Secondary Eclipse of Exoplanet TrES-1

Transcription

1 Secondary Eclipse of Exoplanet TrES-1 Patrick Herfst Studentnumber Sterrewacht Leiden, room 441 Supervised by dr. Ignas Snellen

2 Contents 1 Summary 3 2 Introduction Exoplanet research Transit method Secondary eclipse The TrES-1 system Observations and data reduction Observations Background removal Flatfielding The light curve Integration radius and calibration Seeing adjustment Fitting an eclipse model Conclusion and Further work 24 6 References 25 7 Abbreviations 25 1

3 List of Tables 1 TrES-1 properties Fitted secondary eclipse parameter values Parameter values for binned data List of Figures 1 Illustration of a transit Eclipse model fit onto artificial data set Image of an original data file Bias current removal per pixel Ring-like structure around tilting positions Attempted adjustment of overestimated removal Example of a reduced field Effect of calibration by reference star Correction of jitter bias Determining the optimal integration radius Contour plot of TrES-1 with Gaussian fit Seeing values of both sources Seeing correction for both sources The obtained light curve of TrES Best fitted partial eclipse Binned measurements with resulting fit

4 1 Summary This report has been written on account of a small astronomical research project (Klein Sterrenkundig Onderzoek), being part of the mandatory curriculum of the Astronomy Masters programme at Leiden University. It was carried out under the supervision of dr. Ignas Snellen at the Sterrewacht Leiden. The main goal of the project was to investigate the secondary eclipse of exoplanet TrES-1 in the near-infrared region of the spectrum, from reducing observations to obtaining and analysing the light curve. K band measurements of TrES-1 were taken on the Nordic Optical Telescope at La Palma in August It consisted of a three hour observation of TrES-1 and a nearby reference star using the NOTCam instrument. This data was first reduced by removing bias current from the array. Then the sky background was carefully modelled and subtracted from the data files. Remnants of the edges of the stellar disks remain visible, yet should have a minor effect. A sensitive flatfield was made to eliminate pixel sensitivity variations, which provided the reduced data frames. To calculate the total flux levels per interval, the APER routine of IDL was invoked. The appropriate integration radius was determined by performing a χ 2 test, providing an optimal value of 15 pixels. By taking the flux count ratio of both stars, the flux counts were calibrated and normalised. Intrinsic bias for alternate jitter positions was attempted to be removed, although remnants are clearly still present. Atmospheric seeing was counteracted by Gaussian fits to obtain a final light curve. An IDL program was written to fit a typical eclipse shape to this data set. It showed that the optimal model has parameters consistent with earlier results such as Charbonneau et al. 2005, although a higher upper limit value to the eclipse depth of 0.4% was found. However, statistics show that the detection of the transit is not a valid one; it provided only a 1.2σ detection, so random distributions could not be fully excluded. 3

5 2 Introduction This chapter gives an overview of the processes behind the project. It will provide a short overview of exoplanet research, especially using the transit method, and take a look at the general properties of the TrES-1 planetary system. 2.1 Exoplanet research The search for planetary systems is one of the most exciting fields in astronomy today. Searching for alien worlds dates back to ancient times, and is a direct result of mankind s age-old quest for answers to fundamental and highly philosophical dilemmas. Only recently the available observational techniques have developed far enough to actively go in search of planets beyond our solar system. It will perhaps one day answer the most important question of all - whether or not we are alone in the universe. The first exoplanet was discovered in 1992 by Wolszczan and Frail. Using pulsar timing, they found evidence of a large body orbiting pulsar PSR B The first verified discovery of an exoplanet orbiting a main sequence star (51 Pegasi) was announced by Mayor and Queloz in Astronomers soon set out to find other similar planets, with overwhelming success. We now know of 268 extra-solar planets, and that number is expected to dramatically increase as several space-based missions, such as the newly launched COROT and the expected Kepler satellite, start giving results in the next few years. The large majority of known exoplanets have been discovered with the radial velocity method. A planet orbiting a star exerts a slight gravitational pull, which causes the star to wobble very slightly about the solar system s centre of mass. The star s spectrum would exhibit periodic shifts due to the added Doppler effect in the star s emitted light. With very accurate spectroscopic measurements over a length of time, the presence of another body can be confirmed. It is possible to determine the exoplanet s orbital period but only a minimum mass, as the system s inclination remains unknown. Recently a super-earth planet was discovered surrounding the red dwarf star Gliese 581 by Udry et al It is the smallest exoplanet known to date, with a lower limit mass of only 5 Earth masses. Since it actually lies within the star s habitable zone, it is capable of having liquid water and could therefore possibly support or even contain life. The possible discovery of such environments in the foreseeable future makes exoplanet research one of the most interesting and relevant topics in contempory astronomy. 2.2 Transit method The detection of extra-solar planets via primary eclipses is a simple one to envision. A planet orbiting the star moves (partially) across the stellar disc, blocking starlight in our line-of-sight. This causes a measureable decrease in the observed photometric signal of the system with a 4

