Topic Four Astrophysics
Contextual Outline
The wonders of the Universe are revealed through technological
advances based on tested principles of physics. Our understanding
of the cosmos draws upon models, theories and laws in our endeavour
to seek explanations for the myriad of observations made by various
instruments at many different wavelengths. Techniques, such as
imaging, photometry, astrometry and spectroscopy, allow us to
determine many of the properties and characteristics of celestial
objects. Continual technical advancement has resulted in a range of
devices extending from optical and radio-telescopes on Earth to
orbiting telescopes, such as Hipparcos, Chandra and HST.
Explanations for events in our spectacular Universe, based on
our understandings of the electromagnetic spectrum, allow for
insights into the relationships between star formation and
evolution (supernovae), and extreme events, such as high gravity
environments of a neutron star or black hole.
This module increases students understanding of the nature and
practice of physics and the implications of physics for society and
the environment.
Note stars are all in a state of equilibrium with gravity
pushing inwards and radiation and gas pressure pushing out
Galileo was the first person to point a telescope into the night
sky after refining the design. He built the refracting telescope
that produced an upright image and masked out the edge of the front
lens of his telescope to overcome spherical aberration. As a
result, he was able to make systematic astronomical observations
and deductions of the features of the moon.
Galileo made the following qualitative observations of the
moon:
The moon was rough like the earth
Had vast plains (mare), high mountains and deep valleys
Quantitative:
Calculating the height of a mountain from a measurement of its
shadow when they were near the edge of the shadow and directly
facing the earth, estimated they were at least several kilometres
high
Other important observations
Moons of Jupiter
Phases of Venus
Sunspots on the sun
Thousands of new stars that were not visible by the naked
eye
Implications:
These observations provided evidence that challenged the
prevailing Aristotelian view that was endorsed by Church of Rome
where the heavens were perfect and unchanging, where earth was the
centre of the universe (heliocentric model)
These observations were evidence for the Copernicus geocentric
model as the moons of Jupiter were as predicted in the Copernican
system
The phases of Venus showed that Venus must orbit the sun as
Copernicus had suggested
Galileos contributions would fundamentally challenge the way in
which science regarded space and astronomical bodies
This was a result of an advance in technology where the
telescope allowed distant objects to be seen closer
Information on the cosmos comes entirely from the analysis of
the electromagnetic radiation. However, the Earths atmosphere and
ionosphere prevent certain EM waves from either completely or
partially reaching the earths surface. As a result, ground based
astronomy is restricted to wavebands (part of electromagnetic
spectrum covering a specific range of wavelengths) primarily to
visible light and radio waves.
Problems associated with the detection of EM waves from the
atmosphere:
Selective absorption
The highly energetic gamma rays and x-rays ionise molecules
making up the atmosphere and are therefore strongly absorbed in the
upper atmosphere
Some bands of UV radiation are strongly absorbed by the ozone
layer of the atmosphere while others penetrate to the ground
Infrared wavelengths are partially absorbed
*Long wavelength radio waves are reflected by the ionosphere
Implications:
The atmosphere does not scatter or absorb the visible and radio
band very much, consequently, optical telescopes can be effectively
used at ground level e.g. Anglo-Australian Telescope or radio
telescopes e.g. Parkes
In order to be able to study and analyse these absorbed
wavebands/study the cosmos;
Telescopes must be placed in space above the Earths
atmosphere
E.g. Hubble space telescopes are used to make observations of
every region
Instead of the expensive procedure of placing them into space,
infrared sensitive telescopes may be placed on mountains tops
This means less light pollution and temperature fluctuations
experienced by the instruments are less. This minimises the time to
stabilise expansion or contraction initiated shake in the telescope
lens and mounting
For:
To be able to study the electromagnetic spectrum
Improve our knowledge of the universe e.g. the discovery of a
quasar
Sensitivity this is the measure of its light gathering power
A telescope with high sensitivity means that I can collect large
amounts of light, hence allowing very faint objects to be
observed
Sensitivity is directly proportional to the diameter of the
lens/mirror
Resolution - this is the ability of a telescope to clearly
distinguish between two very close objects
Resolution is usually described in terms of the smallest angle
of separation between two points of light such a two stars close
together. Resolution depends on the diameter of the objective lens
and the wavelength of the light. A telescope with low resolution
will see closely positioned stars as fuzzy and blurred.
Theoretical resolution = 2.1 x10^5 x
D
Atmospheric distortion and resolution:
Ground-based astronomy is beneath a constantly changing sea of
air, water vapour, other gases and dusts. This means that there
will be variations in temperature and pressure and thus will alter
the density of the atmosphere. This causes corresponding changes in
the refractive index which causes stars to twinkle (exhibiting
rapid variations in colour and intensity). As a result, this
atmospheric distortion causes images to shimmer and go in and out
of focus, thus lowering the overall theoretical resolution of the
telescope
Aberrations caused by impurities in the medium (air) as the
radiation passes through it. This has the effect of reducing the
ability to clearly resolve detail in distant objects by scattering
the EM wave.
The true colour of images is altered because at ground level the
variations in absorption with wavelength mean that we are not
seeing an accurate reproduction of the intensity of the spectrum.
