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Chapter 6 Astrophysics Study Notes
Astrophysics
Galileo’s Moon observations
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Galileo refined contemporary telescope design, improving its magnification to over 20
his telescopes had a positive lens objective and a negative lens eyepiece, with a narrow field of view
he used these to systematically observe objects in the night sky and recorded his observations
he observed that the Moon was rough, with plains and mountains (challenging the prevailing Aristotelian view
that celestial objects were ‘perfect’)
he calculated (from their shadows) the heights of mountains on the surface of the Moon
some were several kilometers high (the highest is 5.5 km high)
Wavebands from space
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information about the universe comes to us predominantly as electromagnetic radiation
some wavelengths are absorbed strongly, others penetrate freely; see the table below
Waveband name
gamma rays
X-rays
UV
visible
IR
microwaves
radio waves
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Wavelength range
Less than ~10-11 m
~10–7 to ~10–11 m
400 nm to~10–8 m
700 nm to 400 nm
70 nm to ~1 cm
~ 1 cm to ~1 m
Longer than 1 m
absorption by the atmosphere
absorbed
absorbed
partially absorbed
not absorbed
partially absorbed
not absorbed
not absorbed (except for very long wavelengths)
waveband boundaries are approximate
gamma and X-rays ionize atoms at the ‘top’ of the atmosphere; bets detected by telescopes in orbit
the ozone layer absorbs some parts of the UV spectrum; others reach the ground
IR telescopes work better on high mountains (or in orbit)
Telescopes; resolution and sensitivity
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most telescopes are reflecting(using mirrors)or refracting (using lenses)
both types gather light from the ‘front’ lens/mirror (the objective) to form a small image that the ‘back lens’ (the
eyepiece) magnifies
the larger the objective lens or mirror is, the more light will be gathered, hence the more sensitive the telescope
will be; the sensitivity is proportional to the area of the objective
larger objectives will also increase the resolution of the telescope (the ability to distinguish between close objects
– like binary stars); sometimes described as the resolving power of the telescope
the maximum resolution of a telescope is related to the diameter of the objective by the formula:
R=
2.1´10 5 l
D
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where D is the diameter in metres,  is the wavelength of the light, and R is the smallest angle between two
distinguishable objects (measured in arcseconds)
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the magnification possible is also described (for simple two component telescopes) by
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fO is the focal length of the objective and fE the focal length of the eyepiece
m=
fO
fE
Problems with ground-based telescopes
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absorption of wavebands and parts of wavebands stops observation of the full electromagnetic spectrum
atmospheric conditions above ground-based telescopes are constantly changing (this is the source of ‘twinkle’ in
stars)
light ‘pollution’ from towns and cities reduces contrast of visible light telescopes
interference from human-made sources of other electromagnetic wavebands can also interfere
colour of visible images can altered by differing absorption of different colours
Improving ground-based telescope observation
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locating telescopes (particularly optical ones) on very high mountains (e.g. Mauna Kea, in Hawaii, is over 4000
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Chapter 6 Astrophysics Study Notes
m above sea level) eliminates most of the normal atmospheric distortions
locating telescopes away from human-made electromagnetic ‘pollution’ (e.g. light, radio waves) can also assist
adaptive optics incorporates a device that measures the distortions caused by the atmosphere; this information
is used by a secondary deformable mirror to correct for these distortions; this occurs up to 1000 times per
second
interferometry uses several primary telescopes, combining their signals; this produces the same effect as a
single much larger telescope; this is often used with radio telescopes (but also with optical ones e.g. the Keck
telescopes on Mauna Kea)
active optics is used in telescopes with very large objective mirrors; however, these often flex or distort from
