Module Code: PHYS201501
Module Title: High Energy Astrophysics © UNIVERSITY OF LEEDS
Resit End of Module Assessment
School of Physics and Astronomy Semester Two 2020/2021
Assessment information:
Calculator instructions:
You are allowed to use a calculator or a computer calculator in this assessment.
Dictionary instructions:
You are allowed to use your own dictionary in this assessment and/or the spell-
checker facility on your computer.
Assessment information:
• This assessment is made up of 5 pages and is worth 70% of the module mark.
• You have 48 hours to complete this open book online assessment.
• You are recommended to take a maximum of 2 hours within the time available to
complete the assessment.
• You must answer all of the questions in this assessment.
• You should indicate the final answer to each question by underlining it. At the end
of each answer you should cite any websites or textbooks other than the course ma-
terials and recommended text books that you have used specifically to answer that
question. You should always answer in your own words and not repeat material ver-
atim and you should explain each step of your working.
• You must upload your answers via Minerva to GradeScope within the time al-
lowed. You are advised to allow up to four hours to photograph your answers, and
upload as a PDF to GradeScope.
• When submitting your work, you must identify which questions are answered on which
uploaded pages. You must also check that you have uploaded all the work you wish
to be marked as part of this assessment and that the answers uploaded are clearly
legible. Failure to do so may result in your work not being marked.
• If there is anything that needs clarification or you have any problems, please email the
module leader or XXXXXXXXXX and we will respond to you as quickly
as possible within normal working hours UK time (9:00-17:00 hours, Monday-Friday).
• This is a formal University assessment. You must not share or discuss any aspect
of this assessment, your answers or the module more generally with anyone
whether a student or not during the period the assessment is open, with the exception
of the module leader and Physics exams team.
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Module Code: PHYS201501
Approximate values of some constants
Speed of light in a vacuum, c 2.998 × 108 m s−1
Electron Charge, e 1.602 × 10−19 C
Electron rest mass, me 9.11 × 10−31 kg = 0.511 MeV c−2
Proton rest mass, mp 1.673 × 10−27 kg = 938.3 MeVc−2
Unified atomic mass unit, u 1.661 × 10−27 kg = XXXXXXXXXXMeVc−2
Fine structure constant, α 1/137.036
Planck constant, h 6.626 × 10−34 J s
Boltzmann constant, kB 1.381 × 10−23 J K−1 = 8.617 × 10−5 eV K−1
Coulomb constant, k = 1/4π�0 8.987 × 109 N m2 C−2
Rydberg constant, R XXXXXXXXXX × 107 m−1
Avogadro constant, NA 6.022 × 1023 mol−1
Gas constant, R 8.314 J K−1 mol−1
Stefan Boltzmann constant, σ 5.670 × 10−8 W m−2 K−4
Bohr magneton, µB 9.274 × 10−24 J T−1
Gravitational constant, G 6.673 × 10−11 m3 kg−1 s−2
Acceleration due to gravity, g 9.806 m s−2
Permeability of free space, µ0 4π × 10−7 H m−1
Permittivity of free space, �0 8.854 × 10−12 F m−1
1 Parsec, pc 3.086 × 1016 m
Solar mass, M� 1.99 × 1030 kg
Solar radius, R� 6.95 × 108 m
Solar luminosity, L� 3.85 × 1026 W
Magnetic flux quantum, Φ XXXXXXXXXX × 10−15 W
Some SI prefixes
Multiple Prefix Symbol Multiple Prefix Symbol
10−18 atto a 10−9 nano n
10−15 femto f 109 giga G
10−12 pico p 1012 tera T
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Module Code: PHYS201501
SECTION A
• You must answer all the questions from this section.
• This section is worth 20 marks.
• You are advised to spend 30 minutes on this section.
A1. Sketch the
emsstrahlung spectrum for a single electron. Explain the shape and
work out the highest energy
emsstrahlung photon which could be produced by a 10
MeV electron. [5 Marks]
A2. The Crab Nebula is a supernova remnant. Its energy output peaks in two different
egions of the electromagnetic spectrum and it is thought that both peaks are due to
the same population of high energy electrons. Give a qualitative explanation of this
statement. [5 Marks]
A3. Matter accreting onto a white dwarf is generating 1025 W of thermal X-ray emission.
What is the minimum mass transfer rate (in solar masses per year) needed to sustain
this X-ray luminosity? [5 Marks]
A4. What is the Greisen–Zatsepin–Kuzmin (GZK) effect? How does it affect our ability to
identify sources of the very highest energy cosmic rays? [5 Marks]
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Module Code: PHYS201501
SECTION B
• You must answer all questions from this section.
• This section is worth 60 marks.
• You are advised to spend 90 minutes on this section.
B1. This question concerns supernova remnants.
