Download Investigation of Extrasolar Planets Using Radial Velocity Technique

Republic of Iraq
Ministry of Higher Education & Scientific Research
University of Baghdad - College of Science
Department of Astronomy
Investigation of Extrasolar Planets
Using Radial Velocity Technique
A Thesis
Submitted to the committee of Department of Astronomy,
College of Science, University of Baghdad,
In Partial Fulfillment of the Requirements for
The Degree of Master of Science in Astronomy Science
By
Carmen Samir Shimon
B.Sc. Astronomy (2005), College of Science, University of Baghdad
Supervised By
Prof. Dr. Layth Mahmood Karim
2010 A.D
1431 H.
To The Causes of
My Existence, Success and Ambition
My parents
To The One Who Gave My Life
Its Brightness, Happiness and Beauty
My Sister
Acknowledgment
First I would like to express my sincere thanks and deep gratitude to
my supervisor Dr. Layth Mahmood for his help, advice and guidance
through the research time which lead to successful completion of this thesis.
I owe special thanks to Dr. Ali Talib head of Astronomy Department
and the rest of the Department staff who never hesitated in offering their
help when I need it.
I would like also to thank and express my deep gratitude to Dr.
David Turner who is a professor in Saint Mary University in Canada for
his help and cooperation during my training in Canada.
Next, I would like to thank my sister Ms. Caroline Samir for her help
and support during the completion of this work.
Also, I would like to thank all my friends, colleagues and all the
people who assisted me and I forget to mention for their help,
encouragement during hard times, understanding and for the useful time
that we spent in the discussions and sharing ideas.
Finally, I may not forget the patience and the help of my family to
succeed in this work; I would like to thank them for their confidence in me
over the years. I will not forget their kindness, supports, patience and
encouragement to reach this stage of education.
I pray to God to enable me showing them my graceful gratitude.
Abstract
Extrasolar planets are planets orbiting around star(s) outside the solar
system. Their numbers reached 473 planets till July 2010.
The history of Extrasolar planets research belong to a long time since the early of
1900’s. During that time many discoveries have been appeared, but the real
discovery came in 1995 when the first Extrasolar planet was discovered orbiting
around 51 Pegasi star.
Radial velocity technique is considered as one of the most important methods for
detecting Extrasolar planets, which was used in this research.
The interdependent techniques in Saint Mary Observatory in Canada
were used in this research, which helped gaining an astronomic scientific
knowledge to calculate the mass of planet that needed to prove its existence
around a star. By taking specific date observations and radial velocity
observations for the star, results for the seven stars chosen for this purpose were
reached and from several parameters the mass was calculated.
Two stars were unconfirmed its discovery, while the rest five stars were
confirmed. The results obtained for confirmed stars are found in a good
agreement with the published results, while the unconfirmed stars’ results there
were diverging in the calculated results. That diverging is due to the modicums
in the requisite observational data.
Estimating the mass of planet will help the astronomers to know whether
the companion to the star is a planet or a dim star that can’t be seen. Therefore
this will prove the existence or the absence of the planet around a star.
aim of the thesis
The aim of this research is attempting to put a formula that proves the existence
of Extrasolar planets to be applied by observers who are willing to look for
new Extrasolar planets. That will be investigated by estimating the mass of the
companion to the star to determine whether the companion is another star that
is too dim to see or a planet.
layouts of the thesis:
This thesis is divided into four chapters; each one demonstrates some
topics related to the theoretical and experimental framework of this research:
Chapter one: This chapter gives a brief introduction to the subjects are dealing
with. An introduction concerned with the definition of Extrasolar planets and
the history of the beginning of detecting Extrasolar planets. Besides that, this
chapter gives a short survey about most literatures including information about
Extrasolar planets like: the types of Exoplanets and why Extrasolar planets are
studied.
Chapter two: In this chapter different techniques that used to detect Extrasolar
planets are introduced and discussed with details.
Chapter three: This chapter concerned with computational work which
includes mathematical formulae to calculate the mass of Extrasolar planets.
This will put a criteria for observing Exoplanets to be applied by observers to
study new Extrasolar planets.
Chapter four: This chapter includes discussions and conclusions about present
work and suggestions for future works.
References and Appendices were given in the end of the thesis.
i
list of figures
Figure
number
Figure description
Page
number
1.1
Hot Jupiter planet
6
1.2
Inferred size of the super-Earth GJ 1214 b in comparison
with Earth and Neptune
8
1.3
Conception of PSR 1257+12's system of planets
10
1.4
Hypothetical ocean planet with a terrestrial atmosphere
and two satellites
11
2.1
The orbit of planet around its parent star
16
2.2
The Doppler blue shift and red shift
19
2.3
2.4
The number of discovered Extrasolar planets by Radial
velocity method
The number of discovered Extrasolar planets by pulsar
timing method
24
26
2.5
The transit of a planet in front of its star
27
2.6
Schematic diagram of the geometry of a planet transit
28
2.7
The Kepler Mission Telescope
31
2.8
The number of discovered Extrasolar planets by transit
method
32
2.9
Schematic diagram for Gravitational Microlensing
33
2.10
2.11
The geometry of the gravitational lens with the distances
between lensing star, source star and observer
The number of discovered Extrasolar planets by
Gravitational microlensing method
34
36
2.12
Two Pluto-sized dwarf planets in a collision around Vega
38
2.13
Discovery image of the GJ 758 system
40
ii
Figure
number
Figure description
Page
number
2.14
The number of discovered Extrasolar planets by Direct
imaging method
40
2.15
Kepler's photometer
45
2.16
The Hubble Space Telescope
47
2.17
The Spitzer Space Telescope
48
2.18
The number of discovered Extrasolar planets by all
established detection methods
50
3.1
Schematic organization of the practical work
59
3.2
3.3
3.4
3.5
3.6
3.7
3.8
Shows the radial velocity vs phase, and the generated sine
wave for the star HD 150706
Shows the radial velocity vs phase, and the generated sine
wave for the star HD 24040
Shows the radial velocity vs phase, and the generated sine
wave for the star 51 Pegasi
Shows the radial velocity vs phase, and the generated sine
wave for the star HD 81040
Shows the radial velocity vs phase, and the generated sine
wave for the star HD 118203
Shows the radial velocity vs phase, and the generated sine
wave for the star HD 33564
Shows the radial velocity vs phase, and the generated sine
wave for the star HD 190228
60
61
61
62
62
63
63
iii
list of tables
Table
number
Table description
Page
number
2.1
General information about some space missions
51
3.1
Data of HD 150706 star
54
3.2
Sine wave data for HD 150706 star
57
3.3
Parameters and results of masses calculations for
some stars
64
iv
list of abbreviations
The abbreviations
Astronomical Unit
Brief
AU
Center National d’Etudes Spatiales
CNES
Charge Coupled Device
CCD
COnvection ROtation and planetary Transits
COROT
Distance from the star
D
Einstein angle
θE
Einstein radius
RE
European Southern Observatory
ESO
European Space Agency
ESA
Faint Object Camera
FOC
Faint Object Spectrograph
FOS
Gliese-Jahreiss compilation
GJ
Goddard High Resolution Spectrograph
Gravitational constant
GHRS
G
Haute-Provence Observatory
HPO
Henry Draper catalog
HD
High Accuracy Radial velocity Planet Searcher
HARPS
High Contrast Instrument with Adaptive Optics
HiCIAO
v
The abbreviations
Brief
High Speed Photometer
HSP
HIPparcos catalog
HIP
Hubble Space Telescope
HST
Hungarian Automated Telescope - Planet
Inclination of the planet’s orbit
HAT-P
i
Julian day
JD
Luminosity
L
Mass of Jupiter
MJup
Mass of Sun
MSun
Mass of the planet
Mp
Mass of the star
M*
Near Infrared Camera and Multi-Object Spectrometer NICMOS
Optical Gravitational Lensing Experiment
OGLE
Planet Albedo
A
Planetary orbital eccentricity
e
Planetary orbital period
P
Pulsar
PSR
Radial Velocity
RV
Radius of the planet
RP
Radius of the star
R*
Sagittarius Window Eclipsing Extrasolar Planet
Search
SWEEPS
vi
The abbreviations
Semi-major axis
Space Infrared Telescope Facility
Speed of light
Spitzer Space Telescope
The amplitude of this periodic radial velocity
variation for the star
Brief
a
SIRTF
c
SST
K
Trans-atlantic Exoplanet Survey
TrES
Very Large Telescope
VLT
Wide Angle Search for Planets
WASP
Wide Field and Planetary Camera
WF/PC
XO survey
XO
vii
Contents
Contents
Aim of the thesis ………………………………………………………
i
Layout of the Thesis …………………………………………………..
i
List of figures ………………………………………………………….
ii
List of tables …………………………………………………………...
iv
List of abbreviations …………………………………………………...
v
Chapter one
General introduction
No
1.1 Introduction …………………………………. …
1
1.2 History of Extrasolar planets research …….……
3
1.3 Types of Extrasolar planets …………………….
5
1.3-1 Hot Jupiter ………………………………..
6
1.3-2 Hot Neptune ………………………………
7
1.3-3 Super-Earth ………………………………..
8
1.3-4 Pulsar planets ……………………………...
9
1.3-5 Ocean planets ……………………………...
11
1.4 Studying Extrasolar planets ……………………..
12
Contents
Chapter Two
Detection methods of Extrasolar planets
No
2.1 Introduction ……………………………………...
14
2.2 Established detection methods …………………..
16
2.2-1 Astrometry …………………………………
16
2.2-2 Radial velocity …………………………….
18
2.2-3 Pulsar timing ………………………………
25
2.2-4 Transit ……………………………………..
27
2.2-5 Gravitational microlensing ………………… 33
2.2-6 Circumstellar disks ……………………….... 37
2.2-7 Direct imaging ……………………………... 38
2.3 Other possible methods …………………………... 41
2.3-1 Eclipsing binary minima timing ……………. 41
2.3-2 Orbital phase reflected light variations …….. 41
2.3-3 Polarimetry ……………………….………… 42
2.4 Observations space missions …………………….. . 42
2.4-1 Previous space missions …………………...... 43
2.4-1-1 COROT Mission ……………………. 43
2.4-1-2 Kepler Mission ……………………..
44
2.4-1-3 Hubble Space Telescope …………… 46
2.4-1-4 Spitzer Space Telescope ……………. 48
2.4-2 Future space missions …………………….... 49
Contents
Chapter Three Data processing, calculations and results
No
3.1 Introduction ………………………………………
52
3.2 Data processing …………………………………..
52
3.3 Calculations of Extrasolar planets mass …………. 64
Chapter Four
Discussion, conclusions and future work
No
4.1 Discussion and Conclusions ………………………. 65
4.2 Future work ……………………………………….
References ……………………………………………………………….
66
67
Appendix A …………………………………………………………….... 74
Appendix B ………………………………………………………………
93
Chapter One
General Introduction
1.1 Introduction
The Sun is a star like all others, so it is natural to wonder if some
planets move around other stars, like they do around the Sun. Moreover we
can wonder whether there is life on some of these "Extrasolar Planets". The
search for ‘other worlds’ is one of the oldest scientific questions ‘is there life
elsewhere in the universe?’ This question raises the problem of the different
forms of life that had been expected outside the solar system and the problem
of the definition of life [1].
An Extrasolar planet, or Exoplanet, is a planet outside the solar
system. As of July 2010, 473 Extrasolar planets have been confirmed [2]. The
vast majority have been detected through radial velocity observations and
other indirect methods rather than actual imaging.
