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RSAA SUMMER RESEARCH SCHOLARSHIP REPORT

PHILIP LAH
Project: Extra-Solar Planets Supervisors: David Weldrake & Penny Sackett Scholarship from Wed 20th Nov 2002 to Fri 31st January 2003 ABSTRACT For my Summer Research Scholarship Project I searched for transiting, `Hot Jupiter' planets in the globular cluster 47 Tucanae. I analysed part of a set of observational data taken by David Weldrake, looking through it for planetary transits and variable stars. The probability of finding a planetary transit in my small part of this large observational data set was low, however their was a better probability of finding a few, previously undetected short period variable stars. Due to time constraints only half of my part of the data was analysed. In the half that was finished no planetary transits or variable stars were found; a null result. I also created fake light curves of variable stars, including planetary transits, so that I would have a better understanding of how the light curves of real objects would behave. I have also included with this report a section on the many things I learned during my Summer Scholarship. 1. INTRODUCTION The aim of the project was to see if there were any observable planetary transits in 47 Tucanae. 47 Tuc (NGC 104) is a nearby globular cluster (only 4.11 kpc away), bright (V~4 mag) and is ~30' across (actual size ~37 pc across). 47 Tuc is only visible from the Southern Hemisphere. The goal of looking for planetary transits in 47 Tuc was to see whether planets could form and survive in globular clusters, regions of low metallicity and high stellar density. The advantage of using globular clusters for a planet search is that one can observe many stars with a single pointing. The more stars observed the higher the probability of finding a transit. David Weldrake observed 47 Tuc for 33 nights at Siding Springs Observatory using the SSO 40" (1 m) telescope in August and September of 2002 (80% of the nights were usable). He used the Wide Field Imager made up of 8 CCD chips using a special V+R filter that allowed an increased signal to noise ratio. Each night a series of 5-minute (300s) exposures of 47 Tuc were taken. This series of observational images are turned into light curves for each star that show the change in flux of the star as a function of time. Once the light curves have been obtained they are analysed for any periodic variations in the flux that could be the signature of a variable star or a planetary transit. A planetary transit occurs when a planet passes in front of the star it orbits, reducing the flux that we can measure for that star for a short time period of time. This change in flux of the star will only be observed if the plane of the planets orbit is in line with us, limiting the number that can be seen. Planetary transits that would be detectable in the observation data would involve Hot Jupiters, planets with masses equal to or greater than Jupiter's with orbital periods between 3 and 5 days that lie very close to their parent star. These are the types of planets that have already been observed using the Radial Velocity method that looks at the movement of the spectral lines of a star to determine if any low mass companions are present. The Radial Velocity method is only useful for finding planets in the nearby solar neighbourhood while the method of detection of planets from transit can be used out to much greater distances. A planetary transit due to a Hot Jupiter would reduce a main sequence star's luminosity by ~2%. This is comparable to the size of the errorbars in the observational data. The good temporal resolution of the data over the 33 nights of observations should make it possible to detect the 3 consecutive transits required for confirmation of a planetary transit. A previous series of observations of 47 Tuc were done by Gilliland et al. (1999) using the Hubble Space Telescope specifically looking for planetary transits. For 8.3 days they observed a 0.6' size part of the core of 47 Tuc which had ~34,000 main sequence. They did not find any planetary transits and concluded from their null result that the frequency of planets in 47 Tuc is at least an order of magnitude lower than in the solar neighbourhood. David's observational data covers the entire globular cluster resulting in ~129,000 light curves that each run for 33 days. There are 40,000 main sequence stars in this set of data but these are spread across the whole of the globular cluster. Theoretically planets have a better chance of forming and surviving in the outer, lower stellar density regions of a globular cluster. This is due to the lower probability of a planet being perturbed out of its orbit around its star by a close encounter with another star. This fact as well as the longer length of observation than Gilliland et al. (1999) should result in a higher probability of finding planetary transits. The other stars in the ~129,000 light curves are mostly giants which are analysed because they could be variable stars. 2. PRODUCING THE LIGHT CURVES
Fig 1. Negative image of Globular Cluster 47 Tucanae (from Antilhue - Chile) .

