Astrophysics 18 lecture introduction -10 lectures on cosmology -8 lectures on stellar evolution one...

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@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,

astrophysics lectures 1and 2 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.


Major AssignmentThe major assignment asks you to write an investigation on one of

three topics based on recent research

a) dark energy and the missing mass

b) intermediate mass black holes. ( eg 1000 solar mass near galactic centre)

c) 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.


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


History of the Universe


Cosmology and Dark MatterCosmology and Dark Matter

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

• First 2 lectures


IntroductionFirst hints for ‘dark matter’ (1844):1. It was noticed that planet Uranus had moved from its

calculated position by 2 arc minutes.2. 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.


Redshift

z em

obs em

wavelength at the point of observation

wavelength at thepoint of emission.

In terms of the velocity of the receding object red shift is given by:

1 z 1 v / c1 v / c

z ≈vc


v H0 r

The Hubble Law

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:

QuickTime™ and aGIF decompressor

are needed to see this picture.

1 parsec = 3.25 ly.

Stellar parallax from earth orbit.

Cepheid variables standard candles


h 100 km s 1

Mpc 1

H0

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

Hubble thought H0 was 540 km s-1 Mpc-1

Hubble’s Law

H0 is the Hubble constant - the rate of expansion at the present time.

z ≈v

c=

H0

cr

hh = 0.70 ± 0.05 = 0.70 ± 0.05


Critical densityThis requires the famous Newtonian

result: a) 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.

dr

Mass m

contributing mass


Critical DensityCritical Density cc

The critical density of the Universe is the density which gives E = 0

c = 8G

3H0

2

From known H0 we can compute the value of the critical density:

c(t0) = 1.88 h2 10-26 kg m-3 (i.e. small)

critical density

6 H atoms per m3

Consider the motion of a galaxy of mass m at the edge of a spherical region of mass M and radius r :

Kinetic energy T = mv2/2 Potential energy at the edge of a sphere U = -GMm/r

Total energy E = T + U = mv2/2 - GMm/r The mass of the sphere can be calculated from its volume and mean density M = 4r3 / 3

c = 8G r 2

3v2


Density ParameterDensity Parameter 00

The density parameter 0 is the ratio of the true density of the Universe at the present time to the critical density:

0 c

0 density parameter

Open Universe:

Flat Universe:

Closed Universe:

0 < < 1 c

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. rad, matter, halo, etc.

= 1

> 1

c

c


Fate of the Universe

empty

open

flat

closed

Open Universe:will expand forever

Flat Universe:will expand forever(but the expansionrate slows to zero at infinite size)

Closed Universe:will end in a Big Crunch

The fate of the Universe, as well as many other things, depend on the density (density parameter).

Can we measure it?

The Friedmann Equations


Age Size and Lifetime of Closed UniversesAge Size and Lifetime of Closed Universes

For closed solutions the size of the Universe will reach a maximum

also we can calculate the lifespan of the Universe - the time from birth to

recollapse, e.g. for q0 = 1.

empty

open

flat

closedt0=

23H0

2cH0

amax

q0 = 1

t L=2H0

decelleration parameter qo


A crude estimate of the densityA 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.

~ 1


Mass to light ratioMass to light ratio can help us to find the density or 0.

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.

MSun

LSun

We define the mass to light ratio as:

M

L= where = 1 for the Sun

MSun

LSun

= 0.51g

erg/s


Mass to light ratio

Two examples: i) <<1 :a system is composed of massive , young and luminous main sequence stars; i) >>1 : 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.

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.


Consider motion of the stars perpendicular to the Galactic plane.

Assume this motion is independent of the conventional circular motion around the Galactic centre.

Dark Matter in the Galaxy


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.


The Oort limit

The acceleration due to gravitational attraction is thus:

dgz / dz = - 4 G

where is the average density of gravitating matter.

Thus near the Sun (Oort limit - 1932, 1965):

= g0 / 4 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).


Density in stars and other luminous matterDensity 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.

