. Each
star is assigned a letter (a through o); for example,
star a has a surface temperature of about 10000 °K and
a luminosity of about 80 L.| Name: ________________________ | Due 10/31 | ID Number: ________________________ |
The HR diagram below shows ``surface'' temperatures and and
luminosities for a sample of fifteen stars. Here, temperature is
measured in °K, and luminosity is measured in units of the Sun's
luminosity, L. Each
star is assigned a letter (a through o); for example,
star a has a surface temperature of about 10000 °K and
a luminosity of about 80 L.
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As usual, this HR diagram uses logarithmic spacing along both
axes. Each step leftward is factor of 2 increase in T,
and each step upward is a factor of 10 increase in L.
For example, a star which is plotted halfway between
102 and 103 on the vertical axis has
a luminosity of roughly
3.2×102 L |
1. List these fifteen stars in order of increasing temperature:
10 = 3.162...
increase.
________________________________________________
2. List these fifteen stars in order of increasing luminosity:
________________________________________________
3. The two lists you've just made should be nearly identical, but there will be a few stars (exactly three, in fact), which don't appear in the same order in the two lists. Eliminate these stars from the sample, and list the remaining twelve stars in order of increasing temperature and increasing luminosity:
________________________________________________
4. List the stars on the main sequence in order of increasing luminosity:
________________________________________________
5. The next part of this assignment asks you to calculate
the lifetime of each main-sequence star. To do this, you'll need to
know the mass M of each star in units of the Sun's mass,
M. This information is
given in the following table:
| star | M | star | M | star | M | star | M | star | M | ||||
| a | 3.5 | b | 4.2 | c | 0.77 | d | 1.38 | e | 10.8 | ||||
| f | 0.27 | g | 3.4 | h | 25.2 | i | 0.63 | j | 6.2 | ||||
| k | 1.08 | l | 1.69 | m | 0.14 | n | 16.9 | o | 0.52 |
To calculate the lifetimes, begin by listing the main-sequence
stars, in order of increasing luminosity, in the ``star'' columns of
the table below. Next, use the HR diagram on the other side of this
paper to find the luminosity L of each star you've just listed,
and fill in the L columns of the table. Now suppose, for a
moment, that each star has exactly the same amount of fuel as
the Sun; the star will use up this amount of fuel in a ``reference''
time tref = tlife, ÷ L, where
the Sun's lifetime is tlife, = 1010 yr,
and L is expressed in units of the Sun's luminosity,
L. Finally, use the
values of tref to compute each star's main-sequence
lifetime
tlife = tref × M,
where the star's mass M is taken from the table above and
expressed in units of the Sun's mass, M. For example, star a has
L = 80 L and M =
3.5 M, so
tref = (1010 yr) ÷ 80
= 1.25×108 yr, and
tlife = (1.25×108 yr) × 3.5 =
4.4×108 yr.
| star | L | tref | tlife | star | L | tref | tlife | |
| ___ | __________ | __________ | __________ | ___ | __________ | __________ | __________ | |
| ___ | __________ | __________ | __________ | ___ | __________ | __________ | __________ | |
| ___ | __________ | __________ | __________ | ___ | __________ | __________ | __________ | |
| ___ | __________ | __________ | __________ | ___ | __________ | __________ | __________ | |
| ___ | __________ | __________ | __________ | ___ | __________ | __________ | __________ | |
| ___ | __________ | __________ | __________ | ___ | __________ | __________ | __________ |
6. Use the numbers you just worked out to determine how stellar lifetimes vary along the main sequence. Which stars have the longer lifetimes: high-mass main sequence stars or low-mass main sequence stars?
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Joshua E. Barnes
(barnes@ifa.hawaii.edu)
Last modified: October 23, 2006 http://www.ifa.hawaii.edu/~barnes/ast110_06/homework/hw09.html |
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