their design shape; so actuators are fitted to a flexible thinner mirror that correct for these problems; the
actuators can also correct for atmospheric distortions (though more slowly than an adaptive approach
Parallax
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parallax is the shift in the apparent position of a close object compared to the viewed position of a distant object
as the position of the observer changes
for astronomical measurements, the annual parallax, pis measured as half the angular displacement of a star
compared to the position of more distant stars, as seen from the surface of the Earth in orbit around the Sun
over a sixth month period (as in the diagram below)
since R/x = sinp, and the angles are small, R/x = p
if distances are measured in AU (astronomical units), then R = 1, and p = 1/x
a useful astronomical unit is the parsec (pc); when stars are one pc away, the annual parallax is one second of
arc (1 arcsecond)
also in common use is the light-year (ly); the distance light travels in one year ) 1 ly = 9.46 1015 m
1 pc = 206 265 AU = 3.09  1016 m = 3.26 ly
hence parallax can be used to measure x, the distance to closer stars
not all stars are conveniently on an axis perpendicular to the plane of the Earth’s orbit (as in the diagram
above), where the star apparently moves through a circular path
in this case any six-monthly period will do
when the star is in some other position it traces out an ellipse; in this case the six-monthly period is between the
times the star is at each end of the major axis
when the star is in the same plane as the Earth’s orbit, it traces out a line; here the correct period is between the
times the star is at the ends of the line
if the smallest angle that can be measured from ground is about 0.05 arcseconds, then only stars within 50 pc
could be measured in this way (I.e. about 1000 stars)
space-based telescopes can measure angles to better than 0.001 arcseconds, which extends the distance to
1000 pc (one is planned for 2012, Gaia, which should measure down to 5  10-5 arcseconds; its orbit will be
much larger that the Earth’s orbit)
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Chapter 6 Astrophysics Study Notes
Astronomical spectra
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‘black body’ radiation comprises the electromagnetic emissions from perfect emitters (see notes under Ideas to
Implementation earlier); these spectra consist of a continuous range of wavelengths and can be described as
continuous emission spectra
the peak wavelength of a black body radiator is given by Wien’s Law, max = b/T; where T is in K,  in nm, and b
= 2.9  106 nm K.
the energy output of a black body radiator is given by Stefan’s Law, j = T4, where T is in K, and
j is in J s–1 m–2, and  = 5.67 10–8 J s–1 m–2 K–4
the Sun behaves very much like a black body radiator at a temperature of ~5800 K
line emission spectra comprise the electromagnetic emissions from hot gases (e.g. from a gas discharge tube);
these are line spectra, with a limited number of specific wavelengths
the specific wavelengths identify the atoms or molecules involved
the heat energy or electrical energy supplied to the gas excites some of the atoms or molecules into higher
energy levels; they then decay back to lower energy levels, emitting a photon with each transition
the frequency of these photons is given by hf = E (the energy difference between the energy levels involved)
line absorption spectra can occur when a continuous electromagnetic spectrum is passed through a gas;
photons whose energy corresponds to the energy gap between energy levels can be absorbed, leaving a ‘line
gap’ in the continuous spectrum
they do re-emit these wavelengths; however they re-emit in all directions, and hence are effectively removed
from the transmitted light
an example of this is in the spectrum of sunlight, which has dark lines (Fraunhofer lines); these are associated
with absorption by hydrogen, oxygen and other elements
this means that between the emission of these photons by the sun and our observation of them, there must be
substantial numbers of atoms of these elements (e.g. hydrogen in the Sun’s outer layers, and oxygen in the
Earth’s atmosphere)
Measuring astronomical spectra
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a spectrometer (spectrograph, spectrophotomer, spectroscope) can be mounted at the focus of a telescope
these normally comprise a collimator (to form a narrow parallel beam), a device to disperse the light into its
different wavelengths (a prism or a diffraction grating), and finally a device to record the wavelengths involved (a
camera, a photomultiplier or a charge-coupled device – a CCD).
