Investigating the Galaxy Distribution Using Redshift Surveys (3)

8/10/2019 Investigating the Galaxy Distribution Using Redshift Surveys (3)

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Investigating the Galaxy Distribution using

Redshift Surveys

Sara Nabhan Al-Battashi

A thesis submitted on partial fulfillment of the requirements for

the degree of

Master of Sicence

in Physics

Department of Physics

College of ScienceSultan Qaboos University

Sultanate of Oman

(October, 2014)


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Thesis Committee


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Thesis Examining Committee


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Acknowledgment

Firstly and above all else, praise and thanks to Allah, the almighty for His

guidance throughout my research and for granting me the capability to proceed

successfully.

My thanks go to everyone who helped me in the completion of this project,

beginning with my thesis supervisor, Dr. Saleh Al-Shidhani, for initially introducing

me to the field of cosmology, suggesting it as a topic for my project, responding to my

questions and queries in such a prompt manner and finally his patience in resolving the

technical problems that I faced along the way. Without his help I would not have been

able to complete the project in the amount of time that I did.

I would also like to express my deep and sincere gratitude to Dr. Laila Alabidi

for the fruitful discussions that I had with her, as well as for her assistance with the

statistical techniques used in the project. Many thanks to Dr. Randa Asaad for her

sheer interest in the subject matter of this research, and also for the valuable time that

she put into our insightful discussions about this project.

I would also like to thank my examiners, Dr. Milan Bogosavljevic and Dr.

Zacharias Ioannou for the time they gave up to read my thesis and giving the valuable

suggestions and corrections to this work.

My sincere thanks also goes to Prof. Matthew Colless for his help with the

transformations of the coordinates.

I submit my highest appreciation to my academic advisors, Prof. Abraham

Georgeand Dr. Salim Al-Harthi, for their valuable advice and their help along every

step of the way.

I am extremely grateful to my family, particularly to my motherfor her prayers

and her caring, along with the sacrifices that she has made to educate and prepare me for

my future. A warm thanks to my brothers and sisters and their families for their

encouragement and support in so many ways.

I also wish to extend my thanks to Oliver Allanfor the linguistic support during

the writing process and over the past two years, and Muna Al-Sawafi, for allowing me

to learn from her experience.


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IV

Abstract

Understanding the structure and evolution of the universe has been and remains avery interesting area of research. Many researchers carried out several analyses with

different sky survey sizes. In this study, a large sample of galaxies and QSQs has beenconstructed from ten redshift sky surveys to study the distribution of the galaxiesthroughout universe. The sample covers a large area of the sky and comprises of

2763064 objects, mostly obtained from the SDSS Survey. The study is focused on the

radial distribution of celestial objects, specifically in testing the claim of periodicity(also referred to as the quantization) in the galaxy redshifts. The phenomenon of

periodicity was investigated using an unbiased sample of high quality redshift

measurements and with periodogram spectral estimation. The radial distribution in the

comoving scale was found to exhibit a periodic separation of about ~167 Mpc. No

evidence for a periodicity has been found in the redshift (z) scale.


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Table of Contents

Chapter 1: Introduction ...................................................................................................... 1

Chapter 2: The Expanding Universe and the Large-Scale Structure Formation ................ 3

2.1. History of the Big Bang Theory .............................................................................. 3

2.2. Large-Scale Structure Formation and Evolution ..................................................... 5

2.3. Structure Periodicity ................................................................................................ 7

Chapter 3: Redshift and the Hubble Law ......................................................................... 10

3.1. Redshift Effect ....................................................................................................... 10

3.2. Redshift Measurements ......................................................................................... 12

3.3. Discovery of the Hubbles Law............................................................................. 13

3.4. Hubbles Constant................................................................................................. 15

Chapter 4: The Redshift Surveys, Past, Present and Future ............................................. 18

4.1. The Survey Methods ............................................................................................. 18

4.1.1. Pencil-beam Surveys................................................................................... 18

4.1.2. Slice Surveys............................................................................................... 19

4.1.3. All-Sky and Large Surveys. ............................................................................ 19

4.1.4. Targeted Surveys with special kinds of objects. . .......................................... 19

4.1.5. Blind Redshift Surveys carried out in the 21 cm line of natural hydrogen

(HI)............................................................................................................................ 20

4.2. Sloan Digital Sky Survey (SDSS) ......................................................................... 20

4.3. Two-degree-Field Galaxy Redshift Survey (2dFGRS) ......................................... 21

4.4. Six-degree-Field Galaxy Redshift Survey (6dFGRS) ........................................... 22

4.5. VIMOS-VLT Deep Survey (VVDS) ..................................................................... 23

4.6. The Deep Extragalactic Evolutionary Probe project (DEEP) ............................... 23

4.7. Two Micron All-Sky Survey (MASS) .................................................................. 24

4.8. VIMOS Public Extragalactic Redshift Survey (VIPERS)..................................... 244.9. Galaxy And Mass Assembly Survey (GAMA) ..................................................... 24

4.10. FORS Deep Field (FDF) spectroscopic survey ................................................... 25

4.11. Team Keck Redshift Survey (TKRS) .................................................................. 25

Chapter 5: Data Collection and Statistical analysis ......................................................... 26

5.1 Checking data consistency ..................................................................................... 26


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5.1.1 Coordinate Transformations. ........................................................................... 27

5.1.2 Duplication checking ....................................................................................... 29

5.2 Checking for periodicity ......................................................................................... 30

5.2.1 Histogram......................................................................................................... 31

5.2.2 Periodogram ..................................................................................................... 31

Chapter 6: Results and discussion .................................................................................... 33

6.1 Radial Distributions ................................................................................................ 34

6.1.1 Histograms. ...................................................................................................... 34

6.1.2 Periodograms ................................................................................................... 53

6.2. Visual explorations of clustering and connectivity ............................................... 64

Chapter 7: Summary and Conclusion .............................................................................. 72

Appendix A: ..................................................................................................................... 73

A MATLAB program for the periodogram calculations ................................................. 73

References ........................................................................................................................ 75


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List of Tables

Table 6.1: Summery of the redshift measurements before and after filtering process. 33


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List of Figures

Figure 2.1:Computer simulation of structure formation. Each side of the boxes are 43

Mpc wide. The left-most frame is simulation of the universe when it was less than 1%

of its current age (z=30) and the right-most frame is the illustration of the present day

universe. 6

Figure 2.2:Galactocentric differential redshifts of the 48 Virgo spirals, in bins 11 km s-1

wide. No data smoothing has been applied. Dotted vertical lines represent periodicity

71.1 km s-1

and zero phase. ..7

Figure 2.3: Galactocentric periodicity of ~ 37.5 km s-1

observed in the differential

redshifts of 97 bright spiral galaxies scattered throught the Local Supercluster. . 8

Figure 3.1:The original Hubble diagram of 1929. The plot gives the observed redshift

(again expressed as a Doppler shift given in km s-1

) as a function of distance in (parsec)

. 15

Figure 3.2:Cosmic Microwave Background seen by Planck. ......17

Figure 4.1:The first set of observations done for the CFA redshift survey in 1985 by

Valerie de Lapparent, Margaret Geller and John Huchra. ..19

Figure 4.2:The distribution of 63000 2dFGRS galaxies in the NGP (left panel) and SGP

(right panel) strips. ..22

Figure 5.1:The commoving distance as a function of z, based on equation 5.1. .. 28

Figure 5.2: The difference between the redshifts with respect to the equatorial and

galactic coordinates. ... 30

Figure 6.1: The collective sample redshifts represented using histograms with four

different bin sizes: 0.2, 0.1, 0.01 and 0.001 (From up to bottom). .36

Figure 6.2:Histogram of the collective sample redshifts with bin size of 0.01. ...37

Figure 6.3: Histogram of the collective sample redshifts with bin size of 0.01. The

Frequency is represented using the logarithmic scale. ... 38

Figure 6.4:Histogram of the SDSS sample redshifts with bin size of 0.01. .39


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Figure 6.5: Histogram of the SDSS sample redshifts with bin size of 0.01. The

Frequency is represented using the logarithmic scale. ... 40

Figure 6.6:Histogram of the 2MASS sample redshifts with bin size of 0.01. .. 41

Figure 6.7: Histogram of the 2MASS sample redshifts with bin size of 0.01. The

Frequency is represented using the logarithmic scale. ...42

Figure 6.8:Histogram of the 2dF sample redshifts with bin size of 0.01. 43

Figure 6.9:Histogram of the 2dF sample redshifts with bin size of 0.01. The Frequency

is represented using the logarithmic scale. . 44

Figure 6.10:Histogram of the 6dF sample redshifts with bin size of 0.01. ..45

Figure 6.11: Histogram of the 6dF sample redshifts with bin size of 0.01. TheFrequency is represented using the logarithmic scale. ...46

