Download PHYSICS – Astrophysics Section I

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PHYSICS – Astrophysics
Section I- Our understanding of celestial objects depends upon observations
made from Earth or from space near the Earth
Discuss Galileo’s use of the telescope to identify features of the Moon
In 1609, Galileo constructed his own powerful telescope after hearing about its ability to make
objects look closer. He used it to observe many phenomenon of the Solar System, including features
of the Moon. Galileo saw that the Moon was not perfect and unchanging as was the prevailing
Aristotelian view, but in fact had a very rough surface. He observed the “seas” and mountains on the
surface of the Moon as well as craters. These observations blatantly contradicted the Church’s
Aristotelian beliefs at the time, and were some of the reasons leading to his arrest by the Church.
[NOTE]- Be careful not to discuss Galileo’s more famous observations of the moons of Jupiter or the
phases of Venus. This dot-point clearly states “the Moon”.
Discuss why some wavebands can be more easily detected from space
Different wavebands (a range of wavelengths) of light have differing properties. One of these
properties is absorption by the Earth’s atmosphere. Gamma and x-rays are strongly absorbed by the
upper atmosphere, and very little of these wavebands reach the surface of the Earth. Most of the
ultraviolet radiation is absorbed by the ozone layer, with some reaching the surface. Almost all
visible light reaches the surface of the Earth, although some wavelengths are scattered more easily
than others. Infra-red and microwaves are partially absorbed by the atmosphere, and most radio
waves are allowed through to reach the surface.
With this, it can be deduced that detecting the wavebands to which the Earth’s atmosphere is
partially or almost totally opaque (gamma, x-ray, UV, infra-red and microwave) from the surface of
the Earth is very difficult. It is much easier to detect such wavebands of electromagnetic radiation
from space, as then there is no (or very little) atmosphere to absorb these wavebands.
Define the terms ‘resolution’ and ‘sensitivity’ of telescopes
The sensitivity of a telescope is its ability to detect light. The higher the sensitivity, the fainter the
star (or galaxy, planet, etc.) can be detected. The sensitivity of a telescope is dependent on its
aperture (more specifically, the surface area of the lens/mirror). Sensitivity is sometimes referred to
as “light-gathering ability”.
The resolution of a telescope is its ability to clearly distinguish between two very close objects. The
higher the resolution, the closer and smaller the two objects can be and still be distinguished from
each other. A high resolution is required to view celestial objects because otherwise close objects’
diffraction fringes overlap with a low resolution, and this makes them appear as a single “blob”
rather than several distinct points.
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Identify data sources, plan, choose equipment or resources for, and perform an investigation to
demonstrate why it is desirable for telescopes to have a large diameter objective lens or mirror in
terms of both sensitivity and resolution
Aim: To determine the relationship between diameter and surface area of a circle (representing the
lens/mirror)
Materials: Paper rings of various diameter, M&Ms
Procedure:
1. Measure the diameters of each paper ring
2. Place as many M&Ms as possible within the ring without overlapping
3. Count the number of M&Ms that fit
Results: You should have a table of diameter and number of M&Ms. This can be plotted as a line
graph.
Conclusion: the number of M&Ms was directly proportional to the square of the diameter. Thus it
can be deduced that a small increase in the size of a telescope’s lens/mirror diameter has a large
increase in its sensitivity (increase in resolution is directly proportional to the increase in diameter).
Discuss the problems associated with ground-based astronomy in terms of resolution and absorption
of radiation and atmospheric distortion
Ground-based astronomy is strongly affected by atmospheric distortion, which includes problems
such as “seeing”, dust and gases. Incoming light must travel through kilometres of the Earth’s
atmosphere. The variations in temperature, density and other properties of the atmosphere
constantly alters the refractive indices, and this causes the object being viewed to flicker and change
colour constantly, which presents a major problem in observing the object as it drastically reduces
resolution.
In addition, the Earth’s atmosphere selectively absorbs and/or scatters many wavelengths of light,
preventing these wavelengths from being detected properly with ground-based astronomy. This
strongly limits the sensitivity of ground-based methods of detection for wavelengths that are
absorbed. The atmosphere also absorbs different wavelengths to different extents. This distorts
incoming radiation, effectively limiting the resolution of ground-based telescopes to approximately
0.01 arc seconds.
