E1 Introduction to the universe

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E1 Introduction to the universe


T
he planets orbit the

Sun in ellipses and moons orbit planets. (Details of

Kepler’s laws are not required.)

Students should also

know the names of the planets, their approximate

comparative sizes and comparative
distances from

the
Sun, the nature of comets, and the nature and

position of the asteroid belt.


4 terrestrial planets
:


Mercury, Venus, Earth and Mars


then the asteroid belt.


4 gas giants
:


Jupiter, Saturn, Uranus and Neptune

















E.1.2 Distinguish between a
stellar cluster

(
a group of stars and gas and dust that experience
gravitational attraction)




and a
constellation

(a recognizable group as viewed from the Earth.)


(Interstellar
dust

grains are typically a fraction of a micron across (approximately the wavelength of blue light), irregularly
shaped, and composed of carbon and/or silicates.)


E.1.3 Define
the light year.


(
One l.y. is the distance light travels in a year.)


E.1.4


Compare the relative distances

between
stars within a galaxy

and

between galaxies
, in terms of order of

magnitude.










(Distance between clusters).








T
he apparent motion of the

stars/constellations

(i)


over

one

night




The earth seems to be at the centre of a great sphere.

Each star appears to rotate in


a great circle about an axis through the
geographic
poles
. In the Northern Hemisphere,


the

star Polaris is currently within approximately one degree of the north celestial pole


and thus, from the Northern Hemisphere, all stars and other celestial objects appear


to rotate about Polaris and, depending on the latitude of observation, stars loc
ated


near Polaris may never "set."


(ii)

over
one

year

the earth revolves around the Sun, with the


earth's polar axis


remaining parallel to Polaris.





E2 Stellar radiation and stellar types


Mercury

Venus

Earth

Mars

Jupiter

Saturn

Uranus

Neptune

Pluto

Mean Distance From Sun

(millions of km)

57.9

108.2

149.6

227.9

778.3

1427

2871

4497

5914






m







G


G


C


C







one AU is one astronomical unit


(150 million km = 1.5 x




)


Venus Mars


Mercury

Comets
are lumps
of ice and dust, which are a few km in
diameter. Near the sun a coma forms from liberated gases.

Tails are up to 100 million km long.



Transit of Venus
June 2011


F
usion is the main energy

source of
stars.

(
H
ydrogen is converted into helium.
)



E.2.2 Explain that, in a stable star (for

example, our Sun), there is an

equilibrium between
radiation

pressure

and
gravitational
pressure
.


E.2.3 Define
Luminosity
:
"The total
power

radiated by a star in all directions
.
"



E.2.4 Define
apparent brightness
and state

how it is measured.



The
apparent brightness

(
b
) is how much energy is coming

from
a

star per square meter per second, as measured on Earth.
(
This can be done with a CCD camera
.)



T
wo stars with very different luminosities
may

have the same brightness

as viewed from Earth, if

the more luminous star
is

further away.


Wien’s law and the
Stefan

Boltzmann law


E.2.5 Apply
the

Stefan

Boltzmann law









to

compare the luminosities of different

stars.



E.
2.6 State
Wien’s
law








and

apply it to explain the
connection

between










the colour and temperature

of
stars.




E2.7

Stellar spectra

may be

used to deduce





chemical

data
for stars



The continuous spectrum of a star has absorption lines
,

caused by radiation passing through
gases in cooler
outer layers.



This lets us
identify the gases

in the star.










AND


physical


data

for stars.


The spectra of stars is similar to the spectrum of a black body.


So look at the spectrum and find





W
e
can use
this to
find the temperature
. (Wein's Law).



Students must have a qualitative appreciation of

the Doppler effect as applied to light, including the

terms red
-
shift and blue
-
shift.


(We later meet gravitational redshift, so always refer to Doppler redshift as
DOPPLER redshift
)


E.2.8 Describe the overall classification

system of spectral classes.

(OBAFGKM).



(
decreasing temperature

… our sun is G
2

class).




E.2.9 Describe the different
types of star
.


Students need to refer only to


binary

stars



….
A binary star is a stellar system consisting of two stars orbiting around their center of mass


Cepheid

variables


….. luminosities vary regularly (

Knowledge of different types of Cepheids is not required.)


red giants



….
very large
,
but low surface temperature
.
They have
exhausted their supply of hydrogen in




their cores and switched to fusing hydrogen in a shell outside the core. Since the inert helium core has
no source of energy of its own, it contracts and heats up, and its gravity compresses the hydrogen in the
layer immediately above
it,

causing it to fus
e faster. This in turn causes the star to become more luminous (from 1,000


10,000 times brighter)

and expand; the degree of expansion outstrips the increase in luminosity, thus causing the effective temperature to decrease
)
.

w
hite dwarfs
.


