Download 2900 K micrometers T

!
Astro 1105/1107 Summer 08
Homework
Name____ANSWERS__(25 points total)___
Stellar Spectra. You are an astronomer! Estimating Stellar Surface
Temperatures, Chemical Compositions, and Motion from Spectra of Stars
Write your answers on this page. Due by the BEGINNING of class Monday 7/7/2008. You may
hand it in early anytime in class. Late = zero credit. See helpful HINTS on course webpage.
You already know that as the temperature of an object emitting a thermal (continuous)
spectrum increases, the wavelength corresponding to the intensity peak of the spectrum
gets shorter (“bluer”). You also know that Wien’s law is the equation that relates the
temperature and the wavelength where a thermal spectrum peaks ( " peak , or "max , same thing):
" peak =
2900 K # micrometers
T
-6
(where 1 micrometer is equal
! meters)
! to 10
(Note: Here Wien’s law is expressed in different units than we used in class (meters) or in your
textbook (nanometers). It’s the same law! Some books just prefer to express it this way. They just
used a conversion factor to change the units from meters to micrometers. Both ways are correct.)
Using the equation: For example, if the temperature of the object is 6000 K, then peak intensity of
the spectrum is located at a wavelength of 2900 K micrometers / 6000 K = 0.4833 micrometers.
(Visual: on the middle, dashed spectrum below, the location of " peak is marked with the downward arrow.)
!
0.4
0.5
λ (micrometers)
1. Calculate the peak wavelengths for two objects of T = 5000 K and T = 7000 K: (4 pts)
" peak =
2900 K # micrometers 2900 K # micrometers
=
= 0.58 micrometers (correct units required for full credit)
T
5000 K
2900 K " micrometers
= 0.41 micrometers
7000 K
2. On the next page you will find real spectra taken from six different stars and plotted on the same
graph for ease of comparison.
(a) Which of the three basic types of spectra do you see in these stellar data? (There is more than
one) (3pts)
continuous (thermal) and absorption line
(b) Calculate the temperature of the stars labeled A7IV and G8IV using the spectra and the
equation from page 1. HINT: Estimate the continuous spectrum for each star as demonstrated
in class by drawing a “best fit” curve through the spectrum. (4pts)
For A7IV: T =
2900 K " micrometers 2900 K " micrometers
=
= 7250 K (correct units required for full credit)
# peak
0.4 micrometers
2900 K " micrometers 2900 K " micrometers
For G8IV: T =
=
= 6300 K
# peak
0.46 micrometers
!
(λpeak values - and therefore Temperatures - are approximate; anything close is fine)
!
3. Chemical composition. Now you will determine the chemical composition of the surfaces
(photospheres) of the stars. Use our on-line laboratory spectra of different gases; we call these
“comparison spectra”: http://www.radiochemistry.org/periodictable/gas_spectra/index.html (this
site is also linked from our course web site on the “Homework” page).
(a) Which of the three basic types of spectra do you see in the COMPARISON spectra? (There is
more than one.) (3pts) continuous
(thermal) and emission line
(b) Use the comparison spectra to determine which chemical element is present in the star, A7IV,
and write the name of the element below: (2pts)
^
^
^
hydrogen
^
Why, FYI: Hydrogen has 4 spectral lines in the visible range (marked above on the comparison spectrum),
corresponding to the 4 big dips in the A7IV spectrum on the next page (also marked). No other element has
only these four prominent lines, as A7IV does. Moreover, note that 3 of these lines are toward the blue end,
and the last one is alone toward the red end of the visible range, matching the pattern spacing in A7IV.
(c) Which of the other stars also contains that element? Do the others stars contain other
elements? Very briefly, explain how you can tell. (3pts)
All the stars have hydrogen, because they all show the same pattern of 4 dips (that is, they have
absorption lines in the same locations as A7IV, which are also the same locations as the
EMISSION lines in the hydrogen comparison spectrum). Other stars have additional elements too,
because they have more absorption lines that are not accounted for by hydrogen.
0.4
0.5
0.6
0.7
Wavelength (micrometers)
0.8
0.9
NOTE: The shaded region indicates the extent of the visible spectrum, which is also the extent of
the comparison spectra.
intensity
Here is a real spectrum of the star Sirius (Alpha Canis Majoris), followed by a hypothetical star, Bob.
intensity
λ
λ
4. Motion. Star Bob (lower spectrum) is identical to Sirius in luminosity, surface temperature,
composition, and distance from Earth. Assume no dust between us and either star.
(a) In which direction (relative to Earth) is star Bob’s motion? How can you tell? (3pts)
Away, because the spectrum is shifted to longer wavelengths. (redshifted)
(b) Sketch what star Bob’s spectrum would look like if Bob’s motion had the same speed but in the
opposite direction. (Draw it directly on one of the above graphs.) (3pts)
[The spectrum would look roughly as below: same shape as Sirius’s spectrum, but shifted to the LEFT
(shorter wavelengths, or blueshift) instead of to the right.]