As a result of these problems, many telescopes are built at high altitude (atop a mountain) or placed
into Earth’s orbit to overcome these problems.
Outline methods by which the resolution and/or sensitivity of ground-based systems can be improves,
including
 adaptive optics
 interferometry
 active optics
Adaptive Optics
Adaptive optics is a technique utilised in telescopes and radio dishes to significantly reduce the
effects of atmospheric distortion (seeing) by constantly correcting the incoming perturbed
wavefronts. Adaptive optics systems sample light from a nearby bright star, detecting the effects of
atmospheric distortion in real-time. A computer processes this information, and corresponding
signals are sent to a tilt-tip and/or a deformable mirror (with piezoelectric actuators that push and
pull on the mirror by as little as 4 nanometres), which then correct the distorted light waves. By
sampling the light up to 1000 times per second and adjusting the mirror(s) to compensate for any
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atmospheric distortion, the adaptive optics system effectively straightens out the incoming light
rays, drastically improving image resolution (sensitivity is improved slightly).
Interferometry
Interferometry is based on the fact that although a telescope’s sensitivity is based on its surface
area, its resolution is based only on its diameter. A telescope reflects the incoming wavefronts to
add up (via the law of superposition) in such a way as to produce a sharper image (higher
resolution). By having multiple telescopes (or radio dishes) in an array, the individual waves detected
by each telescope can be carefully combined by a computer to give image resolution exactly like that
of a larger telescope. Thus, two telescopes (or radio dishes) placed 100m from each other together
will have the same resolving power as a telescope (or radio dish) with a diameter of 100m.
Interferometry allows high-resolution images to be much more attainable, as building telescopes (or
radio dishes) with diameters the same as modern arrays would be completely impractical. However,
interferometry does very little to improve sensitivity.
Active Optics
Active optics is a technique similar to adaptive optics, except it is not designed to correct
atmospheric distortion. Instead, many actuators make minor adjustments every minute or so to
correct the shape of the mirror. Unlike adaptive optics, active optics works on a far slower basis,
correcting imperfections in the actual mirror due to sagging, heat expansion, etc. This means that
telescopes and dishes can be made bigger, as shape distortion due to weight can be corrected.
Active optics improves resolution significantly as well as sensitivity, as mirrors can be made larger.
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Section II- Careful measurement of a celestial object’s position in the sky
(astrometry) may be used to determine its distance
Define the terms parallax, parsec and light-year
Parallax is the apparent movement of an object relative to the background due to a change in
position of the observer.
A parsec is a unit of astronomical measurement. One parsec is the distance of the hypotenuse at
which the radius of the Earth’s orbit (1 AU) subtends an angle of one second of arc (arc second).
A light-year is another unit of astronomical measurement. One light-year is the distance that light
moves in a year (through vacuum).
Explain how trigonometric parallax can be used to determine the distance to stars
By observing a nearby star against the background of more distant stars on two separate occasions
when the Earth is at the opposite end of its orbit, we can measure the parallax (the subtended
angle). Using basic trigonometry, the adjacent side of this triangle (i.e. the required distance) can be
calculated as one side and two angles are known on a right-angled triangle.
Solve problems and analyse information to calculate the distance to a star given its trigonometric
parallax using:
1
𝑑=
𝑝
This formula requires either the distance (in parsecs) or the parallax angle (in arc seconds) to work.
Shouldn’t be hard.
Discuss the limitations of trigonometric parallax measurements
Trigonometric parallax, although useful, has several limitations on its usefulness in finding distances
to other stars. Atmospheric distortion (seeing) effectively limits the parallax angle measurable by
ground-based telescopes to 0.01 arcseconds. This translates to a distance of only 100 parsecs, which
accounts for approximately 700 stars.
[NOTE]- Although the dot-point requires plural, I really can’t think of any others that are significant.
Gather and process information to determine the relative limits to trigonometric parallax distance
determinations using ground based and space based telescopes
Ground based telescopes suffer from the problems of seeing and light pollution, and their effective
resolution is limited to 0.01 arcseconds (usually not even that).
