astrophysics repaired)
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1. Earth-based observations Discuss Galileos use of the telescope to identify features of the Moon
Galilei Galileo did not invent the telescope, but he improved its design. He built refracting
(lens) telescopes, which formed upright images and also covered the edges of his telescope toreduce spherical aberration and form clearer images.
Galileo identified and gather evidence on:
-the moons of Jupiter
-the phases of Venus
-sunspots on the sun,
-many new stars
-the rings of Saturn
-features of the moon
In particular, he was able to make qualitative and quantitative observations of geographicalfeatures of the moon. This included mountains, craters and lava flows which he called seas.
This provided evidence against the (then) popular view that all heavenly objects were perfect
and unchanging.
Discuss why some wavebands can be more easily detected from space
Almost all information from space comes in the form of EMR. The EMR spectrum is divided
into wavebands. Each particular waveband covers a specific range of wavelengths in the
EM spectrum. The Earths atmosphere absorbs, diffracts and scatters some wavebands more
than others.
The high energy gamma and x-rays ionise molecules and are therefore strongly absorbed by
the upper atmosphere. Most UV radiation is absorbed by the ozone layer while some
penetrates to the ground. Water vapour and gases in the atmosphere reflect most of the
infrared radiation. Visible light and most radio waves are able to fully penetrate to the ground
This limits ground-based astronomy to the visible and radio wavebands. In order to study the
other EMR effectively, one must go above the atmosphere. Infrared radiation can be studied
by placing infrared telescopes on mountaintops above the densest regions of the atmosphere.
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Absorption of EMR wavebands by the Atmosphere:
Define the terms resolution and sensitivity of telescopes
Resolution
Resolution aka resolving power is a measure of a telescopes ability to clearly distinguishbetween two very close objects in space. When this occurs, the objects are said to be resolved.
0
10
20
40
70
80
90
30
MicrowaveUVGamma
Ozone layer
X-rays
100
Visibl
e RadioInfrared
50
60
Altitude (km)
Wavelength
Ionosphere
Mesosphere
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Telescope resolution is limited by:
-imperfections in the lens/mirror
-diffraction i.e. bending of light around objects or through gaps
Resolution is quantitatively defined by the angle of separation between two light wavefrontse.g. a binary star. It is measured in radians or arcs seconds. The resolving power of a
telescope is given by. The smaller the angle of resolution, the greater the resolving power.
Hence, a smaller wavelength and larger diameter size improve resolution.
Sensitivity
Sensitivity is a measure of the light gathering power of a telescope i.e. its ability to clearly
detect photons from sources in space- the more light that can be detected, the fainter the
object that can be seen. The sensitivity of a telescope is the minimum intensity of light that
needs to be detected to form a suitable image. Quantitatively, sensitivity is proportional to the
surface area of the aperture. Telescopes with large apertures are nicknamed light buckets
Discuss the problems associated with ground-based astronomy in terms of resolutionand absorption of radiation and atmospheric distortion
Atmospheric Distortion
Ground-based telescopes view space from beneath the dynamic mixture of gases, dust and
water vapour of the atmosphere. Variations in temperature and pressure with altitude cause
corresponding changes in the refractive index, causing stars to twinkle. Or more correctly,
the object shimmers in and out of focus, lowering the resolution of the telescope. The true
colour of images is altered due to variations in absorption with wavelength. Objects lower in
the sky are even more susceptible because the light has to travel through more atmosphere to
reach the ground. The atmosphere also scatters unwanted light from nearby cities and vehiclesinto the telescope.
Absorption of radiation
Gamma rays, x-rays, UV, some infrared and the longer wavelength radio waves are absorbed
and scattered by the atmosphere. This means the intensity of these EMR reaching the ground
is very low, so ground-based astronomy is very difficult. Furthermore, much light from the
violet end of the visible waveband is scattered (making the sky blue) so optical astronomy is
impossible during daytime.
Outline methods by which the resolution and/or sensitivity of ground-based systemscan be improved, including:
Two light sources that have been
resolved have separate diffraction
Two light sources with overlapping
diffraction fringes cannot be resolved
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-adaptive optics
-interferometry
-Active optics
The easiest approach to reduce atmospheric distortion is to place the telescope as high in the
atmosphere as possible. This means placing telescopes on very high mountaintops, above thedensest regions of the atmosphere. Another advantage is the remoteness means there are no
unwanted light sources from human activity.
Active Optics
Active optics aims to increase sensitivity by compensating for imperfections in the telescope
mirror. Sensitivity is proportional to the surface area of the mirror; however, larger mirrors
are more susceptible to distortion and the thicker it needs to be. Active optics uses many
small composite mirrors, each controlled by its own actuator which pushes or pulls on the
back of the mirror to actively adjusting its shape accordingly. The mirrors are adjusted about
once a minute.
One of the best examples is the Keck observatory, at the top of an extinct Hawaiian Volcano,
Mauna Kea. It comprises of 36 hexagonal mirrors to give the same sensitivity as a 10m
diameter mirror.
Adaptive O
Adaptive optics aims to increase resolution
by measuring and compensating for atmospheric
distortion. Similar to active optics, adaptive optics
uses actuator-controlled composite mirrors but has much faster
response speed. It involves sampling part of the incident light using a wavefront
sensor to measure the amount of atmospheric distortion. The system relies on a bright
reference star or artificial laser pulse to detect this distortion. The mirrors are adjusted using
actuators, up to 1000 times per second, effectively neutralising atmospheric changes.
The Keck
Observatory
telescope mirror
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Interferometry
Resolution depends on the diameter of the
aperture. Interferometry uses the principle of
several small telescopes linked in an array to
give a higherresolution
. The device
used is called
an
interfero
meter and is most
commonl
y used in radio telescopes because they can be linked over
great distances.
Radio interferometry works by combining the same radio sources (which are slightly out of
phase due to time differences) electronically, so that they interfere by superposition.
Radio telescopes in different continents (and even satellites) can be linked to from a very long
baseline (up to 3 times the Earths diameter). This technique is called very large baseline
interferometry (VLBI) and it used to produce extremely high resolutions.
Optical interferometry aims to produce a brighter image by using constructive interference of
the incoming wavefronts. It is mainly used for determining stellar distances and diameters.
Gather, process and present information on the next generation optical telescopes
The next generation telescopes are designed to have lighter, larger mirrors than before. This
allows astronomers to view fainter objects with higher resolution and ensures stability in the
mirrors.
Spin casting and rotating mercury
The shape of the mirror constantly changes to
keep the rays of light at one focal point Diameter x
Resolution of two mirrors in interferometer
mode separated by x is equal to a single
mirror with diameter x
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Lighter mirrors can be made by spinning the glass into a hyperbolic shape as it cools.
A new generation of parabolic mirrors uses rotating liquid mercury and gallium alloys. The
layer is only 2mm thick and they are low cost compared to conventional mirrors. They are
restricted to facing only directly upwards and objects cannot be tracked.
Thin and replica mirrors
A recent development in mirrors is the production of 1mm thick mirrors made from curved
sheet-glass attached to a honeycomb backing structure. A prototype has already been
fabricated for the HSTs successor, the James Webb Space telescope, expected to be launched
in 2014.
Another technique involves replicating pre-existing mirrors by applying a graphite reinforced
honeycomb composite (GRHC). When the GRHC cures, it is used as a template for new
mirrors.