The observational data is broken up into 8 parts, each corresponding to a CCD chip on the Wide Field Imager. David 1


Fig 4. One of the raw images and the template image for Section 4 subsection 3,1. Fig 2. All the CCD chips of the Wide Field Imager with the sections and sub-sections of CCD 5.

was in the process of completing his analysis of CCD 3 and I was to analyse CCD 5. The centre of 47 Tuc is in the centre of the CCD chips so that CCD 5 lay on the outer edge of the globular cluster, meaning that it is a lower stellar density region. This meant that it contained fewer stars so could be more quickly analysed during the nine weeks of my Summer Scholarship and also increased the survivability of any planets in that region. I analysed only the last 11.4 days of the observational data (the best seeing data) to help reduce the time needed to run the analysis programs. My raw data consisted of 581 fits images from CCD 5 with the time (as a Modified Julian Date) at which each image was taken. To simplify the computer analysis the fits images where broken up into 4 sections and then each section was broken up into 8 subsections as seen in Fig 2. Each of the CCD chips has a width of 2044 pixels and a height of 4096 pixels. The sub-sections are each 512 pixels square. The resolution is 0.4" per pixel. I started my analysis on section 4 of the CCD and then moved on to section 3. I started with these sections first as they contained fewer stars so that I initially would have less light curves to work with while I was still learning how to analyse them. Time constraints meant that work was unable to be started on section 1 and 2. This was unfortunate as there were more stars in these sections as they are closer to the high stellar density centre of the globular cluster as can be seen in the fits image of CCD 5 (Fig 3.). There were ~3000 distinguishable stars in section 3 and 4 combined (2993 actual light curves). A rough estimate of the number of distinguishable stars in section 1 and 2 combined gives ~8000 stars, almost three times as many stars as in the sections that where completed. Completing the Fig 3. One of the 300s exposures analysis on so many extra of 47 Tuc from CCD 5. light curves would not have

taken that much extra time as I had developed my skills to the point where I could do the analysis much quicker than I did for the initial sections. There are many different conditions that can affect the flux of non-varying stars. The flux from a star can be affected by the amount of atmosphere between the telescope and the star that varies throughout the night (the air mass), whether the moon was up or not, the presence of faint clouds etc. To overcome these factors all of the fits images were rescaled in flux to match that of a reference frame (the best seeing fits image which had seeing of 1.14"). This was done in such a way that the whole fits image was rescaled not each individual stars so that any real stellar variation between images would not be lost. The position of a star on the fits image can also vary. This may be due to variations in seeing between exposures, problems in exactly aligning the telescope at exactly the same direction for each observation or other problems. To correct for this a template fits image for each sub-section was created by combining 43 of the best seeing images. This combined image shows much clearer the location of each of the stars, even the faint ones, as seen in Fig 4. All of the fits images are aligned to the template image so that the same star in every image has the same position. Once these calibrations were completed the fits images were run through a photometric pipeline script using the Difference Image Analysis method (also known as Image Subtraction) from WoY niak (2000) to look for possible variable star candidates. This pipeline script took about 3 days of computer time to run per section. The light curves of these variable star candidates where then produced and viewed by eye to see if they were actual variable stars or merely junk. Since it was unlikely that the image pipeline script was sensitive enough to detect the faint variation of a planetary transit, light curves of all the stars in the fits images where also made. To do this a file with the coordinates of all the stars in a subsection fits image was manually created from the template image. This file was then used as the input into part of the photometric pipeline script restant_subtraction_photomerty to create light curves for all the stars in that subsection. This process generates too many light curves to easily and accurately analyse by eye. A periodogram program was therefore used to take the Fourier transform of each of the light curves using a normalised Lomb-Scargle Periodogram algorithm (from the book Numerical Recipes) that takes the Fast Fourier transform of non-equally spaced data. Periodic patterns in the light curve are seen in the Fourier frequency domain as high power peaks indicating a possible variable star candidate that can then be 2


Fig 5. The light curve of the best candidate for a variable star in my data set from section 3, subsection 1,2, the number 2 light curve shown over 11.4 days. The starting date is MJD 52528.453.