Space telescopes are able to have much greater resolution. For example, the Hipparcos satellite
launched in 1989 has a resolution of 0.001 arcseconds, allowing it to view stars that are much
further away.
The successor to Hipparcos is called GAIA, and is expected to measure parallax of up to 0.000007
(seven-millionths) of an arcsecond.
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Section III- Spectroscopy is a vital tool for astronomers and provides a wealth of
information
Account for the production of emission and absorption spectra and compare these with a continuous
black-body spectrum
Continuous Spectrum
A continuous black-body spectrum is a full spectrum of all wavelengths within a range, lacking bright
emission lines or dark absorption lines. A continuous spectrum is given off by hot solids, liquids and
high pressure gases, where there is constant interaction between atoms and molecules. The peak
wavelength and range of wavelengths of the continuous spectrum is given by the Planck black-body
radiation curves.
Emission Spectrum
An emission spectrum appears as multiple bright lines against a dark background. An emission
spectrum is given off when atoms, molecules or nuclei are energised with minimal interaction with
neighbouring particles, for example in diffuse gases. In the Bohr model of the atom, there are
discrete energy states (orbitals) at which electrons can exist. Electrons cannot exist between these
states and movement from one state to another requires either gaining or releasing a specific
amount of energy (for electromagnetic radiation this translates to a specific wavelength of light).
Emission spectra are formed when energised particles (atoms, molecules or nuclei) have their
electrons move into a lower energy state. Because energy states are discrete, each movement
corresponds to a specific amount of energy, i.e. a specific wavelength of light. Molecules tend to
emit bands rather than lines since they have interaction of atoms within themselves. Every atom has
distinct emission lines, and these are used to identify the element.
Absorption Spectrum
An absorption spectrum is the opposite of an emission spectrum, with dark lines against a
continuous spectrum. Just as atoms can only emit certain wavelengths of light, similarly they can
only absorb these wavelengths. When a continuous spectrum of light is passed through the atom,
the electrons absorb certain wavelengths and re-emit them in all directions, so in the view of the
detecting equipment the spectrum appears incomplete, with several discrete wavelengths missing.
Describe the technology needed to measure astronomical spectra
To measure astronomical spectra, astrophysicists use spectroscopes (AKA spectrometer). The two
main types of spectroscopes are prism spectroscopes and diffraction spectroscopes. A prism
spectroscope allows the light to pass through a prism, which spreads the light into a band of
wavelengths. A diffraction spectroscope is similar, but instead of a prism it utilises a diffraction
grating for the same effect.
Computers are then used to refine and analyse the data collected by spectroscopes.
Perform a first-hand investigation to examine a variety of spectra produced by discharge tubes,
reflected sunlight or incandescent filaments
In this “prac” you used spectroscopes and stared at different light sources such as mercury discharge
lamps, sodium discharge lamps, fluorescent lights and incandescent lights. You should’ve seen the
various spectral lines exhibited by these lights.
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Identify the general types of spectra produced by stars, emission nebulae, galaxies and quasars
Stars produce absorption spectra. The light actually produced by nuclear fusion is continuous, but
the atmosphere of the star selectively absorbs wavelengths, forming an absorption spectrum. This is
used to identify elements on the surface of the star.
Emission nebulae produce emission spectra. The spectra result when interstellar gas clouds
surrounding hot stars are excited by radiation from the star. The elements present in the nebula
then emit their characteristic emission lines.
Galaxies produce continuous spectra. Because there are stars of all types as well as different nebulae
and quasars, galaxies emit radiation across the entire electromagnetic spectrum.
Quasars produce emission spectra. Quasars emit enormous amounts of energy, mostly from gases
that are highly energised. Quasars exhibit a continuous spectrum with very strong emission lines,
and thus are classified as producing emission spectra.
Describe the key features of stellar spectra and how these are used to classify stars
Stellar spectra consist of a continuous spectrum superimposed with dark absorption lines. The main
feature of stellar spectra is the wavelengths at which the absorption lines are present (i.e. the
missing wavelengths). By analysing the combination of absorption lines and comparing them to the
known absorption lines of elements (and some molecules/ions), the atmospheric composition of the
star can be deduced. The different classifications (OBAFGKM) of stars exhibit different spectral lines
(mostly due to the temperature of the star), so knowing the spectrum of a star will allow its spectral
class to be deduced. The spectral features of different spectral classes are below:
Spectral Class
O
Colour
Blue
Colour Index
-0.30
Surface Temp.