Extremely large telescopes: The Giant Magellan telescope (GMT), Thirty Meter
Telescope (TMT) and European-Extremely large telescope (E-ELT)
The largest, the E-ELT has a diameter of 42 metres and is predicted to be 15 times more
sensitive than the current largest 10 metre Keck telescopes. The TMT has a 30 metre diameter
and the GMT has a 24.5 metre mirror. They are expected to be completed by 2020.
All rely on adaptive optics to make their resolution as powerful as any space based
observatories.
Identify data sources, plan, choose equipment or resources for, and perform aninvestigation to demonstrate why it is desirable for telescopes to have a larger
diameter objective lens or mirror in terms of both sensitivity and resolution
Investigation: Aperture size and its effect on sensitivity and resolution
Aim: To demonstrate why it is desirable for telescopes to have large diameter aperture in
terms of sensitivity and resolution
Resolution
The following table summarises data on a range of telescopesTelescope Primary mirror
diameter (m)
SA primary
mirror (m2)
Theoretical
resolution
(arcseconds)
Theoretical
gain in
magnitudes
Human eye 0.007 0.001 17 0
6 inch refractor 0.15 0.02 0.8 7
Faulkes
Telescope
2.0 3 0.06 12
Anglo-Australi
an telescope
3.9 12 0.03 14
Keck telescope 10 79 0.01 16
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Note: The gain in magnitudes is related to the sensitivity. A more sensitive telescope can
detect objects many magnitudes fainter than the human eye.
Describe the relationship between sensitivity and mirror diameter.
As mirror diameter increases, the sensitivity increases.
Plot the theoretical gain in magnitude against SA primary mirror and describe the
relationship
As the SA increases, the gain in magnitude (i.e. the sensitivity) increases.
Plot the theoretical resolution vs. Aperture diameter and describe the relationship
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It is observed that as the mirror diameter increases, the angle of theoretical resolution
decreases i.e. as diameter increases, resolution increases.
2. Parallax
Define the terms parallax, parsec, light-year
Parallax is the change in apparent position of a nearby object viewed along two different lines
of sight. Quantitatively, it is measured as the angle between the two lines. Trigonometric
parallax is half the annual parallax.
A parsec is an astronomical unit of distance. It is defined as the distance away a star would
need to be in order for its annual parallax to be 1 degree. In terms of annual parallax, a parsec
is the distance at which the radius of Earths orbit subtends and angle of 1 degree.
Definition of a parsec:
Viewpoint A
Viewpoint B
Viewpoint BViewpoint A
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A light year is an astronomical unit of distance. It is defined as the straight line distance light
travels in a vacuum in 1 year. .
Converting AU to parsecs
Explain how trigonometric parallax can be used to determine the distance to stars
Trigonometric parallax is half the angular shift of a star (in arc seconds) as observed from
Earth over a period of 6 months i.e. half the annual parallax. Because even our closest stars
are so distant, a considerable change in the observers position is required to notice any
change in the stars relative position. By observing parallax in 6 month intervals (from
opposite points of the Earth), the change in the observers position becomes twice
Earth-to-Sun distance or 2 Astronomical Units (AU). Observing 6 months apart maximises
the parallax angle by maximising the baseline and neutralises the slight eccentricity of Earthsorbit
1 AU
1 arc second
1 parsec
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Using trigonometry,, dis the unknown distance from the Sun to the Star andp is the
trigonometric parallax angle. Therefore dcan be calculated by .
Solve problems and analyse information to calculate the distance to a star given itstrigonometric parallax using:
Using the above example, when the parallax of the star (p) is 1 arc second, then the distance d
in parsecs is given by . Remember:
Examples:
1) The star 40-Eridini is 5 pc away. Calculate its parallax in:
a) Arc seconds.
b) Degrees
c) A star has a parallax of 0.3 arc seconds. Calculate its distance from the Earth
in:
a) parsecs
d
2 AUp
= Sun
= Earth
= nearby star
= distant star
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b) light years
Discuss the limitations of trigonometric parallax measurements
The seeing or shimmering effect of Earths atmosphere limits the precision of parallax
measurements. The smallest parallax that can be observed from Earth is 0.01 arc seconds.
This means only about 700 of the closest stars (within 100 pc) can be measured by
Earth-based telescopes. The limitations can be lessened by using space-based telescopes
above the atmosphere or by using a larger baseline for the annual parallax e.g. placing a
satellite in orbit around the sun at a distance from Earths orbit.
Gather and process information todetermine the relative limits to trigonometric parallax distance determinations using
recent ground-based and space-based technologies
Resolution of ground-based telescopes is currently limited to 0.01 arcseconds (100 pcs), due
to atmospheric distortion. Only about 1000 stars within 20 parsecs can be accurately
measured.
Space based telescopes do not suffer atmospheric distortion, so parallax measurements are
determined by the quality and size of the aperture. In 1989, the European Space Agency
(ESA) launched the Hipparcos satellite, which has catalogued accurate parallax
measurements down to 1 milli-arcsecond (mas) for distance measurements of 120 000 stars
out to about 1000 pcs.
Future space telescopes include Gaia and the Space Interferometry Mission (SIM). GAIA has
an accuracy of 10 micro arcseconds (10-5 arcsec) and will catalogue over 1 billion stars
within distances of 100 000 pcs while SIM will use optical interferometry to give parallax of
4 micro arcseconds within 10% accuracy of distances up to 25 000 pcs. The data collected
will allow for a dynamic 3D map of the Milky Way.
Using a satellite to give a
larger baseline
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3. Spectroscopy
Account for the production of emission and absorption spectra and compare thesewith a continuous blackbody spectrum
Emission Spectra
Emission spectra of a chemical element/compound consist only of radiation of a discrete
number of wavelengths. It appears as bright lines against a dark background. This radiation is
produced by hot diffuse gases, such as in a gas discharge tube.
Electrical/heat energy supplied to the atoms/molecules raises the energy level of the electrons.
As the electrons fall back down to their ground state, they emit a quantum of energy which
corresponds to one of the observed wavelengths. The bright lines of emission spectra
correspond to all of the possible energy transitions. The relative intensity of each line depends
on the composition of the gas.
Emission Spectra for Hydrogen:
Absorption Spectra
Absorption Spectra
consist of a
continuous range of
wavelengths, with
discrete gaps at particular wavelengths. It appears as dark lines on a continuous background
of colours. It is produced when a continuous spectrum of light passes through cool gas e.g. in
the Sun, the dark lines result from specific wavelengths being absorbed by cooler gases in the
outer layers.
Atoms/molecules in the gas absorb quantum of energy which corresponds to specific
wavelengths of light. This causes the energy level of the electrons to jump before falling
back to ground state, remitting absorbed wavelengths in all directions. Thus, the intensity of
light transmitted at these wavelengths is reduced. The relative intensity of the lines depends
on the size and density of the gas cloud.
Hot gasSpectrograph
Wavelength (nm)
Each element has its own unique emission spectra
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Absorption spectra for hydrogen:
Continuous Blackbody Spectrum
Blackbody spectrum consists of a continuous range of wavelengths with no lines. It appears
as a continuous rainbow of colours. It is produced by thermal emission of hot substances
e.g. the surface of the Sun acts as a blackbody at high temperatures.
