hw2 - Physics 160: Stellar Astrophysics Homework #2...

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Unformatted text preview: Physics 160: Stellar Astrophysics Homework #2 Due Tuesday October 11th at 5pm in SERF 340 Reading: Carroll & Ostlie sections 5.1-5.4, 8.1-8.2, 9.5 (line broadening) Exercises [90 pts total]: (1) [20 pts] Teegarden’s Star is a recently discovered red dwarf with a high proper motion, µ = 5.05 “/yr, and a large parallax, π = 0.259”. While measuring its Hα line, we find an observed wavelength of 656.52 nm (assume this is a “vacuum” wavelength). (a) [5 pts] What is the radial velocity of Teegarden’s Star? (b) [5 pts] What is its tangential velocity (i.e., in the plane of the sky)? (c) [5 pts] What is its total speed relative to the Sun? (d) [5 pts] The star has an apparent magnitude of V = 15.4. Using Figure 8.16 in Carroll & Ostlie, estimate the spectral type of this star (2) [15 pts] Ap stars are a peculiar class of hot star with strong magnetic fields, usually of order 1 T at the photosphere. (a) [10 pts] Determine the wavelengths of the three components of the Hα line that are produced as a result of Zeeman line splitting (note: the µ in Eqn. 5.22 is the reduced mass of the proton-electron system of a hydrogen atom). (b) [5 pts] The resolution of a spectrograph is typically quantified as R = λ/Δλ, where Δλ is the smallest wavelength range that can be separated at a given wavelength λ. What resolution of spectrograph is needed to resolve the two outer Zeeman lines in these stars? (3) [35 pts] Using the data from Appendix F and G that is provided on the course website, do the following (it may be helpful to use a spreadsheet/plotting program like Excel or OpenOffice): (a) [10 pts] Using data from Appendix G, plot a “theorist’s” HR diagram, comparing log10(L/L) (y-axis) against log10(Teff) (x-axis) for dwarfs, giants and supergiants; remember temperature is plotted from right to left! Label each “0” type in each sequence (i.e., M0, K0, etc.) and the Sun. (b) [5 pts] On this same plot, indicate lines of constant radius based on the Stefan-Boltzmann equation. What are the typical radii of giant and supergiant stars? (c) [10 pts] Again using data from Appendix G, plot an “observer’s” HR diagram for the same spectral types, comparing MV (y-axis) against B-V (x-axis). Again, label the “0” spectral types and the Sun. (d) [5 pts] How do these two plots differ? What are some of the possible reasons behind these differences? Pay particular attention to the shape of the dwarf, giant and supergiant sequences. (e) [5 pts] On the observer’s plot, add in the data for the nearest stars from Appendix F (plot as a different symbol). In general, what kind of stars are these? Are there more cool/faint stars or more hot/bright stars? (4) [10 pts] The Hβ line at 486.1 nm arises from the 4→2 electron transition. We measure the profile of this line form the Sun (T = 5800 K, density of H atoms = 1.5x1023 m-3). What is the line broadening arising from: (a) [5 pts] Natural broadening (b) [5 pts] Doppler broadening (assume vturb = 0) (5) [10 pts + prize!] As discussed in class, the spectral sequence of stars is ordered OBAFGKMLTY, with O-type stars being the hottest and most luminous, and Y-type brown dwarfs being the (recently discovered!) coldest and least luminous. There are many mnemonics that are used to remember this seemingly random string of letters, such as Oh Be A Fine Girl/Guy Kiss Me, Less Tongue, Yuck! Only Boring Astronomers Feel Giddy Knowing Mnemonics Like These (Yawn) Our Buddy Adam Feels Great Knowing Maui Life Tops Yours Obama’s Bailout A Federal Government Killer, Much Luck To You A list of mnemonics created by Physics 160 students is linked off of the course website. Your assignment: come up with a new mnemonic. There will be a prize for the best one as voted on by the class! ...
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This note was uploaded on 02/26/2012 for the course PHYS 160 taught by Professor Norman,m during the Fall '08 term at UCSD.

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