30 000+ K
B
Blue-white
-0.15
15 000 – 30 000 K
A
White
0.00
10 000 – 15 000 K
F
White-yellow +0.40
7 000 – 10 000 K
G
Yellow
+0.80
5 000 – 7 000 K
K
Orange
+1.20
4 000 – 5 000 K
M
Red
+1.80
3 000 – 4000 K
Spectral Features
-strong lines of ionised He
-lines of doubly ionised O, N,
C
-neutral He lines most
prominent
- H lines stronger than O lines
-H lines most prominent
-singly ionised Mg, Si, Fe, Ca,
Ti present
-slightly weaker H lines
-neutral metals are stronger
-ionised Ca most prominent
-weak H lines
- neutral and singly ionised
metals present
-neutral metals most
prominent
-H almost non-existent
-molecular bands present
-molecular bands most
prominent
-TiO bands very prominent
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Describe how spectra can provide information on surface temperature, rotational and translational
velocity, density and chemical composition of stars
Surface temperature- by finding the dominant wavelength in the spectra emitted by stars, the
temperature of the star can be deduced from the Plank black-body radiation curves. The closer the
dominant wavelength is to the blue end of the spectrum the higher the surface temperature.
Rotational velocity- If a star is rotating, one side will be red-shifted and one side will be blue-shifted.
This will cause the spectral absorption lines to broaden. The rate of rotation can be deduced from
the extent of the broadening.
Translational velocity- A star that is moving away from us will have its spectral lines all red-shifted. A
star moving towards us will have its spectral lines blue-shifted. The velocity at which they are moving
away from us can be deduced by the extent of the red/blue-shifting.
Density- A denser star will have more interactions between surface molecules due to the increased
gravitational pull. This causes the spectral lines to broaden (though in a different way to rotational
velocity) similar to the way molecules’ lines are broad. The denser the star, the broader the spectral
lines become.
Chemical composition- stellar spectra can only provide information on the chemical composition of
the surface of the star (other techniques must be used for internal processes). The absorption lines
given off by a star is a combination of all the individual atoms’ (or molecules’/ions’) spectral lines. By
comparing the lines to the known spectral lines on elements (or molecules/ions) the elements
present in the atmosphere of the star can be deduced.
Analyse information to predict the surface temperature of a star from its intensity/wavelength graph
Graphs of black body radiation curves such as the one below can be used to predict the surface
temperature of a star given its dominant wavelength.
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Section IV- Photometric measurements can be used for determining distance and
comparing objects
Define absolute and apparent magnitude
Absolute magnitude is the brightness a star would have if it were a standard distance of 10 parsecs
away from Earth.
Apparent magnitude is the brightness as seen by an observer on Earth. It is based on luminosity of
the star as well as distance.
[NOTE]- For apparent magnitude you must say “from Earth” despite the fact that humans haven’t
placed telescopes anywhere else.
Explain how the concept of magnitude can be used to determine the distance to a celestial object
If a star’s absolute and apparent magnitudes are known, the formula
𝑚 − 𝑀 = 5 log10
𝑑
10
can be used to determine its distance away from Earth. This is related to the inverse square law. The
difference between its absolute magnitude and its apparent magnitude is mostly affected by
distance (some is due to dust, gas and other interstellar particles, but this is usually ignored as it is
negligible), and thus distance can be calculated if the absolute and apparent magnitudes are known.
Solve problems and analyse information using:
𝑑
𝑀 = 𝑚 − 5 log
10
𝑀𝐵 −𝑀𝐴
𝐼𝐴
= 100 5
𝐼𝐵
to calculate the absolute or apparent magnitude of stars using data and a reference star
The first equation is used to calculate the absolute magnitude given the distance and apparent
magnitude (often it is used to calculate distance given M and m).
The second equation is used to calculate the ratio of luminosities of two stars given their absolute
magnitudes.
