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Astrophysics

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Title: Astrophysics


1
Astrophysics
  • 18 lecture introduction
  • -10 lectures on cosmology
  • -8 lectures on stellar evolution
  • one guest lecture by Matthew Young on Pulsars
  • Power point slides plus one lecture from a PDF
  • Two minor, one major assignment see handout
  • Slides will be put on web
  • Text Carroll and Ostlie Modern Astrophysics
  • Contact me whenever necessary ext 2736, mob
    0409687703,dgb_at_physics, rm4-67, basement lab,
    Gingin 95757591

This course includes material from lectures at
many major universites and institutes including
Chicago, Fermilab, Stanford, Sheffield. Authors
include R Kolb, Mohr, W.Hu, V Kudryavtsev,
2
Course Outline
See handout Cosmology 10 lectures Stellar
Evolution 8 lectures Excursion Wed 16 March
barbeque, cosmology and astronomy field
night. Time leave UWA 4.30pm bus and car pool.
Return by 11pm. Major Assignment Dark Energy,
Black hole binary systems and Intermediate mass
black holes.
3
Major Assignment
  • The major assignment asks you to write an
    investigation on one of three topics based on
    recent research
  • dark energy and the missing mass
  • intermediate mass black holes. ( eg 1000 solar
    mass near galactic centre)
  • stellar mass black hole binary systems
    (predicted, none discovered, many expected in
    gravitational wave signals)
  • The investigation should be based on recent
    discovery papers. In your investigation you must
    demonstrate that you have read and understood at
    least 3 research letters. Show how they relate to
    each other. Use Nature, Astrophysical Journal
    Letters, Science and arXiv Astro-ph or gr-qc
    preprints.

4
Looking into the past
  • Telescopes are time machines
  • Looking into the past we see a universe that is
  • Hotter - thermal background radiation rising in
    temperature
  • Denser -galaxies are closer together
  • Expanding-Everything is receeding

5
History of the Universe
6
Cosmology and Dark Matter
  • First 2 lectures

Hubble law
Critical density
Density parameter
Mass to light ratio
Dark Matter in solar system
Dark Matter in galaxies
Dark Matter in clusters of galaxies and
superclusters
Conclusions
7
Introduction
  • First hints for dark matter (1844)
  • It was noticed that planet Uranus had moved from
    its calculated position by 2 arc minutes.
  • F. W. Bessell found the strange motion of the
    star Sirius.

By 1846 the planet Neptune was discovered (no
longer a dark matter).
In 1862 the faint companion to Sirius (Sirius B -
a white dwarf) was discovered.
8
Redshift
z

In terms of the velocity of the receding object
red shift is given by
9
The Hubble Law
1 parsec 3.25 ly. Stellar parallax from earth
orbit. Cepheid variables standard candles
In 1929, based on the observation that the
universe is expanding it was further realised, by
Hubble, that the expansion velocity v is
proportional to distance away from the observer
(Earth) r
10
Hubbles Law
H0 is the Hubble constant - the rate of expansion
at the present time.

The precise value of H0 was disputed for many
years. Today cosmologists agree H0 70 km s-1
Mpc-1
h

h 0.70 0.05
Hubble thought H0 was 540 km s-1 Mpc-1
11
  • This requires the famous Newtonian result
  • a particle inside a spherical mass distribution
    feels no gravitational force.
  • b) For a particle outside a spherical mass
    distribution the gravitational force is as if all
    the matter were concentrated at central point.
  • e.g. 1) The force exerted on the Earth by the
    moon depends on the mass of the moon and not on
    its density profile.
  • 2) The gravitational acceleration of the
    earth falls to zero as you approach the core.

Critical density
Mass m
r
contributing mass
12
Critical Density
rc
Consider the motion of a galaxy of mass m at the
edge of a spherical region of mass M and radius r