All these affects are accentuated if the object being observed is
lower in the sky because the path length the light has to travel
through the atmosphere is greater. E.g. the reason why a blue sky
is seen is because the atmosphere scatters light
Absorption of radiation:
Gamma rays, x-rays, ultraviolet, infrared and parts of the radio
region of the electromagnetic spectrum are absorbed and scattered
to different extents by the atmosphere. Ground-based astronomy in
these wavebands is very difficult because of the low intensity of
radiation reaching the ground. So much light from the violet end of
the visible waveband is scattered, making the daytime sky bright
blue, that optical astronomy is virtually impossible other than at
night.
Other:
The atmosphere also scatters extraneous light into the telescope
from unwanted sources such as nearby houses, cars and towns. This
light pollution is increasingly becoming a major problem for
astronomers.
Adaptive Optics:
This uses a system of electronically controlled thrusters
(actuators) of supports which adjust the shape or angle of the
telescope mirror to correct the effects of atmospheric turbulence.
It uses a fast feed back system as sensors quickly detect
atmospheric distortion (such as absorption and scattering) which is
analysed by a computer. Thrusters are then used to bend the
flexible mirror into the shape that produces the best possible
image in order to improve resolution. These corrections are made up
to 1000 times per second and can be as small as 0.02 microns to
minimise loss of scattered photons.
The success of adaptive optics relies on the detection and
correction taking place every quickly compared to the length of
time over which the distortion lasts. The image correction relies
on the presence of a bright point source or star in the field to be
imaged. Where such a star does not exist, a laser beam is fired
into the atmosphere to provide an artificial star.
Active Optics:
Active optics systems are designed to correct changes in the
surface shape of large primary mirrors that occur as the telescope
tilts or the mirror temperature changes or due to gravity. It uses
a slow feedback system to correct the sagging or deformities in
order to retain the sensitivity of the telescope. By slowing
monitoring the reflection of the wavefront off it, its possible to
apply pressure to various parts of the primary and correct the
deforming effects by using actuators to ensure a sustains its
original resolution
When light leaves the primary mirror, it is slowly sampled by a
wavefront sensor. This can detect how incoming light has been
altered, and by sampling slowly, changes observed n the wavefront
is due to deformities in the primary mirror, rather than
uncontrollable atmospheric effects. Therefore it must be done
slowly in order to eliminate the effect of atmospheric
turbulence.
Interferometry:
Interferometry is a technique used to study optical or
radio-wave interferences (it is more effective with radio waves).
Interferometry works by the superposition of signals/wavefronts in
order to create a sharper image and thus improve the resolution and
sensitivity.
It is based on the principle of a large diameter mirror that
gives a sharper image because the reflections of the wavefront at
various points across the diameter add via the law of
superposition. The resolution of such an instrument is similar to
that of a telescope with a diameter equal to the separation of the
two antennae.
It is used to unblur images from large optical telescopes and
process information about the source of the radio wave e.g. size
and separation of stars. Very Large Array (VLA) is an example of
interferometry
The telescope is a device used for helps to overcome the
limitations of the human eyes for astronomical studies. There are 2
types of telescopes: refracting and reflecting
Reflecting telescope
This applies the principle of refraction to obtain images. It
consists of 2 lens:
Object lens used to gather/collect light
Eyepiece lens used to magnify the image
Disadvantages
Light must pass through the objective lens for an image to be
obtained
The lens can only be supported at the edge
Large, heavy lens will deform under its own gravity and heat.
The deformity of the objective lens cause a distortion to the image
obtained
Reflecting telescope
This applies the principle of reflection of light to obtain
images
Advantage this is that it reflects rather than reflects, hence
can be fully supported
Disadvantage a large objective mirror also deforms to an
extent
Possible Solutions
Many small mirrors appropriately connected to form a large
objective mirror. This reduces the deformities
Using active optics as explained previously
Larger telescopes with lens/mirrors of larger diameter will have
a higher sensitivity and resolution. This can be investigated by
placing a black iris in front of the objective lens of a small
telescope. Use the telescope to bring a page of writing on a wall
some distance away into focus. Then slowly close the iris to reduce
the effective diameter of the objective lens. It is noticed that
the letters begin to become blurred, indicating the resolution is
decreasing. Further more, as the amount of light gathered
decreases, the letters rapidly reduce.
Parallax this is the apparent change in position of a nearby
object as seen against a distant background due to the change in
position of the observer
Parsec One parsec is the distance that corresponds to an annual
parallax of 1 arc sec
Light year this is the distance light travels in a year
1pc = 3.26 light years = 206265 AU
1AU = 1.5 x 1011 m (distance between earth and sun
Trigonometric parallax is the technique used to calculate the
distance to an object from the observer using trigonometry and
parallax
Annual parallax is half the angle through which the star appears
to shift as the earth moves from one side of its orbit to the
other
Parallax data is collected by photographing the same star field
twice, from opposite points of earths orbit in order to use the
baseline of and then measuring the annual shift of stars against a
background of distant stars. This allows the parallax to be
calculated. The annual parallax can be calculated from half this
angle, giving a right angled triangle with a baseline of 1 AU.
Basic trigonometry can then be used to determine the lengths of the
sides and hence the distance to stars.
For example, a star that has a parallax of say 1 arc second will
be at a distance of:
Tan P = D/d
d = D/tanp
= 1.5 x10^11/tan (1/3600)
= 1pc
A large number of relatively near stars, whose distances can be
calculated accurately from parallax measurements, are used as
reference stars for a range of techniques to estimate distances to
much more distant stars, including some in neighbouring
galaxies.
