Download SOLUTIONS ASTROPHYSICS – OPTION D 2015-17

SOLUTIONS ASTROPHYSICS – OPTION D
ASTROPHYSICS OPTION D – PART 1
INTRODUCTION AND STELLAR RADIATION
E.2.5:
Apply the Stefan-Boltzmann law to compare the luminosities of different stars.
Luminosity is dependent on the temperature and
the surface area of a “glowing” object:
L = s AT 4
with
Given
s = 5.67 ´ 10 Wm K
-8
-2
-4
Examples: Stephan-Boltzmann Law
1.
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2.
3.
2
4.
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Black Body and Wien’s Displacement Law pp. 496-497
Examples: Wien’s Law
5.
6.
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More Examples
1.
This question is about the Hertzsprung–Russell (HR) diagram and using it to
determine some properties of stars.
The diagram below shows the grid of an HR diagram, on which the positions of
selected stars are shown. (LS = luminosity of the Sun.)
(a)
(i)
Draw a circle around the stars that are red giants. Label this circle R.
(ii)
Draw a circle around the stars that are white dwarfs. Label this circle W.
(1)
(iii)
Draw a line through the stars that are main sequence stars.
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(1)
(b) Explain, without doing any calculation, how astronomers can deduce that star
B has a larger diameter than star A.
star B has lower temperature;
star B has (slightly) larger luminosity / stars have approximately
same luminosity;
surface area calculated from L = σAT4, so star B has larger
surface area/diameter / to give the same/similar luminosity
at lower temperature, star B must have bigger diameter/
surface area;
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(c)
Using the following data and information from the HR diagram, show that star
A is at a distance of about 800 pc from Earth.
Apparent brightness of the Sun
Apparent brightness of star A
Mean distance of Sun from Earth
1 pc
= 1.4 × 103 W m–2
= 4.9 × 10–9 W m–2
= 1.0 AU
= 2.1 × 105 AU
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b=
L
4 πd 2
used;
to give
dA

dS
L A bS
1.4  10 3

 10 5 
;
LS b A
4.9  10 9
hence dA = 1.7 × 108 AU;
= 800 pc
Do not award a mark for the conversion from AU to pc.
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2.
3.
8
4.
5.
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6.
7.
10
8.
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9.
(1)
Non rotating star = straight line = no movement = no Doppler shift
Rotating star = moving toward and away = Doppler Shift
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ASTROPHYSICS OPTION D – PART 2
STELLAR OBJECTS
1.
2.
1 parsec (pc) = 3.26 light years (ly) = 3.09 ´1016 m
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Review Problem
1. Some data for the variable star Betelgeuse are given below.
Average absolute magnitude
Average apparent magnitude
Average apparent brightness
Radius
= –5.1
= + 0.60
= 1.6 × 10–7 W m–2
= 790 solar radii
The luminosity of the Sun is 3.8 × 1026 W and it has a surface temperature of
5700 K.
SEE NEXT PAGE
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a)
Determine, in terms of the luminosity of the Sun, the luminosity of
Betelgeuse.
b) Calculate the surface temperature of Betelgeuse.
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Spectroscopic Parallax and the Cepheids pp. 510-512
1.
.
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Cosmology: The Expanding Universe , the Big Bang
and Cosmic Background Radiation ( CMB) pp. 516-520
Review Questions
1.
See pp. 506-507
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2.
(a) Apparent magnitude is a measure of the brightness of the star, on a logarithmic
scale, as it appears from earth. (b) Absolute magnitude is the apparent magnitude a
star would have when observed from 10 pc away
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3.
4.
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5. The parallax of a star is 0.025 “. Calculate the distance to the star.
6.
(a) Star A appears brighter because its apparent magnitude is smaller. (b) The
distance of star A is larger since its parallax is smaller. Since it appears brighter and
it is further away it must have a larger luminosity than star B.
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7.
(a) the luminosity is the same since the absolute magnitude is the same. (b) Star
B has a larger parallax so it is closer. Hence it appears brighter.
8.
The three standard pieces of evidence in favor of the big bang are (1) the cosmic
background radiation, (2) the expansion of the universe and (3) the helium
abundance in the universe.
Detailed discussions of these are on page 517 of the textbook:
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9.
(a) The temperature would keep falling to absolute zero. (b) The temperature
would increase as the collapse begins.
10.
The big bang signifies the beginning of time and space. At the big bang the
universe was a point and so the big bang happened everywhere in the universe.
The question is meaningless within the big bang model since by definition time
started with the big bang. It is as meaningless as to ask for a place 1 km north of the
north pole. However, recent developments within string theory suggest that the
question may not be as meaningless as it appears. See the very interesting article
“The time before time”, by Gabriele Veneziano (one of the true greats of theoretical
physics) in the May 2004 Scientific American.
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Cosmology : Galaxies and the Expanding Universe pp. 533-541
Tsokos.
ALSO: Read Oxford New Text pp. 660 - 665
Questions
1.
v = Ho d
2.
Hint : nearby galaxies may move toward us.
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3.
State age of universe in years: Assume 1 year = 365 days. Round off to 1 sig. digit.
1 parsec (pc) = 3.26 light years (ly) = 3.09 ´1016 m
1Mpc = 1x 106 pc
Time = 1
H
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4.
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5.
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Stellar Evolution pp. 521-522 Tsokos
Questions
1. Example Problem HR Diagram - answer a-d below:
a) State the necessary condition of the Sun in order to for it to move from
position S.
b) State and explain the change in the luminosity of the Sun that occurs between
positions S and I.
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c) Explain, by reference to the Chandrasekhar limit, why the final stage of the
evolutionary path of the Sun is at F.
d) On the diagram, draw the evolutionary path of a main sequence star that has a
mass of 30 solar masses.
2.
L ∝ mn
(mass)
The 1 solar mass because it will consume energy ( burn) at a slower rate.
3.
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4.
The Chandrasekhar limit is a mass of about 1.4 solar masses. It represents the
largest mass a white dwarf star can have. If the mass that is left behind after a
planetary nebula or supernova is less than this limit the star will become a stable
white dwarf star.
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ASTROPHYSICS OPTION D – PART 3 – HL ONLY
STELLAR POCESSES
Stellar Evolution Review pp. 521-522
Questions
1. Describe the evolution of a main sequence star of 1 solar mass. See table -
nucleosysnthesis
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2. a) Explain why a star having a mass of 50 times the solar mass would be extected to have a
lifetime of many times less than that of the Sun.
b) By referring to the mass-luminosity relationship , suggest why more massive stars will have
shorter lifetimes.
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Supernovae
Questions
1. Outline the difference between a Type Ia and a Type II supernova.
2. What is meant by a standard candle?
3. Explain how a Type Ia supernova can be used as a standard candle?
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Closed , Open and Flat Universes
Questions
1. Explain what is meant by a closed universe.
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2. On the diagram above draw the variation based on the open model of the
universe.
3. Explain , by reference to your answer in 2, why the predicted age of the
universe depends upon the model of the universe chosen.
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4. a) What evidence suggests that the expansion of the universe is accelerating?
b) What is believed to be the cause of the acceleration?
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