mass of the Milky Way (2) Total mass in the disk of the Milky Way: Approx. 200 billion solar masses Additional mass in an extended halo: Total: Approx. 1 trillion solar masses Most of the mass is not emitting any radiation: Dark Matter!

23. 0 Stellar Populations Population I: Young stars: metal rich; located in spiral arms and disk Population II: Old stars: metal poor; located in the halo (globular clusters) and nuclear bulge

24. 0 A Black Hole at the Center of Our Galaxy By following the orbits of individual stars near the center of the Milky Way, the mass of the central black hole could be determined to ~ 2.6 million solar masses

25. 0 Rotation Curves of Galaxies From blue / red shift of spectral lines across the galaxy infer rotational velocity Plot of rotational velocity vs. distance from the center of the galaxy: Rotation Curve Observe frequency of spectral lines across a galaxy.

26. 0 Galaxy Classification Ellipticals: Spirals: Large nucleus; tightly wound arms Sa E0, …, E7 E0 = Spherical E1 Sb Sc Small nucleus; loosely wound arms E7 = Highly elliptical E6

27. 0 Interacting Galaxies Cartwheel Galaxy Particularly in rich clusters, galaxies can collide and interact. Galaxy collisions can produce ring galaxies and tidal tails. NGC 4038/4039 Often triggering active star formation: starburst galaxies

28. 0 Starburst Galaxies Starburst galaxies: Galaxies in which stars are currently being born at a very high rate. Starburst galaxies contain many young stars and recent supernovae, and are often very rich in gas and dust; bright in infrared: ultraluminous infrared galaxies

29. 0 Cepheid Distance Measurement Repeated brightness measurements of a Cepheid allow the determination of the period and thus the absolute magnitude. Distance

30. 0 Model for Seyfert Galaxies Seyfert I: Strong, broad emission lines from rapidly moving gas clouds near the BH Gas clouds Emission lines UV, X-rays Seyfert II: Weaker, narrow emission lines from more slowly moving gas clouds far from the BH Supermassive black hole Accretion disk Dense dust torus

31. 0 Quasar Red Shifts z = 0 Quasars have been detected at the highest red shifts, beyond z ~ 6 z = 0.178 z = 0.240 z = 0.302 z = 0.389 z = Dl/l0 This indicates distances of several Gigaparsec

32. 0 Hubble’s Law Distant galaxies are flying away (= receding) from us with a speed proportional to distance Recession Velocity (km/s) Distance (Mpc)

33. 0 The Necessity of a Big Bang If galaxies are moving away from each other with a speed proportional to distance, there must have been a beginning, when everything was concentrated in one single point: The Big Bang! Time ?

34. 0 The Cosmic Background Radiation (2) After recombination, photons can travel freely through space. Their wavelength is only stretched (red shifted) by cosmic expansion. Recombination: z = 1000; T = 3000 K This is what we can observe today as the cosmic background radiation!

35. 0 The Accelerating Universe Apparent Magnitude of Type Ia Supernovae Red Shift z In fact, SN Ia measurements showed that the universe is accelerating!

36. 0 The Cosmological Constant • Cosmic acceleration can be explained with the “Cosmological Constant”,L (upper-case lambda) • L is a free parameter in Einstein’s fundamental equation of general relativity; previously believed to be 0. • Energy corresponding to L can account for the missing mass/energy (E = m*c2) needed to produce a flat space-time. “Dark Energy”

37. 0 The Contents of the Universe • We only “see” about 4 % of all the mass and energy in the Universe! • The nature of about 96 % of our Universe is yet mysterious and unknown!