Web viewThe term planet is an ancient Greek word for ‘wandering star’. Some of the...

Observation and Modelling Study of Exoplanet HAT-P-10b


By Vinh Trung Ton

Student I.D.: 486565

M301

Supervisor: Dr Michael McCabe

Mentors: David Harris, Chris Priest and Steve Futcher

1


Abstract

This project is based on the observation, analysis and modelling of a specific exoplanet. I will also be talking about the exoplanatory system as well. This project is to show in depth on how mathematics is very important in the detection of exoplanets. Using mathematics we can calculate many different properties for the planets and stars outside of our solar system.

Firstly my project starts with an introduction which will explain more about exoplanets. I will then discuss about the different methods of exoplanet detection. Though I never got the chance to observe a specific exoplanet myself at an observatory, I will then use results that my mentor David Harris has given me. Using these results I will then analyse them by using a windows software which will produce light curves. I will then use mathematical programs to create models that will simulate transits and then compare and apply them to my observed exoplanet. I will then go a bit deeper into explaining more about transits using the data I have found.

There are different types of calculations to calculate all the aspects of a specific exoplanet, for example is how fast the planet is transiting or how long it takes for a full transit.

At the end I will gather all the information I have researched and conclude my findings.

2


Contents

Nomenclature 4

Chapter 1: Introduction 5

Chapter 2: Exoplanet Detection Methods 8

2.1: Direct Imaging 8 2.2: Coronagraphy 9 2.3: Gravitational Microlensing 10 2.4: Astrometry 13 2.5: Radial Velocity 14 2.6: Transit 15

Chapter 3: Observation and Light Curves 16

3.1: Clanfield Observatory 16 3.2: Chosen Transit 16 3.3: Observations 18 3.4: AIP4Win Analysis 20 3.5: Excel Data Analysis 26

Chapter 4: Data Analysis 29

4.1: HAT-P-10 29 4.2: Orbit Period 29 4.3: Semi-Major Axis 29 4.4: Orbit Speed 31 4.5: Impact Parameter and Transit Duration 31

Chapter 5: Modelling HAT-P-10b 36

Modelling with Maple 36

Chapter 6: Final Analysis 44

Comparing Light Curves 44

Chapter 7: Conclusion 46

7.1: Result Discussion 46 Bibliography 47 Appendix 49

Nomenclature

3


This is a list of symbols that I have used in my project. It shows what each symbol represents.

K= Kelvin

M= Mass

G= Gravitational Constant

C= Speed of light

RE= Einstein’s Ring Radius

θE= Angular Einstein Radius

DL= Distance between observer and star (in the foreground)

DS= Distance between observer and star (in the background)

P= Orbital Period

a= Semi-Major Axis of the orbit

M ¿ or M⨀= Star Mass

R¿ or R⨀= Star Radius

V= Magnitude

RP= Radius of Planet

R¿= Radius of host star

m= Apparent Magnitude

F= Flux

∆ F= Change in Flux

i= Orbital Inclination

T dur= Transit Duration

π= 3.142 (Pi)

b= Impact Parameter

JD= Julian Day

AU= Astronomical Unit

4


Chapter 1: Introduction

1.1: Introduction to Exoplanets

“There are many unanswered question that most people would ask when it comes to our universe. The question of how unique our Solar System has been clearer and clearer each year. It has always been assumed that there are certainly other planets orbiting other stars and that was made clear by Mayor and Queloz who discovered 51 Pegasi b in 1995. Earth itself is only a mere spot in our solar system. There is much more outside our solar system which makes our universe what it is” (Mason, 2008). For years mankind has asked, are we truly alone in this universe? To be honest there is no answer to that yet. The good news is we have the technology to keep searching for other exoplanets outside our solar system, which have the same properties as our very own Earth. Astronomers until now since the first exoplanet was discovered in 1992 have been searching for years for more answers. Many exoplanets have been found and each have many different properties which makes them each unique.

The first exoplanet which was discovered as said above was found by Aleksander Wolszcan and Dale Frail. The exoplanet which was discovered orbited the star called PSR B1257+12. This is a neutron star. The exoplanet orbiting this star was then named PSR B1257+12 b. The b stands for the secondary figure. In other words the centre star is classed as A and the planet/exoplanet which orbits it, is called B, then C, D etc… This of course then followed by a confirmation of detection of 51 Pegasi in 1995. Though in those times, the rate of detection was quite low and now rapidly increasing since then. The idea was to find a planet which is habitable. The first sign for a habitable planet is water. A sign of H2O will help scientists and astronomers look into other life forms of living things or in this case a reliable place for us to be able to live on. Though we cannot technically look for something that we do not know exists. Scientists and astronomers looked at attributes like satellites, gravitation, atmosphere, compound etc… These attributes are looked upon to show if there is a possibility of life.

There are different types of planets. The term planet is an ancient Greek word for ‘wandering star’. Some of the planet classifications are:

Terrestrial Planets

“These are made up of mostly rocks and heavy metals. The core is made up of heavy metals, but most of it is made up of iron and the core also is surrounded by a mantle of silicate rock. These planets have a varied terrain, which includes volcanoes, mountains, canyons and craters. The atmosphere of each terrestrial planet varies from thick carbon monoxide atmosphere to almost nothing. Unlike gas giants, these planets are much smaller” (Cessna, 2010).

5


Gas Giants

“These planets have uniqueness to them. They are almost entirely made up of various gases. Though of course they are not all made up of just gas. The centres of these planets are made up of liquid compound. It is said that astronomers describe the centre as rocky. This was very misleading because as said above it is made up of liquid compound and also of molten heavy metals. These planets also have another name. Jovian planet is the name of these planets named after Jupiter, which is the prototype of the gas giants in our solar system. The different between Gas Giants to Terrestrial Planets are that they are much larger and they are farther away from the sun. They also rotate much faster and are extremely cold being so far away from the sun” (Cessna, 2009).

Ice Giants

These planets are very similar to Gas Giants. The difference is they are enveloped of hydrogen and helium. They are mainly made up of water, ammonia or methane (Ingersoll, 2012).

“Though we are a bit off topic of exoplanets, this is more of an insight of our solar system itself. There is up to a total of 861 such planets (in 677 planetary systems, including 128 multiple planetary systems) which have been identified as of March 1st, 2013” (Schneider, 2012). In the Milky Way galaxy, it is said that there are billions of planets (at least one planet, on average, orbiting around each star, which results in about 100-400 billion exoplanets), with much more free-floating planetary-mass bodies which are orbiting the galaxy directly. The Kepler mission has now detected over 18,000 additional candidates, which includes potential habitable ones (262 to be exact) (BBC News, 2013).

6


This now leads us towards talking about the habitable zone.

Figure 1.1 image of the habitable zone (Habitable Zone, 2013)

“One of the main ingredients for life as we know it is liquid water. Water can only exist as a liquid between 273K and 373K (if the pressure is too low, in which case the water sublimates into gaseous water vapour). If the temperature is between this range somewhere in the region of the solar system (or any planetary system), we call this the habitable zone. I could go on more and more about the habitable zone, but the main points are most important” (Williams, 2013).

