Download E1 Introduction to the universe

E1 Introduction to the universe
The 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
4 gas giants:
Jupiter, Saturn, Uranus and Neptune
Asteroid belt is in between.
Comets are lumps of ice and dust.
A few km in diameter.
Near the sun a coma forms from
liberated gases.
Tail up to 100 million kilometres.)
one AU is one astronomical unit
(150 million km = 1.5 x 1011 𝑚)
Mercury Venus
Mean Distance
From Sun
(millions of
km)
57.9
108.2
Earth Mars
Jupiter Saturn
149.6 227.9
778.3
1427
Uranus Neptune Pluto
2871
4497
5914
E.1.2 Distinguish between a stellar cluster (gravitational attraction) and a constellation (a recognizable group as viewed from the
Earth.)
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).
G
1017 m
G
C
1023 𝑚
The 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 located
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.
C
1024 𝑚
E2 Stellar radiation and stellar types
Fusion is the main energy source of stars. (Students should know that hydrogen is converted into helium. They do not
need to know about the fusion of larger elements. )
E.2.2 Explain that, in a stable star (for example, our Sun), there is an equilibrium
between radiation pressure and gravitational pressure.
Luminosity
E.2.3 Define the luminosity of a star.
"The total power radiated by a star in all directions is known as its luminosity".
E.2.4 Define apparent brightness and state how it is measured.
The apparent brightness (b) is how much energy is coming from the star
per square meter per second, as measured on Earth.
𝐿=
𝑏=
[W.𝑚
𝑡𝑜𝑡𝑎𝑙 𝑒𝑛𝑒𝑟𝑔𝑦
𝑡𝑖𝑚𝑒
[watts]
𝐿
4𝜋𝑑 2
−2
]
Two 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
stars.
E.2.6 State
between
of stars.
E2.7
Stefan–Boltzmann law
𝐿 = 4𝜋𝑟 2 𝜎𝑇 4
Wien’s law 𝜆𝑚𝑎𝑥 . 𝑇 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 = 2.9 𝑥 10−3 𝑚𝐾
to compare the luminosities of different
and apply it to explain the connection
the colour and temperature
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.
(i)
So look at the spectrum and find 𝜆𝑚𝑎𝑥
(ii)
Use this to find the temperature. (Wein's Law).
(iii)
Use this to find the luminosity. (Stefan-Boltzmann Law.)
(iv)
Measure the apparent brightness.
(v)
Use this to calculate distance to the star.
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
class).
http://www.setileague.org/songbook/obafgkm.htm
Types of star
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.)
…. 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 fuse 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).
red giants
…. smaller than 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.
white dwarfs.
E.2.10 Discuss the characteristics of spectroscopic and eclipsing binary 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 star
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 …..
main sequence, red giant, red supergiant, white dwarf and Cepheid stars
scales of luminosity and/or absolute magnitude, spectral class and/or surface temperature
Students should be aware that the scale is not linear.
Students should know that the mass of main sequence stars determines their position on the HR diagram.
O
B
A
F
G
K
M
M
Cepheids
30 solar masses
-10
-5
0
5
If two stars have the
same luminosity, they
also have the same
absolute magnitude.
𝐿1
𝑀1
=
𝐿2
𝑀2
10
0.1 solar masses
15
The temperature of
our Sun is 5800 K
E3 Stellar distances
The parsec is the distance at which one AU subtends an angle of one second.
1 AU
1 pc
Note: One parsec = 3.26 light years, One light year = 9.46 x 1015 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
1
So there is a factor of 1005 (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."
m - M = 5 log
𝒅
𝟏𝟎
(d is measured in
parsecs)
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
𝑑
10
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 = -4 appear than a star with M = 3?
Ex 5. If
Ex 4. A star has M = 0. What colour is it?
𝐿1
𝐿2
=
𝑏1
𝑏2
what can you conclude about star 1 and star 2?