6 highly regular frequency, namely the planet s orbital period. For a Jupiter-sized planet in front of a solar type star, this dip amounts to 1% of the stellar intensity. Although relatively simple, this method recieved serious attention only after the detailed quantification of its possibilities by Borucki and Summers (1984). Figure 1: Illustration of the effect of a transit on the star s light curve. Transits provide a sensitive way to detect planets orbiting other stars. Other than the radial velocity method, eclipses can provide us with information about the planet itself. The duration of a transit depends on the size of the stellar disk and the size and inclination of the stellar orbit. Together with an accurate stellar typing of the parent star, measurement of the transit duration and period yields an estimate for the radius and inclination of the planet s orbital plane. These can be refined by spectroscopic observations, making it possible to make crucial tests of giant planet formation, migration and evolution. Numerous ground-based photometric searches are underway that try to find exoplanets by means of their photometric signal. Since large planets in tight orbits will create the most significant and frequent occultations, these are the easiest to detect. Using better than 1% photometry, several of these so-called hot Jupiters have been found in wide-field surveys. Future space-based projects such as the Terrestial Planet Finder (TPF) provide one of the most promising chances of detecting planets with similar mass and environments as Earth. The principal disadvantage of this method is that it requires a suitable alignment of the viewing direction with the orbital plane. Given a random distribution of configurations, the probability of such an alignment is very low. Although a method for pre-selection exists using 5

7 rotational spin measurements, surveys without previous knowledge about system configuration are time-consuming and inefficient. Only 34 exoplanets have been discovered using the transit method so far. In general, a model of the flux dimming by an eclipse consist of five seperate phases, labelled A through E in Figure 2. This shows a fitted eclipse model onto an artificial data set with added random noise. Stages A and E represent the unocculted photometric signal from the parent star, while stage C is the total eclipsing period, when the planet is fully in front of the star along our line of sight. In between are the transitional phases, when the planet is moving into (B, called the ingress) or out of (D, egress) the stellar disk. It was assumed here that the transitions between phases are sharp, ignoring additional effects such as limb darkening. Figure 2: An eclipse model fit onto an artificial data set with added random noise. Stages A and E are the stellar flux level, B the ingress, D the egress and C the total eclipsing period. Short-term variations in transit timing may indicate the presence of moons or other planets, while long-term variations in the lightcurve could result from orbital precession or migration, although neither effect has yet been confirmed. 2.3 Secondary eclipse This research project focusses on measurements of the secondary eclipse. This phenomenon occurs when a transiting exoplanet moves behind its parent star instead of in front of it, which is described above. The light that was previously reflected or re-emitted by the planet s atmosphere, adding to the total observed flux, is now being blocked by the star. This causes 6