….
smaller t
han Sun, very hot

….
produced when a low or medium mass star dies. These stars are
not heavy enough to generate the core temperatures required to fuse carbon in nucleosynthesis reactions
.
Eventually, over
hundreds of billions of years, white dwarfs will
cool to temperatures at which they are no longer visible. As a class, white dwarfs are
fairly common; they comprise roughly 6% of all stars.

(
Q. Why are white dwarfs so hard to find?
)


O

B

A

F

G

K

M

blue


white


yellow


red









[watts]










[W.



]

































these colours are opposite
to

the

labeling of hot and cold water taps!!


E.2.10 Discuss the characteristics of

spectroscopic and eclipsing bin
ary

stars.


A visual binary star

is a binary star for which
the angular separation is great enough

to permit them to be observed as a
double star in a telescope. The resolving power of the telescope is an important factor in the detection of visual binaries,
and as
telescopes become larger and more powerful an increasing number of visual binaries will
be detected. The brightness of the two
stars is also an important factor, as brighter stars are harder to separate due to their glare than dimmer ones are.







A spectroscopic binary star

is a binary star in which the separation between the stars is usually very small, and the orbital
velocity very high
.
A Doppler shift occurs when they move towards/away from you so the spectrum regularly changes.


An eclipsing binary star

is a binary sta
r

in which the orbit plane of the two stars lies so nearly in the line

of sight of the observer that the components undergo mutual

eclipses. Eclipsing binaries are variable stars, not because the

light of the individual components vary
,

but because of
the eclipses.







The Hertzsprung

Russell diagram

E.2.11 Identify the general regions

….
.


m
ain sequence, red giant, red supergiant, white

dwarf and Cepheid stars


S
cale
s are

not

linear
.


Students should know that the mass of main

sequence stars
determines their

position on the HR

diagram.































E3 Stellar distances


1 AU

1 pc




Cepheid
s

O B A F G K M

30 solar masses


0.1 solar masses


M

-
10

-
5

0

5

10

15



The
temperature of
our Sun is 5800 K

A red star produces little of other colours. A blue star
is producing a lot of the other colours, but mainly blue
.

The

parsec

is t
he

distance at which

one AU

subtends an angle of one second.


Note:
One parsec = 3.26 light years, One light year = 9.46 x




m

(
both
in the data booklet)



Apparent magnitude (
m
)
depends upon

luminosity and distance
. "A measure of how bright a star appears
from the
Earth
."


a magnitude 1 star is 100 times brighter than a magnitude 6 star



1



6


So there is a factor of




(approx
2.51
) increase as you step up the apparent magnitude scale.






Absolute magnitude (
M
)
depends only on

luminosity
.

"A measure of how bright a star would appear if
10 parsecs from
earth
."






Ex 1.

Show that if a star's apparent magnitude is 1.25 and its absolute magnitude is
-

3.92, then it is 108 pc from the Earth.


Ex 2.
m

-

M

= 5 log



can be written in the form

m

-

M

= 5 log d + k
.
Find the value of k.


Ex.3. How many times brighter does a star with
M

=



appear than a star with
M

= 3?


Ex 4. A star has
M

= 0. What colour is it?


Ex 5.
If














what can you conclude about star 1 and star 2?



STELLAR
P
ARALLAX


method

(do not just say
"parallax")

for determining distances to stars.




It relies on the
apparent movement

of the stars

against the

background of further stars as the earth orbits the sun.


The parallax angle θ is observed and measured as the star position changes over the
period of a year.








The parallax movement
s

are very small and are measured in seconds (3600 seconds = 60 minutes = 1 degree
)












































=







































For small angles tan θ = sin θ = θ in radians
.




So



which you can use to find
d
.




(

if p is in radians


then

d

is

in

AU
)



i
f p is in arcseconds

then

d

is

in

parseconds


S
tellar

parallax

is limited to measuring stellar

distances
up to 100

parsecs
.

(
If a star is extremely distant
,

there is very little
parallax.
)


Example:

A star has a parallax angle of 0.2 seconds.

Show its distance from the earth is
16.4 ly
.