The higher the temperature, the shorter wavelength of peak intensity emission i.e. the
maximum intensity is inversely proportional to the temperature of the hot surface. This is
shown by: where, is the wavelength (nm) and T is the temperature (K). This
is also why hotter stars appear blue and cooler stars red.
Spectrograph
Cool
gas
Wavelength (nm)
Wavelength (nm)
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Emission Spectra Absorption Spectra
Continuous Blackbody
Spectrum
Consists of radiation of only
a discrete wavelengths
Consists of a continuous
range of wavelengths, with
gaps corresponding to
discrete wavelengths
Consists of a continuous
range of wavelengths, with
no gaps
Appears as white linesagainst a dark background
Appears as dark lines againsta continuous background of
colours
Appears as a continuousrange of colours
Produced by hot diffuse
gases
Produced when light from a
hot source passes through
cool gas
Produced by thermal
emission from. solids, liquids
& high-pressure gases
Wavelengths emitted depend
on electron energy
transitions of gas atoms
Wavelengths absorbed
depend on electron energy
transitions of gas atoms
All wavelengths produced at
varying intensities
Intensity varies with
wavelength, depending ongas composition
Intensity varies with
wavelength, depending ongas composition and density
Intensity varies smoothly
with wavelength. The peakemission is inversely
proportional to the
temperature
Describe the technology needed to measure astronomical spectra
A spectroscope is a device used to visually observe spectra. A spectrograph is a device
mounted onto a telescope used to record and measure spectra and the recorded photograph is
called a spectrogram.
A spectrograph or spectroscope consists of three parts:
Intensity of
radiation
emitted
Wavelength (nm)
30001000 2000IRUV
Visible
4000 K
5000 K
3000 K
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The collimator uses a narrow slit and mirrors or lenses to form a parallel beam of light from a
light source.
The second part disperses the light into its component wavelengths to produce the spectra. It
consists of wither a triangular prism or a diffraction grating which can be further subdividedinto transmission or reflection gratings. Diffraction gratings consist of thousands of parallel
slits per cm which cause the light to spread out into a spectrum. Most modern spectroscopes
use diffraction gratings because they scatter less light and give better resolving power than
prisms.
The third part allows the spectra to be viewed or recorded. It consists of either a telescope, a
focusing mirror with a photographic plate or an electronic image device such as a charged
couple device (CCD). Fibre optics may be used to simultaneously obtain multiple spectra.
Prism spectroscope:
Transmissi
on grating:
Reflection grating:
Identify the general types of spectra produced by stars, emission nebulas, galaxiesand quasars
Stars
Stars act as blackbodies and therefore produce spectra that depend on their surfacetemperature according to Planks Blackbody radiation. Absorption spectra are produced as the
result of the radiation passing through the stars cooler atmosphere.
Emission nebulas
Emission nebulae are regions of hot gas (mainly hydrogen) and dust that become heated by
radiation from nearby hot stars. As the electrons in the nebulae drop back to their lower
energy level, they produce emission spectra in the UV, visible, infrared and radio bands
(depending on the nebula composition).
Galaxies
Galaxies consist of up to billions of stars, nebula and planets all circling a common centre.Therefore, the spectra for galaxies combine the spectra of all these celestial objects. They
Collimator
Viewing
slit
Focussing
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emit light from the entire EM spectrum, particularly infrared and radio. Absorption lines of B
and K type stars are common, along with emission lines for hydrogen, nitrogen, carbon and
silicon. Almost all galaxies are moving radially away from the Milky Way, so the spectra are
red-shifted.
QuasarsQuasars are distant point sources producing vast amount of radiation across the entire EM
spectrum, but mostly in the radio band. The spectra consist of broad, high-intensity emission
lines that are extremely red-shifted. There are only 1-2 LY across and are believed to be
formed by gas being swallowed up by black holes,
Describe the key features of stellar spectra and describe how this is used to classifystars
A stellar spectrum is the spectrum of radiation emitted by a star. Stellar spectra consist of a
black body spectra superimposed with absorption lines characteristic of the elements in thestars atmosphere.
The shape of the curve, particularly the position of the peak emission wavelength and the
absorption lines for specific elements indicates the surface temperature.
To produce lines for hydrogen, the temperature must be in the range of 4000-12000K while
helium must be in the 15000-30000K range. Too low temperatures and the electrons will
produce faint absorption lines, too high and the atoms will be completely ionised, again
resulting in no absorption lines.
When different stars are compared, there is a change in colour as luminosity increases. Thecoolest stars are red, then orange, yellow, white and blue for the hottest stars.
Stars can thus be classified into spectral class: O, B, A, F, G, K, M (mnemonic: Oh Be A Fine
Girl Kiss Me) from hottest to coolest. There are 10 further subdivisions from hottest to
coolest: A0-A9.
Spectral Class Colour Surface
Temperature
Absorption line Spectral Features
O Blue
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F White-yellow 10 000-7000 K Weakly neutral H
Stronger neutral Mg, Si, Fe, Ca, Ti
G Yellow 7000-5000 K Strong metals esp. Ca
Weak H
Many single lines ionised and neutralmetals
K Orange 5000-4000 K Strong metals
Molecules e.g. CH, CN
Almost nonexistent H
M Red 4000-3000 K Strong molecules esp. TiO
Spectral Class Example Star
O5 Naos
B3 Achermar
A7 Altair
F0 Canopus
G5 Capella
K2 Arcturas
M1 Autares
Describe how spectra can provide information on surface temperature, rotationaland translational velocity, density and chemical composition of stars
Surface Temperature
The surface temperature can be determined by observing the position of the peak wavelength
emission. According to Wiens Displacement law, where
peak wavelength is inversely proportional to the surface temperature. Therefore stars that are
blue are hotter than stars that are red.
Translational Velocity (relative motion)
The proper velocity of a star relative to the sun is made of two components: the radialvelocity and the translational velocity. The radial velocity is a measure of whether the star is
moving towards us or away and how fast it is moving. Translational velocity is a measure of
the motion of a star across our line of sight.
The radial velocity obtained by observing the Doppler shift of a star, compared to
laboratory-measured spectra. If a star is moving towards us, the wavelengths will contract and
there will be a blue-shift. Conversely, if a star is moving away the wavelengths will stretch
out and there will be red-shift. A red-shift indicates the star is moving away while a
blue-shift indicates a star is moving towards us. The faster the radial velocity, the greater the
Doppler shift.
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The translational velocity is measured by determining the change in position of the star over
long time periods. The distance of a star obtained from parallax measurements is used to
determine the translational velocity.
Velocity components of a star:
Rotational velocity
If a star is rotating,
then one edge is moving
towards us while the other
is receding. One edge will
therefore be red-shifted and
the other side will be
blue-shifted by the same amount. The centre will not exhibit Doppler shift. Individual
spectral lines are broadened by an amount dependant on the rotational velocity of the star- the
faster it rotates, the more the lines broaden.
In the case of binarystars, the rotational
velocity around their
centre of mass can be determined using the Doppler Effect. The two stars periodically
approach and recede; hence the spectral lines will be alternately blue-sifted and red-shifted.
From this, the speed of approach and recession can be calculated, which is then used to
determine orbital periods and rotational velocities.
Density
The surface density and therefore surface pressure of a star broadens the spectra lines.
