Po G Lec1slides - PoG Lecture 1 - Slides PDF

Preview

Summary

PoG Lecture 1 - Slides...

Description

Physics of Galaxies : Chapter 1

The Discovery of Galaxies

1

A dark night sky observation often shows almost continuous band of light inclined at an angle 63o with respect to celestial equator. Galileo Galilei (1564 -1642) was first to realise that Milky Way is vast collection of stars. PoG Chapter 1

2

ne Ga l

ac ti c

Pl a

w.r.t. Celestial Equator Ecliptic =23.5o Galactic Plane=63o

Celestial Equator = projection of earth's equator on the sky In class question: what are the Earth rotation axis inclination angles w.r.t. ecliptic and 3 galactic plane normals?

Immanuel Kant (1724-1804) and Thomas Wright (1711-1786) proposed that the Galaxy must be a stellar disc and the Solar System is simply a tiny component of it. First quantitative study was performed by William Herschel (17381822) in the 1780's by counting numbers of stars in 683 regions of sky. Figure: Herschell’s map of the milky way by counting stars – dust and gas obscured distant stars, placing the Sun at the centre. PoG Chapter 1

4

Herschell’s assumptions: (a) all stars have the same absolute magnitude M (see below) (b) number density of stars in space is constant (c) no interstellar extinction (reduction of brightness of stars along the line of sight) (d) that he could see all the way to edges of the stellar distribution. Herschell: (i) Sun in the middle; (ii) diameter /thickness  5 Jacobus Kapteyn (1851-1922) confirmed Herschell’s model but used more advanced methods. Hence main step forward was (i) specifying distance scale of the galaxy  10 kpc and (ii) producing contours of constant stellar number density (see Kapteyn, Astrophys. J. 55, 302, (1922)) PoG Chapter 1

5

Kapteyn Universe Method used: Based on formula d = 10( m − M +5) / 5 (details discussed below) assuming a value for (absolute magnitude), M, ( e.g. when spectral class and luminosity class are known) measuring (apparent magnitude), m, with a telescope gives distance to the star d.

Solar System

~ 10 kpc PoG Chapter 1

6

Harlow Shapley (1885-1972) estimated distances to 93 globular clusters using LL Lyrae and W Viginis variable stars.

PoG Chapter 1

7

Henrietta S. Leavitt (1868-1921) discovered 2400 classical Cepheid stars with periods 1-50 days. Then she plotted period vs magnitude (luminosity). Nearest Cepheid is Polaris some 200 pc away -- distance to large too be measured by stellar parallax. Data from Sandage & Tammann, ApJ, 151, 531(1968)

M V = −2.81 log Pd − 1.43 PoG Chapter 1

Comparing absolute M and apparent m magnitude of a star, we can calculate its distance. 8

PoG Chapter 1

9

Population I – metal reach stars Z=0.03 Population II, - metal poor stars Z=0.001 PoG Chapter 1

10

1.6 m telescope, 1845 William Parsons (Earl of Rosse)

11

PoG Chapter 1

12

M51

M51 imaged by a modern telescope PoG Chapter 1

13

M51 HST, May 2005 PoG Chapter 1

14

Modern (cartoon) View of Galaxy 163,000 lyr = 50 kpc

1 pc = 3.26 lyr

PoG Chapter 1

15

Mapping the Three-Dimensional Density of the Galactic Bulge with VVV Red Clump Stars by C. Wegg, O. Gerhard http://arxiv.org/abs/1308.0593, August 2013

Main Result: 3D Density map of the Galactic Bulge prominently displays a boxy/peanut-like structure as predicted by N-body simulations e.g. Martinez-Valpuesta et al (2006), ApJ, 637, 214

16

cross-section of our galaxy based on http://arxiv.org/abs/1308.0593

and "3D kinematics through the X-shaped Milky Way bulge", S. Vásquez Astron. & Astrophys. 555, A91 (2013)

18

As we can see both Kapteyn and Shapley were in error: Kapteyn's universe was too small (10 kpc) while Shapley's Galactic model was too large (100 kpc) compared to the true size (50 kpc). Surprisingly both models were wrong for the same reason -- failure to include effects of interstellar extinction. Kapteyn looked mostly in the galactic plane (called zone of avoidance, ± 10o from galactic plane) where the extinction is most severe. Shapley looked mostly away from the galactic plane, but since he did not account for the interstellar extinction, he overestimated distances by a factor of 2. PoG Chapter 1

19

In class question: Interstellar extinction always results in the absorption of starlight (i.e. dimming), and yet in the case of Kapteyn and Shapley studies, the size of the Galaxy was under- and over- estimated. Why? (think why under- estimated) (think why over- estimated)

PoG Chapter 1

20

The Nebulae 

Fuzzy objects known in 18th century not stars, which were always point-like  all called nebula (i.e. “mist”, plural nebulae) 

Some featureless:  Some structured:  Immanuel Kant 



spirals are “island universes”?