Figure 6.12:Histogram of the GAMA sample redshifts with bin size of 0.01. 47

Figure 6.13:Histogram of the VIPERS sample redshifts with bin size of 0.01. ...48

Figure 6.14:Histogram of the DEEP sample redshifts with bin size of 0.01. ......49

Figure 6.15:Histogram of the VVDS sample redshifts with bin size of 0.01. ..50

Figure 6.16:Histogram of the TKRS sample redshifts with bin size of 0.01. ..51

Figure 6.17:Histogram of the FDF sample redshifts with bin size of 0.01. .52

Figure 6.18: Periodograms of the collective sample redshifts calculated using four

different sampling rates. . 56

Figure 6.19: The corresponding cumulative periodograms of Figure 6.18s

periodograms. . 57

Figure 6.20: Periodograms of the redshifts of sample 2 (the well-sampled region)

calculated using four different sampling rates. ...58

Figure 6.21: The corresponding cumulative periodograms of Figure 6.20s

periodograms. . 59


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Figure 6.22: Periodograms of sample 1 (upper panel) and sample 2 (lower panel)

represented using the logarithmic scale. ..... 60

Figure 6.23:Periodogram of sample 1 for the high frequency range. ... 61


Figure 6.25:Theperiodogram of sample 3s data. 63

Figure 6.26:The cumulative periodograms of sample 3s data. ... 64

Figure 6.27: Periodogram of sample 3 represented using the logarithmic scale.

..... 65


Figure 6.29: The 3-D distribution of galaxies covered by the sample, represented in the

Cartesian coordinates converted from equatorial coordinates. ...68

Figure 6.30: The 3-D distribution of galaxies covered by the sample, represented in the

Cartesian coordinates converted from galactic coordinates ...69

Figure 6.31: The 2-D distribution of galaxies covered by the sample along the

equatorial coordinates; ra and dec. ..... 70

Figure 6.32: The 2-D distribution of galaxies covered by the sample along the galactic

coordinates; l and b. ....71


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Chapter 1: Introduction

The curiosity about the structure, history and state of the universe has always

encouraged the scientists to investigate the galaxy distribution in the universe, as it is the

key to understand it. However, the distance estimation of astronomical objects was

always the prime challenge that limited our ability to map the structure. Throughout

history, astronomers developed various techniques to measure distances to the

astronomical objects at different ranges, starting from the radar ranging technique which

is limited to the solar system studies and ending with the application of the Hubbles law

(or the redshift phenomenon) that allows measuring the distance to very far extragalactic

objects.

By the 1970s, projects called Redshift Sky Surveys were established to

measure the distances of a large number of astronomical objects, based on Hubbles law

and the redshift phenomenon. The survey catalogues provide the redshifts of the

astronomical objects (usually galaxies) combined with their angular positions and some

photometric properties. Therefore, they can be used to construct a comprehensive

picture of the universe. From such picture, the aim was to examine the Large Scale

Structure (LSS) distribution and features as well as to inform the modeling of the LSS

evolution.

Many studies (e.g. (Hawkins, Maddox, & Merrifield, 2002) and (Tang & Zhang,

2005)) used various methods to quantify the LSS of the universe and trace its evolution

and origin, such as the implementation of the statistical analysis on the data provided by

the Redshift Sky Surveys to examine specific features of the spatial distribution of the

astronomical objects like the degree of clustering and connectivity, looking for the

presence of voids and the detection of periodic structures. In many cases, the sample

selection procedures and the statistical effects can significantly bias the results of the

study and lead to draw unreliable conclusions. Therefore, the selection of a

representative sample of the universe and the application of the appropriate statistical

technique are critical for providing accurate results that can be generalized to the whole

universe.

In this study, we used a collection of ten publicly available Redshift Survey data

releases, namely: Sloan Digital Sky Survey (SDSS, 10th

Release), Two Micron All-Sky


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Survey (2MASS, the final data product), Two-degree-Field Galaxy Redshift Survey

(2dFGRS, the best spectroscopic observations of the final release), Six-degree-Field

Galaxy Redshift Survey (6dFGRS, Data Release 3), Galaxy And Mass Assembly survey

(GAMA, Data Release 2), VIMOS Public Extragalactic Redshift Survey (VIPERS,

PDR-1), The Deep Extragalactic Evolutionary Probe project (DEEP, Data Release 4),

VIMOS-VLT Deep Survey (VVDS, First Epoch sample), Team Keck Redshift Survey

(TKRS) and FORS Deep Field spectroscopic Survey (FDF). We used this collection to

examine a controversial issue regarding the structure of the universe: The claim of the

periodic distribution of galaxies in space, which is known as the redshift periodicity

phenomenon. Most of the previous studies on the phenomenon (e.g. (Napier & Guthrie,

1997)) used relatively small and biased samples, however with this project we aim to

test the hypothesis using a large data set and by using suitable statistical techniques.

After this introductory chapter, the dissertation will briefly discuss the

development of the Big Bang Theory from a historical angle as well as the evolution of

the Large Scale Structure of the universe in chapter 2. The last section of chapter 2

(section 2.3) will introduce the problem that we have studied in this project: the Redshift

Periodicity, as well as the previous researches that pertain to it. In chapter 3, the redshift

phenomenon and the discovery of the Hubbles Law will be explained in some detail .

Chapter 4 is dedicated to the Redshift Surveys: their development, the types of

Redshift Surveys and details about the ten redshifts surveys which have been used in this

project. The methodology that is used in this research to collect the data, ensure its

reliability and test the redshift periodicity will be provided in chapter 5. The results of

the work and the discussion will be presented in chapter 6. Finally, chapter 7 will

contain a summary of the work that has been carried out, the conclusion we have

reached and suggestions for further work.


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Chapter 2: The Expanding Universe and the Large-Scale Structure Formation

For thousands of years, astronomers wondered about the universe, questioning a

number of things regarding its age, size, structure and our place within it. Moreover,

they were curious to know how it began (if it has a beginning) and how matter came to

exist. Throughout history, there have been many attempts to answer these questions, but

before the twentieth century, most of the attempts failed to yield an integrated idea about

the universe that gives consistent answers to all of the questions. At the beginning of the

twentieth century, several observations supported by theoretical considerations led to the

establishment of todays best explanation for how the universe began; the Big Bang

theory. According to this theory the universe began at a moment in the distant past and

evolved from a very hot, dense and almost uniform structure into the complicated

system that we see today.

In this chapter, a brief history of the Big Bang theory and the evolution of the

Large-Scale structure according to it will be presented in the first section. The next

section will focus on an issue concerning the distribution of matter in space: The redshift

quantization, also known as redshift periodicity.

2.1. History of the Big Bang Theory

The seed for the idea of the Big Bang came from Albert Einstein in his field

equations of general theory of relativity in the early twentieth century, but Einsteinhimself didnt like it because he was convinced; as was everybody at that time, with the

model of a static and eternal universe. In general relativity, he proposed that mass warp

space and time to create gravity, but if gravity is always pulling in, then what keeps

everything from ultimately fusing together into one massive object. Einstein believed

that there must be another equal counter force pushing out in opposition to gravity,

keeping the eternal universe in perfect balance. Therefore, in 1917 he inserted a positive

cosmological constant into his general theory of relativity to force the equations to

predict a stationary universe and match the observations of that time that strongly

favoured a steady universe (Straumann, 2002). A few months later in the same year,

1917, Willem de Sitter proposed another solution to the field equations that produced a

non-expanding, static universe if it contains no matter. In contrast to Einsteins universe


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that contained matter but no motion, de Sitters universe involved motion without matter

(Encyclopedia of Time, 1994).

In 1922, a Russian mathematician called Alexander Friedmann derived a solution

to the general relativity field equations that described mathematically a model of an

expanding universe, before there was any observational evidence (Tropp, Frenkel, &

Chernin, 2006). In 1924 he published a paper that described a homogenous, isotropic

and expanding or contracting universe; the Friedmann-Lemare-Robertson-Walker

universe, which is named after the four astronomers: Alexander Friedmann, George

Lemare, Howard P. Robertson and Arthur Geoffrey Walker, who developed the model

independently (Godart & Heller, 1985).

Five years later, Lemare published his Ph.D. research in which he concluded

that the universe was expanding based on Einsteins general theory of relativity and the

redshift measurements of the extragalactic nebulae (L'Annunziatea, 2007).