The fact of the solar system existence raised a question whether or not planets
exist around stars other than the solar system. This is based on the size of the
universe and the laws of probability. The logic answer is that the solar system
is not unique in the universe, since the size of the universe, at the present time
estimated the existence of 50 billion galaxies; the largest of which contain
thousands of billions of stars, are visible to modern telescopes including the
Hubble Space Telescope [3].
In order to determine the existence of Extrasolar planets it is important to
consider one minor and one major premise. The minor premise, and to a large
degree a philosophical one, is to consider the existence of additional solar
systems based on the probability factor. As stated above, with the number of
galaxies and the number of stars contained within each of the galaxies, the
probability of another solar system existing is excellent. The major premise,
and certainly the most important, is to ascertain the existence of Extrasolar
planets by direct astronomical observations [٤].
۱
Chapter One
General Introduction
The system used in the literature for naming Extrasolar planet is
almost the same as the system used for naming binary stars not like the
system used for naming the planets in the solar system, Exoplanets do not
have complicated creative names; they are named after the stars that they orbit
in the order of discovery so the only modification is that a lowercase letter is
used for the planet instead of the uppercase letter used for stars. A lowercase
letter is placed after the star name, starting with "b" for the first planet found
in the system (for example, 51 Pegasi b); "a" is skipped to help prevent
confusion with the primary star. The next planet found in the system would be
labeled with the next letter in the alphabet. For instance, any more planets
found around 51 Pegasi would be catalogued as "51 Pegasi c" and then "51
Pegasi d", and so on. If two planets are discovered at about the same time, the
closer one to the star gets the next letter, followed by the farther planet.
If a planet orbits around one member of a multiple-star system, then an
uppercase letter for the star will be followed by a lowercase letter for the
planet. Examples include the planets 16 Cygni Bb and 83 Leonis Bb.
However, if the planet orbits the primary star of the system, and the secondary
stars were either discovered after the planet or are relatively far from the
primary star and planet, then the uppercase letter is usually omitted. For
example, Tau Boötis b orbits in a binary system, but because the secondary
star was both discovered after the planet and very far from the primary star
and planet, the term "Tau Boötis Ab" is rarely if ever used [5].
۲
Chapter One
General Introduction
1.2 History of Extrasolar planets research
In the early of 1900’s, measurements of distance to other stars and
galaxies changed traditional views of the solar system’s place in the universe.
For the first time, astronomers found evidence that the solar system is not in
the center of the galaxy and that the Milky Way occupies no special place in
the universe. Earth seems to have no special significance to the rest of the
universe. This knowledge made it seem more likely that many other stars
should have solar systems and that some of those solar systems might have
Earth-like planets, so a great deal of study focused on the search for
Exoplanets; with a number of confirmations.
Speculations about the existence of Exoplanets have been ongoing
since the time of Newton’s General Scholium (1713). Newton hinted that
other stars had planets orbiting them just as our Sun [6]. The first claims of a
detection of an Exoplanet were centered on the star 70 Ophiuchi. In 1855
Jacob claimed that the orbit of the binary system exhibited an anomaly. A
third body, an Exoplanet, was held responsible [7]. In the 1890’s, Jackson
supported these claims based on orbital movement as well when the orbital
anomalies proved the existence of a dark body in the 70 Ophiuchi system with
a 36 year period around one of the stars [8]. In 1899, his claims were
disproved by Moulton. Moulton analyzed the triple system and demonstrated
that it would be unstable under the orbital parameters put forth [9].
In the 1960’s, Kamp claimed that Barnard's star had an Exoplanet.
This claim had been based on an apparent wobble in the star’s motion [10].
Kamp spent 40 years studying the Barnard star. Observations made by other
telescopes were never able to replicate the date of the wobble.
۳
Chapter One
General Introduction
It is believed that the wobble was an anomaly of equipment at Sproul
Observatory. There are still no conclusive evidences for or against a planet
existing around Barnard’s star [4].
The first detection to be later confirmed of an Exoplanet was made in
1988 by Campbell et.al. The star Gamma Cephei was tentatively proposed to
have an Exoplanet based on radial velocity observations. It was given a
tentative status because the observations were made at a very limit of the
capability of the instruments at the time [11].
In the early 1990’s, Wolszczan and Frail (1992) made an exciting
discovery of planets far from the solar system in orbit around the pulsar PSR
B1257+12 [12]. They proved there were two planets of 2.8 and 3.4 Earth
masses orbiting the pulsar PSR B1257+12 at 0.46 and 0.36 AU respectively
[13]. A third planet was discovered later of 0.025 Earth masses orbiting at
0.19 AU. This discovery is considered to be the first definitive detection of an
Exoplanet, because the Campbell et.al discovery was not confirmed till 2003.
This was a rather strange discovery because it was revolving around a pulsar
rather than a main sequence star like the Sun [14]. It is worth mentioning,
pulsars are different from the Sun and any planets orbiting them would not be
expected to harbor life as in the solar system [12]. The first discovery of an
Exoplanet orbiting a main sequence star, 51 Pegasi, was announced on
October 6, 1995 by Mayor and Queloz [15]. They used the radial velocity
method to detect the planet. After their discovery numerous Exoplanets have
been detected as a result of improved telescopes with higher resolutions and
more powerful data processing computers [14].
Most Exoplanets detected were massive Jupiter-like planets. Most
likely this is due to the ease of detecting Jupiter-like planets in comparison to
smaller terrestrial planets. New kinds of planets not found in the solar system,
٤
Chapter One
General Introduction
labeled Super-Earths, have also been detected. They are about 5 to 10 Earth’s
mass [16].
In 2008, NASA announced the discovery of an Extrasolar planet orbiting just
around a star Fomalhaut [17]. This was the first Extrasolar planet to be
directly imaged by Hubble Space Telescope. In 2009, Fischer et.al announced
the discovery of five Extra-solar planets revolving around the star (HD
196885Ab) [18].
The rate of discovery of Exoplanets has been steadily increasing each
year due to improved technology and a greater interest in Exoplanets, with 61
planets being detected in 2007 [14] to 473 planets being detected till 2010. As
techniques and technology improve, astronomers may be able to find smaller
planets in more distant orbits around other stars. The space telescopes Kepler
and COnvection ROtation and planetary Transits (COROT) are designed to
detect planets about the size of Earth or smaller.
1.3 Types of Extrasolar planets
Scientists divide the major planets found in the solar system into
different categories. The inner planets Mercury, Venus, Earth, and Mars are
rocky or terrestrial planets. The outer planets Jupiter, Saturn, Uranus, and
Neptune are giant worlds surrounded by thick, primitive atmospheres mainly
made of hydrogen and helium. Planets around the other stars likely fall into
some of these categories.
Some of these types are:
·
·
·
·
·
Hot Jupiter
Hot Neptune
Super- Earth
Pulsar planet
Ocean planet
٥
General Introduction
Chapter One
1.3-1 Hot Jupiter
Hot Jupiters (also called epistellar jovians, pegasids or pegasean
planets) are a class of Extrasolar planets whose mass is close to or exceeds
that of Jupiter (1.9 × 1027 kg), but unlike in the solar system, where Jupiter
orbits at 5.2 AU, the planets referred to as hot Jupiters orbit between 0.15 and
0.5 AU of their parent stars, figure (1.1) shows a hot Jupiter planet. One of the
most well-known hot Jupiters is 51 Pegasi b, discovered in 1995 [19].
Figure (1.1) Illustrates a hot Jupiter planet.[19]
Hot Jupiters have some common characteristics:
1. They have a much greater chance of transiting their star as seen from a
farther outlying point than planets of the same mass in larger orbits.
The most famous of these are HD 209458 b, the first transiting hot
Jupiter found, and HAT-P-7b, which was observed by the Kepler
mission.
2. Due to high levels of insolation they are of a lower density than they
would otherwise be. This has implications for radius determination,
because due to limb darkening of the planet against its background
٦
Chapter One
General Introduction
star during a transit, the planet's ingress and egress boundaries are
harder to determine.
3. They all have low eccentricities. This is because their orbits have been
circularized, or are being circularized. This also causes the planet to
synchronize its rotation and orbital periods, so it always presents the
same face to its parent star - the planet becomes tidally locked to the
star.
Hot Jupiters are the easiest Extrasolar planets to detect via the radial
velocity method, because the oscillations they induce in their parent stars'
motion are relatively large and rapid, compared to other known types of
planets.
Hot Jupiters are thought to form at a distance from the star beyond the ice
line, where the planet can be formed from rock, ice and gasses. The planets
then migrate inwards to the Sun where they eventually form a stable orbit
[19].
1.3-2 Hot Neptune
A hot Neptune is a theoretical Extrasolar planet in an orbit close to its
star (normally less than one astronomical unit away). The mass of a hot
Neptune resembles the core and envelope mass of Uranus and Neptune [20].
۷
General Introduction
Chapter One
1.3-3 Super-Earth
A super-Earth is a class of Extrasolar planet with a mass between that
of Earth and the solar system's gas giants [16], figure (1.2) shows a superEarth planet between Earth and Neptune. In general, super-Earths are defined
exclusively by their mass, and the term does not imply temperatures,
compositions, orbital properties, or environments similar to Earth.
Figure (1.2) Illustrates the inferred size of the super-Earth GJ
1214 b (center) in comparison with Earth and Neptune.[23]
A variety of specific mass values are cited in definitions of super-Earths.
Generally the mass upper bound to 10 times Earth’s mass [16, 21, and 22], the
lower bound varies from 1 [16] or 1.9 [22] to 5 [21].
Solar system does not contain examples of this category of planets, as the
largest terrestrial planet in the solar system is the Earth, and all larger planets
have at least 14 times Earth's mass [23].
۸
Chapter One
General Introduction
The first super-Earths were discovered in 1992 around the pulsar PSR
B1257+12. The two outer planets of the system have masses approximately
four times Earth, too small to be gas giants [23].
The first super-Earth around a main sequence star was discovered in 2005. It
orbits Gliese 876 and received the designation Gliese 876 d (two Jupiter sized
gas giants had previously been discovered in that system). It has an estimated
mass of 7.5 times Earth’s mass and a very short orbital period of just about 2
days [24].
1.3-4 Pulsar planet
Pulsar planets are planets that are found orbiting pulsars, or rapidly
rotating neutron stars. The first such planet to be discovered was around a
millisecond pulsar and was the first Extrasolar planet to be discovered.
Pulsar planets are discovered through pulsar timing measurements, to detect
anomalies in the pulsation period. Any bodies orbiting the pulsar will cause
regular changes in its pulsation. Since pulsars normally rotate at near-constant
speed, any changes can easily be detected with the help of precise timing
measurements. The discovery of pulsar planets was unexpected, because since
pulsars or neutron stars have previously gone supernova, any planets orbiting
such stars would have been destroyed in the explosion [25].
The first Extrasolar planet had been discovered orbits around PSR
1829-10 in 1991 by Lyne [26], but this discover was later retracted [27], just
before the first real pulsar planets were announced. In 1992 where Wolszczan
and Frail announced the discovery of a multi-planet planetary system around
the millisecond pulsar PSR 1257+12 [13] as shown in figure (1.3).
۹
Chapter One
General Introduction
Figure (1.3) Illustrates the conception of PSR 1257+12's
system of planets.[25]
These were the first two confirmed Extrasolar planets discovered, and
thus the first multi-planet Extrasolar planetary system discovered, and the first
pulsar planets discovered. There was doubt concerning the discovery because
of the retraction of the previous pulsar planet, and questions about how
pulsars could have planets. However, the planets proved to be real. Two
additional planets of lower mass were later discovered by the same technique
[28].