Increased gas pressure produces more rapid collisions between atoms during emission orabsorption of radiation. These collisions result in electrons shifting energy levels, hence
Proper Velocity
Translational
Velocity
Distant
Star
Radial Velocity
Proper
motion
Sun
Increasing wavelength (nm)
Laboratory measured
Red shift spectra
Blue shift spectra
Non-rotating spectra
Increasing wavelength (nm)
No Doppler
Blue-shift
Red-shift
Star Earth
Combined blue and red shift broaden the spectral lines
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producing broader spectral lines. Dwarf stars with high density produce the broadest spectral
lines whilst super giants produce narrow spectral lines.
Chemical Composition
Each element, ion or molecule has its own characteristic emission lines which represent the
various electron energy levels. These lines are in the same position in a stars absorptionspectrum. Comparing a stars absorption lines with the emission lines for known elements
allows the stars composition to be determined.
Perform a first-hand investigation to examine a variety of spectra produced bydischarge tubes, reflected sunlight or incandescent filaments
Investigation: Using a CD as a Spectroscope
Aim: To observe and examine a variety of spectra produced by discharge tubes, reflectedsunlight or incandescent filaments.
Equipment:
For the spectroscope:
-a silvered CD
-cardboard box
-cardboard tube
-craft knife
-aluminium foil
-sticky tape
-digital camera
-computer, for analysing spectra images
Method:
1/ At night stand 20m from the light source and holding the CD 40cm in front of your
chest look at the reflection of the light on the silvered side of the CD. The bright and
dark lines or regions are emission and absorption lines respectively.
2/ Take a picture of the reflection for later analysis and comparison
Results:
Light source Spectra Features
Tungsten filament light
bulb (argon gas)
argon
Light sources:
-tungsten filament light bulb
-Neon light sign
-Yellow-orange street light (sodium vapour lamp)
-Mercury vapour lamp
-Halogen car light
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Neon light sign
Sodium vapour lamp Strong peaks in yellow,
Mercury vapour lamp Strong peaks in yellow,
orange, yellow-green
Halogen car light (xenon
gas)
xenon
Conclusion:
Analyse information to predict the surface temperature of a star from itsintensity/wavelength graph
Examples:
1) The graph shows blackbody radiation curves for three temperatures:
Energy radiated (K) vs. (nm)
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a) Define a black body
A black body is an object that is emits or absorbs radiation perfectly i.e. it emits or absorbs
radiation across the entire EM spectrum, at varying intensities.
b) Explain the relevance to astrophysics of black body radiation
The black body radiation curve can be used to determine the surface temperature of stars.
c) Explain how Wiens law is used to determine the temperature and composition
of a star
Wiens law states that the peak wavelength emission of a blackbody is inversely proportional
to its surface temperature i.e. Rearranging, It can be used to predict the surface temperature
of a star:. From the surface temperature and the colour of the star, the stars
chemical composition and spectral class can be predicted.
4. Determining distance using photometric measurements
Luminosity is the measure of the power emitted by a star and depends upon the size (radius)
and surface temperature of the star. Given the same temperature, large stars are more
luminous than small stars and given the same radius, hotter stars are more luminous than
cooler stars.
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Brightness (I) of a star is a measure of the intensity of radiation reaching Earth from a star.. It
depends on the intrinsic luminosity (L) of the star and its distance (d) away.
Mathematically:
Define absolute and apparent magnitude
Apparent magnitude (m) is the brightness of a star as observed from Earth. Brighter stars have
lower magnitude and an increase in 1 represents a decrease in apparent brightness of 2.512.
Absolute magnitude (M) is the brightness a star would have when observed from a distance
of 10 parsecs. Absolute and apparent magnitude use the same scale, therefore, more negative
number correspond to higher luminosity. It is estimated by comparison with reference stars of
the same spectral class and known distance (from parallax).
Explain how the concept of magnitude can be used to determine the distance to acelestial object
If a star is closer than 10 pc, m is larger than M and if it is further than 10 pc., the reverse is
true. The amount by which the absolute magnitude (M) and apparent magnitude (m) differ
depends on the star. If both m and M are known, the difference modulus can be used to
calculate the distance to a star:
For stars closer than 10 pc, the distance modulus is negative, while for stars further than 10
pc, it is positive.
Solve problems and analyse information using and
to calculate the absolute or apparent magnitude of stars using data and a reference
star
Examples:
1) Our Sun has an apparent visual magnitude of -26.5 and an absolute visualmagnitude of +4.83. Explain why these magnitudes are different
Apparent magnitude is a measure of the intensity as viewed from Earth whereas absolute
magnitude is a measure of the intensity when viewed at a distance of 10 parsecs. The more
negative the value for absolute or apparent magnitude the more negative the value. Therefore,
because we are closer to the Sun than 10 pc, the apparent visual magnitude of the Sun is
negative while its absolute magnitude is positive i.e.
2) A star of the sixth magnitude is located 40pc from the Sun. Calculate its absolute
magnitude
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A star has an apparent magnitude of +8 and an absolute magnitude of 0. Calculate the
parallax of them star.
3) Use the table to answer the following questions
Star Apparent magnitude (m) Absolute magnitude (M)
Arcturus 0.00 -0.3
Betelgeuse +0.41 -5.6
Hadar +0.63 -5.2
Sirius -1.51 +1.4
Vega +0.04 +0.5
a) Identify which star is the brightest to an observer on the Earth. Explain your
answer.
For an observer on Earth, we use the apparent magnitude. The more negative the value, the
brighter the star appears. Therefore, the brightest star to an Earth observer is Sirius, with
m=-1.51
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b) Calculate the distance to Vega
c) Calculate how much brighter Betelgeuse appears than Hadar
d) Calculate how much brighter Betelgeuse actually is compared to Hadar.
Outline spectroscopic parallax
Stereoscopic parallax is a technique used to determine the distance to a star by comparing the
absolute and apparent magnitude. The term parallax is simply an analogy for distance.
A stars spectrum indicates its spectral class or temperature, which are located on the
horizontal axis of a Hertzprung-Russel diagram and its luminosity, located on the vertical
axis. By finding the position where the lines intercept, the absolute magnitude (on verticalaxis) can be determined. The apparent magnitude can be directly-measured using photometry.
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The distance modulus equation can then be used to determine the distance in pc. This method
is not precise, but is useful as an estimation of distances to stars.
Explain how two-colour values (i.e. colour index, B-V) are obtained and why theyare useful
Colour index values are useful because they allow the surface temperature of starts to be
determined without spectra.
Stars may have 3 different magnitudes depending on the instruments used to view them: the
human eye, a photographic emulsion (light-sensitive colloid) or a photocell. The eye is most
sensitive to yellow-green light; photographic emulsions are most sensitive to blue-violet light;
photocells perform well at all wavelengths. Hence, a blue star would appear brighter on a
photograph than to the eye.
Blue or photographic magnitude (B) is the magnitude of a star measured through a blue filter
so it only allows wavelengths of ~440 nm to pass through. The visual magnitude (V) is
measured through a yellow-green filter which allows wavelengths of 550 nm to pass
through.
The colour index is the difference between the photographic and visual magnitude i.e. . It
follows that if is positive (, then the star will be redder and therefore, cooler. If is negative (,
then the star will be bluer and therefore, hotter.