8 a slight deminishment of 0.1% of the photometric signal for Solar System parameters, which increases again when the transit ends. Because of this faintness, the study of secondary eclipses is a relatively new area in exoplanet research. The size and mass of a planet, as well as several orbital parameters, can be determined via a detection of the primary eclipse. A secondary eclipse is worthwhile because it directly measures the planet s radiation. This can be compared to models to retrieve the planet s effective temperature and albedo, and possibly estimates of the orbit s inclination and eccentricity. For a mathematical description of secondary eclipses, see Sackett Observations at a range of wavelengths could in the future study the composition of the atmosphere. The dip in the light curve caused by a secondary eclipse is necessarily an order of magnitude less than that of a primary eclipse. Earlier researches in the NIR failed to provide results that exceed the statistical noise adequately. In other wavelength regions, such as the FIR, such projects met with more success. By observing secondary eclipses of the brightest known transiting exoplanets, the light contributions of TrES-1 (Charbonneau et al. 2005), HD b (Deming et al. 2005) and HD b (Deming et al. 2006) have recently been determined with the Spitzer Space Telescope. Measurements in the NIR are wanted because of the difficulty distinguishing between the planet s emission and the stellar output, because the planet is overwhelmed by its parent star. One of the objectives of this project is to detect the eclipse on a 3σ level. This complements known data at other wavelengths, ensuring better models of the TrES-1 system and a further understanding of planet formation. 2.4 The TrES-1 system The TrES-1 extra-solar planetary system was the first to be discovered with the Trans-Atlantic Exoplanet Survey (TrES). This is a network cooperation of three ground-based, small aperture (4 inch), CCD-based telescopes: STARE, PSST and Sleuth. Combining their efforts, they target the sky in wide field ( 6 deg) photometric surveys in search of low-amplitude periodic variations in the light curves of bright stars. The subsequent discovery of TrES-1 in the summer of 2003 was a results of a total of 74 good nights of observations. It was confirmed with radial velocity measurements by the Keck Observatory, and results published by Alonso et al. in To date, the TrES program has yielded four discoveries of transiting exoplanets. TrES-1 is an extrasolar planet orbiting the K0V star GSC , located at 157 parsec (Charbonneau et al. 2005) in the constellation of Lyra. Similar to many other planets detected around other stars with the transit method, TrES-1 belongs to the class of hot Jupiters. Its mass is less than that of our system s giant, yet its radius is somewhat larger, which may be the result of tidal effects. Properties of the TrES-1 parent star and its surrounding planet taken from Alonso et al are shown in Table 1. It is only the second transiting planet orbiting a star bright enough to allow for a variety of follow-up analyses similar to those conducted for HD b (eg Charbonneau 2003). Two 7

9 stars with similar magnitudes and colors lie nearby, which can be observed in the same frame as the target. They can act as reliable calibration sources, as Section 4.1 shall utilize. Table 1: TrES-1 properties, taken from Alonso et al Parent Star Planet Parameter Value Parameter Value R.A. 19 h 04 m 09 s.8 (J2000.0) P (8) days Decl (J2000.0) a ± AU K mag i deg Spectrum K0 V K ± 6.2 m/s M s 0.88± 0.07 M Sun M p (0.75 ± 0.07)M Jup R s R Sun R p R Jup 2MASS R p /R s

10 3 Observations and data reduction This chapter will explain how the data measurements delivered by the NOT were reduced. The bias current and sky background was removed from the images, and a flatfield made to produce the final images. First the specifications of the telescope used and the supplied data will be elaborated on. 3.1 Observations This project is based on photometric measurements of the TrES-1 system while the planet undergoes a secondary occultation. These observations were produced by the Nordic Optical Telescope (NOT) in La Palma on Tenerife, one of the Spanish Canary Islands. The NOT is a Ritchey-Chretien optical system with a 2.56 meter diameter primary mirror. Our measurements were taken with NOTCam, a multi-mode instrument for use in the short-wave infrared region (SWIR) of the electromagnetic spectrum ( µm). It uses a CCD with µm pixels in HgCdTe and is capable of wide-field imaging (4 4 ) at a range of different resolutions and polarities. Figure 3: Image of a data file, plotted in DS9. TrES-1 is the source on the right hand side. 9

