Cosmology part II
Marlinde Drent et al
Contents
1 Galaxies 3
1.1 Types of galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Gravity 3
2.1 Basics of gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3 Light 4
3.1 Doppler effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.2 Fluxes, luminosities and magnitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.3 Filters and colors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.4 Surface brightness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.5 Metalicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4 The Milky Way 6
4.1 Structure of the Milky Way . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
4.2 Galactic discs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
4.3 Velocity dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
4.4 Galactic bulge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4.5 Globular clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4.6 Dust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4.7 Dark halo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
5 The diversity of galaxies 8
5.1 Hubble classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
5.2 Properties of galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
5.3 Surface photometry of galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
5.3.1 Surface photometry of elliptical galaxies . . . . . . . . . . . . . . . . . . . . . . 10
5.3.2 Surface photometry of spiral galaxies . . . . . . . . . . . . . . . . . . . . . . . . 11
5.4 Dynamics of elliptical galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
5.5 Dynamics of spiral galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
6 Scaling relations 13
6.1 Scaling relations of galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
6.2 Splitting by galaxy type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
6.2.1 Scaling relations of elliptical galaxies . . . . . . . . . . . . . . . . . . . . . . . . 13
6.2.2 Scaling relations of spiral galaxies . . . . . . . . . . . . . . . . . . . . . . . . . 13
6.3 Cosmological applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
6.3.1 Tully-Fisher as distance indicator . . . . . . . . . . . . . . . . . . . . . . . . . . 14
6.3.2 Dn − σ as a distance indicator . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
6.3.3 Fundamental plane as a distance indicator . . . . . . . . . . . . . . . . . . . . . 14
1
,7 Supermassive black holes 15
7.1 A black hole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
7.2 The Galactic Center . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
7.3 Extragalactic supermassive black holes . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
7.4 Active galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
7.5 Scaling relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
8 Stellar populations 19
8.1 Basics of stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
8.2 Blackbody radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
8.3 HR diagram and the stellar main sequence . . . . . . . . . . . . . . . . . . . . . . . . . 20
8.4 Initial mass function (IMF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
8.5 The N-star just-born galaxy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
8.6 Simple stellar population . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
9 Evolutionary processes 24
9.1 Formation of galaxies and the dark matter halo . . . . . . . . . . . . . . . . . . . . . . 24
9.1.1 The ELS collapse model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
9.1.2 Hierarchical merger model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
9.2 Formation of the gas disk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
9.3 Evolution of galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
9.3.1 Gas cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
9.3.2 Ageing in isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
9.4 Chemical evolution: closed box model . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
9.5 Feedback processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
10 Groups and clusters of galaxies 27
10.1 Groups and clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
10.2 The Milky Way and its neighbors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
10.3 Mass of the Local Group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
10.4 Tidal disruption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
10.5 Clusters: light and dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2
, 1 Galaxies
1.1 Types of galaxies
There are two types of galaxies; elliptical galaxies and spiral galaxies. In elliptical galaxies stars orbit
all around the galaxy. In spiral galaxies stars orbit in a plane around the center.
2 Gravity
2.1 Basics of gravity
To describe the motion of objects under gravity we use the following equations:
F⃗ (⃗x) = −m∇Φ(⃗x) (1)
∇2 Φ(⃗x) = 4πGρ(⃗x) (2)
We will be using these two equations to describe stars and galaxies. We will not need general or
special relativity as the speeds we are working with are well below the speed of light.
The point-mass potential is given by:
GM
Φ(r) = − (3)
r
This is also the potential outside any spherical mass distribution. It does not matter how it is
distributed inside that boundary.
The circular velocity, also known as Keplerian velocity, is described by:
r
GM
vc (r) = (4)
r
This equation is equivalent to Kepler’s third law. Equation 4 implies that when vc is constant, the
mass of a galaxy M is proportional to its radius r. However we know that the mass does not increase
with the radius, so we are missing a component; dark matter.
The time it takes to complete an orbit at a given circular velocity is given by the dynamical or crossing
time:
2πr
tdyn = (5)
vc
The dynamical time of the Milky Way is approximately 225 Myrs, which is short compared to the age
of the Universe. This means there has been enough time for galaxies to reach dynamical equilibrium.
If the dynamical time long, we would see galaxies as they were forming.
