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    Astrophysics

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    From VCAA

    This detailed study focuses on the development of

    cosmology over time, but with a particular emphasis on the

    twentieth century. In particular, the study looks at the

    nature of stars, galaxies and their evolution, as well as

    evidence about the steady state and Big Bang models ofthe Universe. Light is the basic tool of astrophysicists and

    it is assumed that the nature of the nuclear atom is the

    same throughout the Universe. While Einsteins relativity is

    needed for the details, the Newtonian understanding ofmotion is sufficient to establish the basic ideas.

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    Outcome 3.2

    On completion of this unit the student should be able todescribe and explain methods used to gather information

    about stars and other astronomical objects and apply this

    information to models of the nature and origin of the

    Universe. To achieve this outcome the student will draw

    on the following key knowledge and apply the key.

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    describe characteristics of the Sun as a typical star, including size, mass, energy

    output, colour and information obtained from the Suns radiation spectrum;

    describe the properties of stars: luminosity, radius and mass, temperature and

    spectral type;

    explain fusion as the energy source of a star;

    apply information from the HertzsprungRussell diagram to describe the

    evolution and death of stars with differing initial mass;

    analyse methods used for measurements of the distances to stars and galaxies;

    explain the link between the Doppler Effect and Hubbles observations;

    explain the formation of galaxies, stars, and planets;

    compare the Milky Way galaxy to other galaxies such as those with differentshape, colour or size;

    explain the steady state and Big Bang models of the Universe;

    compare two or more explanations of the nature and origin of the Universe;

    interpret and apply appropriate data from a database that is relevant to aspects

    of astrophysics.

    Key knowledge

    To achieve this outcome the student should be able to:

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    How Far, How Bright?

    Which of the stars A or B are closer to the earth? Give reasons for your choice.

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    How Far, How Bright?

    To determine which is closer we can useparallax.

    Hold out your thumb at arm's length, close one of your eyes, and examine

    the relative position of your thumb against other distant (background)

    objects, such as a window, wall, a tree, etc. Now look at your thumb withyour other eye. What do you notice?

    Move your thumb closer to your face and repeat the experiment. What was

    different this time?

    http://www.astro.ubc.ca/~scharein/applets/Sim/new-parallax/Parallax.html

    Watch this applet to see how parallax works in Astrometrythe measurement

    of distance and position in Astronomy.

    http://www.astro.ubc.ca/~scharein/applets/Sim/new-parallax/Parallax.htmlhttp://www.astro.ubc.ca/~scharein/applets/Sim/new-parallax/Parallax.htmlhttp://www.astro.ubc.ca/~scharein/applets/Sim/new-parallax/Parallax.htmlhttp://www.astro.ubc.ca/~scharein/applets/Sim/new-parallax/Parallax.html
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    The formula of a trigonometric parallax distance is given below:

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    We need to be careful here because these diagrams are not to scale. The parallax

    to the nearest star system, Alpha Cenauri, is 0.74212 arcseconds.

    1 arcsecond = 1/3600 of a degree

    1 parsec = 3.26 light years

    1 light year = 9.46 x 1012

    km1 parsec = 3.086 x 1016 m

    1 parsec = 3.086 x 1013 km

    1 Astronomical Unit (AU) = 1.496 x 1011 m

    1 parsec = 2.063 x 105AU

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    The parallax to the nearest star system, Alpha Cenauri, is 0.74212 arcseconds.

    Using the previous data, calculate the distance of Alpha Centauri in parsecs.

    parsecs35.1

    74212.0

    1

    1

    d

    d

    pd

    If we drew a baseline of 2 cm (i.e. 1AU = 1 cm) on an accurate scale diagram, how

    far away would the star be?

    d = 1.35 x 2.063 x 105= 277, 987 cm = 2.8 km

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    Can you think of a problem with parallax?

    For stars that are very far away, parallax is too difficult to determine. Even most

    stars within our own galaxy cannot have their distance measured using

    parallax.

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    Determining the distance to more distant stars, galaxies and quasars is relies

    on a variety of methods. Detail as to the methods goes beyond the scope of

    this course. Key methods, however include radar measurements (within our

    solar system), spectroscopic parallax, various period-luminosity relationshipsfor different types of intrinsic variable stars, integrated magnitude for globular

    clusters, methods based on galaxy brightness, the Tully-Fisher method and

    the Sunyaev-Zeldovich effect.