۱۰
General Introduction
Chapter One
1.3-5 Ocean planet
An ocean planet (also termed a waterworld) is a hypothetical type of
planet whose surface is completely covered with an ocean of water. Figure
(1.4) shows a type of ocean planet [29].
Figure (1.4) Illustrates a hypothetical ocean planet
with a terrestrial atmosphere and two satellites.[29]
Planetary objects that form in the outer solar system begin as a comet-like.
Simulations of solar system formation have shown that planets are likely to
migrate inward or outward as they form, presenting the possibility that icy
planets could move to orbits where their ice melts into liquid form, turning
them into ocean planets. This possibility was first discussed in the
professional astronomical literature by Kuchner. Such planets could therefore
theoretically support life [29].
The Extrasolar planet GJ 1214 b is the most likely known candidate
for an ocean planet [30]. Many more such objects are expected to be
discovered by the ongoing Kepler spacecraft mission [29].
۱۱
Chapter One
General Introduction
1.4 Studying Extrasolar planets
Extrasolar planets are fascinating because they may solve mysteries
about the solar system. There is a wealth of data available to study different
types of galaxies and stars, which have enabled astronomers to develop
models and theories about star and galaxy formation and to place our galaxy
and stars amongst them. The solar system is 4.6 billion years old, but there is
no way to measure directly how it formed and it was, until recently, the only
planetary system that we knew of, so there was nothing to compare it with.
We had no idea if it was one of many, a typical example of a planetary system
or a unique one-off. Studying the formation of other young planetary systems
may give us answers.
Protoplanetary discs are regions of dust and gas orbiting very young stars,
where planets are formed. Current theories of planetary formation suggest that
dust particles start to collapse under the power of gravity and stick together,
forming bigger and bigger grains. If young protoplanetary discs survive the
threat of stellar radiation and impacts by comets and meteorites, then matter
continues to clump together and eventually planetoids may form. Planetoids
are celestial objects bigger than meteorites and comets, but smaller than
planets. After a few million years, most of the circumstellar dust will have
been swept away as planetoids accumulate mass and grow into planets [31].
۱۲
Chapter One
General Introduction
Most of the planets found so far are large, gaseous and very close to
their star, unlike the situation in the solar system. The concept of orbital
migration has been revived to explain the close proximity of some giant
planets to their star: these planets may have formed undisturbed relatively far
from the star and then slowly spiralled inwards over time [31].
The ultimate goal of searching Extrasolar is to find a planet that would
be capable of supporting life, and for more reason's search for Extrasolar
planet which considered important. These reasons can be scheduled as:
1.
To test the current understanding of the formation of (extra) solar
systems.
2.
To develop the insight into the formation of individual planets.
3.
To assist in the search for extraterrestrial life [32].
Different techniques were used for the detection of Extrasolar planets by
researchers, which will be discussed in details in chapter two.
۱۳
Chapter Two
Detection methods of Extrasolar planets
2.1 Introduction
Within the last several years a great deal of study has been focused on
the search for Extrasolar planets; the discovery of the first planets around a
pulsar (1992) and around a main sequence star different from the Sun (1995)
has opened, after centuries of speculation, a new era in astronomy. The
motivations for the search are continued. A comparative review has been
given for different techniques for their detection. Special attention is paid to
the planetary parameters for each detection method [1].
In this chapter, each detection method will be described in general manner
and the explanation of the general astrophysical parameters is given.
Planets reflect light from their parent star, and approximately one billion
times less luminous. So planets are extremely faint light sources compared to
their parent stars. In addition to the difficulty of detecting such a faint light
source, the parent star causes a glare that washes it out.
Therefore the direct detection of Extrasolar planets is extremely difficult. This
is primarily due to:
1.
Exoplanets appear extremely close to their host stars when observed at
large astronomical distances. Even the closest of stars are several light
years away. This means that while looking for Exoplanet, one would
typically be observing very small angles from the star.
2.
Exoplanets are extremely dim compared to their host stars. The star
will be approximately a billion times brighter than the orbiting planet.
This makes it near-impossible to see planets against the star's glare [33].
For those reasons, current telescopes can only directly image Exoplanets
under exceptional circumstances because they are very unusual planets.
Specifically, it is most likely to be possible when the planet is especially large
(considerably larger than Jupiter), widely separated from its parent star, and
hot enough so that it emits intense infrared radiation [5].
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The search for Extrasolar planets was unsuccessful until recently,
because the different methods of detection were not sensitive enough. But
today the instrumentation has reached a level of sensitivity sufficient to
enable the first discoveries. This difficulty of observing such a dim planet so
close to a bright star is the drawback that has prevented astronomers from
directly imaging Exoplanets. Therefore astronomers resort to indirect methods
to detect Extrasolar planets. However Extrasolar planets can be detected
either by direct or indirect methods. Each detection method is characterized
by some observables which are related to the intrinsic physical parameters of
the planet. These parameters are: their mass MP, radius RP, temperature TP,
distance aP (semi-major axis) from the parent star, orbital period P,
luminosity LP and distance D from the solar system, it is considered that the
majority of Exoplanets orbits are circular, since the planets are very closer to
their stars mother [34].
To investigate these planetary systems, several methods of detection and
observation had been used as listed below:
1. Established detection methods
§
§
§
§
§
§
§
Astrometry
Radial velocity
Pulsar timing
Transit
Gravitational microlensing
Circumstellar disks
Direct imaging
2. Other possible methods
§
§
§
Eclipsing binary minima timing
Orbital phase reflected light variations
Polarimetry
3. Observation space missions
§
§
Previous space missions
Future space missions
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2.2 Established detection methods
2.2-1 Astrometry
Astrometry is the oldest method to search for Extrasolar planets and
originally popular because of its success in characterizing astrometric binary
star systems. It dates back at least to statements made by Herschel in the late
18th century. Herschel claimed that an unseen companion was affecting the
position of the star he cataloged as 70 Ophiuchi. The first known formal
astrometric calculation for an Extrasolar planet was made by Jacob in 1855
for this star.
This method consists of precisely measuring a star's position in the sky and
observing how that position changes over time. If the star has a planet, then
the gravitational influence of the planet will cause the star itself to move in a
tiny circular or elliptical orbit. Effectively, star and planet each orbit around
their mutual center of mass (barycenter), as explained by solutions to the twobody problem. An example is given in the image presented in figure (2.1).
Since the star is much more massive, its orbit will be much smaller [35].
Figure (2.1) Illustrates the orbit of planet around
its parent star, a center of mass marked as (+) [35].
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This method measures a periodic variation in the position of the star on the
‘plane of the sky’, subtracting out the star’s apparent motion due to the yearly
parallax motion and the projection of its real proper motion through space.
The motion of a star around the barycenter thus describes an elliptical motion
with semi-major axis (in arcseconds) of:
………………………………… (2.1)
Where: ap is the semi-major axis of the orbit, D the distance to the stellar
system, is given in parsecs, Mp is the mass of planet, M* is the mass of the
star.
This technique measures the motion of the photometric centroid
position of the star in images taken over at least a large fraction of a planet’s
orbit. It is complementary, for example, to the radial velocity detection
method in that it is most sensitive to long period (large semi-major axis)
planets, while the radial velocity method is most sensitive to short-period
planets with higher velocity variations [36].
In 2002, however, the Hubble Space Telescope succeeded in using
astrometry to characterize a previously discovered planet around the star
Gliese 876 [37].
Upcoming wide field searches for transiting planets (for example, the
National Aeronautics and Space Administration (NASA) Kepler mission
2009) may also allow astrometric searches for planets to take place using the
same photometric data, since the pointing precision as well as the photometric
centroiding of star images should be near the one milliarcsecond precision
required for astrometry. Near-term spacecraft missions such as Space
Interferometry Mission (SIM) will be specifically designed to optimize
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astrometric measurements both for stellar parallax determinations and the
detection of Extrasolar planets in the solar neighbourhood astrometrically.
SIM should be able to detect nearby Extrasolar planets while mapping exact
distances to stars by using interferometry to accurately measure astrometric
wobbles of stars, caused by orbiting planets, to about one microarcsecond in
angular resolution [36]. SIM devoted mainly to astrometry and, secondarily,
to imaging.
The advantage of the astrometric method is that it is most sensitive to
planets with large orbits as mentioned before. This makes it complementary to
other methods that are most sensitive to planets with small orbits. However,
very long observation times will be required years, and possibly decades, as
planets are far enough from their star to allow detection via astrometry also
take a long time to complete an orbit.
In 2009 the discovery of the planet VB 10 b by astrometry was announced.
This planetary object was reported to have a mass 7 times that of Jupiter and
orbiting the nearby low mass red dwarf star VB 10 [35].
2.2-2 Radial velocity
The radial velocity method also known as Doppler spectroscopy uses
the fact that a star with a planet will move in its own small orbit in response to
the planet’s gravity similar to the theory in the astrometric method. The goal
from this technique is to measure variations in the speed with which the star
moves toward or away from Earth. In other words, the variations are in the
radial velocity of the star with respect to Earth. The radial velocity can be
deduced from the displacement in the parent star’s spectral lines due to the
Doppler Effect as shown in figure (2.2) [35].
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Figure (2.2) Illustrates the Doppler blue shift and red shift [35].
The stellar spectral lines will move periodically redward or blueward
due to the Doppler shift caused by the periodic motion, with a maximum
velocity v of the star about the barycenter. The Doppler shift for ordinary
objects can be expressed by:
; v << c …………………………….. (2.2)
Where: Z is the Doppler shift, v is the velocity of the object, c is the velocity
of the light, λ is the rest wavelength and Δλ=λ̀ – λ (λ̀ is the observed
wavelength).
While the relativistic Doppler shift can be expressed by:
; v < c ………………………… (2.3)
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The equation above used for object like quasars moving with a velocity
comparable with the velocity of light.
Again, the spectral line variations only measure the component of the motion
directly towards or away from the observer, and hence the mass of the body
(planet) causing the reflex motion of the star is a minimum mass measurement
for the planet, (Mp sin i).
The maximum amplitude of this periodic radial velocity variation for the star
K* is given by:
.…………… (2.4)
Where: P is the planetary orbital period, i is the inclination of the planet’s
orbit (i = 90◦ being edge-on), e is the planetary orbital eccentricity, and G is
the gravitational constant [36].
The derivation of equation (2.4) is explained in the following:
The radial velocity amplitude of the host star is expressed by:
…………………………………………. (2.5)
Where a* is the semi-major axis of the star.
The radial velocity amplitude of orbiting planet is expressed by:
………………………………………… (2.6)
Radial velocity method involves taking precise measurements of the star’s
radial velocity; therefore equation (2.5) is used to determine the radial
velocity amplitude.
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From Kepler’s 3rd law
…………………………………… (2.7)
Solving equation (2.7) for ap gives:
……………………………….. (2.8)
From the definition of center of mass
Solving for a*
…………………………………………….. (2.9)
Substituting equation (2.9) into equation (2.5)
…………………………….... (2.10)
Substituting equation (2.8) into equation (2.10)
………………… (2.11)
Simplifying equation (2.11)
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Then
For more simplifying
When M* >> Mp then
M*+Mp ≈ M*
………………….. (2.12)
The velocity of the star around the center of mass is much smaller
than that of the planet because the radius of its orbit around the center of mass
is so small. Velocity variations down to 1 m/s can be detected with modern
spectrometers, such as the High Accuracy Radial velocity Planet Searcher
(HARPS) spectrometer at the European Southern Observatory (ESO) 3.6
meter telescope in La Silla Observatory, Chile.