Outline spectroscopic parallax
Spectroscopic parallax is an extremely approximate method of determining the distance to another
star, used only when there are no other options due to its lack of precision. The name “spectroscopic
parallax” is also misleading since it doesn’t utilise the principle of parallax at all. In spectroscopic
parallax, first the spectra of the star is analysed to determine its spectral class. Using the H-R
diagram, an approximation of the star’s absolute magnitude can be made. Since apparent magnitude
can always be measured, the distance modulus formula (above) can then be used to determine the
distance.
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Explain how the two-colour values (that is, colour index, B-V) are obtained and why they are useful
The human eye is most sensitive to colours in the yellow-green spectrum whereas photographic
emulsions are most sensitive to blue-violet light. This discrepancy means that a blue star will appear
brighter on an image than to a human observer. B is the brightness of the star measured through a
blue filter (lower number means brighter) and V is the brightness of a star measured through a
yellow filter (V for visual). The colour index is found by subtracting the two values, giving a negative
value for blue stars and a positive number for redder stars. Colour index is useful because it provides
a quick way of determining a star’s spectral class.
Perform an investigation to demonstrate the use of filters for photometric measurements
Aim: To observe the effect of different coloured filters on the brightness of different colour lights.
Materials: light meter, red light, blue light, yellow light, red filter, blue filter, yellow filter
Procedure:
1. Set up the light sources separately.
2. Aim the light meter at the red light and record the reading (this is the control for red light)
3. Place each of the three filters between the light and the meter, recording each respective
reading
4. Repeat steps 2 and 3 but with the blue and yellow lights
Results: Each light’s respective filter should affect the light reading the least (i.e. red for red, blue for
blue, yellow for yellow). The yellow filter did not affect the others as much, but the blue filter
strongly limited the amount of light coming through.
Conclusion: Use of different colour filters affects the intensity of the light. This discrepancy can then
be used to calculate colour index.
Describe the advantages of photoelectric technologies over photographic methods for photometry
Photoelectric photometry utilises either a photomultiplier tube or a charge-coupled device (CCD) to
detect photons can convert the light into an electric current. A photomultiplier tube uses an array of
sequential dynodes, which detect light and amplify it, producing a strong, measurable current. A CCD
uses circuitry to detect individual photons and arranges the signal in either a line or grid of pixels.
Photographic photometry relies on visual comparisons of photographs of stars, where the diameter
of the star is related to its brightness. There is a complex relationship between the size and density
of the image and its brightness, and this reduces the accuracy of photographic photometry.
Photoelectric photography has numerous advantages over photographic photometry:
 far greater sensitivity (resolution is lower however) because of the electronic amplification
techniques
 sensitive to a wider range of wavelengths
 much more information can be stored digitally than physically
 information can be retrieved and analysed easily in a digital format
 faster and more accurate
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Identify data sources, gather, process and present information to assess the impact of improvements
in measurement technologies on our understanding of celestial objects
This is a very broad dot-point. Some of the things you can discuss (from other parts of this topic) are:
 Adaptive and active optics, interferometry
 Space telescopes such as Hipparcos
 Spectroscopy improving our understanding of stars and their properties (and spectroscopic
parallax)
 Colour index
 Binary and Cepheid variable stars
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Section V- The study of binary and variable stars reveals vital information about
stars
Describe binary stars in terms of the means of their detection: visual, eclipsing, spectroscopic and
astrometric
Binary stars are systems where two stars are orbiting around each other (technically around a
common centre of mass). Known binary stars fall into four categories:
1. Visual
2. Eclipsing
3. Spectroscopic
4. Astrometric
Visual Binaries
Visual binaries, as their name suggests, can be seen as two stars orbiting each other.
Eclipsing Binaries
Eclipsing binaries are stars that are eclipsing each other from the perspective of Earth (i.e. the Earth
must lie on their orbital plane). Eclipsing binaries are detected by a periodic changing in the intensity
of the point (which is actually two stars). Maximum brightness occurs when there is no eclipsingboth stars contribute their brightness in the intensity of the light. When the brighter star moves in
front of the duller star, some light is lost, so the intensity decreases slightly (secondary eclipse). The
star then moves away, ending the eclipse and maximum brightness is restored. Then the brighter
star moves behind the duller star, leading to a bigger decrease in intensity than before (the primary
eclipse). This pattern of primary and secondary eclipses occurs regularly, and when it is detected, the
stars are classified as eclipsing binaries.