Fig 6. The wrapped light curve for the best candidate for a variable star in my data set with wrapped period of 2.407 days.

checked by eye. Examples of the Fourier output from this program can be seen in the next two sections (Figs 9 and 12). 3. THE LIGHT CURVES The light curves that are produced are functions of delta flux versus time (in days). The delta flux is a ratio unit that is defined such that for a non-varying star the delta flux will always be zero independent of the stars magnitude. One can convert the delta flux into a percentage change in flux if one knows the magnitude of the star as defined by the reference image. It is interesting to note that the error in the delta flux for different stars seems to be approximately the same at a particular time with no dependence on the magnitude of the star. The error seems to depend strongly only on the seeing at the time of measurement. This is a property of how the delta flux is calculated and the error will in fact depend on the star's magnitude when the delta flux is converted from the ratio unit to an actual flux using the star's actual flux. Neither looking through my light curves by eye or using the periodogram program found any evidence of any real variable stars. There were strongly varying, periodic light curves but they either increased each night or decreased each night or had some other repeated pattern that occurred each night. These and other periodic variations were discounted as junk as the same pattern occurred in more than one light curve. This type of varying light curves are most likely the result of errors in matching the Point Spread Function of the star cause by a nearby bright star (the program gives a very high В2 value for these points). A star's apparent size on the fits images increases in size when the seeing is bad. A bright star may increase enough in size so that its flux enters into the Point Spread Function of nearby stars causing an apparent variation. The repeated variation of the seeing each night due to the air mass in front of 47 Tuc changing as it rose and set could be responsible for these one-day period varying light curves.

The frequency analysis using the periodogram program also found evidence of periodic behaviour in multiple light curves. However, as the first and second highest power peaks in the frequency spectrum where the same in more than one light curve, these can also be discounted. The most commonly detected highest peak power frequency was the one-day period that corresponds to the regular spacing between observing nights. The best candidate for a variable star in my data is shown in Fig 5. The plot of the light curve looks very jumbled and chaotic. However it is difficult to determine from this plot whether this is a property of the star or due to the discontinuities in the curve from non-observing time from daytime or missed observing time when it was clouded over. To get a more continuos light curve the data is broken up into sections of one period length and super-imposed on one another to create a wrapped light curve as seen in Fig 6. The wrapped light curve does show a rather chaotic periodic light curve. From the periodogram program the highest peak in the frequency spectrum had power 16.1 with a corresponding period of 2.407 days, which is the period used in the wrapped light curve in Fig 6. The highest peak in the frequency spectra of non-varying stars was at most 8 and was usually lower than this meaning that the 16.1 is a significant frequency power. The reason this star was my best candidate was that it was the only light curve with a reasonably high peak power that had didn't have a peak period that was shared by another light curve. However the next highest peak in the frequency spectrum of this light curve had power 15.3 with a corresponding period of 1.742 days. This power is very close to the highest peaks power. This fact, with the messy wrapped light curve, suggests that the variation in the light curve is not due to a physical effect, i.e. the star is not a variable star. The star was located close to the edge of its subsection. There were sometimes problems with matching up stars between fits images near the edges of subsections and this may be related to the apparent variation in the light curve of this star. 3


Fig 7. The light curve of a RR Lyrae Star from CCD 3 over the full 33 days of observations. The starting date is MJD 52509.488.

Fig 8. The wrapped light curve of the RR Lyrae Star with wrapped period of 1.524 days, which is 4 times one period of the main oscillation of 0.3809 days.

An example of a light curve of an actual variable star is shown in Fig 7. for a RR Lyrae star located in the Small Magellanic Cloud that lies behind 47 Tuc. This RR Lyrae star comes from David's analysis of CCD 3 and so runs the full 33 days of observations. The wrapped light curve of the RR Lyrae star (Fig 8.) clearly shows the distinctive fast rise and slow decline in the flux of this type of variable star. RR Lyrae stars are population II stars on the horizontal branch (they burn Helium in their core) and they all have the same intrinsic luminosity. They have short periods of variation; the period of the main oscillation of this star is 0.3809 days. However the period used in the wrapping of the light curve is actually 4 times the actual period of one oscillation. This was done so that one can see that the peak flux of each oscillation is not the constant. This is unusual and is an example of the Blazhko effect, a regular changing in the amplitude of variation that has been discovered in some RR Lyrae stars. The Fourier frequency spectrum for this RR-Lyrae star was also generated and a plot of it can be seen in Fig 9. The highest power peak in the frequency spectrum has power 25.7 and corresponds to a period of 0.3809 days, which is the period of the main oscillation of the star. This with other tests of the periodogram program on the light curves of other known variable stars from CCD 3 demonstrates that this program could detect the periodic behaviour in a light curve that indicates that the presence of a variable star. The expectation before the start of the project was that there would be a few variable stars in my data, i.e. a null result was not expected. David has found in CCD 3 that roughly 0.1% of the stars are variable stars. This lead one to expect to find ~3 variable stars in my ~3000 light curves. The null result may indicate a difference in the environments between CCD 3 and CCD 5 (the inner and outer regions of the globular cluster) that affects the number of variable stars that exist in each. However finding no variable stars in this particular region may not be statistically significant. As one only expects to find ~3 variable stars (a small number) the random statistical variation may be enough to make a null result a plausible outcome without