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Finding massive planets that are close to stars are easy, but detection of those
orbiting at great distances requires many years of observation. Planets with
orbits highly inclined to the line of sight from Earth produce smaller wobbles,
and are thus more difficult to detect [35].
The disadvantage of the radial velocity method is that it can only estimate a
planet's minimum mass, because can’t defined the orbital plane orientations.
If the planet's orbit is almost perpendicular to the line of sight, then the true
mass will be much higher [35].
As mentioned before, the first confirmed use of the radial velocity
technique to detect a planet orbiting a distant star was in 1995. The star was
51 Pegasi, and the planet was named 51 Pegasi b, also unofficially named
Bellerophon and abbreviated as 51 Peg b.
51 Peg b is an Extrasolar planet approximately 50 light years away in the
constellation of Pegasus. It was the first ever planet to be discovered orbiting
a Sun-like star. It is the prototype for a class of planets called hot Jupiters
[38].
The Doppler measurements were sensitive enough to measure radial
speeds down to 12 m/s. The orbital period was 4.2 days, and the calculated
mass of the planet was, at a minimum, half the mass of Jupiter [39].
The planet lies about 0.05 AU from 51 Peg, with a temperature of 1,300 Kº,
and an orbit having an eccentricity of approximately 0.09, indicating a near
circular orbit. It should be noted that Mercury lies between 0.3 and 0.4 AU
from the Sun, making 51 Peg b much closer to 51 Peg than Mercury is to the
Sun. [4] This make us to wonder how could a planet as large as Jupiter form
so close to its Sun?
Lin and others [40] believe that 51 Peg b did not form at its current location.
Instead, it formed from an amassing of solids and gases at about 5
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Detection methods of Extrasolar planets
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astronomical units from 51 Peg. They feel that it began to approach the star,
stopping at its present location due to the result of tidal interactions (inward
and outward forces on the planets orbit) [4].
Since the discover of 51 Peg b, the radial velocity technique has been the
most productive means of detecting Extrasolar planets [39].
Figure (2.3) illustrates the number of planets discovered by this method which
reached to (442) [2].
Figure (2.3) Shows the number of discovered Extrasolar planets by Radial
velocity method till July 2010 [2].
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Detection methods of Extrasolar planets
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2.2-3 Pulsar timing
A pulsar is a neutron star: the small, ultradense remnant of a star that
has exploded as a supernova. Pulsars emit radio waves extremely regularly as
they rotate. Because the intrinsic rotation of a pulsar is so regular, slight
anomalies in the timing of its observed radio pulses can be used to track the
pulsar's motion. Like an ordinary star, a pulsar will move in its own small
orbit if it has a planet. Calculations based on pulse-timing observations can
then explain the parameters of that orbit [35].
The variation in timing can occur due to a positional shift in the pulsar around
the pulsar–planet barycenter. If such a second mass (planet) is in orbit around
the pulsar, the two bodies will orbit around a mutual barycenter, each distance
from the barycenter being determined directly by their mass-ratios, where M*
and a* are the mass and distance (semi-major axis) from the barycenter to the
center of the pulsar and Mp and ap are the mass and distance from the
barycenter to the planet. The motion of the pulsar around the barycenter
causes the addition of (or subtraction of) the light travel time across this
distance, which will result in a delay (or early) arrival of the periodic
variations in the timing of the pulsar pulses [36].
For a planet in a circular orbit, the maximum amplitude of the delay time
(τ) will be [36]:
……………………………. (2.13)
This method was not originally designed for the detection of planets, but is so
sensitive that it is capable of detecting planets far smaller than any other
method can, down to less than a tenth the mass of Earth. It is also capable of
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Detection methods of Extrasolar planets
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detecting mutual gravitational perturbations between the various members of
a planetary system, thereby revealing further information about those planets
and their orbital parameters.
The drawback of the pulsar-timing method is that pulsars are relatively rare,
so we can't find a large number of planets by this way. Also, life could not
survive on planets orbiting pulsars where high-energy radiation is extremely
intense [35].
In 1992 Wolszczan and Frail used this method to discover planets
around the pulsar PSR 1257+12 [13]. Their discovery was quickly confirmed,
making it the first confirmation of planets outside the solar system.
Figure (2.4) illustrates the number of planets discovered by this method which
reached to (8) [2].
Figure (2.4) Shows the number of discovered Extrasolar planets by Pulsar timing
method till July 2010 [2].
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Detection methods of Extrasolar planets
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2.2-4 Transit
When a planet crosses the stellar disk as seen from observer, it will
block part of the star’s light. This phenomenon, called a transit, can be
observed if the orbital axis of the planet is closely perpendicular to the line of
sight, figure (2.5) shows the transit of the planet in front its star [12].
Figure (2.5) The transit of a planet in front its star
(upper) [35] the photometry of this transit is also
shown (lower) [41].
This photometric method can determine the radius of a planet. If a planet
crosses (transits) in front of its parent star's disk, then the observed visual
brightness of the star drops a small amount. The amount the star dims
depends on the relative sizes of the star and the planet [35].
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In the solar system, Mercury transits the Sun several times per century
and Venus transits the Sun only once (or twice) every 100 years. For
Extrasolar planets, the probability to transit depends on the orientation of the
planet-star system [41] as shown in figure (2.6b).
Figure (2.6) (a) Schematic diagram of a planet transit. When a
planet (represented by the small, dark disk) passes in front of its
parent star, the stellar flux (lower part of a) drops by the ratio of
the planet-to-star areas. This is the case even though stars cannot
be spatially resolved as shown in this diagram.
(b) An Extrasolar planet transit will occur only when the planetstar geometry is favorable. Upper diagram shows such a system.
In contrast, the lower diagram shows a planet orbit that will never
pass in front of the parent star. In reality geometries anywhere in
between these will occur [41].
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The geometric probability for a planet-star system to be oriented to
show transits is the ratio of the stellar radius to planet semi-major axis and
expressed by:
…………………………………….. (2.14)
Where R* represent the stellar radius and a is the semi-major axis. This
formula is valid for the case of a circular orbit. From this equation it can be
seen that the transit technique is more sensitive to short period planets. While
for a 3 day short period orbit hot Jupiter P is close to 10%, for a planet at one
AU from its parent star (Period close to one year) P goes down to 0.5%.
If a transit event is observed, the expected luminosity variation can be derived
to be of the order of:
………………………………….. (2.15)
For a Jupiter like planet, Rp ≈ 0.1 R*, inducing thus a photometric variation of
the order of 1%. Much lower values are expected for transits of Neptune or
Earth like planets.
Finally, in the case of an equatorial transit (best case scenario), the transit
duration (t) can be derived from:
……………………………. (2.16)
Where R*, M*, and a are expressed in solar units and AU, respectively.
Usual transit times are of a few hours for short period planets [12].
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This method has two major disadvantages. First of all, planetary
transits are only observable for planets whose orbits happen to be perfectly
aligned from astronomers' vantage point. About 10% of planets with small
orbits have such alignment, and the fraction decreases for planets with larger
orbits. Secondly, the method suffers from a high rate of false detections.
Transit detection requires additional confirmation, especially from the radial
velocity method [35].
The advantage of the transit method is that the size of the planet can be
determined from the light curve. When combined with the radial velocity
method (which determines the planet's mass) one can determine the density of
the planet, and hence learn something about the planet's physical structure
[42].
The transit method also makes it possible to study the atmosphere of
the transiting planet. When the planet transits the star, light from the star
passes through the upper atmosphere of the planet. By studying the highresolution stellar spectrum carefully, one can detect elements present in the
planet's atmosphere. A planetary atmosphere could also be detected by
measuring the polarization of the starlight as it passed through or is reflected
off the planet's atmosphere. In the secondary eclipse (when the planet is
blocked by its star) allows direct measurement of the planet's radiation. If the
star's photometric intensity during the secondary eclipse is subtracted from its
intensity before or after, only the signal caused by the planet remains. It is
then possible to measure the planet's temperature and even to detect possible
signs of cloud formations on it [35].
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A French Space Agency mission, COROT, began in 2006 to search
for planetary transits from orbit as mentioned before, where the absence of
atmospheric scintillation allows improved accuracy. This mission was
designed to be able to detect planets "a few times to several times larger than
Earth" and is currently performing , with two Exoplanet discoveries [43]
(both "hot Jupiter" type).
In March 2009, NASA Kepler Mission was launched to scan a large
number of stars in the constellation Cygnus with a measurement precision
expected to detect and characterize Earth-sized planets. The NASA Kepler
Mission Telescope as illustrated in figure (2.7) uses the transit method to scan
a hundred thousand stars in the constellation Cygnus for planets [35].
Figure (2.7) The Kepler Mission Telescope, a NASA mission
which is able to detect Extrasolar planets [35].
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Kepler Telescope will be sensitive enough to detect planets even
smaller than Earth. By scanning a hundred thousand stars simultaneously, it
will not only be able to detect Earth-sized planets, it will be able to collect
statistics on the numbers of such planets around Sun-like stars [35]. The
COROT and Kepler Missions will be explained in some details later in this
chapter.
Figure (2.8) illustrates the number of planets discovered by this method which
reached to (91) [2].
Figure (2.8) Shows the number of discovered Extrasolar planets by Transit
method till July 2010 [2].
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Chapter Two
2.2-5 Gravitational microlensing
When two stars become closely aligned, the one in front (the lens)
bends the light from the one in back (the source), the source is then broken up
into two images, each of which is distorted and magnified [44] as shown in
figure (2.9).
Figure (2.9) Schematic diagram of Gravitational
Microlensing [35].
The planet can produce a gravitational amplification of the light of
background stars, increasing with the planet’s mass and its distance to the
observer. This amplification can reach factors up to 100 when the planet lies
at several kiloparsecs, i.e. as far as the galactic center. The Gravitational
microlensing method is thus suitable only for very distant planets, difficult to
observe afterwards by any other method. Furthermore, a lensing event is seen
only once and it is not possible to investigate a planet at 4 kpc any further by
any other method. This makes the lensing method less attractive [1].
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This method is most fruitful for planets between Earth and the center of the
galaxy, as the galactic center provides a large number of background stars
[35].
Due to general relativistic effects of bending spacetime, a star moving very
close to alignment with a background star will bend that is; focus the light of
the background star, causing a temporary increase in the combined brightness
of the stars by amplifying the light from the background star [36]. The
phenomenon, first observed with galaxies, is known as Gravitational lensing.
A perfect stellar alignment will cause symmetric images around the lensing
star; this is known as the ‘Einstein ring’ (or sometimes an ‘Einstein cross’).
The Einstein ring radius is given by:
………………………. (2.17)
Where: M*L is the mass of the lensing star, DL is the distance to the lensing
star, DS is the distance to the source star, G is the gravitational constant and c
is speed of light. Figure (2.10) illustrates the geometry of the gravitational
lens with the distances between lensing star, source star and observer.
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Detection methods of Extrasolar planets
Chapter Two
Einstein Ring
θ
O
obsever
Sourec (star)
Lens (star)
DL
DLs
Ds
Figure (2.10) Illustrates the geometry of the gravitational lens with the
distances between lensing star, source star and observer.
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The angle on the sky of the Einstein radius (the Einstein angle) is then given
as:
………………………………………. (2.18)
The microlensing magnification, which varies with time, is given by:
………………………. (2.19)
Where: u(t) is the projected distance between the image of the lensing star
and the source star in units of the Einstein radius.
If a planet is in orbit around the lensing star, then observable deviations from
the amplification pattern given by equation (2.19) may occur, which are
caused by a planet-mass distorting the stellar gravitational field.