Spectroscopic Binaries
Spectroscopic binaries cannot be resolved by telescopes but are detected and classified by the
Doppler shifting of their spectral lines. Like eclipsing binaries, the Earth must not lie perpendicular to
the orbital plane for spectroscopic binaries to be detected. Because the two stars are orbiting
around each other, one will exhibit red-shifting at any one time while the other exhibits blueshifting, then switching over. This cycle repeats, and is detected by the doubling of spectral lines,
one which moves towards the red end and one which moves towards the blue end. They then move
back towards the neutral position and swap over, repeating this pattern periodically. If this pattern
of spectral lines is detected then the system is classified as a spectroscopic binary.
Astrometric Binaries
Astrometric binaries are not visual since the two stars cannot be resolved. In astrometric binaries, a
small “wobbling” of a star indicates the gravitational presence of another star (or planet, but there
are techniques to determine which).
Binaries can be all of visual, eclipsing and spectroscopic, but an astrometric can only also be
spectroscopic.
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Perform an investigation to model the light curves of eclipsing binaries using computer simulation
The explanation for the light curve is given above. The graph is shown below:
In class you should’ve been shown a computer simulation of this (type “eclipsing binary” into
Wikipedia if you didn’t or don’t remember).
Explain the importance of binary stars in determining stellar masses
Binary stars are important in determining the masses of stars because the mass of a solitary star
cannot be calculated with any degree of accuracy (gravitational lensing is possible but current
technology is insufficient to for this method to be practical). Because binary stars are orbiting around
each other and their combined mass can be calculated from their orbital radii and period, they
provide astrophysicists with an important tool to measure the masses of stars.
Solve problems and analyse information by applying:
𝑚1 + 𝑚2 =
4𝜋 2 𝑟 3
𝐺𝑇 2
In this equation, m1 and m2 are the masses of the stars (linked together in this equation), r is the
average distance between them, G is the universal gravitational constant and T is the period for a
complete revolution around each other.
Classify variable stars as either intrinsic or extrinsic and periodic or non-periodic
Variable stars are stars whose properties, such as size, intensity or colour changes with time. An
intrinsic variable star is one that changes due to internal processes within, e.g. a Cepheid variable
star. An extrinsic variable star is one that changes due to external factors, e.g. an eclipsing binary
star. A periodic variable is one that repeats itself at regular intervals, e.g. Cepheid variable stars. A
non-periodic variable star is one that does not repeat at regular intervals, e.g. supernovae.
Explain the importance of the period-luminosity relationship for determining the distance of Cepheids
Cepheid variable stars are a special type of star that pulsates regularly. Normally a star is held at a
constant size because the outward force produced by fusion is at equilibrium with the force of
gravity that acts inwards. However, for Cepheids the forces are not at equilibrium. When the star is
small, contraction increases the rate of fusion, increasing the outward force. This causes the star to
expand, which then reduces the rate of fusion. The star then shrinks, and the cycle is repeated. The
period of this expansion-contraction is related to the absolute magnitude of the Cepheid. By
knowing the period, the absolute magnitude of the star can be deduced, and since apparent
magnitude is always known, its distance can be calculated.
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Section VI- Stars evolve and eventually die
Describe the processes involved in star formation
Stellar formation occurs in large clouds of gas known as a stellar nursery or molecular cloud. A
passing disturbance agitates the gas particles, creating localised regions of slightly greater density.
These areas then attract more surrounding gas, which further increases the density, attracting more
gas, etc. This process is known as accretion. Eventually a region in the gas cloud condenses and
begins to heat up (gravitational potential energy is converted to thermal energy), creating a
protostar. Gravity continues to force pressure on the protostar, increasing its core temperature as it
shrinks and making it glow red. Eventually the core becomes hot enough to initiate hydrogen fusion,
forming a star.
Outline the key stages in a star’s life in terms of the physical processes involved
Creation and Protostar
This is described above.