11 Observations of the secondary eclipse of TrES-1 were made beginning at 22:33 UT on August and lasting until 01:28 UT on August 24. The scheduled observation was postponed due to local weather and telescope cooling problems. When observing could commence, the occultation was already in progress, so the first part has not been detected. A total of 155 measurements have eventually been taken in the high-resolution mode of arcsec fields. From the precise eclipse timing in Charbonneau 2005, the secondary eclipse can a priori be calculated to have a central time at 23:25 UT on August 23, which lies well within the observing time-frame. Due to accumulated uncertainty in the period length, timing of the eclipse could be somewhat off. To the date of our measurements, only 98 orbital periods have passed. The accumulated error due to the uncertainty in the period (see Table 1) affects this timing by 67 seconds maximal, not enough to disturb the measurements. TrES-1 was observed in a single field with a reference star at a distance of 44 arcsec, known only as 2MASS J This star will function as a calibration tool, as Section 4.1 shall show. Successive exposures have been nodded in a cycle of five points about 16 arcsec apart for a more effective background removal. Every observation shows a large anomaly at the top-centre area of the field, believed to be an array malfunction. They also contain a number of light and dark columns, luckily none of which cross stellar positions. An example of a data fits file, plotted in DS9, is shown in Figure 3. The supplied observations had a 40 second total exposure time, in which the CCD array is read out five times. A straight line was fitted through these readouts, and its slope used to Figure 4: Bias current removal for a single pixel by fitting a straight line to five read-outs. The left data point is the resulting photon count. 10

12 yield a total photon count of each pixel during measurement time. Thus the bias current of the CCD array is effectively removed. This is illustrated for a single pixel in Figure 4. Total timescales for a single measurement vary somewhat, yet are typically 57 seconds. 3.2 Background removal The first step that has to be taken in data reduction is the determination of the sky background level. The sources and short-term event like cosmic rays need to be separated from the total image. This can be done by utilizing the tilting of the aperture beam, already mentioned in Section 3.1. The placement of TrES-1 and the reference source on the array is circulated in cycles of five successive data files. Each individual pixel within one of these cycles provides a set of five photon counts. If one of these counts is higher than a threshold value, it is assumed that a source or event was positioned on the pixel, and it is subsequently removed. The average of the remaining counts was taken as the normal sky value for the entire cycle and subtracted from the original images. All fields were normalised for this procedure. The threshold value that was implemented corresponds to 50% above the average count number. Bad pixels, such as light or dark columns or containing negative counts, were replaced with the average of the surrounding datapoints. If any of these were also corrupted, they have been ignored. Individual pixels still show variations in the order of counts after background removal, not including the area around the sources positions, due to natural variations. However, when averaged over a larger area, the mean residual sky value drops rapidly to 0.2 counts per pixel. This is a satisfactory result, and more than adequate for Figure 5: A ring-like structure appears around currently non-occupied tilting positions due to insufficient removal of the sky background. 11

13 further procedures. The background removal has an unwanted side-effect. At the edge of the sources at other tilting positions, the background is overestimated because the algorithm could no longer sufficiently distinguish between the lower stellar counts and the background level. This produces a ring-like structure, as can be seen in Figure 5. The number of pixels affected is relatively small, and they contain only the edge of the stellar disc, so the total amount of counts should be only slightly altered. A rough geometrical calculation shows that the relative inaccuracy would be 0.03%. However, since both sources are affected by this and the interesting quantity is the ratio between the two, as will be explained in Section 4.1, this overestimation should not have a significant effect. An interesting feature is shown in Figure 6. The first panel shows a cross section of a stellar position after background removal, fitted with a Gaussian shape. For several data files, the mentioned overestimation was attempted to be countered by taking a similar cross section of a non-occupied tilting position in the same field, shown on the second panel, and adding this to the flux counts of the sources. However, as can be seen on the fourth panel of Figure 6, the data actually is less well fitted by a Gaussian curve than before. Apparently, the background removal was successfull enough. Figure 6: The attempted adjustment of overestimated background removal failed, since a Gaussian shape fits a cross section better without correction. 12

