Hertzsprung-Russell Diagram

1.  Stellar Classification
    *  O, B, A, . . . temperature sequence
2.  Hertzsprung-Russell (HR) Diagram
    *  Correlates luminosity & temperature
    *  Main sequence (most stars), giants, supergiants, white dwarfs
    *  Giants , supergiants really are big
    *  Luminosity class (I, II, . . . )
        - From width of spectrum lines
3.  Mass-Luminosity Relation
    *  L  a M3.5
4.  Nearest stars mainly dim & cool; brightest-appearing stars are distant & luminous



Questions

1.  Ques. #5, pg. 274.

2.  What kinds of stars are most numerous in the Galaxy?  Why don't you see many of these stars in the night sky?

3.  The diagram above shows an HR diagram with five stars (A - E) along with the main sequence indicated.

a)  Which star has the largest diameter?
b)  Which star has the smallest diameter?
c)  Which is the hottest star?
d)  Which is the star most like the sun?
e)  Which star is a cool supergiant?
f)  Which star has strong lines of ionized helium in its spectrum?
g)  Which star is the white dwarf?
h)  Which star has spectrum lines due to molecules?

4.  Explain how you know that a K5 giant star must be larger in diameter than a K5 main sequence star.  Hint:  plot both stars on an HR diagram and note how their temperatures and luminosities compare.

5.  Suppose the following stars all have the same apparent brightness.  Which is farthest away?  Which is nearest?  Why?

(a)  G2 V    (b)  B3 III    (c)  F0V    (d)  B0 I    (e)  White dwarf

6.  A star 10 times more massive than the sun (spectral type B3 on the main sequence) would be how much more luminous than the sun?


Answers

1.  Here's an HR diagram, showing all the important regions:


 

2.  The coolest main sequence stars ('red dwarfs') are the most numerous stars in the galaxy.  You see none of these in the night sky (viewed from Earth) because of their very low luminosities. The closest of these, Proxima Centauri, though it lies only 4 ly from Earth, is more than 100 times too dim to be viewed with the naked eye.

3.  a)  B has the largest diameter.

b)  C has the smallest diameter.

c)  It looks like A is the hottest star, though C is close.

d)  It looks like D is the star most like the sun (in luminosity and temperature).

e)  B is a cool supergiant.

f)  Lines of ionized helium occur only in hot stars, so stars A and C could show strong lines of ionized helium.

g)  C is a white dwarf.

h)  Stars B and E could have lines due to molecules in their spectra because only very cool stars show molecular lines.

4.   K5 main sequence and giant stars have the same surface temperature; that's what 'K5' means.  Same temperature means same amount of energy radiated per second from each square meter of surface.  So, for the giant to be more luminous than the main sequence star, it must have a larger surface area, thus a larger radius.  (Recall that luminosity (L) is related to radius (R) and temperature (T) thus:  L  = 4pR2sT4.)

5.  The B0 I star is farthest away, as it has the largest luminosity among the stars listed.  The white dwarf star is nearest, as it has the lowest luminosity.  (Recall the inverse-square law relating flux (F), luminosity (L) and distance (d):  F = L/4pd2.  The problem states that the stars listed are equally bright (have the same value of F, as observed from Earth), so to keep the ratio on the right-hand side of the inverse-square law the same in all cases requires that larger L means larger d, and so on.)

6.  The mass-luminosity relation goes like this:  L  M3.5.  So. relative to the sun's luminosity, a 10 solar-mass star has luminosity given by:  L = 103.5  =  3162; i.e., this star is 3162 times more luminous than the sun (!).