PoG Chapter 1

21

NGC 7027 Planetary nebula = remnant of stellar evolution when star casts off its outer envelope. Planetary nebula has nothing to do with planets!

PoG Chapter 1

22

NGC 2997

PoG Chapter 1

23

Andromeda M31 and its neighbours: the nearest galaxy comparable to ours M32

M110

24

The Great Debate in 1920 

Harlow Shapley (1885-1972)  



Heber Curtis (1872-1942) 



had shown Galaxy to be bigger that previously thought believed it unlikely that nebulae could be outside it led group supporting “island universe” idea

Reference: 

Bull. Nat. Res. Council 2 171-217 (1921)

Good further reading: http://apod.nasa.gov/diamond_jubilee/debate_1920.html

PoG Chapter 1

25

Resolution of Debate 

Edwin Hubble (18891953) 

 

measured distance to M31 (Andromeda) in 1925 using Cepheid variable stars 500 kpc – outside Galaxy (50 kpc in diameter)

Hubble, H P, Proc.Am.Astr.Soc. 48 139-142 (1925)

PoG Chapter 1

26

The Local Group of Galaxies ANDROMEDA

do you spot a problem with this plot? (if not, convert distance to M31 in kpc)

Lecture 2

PoG Chapter 1

29

The recession of the Galaxies The key difficulty is in measuring the distances, d of far-away galaxies.

PoG Chapter 1

30

The Red shift • Speed of source is v • the rest wavelength is

λ0

• the observed wavelength is

λ

Measure the red shift z to deduce v for e.g. z = 6.58

z=

λ − λ0 v ≈ c λ0

(*)

Is v=6.58c ?! No! Eq. (*) is applicable to non-relativistic case only. In general, if one has an electromagnetic wave propagating away from the observer, Doppler shift reduces its frequency (and amplitude) according to

f = f0

1− v / c 1+ v/ c

(**)

(On whiteboard to show that Eqs. (**) and (*) are consistent). PoG Chapter 1

31

Red shift – radial velocity relation

**

PoG Chapter 1

32

On whiteboard:

PoG Chapter 1

33

If  is the angle between the direction of relative motion and the direction of emission in the observer's frame (zero angle is directly away from the observer), the full form for the relativistic Doppler effect becomes: and for motion solely in the line of sight ( = 0°), this equation reduces to: . For the special case that the light is approaching at right angles ( = 90°) to the direction of relative motion in the observer's frame, the relativistic redshift is known as the transverse redshift, and a 1 redshift:

1+ z =

1 − v2 / c2

PoG Chapter 1

34

The Expanding Universe 

Vesto Slipher (18751969) 



observed (1917 - pre debate) that the light from most galaxies was redshifted mean velocity (520 km s-1 suggested spiral nebulae not part of Galaxy 

stellar velocities ~ 20 km s-1

PoG Chapter 1

36

The recession of the Galaxies The Red-Shift Distance Relation

Hubble’s Law 1920’s

PoG Chapter 1

37

Hubble’ Velocity-Distance Law • From the figure, velocity of recession is proportional to distance • Hubble obtained: H o = 465± 50 km s−1 Mpc-1 [Individual galaxies] = 513± 60 km s−1 Mpc-1 [Groups of galaxies]

• See that this about order of magnitude too large • Hubble used “wrong” Cepheids. Reason for inaccuracy was that period-luminosity relationship of Cepheid variable (he used as a reference) was based on inaccurate photometric results interfered by Earth's atmosphere and disregarding interstellar absorption. PoG Chapter 1

38

Hubble’s original 1929 plot

6×106 yrs

PoG Chapter 1

39

Modern Hubble Plot going out to larger distances 12% c

2×109 yrs

Hubble 40

Out to larger distances using Supernovae as standard candles Type Ia Supernovae show possible evidence for speeding up of expansion

