duke astro homework 2 summer 2006

duke intro to astro, summer 2006                      homework 2 (assignment 3)                                    due: tuesday, july 18

1) text, question 19-18

2) text, question 19-49

3) this is a re-arrangement of questions 19-51, -52:

a) the color of a given star is mathematically expressed by a quantity called the color index, defined by

                       color index = m_B - m_V = 2.5 log (b_V/b_B)

[here b_B stands for the flux of the star's light in the blue (B) part of the spectrum; b_Vis the flux of the star's light in the yellow-green (V because it matches the our eyes' peak sensitivity in the Visible part of the spectrum; for more details you can read section 19-4, which we skipped)]

b) Convince yourself (and me) that this formula follows from the formula in the first column of box 19-3, page 418

(heretofore, we have usually applied this equation to two different stars; how is it applied above?)

c) Now let's apply this formula, one at a time, to two different stars: a 12,000-K star (spectral class B9) and a 3000-K star (spectral class M8);
note that the blackbody curves for these two stars were drawn in figure 5-10, page 98.

    (1) What can you say about the ratio of b_V/b_B value for the hotter (12,000-K) star?

        Consequently, what is the sign of the color index for this star?

        What else about the 12,000-K blackbody curve is this same sign?

    (2) Same questions as above for the 3000-K star.

4) Cepheids are stars that (due to their interior structure) pulsate (expand and contract) for a small portion of their lives. They are extraordinarily useful for obtaining distance to galaxies and for determining our location in the our galaxy, the Milky Way. The first Cepheid discovered goes by the prosaic name of d Cephei. d Cephei's properties are graphed on page 480.

a) How many times fluxier is d Cephei at its brightest than at its faintest?
b) Is this also how many times more luminous d Cephei is at its brightest than at its faintest?
    why or why not?
c) Use graph (b) and figure out the time(s) when d Cephei has its smallest size.
d) How did they know that d Cephei was the temperature it was where they drew the red arrows
    in graph (c)? What did they look at it, and how was what they looked at different when the star
    was hottest than when the star was coolest?
e) The neat part about cepheids is that period of light (or temperature or luminosity or radius)
    variation is related to its intrinsic average luminosity: see figure 21-17 on the adjacent page
    It turns out that d Cephei is a type I Cepheid [we know because the light variation in graph (a)
    is very smooth; type II Cepheid light variations have a very characteristic bump in the curve]
    First, determine a rough luminosity for the d Cephei from figure 21-17.
    Then use that to determine d Cephei's distance form us.

5) Question 26(35) on the distance to the Hercules cluster. Do NOT read box 26-2; it is absolutely bogus!

6) Question 5(34) on why hydrogen in interstellar space can absorb, but not emit.