Chapter 18 Eruptive and Violent Stars PROBLEM SET HINTS Assigned: 1-12 EXCEPT 3 & 8 18-1: construct a dimensionally appropriate length using the given period (unit of time) and velocity (unit of length per time). 18-2: remember the formula for Luminosity 18-4: a simple distance modulus (DM) calculation (m-M=5logd-5). In this case, V=22 --> m = 22. Express your answers in kpc, Mpc or Gpc as needed. 18-5: Two approaches, either v*t=d or apply eqn. 18-3, then use DM. 18-6: recall that a magnitude difference is simply -2.5 log (Lum1/Lum2). 18-7: Typical solar flare output is about 10(25)J over no more than 10(4) sec. Hence the flare luminosity is ratio (J/s). Use values in Appendix A4-3 for the stars and recall that M(bol)=M(V)+BC and Log L*/Lo = 1.9 - 0.4M(bol). 18-9: Apply the Virial theorem, eqn. 16-15, to find the efficiency is somewhat under 10%. Show your work! 18-10: Similar argument as above (eq.16-15), to deduce the mass loss rate is somewhat typical of red giants, of order 10(-8) Mo/yr. Show your work in deducing this! 18-11: Wind ÒluminosityÓ is still [J/s] which can be constructed from kinetic energy, except using dm/dt instead of m in 1/2 mv2. Use v=100km/s for the T Tauri star, and v=30km/sec for the M stars. 18-12: (a) compute the energy per reaction via the mass deficit (do you get 1.11 x 10(-12)J/reaction?); (b) next, figure the number of reactions possible in the 2Mo shell, assuming equal numbers of Si and He nuclei (should be a large number!); (c) compute the total energy by multiplying a*b and compare with the observed supernova energy of 10(44)J. Done! Note Mo means solar mass. ---------- Hints on even-numbered problems CHAPTER TEN -- THE SUN 10-2: The thermal Doppler width of a spectra line was described in section 8-5B. Remember that the full width is twice the Doppler shift (note eqn. 8-13). 10-4: Recall the Saha equation, 8-31 and section 8-4B for definitions of variables. Fe I is the neutral iron spectrum, Fe II is once ionized. 10-6: Consider Wien's law (eqn.8-39) which allows the wavelength of peak flux output to be related to temperature. 10-8: Escape speed was discussed in chapter 2. How does the solar escape speed compare with Earth's? 10-10: Scale height was defined in section 4-5B. The mean molecular weight (mu) for ionized H is 0.5. Use the following temperatures: 5800K for photosphere; 10,000K for chromosphere and one million K for the corona. 10-12: Use eqn. 8-37b to compute the monochromatic intensity, but consider RATIOS first, I(umb)/I(phot). 10-14: A simple calculation using Wien's law. 10-16: (a) Integrate the optical depth equation, eqn. 10-3, from tau(x=0) to tau(x=d); (b) assume both kappa and rho are depth independent in getting the derivative; (c) re-read sect. 10-2B concerning limb darkening and review Fig.10-5 in formulating your answer.