H205 – Cosmic Origins
Your Name _____________________________
Exploration Packet 4: Galaxies
Due April 8, 2009
Part 1 – Classifying Galaxies
Sketch each of the galaxies shown in the PowerPoint slide, and classify each according to the
scheme shown above. Identify whether the stellar population of each is predominantly old or young,
and whether each galaxy is gas-rich or gas-poor. In each sketch, identify the features that led to your
classification.
Galaxy 1
Classification________
Old stars Young Stars
Gas-rich Gas-poor
Galaxy 2
Classification________
Old stars Young Stars
Gas-rich Gas-poor
Galaxy 3
Classification________
Old stars Young Stars
Gas-rich Gas-poor
Galaxy 4
Classification________
Old stars Young Stars
Gas-rich Gas-poor
Galaxy 5
Classification________
Old stars Young Stars
Gas-rich Gas-poor
Galaxy 6
Classification________
Old stars Young Stars
Gas-rich Gas-poor
Galaxy 7
Classification________
Old stars Young Stars
Gas-rich Gas-poor
Galaxy 8
Classification________
Old stars Young Stars
Gas-rich Gas-poor
Part 2: The Distance to the Galaxy M100 using Cepheid Variables
(This exercise is based on an ESA/ESO Astronomy Exercise, Series 2, and has been adapted for use in our
class. The original data on which the exercise is based were taken from Freedman et al. 1994, Nature, 371,
757)
From repeated observations of the galaxy Messier 100 using the Hubble Space Telescope,
astronomers were able to identify more than a dozen Cepheid variables, and measure their brightness
as a function of time. Cepheid variables are pulsating stars with regular periods of a few weeks.
Henrietta Leavitt, working at the Harvard College Observatory early in the 20th century, discovered
that the period of a Cepheid variable is related to its brightness. Brighter Cepheids pulsate with
longer periods. From the Hubble measurements of Cepheid variables in M100, the periods of the
variables, and hence the absolute magnitudes of the variables, could be determined. Once both the
absolute magnitudes and the apparent magnitudes are known, the distance to M100 can be
calculated.
The relation between a Cepheid's period and its absolute magnitude is given by the “Leavitt Law:”
Mv = -2.8 log(P) -1.4
Where Mv is the absolute magnitude and P is he period in days.
For convenience, this expression is shown in graphical form in the plot below.
Determining the distance to M100 - Use the light curves given in the ESO materials to determine
the periods of each of the Cepheids, as well as the average apparent magnitude of each one.



The period is the time between successive maxima of the Cepheid variable.
The absolute magnitude can be determined from the period using either the chart above or the
expression on the previous page.
The average apparent magnitude is half way between the maximum and minimum brightness in
the light curve.
Work in pairs to enter the period, absolute magnitude, and average apparent magnitude for three
more Cepheids in the table below. The measurements for Cepheid No. 1 have already been entered.
Cephei
d
Number
Period
(days)
Absolute
Magnitude
(M)
Maximu
m App.
Mag.
(mmax)
Minimum
App. Mag
(mmin)
Average
App. Mag.
(mave)
Distance
Modulus
(mave-M)
Distance (Mpc)
1
53.4
-6.2
24.5
25.3
24.9
24.9-(-6.2)=31.1
16.6
2
3
4
5
6
7
8
9
10
11
12
Average distance to M100 in Megaparsecs:
In astronomy, the "absolute magnitude" of a star is the apparent magnitude that star would have if it
were at a distance of 10 parsecs (a parsec is 3.26 light years). Thus the difference between the
absolute magnitude and the apparent magnitude is related to the distance. The relation can be
written mathematically as:
Distance in parsecs = 10(mave -M+5)/5
where mave is the average apparent magnitude and M is the absolute magnitude.
The Cepheid variables in M100 give a wide range of distances. What are some possible reasons why
the distances might vary so much from star to star?
Compare the size of M100 to its distance (M100 is similar in size to our own Milky Way, with a
diameter of about 30 kiloparsecs). Could the variation in the distance to M100 from the different
Cepheid period measurements result from the difference in location of the Cepheid variables within
M100? Why or why not?
In the original scientific paper reporting on the distance to M100 using the Hubble observations, the
distance was calculated to be 17.1 ± 1.8 Mpc (about 56 million light years). The presence of
interstellar dust within M100 causes the apparent magnitudes of the Cepheids to be dimmer than they
should be, so that they appear to be more distant than they really are.
Part 3: Distances from Apparent Diameters of Spiral Galaxies
We can measure the distances to spiral galaxies by measuring their angular diameters, and assuming
that most spiral galaxies have about the same radius, about 22 Kpc.
Visit the website http://www.astro.washington.edu/courses/astro211/HubbleLaw/galaxies.html
and select Image for two of the following galaxies. (Please work in pairs and select galaxies so that
all are measured by some group:
NGC 1357, NGC 1832, NGC 2276, HGC 2775, NGC 2903, NGC 3034, NGC 3147, NGC 3227, NGC
3368, NGC 3623, NGC 3627, NGC 4775, NGC 5248, NGC 5548, NGC 6181, NGC 6217, NGC 6643,
NGC 6764.
