Download Astrophysics

PHYS4: Astrophysics
1.
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
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Galileo built his own telescopes, working out the optics and grinding
lenses. He refined telescope design.
o Built refracting telescopes which produced an upright image
o Masked out edge of the front lens of his telescope to
overcome spherical aberration
Qualitative observations of the Moon
o Galileo saw dark lines defining spots on the Moons changing
with angle of solar illumination, and concluded that these dark
lines were shadows of the moon’s irregular surface. He drew
sketches of vast plains and mountains.
o Galileo: “the surface of the moon is not smooth, uniform and
precisely spherical as a great number of philosophers believe it
(and other heavenly bodies) to be, but is uneven, rough and
full of cavities and prominences, being not unlike the face of
the Earth, relieved by chains of mountains and deep valleys”
Quantitative observations of the Moon
o Measured lengths of shadows cast by mountains of the Moon
when they were near the edge of the shadow and directly
facing earth. From these, he estimated that these mountains
were at least several kilometres high
Galileo was the first to use a telescope to make systematic
astronomical observations of the Moon, phases of Venus, moons of
Jupiter, rings of Saturn, and sunspots.
o His observations of the moon and Jupiter challenged the prevailing Aristotelian view, endorsed by the
Church of Rome, the heavenly bodies were perfectly spherical, smooth, and unchanging.
DISCUSS WHY SOME WAVEBANDS CAN BE MORE EASILY DETECTED FROM SPACE
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A waveband is a part of the EM spectrum covering a specific range of wavelengths. The Earth’s atmosphere
absorbs, scatters, or reflects some wavelength bands more than others. Wavebands which do not reach the
ground are more easily detected from outside the atmosphere
Gamma rays ionise molecules in the atmosphere, and therefore are
strongly absorbed in the upper atmosphere. More easily detected by
telescopes placed outside Earth’s atmosphere, e.g. Compton Gamma
Ray Observatory
X-rays also ionise molecules in the atmosphere, and so are more
easily detected by space telescopes e.g. Chandra X-ray telescope
Ultraviolet radiation is mostly absorbed by the ozone layer of the
atmosphere.
Visible light is not excessively scattered or absorbed by the
atmosphere. These wavelengths mostly reach the ground, so optical
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telescopes such as the Anglo-Australian telescope can be used effectively at ground level.
Infrared wavelengths interact with water vapour and carbon dioxide, and are partially absorbed by the
atmosphere. Hence, infrared sensitive telescopes may be placed on mountain tops above the densest regions of
atmosphere.
Radio waves mostly pass easily through the atmosphere, allowing detection by ground telescopes such as the
Parkes Observatory. Very long wavelength radio waves (long waves) are reflected by the ionosphere.
DEFINE THE TERMS ‘RESOLUTION’ AND ‘SENSITIVITY’ OF TELESCOPES
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Refracting telescopes focus incoming light by refraction. They have greater image contrast due to unobstructed
light path, but can produce image errors (aberrations) and large refractive lenses are expensive to manufacture
accurately, Hence, refracting telescopes are preferred
for planetary/lunar observations but not for observing
stars.
o Chromatic aberration: lens refracts different
wavelengths by different amounts and so each
colour ends up with a different focal point,
resulting in fuzzy halos around stars
Reflecting telescopes use a parabolic concave mirror to
focus light by reflection. Large reflecting telescopes can
be produced less expensively than similarly sized
refracting telescopes.
o Prime focus: photographic film or electronic
detection device is placed at the focus of the
primary mirror
o Newtonian: plane secondary mirror at the focus
of the primary mirror reflects focused light to
the side of the telescope
o
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Cassegrain: hyperbolic secondary mirror reflects light back through a hole at the centre of the primary
mirror
Magnification is the ratio of focal length of objective lens/primary mirror to focal length of eyepiece
o
𝑚=
𝑓
𝑓𝑒
Resolution:
 Resolving power is the measure of a telescope’s ability to reveal
fine detail, or distinguish 2 close objects as separate images. A
telescope with poor resolution will see closely positioned stars
as fuzzy and blurred together.
 Described as the smallest angle of separation (in arc seconds)
between two points of light that can be seen as two distinct
images (1 arc second = 1’’ = 1/3600 degree)
 Diffraction
o When incoming light passes through the
telescope’s circular aperture it tends to spread
out and interfere with itself, forming
concentric circles of maxima/minima, blurring
the image. If two images are so close that the
central maximum (Airy disk) of one image falls
inside the central maximum of the other, the images are said to be
unresolved.
o Radiation with longer wavelengths experience greater diffraction, and
hence poorer resolution
 Resolution depends on wavelength of radiation being collected, and diameter of
telescope.
o
Dawes limit: 𝑅
=
2.1 𝑥 105 𝜆
𝐷
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A smaller angle R (in arcsec) indicates a greater resolution
A radio telescope, since it observes low wavelength radio waves,
has very poor resolution.
Resolution may also be reduced by atmospheric conditions, and quality of
mirrors/lenses
The image on top has better resolution (smaller angle) than the image below
Sensitivity:
 Sensitivity is a measure of a telescope’s ability to produce bright images and
detect fainter objects i.e. the minimum intensity of light from a source that
must fall on the telescope to form a suitable image of that source.
Sensitivity is a telescope’s light-gathering power.
o Sensitivity is proportional to area of the light-collecting surface, and
therefore proportional the square of the mirror diameter.
o If telescope A has a mirror 7 times the diameter of telescope B,
then telescope A is 49 times as sensitive as telescope B. The AngloAustralian telescope, with a 3.9m diameter, is much more sensitive
than a 100mm school telescope
o
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Radio signals from a radio telescope can be amplified with very little increase in noise, so a radio