At the observational level, the most revolutionary step was the discovery of the

linear relationship between the rate of recession of distant galaxies (calculated from their

observed redshifts) with the distance to them, which was made by Edwin Hubble. The

relationship, which is now known as Hubbles Law, was first published by Hubble in

1929 and then refined and published later in association with Milton Lasell Humason, in

1931 (Belenkiy, 2014). The law implies that farther galaxies are going away from us at

higher speeds; hence their spectra are shifted from shorter wavelengths to longer

wavelengths as the light travels from the galaxy to us and the amount of shift is

proportional to distances. This increase in the wavelength is attributed to the expansion

of the space and led to a model of the universe that is consistent with the solutions of

Einsteins General Relativity Equations for a homogenous, isotropic expanding space.

Hubbles observations encouraged other cosmologists such as Arthur Eddington,

de sitter and Einstein to realise that the static models of the universe were unsatisfactory

and to become aware of Lemaitres 1927 paper (Soter & Tyson, 2000).

In 1931, Lemaitre published several papers in which he formulated

mathematically an expanding and homogenous model of the universe and proposed that

it began with an enormous explosion that would start the expansion of the universe


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(Angelo, 2009). The explosion which Lemaitre referred tois what came to be known

as the Big Bang.

From its discovery until the present, the Big Bang is the most popular and

acceptable model of the formation of the universe.

2.2. Large-Scale Structure Formation and Evolution

The Big Bang model assumes that the universe began 13.8 billion years ago

(Bennett, et al., 2013) when space and time were generated in a vast explosion known as

the Big Bang, creating all matter and energy in the known universe via a process called

inflation that lasts until t=10-35

seconds after the Big Bang (Ebrahimi & Riazi, 2012). In

the next one second, the inflation of the universe ended quickly and after the rapid initial

expansion, the universe began to slow down. The four fundamental forces: the

gravitational force, the strong force, the weak force, and the electromagnetic force took

shape and began to hold the universe together . Then in the following three minutes, the

universe as we know today began to take shape; protons and neutrons came together to

form the basic matter and elements (mostly hydrogen and helium). In the next 500,000

years, the universe remained a huge cloud of expanding gas that eventually cooled

enough that celestial bodies could form. Photons from this period have remained as the

Cosmic Microwave Background radiation (CMB) and can still be observed today

(O'Callaghan, 2012).

Initially, the universe was in a very dense, hot, nearly uniform, and isotropically

expanding state (Relativity in General, 1994) , and as time went on, it cooled from 1032

to 2.73 kelvin (Dardo, 2004) and the density fluctuations grew until the universe

structure became the complicated system that we see today. A few hundred million

years after the Big Bang (Bodenheimer, 2011), some matter clumped together to form

stars. Then gravity played new role and galaxies began to form some three billion years

after the Big Bang (Woolfson, 2013). These galaxies interacted gravitationally and

hence grouped into clusters. Clusters can vary from consisting of just a few members,

as in the Local Group that our Milky Way galaxy is a part of (Typically, clusters with

fewer than 50 members are called groups rather than clusters), to clusters containing

thousands of galaxies which are the largest known gravitationally bound systems in the

universe. However, the physical size of all the clusters is typically of the same order,


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regardless of the number of galaxies contained in the cluster, which means that richer

clusters (clusters with large number of galaxies) have higher densities. For example, the

typical cluster size of a few megaparsecs is not much different from the diameter of the

Local Group (Jones & Lambourne, 2004).

Clusters themselves combine to form larger structures called superclusters. In

contrast to the clusters of galaxies, superclusters are non-gravitationally bound and

consequently, they can get involved in the cosmic expansion and are slowly dispersed by

the expansion of the universe (Appenzeller, 2009) . Some of the superclusters have the

shape of a wall (e.g. Northern Great Wall) and some bear a shape closely resembling a

filament (eg. Sculptor Wall), and both surround empty spaces known as voids (Vicent J.

Martine & Enn Saar, 2002).

These stages of the universe evolution can be illustrated using a computer

simulation such as the one shown in Figure 2.1. The left-most frame represents the old

form of the universe when it was very dense and has less fluctuations compared to the

present day universe (right-most frame) where the clusters and filaments can be clearly

seen.

In the prior few paragraphs, we discussed the formation and distribution of the

LSS building blocks in a rather general sense; however in the next sections we are going

to discuss the distribution through a specific topic: The claims for redshift periodicity.

Figure 2.1: Computer simulation of structure formation. Each side of the boxes are 43 Mpc wide. The left-most

rame is simulation of the universe when it was less than 1% of its current age (z=30) and the right-most frame is

the illustration of the present day universe. (Cosmic Web and Formation of Galaxies ).


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2.3. Structure Periodicity

Since the 1970s, claims that galaxies are found in regularly-spaced groups started

to appear by researchers such as William Tifft and his colleagues. They observed that

various astronomical objects tend to favour multiples of some particular values in their

velocities. Tifft, in his 1979 paper Periodicity in the Redshift Intervals for Double

Galaxies (Tifft, 1979) reported finding two possible periodicities:

71 km/s observed for the differential redshifts

* between galaxies in

groups

36 km/s in the redshifts of galaxies measured with respect to our own

galactic centre

Several subsequent studies have confirmed Tiffts findings; such as (Napier &

Guthrie, 1997) where in the galactocentric differential redshifts of the 48 Virgo spirals

were found to be quantized in steps of 71.1 km/s and a galactocentric periodicity of

~37.5 km/s was observed in the differential redshifts of 97 bright spiral galaxies

scattered through the Local Supercluster. The two periodicities found by Napier and

Guthrie are displayed in Figures 2.2 and 2.3.

*The differential redshifts (obtained by subtracting redshifts in pairs) are used to discriminate the local

motions from the recessional velocity due to the cosmic expansion. However, this technique is valuable

only for objects that lie close together in the sky, as with pairs and groups, because when galaxies from

different regions of the sky are involved, different motions contribute differently to the redshifts. In the

latter case, the redshifts themselves must be used.

Figure 2.2: Galactocentric differential redshifts of the 48 Virgo spirals, in bins 11

km s-1

wide. No data smoothing has been applied. Dotted vertical lines

represent periodicity 71.1 km s-1

and zero phase. From (Napier & Guthrie, 1997)


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Later studies indicated that velocity breaks could also occur at submultiples of 71

km/s, like 1/2, 1/3 and 1/6 (Feigelson & Babu, 1996) (Trimble, 2000).

However, even after all of this evidence for periodicity, there is a scientific resistance to

the idea. Many scientists criticize the redshift quantization and ascribe the phenomenon

to statistical artefact and selection procedures. They also point out that the results tend to

come from a small group of astronomers who have a strong prejudice in favour of

detecting such unconventional phenomenon (Hawkins, Maddox, & Merrifield, 2002).

Hawkins, Maddox and Merrifield used Napiers own guidelines for testing redshifts in

much larger sample and they found no evidence for a redshift periodicity and stated that

... The criticism usually leveled at this kind of study is that the samples of redshifts

tended to be rather small and selected in a heterogeneous manner, which makes it hard

Figure 2.3: Galactocentric periodicity of ~ 37.5 km s-1

observed in the differential

redshifts of 97 bright spiral galaxies scattered throught the Local Supercluster.(Napier & Guthrie, 1997).


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to assess their significance (Hawkins, Maddox, & Merrifield, 2002). Also, Su Min

Tang and Shuang Nan Zhang tested the hypothesis in the light of two existing models,

namely the Karlsson log(1+z) model and Bells decreasing intrinsic (DIR) Model, using

the data of Sloan Digital Sky Survey and 2dF QSO redshift survey and the concluded

that there is no evidence for periodicity (Tang & Zhang, 2005).

However, the aim of this project is to examine the periodicity hypothesis without

lending any bias to a specific result, using a large data set and an appropriate statistical

analysis in order to avoid the defects of the previous similar studies.


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Chapter 3: Redshift and the Hubble Law

In 1842 an Austrian mathematician and physicist called Christian Doppler

published a study on coloured light emanating from binary stars. Doppler suggested that

the colour of the light from a star is dependent on the stars velocity relative toEarth.

This theory became known as the Doppler Effect and is extensively used in astronomy

to study the motion of objects across the universe. In the early nineteenth century, the

American astronomer Vesto Slipher observed that the spectra of the vast majority of

distant galaxies are shifted to longer wavelengths, and relying on the Doppler Effect, he

concluded that they are receding. Later on, another American astronomer called Edwin

Hubble made a great discovery when he combined measurements of galaxy distances

with measurements of the redshifts associated with the galaxies, and found a rough

linear proportionality between the objects distance and its redshift. The distance-

redshift relation which is now known as the Hubbles Law has become an import ant tool

for mapping the universe in three dimensions.