7


Chapter 2: Exoplanet Detection Methods

“There is up to a total of 861 such planets (in 677 planetary systems, including 128 multiple planetary systems)” (Schneider, 2012). We are very lucky to have the technology to be able to identify planets and to have the opportunity to understand and find out more about each one. Here I will tell you the different methods of detecting and identifying exoplanets. There are technically two ways of explaining and they are Direct and Indirect observations. Direct observation is probably the most difficult because most of the time exoplanets orbit close to their star. It is less accurate because the light from the star will cause the telescope to leave us with images which are difficult to even see. Indirectly is much more encouraged. In this chapter I will look at the different varieties of methods and techniques which are used to detect exoplanets. We should count ourselves lucky to have the chance to be able to experience this with the amount of technology being built.

2.1 Direct Imaging

Direct imaging is probably one of the easiest methods of detecting exoplanets. Our solar system and all the planets that we know of in this system were detected by using the direct imaging method. “Almost all of the currently known exoplanets were discovered by indirect methods” (Mason, 2008, p14). Direct imaging is only much more effective if the orbiting planet was much brighter and its star was much fainter. One useful tool that astronomers achieved was by observing at the infrared wavelength. Transiting exoplanets have all been discovered at optical wavelengths and most of the characterizations have been performed at infrared wavelengths (Millers, 2012). Optical and infrared wavelengths yield info about the atmospheric albedo. Albedo is the ratio of the light reflected by a planet or satellite to that received by it.

The direct imaging detection method is truly difficult, though it has an advantage of detecting large, hot planets that orbit far from faint stars (those that emit intense infrared radiation). We know that the direct imaging method is probably not favoured among astronomers but despite this astronomers will not give up trying to observe exoplanets directly. This is because it is the best way for astronomers and non-astronomers to understand as much as they can about extrasolar planets.

8


“Using the method above there was a giant exoplanet which was found at an angular distance of 0.78 arcsec from a brown dwarf 2MASSWJ 1207334-393254.” (Haswell, 2010)

Figure 2.1 The Brown Dwarf 2MASSWJ 1207334-393254 (centre) and the giant exoplanet which was found.

We can see that this method is most effective at finding large bright planets at larger distances around dimmer stars. The good news is that astronomers are trying to design an instrument to find Exoplanets using this method by overcoming the light from the stars to reveal planets.

2.2 Coronagraphy

“This technique, which is only suitable for space missions, light from the central star is eliminated using a mask in the focal plane. This method is used to study the corona and prominences of the Sun’s atmosphere, from which its name is derived” (Mason, 2008, p16). The coronagraph is actually a telescopic attachment. It is used to block out intense direct light from a star, which allows the fainter object that are nearby to be easily viewed. As said above, this method was created mainly for the study of the corona of the sun. It is one of the methods which astronomers have invented to detect exoplanets directly as said in 2.1 (Krist, 2006).

“One of the most famous telescopes which use Coronagraphs is called the Hubble Space Telescope. It is the most successful high-contrast astronomical imaging instrument that has yet been built. Since it was build it has provided numerous images of the scattered light from circumstellar disks and the glow from faint substellar companions” (Krist, 2006). The importance of this telescope is the stability and high resolution provided by its placement above the atmosphere.

9


Figure 2.2 Fomalhaut and NASA's Hubble Rogue Planetary Orbit for Fomalhaut B.

Newly released NASA Hubble Space Telescope images of a vast debris disk encircling the nearby star Fomalhaut and a mysterious planet circling it may provide forensic evidence of a titanic planetary disruption in the system (Harrington, 2013).

Moving back to the topic, a stellar coronagraph on ground based telescope can search for exoplanets, but is much more effective when on a satellite based telescope for example the HST. Astronomers still feel that this method is still in its early stages, but they believe that a significant number of exoplanets could be detected through this method.

2.3 Gravitational Microlensing

“The idea with Microlensing is that astronomers wanted to observe galactic bulges, with a view to searching for dark matter and extrasolar planets” (Mason, 2008, p6). Gravitational Microlensing can be used to detect different ranges of celestial objects, though despite the amount of light they emit. Microlensing events occur when the light from a star passes by another near star in the view of the observer from earth.

“The gravitational Microlensing method relies upon chance alignments between background source stars and foreground stars, which may host planet systems. The background source stars serve as sources of light that are used to probe the gravitational field of the foreground stars and any planets that they might host” (Mason, 2008, p47).

10


Figure 2.3 The geometry of gravitational lens of mass, M, that is offset by a distance, b, from the line of sight to the source. (Gravity Lens Geometry, 2011).

The angle of deflected light from the light ray passing the star is calculated by using the equation:

α=4GMc2r

M = the mass of the star

Figure 2.3 is a similar geometry of (Mason, 2008, p49)

If the lens and source are perfectly aligned, the two images merge to form a ring of radius known as the Einstein ring radius. Einstein’s ring will cause the brightness of the star to increase by a factor of just nearly 1000. Even the best telescopes on earth can’t distinguish the images between the source and star. Using the equation below we can calculate Einstein’s ring radius:

RE≡θE DL≡√ 4 GMDL (Ds−DL)c2 D s

(Mason, 2008, p49)

A Microlensing event could take weeks up to months before the source star moves out of alignment. If the star has a planet which orbits it in a position where it crosses the light rays from the source star, then the gravity from the planet will bend the light rays. For a short period it will produce a third image of the source star. From this it will create a spike of brightness on a Microlensing light curve.

11

M


Figure 2.3.1 “The Microlensing process in stages, from right to left. The lensing star (white) moves in front of the source star (yellow) magnifying its image and creating a Microlensing

event. In the fourth image from the right the planet adds its own Microlensing effect, creating the two characteristic spikes in the light curve” (The Planetary Society,

Microlensing, 2012).

Planetary Microlensing events are a subset of multiple lens events where the mass ratio is quite small. Planetary events have light curves that appear quite similar to the single lens light curves, but for a brief period of time they deviate from the single lens form and display the characteristics of a binary lens light curve.

Advantages:

“Microlensing is capable of finding the furthest and the smallest planets of any currently available method for detecting extrasolar planets. In Jan 2006 scientists announced the discovery through Microlensing of a planet of only five Earth masses, which was orbiting a star near the centre of our galaxy, 22,000 light-years away! Microlensing is most sensitive to planets that orbit in moderate to large distances from their star” (Planetary, Microlensing, 2012)

12


Disadvantages:

“Unlike planets that are detected by other methods, planets detected by Microlensing will never be observed again. Microlensing is unique and do not repeat themselves.”

“For example thanks to Microlensing events we know that the planet “OGLE-2005-BLG-390Lb” is a cold rocky world orbiting a small cool star near the centre of the galaxy” (Planetary, Microlensing, 2012).

2.4 Astrometry

“The best way to describe astrometry is that it is the science (and art!) of precision measurement of stars’ locations in the sky. The people who search for planets use astrometry to look for regular wobbles in a stars’ position” (Pravdo, 2009).