Perlmutter et al 1998

54%c 7×109 yrs

Extent of previous slide

Lookbacktime redshift relation clarification

PoG Chapter 1

42

Modern Values of Ho

Until recently, value of Ho uncertain by factor of ~2; see later importance of this. PoG Chapter 1

A value from HST is 72±8 km s-1 Mpc-1 67.80 ±0.77 km s-1 Mpc-1 (2013) from Plank 44

PoG Chapter 1

45

Hubble’s Law

v∝d

•Recession Speed of source is v •Distance of source is d

v = H 0d the ‘Hubble Time’ is (based on Planck 2013 data)

H −0 1 = (13.813 ± 0.058 ) × 10 9 y Compare ages of oldest known stars in Globular clusters (13 ± 2)× ×109 yrs PoG Chapter 1

46

Interpretation of Hubble’s Law

PoG Chapter 1

47

Constant velocity expansion faster

speed

distance

slow

faster still

PoG Chapter 1

48

All galaxies receding from us. Are we at the centre of the universe? No! 3-D model: All currants in the cake see all the other currents going away from them in an infinitely big cake – no centre!

PoG Chapter 1

49

The Cosmological Principle: The Universe remains homogeneous & isotropic at all times. Hubble’s Law is an approximate consequence of this Cosmological Principle. A 2-dimensional model expanding while obeying the Cosmological Principle

PoG Chapter 1

50

Now, at t0 the grid size is 100 units Expanding Universe

It is the fabric of space itself which expands; here represented by the square grid. Later, at t the grid size is 150 units PoG Chapter 1

51

To maintain homogeneity we require a universal universal grid size. All distances everywhere expand at the same rate as the grid. Inhomogeneous expansion

Time

to NOW

t LATER PoG Chapter 1

52

Extrapolating backwards in time.

v d

Now to

Distance = speed × time d = vto

time to Near t = 0 to is the age of the Universe PoG Chapter 1

53

Extrapolating backwards in time.

Hubble’s Law

H0-1 = Hubble Time

to = age of Universe

d = vHo-1

d = vto to = Ho-1 = 13.7 × 109 yrs PoG Chapter 1

54

Clusters of Galaxies

PoG Chapter 1

55

Cosmic (Microwave) Background Radiation Arno Penzias & Robert Wilson 1964-5

Physics Nobel Prize 1978

1965

1985

PoG Chapter 1

56

Bell Laboratories’ Holmdell Horn Antenna. P&W developed a low-noise receiver to study radio emission from our Galaxy.

The Cosmic Background Radiation 1964/65 Intensity 400

2.725 K Black Body Spectrum

300

I( nu) 200

100

0

0

5

10

15

20

25

Frequency (cm-1) nu

Arno Penzias (1933-) and Robert Wilson (1936-)

Measured TCMB=3.5 K at a single frequency 4 GHz PoG Chapter 1

58

COBE SATELLITE (1989)

FIRAS Far Infrared Absolute Spectrometer Measured the spectrum of the Cosmic Background Radiation DMR Differential Microwave Radiometer Looked for variations in CBR temperature from one part of the sky to another

59

COBE spectrum of the Cosmic Background Radiation

PoG Chapter 1

60

61

What does 2.7K mean? At E 13.6 eV (ionization energy of hydrogen), plasma recombines = kBT T = 13.6x1.6x10-19/ 1.38x10-23 = 1.6x105K. The correct treatment requir. Saha eq. yielding T=4000K

Trecomb=2.7(1+z) ,i.e. z = 1500 http://en.wikipedia.org/wiki/Recombination_(cosmology)

62

2003

WMAP After subtractions

The temperature fluctuation in the direction (,) is:

δT (θ , ϕ ) T

∞

= l =1

l l a Y  l ,m m (θ , ϕ ) m = −l

where al,m are complex coefficients and Ylm are spherical harmonic functions. l

Cl = Quantity

1 2 | | a  l ,m 2l + 1 m=− l

l( l + 1) Cl / 2π is then the angular power spectrum. PoG Chapter 1

64

WMAP Fluctuation Spectrum resolves the fine structure of CBR

Statistical frequency of features

1o

l (l + 1)C l / 2π

Angular size of features multipole moment l

2o

1o

0.5o

0.2o

Planck collaboration (2013) data

Planck collaboration (2013). arXiv:1303.5062 http://arxiv.org/abs/1303.5062 updated June 2014...