APAS 1040 Spring, 1997

HOMEWORK No. 5

Due date: Wednesday, April 30


1. The table below provides data on measurements of apparent magnitudes and observed wavelengths of the Ca II K line (rest wavelength 3933.663Å) for a number of galaxies.

(a) Your main job is to use these data to derive the value of Ho, the Hubble constant. To
do so, you will have to convert the given wavelengths into recession velocities and the apparent magnitudes into distances (for this assume that all of the galaxies have the same absolute magnitude, MV = -21.0). Then make a plot of velocity versus distance, draw a straight line through the data points and find the slope of the line (in units of km/sec/Mpc), which will be your value of Ho. If you are able, you could find the straight line by doing a least-squares fit through the points (demanding that the line pass through zero); otherwise, just make an eyeball fit using a ruler.

(b) Use your value of Ho to find the age of the universe (applying the 2/3 correction factor to what you get from 1/Ho). How does your value compare with the estimated age of the galaxy, based on globular cluster ages?

Here are the data:

m_v Wavelength m_v Wavelength

11.12 3961.032 13.32 4007.522
10.70 3954.567 13.64 4019.836
13.60 4023.457 12.79 3992.052
13.40 4013.540 8.60 3939.568
6.39 3936.418 12.21 3983.942
12.96 4004.984 13.82 4033.938
13.20 4010.998 13.17 4005.251
12.27 3979.163 10.55 3955.754
11.94 3975.318 9.19 3946.402
10.05 3951.800 13.82 4030.038
13.25 4005.384 12.91 3997.113
12.39 3983.278 10.15 3949.429
13.45 4018.496 11.83 3969.021
11.64 3970.550 12.55 3993.383
12.67 3987.264 13.49 4016.084


2. The figure below shows the spectrum of a quasar, including both emission lines and
aborption lines. Also given is a table of spectral lines (either emission or absorption) that might appear in the spectrum of a typical quasar. Using this list, identify lines in the given spectrum and determine its redshift (hint: there may be more than one absorption redshift). You will have to use pattern recognition to find the groupings of lines that arise from the same redshifts. One way to do this is to make a template (a piece of paper or cardboard) on which (along one edge) you mark the wavelengths of all the lines from the table (using the same scale as in the given spectrum); then align this template with the spectrum to find sets of lines that match your markings. Note that not all of the lines will appear in each redshift system, so you may have to recognize matches based on only two or three lines in some cases.

In the end you should have a list (it will be short) of all emission and absorption systems represented in this spectrum. For each one, give the recession velocity (using the relativistic Doppler shift formula) and the distance to the object creating the lines (state what value of Ho you are assuming in order to find the distance).

Here is the spectrum:

(NOTE: To do this, you will have to obtain a paper copy of the assignment, which includes a drawing of the spectrum.)

And here is the list of potential lines:

Atom or ion Wavelength (Å)

H I, 1216
Si II 1260
" 1304
" 1526
Si IV 1398
C III 1909
C IV 1549
N V 1240
Mg II 2800