“Given a sequence of observations of a star’s position of sufficiently high accuracy relative to the celestial sphere, the reflex motion of the star caused by the orbit of a planet around it can be detected. Can be used to determine both the absolute mass and orbital inclination of a planet” (Mason, 2008, p4).

“Astrometry is probably one the longest and oldest methods used to detect exoplanets. The earlier date which was recording of using Astrometry was in 1943. It was used by an astronomer named Kaj Strand” (The Planetary Society, 2012). The difference was in those times the results were very hard to prove. Many people were excited, but from the lack of evidence, Kaj’s claims were unproven.

The uses of Kepler’s Laws are very important when it comes to Astrometry. When Kepler published his three laws of planetary motion, at the time it was seen as controversial. Now we can see that it was definitely very useful. I will talk more about Kepler’s Laws later on.

We normally think that a planet orbits a star, but in fact both planet and its parent star have a mass and therefore all entities in planetary system orbit around the barycentre (Haswell, 2010, p26).

“In a regular planetary system, the parent star makes up most of the mass and therefore the barycentre is close to the parent stars own centre of mass. This means that as a planet orbits its parent star, the parent star performs a smaller reflex orbit keeping the centre of mass of the system fixed at the barycentre” (Haswell, 2010, p27).

We can use the equation below to calculate the reflex amplitude of a parent star and its planet orbiting round its barycentre:

a¿=M P

M ¿×aP

(Mason, 2008, p4)

13


“The sun constitutes over 99.8% of the Solar System’s mass, so the barycentre of the Solar System is close to, but not quite at, the Sun’s own centre of mass. During the period of time when the planets are all orbiting around the barycentre, the Sun will execute a small reflex orbit, but always keeping the centre of the mass of the system fixed at the barycentre” (Haswell, 2010, p27).

“From a distance of d when a parent star is being observed, the motion of the parent star in reflex can be detected as an angular displacementβ. This is also called the angle of astrometric wobble and is calculated by”, (Millers, 2012)

β=a¿

d

Now we can use

a¿=M P

M ¿×aP

Substitute in we get

β=M p×aP

M¿×d

(Haswell, 2010, p27)

“This method has only been successful recently; astronomers believe that astrometry can be the key method at finding terrestrial earth like planets that orbit far from their parent star” (The Planetary Society, n.d). Overall Astrometry is very useful because it works well and it applies Kepler’s third law which estimates accurately the planets parameters, such as mass which I will talk about more in Chapter 4.

2.5 Radial Velocity

“Of the extrasolar planets which are discovered to this date, the vast majority have been found using the Radial Velocity Method. This is also known as the Doppler Spectroscopy or the Doppler Method” (Clubb, 2008).

“The radial velocity method is similar to astrometry in that they both use the parent star’s reflex orbit to detect a planet. The difference with the radial velocity procedure is that instead of observing the parent’s star position, we analyse the change in velocity” (Millers, 2012).

14


Both the parent star and planet orbit round the barycentre. Due to the gravitational tug of an orbiting planet it reacts towards the parent star which then performs a smaller reflex orbit. The gravity of the orbiting planet pulls the parent star slightly closer to the earth, compressing the star’s light waves towards the blue end of the spectrum. “As the star moves away from the earth, the light waves are then stretched out towards red end of the spectrum. These shifts in wavelength by the star are called Doppler shifts” (Millers, 2012).

2.6 Transit Method

“This is the most important detection to me because this is what my project is focusing on. We only a minutes chance that the orbital inclination will be close to 90°, this means that the planet will in regular intervals pass between the parent star and of course in the view of us the observer. Once the planet passes in front of its parent star, the planet then occults some of the light rays from the parent star. For instance if the planet was large, the stars light will dip slightly for that period of time that the planets disk is occulting the parent stars” (Millers, 2012).

Astronomers use the transit photometry method to measure the dip in brightness. When the transit occurs it will plot the results as a light curve. The brightness with time of a star will be shown by a graphical light curve.

“Transits by terrestrial planets produce a small change in a star's brightness of about 1/10,000 (100 parts per million, ppm), lasting for 2 to 16 hours. This change must be absolutely periodic if it is caused by a planet. In addition, all transits produced by the same planet must be of the same change in brightness and last the same amount of time, thus providing a highly repeatable signal and robust detection method” (Dijk, 2008).

Figure 2.6.1 A transit which produces a light curve (Dijk, 2008).

15


Chapter 3: Observation and Light Curves

3.1: Observation at Clanfield Observatory

For this project I was told to collect data from Clanfield Observatory. My mentor David Harris who is a member of the Hampshire Astronomical Group has helped me through collecting the data I need for this project. He has shown me how to identify and observe a distant star that has a transiting planet. The idea was to observe a transit through a telescope to fully understand and gain experience. The difficulty for me was I never actually got the chance to collect my own data and take my own images using the telescope. Thanks to David Harris, he has collected his own data on an exoplanet called HAT-P-10b and has explained to me how it was obtained. I used the images that were taken and processed them myself using software called AIP4Win which I will then use to produce a light curve using excel.

3.2: Chosen Transit

Firstly I had to select a suitable observation and from this I will collect some data. Using the Exoplanet Transit Database (ETD) I will select an exoplanet.

Figure 3.2.1 Exoplanet Transit Database

The website shows all the data that is required to find a confirmed transiting planet which astronomers have observed.

First things first on the website I had to insert the longitude and latitude of the Clanfield Observatory. This was explained and shown to me by David Harris while I was at the observatory. I was informed that the longitude was 359° east and the latitude was 51°.

Once I have inserted the location the website will show me a list of planets to be observed and when the transits occur. It also shows what position the exoplanet is in, how long the duration and at what depth. Usually the date today will be highlighted to show you which transits will occur.

Below is an example of this based on the date 20th of March 2013.

16


Figure 3.2.2 A list of observable planets. Position, depth, duration and when the transit occurs.

With the equipment I am using there were a few limitations and reasons why specific exoplanets were only allowed to be used.

Firstly the star had to be of at least magnitude 13 or brighter. If it is not the transit would be very hard to detect.

Secondly the transit had to be at least 30° above the horizon throughout the observations and remote from the Moon.

‘Thirdly the depth has to be at least 0.02 in magnitude so that we could observe it due to available precision of ground based telescope.’ (Stephens, 2012)

The sad news was I never got the chance to observe for myself, though David explained everything to me and how everything worked.

17


Figure 3.2.3 ETD web site, magnification on transit predictions of 20th of March 2013 (Example)

My chosen exoplanet is HAT-P-10 with the transiting planet of HAT-P-10b. Though it doesn’t show in fig 3.2.3, David has kindly given me images taken from Clanfield Observatory of HAT-P-10b.

3.3: Observations

Though I did not take my own images I still had to familiarise myself with the equipment which was used. At Clanfield Observatory David used a 24” telescope which allows for long exposure times. This is used for observing for long period over night. Before proceeding there is stuff that must be checked first.

18


Figure 3.3.1 24” Telescope at Clanfield Observatory.

First things first is the telescope was covered therefore we had to remove the covers. To set up the telescope we had to undo the clamps on the telescope to enable it to be driven. After placing it in the correct position which is shown in Fig 3.3.1, the drive has to be engaged.