The probability of alignment among two stars is, even in the galactic center,
only about one in 106, but once a star is aligned with another star the
probability that a planet may also cause an amplification that exceeds 5% of
the brightness of the star’s amplification itself becomes about one in five. For
this superposition of a brightening due to a planet on top of that due to the
amplified star, the term M*L becomes the mass of the planet, Mp in equation
(2.17) [36].
The duration of a microlensing event is given by:
………………………… (2. 20)
Where: d is the distance to the lensing star in parsecs and V is the orbital
velocity [36].
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In 1991, group of astronomers from Princeton University used
Gravitational microlensing to look for Exoplanets. Successes with the method
date back to 2002, when a group of Polish astronomers during project Optical
Gravitational Lensing Experiment (OGLE) developed a workable technique.
Since then, four confirmed Extrasolar planets have been detected using
microlensing. As of 2006 this was the only method capable of detecting
planets of Earth-like mass around ordinary main-sequence stars [45].
The disadvantage of this method is that the lensing cannot be repeated
because the chance alignment never occurs again. Also, the detected planets
will tend to be several kiloparsecs away, so follow-up observations with other
methods are usually impossible. However, if enough background stars can be
observed with enough accuracy then the method should eventually reveal how
common Earth-like planets are in the galaxy [35].
Figure (2.11) illustrates the number of planets discovered by this method
which reached to (10) [2].
Figure (2.11) Shows the number of discovered Extrasolar planets by
Gravitational Microlensing method till July 2010 [2].
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2.2-6 Circumstellar disks
Disks of space dust (debris disks) surround many stars. The dust can
be detected because it absorbs ordinary starlight and re-emits it as infrared
radiation. Even if the dust particles have a total mass well less than that of
Earth, they can still have a large enough total surface area that they outshine
their parent star in infrared wavelengths [46].
The Hubble Space Telescope is capable of observing dust disks with its Near
Infrared Camera and Multi-Object Spectrometer (NICMOS) instrument.
Even better images have now been taken by Hubble Space Telescope another
instrument just like it, the Spitzer Space Telescope, which can see far deeper
into infrared wavelengths than the Hubble can.
The dust is believed to be generated by collisions among comets and
asteroids. Radiation pressure from the star will push the dust particles away
into interstellar space over a relatively short timescale. Therefore, the
detection of dust indicates continual replenishment by new collisions, and
provides strong indirect evidence of the presence of small bodies like comets
and asteroids that orbit the parent star [47].
More speculatively, features in dust disks sometimes suggest the
presence of full-sized planets. Some disks have a central cavity, meaning that
they are really ring-shaped. The central cavity may be caused by a planet
"clearing out" the dust inside its orbit as illustrated in figure (2.12). Other
disks contain clumps that may be caused by the gravitational influence of a
planet. Both these kinds of features are present in the dust disk around epsilon
Eridani, hinting at the presence of a planet with an orbital radius of around 40
AU [48].
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Figure (2.12) Illustrates two Pluto-sized
dwarf planets in a collision around Vega [35].
2.2.7. Direct imaging
As mentioned previously, planets are extremely faint light sources
compared to stars and the light that comes from them tends to be lost in the
glare from their parent star. So in general, it is very difficult to detect them
directly. In certain cases, however, current telescopes may be capable of
directly imaging planets with developed instrument. Projects to equip the
current
generation
of
telescopes
with
new,
planet-imaging-capable
instruments are underway at the Gemini telescope, Gemini Planet Imager
(GPI), the Very Large Telescope (VLT), and the Subaru telescope High
Contrast Instrument with Adaptive Optics (HiCIAO) [35].
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As explained above planets have generally no intrinsic emission, at
least in the optical wavelength range. One can only detect their illumination
by the parent star. A planet orbiting around a star with a luminosity L*
acquires by reflection a luminosity Lp given by [34]:
………………………. (2.21)
Where A is the planet albedo, φ( t ) is an orbital phase factor given by:
…………………… (2.22)
Where i is the inclination of the orbit with respect to sky plane.
In July 2004, a group of astronomers used the European Southern
Observatory's Very Large Telescope array in Chile to produce an image of
2M1207 b, a companion to the brown dwarf 2M1207 [49]. In December
2005, the planetary status of the companion was confirmed. The planet is
believed to be several times more massive than Jupiter and to have an orbital
radius greater than 40 AU [35].
The first multiplanet system, announced on 13 November 2008, was imaged
in 2007 using telescopes at both Keck Observatory and Gemini Observatory.
Three planets were directly observed orbiting HR 8799, whose masses are
approximately 10, 10 and 7 time that of Jupiter [50]. On the same day, 13
November 2008, it was announced that the Hubble Space Telescope directly
observed an Exoplanet orbiting Fomalhaut with mass no more than 3 times
Jupiter’s mass [17]. Both systems are surrounded by disks not unlike the
Kuiper belt. An additional system, GJ 758, was imaged in November of 2009,
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by a team using the HiCIAO instrument of the Subaru telescope [51] as
shown in figure (2.13).
Figure (2.13) Discovery image of the GJ 758
system, taken with Subaru Telescope HiCIAO in the
near infrared [5].
Figure (2.14) illustrates the number of planets discovered by this method
which reached to (13) [2].
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Chapter Two
Figure (2.14) Shows the number of discovered Extrasolar planets by Direct
imaging method till July 2010 [2].
2.3 Other possible methods
2.3-1 Eclipsing binary minima timing
An "eclipsing binary" star system is a system of a double star aligned
such that the stars pass in front of each other in their orbits. The time of
minimum light, when the star with the brighter surface area is at least partially
obscured by the disc of the other star, is called the primary eclipse, and the
secondary eclipse occurs when the brighter surface area star obscures some
portion of the other star. These times of minimum light, or central eclipse,
constitute a time stamp on the system, much like the pulses from a pulsar
(except that rather than a flash, they are a dip in the brightness). If there is a
planet in circum-binary orbit around the binary stars, the stars will be offset
around a binary-planet center of mass. As the stars in the binary are displaced
by the planet back and forth, the times of the eclipse minima will vary; they
will be too late, on time, too early, on time, too late, etc... The periodicity of
٤٤
Chapter Two
Detection methods of Extrasolar planets
this offset may be the most reliable way to detect Extrasolar planets around
close binary systems [52-54].
2.3-2 Orbital phase reflected light variations
Short period giant planets in close orbits around their stars will
undergo reflected light variations changes because, like the Moon, they will
go through phases from full to new and back again. This method may actually
constitute the most planets that will be discovered by Kepler mission because
the reflected light variation with orbital phase is largely independent of orbital
inclination of the planet's orbit [55].
2.3-3 Polarimetry
Light coming from a star is un-polarized, i.e. the direction of
oscillation of the light wave is random. However, when the light is reflected
off the atmosphere of a planet, the light waves interact with the molecules in
the atmosphere and they become polarized [56].
By analyzing the polarization in the combined light of the planet and star
(about one part in a million), these measurements can in principle be made
with very high sensitivity, as polarimetry is not limited by the stability of the
Earth's atmosphere.
Polarimeters are astronomical devices that used for polarimetry, they are
capable of detecting the polarized light and rejecting the unpolarized beams
(starlight), though no planets have yet been detected using this method [35].
٤٥
Chapter Two
Detection methods of Extrasolar planets
2.4 Observations space missions
Several space missions are planned that will employ already proven
planet detection methods. Astronomical measurements done from space can
be more sensitive than measurements done from the ground, since the
distorting effect of the Earth's atmosphere is removed, and the instruments
can view in infrared wavelengths that do not penetrate the atmosphere. Some
of these space probes should be capable of detecting planets similar to the
Earth [35].
The observation space missions are divided to:
1. Previous space missions
2. Future space missions
2.4-1 Previous space missions used to detect Extrasolar planets
Almost all known Extrasolar planet candidates have been found using
ground-based telescopes. However, many of the methods can yield better
results if the observing telescope is located above the restless atmosphere [5].
COROT (launched in 2006) and Kepler, (launched in 2009) are the only
active space missions dedicated to Extrasolar planet search. Hubble Space
Telescope and Spitzer Space Telescope have found or confirmed a few
planets. Next, these missions will be explained with details.
2.4-1-1 COROT Mission
COROT is a space mission led by the French Space Agency, Center
National d’Etudes Spatiales (CNES), in conjunction with the European Space
Agency (ESA) and other international partners. Table (2.1) illustrates the
general information about the space mission. The mission's two objectives are
٤٦
Chapter Two
Detection methods of Extrasolar planets
to search for Extrasolar planets with short orbital periods, particularly those of
large terrestrial size, and to perform asteroseismology by measuring solar-like
oscillations in stars. It was launched on 27 December 2006, atop a Soyuz 2.1b
carrier rocket [57]. COROT subsequently reported first light on 18 January
2007. COROT is the first spacecraft dedicated to Extrasolar planet detection.
It detected its first Extrasolar planet, COROT-1b, in May 2007. Mission flight
operations were originally scheduled to end 2.5 years from launch but
apparently flight operations have been extended to January, 2010 and then to
2013[58].
COROT will be sensitive enough to detect rocky planets several times larger
than Earth; it is also expected to discover new gas giants, which currently
comprise almost all of the known Extrasolar planets [59]. The mission began
on 27 December 2006 when a Russian Soyuz 2-1b rocket lifted the satellite
into a circular polar orbit with an altitude of 827 km. The first scientific
observation campaign started on 3 February 2007. On May 3, 2007, it was
reported that COROT had discovered a hot Jupiter COROT-1b orbiting a
Sun-like star 1,500 light years away. This planet has a radius approximately
1.4 times that of Jupiter, a mass approximately 1.03 times that of Jupiter, and
orbits its parent star once every 1.5 days. On 20 December 2007, additional
results were published, declaring that a second Exoplanet, COROT-2b had
been discovered, this time with a radius 1.4 times and a mass 3.5 times that of
Jupiter. The orbital period is less than two days [58].
In May 2008, findings of two new Exoplanets, as well as an unknown
celestial object COROT-3b were announced by ESA. In February 2009,
COROT-7b was announced. It is the smallest Exoplanet to have its diameter
confirmed at 1.7 Earth's diameter [60].
2.4-1-2 Kepler Mission
٤۷
Detection methods of Extrasolar planets
Chapter Two
The Kepler Mission is NASA discovery mission which is designed to
discover Earth-like planets orbiting other stars as shown in figure (2.15). The
spacecraft was launched on March 2009. Table (2.1) illustrates the general
information about the space craft mission. The mission is named in honor of
German astronomer Johannes Kepler. With a planned mission lifetime of at
least 3.5 years, Kepler uses a photometer developed by NASA to
continuously monitor the brightness of over 145,000 main sequence stars in a
fixed field of view. The first main results announced on 4 January 2010 [61].
Figure (2.15) Kepler's photometer [62].
The scientific objective of the Kepler Mission is to explore the structure and
diversity of planetary systems. This is achieved by surveying a large sample
of stars to achieve several goals:
1. Determine how many Earth-sized and larger planets in or near the
habitable zone of a wide variety of spectral types of stars.
2. Determine the range of size and shape of the orbits of these planets.
3. Estimate how many planets are there in multiple-star systems.
٤۸
Chapter Two
Detection methods of Extrasolar planets
4. Determine the range of orbit size, brightness, size, mass and density of
short-period giant planets.
5. Identify additional members of each discovered planetary system
using other techniques.
6. Determine the properties of those stars that harbor planetary systems.
Most of the Extrasolar planets detected so far by other projects are giant
planets, mostly the size of Jupiter and bigger. Kepler is designed to look for
planets 30 to 600 times less massive, closer to the order of Earth's mass.