14 3.3 Flatfielding Besides intensity measurements, the NOT also provided flatfield images. These consist of four series of ten fields, each with a 30 second exposure time. Half is taken with a bright lamp switched on, and the other half in the dark. Bright images represent the relative sensitivity of all pixels in the array, while dark exposures constitute the array s dark current. By subtracting a dark image from a bright one, the overall sensitivity of the array is determined. All bright measurements were thus summed, and all dark measurements subtracted from this to provide a sensitive flatfield. The data consists of two layers per exposure, representing high and low count rate flat fields, respectively. Subtracting the latter from the former therefore yields differential flat fields. Bad pixels where again interpolated from surrounding data points, and the entire field is normalised. The skysubtracted fields made in the previous section are now individually divided through the resulting flatfield image. This provides the reduced fields which will be used from now on in further procedures. A typical example of what a reduced field looks like when viewed in the DS9 protocol is shown in Figure 7. Figure 7: An example of a reduced field after data reduction. 13

15 4 The light curve In this chapter the data analysis of the reduced images will take place. The objective is to make a light curve of TrES-1, a curve of the emitted total light during the observation. For this the total flux of the sources must be determined for every field. This can easily be done using the standard APER function from IDL s Astrolib, which integrates the total number of counts within a specified circle. However, the central position and radius of this circle first have to be determined. 4.1 Integration radius and calibration In order to determine an integration radius, first the centre of the circle must be retrieved. This was done manually in DS9, using image circles that were fitted to the sources on the reduced fields by hand. These sources show a slightly elongated shape on the array, with the peak intensity removed from the middle. The centre of the fitted circle was used as the focus position for the integration via the APER function. This actually changes per measurement not only because of the jittering of the aperture beam, but also intrinsically due to insufficient correction for Earth rotation during observing. Centered on these positions, the APER function is now called upon for both sources si- Figure 8: The effect of the calibration by the reference star. The obtained light curve from TrES-1 (top line) is divided by that of the reference star (middle) to yield the corrected light curve (bottom). 14

16 multanously. It calculates the total number of counts within a specified radius, and afterwards the ratio of these counts is calculated per field. Assuming that the reference source has a constant flux throughout the observation time, this calibrates the light curve per measurement by removing temporal effects of the array and the atmosphere. The effect of this can be seen in Figure 8, already using the radius obtained further on. This was done for a range of input radii, creating a database for every value. The shape that results from this calibration shows a highly repetative nature. This is the result of so-called illumination effects that occur when tilting the telescope, resulting in intrinsically disparate flux counts at different tilting positions. Such patterns are common for ground-based infrared observations, yet the underlying reasons are poorly understood. Possible explanations are gravitational differences caused by moving the telescope, unknown gradients in the flat field images or heating effects in the read-out array. Whatever the causes for this effect, it will have to be removed from the fields. This can be done by seperating the measurements according to their jitter position, and then normalising each set by dividing each point by the average value. Afterwards all data points are again repositioned according to measurement time. This calibrates the flux counts with respect to the jitter position and thereby removes the bias. Figure 9 shows the light curve before and after this correction. It is clear that the jitter bias removal was successfull to a large extent, although a remnant of it is still visible. After this correction, the best integration radius can finally be determined. A χ 2 test was used to calculate which radius gave the best fit to the measurements after jitter bias removal. Figure 9: Correction of the bias in jitter position due to illumination effects. 15