Colour Index: Relative size of
magnitudes
Relative Colour Relative
temperature
Relative
Spectral Class
More positive redder Cooler Towards O
More negative bluer Hotter Towards M
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In the above graph, the star emits more energy in the B waveband than the V waveband.
The colour index is calibrated so that a (white) main sequence star (spectral class A,
luminosity class V) has a CI of 0.00. The CI for hotter stars will be negative CI while forcooler stars it will be positive.
Describe the advantages of photoelectric technologies over photographic methodsfor photometry
Photographic photometry
Photographic photometry uses visual comparison of star images on photographic plates.
Brighter stars appear larger and denser on the plate and it is possible to obtain photometry for
thousands of stars using a single image, using a laser to scan and produce a digitised image. It
B intensity
(440 nm)V intensity
(550 nm)
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does not calibrate stars accurately; however, it provides higher resolution than photoelectric
devices.
Photoelectric photometry
Photoelectric devices include: photomultiplier and charged-coupled device (CCD).
A photomultiplier (vacuum tube technology) converts weak light into stronger electrical
current. It consists of an evacuated tube, with a thin glass window that allows photons to enter
and hit a photo-cathode. Electrons are emitted in proportion to the light intensity (termed
secondary emission) and a series of 9-14 electrodes (dynodes), of increasing voltage are
used to accelerate the electrons. Secondary emission creates an increasing the number of
photoelectrons and hence, a larger measurable current.
Photomultiplier:
A CCD (solid-state technology) uses an array of millions of light-sensitive pixels on a
silicon chip to measure current. The pixels act as capacitors, storing charge proportional to
the light intensity. The accumulated charge in each capacitor can be rapidly scanned and
analysed via computer.
Advantages of photoelectric over photographic technologies
-Objects can be scanned extremely quickly with quick response time (due to electronic
detectors
-More uniform response across the entire visible spectrum
-Sensitive to a wider range of wavelengths esp. infrared and can be altered to increase
sensitivity for different wavelengths
-Give more accurate measurements of magnitude
-Data can be collected remotely and transmitted digitally
-Data is processed more easily
+100+200 V
+300 V
+400 V+500 V
+600 V
+700 V
Thinwindow Photo-cathode
Anode to
measuring
device
Incoming
photon
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e) Predict the likely spectral class for Betelgeuse. Explain.
The colour index for Betelgeuse is positive, meaning that it emits more energy towards the
red end of the visible spectrum than the blue end. Red stars are cooler than blue stars; hence
it is a cool red star. Betelgeuse is most likely to be M-type, A1 spectral class.
2) A star is observed to have an apparent magnitude of 6.0 and is 20 parsecs from
Earth. Calculate its absolute magnitude.
3) Use the table below to answer the following questions
Star Apparent visual
magnitude
Absolute visual
magnitude
Spectral Class
Acturus 0.00 -0.3 K2
Betelgeuse +0.41 -5.6 M2
Hadar +0.63 -5.2 B1
Sirius -1.51 +1.4 A1
Vega +0.04 +0.5 A0
a) Predict which star is hottest. Explain.
Stars with a spectral towards O are hotter. The spectral classes, in order of temperature are O,
B, A, G, K, M. Therefore, Hadar is the hottest star.
b) Predict the colour of Arturus. Explain.
Artucus is spectral class K2, which corresponds to a relatively cool star which emits the
orange waveband of the visible spectrum most intensely.
c) Predict which star is the faintest when viewed from Earth. Explain.
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Viewed from Earth refers to the apparent visual magnitude. More positive values for
magnitude correspond to fainter stars. Thus, Hadar is the faintest star when viewed from
Earth.
d) Calculate the distance to Hadar.
Perform an investigation to demonstrate the use of filters for photometricmeasurements.
Aim: To observe the effect of various coloured filters on the brightness of a light source
Equipment:
-Red, Blue and yellow-coloured filters-data logger with light intensity probe attachment
Method:
1/ Place light meter on flat table in a well-lit room (fluorescent lighting)
2/ To simulate a red star,
Results:
Identify data sources, gather, process and present information to assess the impactof improvements in measurement technologies in our understanding of celestial
objects.
Space technology has allowed telescopes to overcome atmospheric distortion. However, these
telescopes are expensive to launch and usually only last several years before falling back to
earth due to orbital decay.
Hubble Space Telescope (HST)
The HST purpose was to photograph nearby stars and distant galaxies to improve ourunderstanding of the universe. It carried 5 scientific instruments:
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Instrument Name Purpose/description Observed
wavebands
Wide Field and Planetary
Camera (WF/PC)
2 optical cameras, each with 4 CCDs
WF: wider viewing angle
PC: greater magnification
Visible
Goddard High resolution
spectrograph (GHRS)
Record spectra in high resolution UV
High speed photometer (HSP) Measure brightness of fast-moving
objects
UV, visible
Faint object camera (FOC)
faint object spectrograph
(FOS)
High-resolution imaging devices. Used
photon-counting digicon rather than
CCDs
Visible
The impact of these technologies has been:
-to constrain the value of the Hubble constant the rate of expansion of the universe.
--However, by observing distant supernovae, it found that the rate of expansion of the
universe may be accelerating
-It demonstrated the connection between galaxies and their central black holes
-High-resolution images of the collision of comet shoemaker-Levy 9 in 1994 were
crucial in developing an understanding of the dynamics of comet collisions with
Jupiter-Discovery of proplyds (dense gas discs surrounding newborn stars) and the optical
sources of gamma-ray bursts
- the Hubble-deep and ultra-deep space field images, which utilised the sensitivity of
the HST to obtain optical images of galaxies billion of years away, which has
generated a wealth of scientific papers.
Cosmic Background Explorer (COBE)
COBEs purpose was to measure the cosmic microwave background radiation (CMB) and
provide measurements to shape our understanding of the cosmos. It carried 3 instruments:
Instrument Name Purpose/description Observed
wavebands
Differential Microwave
Radiometer (DMR)
Microwave instrument designed to map
variations in the CMB.
microwave
Far-Infrared Absolute
Spectrophotometer
(FIRAS)
Spectrophotometer designed to measure the
spectrum of the CMB
Infrared
Diffuse InfraredBackground Experiment
Multi-wavelength infrared detector designed tomap dust emission
Infrared
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(DIRBE)
The DMR provided data on the structure formation of the Universe, indicating cluster so
galaxies and vast empty regions. DIRBE detected 10 new IR-emitting galaxies, which were
able to provide data on very cold dust (VCD). It was also able to collect data on interplanetarydust (IPD) and concluded it originates from asteroids. DIRBE was also able to model the
Galactic disc of the Milky Way, indicating it is not a thick disc. COBE provided important
constraints on the star formation rate, although it was unable to resolve the exact star
formation history, so future observations are necessary.
Wilkinson Microwave Anisotropy Probe (WMAP)
WMAP purpose was to measure temperature variations in the CBM to study the geometry,
content and evolution of the Universe; to test the Big Bang model and cosmic inflation
theory. To achieve this, it had to create an accurate map of the CMB.
Instrument Purpose/description Observed
wavebands
Primary mirror:
Pair of Gregorian
1.4 x 1.6 m
reflecting mirrors
Opposite facing; focus signal into secondary
mirrors.
