Measuring the redshift evolution of Abell clusters and
the density variation of the spiral to elliptical galaxy
ratio in the Sloan Digital Sky Survey
Joe Monegato
Department of Physics, Carthage College, Kenosha, WI
May 4th, 2009
Abstract
From color photometry (Gunn ugr filter bands) of galaxies found in the Sloan Digital
Sky Survey (SDSS) DR6 catalog, I have constructed color-color diagrams for 11 Abell
galaxy clusters ranging in redshift from z=.018 to .375. I have classified the galaxies in
them as spirals and ellipticals using a technique based on the empirically determined ugr
color-color diagrams of known spirals and elliptical. Since star formation has essentially
stopped in gas-poor elliptical galaxies, they have fewer younger blue stars (and more older
red stars) than spiral galaxies, permitting a segregation of the two galaxies by color. I
have measured the number of spiral and elliptical galaxies in each cluster and examine
the behavior of their ratio as a function of cluster redshift. My hypothesis is that the
proportion of spiral to elliptical galaxies in these clusters approximately constant, but may
show some signs of evolution over cosmic time. The Abell clusters that were observed
tended to be towards the 50 percent spiral and 50 percent elliptical galaxies. This was
due to a high-density bias that returns more elliptical than spiral galaxies. The random
search that was conducted returned 67 percent spiral galaxies and 33 percent elliptical,
which is right on with the universal percentages. It was also able to find a few highdensity regions that were rich with elliptical galaxies. However, there was no significant
evolution found over the redshift of z = 0 through z = 0.4.
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1
Introduction
Galaxies
A galaxy is a gravitationally bound system that contains any where from millions to billions
of stars. Along with these stars, galaxies are also comprised of gas and dust that is known
as interstellar medium [1]. Galaxies are found in a variety of different shapes, and that is
typically how they are categorized. Elliptical, spiral, and irregular comprise the three main
types of galaxies. However, irregular galaxies comprise less than three percent of the total
galaxy population.
Elliptical galaxies make up nearly 30 percent of the known galaxy population. These galaxies
tend to be yellow and red in color because the majority of the stars in them are older, as
shown in Figure 1. They also have a wide range in size, as they are both the largest and
smallest known galaxies. The fraction of elliptical galaxies found in a given area can vary by a
large amount depending on where it is. Elliptical galaxies are predominantly in high-density
environments and at the center of large galaxy clusters [1].
Figure 1: Elliptical Galaxy
Spiral galaxies make up approximately 70 percent of the known galaxy population. They are
typically bluer in color because of the high amount of gas and dust in them, which provides
an excellent state for star forming regions [1]. Since they typically have star forming regions
spiral galaxies have a majority of young blue stars, which also contributes to the bluer color,
as seen in Figure 2. These types of galaxies are found in low-density regions in space.
Hubble Tuning Fork
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Figure 2: Spiral Galaxy
Edwin Hubble was one of the most influential scientists of all time. Among his many contributions to Cosmology, Hubble was the first person to devise a classification system for
galaxies, the Hubble Tuning Fork [2]. This classification method is one that is still used
today. The galaxies were separated into two types, spiral and elliptical.
The handle of the tuning fork consists of the elliptical galaxies, while the two prongs show
the two different types of spiral galaxies, barred and unbarred. As seen in Figure 3, elliptical
galaxies are classified from E0 to E7. The E0 galaxies are relatively circular and continue to
get flatter as it moves up the handle of the tuning fork to the E7 galaxies.
The spiral galaxies are found on the prongs of the tuning fork. Spiral galaxies split into
two sections, barred and unbarred galaxies. These are essentially the same, with the only
difference being that the barred galaxies have a visible bar extending from the center before
the arms start to spiral. Spiral galaxies are classified based on how tightly their arms are
wound. As seen in Figure 3 the galaxies are wound tightest at Sa and SBa, but progressively
get looser as they move to Sc and SBc galaxies. Hubble believed that all galaxies started to
the left of his classification system and then evolved over time until they reach the right side
of it. With this notion he called elliptical galaxies early galaxies and spiral galaxies were
called late galaxies [2]. However, this was not actually the case, but the names late and early
galaxies are still used to this day.
Galaxy Clusters
Galaxies are gravitationally bound systems that contain millions to billions of stars. Similarly, galaxy clusters are anywhere from several hundred to thousands of galaxies that are
gravitationally bound within a region of a few mega-parsecs across [3]. Galaxy clusters are
often times found next to other galaxy clusters. This is an enormously high concentration
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Figure 3: Hubble Tuning Fork
of matter in one place. This matter tends to trap in heat and gas, which allows the galaxy
cluster to have x-ray emissions [3].