telescope can be said to have excellent sensitivity.
Sensitivity also depends on quality of the optics
The image on top has greater sensitivity than the image below
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
DISCUSS THE PROBLEMS ASSOCIATED WITH GROUND-BASED ASTRONOMY IN TERMS OF RESOLUTION AND
ABSORPTION OF RADIATION AND ATMOSPHERIC DISTORTION
Absorption, scattering, seeing
 Gamma rays, X-rays, UV, infrared and parts of the radio waveband are absorbed by the atmosphere.
o Gamma rays and X-rays ionise gas molecules in the atmosphere, and therefore are strongly absorbed in
the upper atmosphere. Ultraviolet radiation is mostly absorbed by the ozone layer of the atmosphere.
Infrared wavelengths are partially absorbed water vapour and carbon dioxide in the atmosphere. The
longest radio waves are reflected by the ionosphere.
o Because a low intensity of these wavebands reach the ground, the sensitivity of ground-based
astronomy of these wavebands is decreased
 The atmosphere absorbs different wavelengths to different extents. This variation means that the true colour
of images is distorted at ground level.
o Colour distortion and intensity reduction are worsened is object being observed is lower in the sky,
because light from the object has to travel a greater distance through the atmosphere.
 Scattering effectively decreases the intensity of light coming from astronomical sources
o Mie scattering: suspended dust particles with sizes similar to the light’s wavelength reflect the light
o Rayleigh scattering: molecules of O2 and N2 with sizes much smaller than the light’s wavelength absorb
and re-radiate the light
 The atmosphere also scatters light from unwanted ground sources such as houses and cars into the telescope
 Seeing: Turbulent air with water vapour, other gases and dust, as well as variations in temperature/pressure,
constantly alter the refractive index of the air.
o This distorts the path of starlight through the air into a ground-based
telescope. Hence, stars appear to ‘twinkle’, go in and out of focus, and
exhibit rapid variations in colour/brightness/apparent position
(scintillation), lowering the practical resolution to about 1 arcsec.
o Radio telescopes are not affected as much by seeing, because they
observe longer wavelengths which aren’t refracted as much. However,
water vapour, raindrops, and oxygen in the atmosphere can absorb
wavelengths up to a few millimetres.
o Planets tend not to ‘twinkle’ since their angular size in the sky is usually
larger than the ‘seeing disk’
 The Sun directly interferes with optical viewing, restricting optical astronomers
to night viewing. Rayleigh scattering of the Sun’s visible light from the violet end of the spectrum (making the
daytime sky blue) further restricts optical viewing.
o The Sun is a strong radio source, and interferes with radio sources being observed. This usually prevents
radio telescope observations with 90⁰ of the Sun
o *Note that this problem also applies to space telescopes
 Other Problems:
o Thermal emission of the atmosphere, since the atmosphere is an approximately 300K black body, and
hence will emit infra-red radiation
OUTLINE METHODS BY WHICH THE RESOLUTION AND/OR SENSITIVITY OF GROUND-BASED SYSTEMS CAN BE
IMPROVED, INCLUDING:
–
ADAPTIVE OPTICS
–
INTERFEROMETRY
–
ACTIVE OPTICS
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One method to reduce atmospheric distortion is to place the telescope as high in the atmosphere as possible on
high mountaintops. Placing a telescope above the densest part of the atmosphere, above most air currents
arising from weather patterns, and far away from light pollution due to human activity, allows it to operate near
its theoretical resolution
Coating mirror surface with films of transparent material engineered to maximise reflection would increase
sensitivity
Using new and superior detectors, which count the photons arriving (photoelectric methods) would increase
sensitivity
Interferometry: significantly improves resolution, and moderately improves sensitivity
 Radio telescopes have poor resolution. A larger telescope has a better resolution because reflections of the
wavefront at various points across the diameter add via the law
of superposition to produce a sharper image. However, larger
telescopes are more expensive.
 In interferometry, a cluster of relatively small telescopes are
laid out in a large pattern. By carefully adding the wavefronts of
the same celestial radiation source on all these telescopes, a
sharper image is obtained.
 More precisely, the array combines data about incoming
wavefronts from each telescope, and computers are used to
mathematically analyse interference patterns and reveal
information about the radio source.
 The effective angular resolution of such an array is equivalent to that of a single dish with diameter equal to the
baseline (largest distance between any 2 telescopes). The sensitivity is still proportional to the light-collecting
area.
 Interferometry is mostly done with radio waves, because it is easier to measure the
phase information of longer wavelength radiation.
o The Very Large Array (VLA) is made up of 27 radio dishes, each with
diameter 25m, set out in an array 36 km across. When electronically
combined, the dishes provide the superior resolution of a dish 36 km in
diameter and sensitivity of a dish 130m in diameter.
 Very-long-baseline interferometry (VLBI)
o The Very Long Baseline Array (VLBA) consists of ten 25m dishes at different
locations between Hawaii and the Caribbean, providing a resolution of
0.001 arcsec.
 Speckle interferometry: Many extremely short exposures from a telescope (to
freeze atmospheric distortion) are combined by a computer to extract more precise
information about a star
Active Optics: improves sensitivity (allows larger mirrors) or improves
resolution (prevents mirror distortion)
 A telescope with a larger primary mirror is more sensitive.
However, a larger mirror is more susceptible to becoming
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distorted with changes in temperature and telescope orientation.
o For many years, this presented a limit to largest mirror size, and large mirrors were very thick
In active optics, light that leaves the primary mirror is slowly sampled by a wavefront sensor, which uses
interferometry to detect alterations in incoming light.
o A Shack-Hartmann wavefront sensor splits the wavefront into a number of subapertures using a lenslet