    One particular method uses Photometry, the measurement of the brightness

    of celestial objects.

    The concept of photometry can be traced back to Hipparchus of Rhodes

    (161-126 BC). He developed the concept of magnitude as a measure of a

    stars brightness. His six-point scale classified the brightest stars as being

    magnitude 1 whilst the dimmest stars were magnitude 6. Pogson adapted themagnitude scale in 1856 and proposed a logarithmic scale. As the human

    eyes response is nearly logarithmic, Hipparchus original scheme could be

    easily adjusted to the new standard.

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    Magnitudes are effectively a logarithmic

    scale. The change of 5 in magnitude

    corresponding to a factor of 100 is

    equivalent to the statement b5= 100, or

    5 = logb100, where b is the base of thelog scale. To make this true, b has to be

    close to 2.512 because 2.5125= 100 (try

    it on your calculator). This means that an

    increase in the apparent brightness of 1

    on the magnitude scale corresponds to

    about 2.5 times the brightness.

    Mathematically speaking,

    B

    A

    BA L

    L

    mm log512.2

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    Here is a familiar part of the night sky. Can youidentify any objects? Which are the brightest?

    Alpha Centauri -0.04 Acrux 0.75

    Beta Centauri 3.93 Eta Carinae 6.46

    Becrux 1.25

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    The absolute magnitude, M, of an object given its apparent magnitude, m, and

    distance, d, is given by

    where dis the star's distance in parsecs.

    Alternatively, the distance is given by

    Becrux has an apparent magnitude of 1.25 and an absolute magnitude of -3.92.

    What is its distance from earth in km?

    51010mM

    d

    10log5 d

    mM

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    While the apparent magnitude and absolute magnitude scales are convenient

    for observational purposes, the astrophysicist actually needs to know the

    apparent brightness and intrinsic brightness in SI units; that is, in watts per

    square metre of received radiation, and watts of total radiated power,

    respectively. When measured in this way the intrinsic brightness is called the

    Luminosity (L) and is measured in watts.

    Given that the Luminosity of the sun is 3.86x1026

    W, what is the luminosity ofSirius if its apparent brightness is only 8.8 10-11that of the Sun, and its

    distance is 8.61 l.y.? Hint: find the ratio between the luminosity of the sun and of

    sirius.

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    28

    26

    211

    2

    11

    2

    2

    2

    2

    2

    2

    1000.1

    1086.326

    26

    26

    61.863240108.8

    108.8

    4

    4

    su nsiriu s

    su n

    sirius

    su n

    sirius

    sun

    sirius

    su n

    sirius

    su nsu n

    siriussirius

    su n

    sirius

    siriu ssiriu ssiriu s

    su nsu nsu n

    LL

    R

    R

    R

    R

    b

    b

    L

    L

    Rb

    Rb

    L

    L

    RbL

    RbL

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    Luminosity and brightness are not the only sources of information in the light

    coming from a star. Another incredibly rich source of information is a stars

    COLOUR.

    What it is made of (using spectroscopy)

    What temperature it is (using blackbody radiation)

    The colour of a star can tell us

    http://upload.wikimedia.org/wikipedia/commons/c/cf/EM_Spectrum_Properties_edit.svg
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    Spectroscopy is the technique of splitting light (or more precisely electromagnetic

    radiation into its constituent wavelengths). The energy levels of electrons in atoms

    and molecules are quantised, and the absorption and emission of electromagnetic

    radiation only occurs at specific wavelengths. Consequently, spectra are not

    smooth but punctuated by 'lines' of absorption or emission.

    Spectroscopy

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    Spectroscopy is the technique of splitting light (or more precisely electromagnetic

    radiation into its constituent wavelengths). The energy levels of electrons in atoms

    and molecules are quantised, and the absorption and emission of electromagnetic

    radiation only occurs at specific wavelengths. Consequently, spectra are not

    smooth but punctuated by 'lines' of absorption or emission.