The method used, the transit method, involves observing repeated transit of
planets in front of their stars, which causes a slight reduction in the star's
apparent magnitude. The Kepler Mission has a much higher probability of
detecting Earth-like planets than the Hubble Space Telescope, since it has a
much larger field of view, and will be dedicated for detecting planetary
transits. Since Kepler's detection of planets depends on seeing very small
changes in brightness, stars that vary in brightness all by themselves (variable
star) are not useful in this search. From the first few months of data after
launched, Kepler scientists have determined that about 7500 stars from the
initial target list are such variable stars. These were dropped from the target
list, and will be replaced by new candidates. On November 4, 2009, the
Kepler project publicly released the light curves of the dropped stars. Groundbased follow up studies, reveal five previously unknown planets, all very
close to their stars, one (Kepler-4b) slightly larger than Neptune and four
(Kepler-5b, 6b, 7b, and 8b) larger than Jupiter, including one (Kepler-7b), that
is one of the least dense planets found yet [61].
2.4-1-3 Hubble Space Telescope (HST)
Hubble Space Telescope (HST) is a space telescope that was carried
into orbit by the space shuttle in April 1990 as shown in figure (2.16). It is
٤۹
Chapter Two
Detection methods of Extrasolar planets
named after the American astronomer Edwin Hubble. The HST is Cassegrain
reflector; table (2.1) illustrates the general information about the HST.
The HST is collaboration between NASA and the European Space Agency,
and is one of NASA's Great Observatories, along with the Compton Gamma
Ray Observatory, the Chandra X-ray Observatory, and the Spitzer Space
Telescope [63].
Figure (2.16) The Hubble Space Telescope [63].
When launched, the HST carried five scientific instruments: the Wide Field
and Planetary Camera (WF/PC), Goddard High Resolution Spectrograph
(GHRS), High Speed Photometer (HSP), Faint Object Camera (FOC) and the
Faint Object Spectrograph (FOS). WF/PC was a high-resolution imaging
device primarily intended for optical observations. It was built by NASA's Jet
Propulsion Laboratory, and incorporated a set of 48 filters isolating spectral
lines of particular astrophysical interest. The instrument contained eight
Charge Coupled Device (CCD) chips divided between two cameras, each
using four CCDs. The "Wide Field Camera" (WFC) covered a large angular
field at the expense of resolution, while the "Planetary Camera" (PC) took
images at a longer effective focal length than the WF chips, giving it a greater
magnification. The GHRS was a spectrograph designed to operate in the
٥۰
Chapter Two
Detection methods of Extrasolar planets
ultraviolet, it was built by the Goddard Space Flight Center. Also optimized
for ultraviolet observations were the FOC and FOS, which were capable of
the highest spatial resolution of any instruments on Hubble. FOC was
constructed by ESA, while the Martin Marietta corporation built the FOS. In
February 1997, the GHRS replaced with the NICMOS, this instrument
capable of observing dust disks to detected Extrasolar planets [63].
٥۱
Detection methods of Extrasolar planets
Chapter Two
2.4-1-4 Spitzer Space Telescope
Spitzer Space Telescope (SST), formerly called Space Infrared
Telescope Facility (SIRTF) is an infrared space observatory launched in
2003. It is the fourth and final of NASA's Great Observatories. Figure (2.17)
illustrates Spitzer Space Telescope [64].
Figure (2.17) The Spitzer Space Telescope [63].
The planned nominal mission period was to be 2.5 years with a pre-launch
expectation that the mission could extend to five or slightly more years until
the onboard liquid helium supply was exhausted [64]. Table (2.1) illustrates
the general information about Spitzer Space Telescope.
٥۲
Chapter Two
Detection methods of Extrasolar planets
Spitzer will obtain images and spectra by detecting the infrared
energy, or heat, radiated by objects in space between wavelengths of 3 and
180 microns. Most of this infrared radiation is blocked by the Earth's
atmosphere and cannot be observed from the ground.
Spitzer's highly sensitive instruments give a unique view of the universe and
allow peering into regions of space which are hidden from optical telescopes.
Many areas of space are filled with vast, dense clouds of gas and dust which
block the view. Infrared light; however can penetrate these clouds, allows
peering into regions of star formation, the centers of galaxies and into newly
forming planetary systems. Infrared also brings information about the cooler
objects in space, such as smaller stars which are too dim to be detected by
their visible light, Extrasolar planets, and giant molecular clouds.
The first images taken by SST were designed to show off the abilities of the
telescope and showed a glowing stellar nursery; a swirling, dusty galaxy; a
disc of planet-forming debris; and organic material in the distant universe.
In 2005 the SST directly captured the light from Extrasolar planets, namely
the "hot Jupiters" HD 209458 b and TrES-1. In May 2007, astronomers
successfully mapped HD 189733 b atmospheric temperature, thus obtaining
the first map of some kind of an Extrasolar planet [64].
2.4-2 Future space missions used to detect Extrasolar planets
There are many planned or proposed space missions such as: New
World Mission (will launch in 2014); Darwin (will launch in 2016); Space
Interferometry Mission (will launch between ''2015-2016"); Terrestrial Planet
Finder (will launch between ''2014-2020"); and PEGASE (will launch
between 2010-2012), that will be used to discover Exopalnets.
٥۳
Chapter Two
Detection methods of Extrasolar planets
The number of Extrasolar planets discovered by all mentioned
established methods, reached to (473) planets, and are illustrated in figure
(2.18) [2].
Figure (2.18) Shows the number of discovered Extrasolar planets by all established
detection methods till July 2010 [2].
٥٤
Detection methods of Extrasolar planets
Chapter Two
Table 2.1: General information about some space missions.
Information
COROT [58]
Kepler [61]
HST [63]
NASA
NASA / ESA
2009-03-07
1990-04-24
SST [64]
Center
Organization
National
d’Etudes
NASA /
Caltech
Spatiales, ESA
Launch date
2006-12-27
Baikonur
Launch from
Cosmodrome,
Kazakhstan
Launch
Soyuz
vehicle
2.1b/Fregat
Mission
Space Launch
Complex 17-B,
Cape Canaveral Air
Cape
-
Canaveral,
Florida
Force Station
Delta II (7925-10L)
2003-08-25
Space Shuttle
Delta II
Discovery, (STS-31)
7920H ELV
19 years, deorbited: ~
2.5 to 5
2013-2021
years
950 kg
>2.5 years
>3.5 years
Mass
630 kg
1,039 kg
11,110 kg
Type of orbit
polar
Earth-trailing
Near-circular low
heliocentric
Earth orbit
Orbit height
827 km
1 AU
559 km
-
Location
Earth orbit
-
low Earth orbit
orbiting sun
length
heliocentric
٥٥
Chapter Three
Data processing, calculations and results
3.1 Introduction
From time to time astronomers are discovering Extrasolar planets,
some of which are confirmed while the other are unconfirmed. In order to
confirm the existence of unconfirmed Extrasolar planets available
observational data must be found, with many physical parameters for planet
such as: Mass, Radius, Period, Semi-major axis, Eccentricity, Inclination and
Angular distance, for star: Mass, Radius, Distance, Right ascension,
Declination and Visual magnitude to study these Extrasolar planets.
3.2 Data processing
In this chapter adopted data are chosen for stars and planets from
available published catalogue [2].
These data are used to put criteria that will be used to confirm the presence of
Extrasolar planets by using radial velocity technique which determines the
mass of Extrasolar planets. The presence of Extrasolar planets can be proved
from the value of the mass because if it is smaller than the value of star’s
mass it will be considered to be a planet.
The catalogues of the physical parameters that were mentioned above of
Extrasolar planets are obtained from available online published source which
are divided to many tables depending on the methods of detection. In this
research the physical parameters of Extrasolar planets detected by radial
velocity are listed in appendix-A [2].
٥۲
Chapter Three
Data processing, calculations and results
When a planet is found by the radial velocity method, its orbital
inclination i is unknown [39]. As mentioned in chapter two the radial velocity
method is unable to determine the true mass of the planet, but instead it gives
its minimum mass M sin i which is expressed by [36]:
…………..……… (3.1)
Where: M sin i is the mass of the planet, K* the radial velocity amplitude of
the star, e the eccentricity, M* mass of the star, P the orbital period, and G
gravitational constant.
During the time of training at Saint Mary University observatory in Canada,
for the period from 12-04-2010 to 12-07-2010, knowledge has been gained
for the method of obtaining mass of Extrasolar planet which observed by a
telescope (1.93 m diameter) with high resolution ELODIE spectrograph
instrumentation installed at Haute-Provence Observatory (HPO). The
observed spectrum is recorded on a 1024x1024 CCD [65], where data for
observation are stored in Elodie archive [66]. Then used for further
calculations and manipulations, as follow:
At the beginning Extrasolar planets have been taken and the values of
radial velocity were obtained for several observations for its stars from
available online data that taken from Elodie archive.
HD 150706 has been taken as a sample of the stars that were included in this
research, where its data observations are used to calculate Julian day (JD)
values by using MATLAB program. Results for this calculation are listed in
Table (3.1).
٥۳
Data processing, calculations and results
Chapter Three
Table 3.1: Data of HD 150706 star
A.D (day)
JD-2400000
(day)
RV (km/s)
Epoch
Phase
08/05/1998
50942.05163
-17.19
0.1722333
0.17223
05/06/1998
50970.02858
-17.22
0.2868202
0.28682
05/06/1998
50970.01608
-17.22
0.286769
0.28677
07/06/1998
50972.09229
-17.22
0.2952726
0.29527
08/06/1998
50972.94272
-17.21
0.2987558
0.29876
08/06/1998
50972.95522
-17.19
0.298807
0.29881
31/03/1999
51269.10158
-17.23
1.511751
0.51175
27/06/2000
51722.94335
-17.22
3.3705775
0.37058
02/07/2000
51727.95032
-17.20
3.3910849
0.39108
31/07/2000
51756.90352
-17.22
3.5096702
0.50967
20/06/2001
52080.92627
-17.25
4.8367892
0.83679
22/07/2001
52112.90824
-17.29
4.9677797
0.96778
15/08/2001
52136.88133
-17.26
5.0659676
0.06597
07/09/2001
52159.84467
-17.23
5.1600199
0.16002
10/09/2001
52162.79632
-17.23
5.1721092
0.17211
26/03/2002
52360.15636
-17.27
5.9804483
0.98045
27/03/2002
52361.13940
-17.26
5.9844746
0.98447
19/04/2002
52384.13593
-17.25
6.0786628
0.07866
23/04/2002
52388.10910
-17.25
6.094936
0.09494
19/05/2002
52414.05999
-17.28
6.2012246
0.20122
25/06/2002
52450.94985
-17.28
6.3523166
0.35232
٥٤
Data processing, calculations and results
Chapter Three
25/06/2002
52450.96294
-17.27
6.3523702
0.35237
Table 3.1: continued …
27/06/2002
52452.91360
-17.13
6.3603596
0.36036
27/06/2002
52452.92717
-17.30
6.3604152
0.36042
26/07/2002
52481.89322
-17.30
6.4790531
0.47905
21/08/2002
52507.83195
-17.28
6.5852919
0.58529
17/04/2003
52747.09986
-17.28
7.5652756
0.56528
18/04/2003
52748.06353
-17.27
7.5692225
0.56922
21/04/2003
52751.07653
-17.24
7.5815631
0.58156
22/04/2003
52752.08410
-17.25
7.5856898
0.58569
13/05/2003
52773.03854
-17.25
7.6715142
0.67151
14/05/2003
52774.03600
-17.25
7.6755995
0.67560
16/05/2003
52776.05287
-17.29
7.6838601
0.68386
18/05/2003
52778.06839
-17.27
7.6921152
0.69212
06/06/2003
52796.95400
-17.28
7.7694661
0.76947
09/06/2003
52800.01651
-17.27
7.7820094
0.78201
10/06/2003
52800.93614
-17.27
7.785776
0.78578
12/06/2003
52802.94939
-17.28
7.7940218
0.79402
15/06/2003
52805.94555
-17.28
7.8062933
0.80629
18/06/2003
52808.92337
-17.27
7.8184898
0.81849
21/06/2003
52811.91866
-17.29
7.8307577
0.83076
22/06/2003
52812.97764
-17.29
7.8350951
0.83510
03/06/2004
53159.99191
-17.26
9.2563818
0.25638
07/06/2004
53163.95191
-17.25
9.2726011
0.27260
٥٥
Data processing, calculations and results
Chapter Three
05/08/2004
53222.89376
-17.25
9.5140127
0.51401
Next step the following equations have been used to calculate the Epoch and
the phase values that applied in Excel program:
·
………………. (3.2)
·
………………………………… (3.3)
Where: p is the period of the observations that was determined from the
Peranso program [67].
