Download Lab 9

Astronomy 115
Name(s):
Lab 9: Galaxies and the Hubble Law
Objective: To demonstrate the classification of galaxies and to use a rational
expression to figure out the distances to galaxies using redshift.
The large-scale structure of the universe is governed by gravity. The Sun orbits
the center of our galaxy, the Milky Way. The Milky Way, in turn, orbits the center
of the Local Group, a cluster of galaxies. The Local Group orbits the center of
the Virgo Supercluster, a cluster of clusters of galaxies.
Classifying galaxies
The Hubble Deep Field project, taken by the Hubble Wide Field Planetary
Camera 2, took images of galaxies even more distant than our supercluster. Each
of the three laminated photos (A, B and C) has about 3000 objects in it; the
estimate for the number of galaxies in the universe is between 50 and 100 billion.
Obtain one of the laminated sheets, and classify the numbered objects by color
(hopefully obvious) and by shape:
• stars have spikes due to light scattering in the telescope
• spiral galaxies which have “arms” when viewed from above or look like a “fried
egg” from the side
• elliptical galaxies which have a smooth, featureless appearance, either round or
oval
• irregular galaxies which do not have a uniform or regular appearance
1. Fill in the table below with the number of the object in the appropriate cell.
Color
Blue
White
Yellow
Red
Star
Elliptical
galaxy (E0 to
E7)
Spiral galaxy
(S and SB)
Irregular
galaxy
Pool your data with the class; all of the numbers from 1 to 45 should show up in
your table.
2. Are there any empty cells? Yes. Identify what color and type of objects are
missing from these images.
3. Suggest a reason for the empty cells. In other words, what about those objects
makes them rare and/or nonexistent?
4. Suggest a reason for the large number of blue, irregular galaxies. Hint:
consider current theories of irregular galaxy formation.
5. Do spiral galaxies tend to be a particular color or colors? Suggest a reason for
this trend.
Distances to galaxies
Galaxies are a bit more difficult to determine the distance away that stars. A
quick illustration: Depending on the Hubble Deep Field image you have in front
of you, find the following objects (you only have to do one set):
Camera A: 3, 4, 7, 13, 14
Camera B: 19, 21, 22, 27, 29
Camera C: 33, 36, 41, 42, 44
6. Order one of the sets of objects from nearest to furthest (identify by number).
7. What criterion or criteria did you use to order the objects?
8. The actual order from nearest to furthest are:
Camera A: 4, 14, 13, 7, 3
Camera B: 29, 21, 19, 27, 22
Camera C: 36, 33, 41, 44, 42
How accurate were you? Is the criterion or criteria you used a good way to find
galaxy distances?
In fact, galaxies can be analyzed spectroscopically, so that they can grouped in
such a way that the apparent size of a galaxy is related to its distance from Earth.
This is method similar to the main-sequence fitting we did in an earlier exercise
for star clusters.
Figure 8.1 shows the images and visible spectra of five elliptical galaxies. The
spectrum of each galaxy is shown to the right of the image of the galaxy (the dark
line spectrum sandwiched between emission spectra); all of the galaxy sizes are
on the same scale.
9. Measure the apparent diameter of each galaxy in millimeters, and enter
that information into the appropriate column in the table. If the galaxy is not
round, use an average between the long and short axes of the galaxy.
10. Convert the diameter to the distance the galaxy is away from us by using the
formula, and entering the result in the appropriate column in the table:
dis tan ce =
€
1000
diameter
where the diameter is in units of millimeters and the resulting distance is in units
of megaparsecs (Mpc).
Now, turn your attention to the spectra next to each galaxy shown in figure 8.1.
The spectra show well-defined (laboratory) helium emission lines above and
below the nearly continuous emission spectrum of the galaxy. The leftmost bright
line and rightmost bright line represent, respectively, helium emissions at 388.8
nm and 501.5 nm.
11. Which direction is towards the red end of the spectrum?
On each galaxy’s continuous spectrum, note there are two relatively strong
absorption (dark) lines (there’s a small horizontal white arrow that points
between the lines) which represent the H (the right one) and K (the left one)
absorption lines of calcium, which normally exist at 396.8 nm and 393.3 nm.
12. Is the K line 393.3 nm wavelength the one you would measure in lab (λlab) or
the one the galaxy seems to be emitting (λobs)?
13. What happens to the position of the calcium absorption lines as you go down
the rows of spectra for each galaxy? (Don’t worry about intensity — that has to do
with object luminosity). What is this phenomenon called?
14. Measure the distance d between the K line of calcium of each galaxy (the
right dark line of the pair on the continuous spectrum) and the 388.8 nm helium
emission line (the left bright line) — millimeters is a good unit to use. Enter this
information in the table on the next page.
15. Measure the distance D in millimeters between the leftmost bright line and
rightmost bright line helium emissions. Write the number below for reference.
16. Set up an appropriate proportionality to calculate the observed
wavelength λobs of the calcium K absorption line, and enter the result in the
appropriate table column. Maybe something like:
𝜆!"# =
(𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑛 ℎ𝑒𝑙𝑖𝑢𝑚 𝑤𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ𝑠) lower helium wavelength
!"#$%&'( !" ! !"#$ !"#$ !"#$% !!"#$% !"#$
!"#$%&'( !"#$""% !!"#$% !"#$%
+
17. Now calculate the velocity v that the galaxy is receding from us by using the
Doppler shift formula, and enter the velocity (in km/s) in the appropriate column
of the table:
𝑣 = 𝑐 !!"# ! !!"#
!!"#
where c is the speed of light and is equal to 300,000 km/s.
The factor in the parenthesis in the equation above is called the redshift of the
galaxy, and is value is represented by the letter z.
18. What happens to the value of z as the speed of the galaxy away from us
increases?
Table for results of analyzing figure 9.1
Cluster
d (mm)
λobs (nm)
v (km/s)
Diameter
(mm)
Distance
(Mpc)
Virgo
Ursa Major
Corona
Borealis
Bootes
Hydra
19. Plot distance to the galaxy (in Mpc on the x-axis) versus its recessional
velocity (in km/s on the y-axis) on a piece of graph paper. Make sure to include
units on the axes. Where should the Milky Way be plotted?
20. Describe the mathematical relationship between the distance to a galaxy
and its recessional distance. Congratulations! You’ve discovered the Hubble Law.
21. Since 1 Mpc = 1,000,000 pc, and 1 pc = 3.26 ly, how old (in years) is the light
from the oldest object on your plot?
Figure 9.1 – Visible wavelength images of galaxies (left, note that the smaller
galaxies are indicated by an arrow) and their spectra (right, note the galaxy’s dark
line spectrum is flanked above and below by the emission line spectra of various
gases measured in the laboratory). The arrow in the dark line spectrum shows
how far the calcium H and K lines have been shifted from the laboratory values
for these absorptions.