    Try it yourself with our spectroscopes ,

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    http://www.boston.com/bigpicture/2008/10/the_sun.html

    Early spectroscopy focussed on our closest and favourite star

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    The sun radiates in all parts of the electromagnetic spectrum, not just in the visible

    light that we are accustomed to observing. These images show what the sun

    would look like if we could see at different wavelengths of electromagnetic

    radiation.

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    Spectra of the Elements Applet:

    Here are some examples of what spectroscopy tells us

    Spectral Lines Applet:

    http://jersey.uoregon.edu/vlab/elements/Elements.html http://mo-www.harvard.edu/Java/MiniSpectroscopy.html

    http://jersey.uoregon.edu/vlab/elements/Elements.htmlhttp://mo-www.harvard.edu/Java/MiniSpectroscopy.htmlhttp://mo-www.harvard.edu/Java/MiniSpectroscopy.htmlhttp://mo-www.harvard.edu/Java/MiniSpectroscopy.htmlhttp://mo-www.harvard.edu/Java/MiniSpectroscopy.htmlhttp://jersey.uoregon.edu/vlab/elements/Elements.html
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    Blackbody Radiation Applet:

    http://www.mhhe.com/physsci/astronomy/applets/Blackbody/frame.html

    http://www.mhhe.com/physsci/astronomy/applets/Blackbody/frame.htmlhttp://www.mhhe.com/physsci/astronomy/applets/Blackbody/frame.html
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    The characteristics of blackbodyradiation can be described in terms of several

    laws:

    1. Planck's Lawof blackbodyradiation, a formula to determine the spectralenergy densityof the emission at each wavelength(E

    )at a particular absolute

    temperature (T). (Not examinable!)

    light)of(speedms103

    constant)Boltzman-(StefanKWm1067.5

    constant)s(Planck'Js1005.1

    1

    8

    1-8

    42-8

    134

    5

    c

    k

    h

    e

    hcE

    Thc

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    This applet shows us a practical application of these laws.

    Blackbody Radiation Applet:

    http://www.mhhe.com/physsci/astronomy/applets/Blackbody/frame.html

    http://www.mhhe.com/physsci/astronomy/applets/Blackbody/frame.htmlhttp://www.mhhe.com/physsci/astronomy/applets/Blackbody/frame.html
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    If one assumes that the Sun is a black body with a surface temperature of

    6000K, calculate the energy per second radiated from its surface.

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    Astrophysicists have developed a classification system base on stars spectral

    types. The spectral class is made up of 7 letters as follows.

    Stars in various spectral classes have these characteristics.

    SpectralType

    Temperature (Kelvin) Spectral Lines

    O 28,000 - 50,000 Ionized helium

    B 10,000 - 28,000 Helium, some hydrogen

    A 7500 - 10,000 Strong hydrogen, some ionized metals

    F 6000 - 7500 Hydrogen, ionized calcium (labeled H and K on spectra) and iron

    G 5000 - 6000 Neutral and ionized metals, especially calcium; strong G band

    K 3500 - 5000 Neutral metals, sodium

    M 2500 - 3500 Strong titanium oxide, very strong sodium

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    The following illustration represents star classes with the colors very close to those

    actually perceived by the human eye.

    http://upload.wikimedia.org/wikipedia/commons/8/8b/Morgan-Keenan_spectral_classification.png
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    Given the information about spectral classes, what type of star would give the

    following spectral lines?

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    The star had all the hydrogen lines, so that narrows our choices down to B,

    A, and F. However, it had no helium lines, so that rules out a type B star.

    The star did have ionized calcium (the H and K lines), which are found in

    type F stars. So the star is a type F star.

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    In summary

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    Next lesson: using colour, luminosity, etc to determine the life cycle of starshow

    they are born and die.

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    In 1911 Danish astronomer, Ejnar Hertzsprung, plotted the absolute

    magnitude of stars against their colour. Independently in 1913 Henry plotted

    spectral class against absolute magnitude. Their combined efforts resulted ina chart that is as important to Astrophysicists as the Periodic Table is to

    chemiststhe Hertzsprung-Russell diagram.