In this chapter, we present an overview of the redshift effect and its

measurements and how this lead us to imagine an expanding universe and the theory that

the universe began with the Big Bang 13.8 billion years ago.

3.1. Redshift Effect

The Doppler Effect states that the wavelength of waves changes, hence the

frequency of waves does too if the source and/or observer are moving relative to each

other. If the two are approaching, then the frequency of the wave received by the

observer will be greater than that of the emitted wave; if they move away from each

other, the wave is stretched i.e. its frequency decreases and its wavelength increases.

This effect is applicable for the light emitted by celestial objects and can be seen as a

small shift of the spectral lines in the objects spectrum. For example, if we look for some

particular spectral lines in the suns spectrum, e. g. the sodium doublet in the yellow-

orange portion of the spectrum, we will find that the positions of these lines and all the

other spectral lines are shifted by a small amount; caused by the following factors

(Robinson, 1981):

(a) The rotation of Earth around its own axis that lead to a Doppler

shift of spectral lines, depending on the magnitude and direction of the velocity


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component that is parallel to the Earth-Sun line. In the morning the observer is

on the side of Earth where the radial component of rotation is toward the sun, so

we expect to observe a shift toward the higher frequencies; a blue shift, whereas

in the afternoon the observer moves away from the sun, so the shift is toward the

red. The shift resulted from this particular motion is extremely small (at most 1.4

parts in a million).

(b) The constant motion of the suns surface layer due to the

rotational motion of the solar rotation which has an equatorial velocity of 2000

m/s (Hathaway, 2014) cause a red or blue shift of the spectral lines, depending

on which part of the sun we are looking at.

(c) Einsteins theory of general relativity predicts that there will be a

gravitational redshift by an amount , where z is the gravitationalredshift, G is the Newtons gravitational constant, c is the speed of light and M

and R are the mass and radius of the sun respectively. This shift raised due to the

fact that a proton has to spend energy in order to climb out of the field of the sun,

but at the same time it must remain travelling at the speed of light, so to keep

within these two restrictions, the energy loss occurs as a change in the frequency

instead of a change in speed. Since energy is proportional to the frequency, the

frequency of the photon decreases as it escapes the sun, and this can be seen as a

shift toward the lower frequencies, or red end in the electromagnetic spectrum.

This effect gives rise to a fractional shift in frequency ( ) of about onepart in a million.

(d) Now suppose that we are talking about a star other than the sun; a

star in our own galaxy, orbiting its centre, but unlike the sun, it weaves up and

down through the galactic plane as it goes around the galaxy.

The net shift of frequency due to the above effects is of the order of 10 3.

However, for an integrated spectrum of another galaxy, one would expect to observe an

additional shift due to its relative motion with respect to the Milky Way. The shift could

be in either direction (toward the red or blue end) depending on the radial component of

the motion the galaxy, and this is exactly what has been observed for the nearby galaxies


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so far. For example the spectrum of the Andromeda shows a slight blue shift because it

is moving toward the Milky way at about 250,000 miles per hour (111.750 km/s)

(Garner, 2012), while some other nearby galaxies show redshifts because they are

receding from us. However for more distant galaxies, this isnt often the case, as in

about the year 1912 an American astronomer called Vesto Slipher at Lowell

Observatory in Arizona noticed that almost all the frequency shifts of what were then

called spiral nebulae are redshifts, indicating that the corresponding objects appeared to

be moving away from us (Bartusiak, 2011). In 1929, Edwin Hubble combined his own

distance measurements that are based on Cepheid stars with Sliphers measurements of

the redshifts velocity and discovered that there is a linear proportionality between the

objects distance and the velocity at which it moves away from us. This relationship,

later called Hubbles law, indicates that the universe is expanding and that the redshift

phenomenon is due solely to this expansion and its measurements have now become the

most important tool in mapping the universe. Hubbles law and redshift measurements

will be discussed in more detail in the next sections.

3.2. Redshift Measurements

Usually astronomers measure the redshift of a galaxy or star by comparing its

observed spectrum with the spectrum they would expected based on its chemical

composition. This can be done using various techniques such as photometry and

spectroscopy.

The photometric technique was developed and first described by Baum in the

sixties (Baum, 1962) and is still favoured by many Large Scale Surveys due to its

efficiency in detecting faint objects and short observing time. In photometry, the light

from a galaxy is filtered and measured across specific regions in the electromagnetic

spectrum, usually divided in a color base (e.g. ultraviolet, blue green, red, .. etc.) . Then,

the observed colors are compared to predictions from galaxy spectral energy for various

galaxy types to determine the redshift.

The spectroscopic redshift of a celestial object can be obtained by observing its

spectrum and identifying the spectral lines that correspond to specific elements and

measure the shifts of these lines with respect to their expected positions, as measured in

a laboratory on Earth. In comparison with photometry, the spectroscopic determination


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of redshifts is more difficult and more time consuming, but it provides more reliable

data. However, sometimes a small sample of spectroscopic redshifts is used to calibrate

a large sample of photometric redshifts to reduce the error of the latter.

Astronomers usually express the wavelength (or frequency) change by the

dimensionless quantity redshiftz, which is defined as (Appenzeller, 2009)

Where is the wavelength of the detected light and is the restwavelength that is determined by experiments in a laboratory or by quantum mechanics

calculations. One should notice that z can either be positive or negative depending on

the direction of the spectrum shift, or on the direction of motion of the celestial object in

the first place. Using the relation between the frequency, and the wavelength, , where c is the speed of light), we can rewrite equation (3.1.a) in terms offrequency as follows

Where and are the frequencies of the observed and emitted wavesrespectively. In general, when dealing with objects that are in a non-relativistic motion

(

)

*, the product of z and the speed of light, c, gives the radial velocity between the

object and the observer, For very distant objects, the radial velocity (or sometimes called the redshift

velocity) is nothing but the velocity that the source is moving away from us due to the

expansion of the universe, called the recessional, . In other words, for large distancesthe recession velocity contributes the most to the redshift and any deviation from this

velocity contributes to whats called peculiar velocity.

3.3. Discovery of the Hubbles Law

In the early twentieth century, astronomers wondered about the physical nature

of the cloudy band they see in the night sky, the spiral nebulae. Many of them

*The exact formula that takes into account the theory of special relativity and must be applied for large

distances (high redshifts) is: , where is the recession velocity (Cosmological Redshift).


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believed that the spiral nebulae constituted solar systems in early stages of evolution

(O'Raifeartaigh, 2013). Others thought that they are galaxies in their own right, and are

very distant from our galaxy.This has motivated the young American astronomer, Vesto

Slipher to perform a study on the spectrum of the light from the Andromeda nebula

using a disposal 24-inch telescope at Lowell Observatory in Arizona. By 1912, Slipher

succeeded to obtain the spectra of 41 spiral galaxies (Thompson, 2011) and noticed that

almost all of them are redshifted. With the aid of Sliphers data, in 1922 Carl Wilhelm

Wirtz published a paper in which he concluded that there is a correlation between the

redshifts and the apparent brightness and the angular diameters of the observed galaxies.

Two years later, he argued correctly that since the apparent brightness and the angular

diameter of galaxies decrease with the distance, then the observed correlation must be

due to a possible redshift-distance relationship of galaxies (Appenzeller, 2009). These

were considered to be the first steps toward the discovery of the velocity-distance

relationship. However, Wirtz wasnt able to formulate the relationship because the

distance measurement methods that he was applying gave the relative distances only.

Meanwhile, Edwin Hubble was working on Mount Wilson in California and using a

100-inch telescope, called the Hooker Telescope, which was the most advanced

technology of the time to develop a reliable method to measure large cosmic distances.