Then the phased radial velocity data have been plotted, and a text file of phase
and radial velocities was created then used in another program called
PERIBM that was used to get the zero point and the amplitude which are
used to create a sine wave with the phase offset that set at the beginning to
zero (0.00). Also the amplitude value used in equation (3.1) to calculates the
mass of the planet.
The method of creating a sine wave is made by taking values from 0 to 0.99
in steps of 0.01interval and applying the following equation, using Excel
program:
….. (2.4)
Where n= 0–0.99.
Results for generated sine wave are as shown in table (3.2).
٥٦
Data processing, calculations and results
Chapter Three
n values
Sine wave
0.0000
-17.25812
0.0100
-17.25663
0.0200
-17.25513
0.0300
-17.25362
0.0400
-17.25211
0.0500
-17.25061
0.0600
-17.24912
0.0700
-17.24764
0.0800
-17.24620
0.0900
-17.24478
0.1000
-17.24339
0.1100
-17.24205
0.1200
-17.24075
0.1300
-17.23950
0.1400
-17.23831
0.1500
-17.23718
0.1600
-17.23611
0.1700
-17.23512
0.1800
-17.23419
0.1900
-17.23335
0.2000
-17.23258
0.2100
-17.23190
0.2200
-17.23130
0.2300
-17.23079
0.2400
-17.23037
Table 3.2: Sine wave data for HD
150706 star
٥۷
Data processing, calculations and results
Chapter Three
0.2500
-17.23004
n0.2600
values
0.2700
0.5600
-17.22981
Sine
wave
-17.22967
-17.25818
0.5700
Table 3.2: continued …
n values
Sine wave
0.2800
0.8400
-17.22962
-17.27598
-17.25966
0.2900
0.8500
-17.22967
-17.27538
0.5800
-17.26110
0.3000
0.8600
-17.22981
-17.27469
0.5900
-17.26252
0.3100
0.8700
-17.23005
-17.27392
0.6000
-17.26391
0.3200
0.8800
-17.23038
-17.27307
0.6100
-17.26525
0.3300
0.8900
-17.23081
-17.27215
0.6200
-17.26655
0.3400
0.9100
-17.23132
-17.27008
0.6300
-17.26780
0.3500
0.9200
-17.23192
-17.26894
0.6400
-17.26899
0.3600
0.9300
-17.23261
-17.26775
0.6500
-17.27012
0.3700
0.9400
-17.23338
-17.26650
0.6600
-17.27119
0.3800
0.9500
-17.23423
-17.26520
0.6700
-17.27218
0.3900
0.9600
-17.23515
-17.26385
0.6800
-17.27311
0.4000
0.9700
-17.23615
-17.26247
0.6900
-17.27395
0.4100
0.9800
-17.23722
-17.26105
0.7000
-17.27472
0.4200
0.9900
-17.23836
-17.25960
0.7100
-17.27540
0.4300
-17.23955
0.7200
-17.27600
0.4400
-17.24080
0.7300
-17.27651
0.4500
-17.24210
0.7400
-17.27693
0.4600
-17.24345
0.7500
-17.27726
0.4700
-17.24483
0.7600
-17.27749
0.4800
-17.24625
0.7700
-17.27763
0.4900
-17.24770
0.7800
-17.27768
0.5000
-17.24918
0.7900
-17.27763
0.5100
-17.25067
0.8000
-17.27749
0.5200
-17.25217
0.8100
-17.27725
0.5300
-17.25368
0.8200
-17.27692
0.5400
-17.25519
0.8300
-17.27649
0.5500
-17.25669
٥۸
Chapter Three
Data processing, calculations and results
٥۹
Chapter Three
Data processing, calculations and results
This flowchart explains the précis of the practical work in this thesis:
Figure (3.1) Schematic organization of the practical work.
٦۰
Chapter Three
Data processing, calculations and results
These results of sine wave are plotted as shown in figure (3.2). This figure
shows the values for zero point, amplitude and phase offset.
Zeropoint= -17.25365
amplitude= 0.024029
Phase offset= 0.2202
Figure (3.2) Illustrates radial velocity vs phase data for HD150706.
Again the phase radial values data have been taken and put them into a text
file named PHASE2.DAT. Then a second file was created of the same type of
sine wave generated in Excel named PHASE1.DAT.
Now the two files are used in Force program with a special programming
used to find the best value for the phase offset of the fitted sine wave.
By the same above method, other six stars (HD 24040, 51 Peg, HD 81040,
HD 118203, HD 33564, HD 190228) have been obtained, and the results are
drawn in figures (3.3) to (3.8) respectively.
٦۱
Data processing, calculations and results
Chapter Three
HD 24040
phase
-9.25
0.0000
0.2000
0.4000
0.6000
1.0000
1.2000
Zeropoint= -9.40864
amplitude= 0.058946
Phase offset= 0.04035
-9.30
RV (km/s)
0.8000
-9.35
-9.40
-9.45
-9.50
Figure (3.3) Illustrates radial velocity vs phase data for HD24040.
phase
-33.16
0.0000
-33.18
0.2000
0.4000
0.6000
51 Pegasi
0.8000
1.0000
1.2000
-33.20
RV (km/s)
-33.22
-33.24
-33.26
-33.28
-33.30
-33.32
-33.34
Zeropoint= -33.25802
amplitude= 0.052453
Phase offset= 0.0489
-33.36
Figure (3.4) Illustrates radial velocity vs phase data for 51 Pegasi.
٦۲
Data processing, calculations and results
Chapter Three
HD 81040
49.45
49.40
RV (km/s)
49.35
49.30
49.25
Zeropoint= 49.24692
amplitude= 0.167905
Phase offset= 0.0971
49.20
49.15
49.10
49.05
0.0000
0.2000
0.4000
0.6000
0.8000
1.0000
1.2000
phase
Figure (3.5) Illustrates radial velocity vs phase data for HD 81040.
-29.00
-10.60
0.0000
0.0000
-29.10
-10.70
RV
RV (km/s)
-10.80
-29.20
-50.05
-10.90
0.0000
-29.30
-50.10
-11.00
HD 118203
HD 33564
phase
phase
0.2000
0.2000
0.4000
0.4000
0.6000
0.6000
0.4000
1.0000
1.0000
1.2000
1.2000
Zeropoint= -29.3643
amplitude=
HD
190228 0.202261
Phase offset= 0.0345
phase
0.2000
0.8000
0.8000
0.6000
0.8000
1.0000
1.2000
RV (km/s)
-29.40
-11.10
-50.15
-29.50
-11.20
-50.20
-11.30
-29.60
-50.25
-11.40
-29.70
Zeropoint= -10.96204
amplitude= 0.264124
Phase offset=0.26125
Zeropoint= -50.20556
Figure (3.7) Illustrates radial velocity vs phase data for amplitude=
HD 33564.0.076114
Phase
offset= 0.0652
-50.35
-50.30
Figure (3.6) Illustrates radial velocity vs phase data for HD 118203.
Figure (3.8) Illustrates radial velocity vs phase data for HD 190228.
٦۳
Data processing, calculations and results
Chapter Three
3.3 Calculations of Extrasolar planets mass
In order to calculate the Exoplanet mass equation (3.1) was applied for
this purpose. In order to do so one needs to know the mass of the star (M*),
period of the planet (p), eccentricity of planet orbit (e), amplitude of radial
velocity variation (K*). Some of these values were taken from the table in
appendices A and B [2].
The seven stars of the sample were taken for this purpose, some of which are
unconfirmed and the other are confirmed Exoplanet for comparison. These
parameters and the calculated planets’ masses are listed in Table (3.3).
Table 3.3: Parameters and results of masses calculations for stars with their
planets that chosen in this research.
Unconfirmed star
Confirmed star
Parameters of star and
planet[2]
Name of the
planet
M*
(Msun)
eccentricity
Period
(days)
Ref
This work
Period
applied
(days)
[2]
Amplitude
M sini
M sini
(K*) (m/s)
(MJup)
(MJup)
HD 150706 b
0.94
0.38
264
244.155
24.029
0.65
1
HD 24040 b
1.18
0.277
8000
3776.079
58.946
4.84
9.13
1.11
0
4.2307
4.228
52.453
0.439
0.468
HD 81040 b
0.96
0.526
1001.7
1138.123
167.90
7.13
6.86
HD 118203 b
1.23
0.309
6.1335
6.135
202.26
1.95
2.13
HD 33564 b
1.25
0.34
388
401.606
264.12
10.05
9.10
51 Peg b
(HD 217014 b)
٦٤
Data processing, calculations and results
Chapter Three
HD 190228 b
1.3
0.43
1127
1147.403
76.114
4.21
4.99
٦٥
Chapter Four
Discussion, conclusions and future
4.1 Discussion and Conclusions
Radial velocity technique is one of the principal techniques being
applied in the search for Extrasolar planets that was used by discoverers and
the most successful in terms of the number of confirmed detections.
It’s obvious that the majority of detected planets are of Jupiter mass or larger,
most have circular orbits, most have been detected by radial velocity
technique, the majority of them are less than one astronomical unit from their
star, and the majority of the planets discovered are orbiting stars that are
similar to the Sun.
Stars’ companions which were investigated in this work are nominees
to be Extrasolar planets which were discovered by Radial velocity method.
The stars in this research were chosen from available online internet data.
By estimating the mass of the companion for these stars it can be proved if
they are planets or not.
A form was used to calculate the mass of a companion to the star to
determine or prove if it is a planet or another star.
By taking an available observational data for some stars that were detected via
radial velocity technique from available online data taken from Elodie
Archive, the mass of their planets can be calculated. Then comparing the
results that obtained for calculating the mass of the Exoplanets in this work
with the data obtained by another researchers (e.g. Schneider 2010), from this
comparison it can be noted that the results are approximately the same, except
one result which is (HD 24040 b) from unconfirmed Extrasolar planets where
the difference between the calculated result and that obtained by Schneider is
4.29 MJup and in the confirmed Extrasolar planets is (HD 33564 b) where the
٦٥
Chapter Four
Discussion, conclusions and future
difference amount is 0.95 MJup while the rest of the results were found in a
good agreement.
This difference in the results is due to modicums in observations data, this
leads to the need of more observations to confirm the approach of the
presence confirmation of Extrasolar planets.
The results of calculated masses for the unconfirmed Exoplanets are
approximately between 0.5 and 5 times of Jupiter mass; too small to be a star,
but similar to be a planet. From this can confirming the existence of the
unconfirmed Exoplanets.