Secondary
Mirror:
Pair of 0.9 x 1.0
m reflecting
mirrors
Transmit signal to receivers
Radio, microwave
Polarisation-sensi
tive differential
Radiometers
A set of 20, divided into groups, using 5 discrete
frequencies; Measure differences between two
telescope beams
Microwave,
radio
Low-noise
amplifiers
Amplify weak incoming signal n/A
WMAPs measurements have been key to establishing our current model of the cosmos.Among its achievements include:
-mapping the CMB and producing the first microwave high-resolution map of the sky
-determining the age of the universe to be 13.73 0.12 Billion years
-determining that normal atoms called baryons only compose 4.6% of the universe,
23.31.3% is dark matter and 721.5% is dark energy
-narrowing down the possibilities of what occurred during the first trillionth of a
trillionth (10-24) s, ruling out well-known textbook models
Chandra x-ray telescope
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Chandras purpose was to observe x-rays from high-energy regions of the universe, such as
supernova remnants
Instrument Purpose/description Observed
wavebands
Wolter telescope Consists of nested hyperbolic andparabolic surfaces coated with
iridium/gold, to absorb x-ray photons.
Advanced CCD Imaging
Spectrometer (CIS
10 CCDs
High resolution camera
(HRC)
Has two micro channel plates used to
detect particles and radiation
High- and low-energy
Transmission grating
Spectrometer
Provides high-resolution spectroscopy
over a wide range in the x-ray
x-ray
Data gathered the Chandra has greatly advances the field of x-ray astronomy:
-Images of supernova remnants revealed neuron stars and black holes
-showed for them first time a smaller galaxy being cannibalised by a larger galaxy
-x-ray emissions from main sequence stars
-strong evidence for existence of dark matter
-Observations of neutron stars, pulsars, gamma ray bursts, black holes and possible quark
stars
5. Binary and variable stars
Describe binary stars in terms of the means of their detection: visual, eclipsing,spectroscopic and astrometric
Perform an investigation to model the light curves of eclipsing binaries usingcomputer simulation
Binary stars consist of a pair of stars revolving around a common centre of gravity. They are
grouped according to their method of detection.
Visual Binaries
Visual binaries can be resolved directly via telescope as ellipses traced out relative to
background stars. The mutual separation of the stars is from 100-10 000 AU with an angle of
separation arc seconds. Observations must be made with telescopes of at least 15cm diameter
and a micrometer is used to measure the angle of separation.
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Eclipsing Binaries
Eclipsing binaries cannot be
resolved via telescope and aredetected by fluctuations in brightness when one star moves in front of the other, and vice
versa.
When the brighter star (blue) moves completely in front of the duller star (red), there is a
slight dip in brightness called a secondary eclipse. When the duller star moves completely in
front of the brighter star, there is a larger dip in brightness, called a primary eclipse.
Light curve for total and partial eclipses:
A similar situation occurs for a partial eclipse, with the dips being a V-shape, rather than
flat-bottomed.
Spectroscopic binaries
More massive star
follows a smaller
elliptical orbit
Barycentre
Secondary eclipse
Primary
eclipse
Time
Intensity
Secondary eclipse Primary
eclipse
Time
Intensity
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Spectroscopic binaries cannot be resolved via telescope and are detected by the Doppler shift
of their spectra. When one star is approaching, it will produce blue-shift while the other is
receding from the observer and will produce red-shift. The combination of both broadens the
spectral lines. This technique only works when the motion of the stars is transverse to the
observers line of sight (will not work if motion is perpendicular). This method is preferred
to visual binaries as there are more distant stars than near stars and because their speeds areeasily measured using Doppler shift.
Astrometric binaries
Astrometric binaries cannot be resolved properly because only one star is bright enough to
see. The presence of a companion star is inferred by the oscillation or wobbling of the
visible star from the mean path of motion due to the gravity of its companion.
Red-shift
Blue-shift
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Explain the importance of binary stars indetermining stellar masses
Binary stars provide virtually the only means of directly
measuring the masses of stars other than the Sun. The
mass of a star is key to determining the processes it
undergoes during its lifecycle and endpoint and is
therefore vital in refining our model of stars.
Applying Keplers Laws for a binary system where the
masses of the two stars are similar:
-the stars orbit each other in ellipses with a common centre of motion called the barycentre-the line joining the two stars (radius vector) covers equal area in equal periods.
-The square of the period is directly proportional to the cube of its radius:
Radius of individual star (if M and R are known)By definition, at the barycentre:
Path of mean
proper motion
m1m2
Barycentre
r2r1
R
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Deriving the formula for total mass of system:
Total mass of systemIf T and R are known, use
If T is given in years and R is in AU, use
Individual masses (given M, R and radius of mass)
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Other useful identities
Solve problems and analyse information by applying:
Examples:
1) Two stars in a visual binary system have an orbital period of and are
determined to be apart. Calculate the combined mass of the system.
2) [from Question 30, 2004]
An astronomer made regular measurements of the intensity of a star over the course of several
days and obtained the light curve shown below.
(i) Describe the features of this light curve that suggest the astronomer is
observing an eclipsing binary system.
The light intensity of the system varies periodically with time. The dip in luminosity
represents when one star moves completely in front of the other, resulting in a decrease in the
intensity or amount of light coming from the system.
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(ii) If both starts have equal masses of determine the separation of the two stars.
3) From 2006, Question 30
(a)
(i) Describe the spectroscopic observations that would determine whether a
particular star is really a binary system
The spectra of the system would be observed to show both red-shift and blue-shift as one star
recedes while the other approaches, leading to a broadening of the spectral lines. This would
only occur, however, if the system was viewed transverse to the observers LOS.
(ii) The graph represents the variation in brightness of a binary star systemGiven that the mass of the system is determined to be kg, calculate the average distance
between the stars within the system.
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Classify variable stars as either intrinsic or extrinsic and periodic or non-periodic
Variable stars are stars whose brightness, colour or other property varies with time. They are
classified according to the cause of the variation and the periodic nature of the variation.
The brightness of non-periodic variables varies irregularly with time. These include novae
and supernovae
Intrinsic variables are stars whose variation in luminosity is due to physical changes within
the properties of the star itself. Intrinsic stars may be divided into two main subclasses:
*periodic variables
*non-periodic variables (novae and supernovae)
Periodic variables are variables that expand and contract fairly regularly with a defined
period. They can be further subdivided into two main groups:
*cepheids: those that have short, regular periods of days to months (generally blue
stars towards spectral class O)
*long period (Mira Ceti) variables: those with longer, more irregular periods
(generally red giants of spectral class M) and large variations in luminosity
Other examples include RR Lyrae and RV Tauri variables
Irregular period or non-periodic variables can be subdivided into three main groups:
*semi-regular variables: mainly red stars, giants or supergiants which display small
variations in luminosity and constant brightness
*Irregular variables: include most red giants. They have short periods and display
rapid, although small variations in luminosity (include red giants, white dwarfs)
*Eruptive variables: include the novae and supernovae, which display sudden bursts
in luminosity (typically include giants and supergiants, which emit vast quantities of
energy due to their large mass)
Other examples include flare stars, T-Tauri stars and R Coronawe Borealis variables
Extrinsic variables are stars whose variation is due to external properties. They can be dividedinto two main subgroups:
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*Eclipsing variables: periodic changes in luminosity are due to an eclipsing
phenomena
*Rotating variables: whose variability may be caused by a misalignment of the
rotational axis with the magnetic axis, leading to thermal hotspots on the surface. It
may also be caused by irregularities in the stars chromosphere or an ellipsoidal shape.
