1. Galaxies and Cosmology 5 points, vt-2007 Teacher: Göran Östlin Lecture 6

2. Distances to galaxies (JL 2.4) - Standard candles (& rods) F = L / 4  d 2 inverse square law  = D / dangular diameter vs distance

3. Cepheids P-L relation

4. Cepheid PL relation

5. Type Ia supernovae Exploding white dwarf M CH =1.44 M  Abs mag M B  -19

6. Type II SNe L = 4  R 2  T 4 for black bodies F 1 / F 0 = L 1 / L 0 = R 1 2 T 1 4 / R 0 2 T 0 4 F 1 / F 0 observed photometrically Tfrom Black Body approx R 1 / R 0 from expansion velocity Fainter than Type Ia, less well calibrated

7. Surface brightness fluctuations

8. Galaxies and scaling laws Galaxies have broad luminosity function Spirals: Tully-Fisher: L  V 4 max inclination Ellipticals: Faber-Jacksson: L   v 4 => learn us about galaxies too (3rd) Brightest cluster galaxy Spiral galaxy diameters

9. Other standard candles… - Tip of RGB - Main sequence fitting - eclipsing binaries - Brightest red or blue supergiant - globular cluster luminosity function - planetary nebulae luminosity function -Etc…

10. Redshift

11. Redshifts…

12. Redshisfts… z = ( obs - em )/ em = obs / em - 1 =  / v r = z  c z = H 0  d / c =>v r = H 0  d Valid up to z  0.2 NB Special relativistic formula not more accurate General relativistic description of space-time required

13. Hubble diagram

14. Gravitational lens time delay Einstein cross

15. Cosmic time vs redshift

16. Complications -Deviations from a pure Hubble flow, peculiar motions -Dust extinction -Malmqvist bias -Evolutionary effects

17. Acoustic horizon in CMBR

18. Theoretical cosmology Problems with Newtonian Gravity and Mechanics: Gravity Inertial frames - absolute space and time General Relativity - matter curves space (& time), EP G +  g = -8  G T / c 4 G, g, T are tensors Geometry: line element Cosmological principle: isotropy, homogeneity

19. Gravity can in General Relativity be regarded as a space curvature rather than a force Orbit of earth a straight line in space-time

20. Geometrical cosmology: Line elements 2-dim cartesian 3-dim cartesian 3-dim spherical 2-dim curved space Special relativity Timelike separation Null separation (light) Spacelike separation

21. Robertson-Walker line element Simplest 4-dim (3 space, 1 time) space that fulfills the cosmological principle Only R(t) changes with time -> homogeneously expanding or contracting space