STELLAR PARALLAX 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.
6 months later
Now
The parallax movements are very small and are measured in seconds (3600 seconds = 60 minutes = 1 degree)
tan 𝑝 =
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝐸𝑎𝑟𝑡ℎ 𝑡𝑜 𝑡ℎ𝑒 𝑆𝑢𝑛
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑆𝑡𝑎𝑟 𝑡𝑜 𝑡ℎ𝑒 𝑆𝑢𝑛
For small angles tan θ = sin θ = θ in radians.
So
( if p is in radians
if p is in arcseconds
𝑝=
then
then
1
which you can use to find d.
𝑑
d
d
is in
is in
AU)
parseconds
Stellar parallax is limited to measuring stellar distances less than several hundred 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
E.3.9 State that the luminosity of a star may be estimated
from its spectrum.
How to get luminosity?
(i) Examine spectrum and find
E.3.10 Explain how stellar distance may be determined
using apparent brightness and luminosity.
If we know luminosity L and apparent brightness
𝑏=
𝐿
4𝜋𝑑 2
𝜆𝑚𝑎𝑥 .
𝜆𝑚𝑎𝑥 . T = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
(ii) From Wien's Law
T.
we can find
we can find d, the distance.
(iii) With T you can go to the H-R diagram and find the
luminosity.
it’s anearby
main sequence
star!)
There is an assumption made is that the spectra from distant stars are the same (Provided
as spectra from
stars.
Although this method is not accurate for individual stars, if carried out for many stars it can yield statistically useful values.
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.
The method of spectroscopic parallax is limited to measuring stellar distances less than several thousand parsecs.
Ex.
(i) Which star appears brightest from Earth ?
(ii) Which star is the hottest ?
(iii) Find the ratio of the luminosities of Achernar and Mira. (2.5116 )
(iv) Show that Achernar is approximately 50 parsecs from Earth.
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
Luminosity
or
M
log(period)
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. If 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
Once you know b and L then use
𝑏=
𝐿
4𝜋𝑑 2
3. Directly measure the brightness b.
to calculate the distance to the star.
E4 Cosmology …. The study of the structure and origin of the universe
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 4𝜋𝑟 2 ) surrounding the earth.
If stars are uniformly distributed in the universe, then the number of stars in the shell
is proportional to 𝑟 2 .
But the brightness from that shell is given by
𝑏=
r
𝐿
4𝜋𝑟 2
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
The ‘Big Bang’ theory states that both space and time originated
from a singularity
The universe is not expanding into anything; even a void. It is
simply expanding. There is also no such time as ‘before the Big
Bang’, as time itself was created in the Big Bang.
Edward Hubble's observations of the red-shift of light from distant
galaxies is evidence that the universe is expanding.
We are NOT at the centre of the universe. Consider painted dots
on the surface of a balloon; as the balloon is inflated, the dots
would all move away from each other equally.
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 consistent 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.
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 electron
more, and the gravitational 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.
We 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.
Machos, Wimps and Other Theories
Astrophysicists are attempting to come up with theories to explain why there is so much dark matter and what it
consists of. There are a number of possible theories:




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-mass failed stars or
high-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 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. Many
experimenters around the world are searching for these so-called WIMPs.
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 universe 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.
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
Nucleosynthesis (Nucleosynthesis is the process of combining light elements into heavier elements, also known as
fusion.)
E.5.1 Describe the conditions that initiate fusion in a star.
Start with H, He and dust. As the masses attract, temperature increases. Once nuclear fusion begins, it prevents gravitational
collapse.
E.5.2 State the effect of a star’s mass on the end product of nuclear fusion.
Initial mass ∝ final surface temperature (which determines luminosity)
E.5.3 Outline the changes that take place in nucleosynthesis when a star leaves the main sequence and
becomes a
red
giant.
Once the hydrogen in the core is used up, contraction will occur.
This causes T↑
This causes outer layers to expand.