The telescope is motorised by stepper motors and programmed in to a point targeting system. Once we know what inclination and orientation we want the scope to be positioned we can compute it in. This will then tell the telescope to position itself to observe a specific location. This is done by using the elements co-ordinates from website on Fig 3.2.2.

Figure 3.3.2 Telescope Control Console.

We then attach the CCD camera (Model: SBIG STL-1001E) to the telescope and this is attached to a laptop which will take the images. One of the functions of the camera is temperature. It is important because a lower temperature reduces thermal noise and

19


improves contrast. It is also important that the pixels on the camera will not be saturated otherwise it would not be possible to use the imaging data.

3.4: AIP4Win Analysis

The images that David has taken will now be used and processed digitally. The best way to analyse the images of the chosen transit I used a program called AIP4Win. The images were taken from the CCD camera which was said in 3.3. The images were saved in file formats called FITS (Flexible Image Transport System) files. These files are useful because it allows each image to have information on the GMT time it was taken and the exact Julian Date.

The first thing I did was use the multiple image photometry setting to measure and analyse photons collected from the images.

Multiple Image Photometry

Figure 3.4.1 Multi-Image Photometry

Once the multiple image photometry windows are opened I will now select the images which I will analyse. Before this I will tick the Auto Calibrate function because I do not want to manually calibrate it myself which is a long procedure. After image selection I then uploaded them on to AIP4Win to be analysed.

20


Figure 3.4.2 AIP4WIN with a FITS file image of our observed transit for HAT-P-10b

Now I need to identify which star is the host star HAT-P-10 in the images I have chosen. Only the first image will be shown and once I run the execution it will process all the photos I have chosen. David has shown me a program called Skymap which locates HAT-P-10 for me, but for now I do not have this information. I remembered exactly where HAT-P-10 was, but originally the only way to make sure was to use Skymap.

Figure 3.4.3 HAT-P-10 located on the Skymap Program

21


Figure 3.4.4 AIP4Win image showing the location of HAT-P-10

Now that I have my host star identified, I will now choose comparison stars. Before I do this I must stick to specific criteria to select the right comparison stars.

Choosing a brighter star because the noises square root of photons count. Larger photon count will give a better signal to noise ratio.

A better spacing yet fairly close to the host star. Best to pick stars which do not overlap with other stars. Also once we place a ring and annulus around the chosen stars it must not overlap any other star.

Must not pick a variable star. (Measurably fixed)

Using the comparison stars which I had chosen, the software will detect the change in brightness of the host star by comparing the levels of the light of the comparison stars with that of the host star. The best way to get the best result is to pick more than just one comparison star. I have chosen 4 comparison stars. It is always best to choose a brighter or of similar magnitude as it will help for an accurate analysis. From the first image to the last image the telescope and CCD camera slightly move while the images are taken. This will cause the position of the host star and the chosen comparison stars to slight change while the transit occurs. The radii circles must cover the whole star but has to be clear of any other nearby stars. The good thing is AIP4Win copes no matter if the images change or the

22


position of the stars change. Therefore the Ring and Annulus will follow with the stars that were chosen.

Figure 3.4.5 Screenshot showing the selected host star and the 4 selected comparison stars.

Now that I have chosen 4 comparison stars of the same or similar magnitude as my host star and edited the radii circles using the radii circle control window (settings), it is time to execute the Multiple Image Photometry for my selected images. In this case I had over 300 images, but I split it into two halves.

All images are on Appendix 1 (CD)

23


Figure 3.4.6 Screenshot of the Radii Circle Control Window. This edits the Ring and Annulus which revolves around the chosen stars.

Once I click the execute button it then starts the photometry procedure. AIP4Win will the complete the process for each and every image. Once this is done it will store in a data log with all the photometric measurements and along with all the FITs file info.

24


After the execution is finished another window with two graphs will appear. This is called the Photometry Data. The top graph plots the difference in magnitude between the host star (V) and the first comparison star (C1) which represents (V-C1). I ordered the comparison stars from the brightest as C1 and the least bright as C4. The graph below plots the difference in magnitude between the first comparison star (C1) and the second comparison star (C2) which represents (C2-C1).

Figure 3.4.7 Output graphs of the Multiple Image Photometry of the first half. Photos 1-170.

3.4.8 Output graphs of the Multiple Image Photometry of the second half. Photos 171-332.

25


Now that the analysis had finished, all of the data log will then be imported into Microsoft excel which will process graphs which will show the transit light curves. Before I create my graphs I had to change some of the data from the data log from AIP4Win. This is all explained in 3.5.

3.5 Excel Data Analysis

After my images were processed and executed through AIP4Win I am given a data log. This log is a csv file. This log has all the data which AIP4Win has given for each image.

Please look at Appendix 3 (CD) for the log data for all images which was executed on AIP4Win.

Now I will use the log data and import them all into Microsoft Excel.

Now that the log data has been imported there are only a few data and columns which are most important to me. First of all I converted the Julian Date column into hours. I removed all the data I found unreliable (which is in Appendix …). Now I want to remove errors from the V-C1 column. To remove the errors I found the average of the in-transit magnitude values and took the average away from each magnitude in the V-C1 column. This is useful as it smoothes the data, reducing the variance as you step from point to point through the data. I do this by adding a moving average trend line to a graph. A moving average could be thought of as reducing the errors in (or at least the variability between) the data points. By doing this I worked out a 10 point moving average. Eventually I will input the new data into Maple which I will talk about more in chapter 5.

Finally I converted the averaged V-C1 column values into flux values. I used this equation below to make this a success:

m1−m2=−2.5 log ( F1

F2)

I now substitute V=m2, C1=m2, F2=1 (relative flux).

I then rearranged for F1 which now gives us the equation:

F1=10−(V −C 1)

2.5

I used this formula to make a new column called V-C1 (Average) (Found in Appendix 5 (CD)). Once I found all the flux I can then plot a graph.

Please see Appendix 5 (CD) which shows the excel data after editing. The edit includes the V-C1 average, Julian Date conversion into hours and the flux.

26


0 0.5 1 1.5 2 2.5 3 3.50.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

1.01

1.02Flux

Flux

Julian Date to Hours

Figure 3.5.1 Light curve of the observed transit for HAT-P-10b (V-C1)

“From this light curve I can see that the results I got are quite promising. We can clearly see a definite dip in my light curve which shows the transit of HAT-P-10b” (Millers, 2012).

I also felt that I wanted to look into the V-Ens data as well. I want to do a 10 point moving average for this and compare it with the 10 point moving average data I found for V-C1.

All is found on Appendix 5 (CD)

27


Using the same formulas I used in 3.5 I will interpret this to V-Ens. I will be doing exactly like I did above by finding the flux.

0 0.5 1 1.5 2 2.5 3 3.50.94

0.95

0.96

0.97

0.98

0.99

1

1.01

1.02

Flux

Flux

Figure 3.5.2 curve of the observed transit for HAT-P-10b (V-Ens)

My plan was to do a combination of both (V-C1) and (V-Ens). I am trying to do something called a normalisation. This is when you make the minimal differential value approximately zero so that it is easier to measure the dip, then taking a moving average so it is easier to see the shape of the plot.