If the parallax angle is smaller, then the star is further away,
and if the angle is larger, the star is closer.
d = 1/p
Where d = distance from star
P = parallax angle in arcsecs
The usefulness of trigonometric parallax measurements is limited
because the parallax angle of nearby stars is extremely small.
Current telescopes have a limited resolution and accuracy and hence
limited in measuring small angular shifts
Further more, this is combined with the seeing effect of the
atmosphere, making measurements of small angles very difficult.
The maximum distance of measurements to reasonable accuracy is
approximately 33pc, which is approximately 0.03 arcsec
Solutions
Using a larger baseline, however this is impossible as for this
to happen; earths orbital radius has to be increased.
Putting telescopes above the atmosphere and in the space reduces
the limit to which trigonometric parallax measurements are
restricted by avoiding the effects of the earths atmosphere.
E.g. Hipparcos has precision to 0.01 arcsecs which is 10 times
more accurate than ground based measurements.
Gaia is planned to be launched and intended to have a precision
to 10 microarsecs, 100 times more precise than hipparcos
Spectroscopy is the analysis of spectra produced by an object to
obtain information on its features.
The spectrum is a range of wavelengths of electromagnetic waves.
Under the visible range, these wavelengths are observed as colour.
There are 2 types:
Continuous spectrum e.g. white light, rainbow
Line spectrum e.g. emission and absorption spectrum
Continuous blackbody spectrum
This is produced when an object emits all wavelengths of the
electromagnetic spectrum. Under the visible range, a continuous
band of colours is observed. Black bodies emit a complete spectrum
of electromagnetic waves where the radiation emitted is related to
the temperature of the body. This radiation is produced by the
oscillation of electrons.
Continuous spectra are given off by hot solids, liquids and high
pressure gases. The intensity of the spectrum varies smoothly with
frequency, with a maximum that depends on the temperature of the
body.
R O Y G B I V
Emission Spectrum
An emission spectrum has the appearance of coloured lines as
seen against a dark background.
This is produced when gases or atoms are excited in a flame or
an external energy source that causes the transition of electrons
into higher energy states. When they return to the ground state,
they emit the energy as photons, which form an emission
spectrum.
For this reason, the emission wavelengths are often called the
emission lines. Each element has its own characteristic emission
spectrum
Absorption Spectrum
An absorption spectrum consists of dark lines as seen against a
colourful background
This occurs when white light from a continuous spectrum source
passes through a cool non luminous gas. Some of the components
wavelengths are absorbed by the electrons of the gaseous atoms.
These electrons then make a transition into the higher energy state
and eventually return to their ground state, releasing the energy
as photons. The wavelengths emitted are identical to the ones
emitted.
However, the radiation is emitted in all directions in space,
and hence the energy obtained in the viewing direction is less than
the original directional energy. Thus the spectral lines appear
darker in these wavelengths than others.
A prism spectrometer was used in order to view the spectra
produced by reflected sunlight. It produced an absorption spectrum
due to the earths atmosphere
The device used in spectroscopy is called a spectrometer. There
are 2 types
Prism spectrometer
Diffraction grating spectrometer
Astronomical spectra are examined by using a spectroscope, or
recorded and measured with a spectrograph, mounted at the focus of
a telescope. A spectrograph consists of 3 parts:
1. Collimator This uses a narrow slit and one or more mirrors or
lens to form a parallel beam from a single light source such as a
star
2. Dispersive element Either a prism or diffraction grating
consisting of a thin piece of glass with thousands of lines etched
down it. They both disperse the light beam.
3. Device to view/record the different wavelengths this may be a
viewing telescope, a focussing mirror with photographic plate or
film, or an electronic imaging device such as a charge coupled
device (CCD) detector.
Note: Diffraction grating works by the diffraction of light,
creating an interference pattern. Since the maximum interference
for each wavelength occurs at a different angle, a diffraction
grating effectively disperses the different wavelengths in a light
beam.
Stars These emit a continuous spectrum similar to a black body.
However since light is absorbed by gases in its cooler outer
atmosphere, dark absorption lines appear against the continuous
background of light emitted from each star. The wavelengths of the
absorption lines can be used to determine the elements and
molecules present in the atmosphere of the star
Emission Nebulae These emit an emission spectrum. They are
regions of gas and dust which glow because they are illuminated
with UV light from stars within the nebulae. As excited electrons
in the atoms and ions within the nebula drop to lower energy
levels, line spectra are produced with emission lines in the
ultraviolet, visible, and infrared and radio bands, characteristic
of the elements that make up the nebula along with strong hydrogen
emission lines (red/pink)
Galaxies This emits a continuous spectrum. They are made up of
gas, dust and millions of stars. The spectrum of a galaxy is
generally the composite of various spectra. These are normally red
shifted
Quasar This emits a continuous spectrum with a few emissions
lines that fluctuate in intensity rapidly. They are very distant
objects that produce vast quantities of continuous radiation at all
wavelengths
A stellar spectrum consists of an approximate black body
radiation spectrum for the temperature of the stellar surface,
superimposed with absorption lines characteristic of the elements
present in the stellar atmosphere.