M100 spiralM100 spiral stars ~ 0.005

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:

visible baryons 0.01


Density estimated from galactic dynamicsDensity estimated from galactic dynamics

Rotation curves of spiral galaxiesRotation curves of spiral galaxies

The galaxy "M51". Messier 51 is also known as NGC 5194 and sometimes called the Whirlpool galaxy. The distance to M51 is about 9 Mpc

The first real evidence for substantial dark matter came in 1970 with Freeman’s 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?


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:


vcirc2

r

GM(r)

r 2vcirc

GM(r)r

Keplerian decline v ~ r -1/2 is not observed

=gr

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.


Rotation curves of spiral galaxiesRotation curves of spiral galaxiesIn almost all galaxies the velocity is found to be constant with radius.


10-20

10-21

10-22

10-23

10-24

10-25

10-26

10-27

10-28

10-29

LUMINOUS MATTERactual density (Galactic disk)

mean spherical density

DARK MATTERmean spherical density

mean density (g cm-3)

distance from galactic centre (cm)1.1023 2.1023

Sun LMC~30 kpc

~0.3 GeV cm-3

0

HI (layer)HI (Tangent)HI (Petrovkaya)HII (regions)PNs

0 5 10 15 200

100

200

300

/kms-1

R/kpc

Rotation curve of the Milky Way

Milky WayMilky Way



From the observations we can try to model the density distribution:

The easiest model is to assume the galaxy is spherical (we don’t need to assume that the hidden mass is distributed like the visible mass):



We can use: gr GM(r )

r 2 where M(r) is the mass within radius r.

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:

(r)(r2 r0

2 )0r0

2

o, ro are constants

This yields a typical total mass to light ratio in the halo (lower limit is for visible part of galaxy):

halo~ 10 -100

A similar result is obtained when considering orbiting pairs of galaxies.

halo ≈ 0.1 (maximal)


Density estimates for elliptical galaxiesTo 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:

M87 EllipticalM87 Elliptical

halo~ 10 -100

halo ≈ 0.1 (maximal)


Density of clusters from bulk motionsDensity of clusters from bulk motions

Estimates by the virial theoremEstimates by the virial theorem

Example: Coma

2T V 0

clusters ≈ 0.2

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/r=GmM/r2 Hence twice the kinetic energy T is equal to the negative of the gravitation potential energy V. (Correction factor

T 1

2M v

2 V

GM2

R

0.5 2.0

Cluster mass Mean galaxy velocity

M v

2 R

Gclusters~ 200


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.

• 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).

• Account for total velocity (not just vz).


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.

cluster≈ 0.3

Example: ComaExample: Coma

clusters≈ 300The result is:

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.


Estimates from x-ray observationsEstimates from x-ray observationsChandra 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.


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.


Density estimated from gravitational lensingDensity estimated from gravitational lensing

a distant galaxy lensed by a nearer galaxy cluster

cluster≈ 0.3

clusters≈ 300


Map of a galaxy cluster using gravitational lensing Map of a galaxy cluster using gravitational lensing showing the Dark Matter distributionshowing the Dark Matter distribution

Tyson et al.

Density estimated Density estimated from gravitational lensinggravitational lensing


HST deep fieldHST deep field

Density from supercluster dynamicsDensity 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.

supercluster0.80.5

superclusters= 800±500


Density from supercluster dynamicsDensity from supercluster dynamics


Density from theory - structure and inflationDensity 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).

DM ≥ 0.3

0 1


Solar Neighbourhood

Galaxy: Visible Mass

Galaxy: All Mass

Clusters of Galaxies

Large Scale Structure

1

0.1

0.01

0.001

Scale (Mpc)1 100 100000.010.0001

Theoretical Expectation

Baryonic DM problem

Non-baryonic DM problem

Nucleosynthesis Baryon Limits

ConclusionsConclusions

(i) There is a missing mass (dark matter) in the Universe;

(ii) It is seen at all scales from galaxies to superclusters;

(iii) It is also predicted by the theory (simulations of the structure evolution, inflation).

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