3
Marlinde Drent et al
Contents
1 Galaxies 3
1.1 Types of galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Gravity 3
2.1 Basics of gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3 Light 4
3.1 Doppler effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.2 Fluxes, luminosities and magnitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.3 Filters and colors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.4 Surface brightness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.5 Metalicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4 The Milky Way 6
4.1 Structure of the Milky Way . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
4.2 Galactic discs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
4.3 Velocity dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
4.4 Galactic bulge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4.5 Globular clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4.6 Dust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4.7 Dark halo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
5 The diversity of galaxies 8
5.1 Hubble classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
5.2 Properties of galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
5.3 Surface photometry of galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
5.3.1 Surface photometry of elliptical galaxies . . . . . . . . . . . . . . . . . . . . . . 10
5.3.2 Surface photometry of spiral galaxies . . . . . . . . . . . . . . . . . . . . . . . . 11
5.4 Dynamics of elliptical galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
5.5 Dynamics of spiral galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
6 Scaling relations 13
6.1 Scaling relations of galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
6.2 Splitting by galaxy type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
6.2.1 Scaling relations of elliptical galaxies . . . . . . . . . . . . . . . . . . . . . . . . 13
6.2.2 Scaling relations of spiral galaxies . . . . . . . . . . . . . . . . . . . . . . . . . 13
6.3 Cosmological applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
6.3.1 Tully-Fisher as distance indicator . . . . . . . . . . . . . . . . . . . . . . . . . . 14
6.3.2 Dn − σ as a distance indicator . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
6.3.3 Fundamental plane as a distance indicator . . . . . . . . . . . . . . . . . . . . . 14
1
,7 Supermassive black holes 15
7.1 A black hole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
7.2 The Galactic Center . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
7.3 Extragalactic supermassive black holes . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
7.4 Active galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
7.5 Scaling relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
8 Stellar populations 19
8.1 Basics of stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
8.2 Blackbody radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
8.3 HR diagram and the stellar main sequence . . . . . . . . . . . . . . . . . . . . . . . . . 20
8.4 Initial mass function (IMF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
8.5 The N-star just-born galaxy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
8.6 Simple stellar population . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
9 Evolutionary processes 24
9.1 Formation of galaxies and the dark matter halo . . . . . . . . . . . . . . . . . . . . . . 24
9.1.1 The ELS collapse model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
9.1.2 Hierarchical merger model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
9.2 Formation of the gas disk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
9.3 Evolution of galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
9.3.1 Gas cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
9.3.2 Ageing in isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
9.4 Chemical evolution: closed box model . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
9.5 Feedback processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
10 Groups and clusters of galaxies 27
10.1 Groups and clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
10.2 The Milky Way and its neighbors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
10.3 Mass of the Local Group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
10.4 Tidal disruption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
10.5 Clusters: light and dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2
, 1 Galaxies
1.1 Types of galaxies
There are two types of galaxies; elliptical galaxies and spiral galaxies. In elliptical galaxies stars orbit
all around the galaxy. In spiral galaxies stars orbit in a plane around the center.
2 Gravity
2.1 Basics of gravity
To describe the motion of objects under gravity we use the following equations:
F⃗ (⃗x) = −m∇Φ(⃗x) (1)
∇2 Φ(⃗x) = 4πGρ(⃗x) (2)
We will be using these two equations to describe stars and galaxies. We will not need general or
special relativity as the speeds we are working with are well below the speed of light.
The point-mass potential is given by:
GM
Φ(r) = − (3)
r
This is also the potential outside any spherical mass distribution. It does not matter how it is
distributed inside that boundary.
The circular velocity, also known as Keplerian velocity, is described by:
r
GM
vc (r) = (4)
r
This equation is equivalent to Kepler’s third law. Equation 4 implies that when vc is constant, the
mass of a galaxy M is proportional to its radius r. However we know that the mass does not increase
with the radius, so we are missing a component; dark matter.
The time it takes to complete an orbit at a given circular velocity is given by the dynamical or crossing
time:
2πr
tdyn = (5)
vc
The dynamical time of the Milky Way is approximately 225 Myrs, which is short compared to the age
of the Universe. This means there has been enough time for galaxies to reach dynamical equilibrium.
If the dynamical time long, we would see galaxies as they were forming.
3