17 Figure 10: The internal spread after jitter bias removal was calculated by χ 2 testing for a range of radii, showing a value of 15 pixels (marked in red) to be the most favourable. This measures the internal spread of the resulting light curves, with a higher χ 2 value indicating a less coherent and therefore less plausible distribution. The test shows that the integration area which provides the light curve with the highest signal-to-noise ratio (SNR) has a radius of 15 pixels, as Figure 10 illustrates. This value is consistent with a rough estimate that can be made intuitively with the image circles in DS9. All figures shown in this section were made with this radius known a posteriori for illustration purposes. Another way to determine the integration radius was developed alongside this one. Instead of the centre of a source, this method centered on the peak position of the stellar flux and fitted a circular aperture to the reduced field around it. This procedure turned out to be erroneous because of the non-circular shape. Therefore it either incorporates too much noise or not enough actual signal. Nevertheless, most of the calculations have been made for both alternatives. Because the results using the peak position where obviously false, only those following from the method described above will be presented from here on. 4.2 Seeing adjustment The final correction that has to be applied to the reduced data is the seeing adjustment. Due to rapidly evolving fluctuations in the Earth s atmosphere, line-of-sight photons get perturbed, distorting the measurements on the CCD array as well. More specifically, the point source images of the stars get blurred and smoothed out over an increased angular separation. One of 16

18 Figure 11: A contour plot of a typical field around the TrES-1 position with its 3-D Gaussian approximation overplotted in red. Flux levels at 250, 500, 1000, 1500 and 2000 counts. the most common measurements of seeing is the FWHM of the point spread function (PSF), the diameter of the seeing disc. This represents the best possible angular resolution which can be achieved by an optical telescope in a long photometric exposure. To determine the effect the atmosphere had on the initial observations, the amount of seeing was approximated. This has been done by assuming that the PSF of the sources have the shape of a two-dimensional Gaussian, which is in general a valid one to make, and then fitting such a function over the measured flux counts on the stellar positions. A contour plot of one of the fields can be seen in Figure 11, which shows a good agreement with its Gaussian appoximation. The FWHMs of these fitted functions have been taken as a measure of the atmospheric seeing. A single field was unable to get a Gaussian fit because of a failure to converge, and has therefore been removed. To test of the validity of this procedure, the resulting values were plotted against each other and shown in Figure 12. It clearly illustrates that the seeing of TrES-1 is very strongly correlated with that of the reference star. Values lie in a tight band and the slope of the overplotted linear relation is equal to unity within the accuracy, which is expected when the conditions are assumed equal throughout the field of view. The two outlyers have been disregarded in further calculations, since the Gaussian fit could not be verified in these cases. Now that the procedure of quantifying the seeing has been affirmed, the measurements of both sources can be adjusted. The amount of seeing per data file is plotted against the corresponding flux count ratio obtained after the jitter correction in the previous section, 17

19 Figure 12: The seeing values of the reference star and TrES-1 plotted against each other show a highly coherent linear relation with a slope equal to unity within accuracy. using a 15 pixel integration aperture. This is shown in the top halves of the upper and middle panels of Figure 13 for each source. First-order relations have been fitted through these data sets, which are represented by the red lines. To eliminate the seeing from the measurements, the data is divided by these linear approximations. The resulting values are shown in the bottom halves of the first two panels. With the flux counts of TrES-1 and the reference star both corrected, the rectified ratio of the two can now be calculated, The input and resulting ratio values are shown in the bottom panel of Figure 13. The seeing correction proved to be a minor, but given the accuracy needed in the final light curve, necessary one. 18

20 Figure 13: The input data (top half of panels) is divided by the seeing fitted approximations (red lines) to correct the data for seeing (bottom half). The upper panel is data from TrES-1, the middle from the reference star. The lower panel pictures the total adjustment of the flux ratio. 19

