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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]. ۱٤ Chapter Two Detection methods of Extrasolar planets 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 ۱٥ Detection methods of Extrasolar planets Chapter Two 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]. ۱٦ Detection methods of Extrasolar planets Chapter Two 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 ۱۷ Chapter Two Detection methods of Extrasolar planets 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]. ۱۸ Detection methods of Extrasolar planets Chapter Two 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) ۱۹ Detection methods of Extrasolar planets Chapter Two 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. ۲۰ Detection methods of Extrasolar planets Chapter Two 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) ۲۱ Detection methods of Extrasolar planets Chapter Two 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. ۲۲ Chapter Two Detection methods of Extrasolar planets 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 ۲۳ Detection methods of Extrasolar planets Chapter Two 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]. ۲٤ Detection methods of Extrasolar planets Chapter Two 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 ۲٥ Detection methods of Extrasolar planets Chapter Two 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]. ۲٦ Chapter Two Detection methods of Extrasolar planets ۲۷ Detection methods of Extrasolar planets Chapter Two 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]. ۲۸ Chapter Two Detection methods of Extrasolar planets 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]. ۲۹ Chapter Two Detection methods of Extrasolar planets 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]. ۳۰ Chapter Two Detection methods of Extrasolar planets 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]. ۳۱ Detection methods of Extrasolar planets Chapter Two 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]. ۳۲ Chapter Two Detection methods of Extrasolar planets 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]. ۳۳ Detection methods of Extrasolar planets 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]. ۳٤ Chapter Two Detection methods of Extrasolar planets 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. ۳٥ 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. ۳٦ Chapter Two Detection methods of Extrasolar planets 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]. ۳۷ Chapter Two Detection methods of Extrasolar planets ۳۸ Detection methods of Extrasolar planets Chapter Two 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]. ۳۹ Chapter Two Detection methods of Extrasolar planets 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]. ٤۰ Detection methods of Extrasolar planets Chapter Two 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]. ٤۱ Chapter Two Detection methods of Extrasolar planets 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, ٤۲ Detection methods of Extrasolar planets Chapter Two 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]. ٤۳ Detection methods of Extrasolar planets 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 References [1] Nature Group and Institute of Physics, (2001), Extrasolar Planets, UK. [2] J. Schneider, (2010), Interactive Extrasolar planets Encyclopedia. The Extrasolar planets Encyclopedia version 2.02, Paris observatory. http://exoplanet.eu/catalog.php. [3] J. Gribbin , (1996), Companion to the Cosmos. London: Weidenfed & Nicolson, pp. 156-157. [4] G. 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[67] http://www.peranso.com/ 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