He focused his work on spiral nebulae, including theAndromeda

Nebula andTriangulum (Smith, 2013), specifically concerning himself with a special

class of stars known as Cepheid variables. From their pulsating periods, Hubble was

able to obtain the absolute luminosity of the stars using the period-luminosity relation

accepted at that time and by comparing their brightness with their luminosities, he

calculated their distances. According to Hubbles calculations, the stars and the galaxies

they are a part of were much farther away than anyone had ever imagined, and the

universe was much larger than the Milky Way. In the next few years, Hubble continued

to study distant galaxies, measuring the distances of 33 galaxies for which their redshifts

were already measured by Slipher (Gribbin, 1998). He compared the redshifts and the

distances by plotting a graph of velocity (redshift) against distance, later called the

Hubble diagram (see Figure. 3.1) and noticed that the points lay on a straight line, which

indicates that velocity must be directly proportional to the distance.
http://en.wikipedia.org/wiki/Spiral_galaxy#Spiral_nebulahttp://en.wikipedia.org/wiki/Andromeda_Galaxyhttp://en.wikipedia.org/wiki/Andromeda_Galaxyhttp://en.wikipedia.org/wiki/Triangulum_Galaxyhttp://en.wikipedia.org/wiki/Triangulum_Galaxyhttp://en.wikipedia.org/wiki/Andromeda_Galaxyhttp://en.wikipedia.org/wiki/Andromeda_Galaxyhttp://en.wikipedia.org/wiki/Spiral_galaxy#Spiral_nebula


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In 1929, Hubble published the redshift-distance correlation which is now called

the Hubbles Law and summarised by the following formula(Robinson, 1981)

Where the constant of proportionality, is called the Hubble constant and

and are the radial velocity and the proper distance*of the receding galaxy respectively.This relationship implies that a galaxy twice as far from us than another galaxy is seen to

be receding twice as fast as the nearer galaxy. This conclusion can be considered as the

foundation stone of the expanding universe model and the Big Bang theory.

3.4. Hubbles Constant

In fact, the constant of proportionality in Hubbles Law is not really constant

over time because it does depend upon time, therefore, it should probably be called

Hubble parameter rather than Hubble constant. However, its usually written with a

subscript 0 to denote that it is the value of Hubble parameter at present time.

It is of high importance in cosmology to get an accurate value for the Hubble

constant because it affects the accuracy of determining the size and age of the universe,

*The proper distance is a distance between two nearby events in the frame in which they happen at the

same time (Michel-Marie Deza, 2006) and can change over time, unlike thecomoving distance which is

constant over time.

Figure 3.1: The original Hubble diagram of 1929. The plot gives the observed redshift (again

expressed as a Doppler shift given in km s-1

) as a function of distance in (parsec). (Appenzeller,

2009).
http://en.wikipedia.org/wiki/Comoving_distancehttp://en.wikipedia.org/wiki/Comoving_distance


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but it is somewhat challenging. To obtain the value of the Hubble constant, one needs to

have sets of measurements. The first is the galaxies redshifts (which yield their radial

velocities). The second measurement is one of the most difficult measurements to make

in astronomy; the distance measurements. In addition to this, the sample of galaxies that

are used for the determination of H must be comprised of objects that are far enough

away to avoid the contribution of the peculiar velocities (local motions) on the net radial

velocity. Due to these difficulties, the first values of the Hubble constant were

completely inaccurate; for example, the numerical value of the slope of the original

Hubbles diagram was about seven times too large due to a systematic error he had in his

distance data (Appenzeller, 2009). In the next 30 years, the Hubble constant reduced to

about half of its current value, then the relative error has been reduced to about 10%

during the rest of the 20thcentury (Li, Qin, & Zhang, 2014) (Trimble, 1996). The most

recent value for the Hubble constant is (67.800.77) (km/s)/Mpc, which is obtained by

the Planck Mission and published in March 21, 2013 (Ade , et al., 2013). The Planck

Mission, lunched on May 14, 2009, is a project operated by the European Space Agency

(ESA) and aims to scan the Cosmic Microwave Background radiaton (CMB) using the

dedicated European Space Agencys Planck satellite. As the microwave radiation is

known to be the oldest light in the universe, Plancks measurements are expected to

provide a wealth of information about the early universe and its subsequent evolution.

Specifically, the data can be used to set tight constraints on cosmological parameters and

the ionization history of the universe. Moreover, it can be used to probe the dynamics of

the inhomogeneities produced in the inflationary era and to test the fundamental physics

beyond the inflation. Figure 3.2 illustrates the map of the cosmic microwave background

radiation yielded by the Planck mission.


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Figure3.2:Cosm

icMicrowaveBackgroundseenbyPlanck

.From(CosmicMicrowaveBackgrounds

eenbyPlanck,2013).


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Chapter 4: The Redshift Surveys, Past, Present and Future

The first three-dimensional maps of the universe that combined the

distance information, obtained from the redshifts, with the angular information

obtained from locating galaxies on the celestial sphere were those of Gregory &

Thompson (Stephen A. Gregory & Laird A. Thomson, 1978) and Gregory, Thompson,

& Tifft (Gregory, Thompspn, & Tifft, 1981). They were pencil beam surveys targeting

specific clusters such as Coma, A1367 and Perseus clusters, with the purpose of

identifying superclusters.

Today, there are numerous redshift surveys, the number of which is growing, for

two reasons. The first is that technological advancement in the detectors and

spectrographs employed for the gathering of redshift data. The second is that redshift

surveys have proven that they play a key role in studying the distribution of matter in the

universe and the evolution of the large-scale structure.

This chapter consists of eleven sections; the first is a brief introduction to the

methods of redshift surveys, the following ten sections will highlight the redshift surveys

that are used in this project.

4.1. The Survey Methods

In most cases, the samples of the redshift surveys are selected using quantifiable

selection criteria; i. e the sample is defined as limited by some photometric property,

usually received flux or by limiting angular diameter.

This section introduces the different classes of redshift surveys, classified

according to the selection procedure they follow.

4.1.1. Pencil-beam Surveys. The first redshift surveys that were performed to

study the large-scale structure of the universe i. e. Gregory & Thompson and Gregory

(1978), Thompson, & Tifft (1981) were pencil-beam surveys, where a small area of the

sky that is delimited by specific ranges of the angular coordinates is selected andintensive redshift measurements are made on it. The pencil-beam method is considered

the most economical method since it can yield information on a great depth and achieve

completeness and limited telescope time simultaneously. The 2dF survey (shown in

Figure. 4.2) is an example of a pencil-beam survey.


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Figure 4.1: The first set of observations done for the CFA redshift survey in 1985 by Valerie de Lapparent,

Margaret Geller and John Huchra (Huchra J. ).

4.1.2. Slice Surveys. In this method, galaxies are observed in a thin strip of

the sky with a specified range of declination (from 1 as in CFA1 (Figure. 4.1) to 6 as

first wide slice of a deeper extension of the original CfA survey). The radial coordinate

is the redshift and right ascension is the angular coordinate. The Slice surveys offer

the required resolution and depth for testing the geometry of the galaxian distribution.

4.1.3. All-Sky and Large Surveys. In contrast to the methods mentioned above,

the large surveys extend to large values along all of the three dimensions (RA, DEC and

redshift) to cover a huge volume of the sky. The selection criteria in the large surveys

may be based on the galactic extinction, sky coverage of the telescope used, and limits

of the target catalogue, usually in apparent magnitude, flux, or diameter, and may also

be restricted by morphology or surface brightness constraints on detectability. The

efficiency of each survey is then affected by the biases introduced by selection

procedures (Giovanelli & Haynes, 1988).

4.1.4. Targeted Surveys with special kinds of objects. In this method, targeted

observations are carried out to learn about the properties of galaxies, and hence provide

an important feedback that improves our understanding of the formation and evolution

of the large-scale structure. The surveys may be targeted toward clusters of galaxies,


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active and unusual galaxies of various kinds, or pairs and groups of galaxies. However,

this kind of survey does not provide the sufficient information for studying the large-

scale structure features or layout (Strauss & Willick, 1995).

4.1.5. Blind Redshift Surveys carried out in the 21 cm line of natural

hydrogen (HI). These surveys study the redshift of the 21 cm emission line, which

corresponds to the hyperfine transition of electron in the hydrogen atom between the

parallel spin (triplet) state which has higher energy to the anti-parallel spins (singlet)

state which has lower energy. The strength of the signal at the emission or absorption

lines depends on the relative occupation number of the ground state and the occupation

number of the excited state; hence it gives information about the density of the neutral

hydrogen along the line of sight. This type of survey is one of the fundamental tools for

studying the formation of the first structures during the dark ages and the Epoch of

Reionization (Rhee, et al., 2013).

However, none of the surveys that are used in this project are of the last two

kinds of the above mentioned surveys.

4.2. Sloan Digital Sky Survey (SDSS)

The Sloan Digital Sky Survey is a significant project to produce detailed, 3-

dimensional maps of more than a quarter of the entire sky, using a dedicated 2.5-meter

instrument at the Apache Point Observatory in New Mexico (Lahav & Suto, 2004). The

Survey began in 2000 and started to release data to the scientific community and the

general public periodically.

