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Nuclear Astrophysics

by: Quinn Larkin

Nuclear Astrophysics PHY 983

Quinn Larkin
GPA 3.67


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This 3 page Class Notes was uploaded by Quinn Larkin on Saturday September 19, 2015. The Class Notes belongs to PHY 983 at Michigan State University taught by Staff in Fall. Since its upload, it has received 37 views. For similar materials see /class/207629/phy-983-michigan-state-university in Physics 2 at Michigan State University.


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Date Created: 09/19/15
PHY983 Nuclear Astrophysics Spring 2009 Homework Set 5 Due Feb 20 2009 beginning of lecture Key words hydrostatic equilibrium main sequence absolute and apparent magnitudes globular cluster ages Problem 1a 6 pts Give a ROUGH order of magnitude estimate of central pressure and temperature in the sun just from its observed radius and mass To do this look at a point midway in terms of radius between the center and the surface and assume that the density at this point corresponds to the average density of the sun and that the enclosed mass at this radius is about half the solar mass Use hydrostatic balance at this point and assume further that the pressure gradient is linear from the center to zero at the surface Give the resulting central pressure in CGS units dynescm2 and atmospheres Using the average density of the sun and the assumption of an ideal gas with solar hydrogen and helium composition estimate the temperature The purpose of this is to show that just the assumption of hydrostatic balance maintained by a hot gas sets the scale for the enormous pressures and temperatures in the sun Problem 1b 2pts Compare your result of central pressure and temperature with the standard solar model of John Bahcall BS2005AGSOP Go to his homepage httpwwwsnsiasedujnb and click through Solar Neutrinos Solar models Also check the assumptions made above on enclosed mass and pressure at a mid radius point Problem 2 5pts Derive the absolute visual magnitude of the sun given that the observed visual magnitude is 2673 Also compare the absolute visual magnitude to the absolute bolometric magnitude of the sun see lecture notes and explain the difference qualitatively Problem 3a 10 pts Globular clusters are great laboratories for stellar evolution as they are a group of stars that was born at the same time and that are all at about the same distance from earth In addition distances to globular clusters can be determined relatively accurate as many stars can be used to obtain many measurements Plotting the observed visual magnitude versus the magnitude difference between blue and visual wavelengths BVA measure for the color or effective temperature directly maps out a HertzsprungRussell HR diagram because all stars are at the same distance to the earth and therefore the observed magnitudes do not need to be corrected for distance variations The picture below shows the HR diagram of the globular cluster 47 Tucanae As you can see many of the stars have moved already off me mam sequence Determme the age of 47 Tue from me bservedmamsequencetumoffpomtusmgthefollowmgmethod mptouc 2 gwam branch m non om g 14 bran red gwam E 39 m n g m E 39 subgwam g 3 branch 3 2n Determan me lummosnv ofthe stars at the mam sequence tumon velauve to the sun Luminositerass and Maseram Sequence foeume relations from class to determan conecuon eoneedon to obtam the total observed magutude from he observed msgmmde m the V spectral band The ddstance to 47 Tue 5 o en given m form of a ddstance modulus M rm 13 27 Gas PHY983 Nuclear Astrophysics Spring 2007 Homework set 7 Due Friday March 23 2007 in my mailbox Keywords rpprocess l 10pts Make a graph showing the temperature and mass density conditions needed for breakout of the CNO cycles via a the 150ag reaction and b via the 18Neap reaction assuming a proton abundance of 066 and a helium abundance of 84e2 Mark typical peak conditions for Xray bursts on the graph see lecture notes Document the rates you are using and all equations 150a g rate Use the latest results from the JINA measurement at Notre Dame httppossissaitarchiveconferences028023NICIX7023pdf Use their alpha branching and the total width of the resonance corresponding to the 403 MeV state and use the na1row resonance formalism to calculate the reaction rate Neglect the higher lying resonances to keep it simple they matter a little bit For the total width there is a value from previous work and from the new work use the better value with the smaller error for simplicity don t need to average 18Neap rate Use our new JINA reaction library database to obtain that rate Go to httpwwwnsclmsueduNnerodb and search for the 18Neap rate Click on quotViewquot Data Points and you can copy the values into a spreadsheet or any other program you are using and calculate additional values with the calculator on the page if needed for some reason it doesn39t display the small numbers 2 15 pts Derive a simple estimate for the mass number of the endpoint of the rpprocess in Xray bursts by using the initial hydrogen and helium abundance and the number of ap reactions in the ap process as free parameters Make the following assumptions 0 In a rst step the burst burns instantaneously all the helium via the triple alpha reaction and the alphap process along a SIMPLE alphap process reaction chain alternating alphap and pg reactions starting at 18Ne Neglect the additional proton capture at 12C in this chain assume you have only alphap process and triple alpha 0 Assume all helium is converted into the nucleus at the endpoint of this alphap process instantaneously Assume that only then the hydrogen burning via the rpprocess starts Assume that the burst burns all the hydrogen and that the nal composition is a single nucleus at the end of the rpprocess 0 Assume there are no cycles Hint the critical quantity is the proton to seed nucleus ratio at the onset of the rpprocess 2a Go through all assumptions in the previous subproblem and write one sentence about why you think this is a good or a bad assumption Continued on next page H


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