Redshift
Everything in the universe seems to be moving away from Earth. Redshift allows us to
measure how far a given object is away from us by taking a look at its light waves. If a
galaxy is moving away from us the light waves move apart, which lowers the frequency. Since
red light is at the low-frequency end of the visible spectrum, this is known as a redshift [4].
Redshift is denoted by the letter z and the equation to find the redshift is:
z=
λobsv − λemit
λemit
This means that the higher the z value is the farther the object will be located from Earth.
By looking at different redshifts we will be able to see how galaxies evolve over time.
Sloan Digital Sky Survey (SDSS)
The Sloan Digital Sky Survey is one of the largest astronomical databases that is available
online. The SDSS uses a 2.5-meter telescope that is located on Apache Point, New Mexico.
The goal of SDSS is to map 25 percent of the sky and obtain observations on 100 million
objects [5]. This information can help in a wide variety of studies that will give a better
understanding of our universe.
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Figure 4: Abell 2255 Galaxy Cluster
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Thesis Statement
From color photometry (Gunn ugr filter bands) of galaxies found in the Sloan Digital Sky
Survey (SDSS) DR6 catalog, I have constructed color-color diagrams for 11 Abell clusters
ranging in redshift from z=.018 to .375. They were classified as spirals and elliptical galaxies
in order to see if the ratio of spiral to elliptical galaxies behaves differently as a function of
redshift.
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Method
NASA/IPAC Extragalactic Database (NED)
NED is an on-line astronomical database that allows astronomers to access information on
extragalactic objects. The database contains 10.4 million astronomical objects along with
1.4 million redshift measurements. NED was used to find the exact RA and DEC coordinates
of the 11 Abell galaxy clusters used in this paper. Once the galaxy clusters were found in
NED we were able to view the diameter of the galaxy cluster measured in arcmins, along
with the redshift. This information was recorded in an excel spreadsheet to be used in the
next step of analyzing the galaxy clusters.
Radial Search
The Sloan Digital Sky Survey is another on-line database that is used by astronomers to
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access information on extragalactic objects. The data that was retrieved from NED was
used in the SDSS to receive further information about the 11 Abell galaxy clusters.
The RA and DEC coordinates were used to conduct a radial search in the SDSS of each
galaxy cluster. Along with the coordinates a radius measured in arcmins must be inputted
in order to tell the database how large of an area it must search. For all 11 Abell galaxy
clusters a radius of 5arcmins was chosen.
The radial search outputs all stars, galaxies, and quasars in the area at that given coordinate
and redshift in a comma separated value (CVS) format. The CVS worksheet includes the
type of object it is, RA, DEC, and ugriz filter numbers. The object type is a number, and
that number corresponds to a specific type of object. The type number for a galaxy is 3,
which is what we are interested in. Once the radial search is conducted the type 3 objects,
galaxies, have to be separated in order to learn more about them. These are separated in
excel and then analyzed further.
Color-Color Diagram
One fairly easy way to decide what type of galaxy is being viewed is to look at its color. If a
galaxy has a color that is more white and blue it is typically a spiral galaxy. However, if the
galaxy is more red and orange it is typically an elliptical galaxy. In order to separate each
individual galaxy in a galaxy cluster a Color-Color diagram can be very useful.
A Color-Color diagram is extremely useful in separating spiral and elliptical galaxies based
on their color. After the information from the radial search is compiled in excel there are
only three main categories that are important to view for further analysis. The u, r, and g
filter numbers can be used to create a Color-Color diagram. As seen in Figure 5, a ColorColor diagram is constructed by putting the u-g values on the x-axis and the g-r values on
the y-axis. By doing this it plots every galaxy in the cluster, which will then allow us to
separate them. Elliptical galaxies have u-r values higher than 2.2, and spiral galaxies have
u-r values lower than 2.2. To separate these two galaxy types a trend line must added to
the Color-Color diagram that has the equation y = −x + 2.2. This trend line places the
majority of the elliptical galaxies above the line and the spiral galaxies below it. This system
for classifying the elliptical and spiral galaxies is a technique that is based on the empirically
determined ugr color-color diagrams of known spirals and ellipticals. Experiments have been
conducted and have found that this empirical method is 96 percent reliable for spiral galaxies
and 83 percent reliable for elliptical galaxies [5]. This can be seen in figures 25 and 26. After
all of the Abell clusters were processed and the percentages were found for each type of
galaxy, a histogram was constructed which will be explained later in the Results section.