From figure 3.5.2 I can see that using the data from the flux found using (V-Ens) that the results from this light curve is much more promising. There is a much clearer dip which can help me with modelling.

Equation used:

Normalisation magnitude value NV = sum[seq# = 1 to 10](V-Ens(Seq#)/10

This shows us the sum of the sequence from 1-10 from the column V-Ens which is then divided by 10.

28


Chapter 4: Data Analysis

4.1: HAT-P-10

These are the characteristics of HAT-P-10

Spectral Type

Mass (M ¿¿

Radius (R¿¿

Metallicity

Fe/H

Right Ascension

Declination Magnitude V

HAT P 10

K3V 0.82 0.81 0.13 03:09:29.0 +30:40:25/26 11.89

Right Ascension:

03 represents hours 09 represents minutes 29.0 represents seconds

Declination:

+30 represents degrees 40 represents minutes 25 or 26 represents seconds

(Schneider, 2013) and (Mgr. Poddaný, 2013)

4.2: Orbit Period

“What I know is that the depth of a transit is proportional to the square of the ratio of the planet radius to the host stars radius. We know that the transit light curve allows us to obtain a precise measurement of the orbital inclination, i, of the planet, and consequently it allows an exact value of the planet’s mass to be deduced from the radial velocity curve of the host star” (Haswell, 2010).

The orbit period is the time taken for a specific object to make one complete orbit around another object.

4.3: Semi-Major Axis

When I come to talk about the Semi-Major Axis I must first talk about Kepler’s Laws.

Kepler’s Laws:

1) “The law of orbits: All planets move in elliptical orbits, with the sun at one focus.”2) “The law of areas: A line that connects a planet to the sun sweeps out equal areas in

equal times.”

29


3) “The law of periods: The Square of the period of any planet is proportional to the cube of the semi-major axis of its orbit. “

(Nave, 2012)

“Kepler’s third law represents much of astrophysics. It can be deduced from observations of the Solar System planets, and be derived from Newton’s law of universal gravitation and Newton’s second law of motion. In other words Kepler’s third law is there to provide us a basis for the quantitative analysis of planetary orbits. It is the starting point for analyzing exoplanet transits.” (Haswell, 2010).

Kepler’s third law can be used in relation to the period and semi major axis. Probably one of the easiest things to do is measure the orbital period of a transiting exoplanet:

a3

P2=G(M ¿+M P)

4 π2

In general we know that M ¿≫ M P , so now we can make a fairly good estimate of the mass of the system from the spectral type of the star and ignoring the mass of the planet.

The mass of the Sun is 1.9891×1030kg and the mass of HAT-P-10 is 0.82 times the mass of the Sun.

I can rearrange the equation above to make:

a=(G (M ¿+M P ))13 ( P

2π )23

Now I can substitute each symbol with numbers.

M ¿=1.631062×1030Kg

G = this is the gravitational constant which is = 6.67398 × 10-11 m3 kg-1 s-2

P = 2.77596days … We must change this into seconds = 2.77596x24x3600 = 239842.9s

(Schneider, 2012)

Now that we have all the information and data we need we can finally input them into the formula:

a≈ (GM ¿ ( P2 π )

2

)13

30


a≈ ((6.67×10−11)×(1.631062×1030)×( 239842.92 π )

2

)13

a≈5412070353m

AU=149.60×109 m

a≈0.036 AU

4.4: Orbit Speed

Now to find the orbit speed we must use the values for the semi major axis and the orbit period. We can find the speed at which the exoplanet is orbiting, in other words we must use Kepler’s second law.

v=2πaP

v=2π ×5412070353m239842.9 s

v=141780.48ms−1

v=142 k ms−1

4.5: Impact Parameter and Transit Duration

After finding the period we can now use further data from the transit time of the exoplanet and the radius of the star to find the impact parameter. The definition for impact parameter is the perpendicular distance from the original centre of a set of scattering particles to the original line of motion of a particle being scattered.

Below is an image of Venus. It shows us that a transit has four contacts. (Only an example)

31


Figure 4.5.1 Transit of Venus

First contact is when the limb of the planet’s disc first coincides with the limb of the star’s disc. Second contact is when the whole disk of the planet is just within the stellar disc. Third contact occurs when the limb of the planet’s disc coincides with the limb of the star’s disc. This means the last point when the whole disc of the planet is just within the stellar disc. Fourth contact occurs when the trailing limb of the planet’s disc crosses the limb of the star’s disc. This means at the last instant of the transit.

First things first are to find the Transit duration. The transit duration for a circular model of my chosen exoplanet of its host star with impact parameter b=0.

T dur=P R¿

πa

T dur=66.062304hrs×563355000m

π×5412070353m

R¿=563355000mBecause the radius of the Sun is 6.955×108. Therefore I had to multiply this by0.81 R¿.

32


T dur=2.19hours

To get it into minutes I multiplied the T dur hours by 60.

T dur=131.4mins

Figure 4.5.2 “emphasizing the trigonometryDetermining the impact parameter, b = a cos i” (Haswell, 2010)

The impact parameter, b, represents the vertical distance at mid-transit of the centre of the planet from the centre of the star. The vertical distance is:

b=aCosi

However long the transit lasts for depends on the impact parameter.

Figure 4.5.3 “Pythagoras’s theorem allows us to express the length l in terms ofthe impact parameter, b, and the radii of the star and planet.” (Haswell, 2010)

33


Here we are looking for the length l. Figure 4.5.3 shows a right-angled triangle that has a hypotenuse of length R¿+RP and a vertical side that is equal to the impact parameter, b, and therefore has length acosi. As we can see in this image is that the horizontal line joins the positions of the centre of the planet’s disc at mid-transit and fourth contact.

Figure 4.5.3 uses Pythagoras’s Theorem:

l=√(R ¿+RP)2−a2 cos2 i

Figure 4.5.4 “During transit, the planet moves from A to B around its orbit. If the orbit is circular, the distance around the entire orbit is 2πa, and the arc length between A and B is aα , with the angle α in radians. The distance along a straight line between A and B is2 l.