21 4.3 Fitting an eclipse model Now that all the necessary adjustments to the data have been made, the final light curve of TrES-1 is obtained. This is shown in Figure 14, where the normalised flux count ratio of TrES-1 to the reference star has been plotted against time. The average error on these values is 0.51%. From this light curve concrete evidence for an eclipse must be obtained. As mentioned in Section 3.1, measurements only commenced when the TrES-1 planet was already being eclipsed by the parent star. Therefore the occultation was only partly observed, and the model made for data sets similar to Figure 2 no longer valid. The IDL fitting program was adapted accordingly, leaving out the initial high plateau and ingress period - phases A and B in Figure 2. Also mentioned in Section 3.1 was the central time determined from Charbonneau et al of 23:25±1 UT. This helps with fixing the eclipse in time, if the duration is known. Sackett 1998 derives a total duration of the primary eclipse Θ I (R + R p Θ I = P π a ) 2 cos 2 i (1) Putting in the values and error margins from Table 1 taken from Alonso et al gives a value of Θ I 153.5±1.5 minutes. Winn, Holman & Roussanova (2007) report an ingress and Figure 14: The obtained light curve of TrES-1, with the normalised flux count ratio of TrES-1 to the reference star as a function of time. The dashed line shows the average value of 1. 20

22 egress length of 18.5±0.6 minutes. The time at which egress begins can be calculated by adding half the total eclipse duration to the central time and deducting the egress duration, which yields 00:23±2 UT. This creates a window for the start of the egress between 00:21 UT and 00:25 UT. However, the eccentricity of the orbit must be taken into account. The duration of the secondary eclipse Θ II are related via: Θ I Θ II Θ I + Θ II e sinω (2) Charbonneau et al derive a value for the longitude of periastron ω 274, while putting an upper limit on the eccentricity of e Putting in this upper limit and using ω = 274, the secondary eclipse has a maximal length of 165±1.5 minutes. This expands the original timing window by 6 minutes, so that the beginning of egress occurs at 00:31 UT at the latest. Letting the eccentricity be a free parameter results in a window for the start of the egress between 00:21 UT and 00:31 UT. The adjusted IDL code that determines the best partial occultation model fit to the obtained data set is now called upon. It returns the optimal combination of parameters using a χ 2 test method. Ideally only the height of the unperturbed flux level and the depth of the light curve are free parameters. But since the upper limit on the eccentricity and parameter uncertainties provide a window of times for the egress to start, this range is also taken along in the fitting procedure. The result can be seen in Figure 15, the parameters resulting from it are listed in Table 2. Figure 15: The best fitted model of a partial eclipse to the obtained data set. 21

23 Table 2: Results from secondary eclipse parameter fitting from the model of Figure 15. Parameter Value Parameter Value Stellar flux level ± Transit depth level 0.37±0.35% Egress starting time 00:27±1 UT Duration of egress 18.7±1 min End of transit 00:46±1 UT Total duration eclipse 162±2 min The uncertainties caused by the fitting program are negligible, since it can be run in increasingly narrow ranges. The inaccuracy in time scales is therefore completely determined by the intrinsic duration of the measurements. The accuracy for all original timescales is therefore taken to be the typical time between two measurements, or 1 minute. The error on the flux levels can likewise be taken increasingly small, yet is limited by the accuracy in the original measurements and in the timing, when improvement on these levels is no longer meaningful. The χ 2 value of this fit is , or 9.31 per data point. This indicates that the model is a poor fit for the data supplied. However, the largest part of this value is caused by the highest scattered points. As a cut-off value, a limit on χ 2 of 5 per point has been implemented.if these most outlying datapoints are removed, the χ 2 value drops to 329.2, or 2.33 per measurement. This is a significantly better result, and although not a good fit, it indicates that the error margin per measurement has probably been underestimated. For this reason the individual errors were all increased by a factor of 2.33 = 1.53 so that the reduced χ 2 value becomes unity and the average error comes to 0.78%. Next the fitted eclipse model must be proven statistically, to make sure this is the correct model to adequately match the given data. As a test function a linear fit was made to the entire data set. The eclipse model has a total χ 2 of 141, being the number of remaining data points, where the best linear fit has a χ 2 of The eclipse model fits the data better; in fact, the chance of finding a greater difference in χ 2 values in a is only 78.7%, or within 1.2 standard deviations of a random distribution. This is caused by the scatter in the data points and the relatively large error margins. This means that the eclipse model is the correct model to fit the data set to within 78.7% certainty. Although a relatively high value, it is not accepted as correct within the scientific community. This requires a 3σ detection, corresponding to 99.7% accuracy, which was the a priori aim of this project. It is therefore implausible to distinguish the given data set as a light curve resulting from an eclipse, which is a disappointing result. This is caused by the lacking of the ingress phase measurements and the troubles encountered during the data reduction. In order to provide with less scattered data, the observations were binned into 15 minute intervals. This only leaves 12 datapoints to run into the fitting program, but that is enough for a conservative estimate. The binned measurements are shown in Figure 16. Almost all of 22