array. The tilt of the wavefront across each lens is calculated from the position of the focal spot on each
sensor
o Alterations due to uncontrollable atmospheric effects occur on smaller time scales, whereas correctable
changes due to wind/gravity-induced mirror deformation occur more slowly. Slow sampling (about once
per minute) ensures that detected changes are due to mirror deformation.
Information from the wavefront sensor is processed by a
computer, which calculates optimal mirror shape to correct
distortions. The thin, sometimes segmented primary mirror is
fitted with actuators at the back which push or pull the mirror
back into correct shape.
This slow feedback system changes the primary mirror’s shape
to correct factors that affect image quality at timescales of one
second or more
Adaptive Optics: improves resolution (reducing seeing)
 Adaptive optics operates on much shorter timescales to
compensate for atmospheric distortion rather than mirror
distortion, improving resolution
 A wavefront sensor measures atmospheric distortion of a
reference star’s wavefronts up to 1000 times per second. The information is processed by a computer, which
calculates the necessary corrections.
 Actuators move secondary mirrors to correct the atmospheric distortion, because the primary mirror may be
too heavy to move at such speeds. Detection/correction must occur
much faster than changes in atmospheric distortion for adaptive optics
to be successful.
o A tip-tilt mirror makes small rotations around 2 of its axes,
adjusting for slight changes in position of the light
o A deformable secondary mirror adjusts other deformities in the
light so that images appear sharp
 Adaptive optics only works when a reference star of sufficient luminosity
can be found very near to the object of observation
o As distance from the reference star increases, image quality
degrades (therefore small field of view)
o An alternative is to use a laser beam directed into the
atmosphere as a reference light source, and detecting the
backscatter from altitudes 15-25 km.
2.
Careful measurement of a celestial object’s position in the sky (astrometry)
may be used to determine its distance
EXPLAIN HOW TRIGONOMETRIC PARALLAX CAN BE USED TO DETERMINE THE DISTANCE TO STARS
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Objects which are closer to an observer have greater parallaxes than objects which are further way.
Trigonometric parallax is a method of using parallax measurements and trigonometry to determine the distance
to celestial objects.
A large change in the observer’s position is required to see any appreciable parallax in distant stars. The greatest
baseline achievable for a ground-based telescope is the diameter of the Earth’s orbit around the Sun.
o The position of a star relative to distant stars is photographed at 6-monthly intervals from opposite
points of Earth’s orbit, i.e. the change in observer’s position is twice the Earth-Sun distance (2 AU)
o Actually, the position of a star will annually trace out an ellipse (the parallactic ellipse), because most
stars are at an oblique angle from the plane of the Earth’s orbit. Annual parallax is defined as the angle
subtended by the semi-major axis of this parallactic ellipse. Hence, there is a specific 6-month period
within the year when the star’s position must be photographed
The trigonometric/annual parallax (p) is half the angle through which the star appears to shift as the Earth
moves from one side of its orbit to the other.
o
tan 𝑝 =
o 𝑑=
𝑅𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝐸𝑎𝑟𝑡ℎ′ 𝑠 𝑂𝑟𝑏𝑖𝑡
1 𝐴𝑈
tan 𝑝
𝑑
, where 𝑑 is distance between Earth and the star
o
The angle of trigonometric parallax is very small. Proxima Centauri has the largest parallax of a star at
only 0.772 arcsec. At such small angles, 𝑝 = tan 𝑝
o
∴ distance to the star is given by
𝑑=
1
𝑝
, with ‘d’ in parsecs, and ‘p’ in arcsec
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The unit of distance is a parsec (pc), i.e. the distance between Earth (with orbital radius 1 AU)
and a celestial object that has a trigonometric parallax of 1 arcsec.
Distances to relatively nearby stars can be calculated accurately using parallax measurements. Distances to
distant stars/galaxies can be determined using techniques which use these nearby stars as reference stars.
SOLVE PROBLEMS AND ANALYSE INFORMATION TO CALCULATE THE DISTANCE TO A STAR GIVEN ITS TRIGONOMETRIC
PARALLAX USING: d 
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1
p
p is in arcsec
d is in parsec (pc)
DEFINE THE TERMS PARALLAX, PARSEC, LIGHT-YEAR
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Parallax is the change in apparent position of a nearby object with respect to distant objects as the observer’s
position changes. The apparent change in position is usually given as an angle.
One parsec (pc), or parallax-second, is the distance from the Earth (or Sun) to a point that has an annual
parallax of 1 arcsec. It is also the distance at which the radius of Earth’s orbit (1 AU) subtends an angle of 1
arcsec.
o 1 parsec = 3.26 light years
o Proxima Centauri is 1.29 pc distant from Earth
The light year (ly) is the distance that light (electromagnetic radiation) travels in one year.
DISCUSS THE LIMITATIONS OF TRIGONOMETRIC PARALLAX MEASUREMENTS
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Parallax angles of stars are extremely small. The largest trigonometric parallax, from Proxima Centauri, is
0.772’’. Due to atmospheric distortion (seeing), the smallest parallax measurable by ground-based telescopes is
0.01 arcsec. This corresponds to a maximum accurately measurable distance of about 100 pc.
o This limitation may be alleviated by using known distances to nearby stars (using parallax) to determine
the distance to celestial objects which are >100pc away via other techniques
Placing a telescope in space reduces limitations of parallax measurements due to atmospheric distortion. This
means that sharpness of image is limited mainly by quality of optics and size of telescope objective.
o Moreover, a space telescope can observe shorter wavelength radiation from stars, increasing resolving
power.
Using a larger baseline (e.g. orbit of mars, or satellite’s orbit around the sun) would increase the annual parallax
of celestial objects, resulting in more accurate measurements.
GATHER AND PROCESS INFORMATION TO DETERMINE THE RELATIVE LIMITS TO
TRIGONOMETRIC PARALLAX DISTANCE DETERMINATIONS USING RECENT