Stars can be classified into 7 spectral classes based on their
surface temperatures
O B A F G K M
Oh Boy Angry Fearnside Gonna Kill Me
Higher surface temp ( Lower surface temp
In each spectral class, it is then subdivided from 0 ( 9
Bo B 1 B2 B9
Higher surface temp ( Lower surface temp
By analysing the stellar spectra, we can classify them according
to their surface temperatures and colour
Spectral Class
Spectral Features
Surface Temp
Colour
Mass (sun = 1)
O
Ionised helium
Weak hydrogen
> 25000
Blue
30
B
stronger hydrogen
neutral helium
25000 -11000
Blue white
8
A
Strong hydrogen
Ionised metals
11000-8000
White
2.5
F
Weaker hydrogen
Ionised heavier metals
Neutral metals
8000-6000
Yellow white
1.4
G
Ionised calcium strongest
Many neutral metals
6000-4800
Yellow
12
K
Neutral metals dominate
Hydrogen lines very weak
4800-3500
Orange
0.7
M
Strong neutral metals
Molecules particularly titanium oxide
< 3500
Red
0.3
Surface Temperature
This can be deduced based by using Weins law. A spectroscope is
used to determine the wavelength of maximum output in analysing the
prominence of spectra or by plotting the intensity of the radiation
as a function of its wavelength and using the wavelength when it
peaks.
Weins law : T x peak = 2.89 x10-3
Rotation velocity
This can be determined by analysing the optical Doppler shift
effect caused by the rotation of the star. As a star rotates about
its own axis, the spectral lines will be both blue and red shifted.
This is because one side moves towards the observer (blue shift) ad
the other side moves away from the observer (red shift)
Thus the individual spectral lines will be broadened by an
amount depending on the rotational velocity of the star. The faster
a star rotates, the more broadening of spectral lines is
observed.
Translational velocity
This is also determined by analysing the Doppler effect on the
absorption lines. If a star is approaching the observer, every
absorption line in the spectrum of the star is shifted toward the
blue end of the spectrum by the same amount. If the star is moving
away, all the lines are shifted towards the red end. The amount by
which all the lines are shifted depends on the component of the
velocity of the star along the line of sight.
Density
The broader the spectral lines, the higher the density of the
atmosphere surrounding the stars. This is different to the
rotational velocity analysis as the intensity varies across the
line in different way from the effect of rotation.
Chemical composition
This can be determined by comparing the absorption spetrum of
the star to the absorption spectra on the earth.
First identify the wavelength at which the black body curve is
at its highest intensity. Then use Weins law in order to predict
its surface temperature
Photometry is the measurement of the brightness of stars and
other celestial objects
The brightness of a star depends on its
Luminosity
Radius2
Temperature
Distance-2
Apparent magnitude This is the number given to a star to
indicate its brightness as measured from earth
Absolute magnitude This is the number given to a star to
indicate its brightness as measured at 10 parsecs away
Since the brightness of a star depends on its luminosity and its
distance to the earth, the apparent magnitude will vary with the
distance to the observer. The further the observer is, the fainter
the star and the higher the apparent magnitude. The closer the
observer is the brighter the star and the lower the apparent
magnitude.
Since absolute magnitude is measured from 10pc away, it is a
fixed number and hence the brightness of stars can be properly
compared. Absolute magnitude is estimated for distant stars by
comparison with reference stars of the same spectral class and of
known distance.
Thus if both the apparent and absolute magnitudes were known,
then the distance can be worked out with the formula of
If a star is further away than 10 pc, its apparent magnitude m
is larger than its absolute magnitude M, because the star appears
fainter at the greater distance. If closer than 10 pc, it would
appear brighter and m would be smaller than M.
Where M is the absolute magnitude
M is the apparent magnitude
d is the distance in parsecs
Spectroscopic parallax is the process of using the
Hertzsprung-Russel diagram and the distance modulus formula to
determine the approximate distance of a star.
This method involves
Using photometry to measure the apparent magnitude of the
star
Using spectroscopy to determine the spectral class as well as
the luminosity class in order to determine which group the star
belongs to
Use the H-R diagram to find the absolute magnitude. By drawing a
vertical line up from the position on the horizontal spectral class
axis until it intercepts with the luminosity class, we can read off
the stars luminosity on the vertical axis.
Using the distance modulus formula
The apparent magnitude of a star can vary depending on the
detector used. A human eye is more sensitive to the yellow-green
region of the visible spectrum and hence red and blue stars are not
judged to be as bright as they really are. (Red stars are seen to
be brighter and bluer stars seen to be dimmer)
Similarly, a photographic film or detector is most sensitive to
the blue region of the spectrum.
The visual magnitude (V) refers to the magnitude as judged by
the eye or a photometer fitted with a yellow green filter
The photographic magnitude (B) refers to the magnitude as
detected by photographic film or a photometer fitted with a blue
filter.
Colour index is determined by the photographic magnitude minus
the visual magnitude
CI = B - V
They are useful as they provide a more accurate reading of
magnitude when both values are used. It is a fast and simple method
and can be used to determine the colour and spectral class of a
star.
Photographic photometry
This is the technique used to identify the brightness of a star
based on photographic images. It involves making a photograph of a
portion of the sky and when the image is developed, the size and
density of each spot is measured. Brighter stars expose a larger
area of film and appear as larger denser sports. Each sport is
compared to standard spots and densities to determine the star
magnitude.