effecting the number ratio of variable stars in 47 Tuc. If one analysed the whole of CCD 5 one would expect to find ~11 variable stars as there are approximately 11,000 stars in total. If the number of variable stars were found to be much less than the expected 11 variable stars one would have a stronger statistical argument. Once an analysis of all the CCD chips is completed a better comparison between the inner and outer regions of the globular cluster can be made. The expected number of planetary transits in my data can also be roughly estimated. In the solar neighbourhood about 2% of stars have Hot Jupiters (seen from the radial velocity method) and about 7% of these will have a planetary transit lined up with our line of sight so that it can be seen. This

Fig 9. The frequency spectrum of the RR Lyrae Star displayed as power vs. frequency from the periodogram program.

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Fig 10. Theoretical and observational light curves of a fake planetary transit plotted on the same axes.

Fig 11. Both the theoretical and observational wrapped light curves of the fake planetary transit with wrapped period of 2.25 days.

means that ~0.14% of stars have detectable planetary transits so that one expects ~4 planetary transits in my ~3000 light curves. However this estimate is very poor as it is based on the observations of the solar neighbourhood environment. The environment in 47 Tuc is vastly different in metallicity and stellar density. In fact it is believed by many that the number of planets that can exist in a globular cluster is significantly less than the solar neighbourhood. This means that the expected ~4 planetary transits is best taken as an upper limit on the number of transits not as a measure of how many one expects to find. Once again this is a small number of expect detections so a null result may not be statistically significant. It is possible that there are planetary transits in my data that where not detected by my analysis using the photometric pipeline or by the periodogram program. The small variation in the delta flux of a planetary transit would make it difficult to detect by either method. Hence a match filter algorithm is being developed by David specifically to look for planetary transits. The match filter will generate a series of possible planetary transit light curves and compare them to the actual light curves. A В2 value will be calculated for each comparison and from this one can determine whether that possible planetary transit light curve is a good fit to the observational data. This type of analysis will be expensive in computer time but would provide the best chance of finding planetary transits in the data. 4. FAKE LIGHT CURVES When I produced my first light curves I was unsure how to tell real variable objects from the random noise or junk. I was particularly unclear on how a variable star's light curve would look with the observational data's discontinuities and random errors. To correct this lack of knowledge I decided to create a program to make fake light curves of variable stars. The program starts by making a theoretical continuous light curve using simple mathematical relations between time and delta flux. The points in these theoretical light curves that correspond to the same time values as the observational data are then selected. Random errors are then introduced for each