GROUND-BASED AND SPACE-BASED TELESCOPES
Ground-based Telescopes:
 Royal Observatory of Belgium
 Paris Observatory
 United States Naval Observatory
 Uccle Observatory
HIPPARCOS:
 The orbital satellite HIPPARCOS (1989-1993) carried an astrometric telescope designed to measure star
parallaxes accurately
 Using its 290mm optical telescope, HIPPARCOS could accurately measure parallax to 1 milli-arcsecond (0.001’’).
HIPPARCOS gave distance measurements for nearly 120 000 stars out to about 1000 pc distant, compared to
ground-based telescopes which have an upper limit of about 100 pc.
 After several years of data analysis, the HIPPARCOS Catalogue was produced in 1997, containing the details of
almost 120 000 stars.
GAIA:
 GAIA is a space-based telescope planned for launch in 2012.
 It will be placed in orbit around the sun 1.5 million km further out than
Earth’s orbit. The larger baseline results in larger parallax angles, which
can be measured more accurately.
 Moreover, improvements in technology mean that parallax measurements
as small as 10 micro-arc seconds (0.00001’’) can be achieved, 100 times
more accurate than HIPPARCOS
 GAIA would allow the distances to about 1 billion stars to be measured,
representing about 1% of the stars in our galaxy.
3.
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 BLACKBODY SPECTRUM
Emission Spectra:
 An emission spectrum consists of radiation only at a
few discrete wavelengths, appearing as bright lines
against a long, dark background. It is produced by hot
low-pressure gases
 Energy (electrical or heat) supplied to the gas is
absorbed by atoms, causing electrons to jump from
their ground state to a higher energy level. As the
electron falls back to the stable ground state, it
releases a photon of energy corresponding to the
energy drop: 𝐸2 − 𝐸1 = ℎ𝑓
 When light from a hot low-pressure gas is directed through a spectroscope, the spectrum produced will contain
discrete wavelengths or lines, each corresponding to a possible energy level transition.
 Composition of the gas determines the possible energy transitions and their probability, and hence the relative
intensity of each line.
o Each element has its unique emission spectrum. Therefore, by examining the emission spectrum of an
unknown mix of elements, we can determine the elements present and their concentrations.
Absorption Spectra:
 An absorption spectrum consists of a continuous range of wavelengths with discrete gaps at particular
wavelengths, appearing as dark lines against a continuous background of colour. It is produced when a
continuous spectrum of light passes through a cloud of cool, non-luminous gas.
 Atoms of the gas only absorb photons corresponding to quanta of energy involved in possible transitions of
electrons from ground state to higher energy levels: 𝐸2 − 𝐸1 = ℎ𝑓
o Hence, the wavelengths absorbed by a cool gas are those in its emission spectrum
 As excited electrons drop back to their ground state, they re-emit the absorbed photons in all directions. By
passing a continuous spectrum of light through the cool gas, the absorbed wavelengths have been reduced in
intensity.
 When this light is directed through a spectroscope or prism, the absorption spectrum produced will have dark
lines at the absorbed wavelengths.
o Relative darkness of each line depends on the composition of the gas. The darkness of all the lines
against the background spectrum depends on the size/density of the gas cloud.
Continuous Spectra:
 A continuous spectrum shows a continuous range of frequencies, i.e. all frequencies of EM radiation are
released, albeit at varying intensities. Such a spectrum is produced by a hot solid, liquid or high-pressure gas.
 Objects which release continuous spectra are modelled by
black bodies
o Radiation emitted from a black body has a continuous
distribution of wavelengths. The intensity of the
spectrum varies smoothly with wavelength.
o The wavelength of maximum intensity decreases as
temperature of the body increases. This is given by
Wien’s Law: 𝜆𝑚𝑎𝑥 𝑇 = 𝑊
o By observing the wavelength of maximum output
from a star using a spectrophotometer, the surface
temperature of the star can be calculated
IDENTIFY THE GENERAL TYPES OF SPECTRA PRODUCED BY STARS,
EMISSION NEBULAE, GALAXIES AND QUASARS
Emission spectra are produced by hot low-pressure gases:
Absorption spectra are produced when a continuous spectrum of light passes through a cold, non-luminous gas:
Continuous spectra are produced by a hot solid, liquid or high-pressure gas:
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Stars produce absorption spectra.
o The hot, dense inner body of a star behaves like an approximate
black body, and produces a continuous spectrum. The cooler and
less dense atmosphere absorbs certain wavelengths and remits
them in all directions, producing an absorption spectrum.
o Elements/molecules present in the atmosphere can be determined
from the absorbed wavelengths
Emission nebulae are regions of hot gas, mainly hydrogen, heated by UV
radiation from hot young stars nearby.
o UV radiation from the hot, young stars nearby continually ionise the
gases, which then recombine with free electrons to form excited atoms which emit emission spectra as
they return to their ground states
o As electrons in atoms/ions of the nebula which are excited by UV radiation drop to lower energy levels,
an emission spectrum is produced of predominantly red light, which is characteristic of hydrogen gas
Galaxies release continuous spectra which are a composite of various component spectra.
o Continuous background spectrum, absorption spectra of type B/K stars, emission spectra due to
hydrogen in gaseous nebulae
o As most galaxies are moving away from us, the lines of galaxies are often strongly red-shifted
o Normal galaxies have a red continuous spectrum from old population stars, with strong calcium
absorption lines. Galaxies with massive star formation have strong emission line spectra as young hot
stars ionise surrounding gas. Galaxies with active nuclei and central black holes have emission spectra
from the central region.
Quasars emit continuous spectra at all wavelengths, but spectral
lines are mostly longer radio wavelengths.
o They have significantly red-shifted and broadened
emission spectra superimposed on a continuous
spectrum which is rising towards the blue end.
o Note that quasars show non-thermal spectra, i.e. it is not
a black-body spectrum
o Some quasars also show absorption lines, which may be