Advantages
It is a fast method and the brightness of a large group of stars
can be identified at one time
Fine detail of a star can be recorded photographically, often to
high resolutions achieved electronically
Disadvantages
Restricted to the visible range of the EM spectrum
Sensitive to blue colour which leads to inaccurate measurements
of brightness
Photoelectric photometry
This is the technique used to identify the brightness of a star
by converting the amount of light input into electric signals. They
use a combination of a filter and an electronic sensor such as a
CCD. In general the brighter the star, the greater the electric
signal. (more generally used)
Advantages
Responds uniformly to all wavelengths of the EM spectrum and
hence allows the study of a much broader region of the EMR than
done by photographic film
They are more efficient in catching photons, hence a greater
sensitivity to intensities of light
Fast response for computer analysis, can be done quickly and
remotely
Disadvantages
Slower than photographic for comparison and studying a large
group of stars
Cannot achieve the same resolution
Produce simulated starlight from the incandescent lamp in a ray
box kit, commonly available in school science laboratories. This
has the advantage that coloured filters mounted in 35 mm slide
frames can easily be inserted in the light path. If this is not
available, filters can be held by hand in front of any incandescent
lamp.
Use a light intensity probe attached to a datalogger to measure
the intensity of light at a set distance from the lamp. Set the
datalogger to operate in manual or snapshot mode. A photographers
hand-held light meter is a suitable alternative to measure light
intensity.
Place different coloured filters, one at a time, between the
lamp and the light probe. For each filter, measure the intensity of
light with the datalogger. You should note that the filters used in
photometry, unlike those in a ray box kit, transmit a carefully
calibrated range of frequencies.
For each filter, also observe the light through a hand-held
spectroscope to see qualitatively what effect the filter has on the
spectrum of white light produced by the lamp. Use the in-built
scale to measure the range of wavelengths transmitted.
Record all your observations systematically in a suitable table.
Compare your qualitative and quantitative observations for
different filters.
Use your observations to predict the effect of different filters
on the measurement of apparent magnitude of stars of different
spectral type.
Key discoveries in imaging and measurement of celestial bodies
follow the introduction of improved technology.
Tyhco Brahes large metal and wooden quadrants and scales allowed
an enormous improvement in the measurements of the position of
celestial bodies. Kepler then used Brahes measurements to calculate
that the orbit of Mars was elliptical, undermining the accepted
geocentric belief of circular orbits.
The invention of photography in the 19th century allowed length
and integrated exposures which produced a permanent image that
could be measured and analysed. This allowed starts to be
accurately compared over time, allowing the time-varying phenomenon
such as variable stars to be studied. Measurements of plates
allowed magnitudes of objects to be studied. Measurements of plates
allowed magnitudes of objects to be determined and faint objects
such as galaxies to be discovered. The development of the
spectrograph led to the discovery of helium in the sun before it
was found on earth. Furthermore this has developed into using
photomultipliers and CCDs in photometry that electronically enable
a greater understanding by improving on the measurement
technologies
The Hubble telescope combined long exposure photographic plates
with spectral observations to discover the galaxies were separate
from the milky way and that the universe is expanding. These
discoveries had profound social and philosophical implications.
More recently, developments in electronics have allowed
astronomers to observe wavelengths other than visible light. The
advent of computers and space telescoped has allowed them to detect
and image objects such as nebulae and galaxies across the EM
spectrum.
Binary stars consist of two stars orbiting around their common
centre of mass. Approximately half of all stars are actually binary
star systems. They are classified accordingly to the method used to
detect them
Visual
These are those that can be resolved by a telescope where binary
stars can be actually seen orbiting one another
Astrometric
This consists of 2 stars but one star is too faint to be
detected in anyway. Only one star can be seen
The only means of detection is the wobble effect from the
orbital motion of the visible star. This is deduced from the
periodic perturbation (variation in the designated orbit of one
body due to the influence of another body)
Spectroscopic
These are unresolved pairs of stars that can only be detected
from the shifting of their spectral lines. During its orbit, one
star will be moving towards the observer and the other moving away.
The receding star experiences a red shift while the approaching
star experiences a blue shift in their absorption spectra.
Periodic doubling of the spectral lines indicates it is a
spectroscopic binary
Eclipsing
These are unresolved stars that can only be detected by the
characteristic of the light intensity of the 2 stars. In the
eclipsing binary, one star of the pair eclipses the other at
regular intervals, leading to variations in the brightness of the
light.
When the brighter star (usually the small one) eclipses the
duller star (usually the bigger one), the combined intensity dips
slightly. When the duller star eclipses the brighter star, the
combined intensity drops more steeply. As shown below
The difference between the flat and curved bottom is that a
total eclipse occurs with the flat bottom and a partially eclipses
creates the curved bottom
Binary star systems are important as they enable astronomers to
calculate the mass of stars. By observing the system, we can
determine the period of the motion, the separation and hence the
total mass can be calculated using Keplers law.
Astronomers need to know the mass of stars in order to
understand the processes that that give a star its energy at
different stages of its evolution.
Variable stars are those that vary their brightness
This can be classified into two types
Intrinsic These change their brightness due to processes within
the star e.g. rate of nuclear fusion, surface temperature
Extrinsic These change their brightness due to external
process
Eclipsing binary
Rotating variables (have large and cool spots that change the
stars brightness as they rotate
Intrinsic variable stars are classified into
Periodic These vary brightness in a regular cycle with a fixed
period
Mira
RV tauri
Cepheids
RR lyrae
Non periodic Change their intensity in an irregular way
Super novae
Novae
Flare stars
R coronae Borealis
T Tauri
Cepheids are supergiant stars that are intrinsic periodic
variable stars with a characteristic light curve. They change their
radius and surface temperature periodically which results in a
change in their brightness. The temperature change is due to an
increased rate of fusion during contraction and a decreased rate
during expansion.