Spectroscopic

parallax

…..


has nothing to do with parallax!! ….it is a way of measuring distance to
stars


m

-

M

= 5 log



(
d is measured in
parsecs
)


Now

6 months later











Use



to compare luminosities !!

Eg.


= 4.2


=

2.1





=




















E.3.9 State that the
luminosity of a star may

be estimated


from its spectrum.



E.3.10 Explain how stellar distance may be determined


using apparent brightness and luminosity.


If we know luminosity
L

and apparent brightness











we can find d, the distance.





Th
er
e

is an
assumption made is that the spectra from distant stars are the same as spectra from nearby stars.

Although this method is not accurate for individual stars, if carried out for many stars it can yield statistically useful va
lues.

This method involves quite a lot of uncertainty. Matter between the star and the observer (for example, dust) can
affect the light that is received.
It would absorb some of the light and make the star's apparent brightness less than it should be.


T
he method of

spectroscopic parallax is limited to

measuring stellar distances
less than

several thousand parsecs.


Exercise:





(i) Which star appears brightest from Earth ?





(ii) Which star is the hottest ?



(iii) Find the ratio of the luminosities of Achernar and Mira.

(







(iv) Show that Achernar is approximately 50 parsecs from Earth.

(v) Which star is a white dwarf?


A

Cepheid variables

is a star in which the outer layers undergo a periodic

expansion and contraction, which produces a
periodic variation in its luminosity


E.3.14
State the relationship between period

and absolute magnitude for Cepheid

variables.



Cepheid variables may

be used as “standard candles” to check other methods. I
f a Cepheid

variable is located in a particular galaxy, then the

distance
to the galaxy may be determined by using
the luminosity

period

relationship.


1.

observe the period


2.

use the graph to get the luminosity


3.

Directly measure the brightness b
.

Once you know
b

and
L

then use









to
calculate

the distance to the star.


E4 Cosmology

…. The study of the structure and origin of the universe


Luminosity


or M


log(period)

How to get
luminosity
?



(i
) Examine spectrum and find






(ii) From Wien's Law












we can find
T
.


(
iii)

With T you can go to the H
-
R diagram and find the
luminosity.


(Provided it’s a main sequence star!)




Absolute Magnitude

Apparent Magnitude

Spectral class

Achernar


-

3.0


+ 0.50

B

EG 129

+ 13.0

+ 14.0

B

MIRA


-

3.0


+ 5.0

M


Olbers’ paradox

E.4.1 Describe Newton’s model of the

universe.
Students should know that Newton assumed an

infinite

(in
both
space and time
,

with no centre
and no edge)
,

uniform

and
static

universe.




Principle of isotropy ….universe looks the same in all directions.


E.4.2 Explain Olbers’ paradox.

"If there are infinite stars then the sky should never be dark!"



Imagine a shell (surface area






)
surrounding the earth.


If stars are uniformly distributed in the universe, then the number of stars in the shell



is proportional to





But the brightness from that shell is given by












So there is equal light from all shells.


There is an infinite number of shells, so infinite light, so the sky should always be bright.



HOWEVER



1. The universe is expanding.


2. Gas and dust absorb light.



The Big Bang model


E.4.5 Describe the discovery of cosmic

microwave

background (CMB)

radiation by Penzias and Wilson.

In 1965 they discovered that radiation was coming in all directions from space. The spectrum detected was typical of a black
body
at 3K… this is leftover
heat from the Big Bang.

E.4.6 Explain how cosmic radiation in the

microwave region is consistent with

the Big Bang model.



The universe was hot in its early stages, and has cooled down because of the expansion of the universe.

…. A long wavelength is cons
istent with an expanding and cooling universe.


E.4.7 Suggest how the Big Bang model

provides a resolution to Olbers’

paradox.


If the universe is not infinitely old, light from distant galaxies will not have reached us yet.

(Also universe is expanding)




The development of the universe

E.4.8 Distinguish between the terms open,

flat and closed when used to describe

the development of the universe.

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An open Universe

is one that continues to expand forever. The force of gravity slows the rate of recession of the galaxies

down a little bit but it is not strong enough to bring the expansion to a halt.
A low density universe
.

A closed Universe

is one that is brought to a

stop and then collapses back on itself

( "big crunch"). The force of gravity is enough
to

bring the expansion to an end.
A high density universe
.