The u-g and g-r values on the color-color diagram are actually measuring the magnitude of
each galaxy. Furthermore, what is actually being measured is called the radiant flux. The
radiant flux is the amount of light that arrives in a given area on Earth in a given time. It
is given by the equation m = −log2.51(F/F V ega). By using this equation it can be seen
how much brighter a given galaxy is than another, which ultimately helps in categorizing
the galaxy as either a spiral or an elliptical.
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Figure 5: Color-Color Diagram
Random Search
In order to get a better grasp on the universal percentages of spiral to elliptical galaxies 100
random spots in space were looked at. All 100 random places in space were run through
the same radial search as the Abell clusters and were searched with a radius of 5 arcmins.
The same process was done as with Abell galaxy clusters. The galaxies were separated from
the stars and quasars, and then the u-r values were processed to categorize each galaxy in
the random space as an elliptical or a spiral galaxy. Once again the u-r values greater than
2.2 correspond to the elliptical galaxies, while the u-r values below 2.2 correspond to spiral
galaxies. Once the 100 random places in space were processed and the galaxy percentages
were found, a histogram was constructed which will be explained later in the Results section.
Sort by Redshift
An easy way to tell if galaxies have changed is to see if the colors of the galaxies have changed
over time. All 11 galaxy clusters have a different redshift, which means that they are all
at different distances from Earth. The speed of light is finite, so when you look at larger
distances, you are looking at things as they were in the more distant past. By looking at
galaxy clusters of different redshifts, you can see if galaxies have evolved over time. Drawing
conclusions from the color-color diagrams of the galaxies at different redshifts will allow us
to see if the galaxies have evolved over time.
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Results and Discussion
Abell Clusters
The universal percentages for galaxies are approximately 70 percent spiral and 30 percent
elliptical. The data that was collected on the 11 Abell galaxy clusters can be seen in Figure
6. The figure shows the redshift of the galaxy cluster, the name of the cluster, how many
galaxies where found in the radial search, and the percent of spiral to elliptical galaxies. It
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can clearly be seen that the percentages of spiral to elliptical galaxies for the 11 Abell galaxy
clusters that were observed do not match up to the universal percentages. The clusters
range from 40.5 percent spiral galaxies in Abell 1855, to 65 percent spiral galaxies in Abell
1068. The redshifts that were looked at range from z=0.0301 to z=0.3186. The universe is
approximately 15 billion years old. The redshift values that are used in this paper go up to
5.4 billion years, so it does not cover the whole lifetime of the universe but it does cover a
fairly large portion. In order to find out how far in the past a galaxy is there are a couple
things that need to be looked at. If the redshift is known we can use the following equation
to solve for velocity z = v/c. Once the velocity is known we can use Hubble’s law to find
the distance away from Earth. Hubble’s law states that v = Hod, where Ho is the Hubble
constant and d is the distance. If velocity and the Hubble constant are known it becomes a
very simple equation to get the distance. Throughout this range in redshift the percentages
of spiral to elliptical galaxies that were observed tend to be fairly close to 50/50. Based
on the information that has been obtained from the radial search of galaxy clusters using
the SDSS there can be no clear conclusions drawn that correlate the redshift of the galaxy
clusters to any type of evolution of the galaxies.
Figure 6: Abell Galaxy Cluster Data
Random Search
The random search of 100 areas in space was able to return some very useful data. When
the random places in space were looked at the data agreed with the universal percentages
for spiral to elliptical galaxies. This showed that there was some sort of error in the data
with the 11 Abell galaxy clusters. The error could possibly be the high-density regions which
would return more elliptical galaxies than spiral.
Histograms
With all of the information that was collected histograms were made for the 11 Abell galaxy
clusters as well as for the 100 random places that were looked at in space in order to get a
better understanding of the data. The histograms are Figure 7 for the Abell clusters, and
Figure 8 for the random places in space. The average percentage of spiral galaxies in the 11
Abell galaxy clusters is 50.6 percent with a 7.09 standard deviation. It also has a median
of 51.2 percent spiral galaxies. This does not reflect the universal percentages of spiral to
elliptical galaxies in the universe.
However, the histogram for the random places in space does agree with the universal per8
Figure 7: Histogram of 11 Abell Galaxy Clusters
centages. For the 100 random places in space the average percent of spiral galaxies is 67.08
percent with a 5.61 standard deviation. Furthermore, an interesting discovery was made with
the histogram for the 100 random places in space. It has a tail to the left that represents a
lower percentage of spiral galaxies. This tail represents high-density regions in space where
spiral galaxies are not as predominant. Taking a closer look at these places in space may be
able to confirm a possible source of error that can then be correlated to the 11 Abell galaxy
clusters that were looked at.