From the triangle formed by A, B and the centre of the star, sin(α2 )= la”, (Haswell, 2012)

We can take a transit which corresponds to the lengthl. We can express the transit duration is respect to this length given the angleα . We can see that the exoplanet moves round the system from one point A to another point B subtending the angle α . If we look at Figure 4.5.4 the triangle formed between points A, B and the centre point of the star, we can now do the following substitution to get an overall expression for the transit duration.

sin(α2 )= la

T dur=Pπ [(R¿

a )2

−cos2i ]12

7884 s=239842.9 sπ [( 563355000m

5412070353m )2

−cos2 i ]12

34


7884× π239842.9=[( 563355000m

5412070353m )2

−cos2 i]12

(7884× π239842.9 )

2

=( 563355000m5412070353m )

2

−cos2i

(7884× π239842.9 )

2

−( 563355000m5412070353m )

2

=−cos2i

cos2i=( 563355000m5412070353m )

2

−(7884× π239842.9 )

2

cos2i=0.01083521266−0.01066446917

cos2i=1.707434866×10−4

cosi=0.01306688512

i=89°

From my result I can see that that my value of i is perfect to the value on the exoplanet.eu website of HAT-P-10b which corresponds to 88.5° . I will now use this value of the orbital inclination of ito find a value for the impact parameter b. I will use the formula below:

b=a× cos (i )

b=5412070353m×cos (88.5°)

b=141671485.9m=0.2514781725R ¿

b≈ 14

R¿

35


Chapter 5: Modelling HAT-P-10b

Chapter 5.1: Modelling with Maple

Going back to my excel data, I have added a txt format data from the information on my excel data. Appendix 5 (CD) Is my excel data and Appendix 6 (CD) Is my txt format data from my excel data. Using the information from my txt format data which includes the Julian Date in hours and the flux data, I will now input this into Maple.

Maple is a computer program that most mathematicians use to solve problems and functions. We can also use the program to create animations and to plot a more detailed graph.

A copy of my Modelling with Maple data is found in Appendix 7 (CD).

Figure 5.1.1 Code used to generate the animation of my chosen transiting planetary system

Rstar represents the radius of the host star. This will always be kept constant at 1.

Rplanet represents the radius of the exoplanet as a proportion of the host star.

B represents the Impact Parameter.

X is a variable that we use to calculate the beginning of the transit in other words a starting point that lays on the x-axis.

The display is just commands which represent the animation transit image which I shall talk about later.

36


The dip in brightness is due to the planet occulting some of the nearby star’s light, which relates to the planet and the stars radius.

This then gives us the formula of:

∆ FF

=(RP

R¿)

2

From the light curves of the transit I can find the flux value of the dip brightness. Using this value I can formulate an estimated radius of the exoplanet which is proportion of its host star. Basically I can use my light curve from my exoplanet HAT-P-10b. From this I can estimate a value. So first things first I need to get the flux value (F). To find this I took the average of the starting point of the transit.

¿ . F=1

Now it was time to find∆ F, which is the change in the flux. I took the average of all the flux values and subtracted it from the value of F.

Averageof all the flux=0.986

∆ F=0.014

Finally I can take the ∆ Fvalue and divide this by F and this will then estimate the radius of my chosen exoplanet of HAT-P-10b which is proportion of its host star HAT-P10.

∆ FF

=0.0141

( RP

R¿)

2

=0.014

RP

R¿=0.118

So from this I can see that my result of observing the transit of HAT-P-10b has given an estimation of the radius which gives 0.118.

37


Though I will now check using the values that astronomers have found (Jean Schneider, 2013),

RP

R¿=

1.045R J

0.81⨀

1.045×69911km0.81×695500 km

Therefore

RP

R¿= 73057

563355=0.1297

Looking at the original value from (Jean Schneider, 2013) I can see that the two results are very close. This is telling me that the data that I have collected from my transit is very closely accurate. I did earlier estimate the value for the semi-major axis and orbital inclination, so now I will prove it using the information given to me from (Jean Schneider, 2013).

b=acos ( i )

R¿

acos (i)R¿

=0.0439×cos (88.5)563355

b=0.3051

Looking back at my estimate earlier in Chapter 4.5, I can see that my result was very close.

38


The problem about Maple was that it couldn’t create an animation due to a technical fault, though I still did get an image of the start of the animation.

Figure 5.1.2 An image of the start of transit for HAT-P-10

Now using some more maple commands I will create a code which will generate a light curve for the transit.

39


Figure 5.1.3 Generated code on Maple to create a light curve

(From local to dmax). Here we can see that the impact parameter is not b but instead is y. Ds is used to calculate separation of centres for the exoplanet and the host star. Rmax is used to calculate the maximum radius for both the host star and the exoplanet. Rmin is used to calculate the minimum radius of both the host star and the exoplanet. Dmax is used to calculate the maximum distance between both objects.

(From if y to B1:=subs). Here we have dmin which is used to calculate similar to the dmax but instead the minimal distance between both objects. A is to calculate the previous formulated equation for the area of intersection for two circles. B is used to calculate a constant only when there is completely no circle intersection. B1 is subbed for rplanet as r and Rstar as R on the previous line of codes.

P1 is to plot the egress of the theoretical light curve. P2 is to plot the ingress. P3 is to plot the point before the ingress. P4 is the point after the egress. P5 is to plot the point where the light curve dips which is between the ingress and egress.

The steps explaining each one were ideas linked to (Millers, 2012) and (Weisstein, 2013).

40


Figure 5.1.4 Generated code on Maple to create a light curve (continued)

This part plots everything into one graph. As you can see there is place to import text files (.txt). So I used the (.txt) excel data of the Julian Days in hours and the flux and imported it into Maple (hat10).

From this the output of light curves are now shown.

Figure 5.1.5 Maple light curve with the observed light curve of HAT-P-10b.

Here I can see clearly my results plotted onto a graph. I can see that the dip from my light curve corresponds to the dip of the observed light curve. This shows a definite fit. I can see that maybe a part of the stellar flux is lost during the transit because the curve is flat bottomed which is not the correct shape of a light curve (Haswell, 2010, p97). Most of the light is blocked when the planet is at the furthest point from the limb of the star’s disc. We can see that the light curves dip is very deep at the middle of the curve. From this I can see that it is due to limb darkening.

41


Figure 5.1.6 Generated code on Maple to create a light curve with limb darkening

(From A to i1) Here we can see additional codes, for instance U represents linear coefficient of limb darkening. Ds is used to calculate separating of centres for the exoplanet and host star. i represents intensity and uses the limb darkening law which I shall talk about later in Chapter 6. F is used to calculate the flux.

(From rmax to A1) rmax is used to calculate the max radius for both the host star and the exoplanet. Rmin is used to calculate the opposite of rmax. Dmax is used to calculate the max distance of the host star and the exoplanet. Dmin is the opposite of dmax. A is to calculate a formulated equation for the area of intersection for two circles (Weisstein, 2012). A1 which is said earlier is to sub the value for rplanet as r and Rstar as R.

(The rest) DF1 is to calculate the approx amount of light which is blocked by the exoplanet which is transiting, by multiplying the area of the intersection and the intensity. P1 to P5 is the same as said earlier. DF5 is used to plot the dip which is similar to P5.

Figure 5.1.7 Continued

The rest of the maple code is just used to import the date from my text file and it will then plot an observed light curve with limb darkening involved.

42


Figure 5.1.8 Plot of the Maple light curve with limb darkening and the observed light curve of HAT-P-10b (V-C1 Flux)

Here we can see evidently that with limb darkening, the light curve is a lot more accurate. Now that I compare both the two light curves I can see that the light curve shows that the dip in my observed light curved is not well defined. I can see this because the points of my observed light curve is very scattered and is not following a specific shape of the light curve.

43


Chapter 6: Final Analysis

6.1 Comparing Light Curves

Earlier I input all my excel data into Maple. From this I created a light curve and also a light curve which included limb darkening. I want to compare using the V-Ens Flux data with the V-C1 Flux data to see how similar they are to quote on what I found.