Explain the importance of the period-luminosity relationship for determining thedistance of cepheids.
Cepheids are periodic intrinsic variables whose periods of pulsation are proportional to theirluminosity. As they expand, surface temperature increases while luminosity decreases and as
they contract, their surface temperature increases while luminosity decreases.
Typical light curve for a Cepheid:
It has been
found that the maximum intensity occurs just after the minimum radius. Thus, the steep rise
in luminosity is due to the increase in temperature after the star contracts. In 1912, Henrietta
Leavitt discovered the period- luminosity relation, by plotting the luminosity values of
cepheids on a log-log graph.
The period-luminosity relation is given by the equation: , where
Light
Time
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L is the luminosity, in magnitudes
A is the gradient of the graph
T is the period, in days
B is the y-intercept
Period-Luminosity graph of cepheids:
For cepheids, a definite
relationship exists
between its period of
pulsation and luminosity.
There are two types ofcepheids: Type I
(classical cepheids) and
Type II (younger stars
with lower metal content)
Hence, if we know the
period of pulsation we
can graphically determine
the absolute magnitude. Combining with the apparent magnitude, we can use the distance
modulus to determine the distance.
Cepheid variables are also observed in other galaxies well beyond the scope of parallax
measurements. Thus, if other galaxies contain cepheids, the distances to those galaxies can be
accurately measured. Cepheid variables have been vital in determining the cosmic expansion
of the Universe.
6. Stellar Evolution
Describe the processes involved in stellar formation
Protostar
Type I (classical
cepheids)
Type II
Period, T (days)
Absolute
magnitude
100
-6
10
0
-2
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Gravity causes interstellar nebula of gas and molecules to collapse. These nebulas have
diameters of LY and masses of solar masses. If the mass exceeds the Jeans mass gravity
overcomes any outward thermal pressure and the clouds begin to collapse.
During contraction gravitational potential energy converts into heat- a protostar. The star
begins to faintly emit visible red and infrared radiation. The temperature is too low for
nuclear fusion to begin yet but its vast size means it is luminous, placing at the top RH corner
of the H-R diagram.
Outline the key stages in a stars life in terms of the physical processes involved
Pre-main sequence
Increased temperature increases thermal pressure, opposing gravity and slowing down
contraction. Eventually the protostar reaches a temperature where hydrogen molecules
decompose into atomic hydrogen, allowing further compression and heating to occur. As the
protostar collapses, it rotates and several stars may form by fragmentation to form a cluster.
Surrounding gas and dust are blown away. When maximum luminosity is reached, it is called
a pre-main sequence star.
The mass and composition of interstellar medium determines when and where the star entersthe main sequence (called the Zero-age main sequence). The lower the mass, the longer it
takes the star to enter the zero-age main sequence- stars of less than 0.08 solar masses never
reach the temperatures to begin nuclear fusion.
Protostar:
GPE heat
Pre-Main Sequence: dust
and gas are removed by
the stellar wind
Main Sequence:
Gravity and
outward thermal
pressure are
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Main Sequence
Once temperature and pressure are high enough for nuclear fusion, the star enters the main
sequence. Outward pressure and gravity are balanced, so the star is stable. Dust and gas not
accreted to the core are removed by the stellar wind. The star begins the process of hydrogen
fusion in its core for energy. It becomes slightly hotter and more luminous as radiation andparticles radiate into space in a stable manner.
Describe the types of nuclear reactions involved in Main-Sequence and
post-Main Sequence stars
Main-Sequence
Main sequence stars produce energy from the conversion of hydrogen to helium in its core.
There are two nuclear fusion reactions involving hydrogen:
-the proton-proton chain
-the carbon-nitrogen cycle
In both cases, the net effect is the same: 6 protons are involved, two of which are regenerated
while the other four are converted into two helium nuclei, two neutrinos, two positrons and
gamma radiation. The net reaction is:
Proton-Proton (PP) Chain
The PP chain occurs in lower mass, cooler MS stars (less than 20 million Kelvin) and takes~7 billion years. There are three steps involved:
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1. Fusion of two protons (hydrogen nuclei) into a deuterium (rare isotope of hydrogen)
nucleus. One proton decays into a neutron, releasing a positron and a neutrino.
Positrons (positive charge) readily ionise, emitting gamma radiation. Neutrinos have
no mass or charge and pass out of the core.
2. Fusion of a deuterium nucleus and a proton to form a helium-3 nucleus, with energy
in the form of gamma rays also emitted.
3. Fusion of two helium-3 nuclei to form a stable helium-4 nucleus and two protons.
These protons may strike other protons and begin the chain reaction again.
The Carbon-Nitrogen (CNO) cycle
The CNO cycle occurs in higher mass, hotter MS stars (more than 30 million K) and takes 7million years to complete. There are six steps involved:
1. Fusion of a proton and a carbon nucleus to form a nitrogen-13 nucleus and 2 MeV of
energy I the form of gamma radiation.
2. Nitrogen-13 is unstable and decays into Carbon-13, releasing a neutrino and a
position. The positron annihilates itself when it meets an electron, releasing 1 MeV of
energy
3. Fusion of a proton and Carbon-13 to form nitrogen-14, releasing 8 MeV of gamma
radiation.
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4.Fusion of a proton and Nitrogen-14 to form Oxygen-15 and & MeV of gamma
radiation.
5.Oxygen-15 is unstable and decays into Nitrogen-15, releasing a neutrino, a positron
and 1.7 MeV of energy
6. Fusion of a proton and Nitrogen-15 to regenerate the carbon nucleus, a helium nucleus
and 0.5 MeV of gamma radiation.
Post-Main sequence
Over time, hydrogen-fusion in main sequence stars produces a helium core and an outer
hydrogen-burning shell. When the hydrogen in the core is depleted, hydrogen fusion cannot
occur and gravity causes the core to collapse. GPE is converted into heat, causing the outer
layers to expand. The brightness of the star gradually decreases as the surface area expandsfaster than energy is produced so the star becomes a red giant.
As the core continues to collapse and temperature increases, helium fusion begins explosively
in the helium flash. This causes the star to contract.
Triple Alpha process
End of MS: inner helium
core and outer
energy-producing hydrogen
shell
Core collapses due to
gravity: GPE heat
Heat causes outer layers
to expand- the star
begins the Red Giant
stage
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In Red Giants, three helium nuclei fuse to form a carbon nucleus in the triple alpha process:
When the core is mainly carbon, helium fuses with carbon to produce an oxygen core. Further
exothermic reactions in the outer hydrogen shell form heavier elements up to iron.
Discuss the synthesis of elements in stars by fusion
The heat of the Big Bang synthesised only hydrogen and helium. All other elements have
been created by stellar nucleosynthesis.
Further helium is produced in MS stars via hydrogen fusion (PP chain in cooler stars, CNO
cycle in hotter stars).Helium fusion produces carbon, oxygen, neon and magnesium in post-MS stars via the Triple
Alpha Process i.e. fusion of the product nuclei with alpha particles.