T mv2/2
Kinetic energy
U -GMm/r
Potential energy at the edge of a sphere
E T U mv2/2 - GMm/r
Total energy
The mass of the sphere can be calculated from its
volume and mean density
M 4p r3 r / 3
The critical density of the Universe is the
density which gives E 0
critical density
From known H0 we can compute the value of the
critical density
rc(t0) 1.88 h2 . 10-26 kg m-3 (i.e. small)
6 H atoms per m3
13
Density Parameter
W0
The density parameter W0 is the ratio of the true
density of the Universe at the present time to
the critical density
density parameter
0 lt W0 lt 1
r0 lt rc
Open Universe
W0 1
r0 rc
Flat Universe
r0 gt rc
Closed Universe
W0 gt 1
Note that we can use the density parameter to
quantify components of the density due to
particular types of material in terms of the
ratio to the critical density, i.e. Wrad,
Wmatter, Whalo, etc.
14
Fate of the Universe
The Friedmann Equations
Open Universe will expand forever Flat
Universe will expand forever (but the
expansion rate slows to zero at infinite
size) Closed Universe will end in a Big Crunch
W0
Wlt1
W1
Wgt1
The fate of the Universe, as well as many other
things, depend on the density (density parameter).
Can we measure it?
15
Age Size and Lifetime of Closed Universes
For closed solutions the size of the Universe
will reach a maximum
decelleration parameter qo
also we can calculate the lifespan of the
Universe - the time from birth to recollapse,
e.g. for q0 1.
16
A crude estimate of the density
A crude estimate comes form considering the
typical mass of a galaxy 1011 MSun, and
typical galaxy separation 1 Mpc. Check for
yourself that this gives a density close to the
critical density.
17
Mass to light ratio
Mass to light ratio can help us to find the
density or W0.
There are stars which are intrinsically faint,
such as white dwarfs, brown dwarfs. There are
also dead stars, such as neutron stars and black
holes. Important to distinguish between objects
which are intrinsically dim and those which are
dim because they are very distant.
We can define the mass to luminosity ratio for a
given system (galaxy, cluster of galaxies, any
part of galaxy) relative to the Sun.
We define the mass to light ratio as
where h 1 for the Sun

h
18
Mass to light ratio
Characterise the average density in various
regions of the Universe in terms of mass-to-light
ratio. and contribution to the density parameter.
Note M/L is proportional to h.
Two examples i) h ltlt1 a system is composed of
massive , young and luminous main sequence stars
i) h gtgt1 a system with old white dwarfs and
hidden (dark) matter.
Measurement of M/L depends on location Solar
neighbourhood count up the luminosity of all
stars etc and determine masses from orbital
motions. In galaxies measure total galaxy
luminosity and use rotation curves or virial
theorem (see later) to estimate total mass.
19
Dark Matter in the Galaxy
Consider motion of the stars perpendicular to the
Galactic plane.
Assume this motion is independent of the
conventional circular motion around the Galactic
centre.
20
Dark Matter near the Sun - the Oort limit
The velocity in z-direction vz decreases as z
increases due to the gravitational attraction to
the Galactic plane.
It is impossible to measure vz or gz (the
gravitational force per unit mass).
But assuming the big number of oscillations made
around the plane and mapping the distributions of
stars away from the plane, it is possible to
estimate the average gravitational force.
In general we have
gz g0 (z / z0)
where g0 and z0 are measurable constants of
acceleration and length.
21
The Oort limit
The acceleration due to gravitational attraction
is thus
dgz / dz - 4 p G r
where r is the average density of gravitating
matter.
Thus near the Sun (Oort limit - 1932, 1965)
r g0 / 4 p G z0
Oort estimated this as 0.2 MSun/pc3. Recent
estimates give the total density of 0.15 MSun/pc3
(0.3 GeV/m3) and 0.08 MSun/pc3 for stars and gas
only.
Hence about 1/2 or 1/3 is missing matter. But
this is at a very specific point (near the Sun).
22
Density in stars and other luminous matter
We can estimate the mass contribution from stars
in galaxies. We add up the mass of stars, making
use of the known relationship between stellar
luminosity, temperature and mass. Within the
optical radius of galaxies this yields a
non-dynamical estimate for the mass density.
This provides a lower limit for the baryonic
density. It can be extended slightly by
integrating over the total background luminosity
of the Universe, but it still yields a value no
more than
23
Density estimated from galactic dynamics
Rotation curves of spiral galaxies
The first real evidence for substantial dark
matter came in 1970 with Freemans observation of
the rotation curves of Galactic halos. He showed
that the 21 cm line of neutral hydrogen did not
show the expected Keplerian decline beyond the
optical radii of these galaxies.
What would we expect if all the mass of a galaxy
were accounted for by the visible mass?
24
Rotation curves of spiral galaxies
Assume that stars, gas and dust move in circular
orbits around galaxy. At large distances the
gravitation field would be as if all the mass
were concentrated in the centre Centripetal
force is balanced by gravity
gr
Keplerian decline v r -1/2 is not observed
Doppler shift can be due to several motions i)
motion of the whole galaxy away/towards us ii)
random motions of the clouds iii) rotation of
the galaxy. This can be separated to find the
rotation curve we can measure v0 vcirc and v0
- vcirc . This applies to galaxies seen edge on
or at an angle.
25
Rotation curves of spiral galaxies
In almost all galaxies the velocity is found to
be constant with radius.
26
Rotation curves of spiral galaxies
27
Rotation curve of the Milky Way
Milky Way
28
Rotation curves of spiral galaxies
From the observations we can try to model the
density distribution
The easiest model is to assume the galaxy is
spherical (we dont need to assume that the
hidden mass is distributed like the visible
mass)
29
Rotation curves of spiral galaxies
In this case we can determine the mass
distribution uniquely. The solution is not much
different for the more realistic case of a
flattened spheroid. The best fit mass density
distribution is
ro, ro are constants
This yields a typical total mass to light ratio
in the halo (lower limit is for visible part of
galaxy)
hhalo 10 -100
A similar result is obtained when considering
orbiting pairs of galaxies.
30
Density estimates for elliptical galaxies
To determine the mass of elliptical galaxies we
need to use the virial theorem because there is
not much rotation. Alternatively we can use
X-rays in halos or pairs of galaxies. All this
gives
hhalo 10 -100
31
Density of clusters from bulk motions
Estimates by the virial theorem
In any system of gravitating bodies changes in
size are determined by the balance between
gravitational attraction and the motions of the
bodies.
For orbit, mv2/rGmM/r2 Hence twice the kinetic
energy T is equal to the negative of the
gravitation potential energy V. (Correction
factor a)
Example Coma
2
T
V
0