0 0.5 1 1.5 2 2.5 3 3.50.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

1.01

1.02 Flux

Flux

Julian Date to Hours

Figure 3.5.1 Light curve of the observed transit for HAT-P-10b (V-C1)

0 0.5 1 1.5 2 2.5 3 3.50.94

0.95

0.96

0.97

0.98

0.99

1

1.01

1.02

Flux

Flux

Figure 3.5.2 curve of the observed transit for HAT-P-10b (V-Ens)

44


My plan was to do a combination of both (V-C1) and (V-Ens). I am trying to do something called a normalisation. This is when you make the minimal differential value approximately zero so that it is easier to measure the dip, then taking a moving average so it is easier to see the shape of the plot.

From figure 3.5.2 I can see that using the data from the flux found using (V-Ens) that the results from this light curve is much more promising. There is a much clearer dip which can help me with modelling.

My plan now is to input this data into Maple. I have already done this with V-C1, so now I will do this with V-Ens and compare them both. Appendix 5 for V-Ens Data on Excel and Appendix 6 for the txt file which was input into Maple.

Figure 6.1.1 Plot of the Maple light curve with limb darkening and the observed light curve of HAT-P-10b (V-Ens Flux)

Here we can see evidently that with limb darkening, the light curve is a lot more accurate. Now that I compare both the two light curves I can see that the light curve shows that the dip in my observed light curved is not well defined either. The points are still quite scattered so my results came out very similar.

45


Chapter 7: Conclusion

7.1 Result Discussion

This project has been a very difficult mountain to climb, but I enjoyed every part of it. I chose to observe HAT-P-10b which is a low mass hot Jupiter planet that orbits the star HAT-P-10. I was able to obtain images and data from my mentor David Harris at the Clanfield Observatory for the transit of HAT-P-10b. I went through all the images and analysed them to obtain a light curve of the transit. Some of the results were quite good, but overall I found that because of the errors it pulled me down a bit. The good news was I used a 10 point moving average to lower the amount of errors from occurring. When I compared my observed light curve with amateur astronomers, I definitely felt that my light curve doesn’t even compare. The others showed more of a defined dip and smoother curves while mine were too scattered which was difficult to get a well defined dip. These errors were definitely not easy to fix, though I knew some reasons behind why my results were not as good as I would have expected. One of the reasons would be objects that pass in front of the telescope like a cloud or a plane. I definitely saw a few images with cloud passing by and a streak which probably was a plane. So the points on my light curve that looked a bit out of place probably meant something was in the way. Due to lack of time I was unable to find out other methods to help me remove the errors from my data which may have lead to a better fitting light curve. The weather was not too good either which meant it was very difficult for me to get the chance to observe my own transit of HAT-P-10b.

The use of Maple really helped with my research. I used maple from the data I got from each image that was taken by David of HAT-P-10b. Once I ran this data through maple it automatically created a light curve for me.

The use of AIP4Win was very useful in locating my selected star and comparisons stars. My mentor Chris had told me that a good idea is to pick a comparison which is brighter than the host star. Noises Square rooted of photo count. It always helps for the comparison star to be fairly close by, but with a lot of space for the ring and annulus to easily surround the chosen star. Last of all was to never pick a variable star because it is measurably fixed.

Though I never got the chance to collect more data and take my own images it was a great experience.

I felt the aims of my project were somewhat slightly achieved. All my estimations of HAT-P-10b’s parameters were very promising, including the models I produced. Though some of my results were not up to scale I still had achieved what I still came to do. The animation on maple was quite a letdown because it would have been nice to see an animation of the data I found for HAT-P-10 to transit. Other than that everything else was achieved successfully.

46


Bibliography

Haswell, C. A. (2010). Transiting Exoplanets. Cambridge: University Press Ltd.

Mason, J. W. (Ed.). (2008). Exoplanets: Detections, Formations, Properties, Habitability. Chichester: Praxis Publishing Ltd.

Mgr. Poddaný, S. Exoplanet Transit Database. Retrieved from the website: http://var2.astro.cz/ETD/index.php [Last accessed March 26th 2013]

Nave, R. (2012). Kepler’s Laws. Retrieved from Hyper Physics website: http://hyperphysics.phy-astr.gsu.edu/hbase/kepler.html [Last accessed March 25th 2013]

Schneider, J. (2012). The Extrasolar Planet Encyclopaedia. Retrieved from the exoplanet website: http://exoplanet.eu/catalog.php [Last accessed March 26th 2013]

‘The Planetary Society’. (2012a). Astrometry: The Past and Future of Planet Hunting. Retrieved from The Planetary Society website: http://planetary.org/explore/topics/extrasolar_planets/extrasolar/astrometry.html [Last accessed March 15th 2013]

‘The Planetary Society’. (2012b). Transit Photometry: A Method for Finding Earths. Retrieved from The Planetary Society website: http://www.planetary.org/explore/topics/extrasolar_planets/extrasolar/transit_photometry.html [Last accessed March 20th 2013]

‘The Planetary Society’. (2012c). Microlensing: Beyond Our Cosmic Neighbourhood. Retrieved from The Planetary Society website: http://www.planetary.org/explore/topics/extrasolar_planets/extrasolar/microlensing.html [Last accessed March 17th 2013]

Weisstein, E. W. (2012). Circle-Circle Intersection. Retrieved from the Math World website: http://mathworld.wolfram.com/Circle-CircleIntersection.html [Last accessed March 23rd 2013]

Cessna, A. (2010). Terrestrial Planets. Retrieved from Universe Today website: http://www.universetoday.com/50287/terrestrial-planets/ [Last accessed March 17th 2013]

Cessna, A. (2009). Gas Giants. Retrieved from Universe Today website: http://www.universetoday.com/33506/gas-giants/ [Last accessed March 17th 2013]

BBC News. (2013). Extrasolar Planets. Retrieved from the BBC News Website on Exoplanets: http://www.astro.sunysb.edu/fwalter/AST101/habzone.html [Last accessed March 20th 2013]

Fig 2.2: http://www.nasa.gov/mission_pages/hubble/science/rogue-fomalhaut.html

Krist, J. (2006). Exoplanet Detection with Coronagraphs. Retrieved from the Nasa.gov website: http://exep.jpl.nasa.gov/TPF/Coronagraph_PDFs/CWP2006_15_Krist_pp83-85.pdf

47

http://exep.jpl.nasa.gov/TPF/Coronagraph_PDFs/CWP2006_15_Krist_pp83-85.pdf

http://www.nasa.gov/mission_pages/hubble/science/rogue-fomalhaut.html

http://www.astro.sunysb.edu/fwalter/AST101/habzone.html

http://www.universetoday.com/33506/gas-giants/

http://www.universetoday.com/50287/terrestrial-planets/


Fig 2.6.1: Dijk, V, A (2008). The transit method of detecting extrasolar planets. Retrieved from Nasa.gov website: http://www.nasa.gov/mission_pages/kepler/multimedia/images/kepler-transit-graph.html

Everett, E, M., Howell, B, S. (2001). A technique for ultrahigh-precision CCD photometry. Publications of the Astronomical Society of the Pacific.