different wavebands may require different dispersion devices
modern electronics holds the promise of devices to record single photons, allowing all the functions of a
spectrophotometer in a single chip, using superconducting Josephson junctions
Spectra from astronomical bodies
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stars emit black body-like continuous spectra, varying with the temperature of the star
there will be absorption lines in their spectra (from elements in the outer layers of the star), and elements in the
Earth’s atmosphere
emission nebulae comprise large regions of hot gases and dust particles, that produce line spectra characteristic
of the elements involved
galaxies (e.g. the Milky Way) are collections of large numbers (thousands to billions) of stars; hence the
spectrum of a galaxy is the sum of all the star spectra, complete with absorption spectra and emission spectra
from any hot gases and/or dust particles
quasars are very distant objects that emit very large amounts of energy – more than many galaxies; they are
probably ‘powered’ by large black holes
quasars produce a continuous spectrum of radiation across the electromagnetic spectrum, particularly at radio
wavelengths, combined with strong line emissions, that may vary in intensity
most of the spectra from astronomical bodies show a red shift – a shift of wavelength towards longer
wavelengths; this is caused by the Doppler effect, and indicates that the bodies are receding from us
the stronger the red shift, the faster they are receding
generally the most distant bodies show the greatest red shifts (particularly quasars)
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Chapter 6 Astrophysics Study Notes
Classifying stars from their spectra
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there are seven ‘traditional’ spectral classes of stars (Harvard), as shown in the table below
Class
O
B
A
F
G
K
M
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Temperature
(K)
>33 000
10 000 – 33 000
7500 – 10 000
6000 - 7500
5200 - 6000
3700 - 5200
<3700
‘Colour’;
actual colour varies
blue
blue to blue-white
white
yellowish white
yellow
orange
red
Atoms/molecules (from absorption
lines)
ionised He, weak H; strong UV
He, weak H
strong H, ionised metals
Weak H, metals
Ionized Ca; many metals
metals, weak H
strong metals & molecules
Mass
(solar masses)
>16
2.1 - 16
1.4 – 2.1
1.04 – 1.4
0.8 – 1.04
0.45 – 0.8
<0.45
other classes have been proposed, such as L (T: 1650 – 2500 K) and T (T: 700 – 1300 K)
these classes can be further subdivided
assuming the star to be a black body, Wien’s Law (see earlier) can be used to estimate the surface T
rotating stars will broaden their spectral lines (absorption spectra), due to Doppler shifting; the receding parts
will red shift, the approaching parts will blue shift
in rotating double stars the blue and red shifts can sometimes be distinguished and the direction of rotation
inferred
velocity to and from the Earth: can be determined from the net red or blue shift of spectral lines
‘sideways’ velocity of stars relative to Earth; can only be determined photographically over a longish time
interval
density of stars can also affect the breadth of spectral lines; high density stars have broader lines
elements and molecules in the star’s outer layers cause absorption spectra with the ‘fingerprint’ of the
elements/molecules
Absolute and apparent magnitude
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apparent magnitude (m) measures how bright a star appears viewed from Earth; affected by distance of star as
well as its visible energy output
the brightest stars have a low number (the ancient Greeks scaled to brightest star to 1 and the dimmest to 6,
but we have since seen brighter stars, which have m< 1, and can in fact be negative, and dimmer stars, which
have m > 6)
historically the reference star, with a magnitude of 0 was Vega; currently it is assigned m = 0.03
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the brightness ratio of two stars A and B is given by the formula
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scale can be applied to any celestial object
examples shown in the table below
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Star
Vega
Sun
(full) Moon
(full) Mars
Sirius
Algol
Castor
Barnard’s star
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IA
= 100
IB
(mB -mA )
5
Apparent Magnitude
0
–27
–13
–2.9
–1.4
+2.1
+1.57
+9.5
apparent magnitude is sometimes termed apparent brightness
absolute magnitude (M) measures of the total amount of light a star radiates into space
hence, it is a measure of the star’s actual luminosity.
Magnitude and distance
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apparent magnitude m and absolute magnitude M are related by the relationship below (d is in pc)
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(m – M) is known as the distance modulus; knowing m and M for a star enables calculation of d
this formula is often used together with the parallax formula d = 1/p
Spectroscopic ‘parallax’
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this method can be used to give an approximate value for d, using the Hertzsprung-Russell (H-R) diagram and
spectroscopic information about the star (see below)
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first, determine apparent magnitude m of the star by measuring its brightness (photometry)
secondly, examine its spectrum to determine its spectral class (O B A F G K M – see earlier)
this will locate the star’s position on the horizontal axis of the H-R diagram (if not precisely)
thirdly, determine which kind of star you are observing (main sequence, red giant, white dwarf…); this can be
done from its luminosity class ( from fine details in the spectral lines of the star, such as pressure broadening);
this locates the star on the vertical axis of the H-R diagram, and hence gives M
now use the distance modulus formula to find d
accuracy of this method probably limited to around 10 Mpc (megaparsecs)
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Colour and stars
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the apparent magnitude of a star depends on which wavelengths of the spectrum are observed
comparing magnitudes measured at different wavelengths (using filters) gives useful spectral information about
the star
one such system with widespread recognition is the U (ultraviolet) B (blue) V (yellow-green – to simulate visual
observation), or the UBV system
the value (B – V) gives the colour index
the colour indices can be aligned with the spectral class of the star, as in the approximate values:
Colour Index
– 0.6
–0.3
0
+0.3
+0.6
+0.8
+1.4
Spectral Class
O
B
A
F
G
K
M
(minor adjustments are sometimes necessary for different luminosities)
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this can be a quick way to find the spectral class without the need for detailed spectroscopy
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Photoelectric and photographic methods for photometry
Photographic photometry uses visual comparisons between the images of stars on photographic film. The diameter of
each star’s image on the film is related to its magnitude. It is possible to obtain photometry for thousands of stars
from a single photograph using this technique. Lasers can be used to scan the plate to produce a digitised image
which can then be analysed.