caused by galaxies/gas between Earth and the quasar.
PERFORM A FIRST-HAND INVESTIGATION TO EXAMINE A VARIETY OF
SPECTRA PRODUCED BY DISCHARGE TUBES, REFLECTED SUNLIGHT, OR
INCANDESCENT FILAMENTS
DESCRIBE THE TECHNOLOGY NEEDED TO MEASURE ASTRONOMICAL SPECTRA
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Astronomical spectra can be observed by attaching a simple spectroscope to the eyepiece of a telescope, or a
spectrograph at the focus of the telescope
o A spectroscope is a device used to spread light into its spectrum so that it can be recorded
The first part of a spectrograph is a narrow slit through which light from the telescope enters. This is so that
only a point source of light corresponding to a single celestial object is used
The second part of a spectrograph is a collimator. A collimator uses mirrors or lenses to form the incoming light
into a flat, vertical beam so that the photons are moving parallel to one another
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The dispersive element disperses the flat beam into a rectangular strip, separating its component wavelengths.
It may consist of a triangular prism or a diffraction grating.
o A triangular prism splits light by refraction. Blue light travels more slowly through glass than red light,
and hence is refracted more
o A diffraction grating has thousands of narrow lines ruled on a glass surface
 A prism absorbs some of the light passing through it. There is no loss of photons with a
diffraction grating because it reflects light instead of refracting it
 A prism disperses blue light more than red light. Diffraction grating has linear response
 A glass prism is opaque to UV, while
diffraction gratings can reflect UV light
The spectrum is then viewed/recorded with a
photographic plate, viewing telescope, or electronic
imaging devices
o If a photographic plate is used, the wavelengths
present appear as bright lines on a rectangular
strip
o A photometer can electronically detect the
intensity of each wavelength. This data can be
used to produce a graph of intensity against
frequency (spectrogram) and the whole setup is then called a spectrophotometer.
 A charge coupled device (CCD) can record very faint light signals
 Other modern advances include the use of computer-controlled positioning equipment with
fibre optics, and multiple spectroscopes to obtain multiple spectra in the viewing field.
DESCRIBE THE KEY FEATURES OF STELLAR SPECTRA AND DESCRIBE HOW THESE ARE USED TO CLASSIFY STARS
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A stellar spectrum is the spectrum of radiation emitted by a star. It consists of an approximate black body
continuous spectrum depending on the temperature of the stellar surface, and absorption lines characteristic of
the elements in the stellar atmosphere.
The wavelength of maximum emission depends on the star’s surface temperature. There is a gradual change
from red, for coolest stars, through orange, yellow, white, and blue for the hottest stars.
o Moreover, increasing temperature breaks molecules into atoms, then atoms into ions. The spectral lines
produced are characteristic of the particles present.
Therefore, visible stars can be classified into spectral classes. Each spectral class has characteristic colour,
surface temperature range, and specific absorption line patterns indicating elements in the stellar atmosphere
o Spectral classes: O, B, A, F, G, K, M
 “Oh, Be a Fine Girl, Kiss Me”
o Each class is subdivided into 10 subclasses (…O5, O6, O7, O8, O9, B0, B1, B2, B3, B4…)
There are also stars that radiate predominantly in UV (class W) and infra-red (classes R, N, S) regions of the
spectrum. A new class of stars (L) has been discovered, which are dwarf stars cooler than M-class stars
 Note that ‘metal’ in astronomy refers to all elements other than hydrogen and helium
Spectral Class
Colour
Surface Temperature (K)
Absorption Lines
O
Blue
30 000 – 50 000
Ionised He, weak H (strong UV component)
B
Blue-white
10 000 – 30 000
Neutral He, weak H
A
White
7000 – 10 000
Strong H, ionised metal
F
White-yellow
6000 – 7000
Weak H, strong metal (Ca, Fe)
G
Yellow
5000 – 6000
Strong metal, ionised calcium
K
Orange
4000 – 5000
Strong metal (CH, CN), strong molecules
M
Red
3000 – 4000
Strong molecules (TiO)
DESCRIBE HOW SPECTRA CAN PROVIDE INFORMATION ON SURFACE TEMPERATURE, ROTATIONAL AND
TRANSLATIONAL VELOCITY, DENSITY AND CHEMICAL COMPOSITION OF STARS
Surface Temperature:
 Once a star’s spectral class is identified from its main absorption lines, then its temperature can be deduced
since each spectral class has a characteristic temperature range.
 Alternatively the wavelength of maximum intensity in the star’s continuous spectrum can be found using a
spectrophotometer. A cooler star will appear redder, while a hotter star will appear blue (black body radiation).
Using Wien’s Law, 𝜆𝑚𝑎𝑥 𝑇 = 𝑊, the surface temperature can be calculated.
o W = 2.9 x 10-3 m K
Translational Velocity:
 If the star is approaching the observer, absorption lines will be blue-shifted, appearing at slightly shorter
wavelengths (shifted towards blue end of the spectrum).
 The set of lines for an element is recognised by the spacing between the lines. Knowing what wavelengths the
absorption lines for that element should be at, we can determine how much the spectrum has been shifted.
 If a star is moving away, absorption lines will be similarly red-shifted due to the Doppler effect
 By measuring the direction and extent of wavelength shifts in absorption lines, the radial velocity of a star
(towards or away from us) can be determined.
 The component of a star’s translational velocity perpendicular to the observer’s line of sight cannot be
determined from its spectrum. It can be found by measuring the star’s position relative to more distant celestial
objects over long periods of time.
Rotational Velocity:
 If a star is rotating, one side is travelling away from us while the other side is coming towards us
o Light emitted from atoms on the receding side will be red-shifted by an amount corresponding to the
star’s rotational velocity. Light from the approaching side will be similarly blue-shifted.
 Each individual spectral line will consist of red-shifted light and blue-shifted light depending on where on the
rotating star the light originated. Therefore, the spectral lines will be broadened by an amount depending on
the rotational velocity of the star.
o By measuring this Doppler broadening effect, the rotational velocity of the star can be determined.

