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Galaxies and Cosmology

5 points, vt-2007Teacher: Göran Östlin

Lecture 6

Distances to galaxies (JL 2.4)

- Standard candles (& rods)

F = L / 4 π d2 inverse square law

α = D / d angular diameter vs distance

Cepheids P-L relationCepheid PL relation

Type Ia supernovaeExploding white dwarfMCH=1.44 MAbs mag MB ≈ -19

Type II SNe

L = 4 π R2 σ T4 for black bodies

F1 / F0 = L1 / L0 = R12

T14 / R0

2 T0

4

F1 / F0 observed photometricallyT from Black Body approxR1 / R0 from expansion velocity Fainter than Type Ia, less well calibrated

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Surface brightness fluctuations

Galaxies and scaling laws

Galaxies have broad luminosity function

Spirals: Tully-Fisher: L ∝ V4max inclination

Ellipticals: Faber-Jacksson: L ∝ σv4

=> 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 = (λobs - λem)/ λem = λobs / λem - 1 = Δ λ/ λ

vr = z ⋅ c

z = H0 ⋅ d / c => v r= H0 ⋅ d

Valid up to z ≈ 0.2

NB Special relativistic formula not more accurateGeneral relativistic description of space-time required

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Hubble diagramGravitational 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:GravityInertial frames - absolute space and time

General Relativity - matter curves space (& time), EPG + Λg = -8πG T / c4

G, g, T are tensors

Geometry: line element

Cosmological principle: isotropy, homogeneity

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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

!

ds2

= dx2

+ dy2

ds2

= dx2

+ dy2

+ dz2

ds2

= dr2

+ r2(d" 2 + sin

2" d# 2)

ds2

= r2(d" 2 + sin

2" d# 2)

ds2

= dx2

+ dy2

+ dz2 $ c 2dt 2

ds2

< 0

ds2

= 0

ds2

> 0

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

!

ds2

= c2dt

2 " R2(t)dr

2

1" kr2+ r

2(d# 2 + sin

2# d$ 2)%

& '

(

) *

Simplest 4-dim (3 space, 1 time) space that fulfillsthe cosmological principle

Only R(t) changes with time -> homogeneouslyexpanding or contracting space