Photoelectric photometry uses a photomultiplier to convert weak light into a measurable electric current. Light from a
single star falls through a pinhole, onto a photocathode, causing electrons to be ejected in proportion to the intensity
of the light. A photomultiplier produces a pulse of current for every electron ejected, and pulses are counted to
produce an digital signal which can analysed by a computer. Several photomultipliers can be used simultaneously to
measure the light from different stars.
There are many advantages of photoelectric technologies over the older photographic techniques:
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CCDs have a more uniform response across the visible spectrum than photographic film does, and corrections
must be made for this in photographic photometry.
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CCDs are sensitive to a wider range of wavelengths than photographic film, particularly in the infrared.
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CCDs and photomultipliers are more sensitive than photographic film.
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Modern CCD arrays have a greater resolution than photographic film.
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Information can be collected much more quickly with electronic sensors than from photographs.
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Information can be collected remotely and transmitted digitally.
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Data can be processed more easily and quickly.
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There is more scope for a greater level of analysis because of the increased quantity of data.
Photoelectric photometry allows for a faster and more accurate measurement of magnitude than photographic
photometry; computer-based processing of images also assists speed and quality
Binary stars
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binary stars are two stars orbiting their common centre of mass; they are very common, possibly accounting for
more than half of all stars
powerful telescopes can resolve some of these pairs; they are called visual binaries
some pairs, which cannot be optically resolved, can be detected because they pass in front of each other,
causing regular periodic variation in the light output; these are called eclipsing binaries
provided that the plane of the orbits is not perpendicular to the line of sight from Earth, the stars will alternately
approach and recede from the Earth; this may cause an periodic observable Doppler shift in spectral lines;
these are called spectroscopic binaries even though they cannot be resolves optically or be eclipsing types
spectroscopic binaries can, however, also be eclipsing binaries
some binaries have one member too faint to observe; this can sometimes be detected because the visible star
of the pair follows a ‘wobbling’ path; these are called astrometric binaries
measurement of the period and the separation of a binary star pair allows calculation of the total mass, using
Newton’s Law of gravitation and circular motion theory, as shown following (R is the separation, T the period,
and G the universal constant of gravitation)
M total =
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4p 2 R 3
GT 2
further, if the distance of one of the pair from the common centre of mass is known (say r1), then:
m1 =
M (R - r1 )
R
Variable stars
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called variable when brightness varies with time
this can be caused by internal factors in the star (intrinsic variables), or factors external to the star (external
variables)
intrinsic variations can periodic (brightness variations are regular and recurring; examples are Cepheids) or nonperiodic (variations are irregular; examples are supernovas)
extrinsic variations are generally periodic; examples are eclipsing binaries and rotating stars with hotter and
cooler surface areas; extrinsic variable stars are normally periodic
Cepheid variables
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these are periodic intrinsic variable stars of two kinds: Type Iare luminous yellow young second generation
supergiants, and Type II, that are old first generation red stars.