    H-R Diagrams

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    At the bottom-right of the

    diagram we can see two

    named stars, Proxima

    Centauri and Barnard's Star.These are both cool

    (approximately 2,500 K) and

    dim (absolute magnitudes of

    about -13). Following the

    broad band straight up we

    come across Mira, also coolbut much more luminous.

    Travelling further up we come

    across Antares and

    Betelgeuse. Again these stars

    are cool but they are

    extremely luminous.

    Why do these three groups

    differ so much in luminosity?

    Th t thi ti d d th St f B lt l ti hi

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    The answer to this question depends upon the Stefan-Boltzmann relationship.

    424 TRL

    If two stars have the same effective temperature they each have the same power

    output per square metre of surface area.

    So a star that is much more luminous than the other it must have a much greatersurface area.

    The more lum inous s tar is b igger.

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    If we look at the

    vertical band on the

    H-R diagram for hotter

    stars around type A

    spectral class we see asimilar pattern:

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    If we compare the dimmest stars on the H-R diagram we can also make some

    inferences. The following diagram shows the lower region of the H-R diagram.

    Procyon B andBarnard's Star share

    the same low

    luminosity with an

    absolute magnitude

    of about +13.

    Procyon B is muchhotter than Barnard's

    Star. Given that they

    have the same total

    power output

    Procyon B must

    therefore have lesssurface area than -

    its radius is smaller.

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    Star Formation

    M16, the Eagle Nebula shows newborn stars emerging from "eggs" - not the

    barnyard variety - but rather, dense, compact pockets of interstellar gas called

    evaporating gaseous globules (EGGs).

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    Protostarsform when sections of giant molecular clouds start to collapse due to

    gravitational attraction. Continued collapse leads to higher densities so that

    eventually the cloud becomes opaque, trapping the thermal energy within the

    cloud. This then causes both the temperatureand pressureto rise rapidly. The

    timescale for this is basically a function of the massof the collapsing cloud withmore massive clouds collapsing more rapidly into a protostar. A 15 solar mass

    protostar may collapse in only 105 years whilst a star like our Sun would take

    around 50 million years.

    HST visible and infrared images ofstar forming region, 30 Doradus in

    the Large Magellanic Cloud. The

    arrows point to protostars that are

    obscured in the visible but visible at

    infrared wavebands.

    Credit: NASA , John Trauger (Jet Propulsion

    Laboratory) and James Westphal (California Institute

    of Technology), Nolan Walborn (Space Telescope

    Science Institute) and Rodolfo Barba' (La Plata

    Observatory)

    http://www.nasa.gov/http://www.nasa.gov/
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    Main sequence evolution

    Atoms in proto-starare drawn closer together and reduction in GPE increases KE of

    random disordered movement. i.e. temperature increases.

    At ~3000 K nuclei of hydrogen and helium can no longer hold on to orbiting

    electrons.

    Energy radiated by star exactly balances energy released by thermonuclear

    fusion, so star maintains steady temperature.

    At several million Kelvin nuclear fusion of hydrogen begins. Enormous

    amount of energy released and state of equilibrium reached in which:

    Thermal and radiation pressure acting outwards from core exactly balances

    gravitational pressure tending to collapse stars mass inwards, so star maintains a

    constant size.

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    Animation of the p-p chain:

    http://www.jinaweb.org/movies/pp_chain.html

    Very high temperatures are needed because atomic nuclei are positively charged

    and must have enough kinetic energyto overcome repulsion

    Thermonuclear fusion

    Once close enough the strong forcein enough to hold them together.

    http://www.jinaweb.org/movies/pp_chain.htmlhttp://www.jinaweb.org/movies/pp_chain.html
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    When the hydrogen fuel in the core runs out and fusion stops, it shuts off the

    outward radiation pressure. Inward gravitational attractioncauses the helium

    core to contract, converting gravitational potential energy into thermal energy.The rise in temperature heats up the shellof hydrogen surrounding the core until

    it is hot enough to start hydrogen fusion, producing more energy than when it was

    a main sequence star.