In its first two operational stages (SDSS-I, 2000-2005, SDSS-II, 2005-2008), the

project obtained comprehensive multi-colour images of more than a quarter of the sky

that created 3-dimensional maps containing more than 930,000 galaxies and more than

120,000 quasars. The Sloan Digital Sky Survey is continuing through the Third Sloan

Digital Sky Survey (SDSS-III) that started observations in mid-2008 and will continue

until 2014. This phase consists of four distinct surveys, carried out using the same

facilities. The four surveys are: APO Galactic Evolution Experiment (APOGEE),

Baryon Oscillation Spectroscopic Survey (BOSS), Multi-object APO Radial Velocity

Exoplanet Large-area Survey (MARVELS) and the Sloan Extension for Galactic


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Understanding and Exploration (SEGUE-2). Each of the SDSS-III surveys is designed

for different purposes and operates differently.

The first data collection of SDSS-III (Data Release 8) was released in January

2008. It contains all of the imaging data taken by the SDSS imaging camera which

covers about 14,000 square degrees of the sky in addition to the new spectra taken by the

SDSS spectrograph during its last year of operation for the SEGUE-2 project and

includes imaging of roughly 5200 square degrees.

The second SDSS-III data collection (Data Release 9) was released in August

2012. It contains the first release of BOSS spectroscopy to the public and also includes

all imaging and spectra fromprevious data releases with some important updates such as

providing corrected astrometry for the imaging Data Release 8 by making some

improvements to the astrometric calibration. Data Release 9 covers over 3,300 square

degrees. The median redshift of the SDSS is z=0.1 and the maximum detected redshift

for galaxies is z=0.7 and foe quasars is z=5; and the imaging survey is supposed to

include quasars as far as z=6.

The newest release is Data Release 10 which was completed in July 2014 and

contains the first release APOGEE infrared Galactic spectroscopy as well as hundreds of

thousands of new galaxy and quasar spectra from the BOSS survey and some

modifications to the Data Release 9. The total sky coverage at completion of Data

Release 10 is 14,555 square degrees and optical spectra measurements for 1,848,851

galaxies, 308,377 quasars and 736,484 stellar objects as well as 57,454 infrared stellar

spectra. The SDSS-III will continue operating and releasing data and hopefully be

complete in few more years. The obtained SDSS image is considered to be the largest

colour image of the sky ever made.

The project was managed by the Astrophysical Consortium for Participating

Institutions and named after Alfred P. Sloan Foundation who provided the major Fund

(Sloan Digital Sky Surveys, 2014) (York, et al., 2000).

4.3. Two-degree-Field Galaxy Redshift Survey (2dFGRS)

The Two-degree-Field Galaxy Redshift Survey (2dFGRS) is a major

spectroscopic redshift survey conducted on the 3.4-meter Anglo-Australian Telescope in

the Siding Spring Observatory in Australia. The project started in 1997 and by 11 April
https://www.google.com/search?espv=2&biw=1366&bih=667&q=define+previous&sa=X&ei=ZsamU-65C8r80QXztIBQ&ved=0CB0Q_SowAAhttps://www.google.com/search?espv=2&biw=1366&bih=667&q=define+previous&sa=X&ei=ZsamU-65C8r80QXztIBQ&ved=0CB0Q_SowAA


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2002, the project was completed with spectra measurements of 245591 objects brighter

than magnitude of bJ=19.45, 221414 of them yielded reliable redshifts of galaxies, which

makes it to be considered as the second largest redshift survey next to the Sloan Digital

Sky Survey. The redshifts of almost all galaxies is less than z=0.3 with a median of z =

0.11. The total sky area covered by 2dF survey is approximately 1500 square degrees,

distributed in three regions: two declination strips, in the northern and southern galactic

hemispheres, and 100 random fields scattered around the southern galactic hemisphere

strip as shown in figure 4.2 (Colless, et al., 2003).

4.4. Six-degree-Field Galaxy Redshift Survey (6dFGRS)

The Six-degree-Field Galaxy Redshift Survey (6dFGRS) is aimed to measure

redshifts and peculiar velocities over almost the entire southern sky. The survey was

conducted on the Anglo-Australian Observatorys 1.2-meter UK Schmidt Telescope

between 2001 and 2009. The survey achieved 136,304 spectra measurements that

yielded 110,256 reliable and unique redshifts with median of z=0.053. The survey is the

largest redshift survey of the nearby universe (z 0.15) and the third largest survey next

Figure 4.2: The distribution of 63000 2dFGRS galaxies in the NGP (left panel) and SGP (right panel) strips

(Lahav & Suto, 2004).


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to 2dFGRS and SDSS. The 6dFGRS covers an area of 17000 square degrees of the

southern sky with |b| < 10 which is more than ten times the sky area of the 2dFGRS and

almost twice that of the SDSS (Jones, et al., 2009).

4.5. VIMOS-VLT Deep Survey (VVDS)

The VIMOS-VLT Deep Survey (VVDS) is a comprehensive imaging and

spectroscopic redshift survey, carried out using the VIMOS spectrograph which is built

by the VIRMOS consortium of French and Italian. The aim of the project is to provide a

complete picture of galaxy formation and evolution of large scale structure growth of the

universe over a very broad redshift range (0 < z 6.7) over sixteen square degrees of the

sky in four separate fields. The VVDS is a combination of three nested surveys, selected

on the basis of apparent magnitude as follows: Wide (17.5 iAB 22.5; 8.6 square

degrees), Deep (17.5 iAB 24; 0.6 square degrees) and Ultra-Deep (23 iAB 24.75;

512 square arcmin) with a total of 22434, 12051, 1041 measured galaxy redshifts

respectively. In the redshift scale, the VVDS succeed in measuring high redshifts with

4669 redshifts in 1 z 2, 561 redshifts in 2 z 3 and 468 with z >3 (Le Fvre, et al.,

2005).

4.6. The Deep Extragalactic Evolutionary Probe project (DEEP)

The Deep Survey is a large scale survey of distant galaxies conducted to study

theformation and evolution of galaxies, the origin oflarge-scale structure,the nature of

thedark matter, and thegeometry of the Universe using the twin 10-mW.M. Keck

Telescopes and theHubble Space Telescope (HST).

DEEP project is divided into two phases, the first (DEEP I) used the Low

Resolution Imaging Spectrograph (LRIS) to study a sample of ~ 1000 galaxies to a limit

of I = 24.5 and a median redshift of about unity. Phase 1 was designed to examine the

technical feasibility and establish the scientific scope of the program, prior to conducting

phase 2. The second phase (DEEP II) started in spring 2002 and used the largest

spectrographic detector of its type ever made, which is the Deep Multi-Object

Spectrograph (DEIMOS) that is capable of observing 140 galaxies at a time. The goal

of DEEP II is to include a rage sample of greater than 50000 galaxies brighter than I-

band magnitude 23.5 with high resolution and in the pre-selected redshift range of z =

0.7-1.55 (Davis, et al., 2003).
http://deep.ucolick.org/overview/galevol.htmlhttp://deep.ucolick.org/overview/structure.htmlhttp://deep.ucolick.org/overview/darkmatter.htmlhttp://deep.ucolick.org/overview/geometry.htmlhttp://www2.keck.hawaii.edu:3636/http://www2.keck.hawaii.edu:3636/http://www.stsci.edu/http://www.stsci.edu/http://www2.keck.hawaii.edu:3636/http://www2.keck.hawaii.edu:3636/http://deep.ucolick.org/overview/geometry.htmlhttp://deep.ucolick.org/overview/darkmatter.htmlhttp://deep.ucolick.org/overview/structure.htmlhttp://deep.ucolick.org/overview/galevol.html


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4.7. Two Micron All-Sky Survey (MASS)

The Two Micron All-Sky Survey (MASS) survey was conducted between 1997

and 2001 and covered almost the whole sky (99.998% of the celestial sphere) in three

near-infrared band. Observations were conducted from two dedicated infrared 1.3-meter

m diameter telescopes located at Mount Hopkins, Arizona, and Cerro Tololo, Chile. The

observed wavelengths were 1.25, 1,65 and 2.16 microns.

The project was a collaboration between The University of Massachusetts that

constructed and maintained the observatory facilities and operated the survey, and the

Infrared Processing and Analysis Center (JPL/ Caltech) that had the responsibility of the

data processing and data product generation.

The 2MASS data were release for general public in 2003 release and included

4.1 million compressed FITS images covering the entire sky, 471 million source

extractions in a Point Source Catalogue, and 1.6 million objects identified as extended in

an Extended Source catalogue (Huchra, et al., 2012).