In a rotating double star system, one star will be blue-shifted while the other is red-shifted. After a period of
time, this situation will reverse. By keeping track of this, the rotational period and velocity can be calculated.
Density:
 In high density stars, the increased gas pressure produces more rapid collisions between atoms during radiation
emission/absorption. These collisions cause minor changes in electron orbits, and hence changes in possible
energy level transitions, resulting in the broadening of each spectral line.
o A supergiant star with a low density atmosphere will have narrower spectral lines than those of a
denser main sequence star.
 Therefore, a dense stellar atmosphere broadens spectral lines, while rotational velocity also affects intensity
across each line. By measuring the width/shape of spectral lines, the density and rotational velocity of a star can
be deduced.
Chemical Composition:


Elements in the star’s atmosphere absorb light from the continuous black-body spectrum of the star.

By comparing a star’s absorption spectrum with spectra of known elements, the chemical composition of the
star’s outer layers can be determined.
Each chemical element has a unique absorption spectrum, with lines corresponding to possible electron energy
level transitions in the atom.
ANALYSE INFORMATION TO PREDICT THE SURFACE TEMPERATURE OF A STAR FROM ITS INTENSITY/WAVELENGTH
GRAPH

𝜆𝑚𝑎𝑥 𝑇 = 𝑊
o
o
o
𝜆𝑚𝑎𝑥 is wavelength of maximum intensity
𝑇 is surface temperature of the star
𝑊 is a constant, 2.9 x 10-3 m K
4.
Photometric measurements can be used for determining distance and
comparing objects
Astrometry is the measurement of positions, distances, and movements of astronomical objects.
Photometry is the measurement of the apparent brightness of stars and other astronomical objects. From such
measurements, distance to these objects can be determined.
DEFINE ABSOLUTE AND APPARENT MAGNITUDE

𝐵𝑟𝑖𝑔ℎ𝑡𝑛𝑒𝑠𝑠 = 𝑘 ×
o
o
𝐿𝑢𝑚𝑖𝑛𝑜𝑠𝑖𝑡𝑦
𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 2
Brightness is in units of watts per square metre
Luminosity is total energy radiated by a star per second
Apparent Magnitude (m):
 Apparent magnitude is a relative measure of the brightness of a star to an observer on Earth
o Influenced by distance of the star, luminosity, and any intervening matter which can make the star
appear dimmer
 The brightest visible stars known to the ancients (e.g. the Greek astronomer Hipparchus) were arbitrarily given
magnitude 1, while the faintest visible stars were given magnitude 6.
o In the 1850s, scientists realised that this magnitude scale was not linear with respect to changes in light
intensity. It was observed that a magnitude 6 star was about 100 times brighter than a magnitude 1
star.
o Moreover, the brightest stars known now have magnitudes as low as -1.4. The faintest stars have
magnitudes greater than 25.
 Norman Pogson mathematically related the actual brightness
ratio of 2 stars to the difference in their apparent
magnitudes. He defined that a magnitude difference of 5
corresponds exactly to a factor of 100 in brightness.
o
𝐼𝐴
𝐼𝐵
= 100
𝑚𝐵 −𝑚𝐴
5



mA and mB are the apparent
magnitudes of 2 stars
 IA and IB represent the brightness of
each star
An decrease in magnitude by 1.0 represents
an increase in apparent brightness by a factor
of 1001/5, or 2.512 (Pogson’s Ratio)
A star of magnitude m is 100 times brighter
than a star of magnitude m+5
Absolute Magnitude (M):
 Absolute magnitude is defined as the apparent magnitude a star would have to an observer who is 10 parsecs
from the star, if no intervening dust/gas absorbs or scatters the radiation. Distance does not influence absolute
magnitude since it is set to a standard 10 pc, so absolute magnitude is a relative measure of a star’s true
luminosity, or the amount of radiation released it.
SOLVE PROBLEMS AND ANALYSE INFORMATION USING:
d
M  m  5 log( )
10
AND
IA
 100 ( mB mA ) / 5
IB
TO CALCULATE THE ABSOLUTE OR APPARENT MAGNITUDE OF STARS USING DATA AND A REFERENCE STAR
Proof of Formula 1:

𝐼𝐴
𝐼𝐵
= 100
𝑚𝐵 −𝑚𝐴
5

𝐼
log100 𝐼𝐴 =
𝑚𝐵 −𝑚𝐴
5
𝐵
o Let mB = m, the apparent magnitude of a star at distance d
 IB is ‘brightness’ of the star at distance d
o Let mA = M, the absolute magnitude of the same star (i.e. apparent magnitude at d=10 pc)
 IB is ‘brightness’ of the star at d=10 pc

∴
𝑚−𝑀
5
𝐼
= log100 𝐼𝐴
𝐵
𝑘𝐿

𝐼𝐵 = 𝑑2

𝐼𝐴 = 102

∴ log100 𝐼𝐴 = log100
𝑘𝐿
𝐼
𝐵
𝑘𝐿⁄
102
𝑘𝐿⁄
𝑑2
𝑑2
𝑑
log10𝑑⁄10
= log100 102 = 2 log100 10 = 2 log
10 100
𝑑
= log 10

𝑚−𝑀
𝑑

∴

𝑚 − 𝑀 = 5 log 10

∴ 𝑀 = 𝑚 − 5 log 10
5
= log 10
𝑑
𝑑
o
o
o
o
d is in parsecs*
When d=10, m=M
When d is increased, m increases (star appears fainter)
When d is decreased, m decreases (star appears brighter)
EXPLAIN HOW THE CONCEPT OF MAGNITUDE CAN BE USED TO DETERMINE THE DISTANCE TO A CELESTIAL OBJECT





Apparent magnitude describes how bright the star appears to an observer on Earth. It depends on both the
luminosity of the star, and varies inversely with the square of the distance from the star.
Absolute magnitude describes the brightness of the star to an observer at a fixed distance of 10 pc. Therefore,
the absolute magnitude is a measure of the star’s luminosity.
The relationship between distance and apparent brightness is known (inverse square law). If the brightness of a
star is known at 10 pc (absolute magnitude), then the distance corresponding to any brightness can be
determined.
The difference between apparent magnitude and absolute magnitude (the distance modulus m-M) can be used
to calculate the distance to the star using the distance modulus equation:
𝑑
𝑀 = 𝑚 − 5 log 10
𝑑
o
𝑚 − 𝑀 = 5 log 10
o
log 10 =
o
log 𝑑 − 1 =
o
log 𝑑 = 1 +
o
𝑑
𝑚−𝑀
1+
𝑑 = 10
5
𝑚−𝑀
5
𝑚−𝑀
5
𝑚−𝑀
5
OUTLINE SPECTROSCOPIC PARALLAX
o
We cannot accurately determine the distance to stars that are too far away using parallax because the
annual parallax is too small. Spectroscopic parallax is a technique for calculating the distance to a star
using the H-R diagram and the distance modulus formula, by finding out its absolute magnitude and
apparent magnitude.





