Astrophysics 2 rar
Transcript of Astrophysics 2 rar
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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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