There are two types
Type I massive, young second generation stars
Type II small, old and red first generation stars
It was found that when the absolute magnitude of the cepheids is
graphed against their corresponding periods, a linear relationship
is obtained. This means their period of their brightness is
directly related to their average luminosity. The period varies
from 3-50 days where the longer Cepheids being more luminous than
those with shorter periods.
Thus we can measure the period of variation of a Cepheid
variable, we can easily determine its luminosity immediately. We
can then calculate the distance to the star by using the inverse
square law or by applying the distance modulus equation.
Due to the correlation between their periods and the average
absolute magnitude, they are very useful in determining the
distance to different galaxies
The Hertzsprung Russell diagram is a plot of the surface
temperature/spectral class/colour against their absolute
magnitude/luminosity of stars. The H-R diagram is important since
it enables astronomers to classify stars and understand its
evolution.
Important features
Star temperature decreases towards the right, hence stars on the
left are blue (spectral class O) while those on the right are red
(spectral class M)
The radius of a star increased vertically for each spectral
class. Therefore a red star near the bottom of the diagram will
have a smaller radius than a red star near the top of the
diagram
When a star is plotted, it will fall into one of the main
distinct groups, each characteristic of a specific stage in star
lifetime.
Main sequence This is where the majority of stars ( greater than
90%) lie and most of these are found on the cooler part of the
band
They fuse hydrogen to helium in their cores and exist in a state
of equilibrium between the force of gravity pushing inwards and the
radiation and gas pressure pushing outwards
The point at which the stars joins the main sequence at the
lower edge of the band is called the zero age main sequence
It becomes more luminous and massive in moving from the bottom
right to the top left
Red giants this is when the nuclear fusion of helium occurs at
the core
They are extraordinarily large in size
White dwarfs This is when no more nuclear fusion occurs,
basically a collapsed star corpse.
The vertical axis of the H-R diagram may show the stars mass
relative to the sun, its absolute luminosity or its luminosity
relative to the sun. The horizontal axis may show the stars surface
temperature, its spectral class or its colour index.
Stars fall into distinct groups in the H-R diagram, with common
characteristics of luminosity (hence, mass) and temperature (hence,
colour), and at a similar evolutionary stage. The regions
include:
the main sequence (diagonally from bottom right to top
left),
the red giants (middle to upper right side cool, but very
luminous, therefore very large),
the white dwarfs (bottom middle and left hot, but low
luminosity, therefore small)
the supergiants (across the top of the H-R diagram both very hot
and very luminous).
A higher mass start evolves more quickly than a lower mass
star
Sample analysis
Star A is low and to the right of the main sequence, therefore
it is a protostar, at a very early stage of its life, and heading
for the main sequence. It is very cool, but is nearly as luminous
as the sun, therefore it is very large.
Star B is on the main sequence, so it has begun to produce
energy by fusion of hydrogen into helium. Its low surface
temperature shows it to be a red star, while its low luminosity,
and position at the bottom of the main sequence, show it to be a
dwarf. As a low-mass star, it will consume its fuel very slowly and
spend a very long time on the main sequence.
Star C is on the main sequence and is steadily converting
hydrogen to helium by fusion. Its surface temperature is
approximately 6000 K (remember that the scales are logarithmic), so
it is a yellow star like the sun. It is also approximately as
luminous as the sun, therefore it must be of similar mass to the
sun.
Star D is in the region of red giant stars. It is relatively
cool, but about 1000 times as luminous as the sun, therefore it
must be very large. It has consumed most of its fuel and is near
the end of its life.
Star E is very hot and very luminous, about 10 000 times as
luminous as the sun, but it is on the main sequence. It must
therefore be a very young star, as such a star consumes its fuel
quickly and would not stay on the main sequence very long. It is
very massive and will have a short, violent life, ending in a
supernova.
Star F is a hot white star, but from its low luminosity, and its
position on the H-R diagram, we can see that it is very small. It
is a white dwarf and is at the end of its life.
Blue stars initially have a bigger gas cloud and more fuel and
enter the main sequence at the top left such as the 10 solar mass
star. They burn fuel the quickest and survive as stars only for a
fraction compared to the smaller mass stars.
Stellar formation begins with the gravitational contraction of a
vast nebula of interstellar dust and molecular gas clouds, mainly
hydrogen. This process begins slowly, but quickly speeds up as the
density increases more quickly at its centre and experiences
greater gravity. Also, a shock wave moving through a gas cloud
could trigger the cloud to contract sufficiently to form a
star.*
The cloud now has two parts
A rapidly contracting core
Slower contracting surroundings of gas and dust.
As the core contracts, the gravitational potential energy
converts into thermal energy. This increasing temperature produces
an outward pressure that opposes the gravitational force. This
pressure increases and builds up as the core becomes hotter,
eventually stopping the collapse and stabilising the size of the
core.
This state before a new star begins to produce any nuclear
energy in its core is called a protostar. It eventually develops
strong stellar wind that blows away the remnants of the surrounding
cloud. Hence without an energy source, the contraction of the core
is very slow, ranging from a hundred thousand years for a big star
to several million years for a small star. This decrease in size
causes it become less luminous, but also heats the core.
If the core mass is above between 0.01 to 100 solar mass, it
will eventually reach a temperature high enough to trigger the
nuclear fusion of the hydrogen within it (approx 8 million
kelvins). If the mass were lower, the protostar would not have
heated sufficiently to begin nuclear fusion, and if it were
greater, it wouldve overheated and blown itself up forming smaller
clouds and protostars.