Find the angular size of the galaxy using its image. There may be more than one galaxy in the image;
the galaxy of interest is always the one closest to the center. To measure the size, click on opposite
ends of the galaxy, at either end of the longest diameter. Be sure to measure all the way to the
faint outer edges. Otherwise, you will dramatically underestimate the size of the galaxy, and
introduce a systematic error.
Your measurements are in image pixels. Compute the diameter of the galaxy in pixels using the
Pythagorean Theorem (x2+y2=diameter2). Convert the diameter from pixels to degrees as shown
below.
d (degrees ) 
The distance in Kpc is given by:
5.3x10 5
x 2  y 2
distance (in Kpc) = 22 Kpc / tangent (diameter in degrees)
Galaxy Name ______________________
Diameter in pixels___________________________
Diameter in arc min _________________
Distance in Mpc ____________________________
Galaxy Name ______________________
Diameter in pixels___________________________
Diameter in arc min _________________
Distance in Mpc ____________________________
Part 4: Recession Velocities
The recessional velocity of a galaxy is measured using the Doppler effect and is given by:
velocity = c * (
where v is the velocity in km/sec, c is the speed of light (300,000 km/sec), is the rest wavelength of
the radiation, and  is the amount the radiation has been shifted towards longer wavelengths ( =
the observed wavelength minus the rest wavelength). For these spectra, wavelengths are usually
measured in Angstroms (Å), rather than nanometers. An Angstrom is 1/10 of a nanometer, 10-10
meters. The red-ward shift of a spectral line of radiation relative to its rest wavelength,  is
known as the redshift, and is often denoted by the letter z.
We can determine the velocity and redshift of a galaxy from its spectrum: we measure the wavelength
shift of a known absorption line and solve for v.
Example: An absorption line that is found at 5000Å in the lab is found at 5050Å when
analyzing the spectrum of a particular galaxy. Therefore this galaxy is moving away from us
with a velocity
v = (50/5000) * c = 3000 km/sec
Using the same website as above, click on “spectrum” for the two galaxies whose distances you
measured. The optical spectrum of the galaxy is shown at the top of the spectrum page. Shown are
many different spectral features, including absorption lines and emission lines, superimposed on
continuum emission from the galaxy, over the entire visible-light spectrum. Below the full optical
spectrum are enlarged portions of the same spectrum, in the vicinity of the spectral features of
calcium and hydrogen.
The small dark bars near the lower left corner of the sub-spectrum indicate the rest wavelengths of
particular lines. Measure the wavelength by clicking at the middle of the spectral line in the galaxy's
spectrum. Important note: Ca H and Ca K are “absorption lines” – this means that they look like big
dips in the spectrum. The spacing between these two dips is approximately the same as the spacing
between the two small dark bars that show their rest wavelengths. Try to select the deepest point in
each dip for your measured wavelength. In contrast, H is a strong “emission line” – the tallest sharp
peak in the spectrum. Select the point at the peak for the measured wavelength of this line. Enter the
positions of the two Ca features and the H-alpha feature below.
Galaxy Name __________________________
Position of Ca K ____________________
Velocity from Ca K _____________________________
Position of Ca H ____________________ Velocity from Ca H _____________________________
Position of H-alpha __________________ Velocity from H-Alpha ___________________________
Average Velocity _______________________________
Galaxy Name ______________________
Position of Ca K ____________________
Velocity from Ca K _____________________________
Position of Ca H ____________________
Velocity from Ca H _____________________________
Position of H-alpha __________________ Velocity from H-Alpha ___________________________
Average Velocity _______________________________
The velocities can be calculated from the positions of the spectral lines as follows:
For the Ca K line:
V 
( position  158) x0.76
x300,000 km/sec
3934
For the Ca H line:
V 
( position  204) x0.76
x300,000 km/sec
3969
For the H-alpha line:
V 
( position  195) x0.76
x300,000 km/sec
6563
Part 5: The Hubble Constant
We will collect the velocities and distances for the set of galaxies listed above to plot the recession
velocity vs. distance.
What is the Hubble Constant based on our measurements?
___________________________________
Part 6 -The Age of the Universe
If the universe has been expanding at a constant speed since its beginning, the universe's age would
simply be 1/Ho.
First, convert Ho to inverse-seconds (1/sec). Since 1 Mpc = 3.09 x 1019 km , this entails dividing your
calculated value for the Hubble Constant by 3.09 x 1019 km.
Now calculate the "expansion age" of the universe: t = 1/Ho. This gives an approximate age of the
universe in seconds. To convert this number into years, divide it by 31,536,000 (the number of
seconds in a year).