4.8. VIMOS Public Extragalactic Redshift Survey (VIPERS)

VIMOS Public Extragalactic Redshift Survey (VIPERS) is an on-going survey

started in 2008 and carried out using the European Southern Observatorys Very Large

Telescope (ESO VLT). The aim of the project is to build a large sample of ~100,000

galaxies with red magnitude I(AB) brighter than 22.5 over an area of 24 square degrees.The survey is focused on a long redshift range (0.5 < z < 1.2), hence yielding a large

volume (5 x 107 h-3 Mpc3). The first VIPERS data release includes spectroscopic

measurements for 57204 objects, 54756 of them are galaxies (Franzetti).

4.9. Galaxy And Mass Assembly Survey (GAMA)

The Galaxy And Mass Assembly Survey (GAMA) is a project to study the

structure on scales of 1 Kpc to 1 Mpc. This wide range will be very helpful in studying

the galaxy evolution and the large-scale structure.

GAMA surveys will be carried out using a number of instruments: The Anglo-

Australian Telescope (AAT), theVLT Survey Telescope (VST), theVisible and Infrared

Survey Telescope for Astronomy (VISTA), the Australian Square Kilometre Array

Pathfinder (ASKAP), the Herschel Space Observatory and the Galaxy Evolution

Explorer (GALEX).
http://en.wikipedia.org/wiki/Anglo-Australian_Telescopehttp://en.wikipedia.org/wiki/Anglo-Australian_Telescopehttp://en.wikipedia.org/wiki/VLT_Survey_Telescopehttp://en.wikipedia.org/wiki/VISTA_(telescope)http://en.wikipedia.org/wiki/VISTA_(telescope)http://en.wikipedia.org/wiki/Australian_Square_Kilometre_Array_Pathfinderhttp://en.wikipedia.org/wiki/Australian_Square_Kilometre_Array_Pathfinderhttp://en.wikipedia.org/wiki/Herschel_Space_Observatoryhttp://en.wikipedia.org/wiki/Galaxy_Evolution_Explorerhttp://en.wikipedia.org/wiki/Galaxy_Evolution_Explorerhttp://en.wikipedia.org/wiki/Galaxy_Evolution_Explorerhttp://en.wikipedia.org/wiki/Galaxy_Evolution_Explorerhttp://en.wikipedia.org/wiki/Herschel_Space_Observatoryhttp://en.wikipedia.org/wiki/Australian_Square_Kilometre_Array_Pathfinderhttp://en.wikipedia.org/wiki/Australian_Square_Kilometre_Array_Pathfinderhttp://en.wikipedia.org/wiki/VISTA_(telescope)http://en.wikipedia.org/wiki/VISTA_(telescope)http://en.wikipedia.org/wiki/VLT_Survey_Telescopehttp://en.wikipedia.org/wiki/Anglo-Australian_Telescopehttp://en.wikipedia.org/wiki/Anglo-Australian_Telescope


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The newest GAMA data release (DR2) gives spectra, redshifts and abundance of

information for 72,225 objects from the first phase of the GAMA survey (2008 - 2010,

usually referred to as GAMA I) (Baldry, et al., 2010).

4.10. FORS Deep Field (FDF) spectroscopic survey

Using the visual and near UV FOcal Reducer and low dispersion Spectrograph

(FORS) instrument, the FORS Deep Field (FDF) spectroscopic survey was performed to

improve our understanding of the formation and evolution of galaxies in the young

Universe. The survey began in 1999 and covered a small angular area, 7 7, just

about the size of a large galaxy cluster at high redshift and the targets were selected in

the basis of photometric redshifts. The survey detected 341 reliable redshifts, 98 of them

correspond to starburst galaxies and QSOs at z > 2. The redshift of the observed

extragalactic objects ranges between 0.1 and 5.0 (Noll, et al., 2004).

4.11. Team Keck Redshift Survey (TKRS)

Team Keck Redshift Survey (TKRS) is a project conducted by W.M. Keck

Observatory and used the Keck II telescope to observe the spectra of nearly 3000

sources, yielding secure spectroscopic redshifts for 1536 objects (1437 are galaxies).

The redshifts are accurate to 100 km/sec and the limiting magnitude is R=24.3. The

TKRS results enabled numerous studies of large-scale structure, galaxy dynamics, and

abundances (Wirth, et al., 2004).


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Chapter 5: Data Collection and Statistical analysis

As the aim of this project is to study the distribution of galaxies throughout

universe without focusing on a specific region of the sky or focusing upon a certain type

of celestial object, it was decided that the publicly available data of various Redshift Sky

Surveys would be used that utilise different selection criteria. However, this required

the following of certain procedures to check for data reliability and consistency and for

the existence of duplications, if there should be any. The data was collected from the

following ten Redshift Sky Surveys: Sloan Digital Sky Survey (SDSS, 10th

Release),

Two Micron All-Sky Survey (2MASS, the final data product), Two-degree-Field Galaxy

Redshift Survey (2dFGRS, the best spectroscopic observations of the final release), Six-

degree-Field Galaxy Redshift Survey (6dFGRS, Data Release 3), Galaxy And Mass

Assembly survey (GAMA, Data Release 2), VIMOS Public Extragalactic Redshift

Survey (VIPERS, PDR-1), The Deep Extragalactic Evolutionary Probe project (DEEP,

Data Release 4), VIMOS-VLT Deep Survey (VVDS, First Epoch sample), Team Keck

Redshift Survey (TKRS) and FORS Deep Field spectroscopic Survey (FDF).

This chapter describes the procedures implemented to check that the data

collected from the various databases is consistent and that the two tests performed to

check whether the distribution of the radial dimension, z is periodic.

5.1 Checking data consistency

The high quality and reliable redshifts are extracted from each survey data

collection, such that < 10%, or measurement confidence 90%.In all of the survey catalogues used in this project, the positions of the celestial

objects are given with respect to the J2000 equatorial coordinates. However, we wanted

to examine the periodicity hypothesis in the distribution of the co-moving radial

distance, as well as in the distribution of the z in the equatorial coordinates there arose a

need to perform a conversion from the J2000 equatorial coordinates to the co-moving

coordinates. Moreover, the angular dimensions were converted from the equatorial

coordinates to the galactocentric coordinates so they can be used in any further studies.

The next two subsections discuss the procedures implemented to generate reliable data

sets in different coordinate systems from the original source catalogues.


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5.1.1 Coordinate Transformations. The equatorial coordinate system originates

at the center of Earth and its reference plane is the Earths equatorial plane which is the

projection of the earths equator on the celestial sphere. Based on the equatorial

coordinates, the angular position of any celestial object can be described by two

quantities: right ascension; RA, and declination, Dec. The right ascension is measured

eastward along the celestial equator starting from the vernal equinox. It could be given

in hour angle and its subdivisions (from 0h0

m0

swhich corresponds to the direction of

the vernal equinox, to 24 h

0m

0s) or in degrees (from 0 to 360). The declination

measures the angular distance of an object perpendicular to the celestial equator, and

extends from 0at the celestial equator to +90at the north celestial pole and down to -90at the south celestial pole. For the purposes of consistency, the angular dimensions(RA and Dec) of all of the objects in the data collection have been converted to decimal

degrees.

It must be kept in mind that the orientation of the equator and the ecliptic are not

fixed, but rather they are changing with time due to the precisional motion of the earth.

Thus, a standard reference frame is usually based on the mean equator, the mean

ecliptic, and the equinox of some dedicated epoch. The most commonly used is the

J2000.0 equatorial coordinates which is based on the Julian date calendar and the right

ascension and the declination are defined from the mean vernal equinox and the mean

equatorial plane at 12:00 UTC on January 1st in the year 2000 (Takahashi, Kondo,

Takahashi, & Koyama, 2000).

The radial dimension of an object in the equatorial coordinates is the component

along the line of sight between the observer and the position of the object, measured at a

specific moment. While this distance (called the proper distance) is changing with time

due to the expansion of the universe, there is another coordinate choice, called the

comoving coordinates, which allow us to express the radial distance to an object with

eliminating the increase in the distance due to the expansion. In other words, in the

comoving coordinates the distance to an object (called the comoving distance) is

constant over time despite the expansion of the universe. However, the detailed

definition of the comoving coordinates is beyond the scope of this project, and what we

should concern ourselves with is the conversion of the redshift, z, to the comoving


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distance. This conversion task has been accomplished with the aid of a MATLAB

function that is available online by Instituto de Fsica y Matemtica (Surendran, 2011)

The code is based on the following formula

Where

the comoving radial distance, z is the redshift value that we want to convert,

is the speed of light and is the Hubble constant. The numbers 0.27 and 0.73 referto the fractions of the matter and dark energy respectively. Using the above formula, a

graph or r versus z has been plotted to be used in the reverse conversion; from comoving

distance to redshift (the graph is shown in Figure. 5.1). This relation tells that a fixed

separation in the z scale corresponds to a decreasing spacing in comoving distance scale;

e. g. a spacing of 0.1 between z=1 and z=1.1 is equivalent to ~242 Mpc in the comoving

distance scale, while the same separation in the z scale between z=4 and z=4.1 is

equivalent to ~70 Mpc in the comoving coordinates.