of these points by the equation below to create observational fake light curves. new delta flux = old delta flux + error в a random number with a Gaussian distribution The value of the error was the average error at each point taken from ten real light curves (the error in the real light curves did not vary much from light curve to light curve for the same point in time). To test the validity of this method of generating fake observational light curves I compared the light curve of actual non-varying stars with a fake non-varying light curve and found that the two where essential identical. All of the fake light curves developed have easily varied parameters such as their period and amplitude of variation, enabling one to create a wide variety of light curves. I made fake light curves using simple sine curves as well as light curves matching the expected shape of RR Lyrae stars and occulting binary stars. I also made a series of increasingly more complex models of fake light curves of planetary transits of which the most realistic version is shown in Fig 10. The fake planetary transit in Fig 10. has a transit depth of 1.5 delta flux units and the planet's orbital period is 2.25 days. The planet takes 0.2 days (4.8 hours) to complete its transit in front of the star. The wrapped light curve for the fake transit is shown in Fig 11. The simple model used to generate this fake transit is that of a periodic dip in the delta flux with sides that are sine curves and a flat region in between the sine curves. The sine curve represents regions where the planet is only partially in front of the star and the flat region where the planet is completely in front of the star. No attempt was made to model the actual theoretical model of a planetary transit, as it is fairly complex involving a numerical evaluation of a messy integral. The actually differences between my simple model and this theoretical model would not be significant as the small differences would be blurred out by the random error in the observation fake light curves. I also ran the periodogram program on the fake light curves to test whether the program could detect such variable stars. In Fig 12. the frequency spectrum for both the theoretical and 5


a high peak in the frequency spectrum corresponding to its period as the above example. The peak may not even be the highest peak making the transit even more difficult to detect. Tests with a variety of fake light curves to quantify this effect would help to determine the ease by which the periodogram program can find planetary transits. This problem with the matching of transits and observing times will be less significant in the full 33 days of data as there is more chance that a transit will appear multiple times in the observational data. One thing that did come out of this Fourier analysis of this fake transit is that the periodogram program can detect the small periodic variations of at least some planetary transits. The fact that no planetary transits where found in my ~3000 light curves may therefore indicate that there are none rather than merely being an inability to detect them. 5. WHAT I LEARNED FROM THE SCHOLARSHIP During the Summer Scholarship: I learned how important time management is especially as it applies to large projects. Nothing takes as long as one expects. Constant monitoring of one's progress is necessary so that one can decide what can be completed and what cannot in the time available. I also learned how unexpected complications can arise that can dramatically affect your planned timetable. I came to understand that when you go looking for something you do not always find what you expect, that a null result is a scientifically significant result. I gained knowledge on a wide variety of different areas of Astronomy and Astrophysics from various sources including the Summer Scholar Lecture Series, the Feast of Facts and the Colloquia. I learned in detail the properties of extra -solar planets and planetary transits as well as the different types of variable stars and the shapes of their light curves. I discovered that the hard stuff to learn is not the Astrophysics but the learning of how to do the Astrophysics, i.e. the skills (especially the computer skills) necessary to produce a result. I found out how much larger in quantity and how much messier real scientific data can be compared to my previous experience in undergraduate physics labs. I found out how much processing of scientific data is necessary to remove all the known systematic errors before one can start the interesting analysis. I greatly improved my programming skills so that I am now more confident in my ability to solve problems by either writing my own code or by modifying existing programs. I become skilled at using Super Mongo and Unix including Unix scripts and came to understand the advantages of the Unix operating system. Also I improved my knowledge of Fortran programming (something I wish to improve further). I began to use the Internet as a more effective information resource for Astronomical information as well as starting to use it for detailed information on programming. (Having instant access to the Internet all the time when one is working changes the way one use it.) 6

Fig 12. Frequency Spectrum of Theoretical and Observation Light Curve for Fake Planetary Transit.

observational light curves of the previous fake planetary transit are shown. In the theoretical curve the highest peak's power is 244 with a corresponding period of 2.238 days. This period compares well enough to the actual period of 2.25 days such that a wrapped image at this period will make the transit visible to the eye. The other peaks that are positioned at regular intervals and show a decreasing trend in power correspond to frequencies that are в2, в3, в4, в5, etc. of this highest power frequency. This pattern is due to the way in which a square wave can be formed by a Fourier Series of sine curves. A square wave is built up by taking a sine wave with frequency equal to the square wave's frequency and adding to it an infinite series of sine curves that are integer multiples of the square wave's frequency but with decreasing amplitude as one increases the frequency of the sine curves. The fake transit is not quite a perfect square wave due to the sine curve shaped sides of the transits, which is why there are other small features in the frequency spectrum. The observational curves highest peak's power is 45 with a corresponding period of 2.216 days. This period is close enough to the actual period of 2.25 days to make detection possible. The highest peak power has greatly decreased from the theoretical frequency spectrum, where it was 244, showing how much the added discontinuities and random errors blur the periodic variation. The observational spectrum is a reasonably chaotic mess of peaks but one can see the traces of the regular structure of the theoretical peaks. This messiness in the frequency spectrum is another indication of the detrimental effect that the added discontinuities and random errors have on the periodic variation. To create this well-defined fake planetary transit I had to artificially adjust the period and offset of the theoretical model so that the actual transit occurred on multiple observing nights. A planetary transit in the actual observational data would be unlikely to be as well behaved especially in my 11.4 days of data. A planetary transit that does not have a transit that overlaps as well with the observing times would not have such