Fig 2.1: 2MASSWJ 1207334−393254. [Photograph]. In Encyclopædia Britannica. Retrieved from: http://www.britannica.com/EBchecked/media/123739/The-brown-dwarf-2MASSWJ-1207334393254-as-seen-in-a-photo

Fig 1.1: N/A (2013). Habitable Zone. Retrieved from: https://www.e-education.psu.edu/astro801/files/astro801/image/Lesson%2012/491px-Habitable_zone-en_svg.png

Fig 2.3: N/A (2013). Gravity Lens Geometry. Retrieved from: http://www.physics.wisc.edu/undergrads/courses/fall2011/107/images/25-01-gravity-lens-geometry.png

Fig 3.2.1, 3.2.2, 3.2.3: Mgr. Poddaný, S. Exoplanet Transit Database. Retrieved from the website: http://var2.astro.cz/ETD/index.php [Last accessed March 26th 2013]

Fig Espenak, F. (2012). Transit of Venus. Retrieved from: http://eclipse.gsfc.nasa.gov/OH/transit12.html

48

http://eclipse.gsfc.nasa.gov/OH/transit12.html

http://www.physics.wisc.edu/undergrads/courses/fall2011/107/images/25-01-gravity-lens-geometry.png

http://www.physics.wisc.edu/undergrads/courses/fall2011/107/images/25-01-gravity-lens-geometry.png

https://www.e-education.psu.edu/astro801/files/astro801/image/Lesson%2012/491px-Habitable_zone-en_svg.png

https://www.e-education.psu.edu/astro801/files/astro801/image/Lesson%2012/491px-Habitable_zone-en_svg.png

http://www.britannica.com/EBchecked/media/123739/The-brown-dwarf-2MASSWJ-1207334393254-as-seen-in-a-photo

http://www.britannica.com/EBchecked/media/123739/The-brown-dwarf-2MASSWJ-1207334393254-as-seen-in-a-photo

http://www.nasa.gov/mission_pages/kepler/multimedia/images/kepler-transit-graph.html


Appendix

Appendix 1

All Images of HAT-P-10b which were taken with a CCD Camera by David Harris and image of HAT-P-10 located on Skymap. This is within a CD attached.

Appendix 2

AIP4Win images of step by step Multi-Image Photometry. This is within a CD attached.

Appendix 3

The AIP4Win csv file which shows the data from all the images that were processed of HAT-P-10b. This is within a CD attached.

Appendix 4

Once the csv txt file is input into excel. All data from the csv file which is now spread out nicely on excel for a clear view of what AIP4Win found from each image. This is within a CD attached.

Appendix 5

Excel file of the post-editing. Including V-C1 and V-Ens. Excel light curve photos are also included. This is within a CD attached.

Appendix 6

Only the reliable sources were used which was the flux and the Julian Date in hours. This is the excel notepad txt file which has both the flux and Julian Date in hours data for each image which is input into Maple. This is within a CD attached.

Appendix 7

Pictures of the step by step guide of Modelling HAT-P-10b on Maple. This is within a CD attached.

49


Appendix 8

Project Plan:-

Final Year Project Plan

Date 9/11/2012

Student: Vinh Trung Ton

Supervisor: Michael McCabe

Mentors: David Harris and Chris Priest

Provisional Title:

Observation and Modelling Study of Exoplanet ……..

As you can see I have not chosen a specific Exoplanet yet. Not until I have gone to the observatory where I will ask David which one is best to observe and model.

Project Brief:

The universe has always been an interest to me. I find it amazing to know that technology is always updating itself to be able to find more and more mysterious, yet exciting new discoveries. We all know it is very difficult to calculate the actual size of the universe. The question is, are we alone?

The study of exoplanets is a study to help us find out more about our universe. To see if there is just one other Exoplanet that is capable of habitability. Not just that but also its properties, formation, movement etc…

Due to our technology that is always updating and expanding, it has given us a clearer picture of our universe. With all the new ways of detecting exoplanets we can one day find the truth about our universe. One of the most well known satellites is the Nasa Kepler space satellite. It is designed to detect transiting earth sized exoplanets.

My project will overall connect all the information from my own research to work of previous projects in to this topic, which was carried out by other students. Currently I have not picked a specific exoplanet yet, but when I do I will then use the data and will hopefully be able to make mathematical models.

Before I start by researching and collecting data for one specific exoplanet I will analyse more about the methods of detecting exoplanets. Not all technology is perfect, but there are always advantages and disadvantages when we use them.

50


Using the observatory’s collected data and methods to show how an exoplanet is detected and what I find.

I will use AIP4WIN and Maple to model my findings. Using my findings for the specific exoplanet I will then compare my results with

other Astronomers results over the past years. Then finally I will look about the future observations and Conclude my results and

anaylsis.

Plan:

October Picking Project topic and Supervisor.

November Finalise Project Plan and start finding resources.

December Regular visits with supervisor and journeys to the Observatory. Further data collection

from findings at observatory and references. Use of programs using the data collected.

January Use of AIP4WIN and Maple. Including more further data collection from resources and

observatory visits. Regular visits to supervisor. Looking up books that will be

useful.

February Final visits to the observatory, Final visits to my supervisor. Continue to write up my

project. Use of programs. Looking back at what I have already done.

March Finalise Project to hand in on March 28th. Last visits with supervisor and mentor at the

observatory. Finalise all data found. Complete Project!

April Using the information on my final year project I will create a power point

51


presentation. This will be finalised before April 23rd where I will present this

presentation.

Brief Chapter Plan:

Abstract: A brief review of the whole project Chapter One: Introduction to exoplanets

History from the first exoplanet being discovered Chapter Two: Ways of detecting an exoplanet

Transits Direct Imaging Astrometry Microlensing Radial Velocity

Chapter Three: Observations Transit Options Using AIP4WIN

Chapter Four: Data Analysis Usage of Matlab or Maple

Chapter Five: Limb Darkening Chapter Six: Modelling

Calculations Simulators

Chapter Seven: Conclusion Analysis

Modelling Limb Darkening

Construction and Observation

Resources:

- Kepler.nasa.gov

52


- Mason, J.W.(2008). Exoplanets(Detection, Formation, Properties, Habitability).UK: Praxis Publishing

- Exoplanet transit data base (ETD) (var2.astro.cz/ETD)- Exoplanet.hanno-rein.de- Methods of detecting extra solar planets (Wikipedia)- Thomas Stephens (2011), Observation and Modelling Study of Exoplanet Qatar1b,

University of Portsmouth, Portsmouth. (Dissertation)- Peter Miller (2011), An in-depth study of the detection, observation and modelling of

transiting exoplanatory systems, University of Portsmouth, Portsmouth (Dissertation)

- AIP4WIN and Maple

53

Web viewThe term planet is an ancient Greek word for ‘wandering star’. Some of the...

Documents

Transcript of Web viewThe term planet is an ancient Greek word for ‘wandering star’. Some of the...