It can be noted that there is an error shifting in the sine fitting curve of the
figures (3.4), (3.5), and (3.8) the reason behind that is unknown. Maybe it
belongs to the values of the phase offset, which obtained from specific
programming.
4.2 Future work
In future work the following can be done:
1. Calculating the mass of multiple planets orbit around star instead of
calculating the mass of single planet which have been done in this
research.
2.
Using interferometry technique for detection Extrasolar planets.
٦٦
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۷۳
‫ﺍﻟﺧﻼﺻﺔ‬
‫ﺍﻟﻛﻭﺍﻛﺏ ﺧﺎﺭﺝ ﺍﻟﻧﻅﺎﻡ ﺍﻟﺷﻣﺳﻲ ﻫﻲ ﻛﻭﺍﻛﺏ ﺗﺩﻭﺭ ﺣﻭﻝ ﻧﺟﻭﻡ ﺧﺎﺭﺝ ﺍﻟﻧﻅﺎﻡ‬
‫ﺍﻟﺷﻣﺳﻲ‪ .‬ﺣﻳﺙ ﺑﻠﻎ ﻋﺩﺩﻫﺎ ‪ ٤۷۳‬ﻛﻭﻛﺏ ﻟﻐﺎﻳﺔ ﺍﻟﺷﻬﺭ ﺍﻟﺳﺎﺑﻊ ﻟﻌﺎﻡ ‪.۲۰۱۰‬‬
‫ﺗﺎﺭﻳﺦ ﺍﻟﺑﺣﺙ ﻋﻥ ﺍﻟﻛﻭﺍﻛﺏ ﺧﺎﺭﺝ ﺍﻟﻧﻅﺎﻡ ﺍﻟﺷﻣﺳﻲ ﻳﻌﻭﺩ ﺍﻟﻰ ﺯﻣﻥ ﻁﻭﻳﻝ ﻣﻧﺫ ﺑﺩﺍﻳﺎﺕ ﻋﺎﻡ‬
‫‪ ۱۹۰۰‬ﺧﻼﻝ ﺗﻠﻙ ﺍﻟﻔﺗﺭﺓ ﺍﻟﻌﺩﻳﺩ ﻣﻥ ﺍﻻﻛﺗﺷﺎﻓﺎﺕ ﻅﻬﺭﺕ‪ ،‬ﻟﻛﻥ ﺍﻻﻛﺗﺷﺎﻑ ﺍﻟﺣﻘﻳﻘﻲ ﻛﺎﻥ ﻓﻲ‬
‫ﻋﺎﻡ ‪ ۱۹۹٥‬ﻋﻧﺩ ﺍﻛﺗﺷﺎﻑ ﺍﻭﻝ ﻛﻭﻛﺏ ﺧﺎﺭﺝ ﺍﻟﻧﻅﺎﻡ ﺍﻟﺷﻣﺳﻲ ﻳﺩﻭﺭ ﺣﻭﻝ ﺍﻟﻧﺟﻡ ‪.51Pegasi‬‬
‫ﺍﻛﺛﺭ ﻣﻥ ﺗﻘﻧﻳﺔ ﻭﺍﺣﺩﺓ ﺍﺳﺗﺧﺩﻣﺕ ﻟﻠﻛﺷﻑ ﻋﻥ ﺍﻟﻛﻭﺍﻛﺏ ﺧﺎﺭﺝ ﺍﻟﻧﻅﺎﻡ ﺍﻟﺷﻣﺳﻲ ﻭﻣﻥ ﺍﻛﺛﺭ‬
‫ﺍﻟﻁﺭﻕ ﺍﺳﺗﺧﺩﺍﻣﺎ ًﻫﻲ ﺗﻘﻧﻳﺔ ﺍﻟﺳﺭﻋﺔ ﺍﻟﻧﺻﻑ ﻗﻁﺭﻳﺔ ﻭﺍﻟﺗﻲ ﺗﻌﺗﺑﺭ ﻣﻥ ﺍﻛﺛﺭ ﺍﻟﻁﺭﻕ ﺍﻫﻣﻳﺔ ﻓﻲ‬
‫ﺍﻟﻛﺷﻑ ﻋﻥ ﺍﻟﻛﻭﺍﻛﺏ ﺧﺎﺭﺝ ﺍﻟﻧﻅﺎﻡ ﺍﻟﺷﻣﺳﻲ ﻭﻗﺩ ﺍﻋﺗﻣﺩﺕ ﻓﻲ ﻫﺫﺍ ﺍﻟﺑﺣﺙ‪.‬‬
‫ﺗﻡ ﺍﺳﺗﺧﺩﺍﻡ ﺍﻟﺗﻘﻧﻳﺎﺕ ﺍﻟﻣﻌﺗﻣﺩﺓ ﻓﻲ ﻣﺭﺻﺩ ﺳﺎﻧﺕ ﻣﺎﺭﻱ ﻓﻲ ﻛﻧﺩﺍ ﻭﺍﻟﺗﻲ ﺳﺎﻋﺩﺕ ﻓﻲ ﺍﻛﺗﺳﺎﺏ‬
‫ﻣﻌﺭﻓﺔ ﻋﻠﻣﻳﺔ ﻓﻠﻛﻳﺔ ﻟﺣﺳﺎﺏ ﻛﺗﻠﺔ ﺍﻟﻛﻭﻛﺏ ﺍﻟﻣﺭﺍﺩ ﺍﺛﺑﺎﺕ ﻭﺟﻭﺩﻩ‪ .‬ﺗﻡ ﺍﻟﺗﻭﺻﻝ ﺍﻟﻰ ﻧﺗﺎﺋﺞ ﻟﺳﺑﻌﺔ‬
‫ﻧﺟﻭﻡ ﺗﻡ ﺍﺧﺗﻳﺎﺭﻫﺎ ﻟﻬﺫﺍ ﺍﻟﻐﺭﺽ‪ ،‬ﺑﻌﺩ ﺍﺧﺫ ﺍﺭﺻﺎﺩﺍﺕ ﻣﻌﻳﻧﺔ ﻟﺗﺎﺭﻳﺦ ﺍﻟﺭﺻﺩ ﻭﺍﺭﺻﺎﺩﺍﺕ‬
‫ﻟﻠﺳﺭﻋﺔ ﺍﻟﻧﺻﻑ ﻗﻁﺭﻳﺔ ﻟﻠﻧﺟﻡ ﻭﻣﻥ ﺧﻼﻝ ﻋﺩﺓ ﻋﻧﺎﺻﺭ ﻣﻌﻳﻧﺔ ﻳﻣﻛﻥ ﺣﺳﺎﺏ ﺍﻟﻛﺗﻠﺔ‪ .‬ﺍﺛﻧﺎﻥ‬
‫ﻣﻥ ﻫﺫﻩ ﺍﻟﻧﺟﻭﻡ ﻏﻳﺭ ﻣﺅﻛﺩ ﺍﻛﺗﺷﺎﻓﻬﺎ ﻭﺍﻟﺧﻣﺳﺔ ﺍﻟﺑﺎﻗﻳﺔ ﻣﺅﻛﺩ ﺍﻛﺗﺷﺎﻓﻬﺎ‪ .‬ﻟﻘﺩ ﺣﺻﻠﻧﺎ ﻋﻠﻰ ﻧﺗﺎﺋﺞ‬
‫ﻣﻘﺎﺭﺑﺔ ﻟﻠﻧﺗﺎﺋﺞ ﺍﻟﻣﻧﺷﻭﺭﺓ ﺑﺎﻟﻧﺳﺑﺔ ﻟﻠﻧﺟﻭﻡ ﺍﻟﻣﺅﻛﺩﺓ‪ ،‬ﺍﻣﺎ ﻏﻳﺭ ﺍﻟﻣﺅﻛﺩﺓ ﻣﻧﻬﺎ ﻓﺎﻥ ﻫﻧﺎﻟﻙ ﺗﺑﺎﻋﺩ‬
‫ﻓﻲ ﻧﺗﺎﺋﺞ ﺍﻟﺣﺳﺎﺑﺎﺕ‪.‬‬
‫ﺍﻥ ﺣﺳﺎﺏ ﻛﺗﻠﺔ ﺍﻟﻛﻭﻛﺏ ﺳﻳﺳﺎﻋﺩ ﺍﻟﻔﻠﻛﻳﻳﻥ ﻓﻲ ﻣﻌﺭﻓﺔ ﻓﻳﻣﺎ ﺍﺫﺍ ﻛﺎﻥ ﺍﻟﻣﺭﺍﻓﻕ ﻟﻠﻧﺟﻡ ﻫﻭ ﻛﻭﻛﺏ‬
‫ﺍﻡ ﻧﺟﻡ ﺧﺎﻓﺕ ﻏﻳﺭ ﻣﺭﺋﻲ‪ ،‬ﻟﺫﻟﻙ ﺳﻳﺛﺑﺕ ﻭﺟﻭﺩ ﻛﻭﻛﺏ ﺍﻭ ﻋﺩﻡ ﻭﺟﻭﺩﻩ ﺣﻭﻝ ﻧﺟﻡ ﻣﻌﻳﻥ‪.‬‬
‫ﺟﻤﻬﻮرﻳﺔ اﻟﻌﺮاق‬
‫وزارة اﻟﺘﻌﻠﻴﻢ اﻟﻌﺎﻟﻲ واﻟﺒﺤﺚ اﻟﻌﻠﻤﻲ‬
‫ﻗﺴﻢ اﻟﻔﻠﻚ–ﻛﻠﻴﺔ اﻟﻌﻠﻮم ‪-‬ﺟﺎﻣﻌﺔ ﺑﻐﺪاد‬
‫ﺍﻟﺒﺤﺚ ﻋﻦ ﺍﻟﻜﻮﺍﻛﺐ ﺧﺎﺭﺝ ﺍﻟﻨﻈﺎﻡ‬
‫ﺍﻟﺸﻤﺴﻲ ﺑﺄﺳﺘﺨﺪﺍﻡ ﺗﻘﻨﻴﺔ ﺍﻟﺴﺮﻋﺔ‬
‫ﺍﻟﻨﺼﻒ ﻗﻄﺮﻳﺔ‬
‫رﺳﺎﻟﺔ‬
‫ﻣﻘﺪﻣﺔ اﻟﻰ ﻣﺠﻠﺲ ﻛﻠﻴﺔ اﻟﻌﻠﻮم ﺟﺎﻣﻌﺔ ﺑﻐﺪاد ﻛﺠﺰء ﻣﻦ ﻣﺘﻄﻠﺒﺎت ﻧﻴﻞ درﺟﺔ‬
‫اﻟﻤﺎﺟﺴﺘﻴﺮ ﻓﻲ ﻋﻠﻮم اﻟﻔﻠﻚ‬
‫ﻣﻦ ﻗﺒﻞ‬
‫ﻛﺎرﻣﻦ ﺳﻤﻴﺮ ﺷﻤﻌﻮن‬
‫ﺑﻜﺎﻟﻮرﻳﻮس ﻋﻠﻮم ﻓﻠﻚ‪-‬ﻛﻠﻴﺔ اﻟﻌﻠﻮم – ﺟﺎﻣﻌﺔ ﺑﻐﺪاد‬
‫)‪(٢٠٠٥‬‬
‫ﺑﺄﺷﺮاف‬
‫أ‪.‬د ﻟﻴﺚ ﻣﺤﻤﻮد ﻛﺮﻳﻢ‬
‫‪۱٤۳۱‬ﻫـ‬
‫‪ ۲۰۱۰‬ﻡ‬