Using photometry (photographic plates, photomultiplier tubes, etc.), the star’s apparent magnitude m is
determined.
Using the shape of a star’s black-body radiation spectrum (especially the peak wavelength emitted), its spectral
class/surface temperature (e.g. O, B, A…) is determined.
o Alternatively, the star’s colour index can be
determined using B/V filters
The width of the absorption lines tells us the star’s
luminosity class (e.g. supergiant, main sequence,
etc.)
o A dwarf star with about the same mass as a
giant star may have a far smaller radius, and
hence a greater gas pressure at the surface.
As a result, the spectral lines of such a dwarf
star would have more ‘pressure broadening’
than the lines of a giant star.
On a Hertzsprung-Russel diagram, we draw a vertical
line up from the star’s spectral class on the
horizontal axis until it intercepts with the correct
luminosity class (star group). From this position, a
horizontal line is drawn which meets the vertical axis
at the star’s absolute magnitude M.
Once the apparent magnitude m and absolute
magnitude M are known, the distance to the star
can be found using 𝑀 = 𝑚 − 5 log
o
𝑑
10
The technique is only accurate to 10%, and
to a maximum distance of about 10
megaparsecs. This is because determination
of the absolute magnitude can carry a large percentage error, especially since luminosity classes are
usually broad bands. Interstellar gas/dust may also affect accuracy of brightness measurements
EXPLAIN HOW TWO-COLOUR VALUES (IE COLOUR INDEX, B-V) ARE OBTAINED AND WHY THEY ARE USEFUL

The human eye is most sensitive to yellow-green light, while the photographic emulsions used in astronomy are
most sensitive to the blue end of the spectrum.




Therefore, a hot blue star will appear brighter (lower magnitude) on a photographic plate than to the human
eye because the plate’s maximum intensity is in the blue region of the spectrum.
Depending on its colour, a star will have a different visual magnitude to its photographic magnitude.
Nowadays, magnitudes are measured with photoelectric photometers which are equally sensitive to all
wavelengths. In order to maintain consistency with naked eye or photographic plate observations, coloured
filters which only let through a narrow waveband of the spectrum are used.
The visual magnitude (V) of a star is its apparent magnitude measured through a yellow-green filter. The
photographic magnitude (B) is measured through a blue filter. The V filter centres on a 550 nm wavelength,
while the B filter centres on a 440 nm wavelength.
o An ultraviolet filter (U) utilises the extra sensitivity available from the photometer. Various other filters
which centre on other wavelengths are also used.
Colour Index:
 Colour magnitudes are apparent magnitudes
for a star as observed through coloured filters. We often subtract one colour magnitude from another to
produce a numerical two-colour value that expresses the star’s colour
 The (B-V) colour index is the difference between the photographic magnitude (B) and visual magnitude (V) of a
star. The resulting two-colour value numerically expresses the colour of the star.
o Colour Index = B – V
 By definition, stars of spectral class AO (with surface temperature 10 000K and blue-white colour) have a colour
index of zero
 A red star is brighter through the V filter, has a lower V magnitude. and will have a positive colour index
 A blue star is brighter through the B filter, has a lower B magnitude, and will have a negative colour index
 By measuring magnitude of a star through two coloured filters, we obtain its colour index. From its colour index,
we can determine its spectral class, colour and surface temperature
PERFORM AN INVESTIGATION TO DEMONSTRATE THE USE OF FILTERS FOR PHOTOMETRIC MEASUREMENTS
DESCRIBE THE ADVANTAGES OF PHOTOELECTRIC TECHNOLOGIES OVER PHOTOGRAPHIC METHODS FOR
PHOTOMETRY
Photographic Photometry:
 Specially prepared emulsions are used to make a photograph of a portion of the sky, via photochemical
reactions between incident light and the emulsion/film. When the photograph is developed, brighter stars with
lower magnitude appear as larger and denser spots.
 Each spot can be compared to standard spot sizes/densities to determine the stars’ apparent magnitudes.
o Lasers can scan the exposed film to digitally analyse the image.
 Photographic emulsions are restricted to the visible spectrum, including near-infra-red and near-ultraviolet.
Photoelectric Photometry:



Photoelectric photometry electronic light sensors such as Charge Coupled Devices (CCDs) or photomultiplier
tubes, along with filters
In a photomultiplier, light from a single star falls through a pinhole onto a photocathode, causing electrons to be
ejected in proportion to intensity of the light. These photoelectrons are accelerated towards a metal electrode
(dynode), and strike the dynode with sufficient energy to ‘knock’ many more electrons from its surface through
secondary emission. These new electrons are then accelerated towards the next dynode, and the whole process
typically occurs about 10 times. In effect, the photomultiplier produces a large pulse of current for photon
striking the first cathode, and pulses are counted to produce a digital signal.
In a CCD, light projected onto the capacitor
array causes electron-hole pairs to form,
and each capacitor accumulates electric
charge proportional to light intensity at that point. A control circuit causes these charges to be released into a
charge amplifier, which converts the charges into a sequence of digital voltages.
Advantages of Photoelectric over Photographic Methods:
Range of wavelengths, Uniform detection of wavelengths, narrow waveband, quantum efficiency, dynamic range, linear
response, digital information, storage
 CCDs can detect a wider range of wavelengths than photographic film (especially in the infrared)
 CCDs detect different wavelengths of visible light more uniformly than photographic film. Hence,
measurements of apparent brightness will not be influenced by the star’s colour if photoelectric methods are
used. Corrections must be made for this in photographic photometry, since photographic film is more sensitive
to blue light than red.
 CCDs can accurately detect the intensity of a narrow waveband, useful when searching for the presence of a
particular element in a celestial object
 CCDs and photomultipliers have a greater quantum efficiency (% of incident photons that create an electronhole pair) than photographic emulsions. Photographic emulsions have much less than 10% QE, while
photomultipliers have about 20% QE and CCDs have > 90%. Photoelectric methods are therefore more sensitive
to faint light sources than photographic film.
o This also means the photographic methods need longer exposure times to detect a faint light source,
while electronic sensors collect photometric information more quickly.
o Reciprocity failure: the QE of photographic films decreases further as exposure time increases. Doubling
the exposure time would not record stars twice as faint
 CCDs have a larger dynamic range (range between lowest and highest detectable light intensities). CCDs have a
dynamic range with a factor of 100,000x while photographic emulsions have only 100x. This means CCDs can
detect a greater range of light intensities
 CCDs have a linear response, whereas photographic methods do not. A linear response means that double the
number of incident photons striking the CCD causes the output signal to double.
 Due to the regular pixel arrangement on CCDs as opposed to randomly positioned silver halide grains on
photographic emulsion, photometric measurements from a CCD are accurate and can be more easily quantified.


As information is stored digitally when using photoelectric methods, data can be transmitted to computers and
processed more quickly.
CCDs can be turned on or off as required. Glass photographic plates are heavy, large and fragile, and must be
stored in the dark for long-term stability, making storage difficult and costly
Disadvantages of Photoelectric Method:
 Photographic photometry can often record fine detail with higher resolution than electronic methods, because
a single plate usually has many millions of silver halide crystals and pixels
 CCDs are relatively small, and have a smaller field of view than photographic plates
 A CCD’s performance varies with temperature. This must be taken into account.
IDENTIFY DATA SOURCES, GATHER, PROCESS AND PRESENT INFORMATION TO ASSESS THE IMPACT OF
IMPROVEMENTS IN MEASUREMENT TECHNOLOGIES ON OUR UNDERSTANDING OF CELESTIAL OBJECTS



Interferometry has vastly improved the resolving power of ground-based telescope systems.
o As the radio frequencies commonly used in interferometry are less affected by seeing, radio telescope
arrays using interferometry have better resolution than optical ground telescopes. This has let us see
fine details of distant galaxies, as well as other celestial objects which emit radio waves, such as quasars.
Photoelectric measurement technologies have allowed for increased accuracy, ease, and scope of photometric
measurements
o Charge Coupled Devices (CCDs) and photomultiplier tubes; discussed in previous DotPoint
Modern telescopes have increased our understanding of celestial objects by allowing us to see them in greater
detail, and record non-visible wavebands of radiation emitted.
o Cosmic Background Explorer
 Investigated the cosmic microwave background radiation
o Wilkinson Microwave Anisotropy Probe (WMAP)
 Measures differences in the temperature of the cosmic background radiation across the sky
o Hubble Space Telescope
o Chandra X-ray Telescope
o Compton Gamma Ray Observatory
5.
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
EXPLAIN THE IMPORTANCE OF BINARY STARS IN DETERMINING STELLAR MASSES
CLASSIFY VARIABLE STARS AS EITHER INTRINSIC OR EXTRINSIC AND PERIODIC OR NON-PERIODIC
EXPLAIN THE IMPORTANCE OF THE PERIOD-LUMINOSITY RELATIONSHIP FOR DETERMINING THE DISTANCE OF
CEPHEIDS
PERFORM AN INVESTIGATION TO MODEL THE LIGHT CURVES OF ECLIPSING BINARIES USING COMPUTER SIMULATION
SOLVE PROBLEMS AND ANALYSE INFORMATION BY APPLYING:
4 2 r3
m1  m2 
GT 2
6.
Stars evolve and eventually ‘die’
DESCRIBE THE PROCESSES INVOLVED IN STELLAR FORMATION
OUTLINE THE KEY STAGES IN A STAR’S LIFE IN TERMS OF THE PHYSICAL PROCESSES INVOLVED
DESCRIBE THE TYPES OF NUCLEAR REACTIONS INVOLVED IN MAIN-SEQUENCE AND POST-MAIN SEQUENCE STARS
DISCUSS THE SYNTHESIS OF ELEMENTS IN STARS BY FUSION
EXPLAIN HOW THE AGE OF A GLOBULAR CLUSTER CAN BE DETERMINED FROM ITS ZERO-AGE MAIN SEQUENCE PLOT
FOR A H-R DIAGRAM
EXPLAIN THE CONCEPT OF STAR DEATH IN RELATION TO:
–
PLANETARY NEBULA
–
SUPERNOVAE
–
WHITE DWARFS
–
NEUTRON STARS/PULSARS
–
BLACK HOLES
PRESENT INFORMATION BY PLOTTING HERTZSPRUNG-RUSSELL DIAGRAMS FOR: NEARBY OR BRIGHTEST STARS,
STARS IN A YOUNG OPEN CLUSTER, STARS IN A GLOBULAR CLUSTER
ANALYSE INFORMATION FROM A H-R DIAGRAM AND USE AVAILABLE EVIDENCE TO DETERMINE THE
CHARACTERISTICS OF A STAR AND ITS EVOLUTIONARY STAGE
PRESENT INFORMATION BY PLOTTING ON A H-R DIAGRAM THE PATHWAYS OF STARS OF 1, 5 AND 10 SOLAR MASSES
DURING THEIR LIFE CYCLE