Beyond iron, the reactions are endothermic and occur in the stages beyond Red Giants,
although elements up to lead may be formed by the slow capture neutron process (S-process)
in red giants. All the elements heavier than gold are produced by the rapid capture neutron
process (R-process) in supernova explosions.
explain how the age of a globular cluster can be determined from its zero-age
main sequence plot for a H-R diagram
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Stars in a globular cluster are approximately the same age as they were formed by the same
nebula. This means the stars in the cluster have similar chemical compositions and cover the
entire range of stellar masses. The zero-age main sequence plot shows the stars when they
have just begun the main sequence stage.
Globular clusters are observed to be missing high-mass stars (spectral class O and B). This isbecause high-mass stars use their hydrogen more quickly than smaller stars and move off the
main sequence. As a cluster ages, it appears to form a knee, bending upwards from the right
of the MS. The absolute magnitude at this turn-off position is a function of the age of the
cluster.
Thus, the age of a globular cluster can be determined by the position of the massive stars. If
the cluster is:
-old, there will be less of the high-mass stars on the MS
-young, there will be more high-mass stars on the MS
Explain the concept of star death in relation to:
-planetary nebula
-supernovae
-white dwarfs
-neutron stars/pulsars
-black holes
Star death occurs when nuclear fusion in the core of stars ceases and the outward thermal
pressure due to radiation is overcome by the inward force of gravity. The processes that occurnext depend on the mass of the star.
Low mass stars (2-5 solar masses)
After low-mass stars have begun the helium-burning stage, oxygen and carbon accumulate in
the core. In order to remain stable, the outer hydrogen burning shell moves outwards, ejecting
shells or rings of ionised gas around the core, forming what is known as planetary nebulae.
The core temperature is too low for fusion of oxygen and carbon into other elements, so the
core simply contracts, supported only by the quantum effect called electron degeneracypressure which prevents further core collapse. It is now called a white dwarf. Its high mass
and low surface area means it is hot (~105 K), but low luminosity (therefore very faint). It is
now called a white dwarf.
White dwarfs have no energy source as such, simply relying on residual heat from the core.
Eventually, all this heat is radiated into space and the white dwarf is thought to become a cold
brown or black dwarf. However, no black dwarfs are believed to exist as they would take
longer than the age of the Universe to reach this stage.
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High mass stars (5-8 solar masses)
In more massive stars, nuclear fusion in the core forms elements up to iron. The electron
degeneracy pressure, which prevents electrons from being forced into the nucleus, is
overcome by the inward gravitational force. This causes electrons to be forced into protons,forming neutrons. The core resists further collapse due to the quantum neutron degeneracy
pressure.
Any further collapsing matter simply bounces off the core with an ejection of subatomic
particles called neutrinos, resulting in a supernova explosion. Supernova explosions are
only relatively brief and cannot be seen on an H-R diagram as they are too hot and luminous.
Elements heavier than iron are synthesised during supernova. What occurs next depends on
the core mass of the original star
Neutron stars
If the supernova core mass is 1.4 3.0 solar masses, the neutron degeneracy pressure preventsfurther core collapse, forming a neutron star. Neutron stars are extremely dense, small (10-20
km in diameter), with powerful gravitational and magnetic fields. They emit radiation in the
gamma and x-ray wavebands. Most known neutron stars are called pulsars, which emit beams
of radio waves from their magnetic poles as they rotate (light a lighthouse). When the beams
sweep past the Earth, we detect them as regular radio pulses, hence the term pulsar.
Neutron stars obtain their energy from either from angular momentum from the supernova
explosion which created them, from their intense magnetic fields or from the accretion of
matter from companion stars
Black Holes (>8 solar masses)
For stars that begin greater than 8 solar
masses, the supernova remnant core will be greater than 3 solar masses. At this stage, gravity
completely overcomes even the neutron degeneracy pressure and the core continues to
collapse into a singularity. The gravity is so powerful that not even light can escape its
surface- a black hole is formed!
Gravity
Core mass of 1.4 - 3.0 solar masses:
Electrons stop further collapse
Core mass 1.4 - 3.0 solar masses:
Electrons forced into protons,
forming neutrons i.e. electron
capture. Neutrons prevent
Gravity
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Present information by plotting Hertzprung-Russell diagrams for: nearby or
brightest stars, stars in a young open cluster, stars in a globular cluster
Core mass > 3 solar masses:
Gravity overcomes neutron
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Open Cluster Globular cluster
H-R diagrams vary greatly for different
clusters i.e. some are sparse, others are
densely populated
H-R diagrams are all similar
Giants and supergiants present No supergiants
Giant branch at zero absolute magnitude Giant branch at -3.5 absolute magnitude
Giant branch separate from MS Narrow band connects giant branch with MS
Stars have varying ages Low turn-off point, indicating they are old
clusters
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Globular Clusters
Globular clusters are generally composed of hundreds of thousands of old, low-metal stars.
As a result, there are no supergiants and few dust and gas clouds, as all the stars have
surpassed this stage. All the stars are about the same distance away from us, so the apparent
magnitude and the absolute magnitude for all stars differs about the same amount. Bymatching up H-R diagrams for absolute and apparent magnitude and using the distance
modulus gives an estimate of the age of the cluster.
All the stars in a globular cluster fall upon a well-defined curve. As each star on an H-R
diagram varies with age, this can be used to estimate the age of the star. The highest mass
stars are the most luminous and the first to become red giants. As the cluster ages, lower mass
stars also begin entering the red giant stage- this forms a turn-off point on the diagram. The
absolute magnitude at this turn-off point is a function of the age of the cluster, so an age
scale can be plotted parallel to the magnitude.
If the main sequence contains O-type stars, the cluster is less than 10 million years old
because this is the amount of time it takes for an O-type star to deplete its core hydrogen. If it
contains A- or B-type stars, the cluster is older than 10 million years old.
Open Clusters
Stars in an open cluster are approximately the same age, mass, chemical composition and the
masses of the stars vary greatly.
Present information by plotting on a H-R diagram the pathways of stars of 1, 5
and 10 solar masses during their life cycle
A star of 1 solar mass e.g. the Sun, enters low on the MS (spectral class M). It remains here
for most of its life, slowing moving up the MS to spectral class F. Once it has depleted
hydrogen in the core, it becomes brighter and moves horizontally right to the Red giants
(spectral class K). Once all its nuclear fuel is depleted, its outer layers are radiated off, leaving
a small, hot core. This makes it spectral class F, towards the bottom LH corner of the
diagram.
A 5 solar mass star enters higher on the MS (spectral class F). It spends less time here beforebecoming a red supergiant (spectral class G). Eventually, it moves off the H-R diagram as it
forms a supernova explosion, which is too hot and luminous to graph. The neutron star that
forms next is also too hot and luminous to be graphed.
A 10 solar mass star enters even higher on the MS, for an even shorter time period. There are
two possible stages which occur next:
-the star can become a blue supergiant (spectral class B-A) which forms a supernova
directly before forming a black hole
-the star many become a red supergiant (spectral class G), before becoming a
supernova, and the a black hole
In both cases, the star simply moves upwards off the H-R diagram
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Massive stars (e.g. 10 solar masses) will enter high on the MS and will spend a relatively
short period of time there. Next, it will move to the supergiants (spectral class G) before
moving up off the H-R diagram
Analyse information from a H-R diagram and use available evidence todetermine the characteristics of a star and its evolutionary stage