Furthermore, the measurements have been converted from the equatorial

coordinates to the galactic coordinate system. The galactic coordinates are based on the

galactic plane and centered on the sun. The latitude angle of the galactic coordinates is

denoted by the letter b, and its measured from 0to 90northward and from 0to -90

Figure 5.1: The commoving distance as a function of z, based on equation 5.1.


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southward the galactic equator. The galactic longitude is represented by the letter, andis measured in the galactic plane using an axis pointing from the sun to the galactic

center (where = 0) and extends counter clockwise as seen from the north galactic poleto 360

The conversion from the equatorial coordinate system to the galactic coordinate

system has been accomplished with the aid of a Fortran 95 code emailed to us by

Professor Matthew Colless, which uses the following set of equations:

[ ]

Where Ra, Dec, b and are all given in degrees.Moreover, in some researches such as (Napier & Guthrie, 1997) the existence ofa redshift periodicity has been detected in the galactocentric frame of reference, which

has the galactic center as its origin. However, we have performed a simple test to

determine if whether the difference between the redshifts in the galactocentric

coordinates; zgalactocentric, and the redshifts in the equatorial coordinates (zequatorial) is

significant. The test was as follows: If the galactic center, Earth and the targeted

celestial object are approximated to form a right tringle, then the difference between

zgalactocentricand zequatorialcan be written as,

Where is the galactic center distance from Earth. Using ~ 8.33 kpc

(Gillessen, et al., 2009), the difference can be calculated for a range of values of

as illustrated in Figure 5.2. From the calculations we have concluded that thedifference is too small and insignificant.

5.1.2 Duplication checking

Since we are dealing with a large data set (for ~ 3 million objects), comparing the

coordinates of each object with the coordinates of all other objects would require doing

very heavy computations. To reduce the number of calculations, we have made use of

the following method: the data lines have been ordered and then sorted into 36 groups,


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based on the right ascension values. The three position coordinates (RA, Dec and z) of

each object have then been compared to all of the other objects of the same group that

the object belongs to. Two objects are considered to be duplicate if their redshifts

(and ) match precisely and the difference between their angular dimensions doesn'texceed the approximated angular diameter. These conditions condition can be written as

( ) Where is the galactic diameter and is approximated to be fixed as the diameter

of the Andromeda which is 110 kly (Kambic, 2009) . However, this checking method is

valid for low redshifts only (z


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5.2.1 Histogram

For Large sets of data, the histogram is an efficient method to use in order to

derive various features of the distribution. It uses rectangles to represent the counts of

the data point falling in various ranges. The most common form of the histogram can be

obtained by dividing the data range into equal-sized bins. Then the number of data

points that fall into each bin is counted and plotted against the corresponding interval.

The shape of the histogram and the data features that can be extracted from it are

highly dependent on the bin size. If the bins are wide, the noise due to the sampling

randomness can be reduced, but at the same time, important information might be

omitted. On the other hand, using narrow bins may cause random variation effects to

appear as meaningful information, but it gives greater precision to the density estimation

as a benefit. Therefore, its advisable to trydifferent bin sizes in order to obtain a more

complete picture of the data. In this study, the histogram of the redshift distribution has

been computed for four different bin sizes: 0.2, 0.1, 0.01 and 0.001.

5.2.2 Periodogram

A Periodogram is an efficient statistical tool for examining the periodic (cyclic)

behavior in a time series, where it identifies the dominant periods (or frequencies) of the

sequence. Assume we have a time series of length N; {}

, asmoothed periodogram of the series can be obtained by carrying out the following main

three steps:

1. Multiplying the sequence by a window function to reduce the noise and the

effect of the leakage in the Fourier transform due to sudden changes in the

start and end of the data (Kang, 2008).

2. Computing the discrete Fourier transform (DFT) which is defined as (Vio,

Diaz-Trigo, & Andreani, 2013):

3. Averaging the squared absolute value of the DFT of the signal to obtain the

periodogram, :


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|| A plot of s as a function of frequency is also called the periodogram (also the

power spectrum) of the series, and the analysis is called the periodogram analysis

(Chatfield, 2004). If there is a strong sinusoidal signal in the time series with some

frequency, then there will be a peak in the periodogram at that frequency. If the periodic

signal is non-sinusoidal, then there will be a fundamental peak in the periodogram at the

frequency of the signal but also at multiples of that frequency.

However, if the sampling rate, (which is the reverse of the sampling step) ischosen to be very small, then a phenomenon called aliasing may occur.

Aliasing refers to when the frequencies above a certain frequency, called the

Nyquist frequency ( ) will, after sampling, be indistinguishable fromfrequencies below the Nyquist frequency and distort the spectrum. In order to void thealiasing problem, one can filter out components whose frequency exceeds the Nyquist

frequency prior to sampling. Another solution worth mentioning is to choose a sampling

rate that is sufficiently high (much higher than the frequency of interest) so that the

frequency components produced by aliasing will be far away from the range of

frequency of interest and can be easily discriminated. More details about the aliasing

phenomenon and its solutions can be found in (Hearn & Metcalfe, 1995).

For testing the white noise, one can use the cumulative periodogram which

defined as (Diggle & Fisher, 1991)

For a purely random series, the plot of s against would consist of

a straight line joining (0, 0) and (0.5, 1). If a series has a periodicity with some

frequency, then there will be a jump in the cumulative periodogram at that frequency

(where the periodogram has a peak).

The code that is used in this project to calculate the periodogram, both the

classical and the cumulative periodogram, is attached in Appendix. A.


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Chapter 6: Results and discussion

A total of 2841496 redshift measurements were obtained from ten redshift survey

catalogues. After filtering the redshifts to extract the most reliable values, the number is

reduced to 2763064 redshifts, combined with the angular distances of the associated

celestial objects. The collective sample covers the whole sky area (RA from 0 to 360

and Dec from -90 to 90). Table 6.1 summarizes the number of objects included in each

survey sample, as well as in the collective set before and after the filtering process.

Table 6.1: Summery of the redshift measurements before and after filtering process

Note that the number of reliable redshifts in the collective sample is not the sum

of the numbers of reliable redshifts of the individual sample, because the collective

sample has been subjected to the same filtering process in order to detect the duplicate

objects between the different survey samples.

In this chapter, we present a discussion of the radial distribution of the celestialobjects using the histograms and the periodograms that we have obtained. We also

discuss the main conclusions of the study.

Note that all of the plots have been obtained using MATLAB 2014b, while the

calculations (Filtering, conversions, statistics, .. etc.) have been done using Fortran 95 as

well as MATLAB 2014b.

Sample Number of redshifts (before filtering) Number of reliable redshifts

SDSS 1982640 1979282

2MASS 240510 240291

2dF 245591 227190

6dF 124647 124326

GAMA 90409 83610

VIPERS 61221 45156

DEEP 50319 35752

VVDS 40081 25685

TKRS 5737 1473

FDF 341 299

Collective sample 2841496 2763064


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6.1 Radial Distributions

The distributions of the celestial objects along the radial dimension, z, have been

examined using histograms and periodograms for different bin sizes and different

sampling rates. The next two sections will present the resulted diagrams and the general

conclusions that can be drawn from them.

6.1.1 Histograms.

The z values of the collective sample have been presented using histograms with four

different bin widths: 0.2, 0.1, 0.01 and 0.001, as shown in figure 6.1. Comparing the

four histograms, one can see clearly that the 0.2 and 0.1 bin sizes are too large such that

the resolution of the resultant histograms are not good enough to extract the features of

the distribution. In other words, most of the data fall in the first few bars so we may lose

some details of the shape of the distribution. Also, the 0.001 bin size is too small

because it shows unimportant fluctuations that could have arisen from the error of the

measurements (since 0.001 is comparable with the error of the small values of z, see

section 5.1). The comparison between the histograms with the four different bin sizes is

represented in Figure 6.1.

Most of the z values fall in the interval (0 z 4) as can be

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Investigating the Galaxy Distribution Using Redshift Surveys (3)