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

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Presentation transcript:

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

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

Cepheids P-L relation

Cepheid PL relation

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

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

Surface brightness fluctuations

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

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…

Redshift

Redshifts…

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

Hubble diagram

Gravitational lens time delay Einstein cross

Cosmic time vs redshift

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

Acoustic horizon in CMBR

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

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

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

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