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 “luminosity” 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


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.