The evolutionary stages through which a star passes during its
life depends on the initial mass of the star.
Stellar Formation
Material accumulated at the centre of a nebula collapses under
its own gravity and forms an expanding core of hot dense matter.
The heat radiated from the core causes the surrounding cloud to
become luminous. The luminous cloud with its hot dense core is
known as the protostar as it has not reached the stage in which
nuclear fusion has begun. The increasing density of the core begins
to slow further in falling of matter.
Eventually the protostar ( if it has a mass greater than 0.08
solar mass) will reach a temperature where the fusion of hydrogen
begins, entering the main sequence
Small mass stars
A small star of 0.3 solar masses would take about a billion
years to join the lower right hand side of the main sequence. Since
the star is comparatively small, the rate of hydrogen fusion in the
core is low and the surface temperature also being low. Such stars
are therefore red and very long lived
These small mass stars remain in the main sequence for over 30
billion years. Since they are too small to reach the higher
temperatures required to fuse helium, when a large core of helium
is formed in such stars, fusion ceases. Then the star contracts to
become a white dwarf. Without the fusion to oppose it, gravity
collapses the star and the potential energy is converted into heat,
resulting in a small, very hot white dwarf, which will eventually
radiate its heat away and fade.
Sun-like mass stars
These are stars of about 0.5 to 5 solar masses that have enough
mass to fuse hydrogen to helium and then helium to form carbon and
heavier elements. When a sufficiently large helium core forms,
fusion ceases and gravity collapses the star until a shell of
hydrogen begins to fuse. This expands and cools the star, turning
it into a red giant. When the hydrogen in the shell is used up, the
star collapses again until the temperature is high enough to fuse
helium to carbon. When this occurs, the star expands and cools
again.
Eventually the carbon formed in the core prevents further fusion
and the star once more collapses inwards. The heart produced by
this collapse may blow off the outer layers of the star in a nova
explosion. The outer layers spread away from the star, forming a
planetary nebula while the small core that remains forms a white
dwarf star.
Large mass stars
These are stars with masses greater than 5 solar masses, and
elements heavier than helium can be fused in the core. The star
moves to the left and right of the H-R diagram. This is due to the
fusion of each successive element ceasing, and causing the
collapsing and fusion of the next element. Eventually a core of
iron is formed and fusion ceases (fusion of iron and heavier
elements does not release energy). When the iron core is large
enough, the star collapses and causes a supernova explosion,
blowing away most of the stars mass. The fate of the core depends
on the mass that remains (could become a neutron star, white dwarf
or a black hole)
Smaller and cooler main sequence star (about 20 million
Kelvin)
The predominant type of nuclear reaction is the proton-proton
chain reaction. It is a slow process
1. Fusion of two hydrogen nuclei to form a heavy hydrogen
nucleus. One proton decays into a neutron with the release of a
position and neutrino
2. Fusion of a proton and deuterium nucleus to form helium 3
nucleus, with the release of gamma radiation
3. Fusion of two helium 3 nuclei to form a helium 4 nucleus and
two free protons which may participate in further PP chain
reactions
Bigger and hotter main sequence stars
The predominant reaction is the carbon-nitrogen-oxygen (CNO)
cycle. This requires a higher temperature and also converts 4
protons into 1 helium nucleus. This is fast and releases a lot of
energy. Carbon is used as a catalyst
1. Four successive protons combine with a carbon nucleus to
produce nitrogen, then oxygen and finally carbon again plus a
helium nucleus
2. The first and third collision triggers the decay of a proton
into a neutron and a position, thus increasing the number of
neutrons in the nucleus
3. The second and fourth collision simply increases the number
of protons in the nucleus
4. This process if cyclic as the a carbon nucleus is present at
both the start and the end, allowing the process to be
repeated.
Post main sequence stars
Since helium is plentiful in the core, three helium nuclei can
fuse to form a carbon nucleus through the triple alpha reaction.
This process occurs when a star is at the stage of a red giant
3 42 He ( 126 C + gamma radiation
The carbon atom can then easily fuse with another helium nuclei
to form oxygen
126 C + 42 He ( 168 O + gamma radiation
If a star is massive enough, further exothermic shell-burning
reactions can take place in successively deeper shells within the
star. This converts carbon to neon and magnesium, oxygen to silicon
and sulfur and then to iron. Here ends the energy source as further
fusion will not release anymore energy.
Initially only hydrogen and helium were present in the universe
after the big bang. All other elements were synthesised by fusion
during the life and death of stars. The mass of the star and the
stage of life of the star determine which elements are
synthesised.
Further helium is produced by fusion of hydrogen in main
sequence stars either by PP or CNO chain reactions. The rate at
which fusion proceeds depends on the temperature and pressure at
the core and hence mass of the star. These fusion reactions are
exothermic and the energy is eventually released as radiation
Elements heavier than helium are produced by fusion in post main
sequence stars,
Beyond iron, the reactions are endothermic, but inside red giant
stars, heavier nuclei can still be formed by nucleosynthesis
The first process is a slow capture of neutrons inside red
giants that have achieved a helium burning shell. The neutrons are
captured by nuclei to form heavier ones. This slow process is
capable of generating elements up to lead on the periodic table,
including gold
The second process is a fast capture in a supernova explosion.