Figure 8: Histogram of Random Space
In order to get a more realistic data set for the random search the lowest four percentages
were taken out. The four lowest percentages represent high-density regions in space just like
in the center of the Abell galaxy clusters. A new histogram was composed after the low
percentages were removed, which gave a more accurate measurement of random space as
seen in Figure 9. The new average percent of spiral galaxies went up to 67.8 and the new
standard deviation is 4.29, which is over a point lower than the previous standard deviation.
High-Density vs. Low-Density Regions
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Figure 9: Improved Histogram of Random Space
To further analyze the possible error in the data that was obtained a closer look was taken
of an Abell galaxy cluster, a random place in space that matched the universal percentages,
and a random place in space was on the left tail of the histogram in Figure 8.
High-density regions have more elliptical galaxies that spiral. In order to show this the
SDSS was used to find pictures of the previously mentioned places, which visually showed
the difference between them. Figure 10 shows a picture of Abell 1835. This is a high-density
region in space which has 40.5 percent elliptical galaxies within a radius of 5 armins from
the center of the cluster. This was then compared to Figure 11, which is a picture from the
random search conducted that was on the leftward tail. In these two figures a high-density
region can be seen. This is what skews the data from the universal percentages and allows
for an increased amount of elliptical galaxies.
Figure 12 shows a low-density region in space that was found in the random search. When
this figure is compared to Figure 10 and Figure 11, it can clearly be seen that there isn’t as
many objects in the area. This low-denisty region agrees with the universal percentages of
70 percent spiral and 30 percent elliptical galaxies. This visually proves that the tail to the
left in Figure 8 are high density regions and should be taken out in order to obtain more
accurate results in the random search.
High-density Bias
There is a bias in the data that was collected that may have contributed to the skewed
percentages of spiral to elliptical galaxies in the 11 Abell clusters that we looked at. The
environment that surrounds galaxies contribute to which type of galaxy it is. Elliptical
galaxies are more prevalent in high-density regions in space, while spiral galaxies tend to
be found in low-density regions. The information was gathered with a radius of 5 arcmins
from center of each Abell galaxy cluster. At the center of galaxy clusters there are usually
a majority of elliptical galaxies because it is a high-density region of space. However, spiral
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Figure 10: Abell 1835 High-Density Region
galaxies are rare in the center of galaxy clusters because they are formed in low-density
regions of space. The average diameter of each galaxy cluster that was looked at is 52
acrmins. Since the search was done with a radius of 5 armins from the center of each galaxy
cluster we are looking at a relatively small portion of galaxies in the cluster. To correct this
error a larger radius should be used in the search, which should allow the percentages of
spiral to elliptical galaxies to gravitate closer towards the universal percentages.
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Implications of Research
Once I have finished all of my research and analysis I will have a substantial amount of
information on galaxies. This will help determine whether certain types of galaxies have
been around more today or more in the distant past. This information can be used in the
continual study of galaxies and our universe in order to get a better grasp on what is going
on in our universe. I am currently conducting SQL searches at specific redshifts in order to
see if there is any further evolution of galaxies that can be detected.
References
[1] Robinson, J. Astronomy Data Book. New York: John Wiley and Sons, 1972.
[2] Liddle, Andrew, and Jon Loveday. The Oxford Companion To Cosmology. New York:
Oxford University Press, 2008.
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Figure 11: High-Density Region in Random Search
[3] Mitton, Simon. Exploring The Galaxies. New York: Charles Scribner’s Sons, 1976.
[4] Liddle, Andrew. An Introduction to Modern Cosmology. Second. New York: John Wiley
and Sons, 2003.
[5] Zhang, Yanxia, and Lili Li, and Yongheng, Zhao. ”Morphology Classification and Photometric Redshift Measurment of Galaxies”. Printed 6 October (2008). November 7,
2008 ¡http://arxiv.org/pdf/0810.0867¿
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Diagrams
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Figure 12: Low-Density Region in Random Search
Figure 13: Color-Color Diagram of Abell 2255
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Figure 14: Color-Color Diagram of Abell 0085
Figure 15: Color-Color Diagram of Abell 0963
Figure 16: Color-Color Diagram of Abell 1995
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Figure 17: Color-Color Diagram of Abell 2142
Figure 18: Color-Color Diagram of Abell 1795
Figure 19: Color-Color Diagram of Abell 1835
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Figure 20: Color-Color Diagram of Abell 1413
Figure 21: Color-Color Diagram of Abell 0750
Figure 22: Color-Color Diagram of Abell 1068
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Figure 23: Color-Color Diagram of Abell 2199
Figure 24: Redshift vs. Percent Spiral
Figure 25: Comparison between classification methods for the spectroscopic sample
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Figure 26: Color-Color Diagram
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