Pre-Main Sequence
A protostar begins contracting quickly, since its core temperature is low, but as it shrinks and the
temperature increases, collapse slows down. The force of gravity is counteracted by the pressure
exerted by the excited hydrogen atoms, and once the temperature is high enough, nuclear fusion
begins. The core becomes much hotter but overall it is less luminous, since it is smaller.
Main Sequence
Stars spend approximately 90% of their lives in the main sequence. Once nuclear fusion of hydrogen
begins in the core, equilibrium between gravity and outward pressure is reached and the star
stabilises (except in variable stars). This period is known as the zero-age-main-sequence. The fusion
of hydrogen provides enormous amounts of energy, and this energy is radiated outwards as
electromagnetic radiation and solar wind. All remaining dust and gas is blown away by the solar
wind, leaving the star with a distinct edge. The colour of the star is dependent on its surface
temperature.
Post-Main Sequence
When the helium content in the star reaches about 12%, fusion of hydrogen stops and the star
quickly collapses due to a lack of outward pressure. However, this collapse increases the core
temperature sufficiently to begin helium fusion. In smaller stars this is a gradual process but in larger
stars which collapse faster (greater gravitational attraction), this occurs explosively in an event called
the “helium flash”. The star then rapid expands due to the new source of energy, called a red giant
or supergiant depending on its size.
Star Death
After a star runs out of fuel (heavier elements are more stable), its death begins. Smaller stars shrink
to form white dwarfs, whereas larger stars become neutron stars or black holes. This will be
described in more detail below.
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Describe the types of nuclear reactions involved in main sequence and post-main sequence stars
Main Sequence
The main type of nuclear reaction occurring in the core of a main sequence star is the fusion of
hydrogen. To a much lesser extent, there is minimal helium fusion, but this is usually ignored. There
are two types of hydrogen fusion occurring in stars, the proton-proton chain and the carbon (CNO)
cycle. The proton-proton chain is the main reaction in smaller stars such as the Sun. Larger stars use
the carbon cycle.
The proton-proton chain goes as follows:
1
H1 + 1H1
2
H1 + 1H1
2 3He2
2
H1 + e+ + v + energy
3
He2 + γ + energy
1
2 H1 + 4He2 + energy
1
H1 is hydrogen, 2H1 is deuterium, e+ is a positron, v is a neutrino, 3He2 is helium-3, γ is gamma
radiation and 4He2 is regular helium. The net result is that four protons (hydrogen nuclei) form a
helium nucleus.
The carbon/CNO cycle goes as follows:
12
C6 + 1H1
N7
13
C6 + 1H1
14
N7 + 1H1
15
O8
15
N7 + 1H1
13
13
N7 + γ
C6 + e+ + v
14
N7 + γ
15
O8 + γ
15
N7 + e+ + v
12
C6 + 4He2
13
As with the proton-proton chain, energy is released with every reaction. The net result is also that
four protons form a helium nucleus.
Post-Main Sequence
In post-main sequence stars, most fusion is of three helium nuclei into a carbon nucleus. This
process is known as the three-alpha reaction. As heavier elements are produced, shell-burning
reactions occur as different elements are available at different strata. These reactions do not need
to be known at the HSC level, but involve carbon to neon and magnesium, oxygen to silicon and
sulfur, and silicon and sulfur to iron. Stars are incapable of fusing iron as it is too stable.
Discuss the synthesis of elements in stars by fusion
The model for the early universe as given by Einstein’s equation predicts a high percentage of
hydrogen (~75%), some helium (~25%) and trace amounts of lithium (<1%). The abundance of
heavier elements present in the modern universe is through the process of nucleosynthesis in stars
and novae.
As discussed previously, post-main sequence stars are capable of fusing elements up to iron, and the
abundance (relatively) of these elements can be attributed to first-generation stars creating these
via nucleosynthesis. Different shells of giants contain different elements, and when the star dies,
these elements are ejected out as part of a planetary nebula.
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Elements heavier than iron (e.g. gold and uranium) cannot be created in stars, so their presence
cannot be attributed to stellar fusion. Instead, they are created in the enormous energies of novae
and supernovae, the explosive death of stars. These supernovae emit the energy that a billion stars
give off (over the period of about a month). The tremendous energy levels in these explosions allow
the fusion of heavier elements, synthesising all elements with atomic masses greater than iron.