(a) The evolution of a supernova remnant can be summarised as a transition through
four phases. In phase four the radius of the remnant is constant, i. e. it has
stopped expanding. Which three quantities are considered constant during the
expansion (give one per phase)? Explain why they are considered constant. [5]
(b) A 1600 year old shell-type supernova remnant is known to contain electrons of
energies up to 100 GeV, trapped by a 35 nT magnetic field. Give a numerical
argument to support the statement that particle acceleration is probably still go-
ing on within the supernova remnant, given that the electrons lose energy via
synchrotron radiation at a rate given by
−dE
dt
=
e4B2E2sin2θ
6π�0c5me4
.
Note:
e4
6π�0c5me4
= 2 × 1012Js−1T−2
.
[15]
[20 Marks]
B2. This question relates to X-ray binaries.
(a) In a particular X-ray binary system, how many solar masses of material per yea
have to be accreted onto the compact star of radius 10 km in order to sustain
an observed X-ray luminosity of 1030 W? Discuss two possible scenarios for the
transfer of mass to the compact star from its non-degenerate companion. [10]
(b) An X-ray binary system exhibits flickering on a shortest timescale of about 0.3 ms
ut no coherent X-ray pulse period. Estimate the mass of the compact object in
this system. The optical luminosity of the non-degenerate star exhibits a regula
18 day cycle and a shift in the wavelength of its emission lines of up to 0.025
percent is seen. Estimate its mass. State any assumptions you have made. [10]
[20 Marks]
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Module Code: PHYS201501
B3. This question concerns radio galaxies.
(a) 408 MHz radio maps of another galaxy show that two radio components have
moved apart by a distance of 25 light years between July 2011 and July 2021.
If the true separation of the components is now 40 light years, what must the
frequency of the observed 408 MHz radio emission have been in the rest frame
of its source?
Hint: E
′
= γE(1 − βcosθ) [10]
(b) A particular active galaxy is a
ight X-ray source and contains relativistic elec-
trons of energies of up to 5 GeV. Explain why one might expect a flare from this
object detected in 100 keV X-rays to be accompanied by a gamma ray flare with
photon energies of up to 10 TeV. [10]
Page 5 of 5 End.
Module Code: PHYS201501
Module Title: High Energy Astrophysics © UNIVERSITY OF LEEDS
Resit Mid-term Assessment
School of Physics and Astronomy Semester Two 2020/2021
Assessment information:
Calculator instructions:
You are allowed to use a calculator or a computer calculator in this assessment.
Dictionary instructions:
You are allowed to use your own dictionary in this assessment and/or the spell-
checker facility on your computer.
Assessment information:
• This assessment is made up of 4 pages and is worth 30% of the module mark.
• You have 48 hours to complete this open book online assessment.
• You are recommended to take a maximum of 1 hour within the time available to com-
plete the assessment.
• You must answer all of the questions in this assessment.
• You should indicate the final answer to each question by underlining it. At the end
of each answer you should cite any websites or textbooks other than the course ma-
terials and recommended text books that you have used specifically to answer that
question. You should always answer in your own words and not repeat material ver-
atim and you should explain each step of your working.
• You must upload your answers via Minerva to GradeScope within the time al-
lowed. You are advised to allow up to four hours to photograph your answers, and
upload as a PDF to GradeScope.
• When submitting your work, you must identify which questions are answered on which
uploaded pages. You must also check that you have uploaded all the work you wish
to be marked as part of this assessment and that the answers uploaded are clearly
legible. Failure to do so may result in your work not being marked.
• If there is anything that needs clarification or you have any problems, please email the
module leader or XXXXXXXXXX and we will respond to you as quickly
as possible within normal working hours UK time (9:00-17:00 hours, Monday-Friday).
• This is a formal University assessment. You must not share or discuss any aspect
of this assessment, your answers or the module more generally with anyone
whether a student or not during the period the assessment is open, with the exception
of the module leader and Physics exams team.
Page 1 of 4 Turn the page ove
Module Code: PHYS201501
Approximate values of some constants
Speed of light in a vacuum, c 2.998 × 108 m s−1
Electron Charge, e 1.602 × 10−19 C
Electron rest mass, me 9.11 × 10−31 kg = 0.511 MeV c−2
Proton rest mass, mp 1.673 × 10−27 kg = 938.3 MeVc−2
Unified atomic mass unit, u 1.661 × 10−27 kg = XXXXXXXXXXMeVc−2
Fine structure constant, α 1/137.036
Planck constant, h 6.626 × 10−34 J s
Boltzmann constant, kB 1.381 × 10−23 J K−1 = 8.617 × 10−5 eV K−1
Coulomb constant, k = 1/4π�0 8.987 × 109 N m2 C−2
Rydberg constant, R XXXXXXXXXX × 107 m−1
Avogadro constant, NA 6.022 × 1023 mol−1
Gas constant, R 8.314 J K−1 mol−1
Stefan Boltzmann constant, σ 5.670 × 10−8 W m−2 K−4
Bohr magneton, µB 9.274 × 10−24 J T−1
Gravitational constant, G 6.673 × 10−11 m3 kg−1 s−2
Acceleration due to gravity, g 9.806 m s−2
Permeability of free space, µ0 4π × 10−7 H m−1
Permittivity of free space, �0 8.854 × 10−12 F m−1