Udalski, A. et al. 2002, AcA. 52 317 (astro-ph/0301210) Weldrake, D. T. F. 2002, PhD Thesis Proposal. Giant Planets in Globular Clusters. Westra, E.A.M. 2002, Draft Honours Thesis. A Search for Planets and Other Variables in 47 Tucanae. WoYniak, P. R. 2000, AcA, vol 50 421-450 (astro-ph/0012143) Weldrake, D. T. F. for the template program, photometric pipeline program and other programs to make the light curves that where based on Wozniak (2000) image subtraction method http://astrosun.tn.cornell.edu/~akgun/Fortran/fortran.html The source of the original unmodified Fortran program periodogram.f, which is based on the Normalized Lomb-Scargle periodogram from Numerical Recipes for Fortran, (2001) www.astrosurf.com/antilhue/ngc_104_-_47_tuc.htm Picture of Globular Cluster 47 Tucanae (Fig 1.) from Antilhue - Chile, a website of Antilhue, an amateur astronomical observatory.

7. ACKNOWLEDGEMENTS The following people are to be thanked for their help and support throughout the scholarship: David Weldrake for providing an int eresting project and for his help in learning how to run the various programs. Also for being available so that I could pop in and ask a question when I needed help and for proof reading this report, giving suggestions on improvements. Penny Sackett for her inspiration and her many ideas on how to proceed with the project. Ken Freeman for his additional information on the globular cluster 47 Tuc. The Stromlo staff that gave the lectures to the Summer Scholars. The staff and students of Stromlo for m aking me and the other Summer Scholars feel welcome and an important part of the Stromlo community. Fiona Aplin, Terry Gallagher, Denise Bourne, Peter Walshe, Graeme Blackman and the other administration and computer staff for helping to make the scholarship run smoothly especially after the fire. The various tour guides at the observatories for giving up their time to show a group of students around. Rob McNaught for taking time out of his observing to let us play around with a real research class telescope, the 40" at Siding Springs. The other Summer Scholars: Alicia, Angela Anna, Elizabeth, Jessie, Leith and Patrick for the pleasure of their company and friendship during the Scholarship. And Simon Driver for organising and running the RSAA Summer Scholarship Program in 2002-2003 which I found to be a most productive experience and a useful tool in preparing me for my Honours year on the Mountain.

Fig 13. Four of the images that where taken by the Summer Scholars on the SS0 40 inch telescope during the observatory tour. The top left image is NGC 3132 a planetary nebula in Vela. The top right image is M42 the Orion Nebula. The bottom left image is NGC 1566 a galaxy in Dorado and the bottom right image is NGC 2298 a globular star cluster in Puppis. The rest of the images can be seen at http://www.mso.anu.edu.au/~plah/40_inch_jpeg_images.html

I gained experience in using IRAF as well as other Astronomically specific programs like ds9. I had my first real exposure to front line research and actual Astronomical Papers. I saw on the observatory tour the large variation possible in telescope design among both optical telescopes and radio telescopes. I increased my understanding of what actual observation work is like from the observing the Summer Scholars did at Siding Springs on the 40" with Rob McNaught taking some images of Astronomical interesting objects. Finally I saw first hand how the aftermath of a disaster is successfully managed and gained experience in how to get back to work after such an event. 6. REFERENCES
Costa, G.C. 1977, PhD Thesis. The Structure and Content of Globular Clusters. Davies, M. B. & Sigurdsson, S. 2001, Mon. Not. R. Astron. Soc. 324 (astro-ph/0104336) Gilliland, R. L. et al. 2000, ApJ 545: L47-L51. Konacki, M. et al. 2003, Natur.421..507-509 Sackett, P. S. 1999, poss.conf 189S (astro-ph/9811269)

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