Explain the concept of star death in relation to:
- planetary nebulae
- supernovae
- white dwarfs
- neutron stars/pulsars
- black holes
As with their lives, the deaths of stars are dependent on their mass:
For stars of mass up to 1.4 solar masses, their lives end after helium “burning”. Once there is
insufficient fuel to continue fusion, gravity slowly takes over and crushes the star. At one point the
star will explode outwards, ejecting up to a fifth of its mass as a planetary nebula that slowly drifts
away. This planetary nebula contains heavier elements, and it surrounds a hot, glowing white dwarf.
The white dwarf is prevented from further collapse by electron degeneracy pressure, a consequence
of the uncertainty principle (which states that an electron confined to a small volume has a large
momentum). While this does not need to be known in depth, suffice to say the electrons are pushed
against each other, which causes enough repulsive force to stabilise the white dwarf. The white
dwarf will slowly radiate away its energy and become a brown dwarf.
Stars between 1.4 and 3 solar masses end up as neutron stars. After their supply of fuel is exhausted,
the outer layers rapidly shrink from 8000km to 20km in about a second. The density of the core
“bounces” the outer layers back, resulting in enormous amounts of energy and matter to be
released. This is a supernova, which is bright enough to be seen from another galaxy. The matter
given off by a supernova is later incorporated in a new generation of stars and planets. The
remaining core of the giant becomes a neutron star, named because it is solely composed of
neutrons. Electron degeneracy is insufficient to stabilise the star, and they are forced in the nucleus,
joining with protons to form neutrons. The incredible density then gives neutron degeneracy
pressure, which is stronger than electron degeneracy pressure and thus stabilises the core as a
neutron star. Neutron stars emit radiation, and ones that are spinning are labelled as pulsars
(because from our perspective the radiation appears to pulsate).
Stars greater than 3 solar masses follow a similar death, but even neutron degeneracy pressure is
insufficient. In this scenario, gravity overwhelms the subatomic stability of the core and forms a
black hole. In a black hole, the laws of mathematics and physics break down, as infinite density
cannot be accounted for.
Lok
Present information by plotting Hertzsprung-Russell diagrams for: nearby or brightest stars, stars in a
young open cluster, stars in a globular cluster
AND
Analyse information from a H-R diagram and use available evidence to determine the characteristics
of a star and its evolutionary stage
AND
Explain how the age of a globular cluster can be determined from its zero-age-main sequence plot for
a H-R diagram
This is a standard H-R diagram for nearby stars, of which there is a relatively even distribution of
types:
An open cluster is a cluster of stars that are formed from the same cloud of gas. As such, they have
the same ages but different masses, which allows astrophysicists to investigate the effect of mass on
the evolution of a star.
Lok
As can be seen, an open cluster features a “turn-off” point, since bigger stars progress through their
lives quicker. They move up to the giant area while smaller stars remain on the main sequence, and
the age of the cluster can be determined by the location of the turn-off point. Notice that in the
above graph, apparent magnitude is plotted rather than absolute. This is acceptable since all stars
come from the same cluster, and the difference in distance is negligible.
A globular cluster is a much tighter formation of very old stars that are usually found on the outskirts
of a galaxy. Not much is known about them, but the stars are very old and give information
regarding the age of the universe.
The graph above shows a typical globular cluster. As can be seen, it is noticeably older than the open
cluster, since the turning point is closer to the right. Because the larger stars leave the main
sequence earlier than smaller stars, as time progresses, the H-R plot of a globular cluster shows the
top left stars moving towards the top-right. Stars in the middle follow, and eventually so to do the
small stars. Thus, the age of a globular cluster can be determined from the location of the turning
point.
Present information by plotting on a H-R diagram the pathways of stars of 1, 5 and 10 solar masses
during their life cycle
A star of 1 solar mass will move from the bottom right to join the middle of the main sequence. After
hydrogen runs out, it moves up to become a giant, until helium runs out then rapidly falls to a white
dwarf in the bottom left.
A star of 5 solar masses will enter the main sequence higher and further to the left than the sun, also
moving higher to the supergiants after hydrogen runs out. A star of 10 solar masses is similar, but
even higher and further to the left. These massive stars do not form white dwarfs.