0
.
5
2
.
0
a

-
Cluster mass
Mean galaxy velocity
2
v
R
hclusters 200
lt
gt
M

G
a
0
.
2
W

clusters
32
Problems with clusters
  • We have to be sure that the galaxies are
    actually in the cluster (redshift).
  • Exclude large fluctuactions (fast moving
    galaxies).
  • Carefully treat close clusters moving near each
    other.
  • Account for total velocity (not just vz).
  • Be sure that this is a cluster (not a random
    coincidence) and that the cluster is not
    contracting or flying apart.
  • Take into account cosmological evolution
    (galaxy formation).

33
Estimates from x-ray observations
The properties of the hot gas that emit x-rays
can be used to determine the mass and density
profile of the dark matter, even though they may
not themselves have the same density profile.
The temperature maps can be used to determine the
mass needed to prevent the hot gas and galaxies
from escaping the clusters. One of the best
examples is the analysis for the Coma cluster.
The result is
hclusters 300
34
Estimates from x-ray observations
Chandra X-ray Observatory images (left, X-rays
from hot gas) and Hubble Space Telescope images
(right, massive central regions bend light from
distant galaxies) of the giant galaxy clusters
Abell 2390 and MS2137.3-2353. The clusters are
located 2.5 and 3.1 billion light years from
Earth, respectively.
35
Gravitational lensing
A relatively new technique of measuring the Dark
Matter is to use the gravitational deflection of
light rays by the cluster. This distorts the
image of background objects giving arc-like
features which are magnified images of distant
galaxies behind the cluster.
36
Density estimated from gravitational lensing
hclusters 300
a distant galaxy lensed by a nearer galaxy cluster
37
Density estimated from gravitational lensing
38
Density from supercluster dynamics
The total mass of superclusters is obtained from
deep redshift galaxy surveys, again using virial
techniques. Comprehensive surveys of infra-red
and other galaxies have gone out to distances in
excess of 200 Mpc. From large-scale velocities,
it is possible using linear theory to estimate
the homogeneous mass density.
hsuperclusters 800500
39
Density from supercluster dynamics
40
Density from theory - structure and inflation
There are no current working models of structure
formation that do not require dark matter with
Inflation, the model that may explain the
Universe in its early stages when it undergoes
rapid expansion, predicts that the Universe is
flat. In the simplest form this tells us
However, we could have a lower density of matter
if we assume the presence of dark energy, which
is favoured by recent observations of distant
type Ia supernovae (cosmological constant).
41
Conclusions
  • There is a missing mass (dark matter) in the
    Universe
  • It is seen at all scales from galaxies to
    superclusters
  • It is also predicted by the theory (simulations
    of the structure evolution, inflation).
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