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their magnitude/time graph is characteristic, as shown in the sketch following
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Cepheids are very useful ‘calibration’ stars; the period of their luminosity variation relates directly to their
average luminosity (see trend line graph for Type 1 Cepheids below; Type II stars follows a similar graph)
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the period of a Cepheid variable gives the luminosity of the star, and thus M
combine this results with the apparent magnitude m
use the distance modulus formula (m – M) = 5log(0.1d) to calculate the distance to the star
Cepheids occur in many galaxies, often at distance where other techniques (e.g. parallax methods) do not work;
they have been an important technique in determining the expansion of the universe
Hertzsprung Russell diagram
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vertical axis: units of absolute magnitude (M), absolute luminosity or luminosity relative to the Sun
horizontal axis: units of colour, spectral class or colour index (increases from L to R); alternatively temperature
(in K) increasing from L to R
most stars lie on the main sequence
stars of the same colour (or spectral class, or temperature) with a smaller value of absolute luminosity (or M) will
have a smaller radius than those with larger values
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Chapter 6 Astrophysics Study Notes
Stellar formation
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starts with gravitational contraction of interstellar dust and molecular gas located in ‘clouds’ (or nebulae) –
higher density than other regions of interstellar space
these are composed mostly of hydrogen (typically 70%), with some helium and traces of other elements; much
of the hydrogen is in molecular form in the denser nebulae
gravitational forces will tend to collapse these clouds, but this is opposed by the pressure from the KE of the gas
particles
when the mass reaches a critical value (the Jeans mass), gravitational collapse will start
the cloud may break up into fragments as it collapses (clouds that are too massive do not become single stars)
in these fragments the mass becomes more compact; the density at the centre of the cloud increases more
quickly than in outer regions
the core heats up as GPE is converted into KE; this increases the outward pressure eventually stopping the
collapse; at this stage the core is described as a protostar
the surrounding material is still attracted to the protostar, and its mass increases
as the temperature increases, energy is lost by electromagnetic radiation; hence it is luminous
it continues to collapse slowly until the temperature is high enough to initiate nuclear fusion of hydrogen
at this stage a balance is established between the gravitational forces tending to collapse the star, and the
outward radiation pressure from the internal nuclear reactions
it is now relatively stable and located on the main sequence; it will have a mass of between 0.1 and 100 solar
masses; its position depends on its mass (the mass is connected to the luminosity)
large mass stars reach the main sequence more quickly than low mass stars
it will remain on the main sequence for about 90% of its total lifetime, converting (‘burning’) hydrogen into helium
Stellar life cycle – ‘red’ stars (<0.8 solar masses)
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these are sometimes know as red dwarfs
they are located on the main sequence at the lower left corner of the H-R diagram
they live a very long time, burning their fuel slowly
they probably stay on the main sequence longer than the age of the universe
they may eventually become a white dwarf (left hand lower corner of the H-R diagram)
they probably end ‘life’ as a non-luminous cold black dwarf
Stellar life cycle – ‘yellow’ stars (0.8 – ~5 solar masses)
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hydrogen burning in the core produces helium (mostly as He–3), which pools at the centre of the star
when most of the hydrogen is burnt, the radiation pressure reduces, and the star begins to contract
this contraction heats both the core (of He–3) and the outer shell (unburnt hydrogen)
this outer shell now starts to burn (H); the increased radiation pressure causes the star to expand and cool; it
moves off the main sequence into the red giant region (top right hand corner of the H-R diagram)
as the hydrogen is consumed the star will contract and helium fusion will start, forming carbon
it migrates left on the H-R diagram (but not as far as the main sequence), shrinking slightly and increasing in
temperature; this is followed by further movements on the H-R diagram
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Chapter 6 Astrophysics Study Notes
it then sheds its outer layers as a planetary nebulae
eventually most of its fuel is consumed and it becomes a white dwarf
it ends ‘life’ as a non-luminous cold black dwarf
Stellar life cycle – ‘blue-white’ stars (>~5 solar masses)
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these follow the same path to red giants as the ‘yellow’ stars above, except they are much larger