A flat Universe

is the mathematical possibility between open and closed. The force of gravity keeps on slowing the expansion
down but it takes an infinite time to get to rest. This would only happen if universe were exactly the right density. One ele
ctron
more, and the g
ravitational force would be a little bit bigger. Just enough to start the contraction and make the Universe closed.


A universe with critical density.

E.4.9 Define the term
critical density
by

reference to a flat model of the

development of the universe.


E.4.10 Discuss how the density of the

universe determines the development

of the universe.


E.4.11 Discuss problems associated with

determining the density of the

universe.

W
e can see only 10% of the matter that must exist in the galaxy. This means that
much of the mass of a galaxy and indeed the
Universe itself must be dark matter
-

in other words we cannot observe it because it is not radiating sufficiently for us to detect it.

M
achos, Wimps and Other Theories to explain why there is so much dark matter

and what it consists of.



the matter could be found in
Massive Astronomical Compact Halo Objects

or
MACHOs

for short. There is some
evidence that lots of ordinary matter does exist in these groupings. These can be thought of as low
-
m
ass failed

stars or
hi
gh
-
mass planets. They could even be black holes. These would produce little or no light.



some fundamental particles (
neutrinos
) are known to exist in huge numbers. It is not known if their
rest
masses

are zero

or just very very small. If they turn out to
be the latter then this could account for a lot of the missing mass.



there could be
new particles

that we do not know about. These are the
Weakly Interacting Massive Particles
.



perhaps

our current theories of gravity are not completely correct. Some theories try to explain the missing matter as
simply a failure of our current theories to take everything into account
.

E.4.12 State that current scientific evidence

suggests that the univer
se is open.


E.4.13 Discuss an example of the

international nature of recent

astrophysics research.

It is sufficient for students to outline any

astrophysics project that is funded by more than

one country.

The
Cosmic Background Explorer (COBE)

was launched on 18 November 1989. COBE determined that the CMB exhibits anisotropies at a level of
one part in 10
5

and showed that the CMB spectrum matched that of a black body with a temperature of 2.725 K ± 2 mK.

ESA's
2009

Planck mission

could answer s
ome of the fundamental questions about the nature of dark matter. Its objective is to analyse, with the
highest accuracy ever achieved, the remnants of radiation that filled the Universe immediately after the Big Bang.

E.4.14 Evaluate arguments related to

investing significant resources

into researching the nature of the

universe.

Students should be able to demonstrate their

ability to understand the issues involved in deciding

priorities for scientific research as well as being able

to express their own
opinions coherently.

E5 Stellar processes and stellar evolution


Stars begin as

H, He and dust
. As the masses attract, temperature increases. Once nuclear fusion begins, it prevents gravitational
collapse.

Originally
two
hydrogens fuse to give helium but
then helium nuclei can fuse to give larger nuclei.

(
Light elements combining into heavier elements is called
nucleosynthesis
.
)
The final stage of this process in large stars

is called
silicon burning.


























































Red Giants
. Once a small or medium star has used up most of the hydrogen in its core, contraction will occur.







This causes
the temperature of the core to increase,

so the outer layers expand.




The surface
temperature drops
, but the
luminosity increases

due to greater surface area!


The helium in the core
then
fuses into
carbon and
oxygen
.

The helium in th
e outer layers is then ejected and forms

a

glowing
shell of gas and plasma

(
a

planetary nebula
)

and the core cools to become a
white dwarf.




White dwarfs

are formed from the cores of small stars that have run out of fuel.

They are the final
evolutionary state

of all stars
whose mass is not high enough
(
less than 8 times the mass of the sun
)

to become a
neutron star

97% of the stars in
our galaxy
.


"
White dwarfs are stable due to electron degeneracy pressure
" (
e
lectrons are packed together as closely as possible
)


*
Degenerate matter

is
matter

that has such extraordinarily high
density

that the dominant contribution to its
pressure

is attributable to the
Pauli exclusion principle

(the constituent particles cannot occupy iden
tical
quantum states
.) When particles are forced close together, they are not clearly separated by position, so they
must occupy different energy levels. Therefore, reducing the
volume requires forcing many of the particles into higher
-
energy quantum states.


A white dwarf is very hot when it is formed, but since it has no source of energy, it will gradually radiate away its energy
and
cool down

and become redder
. Over a very
long time

they

will cool to become a cold
black dwarf
. However, since no white dwarf
can be older than the
age of the Universe

(approximately 13.7 billion years) even the oldest white dwarfs still radiate at
temperatures of a few thousand
kelvin
, and no black dwarfs are thought to ex
ist yet.