The surface temperature drops, but the luminosity increases due to greater surface area!
The helium in the core fuses into oxygen and carbon…. They fuse to form silicon.
The helium in the outer layers is then ejected, (A planetary nebula is an astronomical object consisting of a glowing shell of gas
and plasma formed by certain types of stars at the end of their lives. They are in fact unrelated to planets. ) and the core cools to
become a white dwarf.
( White dwarfs are stable due to electron degeneracy pressure … electrons are packed together as closely as possible )
Students need to know an outline only of the processes of helium fusion and silicon fusion to form iron.
Evolutionary paths of stars and stellar processes
𝐿 = 𝑘𝑀3.5 (𝑙 = 𝑘𝑀 2.5 )
E.5.4 Apply the mass–luminosity relation.
can only be applied 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 masses is 243:1
A more massive star generates a stronger gravitational
field than a less massive one. This creates higher
pressures in the stellar core, which means that the star
converts its fuel into energy faster and more efficiently.
Though high mass stars 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.5.5 Explain how the Chandrasekhar (for main sequence stars) and Oppenheimer–Volkoff (for neutron stars) limits are used to
predict the fate of stars of different masses.
Chandrasekhar limit: White dwarfs must have mass less than 1.4 times the mass of the sun.
(all stars with mass less than 8 times the mass of the sun end up as white dwarfs).
Oppenheimer–Volkoff: Neutron stars must have mass less than 2 to 3 times the mass of the sun, or they will become a
black hole.
E.5.6 Compare the fate of a red giant and a red supergiant.
Students should know that:
• a red giant forms a planetary nebula and then becomes a white dwarf
• a white dwarf is stable due to electron degeneracy pressure
• a red supergiant experiences a supernova and becomes a neutron star or collapses to a black hole
• a neutron star is stable due to neutron degeneracy pressure.
E.5.7 Draw evolutionary paths of stars on an HR diagram.
H-R diagram can also be used to plot the evolution of a star from its birth as a protostar until its death as a white dwarf
Proto-star formed from interstellar dust and gas
Main sequence star
less than 4𝑀𝑆
Red Giant
Carbon-oxygen core
Main sequence star
between 4𝑀𝑆 and 8𝑀𝑆
Red Giant
Oxygen-neon core
Main sequence star
above 8𝑀𝑆
Super Red Giant
Iron core
Supernova
Planetary nebula
Neutron star or Black Hole
White Dwarf
A supernova has sufficient energy to fuse elements higher than
iron.
Eventually, over hundreds of billions of years, white dwarfs will cool to temperatures at which they are no longer visible.
However, over the universe's lifetime to the present (about 13.7 billion years) even the oldest white dwarfs still radiate at
temperatures of a few thousand kelvin.
E.5.8 Outline the characteristics of pulsars. ….. rotating neutron stars emitting radio wave pulses. (Neutron stars have strong
magnetic
fields. Magnetic fields accelerate charged particles, which release radiation.)
E6 Galaxies and the expanding universe
Galactic motion
E.6.1 Describe the distribution of galaxies in the universe.
Galaxies form clusters …." Galactic cluster"
Clusters form superclusters.
The existence of superclusters indicates that the galaxies in our Universe
are not uniformly distributed.
There are three types of galaxies ….. spiral (Milky Way),
elliptical,
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 compared 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.
Doppler Effect
∆𝜆
𝜆
=
𝑣
𝑐
Hubble’s lawIn 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.
E.6.4 State Hubble’s law.
𝑣 = 𝐻𝑑
where H is the Hubble constant (difficult to measure)
V is the recessional speed of a galaxy ( due to the expansion of the universe)
E.6.5 Discuss the limitations of Hubble’s law.
1. Distances to galaxies 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.
(Students need only consider a constant rate of expansion.)
Time =
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑠𝑝𝑒𝑒𝑑
=
𝑑
𝐻𝑑
=𝐻
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.