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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- batim 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
[email protected] 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 5 Turn the page over 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 = 931.494 MeVc−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 1.09373 × 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, Φ0 2.0679 × 10−15 Wb 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 Page 2 of 5 Turn the page over 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 bremsstrahlung spectrum for a single electron. Explain the shape and work out the highest energy bremsstrahlung 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 regions 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] Page 3 of 5 Turn the page over 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 year 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 but 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 regular 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] Page 4 of 5 Turn the page over 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 bright 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- batim 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
[email protected] 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 over 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 = 931.494 MeVc−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 1.09373 × 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