the subsequent helium burning (and sometimes carbon, oxygen, neon, silicon burning) will form nuclei beyond
carbon, up to iron, which accumulates in the core
burning (fusion) beyond iron cannot proceed because it consumes energy, rather than produces it
eventually the energy supply in the core is insufficient to prevent catastrophic implosion, and a supernova
explosion occurs
this explosion and its aftermath produces elements up to and beyond iron (most atoms in our bodies, with the
exception of some of the hydrogen, must have come from the remains of such an explosion)
remnant collapses into a very dense neutron star (smaller masses) or a black hole (larger masses)
the neutrons in the neutron star are formed when the electrons are forced, by the huge pressure, to combine
with the protons to make neutrons; further collapse prevented by their outward pressure
rotating neutron stars form pulsars
black holes (singularities in space); have gravitational fields so strong that light cannot escape
Nuclear reactions in stars: Main Sequence (M-S)
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hydrogen ‘burning’ via the PP process the predominant energy source for lower mass, cooler M-S stars;
involves conversion of 4 protons into 1 helium nucleus with emission of energy (from E = mc2); key equations
below:
H + 11H ¾¾
® 12 H + -10 b + n + energy
- H + 12 H ¾¾
® 23 He + g + energy
- He + 23 He ¾¾
® 24 He + 2 11H + energy
-
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1
1
1
1
3
2
in higher mass, hotter M-S stars (containing some carbon); CNO cycle will be predominant; key equations:
H + 126 C ¾¾
® 137 N + g
N ¾¾
® 136 C + +10 b + n
H + 136 C ¾¾
® 147 N + g
H + 147 N ¾¾
® 158 O + g
O ¾¾
® 157 N + +10 b + n
H + 157 N ¾¾
® 126 C + 24 He
1
1
- 137
- 11
- 11
- 158
- 11
-
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note that the carbon is not ‘consumed’, and that 4 protons have changed into 1 helium nucleus
Nuclear reactions in stars: post M-S
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hydrogen burning continues in outer shell; core hydrogen has been replaced by non-burning helium
core contracts and heats; shell expands (to red giant form)
helium in core starts burning, provided star is > about 0.5 solar masses
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6
2
8
in helium burning: 2
; can be followed by 6
further fusion reactions can now add a helium nucleus to carbon (forming oxygen), then neon, then magnesium,
then silicon, sulfur all the way up to iron (‘alpha-particle’ nuclei whose A number is divisible by 4); after iron
fusion is not exothermic so this process stops; these reactions occur in shells (heavier elements being produced
in the inner shells)
in larger stars (> about 5 solar masses) a massive explosion (a supernova) occurs when fusion finishes in the
core; this gives rise to a whole range of new and complex nuclear reactions producing elements with mass
numbers from 12 to 62, which are disperse into interstellar space to mix with the hydrogen and helium gas
clouds
neutron capture reactions from all the elements up to Bi-209 (heaviest stable nucleus); these can occur both
before the supernova and during it
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3 4 He ¾¾
® 12C + g
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C + 4 He ¾¾
® 16O + g
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Chapter 6 Astrophysics Study Notes
Using the H-R diagram; sample star analysis
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star a: protostar, cool but as luminous (nearly) as sun, hence very large
star b: high on M-S, very hot, very large and luminous, hydrogen burning, young (using fuel quickly), will have a
‘short’ life, will become a supernova
star c: very similar to Sun in temperature, luminosity and mass, a ‘yellow’ star, on M-S, hydrogen burning, will
have similar fate to sun (red giant then white dwarf)
star d: red giant, cool, large, luminous, shell burning, most fuel consumed, near end of life
star e: on M-S, hydrogen burning, cool (a ‘red’ star), low mass and luminosity, will burn fuel slowly and last a
long time
star f: hot, small, low luminosity and mass, white dwarf, near end of life
Globular clusters
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stars in a globular cluster are of similar age (formed from a single nebula)
will probably have a large range of masses and hence ages; typical plot (black dots) shown:


stars on MS are younger than those that have left it (at ‘turn-off’ point)
estimate approximate age of globular cluster from ‘turn-off’ point
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Cambridge Checkpoints 2014 HSC Physics
Chapter 6 Astrophysics Study Notes
Open clusters

stars in open clusters tend to be young, so they will be on the M-S or heading towards the M-S
Pathways on the H-R diagram
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always show where:
the star joins the M-S (starts to burn hydrogen)
leaves the M-S to become a red giant
where the red giant pathway turns around (or goes to supernova)
and where it ends (low masses as white dwarf; high masses as neutron star or black hole)
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