In such an environment, there is sufficient energy available to
allow the rapid formation of the elements heavier than lead such as
uranium
A star cluster consists of a few hundred to thousands of stars
that are about the same age. The stars in a cluster are believed to
have condensed from interstellar gas clouds at the same time. The
age of a cluster can be determined by its turn off point the point
it leaves the main sequence.
An old cluster will have a low cut off point. This is because it
contains a high mass stars and hence consumers more energy to
counteract the gravitation collapse. It will evolve off the main
sequence faster than younger stars.
A young cluster will have a higher cut off point
i. is a young star cluster
ii. is a much older cluster
Open clusters these are very young clusters with higher cut off
points than globular clusters in a region of about 25pc
Globular clusters these are older clusters of stars closely
packed together in a spherical or globular shape. It contains
thousands to millions of stars 10-30pc across
The fate of a star when it does depends on its mass.
1. Planetary nebula These are huge clouds of gas and dust
produced when the outer layers of a star are blown away when fusion
ceases in the star and it collapses inwards. Approximately a
quarter of the star can be blown outwards to form a planetary
nebula which expands outwards from the white dwarf that remains
2. Supernovae This is a violent explosion of uncontrolled
nuclear reactions that completely blows away the various layers of
a massive star (occurs when original mass is greater than 5 solar
masses). It occurs when an iron core builds up and fusion ceases in
very large stars. It is in such explosions that nuclear reactions
occur in which elements heavier than iron are created
3. White dwarfs these are small and very hot remnants of stars
in which fusion has ceased. Without fusion to oppose it, gravity
collapses the star and potential energy is converted to heat. It
will eventually radiate its stored heat away and fade away to
become a brown, then black dwarf. The collapse is eventually hated
by quantum effects of matter where closely spaced electrons cannot
be in the same energy level
4. Neutron stars/pulsars This is the extremely dense remnant of
the core where the inward force of gravity exceeds the maximum
force of the outward pressure. Matter is condensed to the density
of nuclear material and a neutron star with a diameter of about
10km is formed. This huge decrease in radius results in a very hot
and rapidly spinning star with an intense magnetic field. They emit
X-rays and as they rotate, sweep across the sky. (also known as
pulsars)
5. Black holes This is the crushed remnant of the core of a very
massive star. The force of gravity is so great that when fusion
ceases, nothing can stop the star from collapsing. The matter is
crushed down to a point of infinite density, known as singularity,
which is infinitely small. Around the singularity is a region
called the event horizon, where the escape velocity required is
greater than the speed of light, thus even light cannot escape from
a black hole. Thus they would appear as small black spheres in
space.
Discuss why some wavebands can be more easily detected from
space
Discuss Galileos use of the telescope to identify features of
the moon
The electromagnetic spectrum is loosely divided into bands
because the range of the wavelength is vast. It is divided based on
wavelengths and on how the radiation can be produced and
detected
Discuss the problems associated with ground-base astronomy in
terms of resolution and absorption of radiation and atmospheric
distortion
Section One
Our understanding of celestial objects depend upon observations
made from earth or from space near the earth
Seeing is the distortion of the image of a distant light source
by the earths atmosphere
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
Outline methods by which the resolution and/or sensitivity of
ground-based systems can be improved including:
Adaptive optics
Interferometry
Active optics
The speed is the major difference between adaptive optics and
active optics
Define the terms resolution and sensitivity of telescopes
Section Two
Careful measurement of a celestial objects position in the
sky(astrometry) may be used to determine its distance
Define the terms parallax, parsec, light-year
Explain how trigonometric parallax can be used to determine the
distance to stars
Discuss the limitations of trigonometric parallax
measurements
Gather and process information to determine the relative limits
to trigonometric parallax distance determinations using recent
ground based and space based telescopes
Section Three
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
Perform a first hand investigation to examine a variety of
spectra produced by discharge tubes, reflected sunlight or
incandescent filament
Describe the technology needed to measure astronomical
spectra.
Identify the general types of spectra produced by stars,
emission nebulae, galaxies and quasars
Describe the key features of stellar spectra and describe how
these are used to classify stars
Describe how spectra can provide information on surface
temperature, rotational and transition velocity, density and
chemical composition of stars
Analyse information to predict the surface temperature of a star
from its intensity/wavelength graph
Section Four
Photometric measurements can be used for determining distance
and comparing objects
Define absolute and apparent magnitude
Explain how the concept of magnitude can be used to determine
the distance to a celestial object
Outline spectroscopic parallax
Explain how two-colour values(ie colour index B-V) are obtained
and why they are useful
Describe the advantages of photoelectric technologies over
photographic methods for photometry
Perform an investigation to demonstrate the use of filters for
photometric measurements
Identify data sources, gather, process and present information
to assess the impact of improvements in measurement technologies on
our understanding of celestial objects
Section Five
The study of binary and variable stars reveals vital information
about stars
Describe binary stars in terms of the means of their
detection
Visual
Astrometric
Spectroscopic
Eclipsing
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
Section Six
Stars evolve and eventually die
Describe the process involved in stellar formation
Present information by plotting Hertzsprung-Russell diagram for:
nearby or brightest stars, stars in a young open cluster, starts in
a globular cluster
Outline the key stages in a stars life in terms of the physical
process involved
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
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
Explain the concept of star death in relation to:
Planetary nebula
Supernovae
White dwarfs
Neutron stars/pulsars
Black holes