The mass


luminosity relationship
.



(
only

applies

to main sequence stars
)





Eg. If star A has
9

times the mass of star B, show that

the ratio of their luminosity per unit mass
es is 2
43
:1










M
ore massive star
s generate

stronger gravitational

f
ield
s,
and
so have

higher

pressures in the
ir

core
s.

Therefore they


convert
their

fuel into energy
faster

and
more efficiently
.
Although t
hey

have larger fuel supplies than low mass stars,

they

burn through it more quickly (hence they are much brighter), so their Main Sequence

lifetimes are
far shorter
.

























)
































E.5.7 Draw
evolutionary paths

of stars on an H R diagram.


















P
ulsar
s
are

rotating neutron stars

emitting radio wave pulses
.


Neutron stars have strong magnetic fields.


Magnetic fields accelerate charged particles, which release radiation.)



This radiation can only be observed when the beam of emission


is pointing toward the Earth, much the way a lighthouse can only


be see
n when the light is pointed in the direction of an observer,


and is responsible for the pulsed appearance of emission.







E
6 Galaxies and the expanding universe


Galactic motion
.
E.6.1 Describe the distribution of galaxies

in the universe.





a neutron star is stable due to

neutron degeneracy pressure

Proto
-
star forms from interstellar dust and gas

Red Giant

Carbon
-
oxygen
core

Red Giant

Oxygen
-
neon core

Red Super Giant

Iron core

White Dwarf

Neutron star or Black Hole


Solar masses

0

4

8

20

Planetary nebula


Supernova


(
A supernova has sufficient energy to

fuse

elements higher than iron.
)


Chandrasekhar limit
:
White

dwarfs must have mass less
than 1.4
4

times the mass of
the sun.


Oppenheimer

Volkoff

lim
i
t
:
Neutron
stars

must have mass less than
2 to 3

times the mass of the sun
,
or they will
become a

black hole.





Galaxies

form
clusters

….
" Galactic cluster"


Clusters form
superclusters
.

The existence of superclusters indicates that the galaxies in our Universe

are not uniformly distributed.


T
here are three types of galaxies …..

spiral (Milky Way),





elliptical,

and irregular







E.6.2 Explain the red
-
shift of light from

distant galaxies.


Students should realize that the red
-
shift is due to

the expansion of the universe.

Doppler

redshift

is a phenomenon in which the visible light from an object is shifted towards the red end of the spectrum. It is an
observed increase in the wavelength, which corresponds to a decrease in the frequency of electromagnetic radiation, received
by a
detector c
ompared to that emitted by the source. The corresponding shift to shorter wavelengths is called blueshift.

E.6.3 Solve problems involving
(Doppler)
red
-
shift

and the recession speed of galaxies.





Hubble’s law
.

In 1929, Edwin Hubble announced that almost all galaxies appeared to be moving away from us. In fact, he
found that the Universe was expanding
-

with all of the galaxies moving away from each other. This phenomenon was observed as
a redshift of a galaxy's
spectrum. This red
-
shift appeared to be larger for faint, presumably further, galaxies.

Hence,
the farther a galaxy, the faster it is receding from Earth
.
If you are asked to state Hubble's Law say







E.6.5 Discuss the limitations of Hubble’s

law.



1.
Distances to
gal
axies are difficult to measure.

2.
It should be noted that, on very large scales, Einstein's theory predicts departures from a strictly linear Hubble law.

3. … and nearby galaxies cannot be used to verify Hubble's Law because they are more affected

by gravitation that expansion.


E.6.6 Explain how the Hubble constant may

be determined.

Find
v

from Doppler shift and measure
d

distance using Cepheids etc


E.6.7 Explain how the Hubble constant may

be used to estimate the age of the

universe.


Time

=



=




=





=






















=














=
































=
15 billion years


E.6.8 Solve problems involving Hubble’s

law.


E.6.9 Explain how the expansion
of the

universe made possible the formation

of light nuclei and atoms.


Students should appreciate that, at the very high

temperatures of the early universe, only elementary

(fundamental) particles could
exist and that

expansion gave rise to cooling

to temperatures at

which light nuclei could be stable.


Doppler Effect





=






where

H is the Hubble constant

(difficult to measure) and






is the recessional speed
of a galaxy

(due to the expansion of the universe)




d

is the distance
of the galaxy from the Earth
.