Expansion age of the Universe = ___________________________________
This is a very simple model for the expansion of the universe. A better model would account for the
deceleration caused by gravity. Models like this predict the age of the universe to be: t = (2/3)Ho.
Re-calculate the age using this relation.
t = _______________________________________
How does this value compare to the age of the Sun, which is about 4.5 billion years old?
For Wednesday, April 8
Part 7: Supernova in M51
At least two supernovae have been detected in recent years in the nearby Whirlpool Galaxy, Messier
51. M51 is located at a distance of about 31 million light years (about 10 megaparsecs) in the
direction of the constellation Canes Venatici.
Stars can explode as supernovae in different ways, and the different explosion mechanisms produce
characteristically different behavior of brightness with time, as the supernova brightens and then fades
again. The two dominant types of supernovae are Type Ia supernova, which are thought to be
exploding white dwarfs, and Type II supernovae, which are explosions of massive stars that run out of
nuclear fuel.
The light curves of supernovae of Type Ia and Type II are
compared in the figure below. Type Ia supernova rise to
maximum and then fall steadily in brightness, fading in just
a few weeks. Type II supernovae remain bright for a
longer period of time as energy is provided by the decay
of radioactive products produced in the explosion.
From observations of the light curve of SN1994i in M51,
determine whether the explosion is a Type Ia (exploding
white dwarf) or a Type II (massive star) supernova. The
observations were obtained with the Leuschner Telescope
between April 2 and May 6 in 1994.
Note: Because sky conditions vary, the brightness of the supernova should be compared to the
brightness of the two stars in the image, in the lower left center and lower right.
Does SN1994i appear to be a Type Ia or a Type II supernova? _______________________________
Part 8: Absolute Magnitudes of Supernovae This exercise is based on one developed by Lindsay Clark
(see http://www.astro.princeton.edu/~clark/SNLab.html), and has been adapted for our use.
On the accompanying pages are the light curves of nine Type Ia supernovae that appear in galaxies
during the years 1994-1996 (Type 1a supernovae are a particular type of exploding star). The units
on the x-axis are days, and on the y-axis are apparent magnitude. Each supernova was monitored for
several weeks so that its rise to maximum light and its subsequent decline in brightness are welldetermined. For each, the apparent magnitude at which the supernova was brightest can be
determined from the light curve. Our goal is to determine the absolute magnitude of each supernova.
Record the brightest magnitude reached for two of the supernova in the table below.
Recession
velocity
(km s-1)
Host
Galaxy
z
1994S
NGC
4495
0.01610
4,463
1995D
NGC
2962
0.00655
1,998
1994ae
NGC
3370
0.06700
1,279
1995al
NGC
3021
0.00514
1,536
1995ac
Anon
0.04900
14,615
1995bd
UGC
3151
0.01520
4,758
1996X
NGC
5061
0.00681
2,034
1996bl
Anon
0.3480
10,598
1996bo
NGC
673
0.01650
5,063
Supernova
Distance in Mpc for
Ho=72 km s-1 Mpc-1
App
Mag
(mmax)
Absolute
Magnitude
(M)
14.8
Mean Absolute Magnitude
Median Absolute Magnitude
The recession velocities of the host galaxy of each supernova were measured from the redshift of
spectral lines. The recession velocity must be measured from the host galaxy, rather than from the
supernova itself, because the gas from which the supernova spectrum arises is expanding explosively
from the original supernova progenitor.
Use the value of the Hubble Law to compute the distance of the host galaxy (and the supernova) from
the recession velocity. Remember that the distance = velocity / Ho.
Calculate the absolute magnitude from the distance and the apparent magnitude using the inverse
square law. Recall that the distance in parsecs is related to the difference between the absolute and
apparent magnitude as follows:
Distance in parsecs = 10(m-M+5)/5
In this case, we know the distance and apparent magnitude and want to determine the absolute
magnitude. The expression can be rewritten as
M = m – 5 log(distance in parsecs) + 5
Use a calculator to obtain the logarithm of the distance in parsecs (the distance in parsecs is 106
times larger than the distance in megaparsecs. The absolute magnitudes of the supernovae should
be negative, since the supernovae are very bright compared to ordinary stars. Remember that
astronomical magnitudes become smaller, and then negative, as objects become brighter. Each 5
magnitudes is a factor of 100 in brightness.
How does the brightness of a Type Ia supernova compare to the brightness of the Sun? The Sun's
absolute magnitude is approximately 5. (The Sun's apparent magnitude is -26.)
What can you conclude about the absolute magnitudes of Type Ia supernovae?
What is peculiar about the supernova 1995bd? What explanation might account for its difference from
other Type Ia supernovae?
How might your conclusions about Type Ia supernovae be useful for determining the distances to
other galaxies?
Part 9: Reflection (5 minutes, max) – Write a short statement (no more than five sentences)
summarizing the basic ideas covered in this Exploration about galaxies and the methods astronomers
use to determine the distances to galaxies.