    When hydrogen runs out

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    The new, increased

    radiation pressure actually

    causes the outer layers of

    the star to expand tomaintain the pressure

    gradient. As the gas

    expands it cools, just as a

    spray can feels colder after

    use as the gas has been

    released. This expansion

    and cooling causes the

    effective temperature to

    drop. Convection transports

    the energy to the outer

    layers of the star from theshell-burning region. The

    star's luminosity eventually

    increases by a factor of

    1000 or so.

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    Helium gets dumped onto the core causing it to heat up even more. When the core

    temperature reaches 100 million K, the helium nuclei now have sufficient kinetic

    energy to overcome the strong coulombic repulsion and fuse together, forming

    carbon-12 in a two-stage process. As three helium nuclei, also known as alpha

    particles, are used it is called the triple alpha process. Fusion with another heliumnucleus produces oxygen-16 nuclei. This process is the main source of the carbon

    and oxygen found in the Universe, including that in our bodies.

    The process initiates in a matter of minutes or hours. Once the temperature is

    hot enough for helium fusion in one part of the core, the reaction quickly spreads

    throughout it. This sudden onset of helium core fusion is called the helium flash.

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    Eventually the outer layers of gas cool and a red giantis produced.

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    D th f t

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    Death of a star

    If red giantshave a mass greater than about 8x Suna supergiantcan allowa series of further thermonuclear reactions after helium:

    If the temperature reaches 600 million K, carbon burning occurs producing neon

    and magnesium.

    If the temperature reaches 1 billion K, neon burning occurs producing oxygen andmagnesium.

    If the temperature reaches 3 billion K, silicon burning involving many nuclear

    reactions finally producing very stable iron nuclei.

    Supernova

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    When the fuel for the supergiants final nuclear reaction is exhausted the core

    collapsesuntil the neutrons are compressedas tightly as they will go.

    A shock wave is producedwhen the very rapid final collapse is suddenlyhalted and the intense radiation pressure from the immensely hot core

    causes the star to explode forming a supernova

    Extreme temperatures and pressure during a supernova further

    thermonuclear fusion reactions occur absorbing rather than releasing

    energy. This is how elements more massive than iron are created.

    The debris disperses into the hydrogen and helium gas in space and eventually

    density variations may cause the clouds of dust and gas to collapse and give

    birth to a new generation of stars.

    Supernova

    Ne tron Star

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    The high rotational speed means that the surface of neutron stars are travelling

    at relativistic speeds. The gravitational pull on the material must be enormous to

    prevent the layer being ripped off. The acceleration due to gravity at the surface

    of a neutron star is of the order of 1012 ms-2compared with 10 m. s-2at the

    surface of the Earth. Any material that falls onto its surface would thus be ripped

    apart and smeared one atom thick on the surface.

    Neutron Star

    After a supernova part of the coreremains intact and is greater than 1.4solar massesit forms a neutron star

    Density would be >100x greater than a white dwarf -

    a teaspoonful would have a mass of several

    hundred million tonnes!

    Until 1967, neutron stars were theoretical but

    Cambridge astronomer Jocelyn Bell used 2048

    dipole antennae array to survey galaxies which

    emitted radio waves and noticed an unusual signal.

    Pulsar

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    Pulsar

    Bell discovered a signal that continuously repeated with

    a period of 1.3373011 seconds. She checked that the

    pulses were not being produced on Earth and foundother pulsating radio sources including one in the Crab

    nebulaa supernova remnantwith a period of one-

    thirtieth of a second.

    The pulsating sources of radio-wave radiationwere

    given the name pulsars.

    The frequency of the pulses

    corresponds to the frequency at which

    a pulsar vibrates or rotates.

    Therefore, Pulsars must be very small

    bodies.

    The intensity is high. Therefore, Pulsars

    must be very massive and very dense.

    The most plausible explanation is that

    pulsars are neutron stars.

    Black Holes

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    Black Holes

    If the mass of a neutron star is greater than about 2.5 solar masses,

    neutrons would not be able to withstand immense gravitational pressure and

    core would shrink to infinitesimally small point with an infinitely high

    density.

    Gravitational fieldwould be so strongthat not even lightand other EM

    radiation could escape.

    This is known as a black hole.

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    http://www.factmonster.com/images/ESCI168NEBULA002.jpg

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    http://www.optcorp.com/images2/articles/full-LivesOfStarsDiagram.jpg

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