24 Table 3: Results from secondary eclipse parameter fitting from the model of Figure 16. Parameter Value Parameter Value Stellar flux level ± Transit depth level 0.43±0.22% Egress starting time 00:24±1 UT Duration of egress 19.0±1 min End of transit 00:43±1 UT Total duration eclipse 156±3 min the scatter has been removed by the binning, and the average error per data point drops to 0.23%. It also shows that the best fit seems very precise at first glance, although it contains a small number of points. Table 3 lists the parameters of this fit. In both this case and using unbinned data, the eclipse depth was calculated to be 0.4%, which is higher than expected, yet has a large error margin. It is probably wise to take this value as an upper limit. Again, this fit has been analysed statistically. The total χ 2 of the eclipse model now is 12.23, so that the reduced χ 2 value is close to unity. The best linear fit has a χ 2 value of It indicates that the eclipse model was with 80.3% certainty not randomly distributed, or providing a 1.3σ detection. This is a similar result as with the unbinned data, as it should be, and is thus still short of the original goal of 3σ. Figure 16: The measurements binned into 15 minute intervals, removing most scatter. In red is plotted the best fitted partial eclipse model, in blue the best linear fit used for statistics. 23

25 5 Conclusion and Further work Flux count measurements of the TrES-1 planetary system during secondary eclipse, taken with the ground-based NOT, were reduced by removing bias current and sky background, and intensity variations eliminated by flatfielding. After calibrating the flux counts using a nearby reference star and determining the integration radius, the atmospheric seeing was compensated for to obtain the star s light curve. An eclipse model was fitted to this profile to procure the physical process of the secondary eclipse. This provided a calculated eclipse depth of 0.4%, although given the error margins probalby best considered an upper limit. The eclipse model was fitted to a 1.6σ detection, which lies below accepted levels. Although it is safe to assume that a trend towards an eclipse is definitely present, a random distribution can therefore not be excluded. This is caused by the lack of ingress phase measurements and the troublesome data reduction. A number of methods used in this project still need improvement, which shall be listed here briefly. The ring structures that result from sky background removal must be looked into more closely. If it interferes with the count levels to within the accuracy, they should be compensated for. A possible answer could be the masking of the stellar disk positions. The removal of the jitter bias due to illumination effects must be done better, since remnants of it can still be seen. This undoubtely contributes to the spread in the final intensity profile. The eclipse shape used for fitting is a simple one. A mathematically more precise model could be used, for instance including limb darkening, instead of the sharp-edge profile invoked here. Further work on these measurements however is not recommended. Given the fact that the ingress phase was not observed due to local weather, it would prove hard to obtain high quality results and the necessary 3σ detection from these measurements. Space-based projects such as the new Spitzer and COROT telescopes provide one of the most promising chances of detecting planets with increasingly smaller masses in Earth-like environments. Within the next decade a series of space based observatories will be launched that will have sufficiently high resolution to detect possible terrestial worlds. Prominent among these are ESA s Darwin mission and NASA s Kepler mission, with the Terrestial Planet Finder being planned on a longer timeframe. Once found we can then try to detect if these planets have atmospheres, and if so, analysing their composition using special spectroscopic techniques at a range of wavelengths in an attempt to determine if they might hold life. 24

26 6 References Alonso et al.; 2004, ApJ, 613, L153 Borucki & Summers; 1984, Icar, 58, 121B Charbonneau; 2003, ASPC, 294, 449C Charbonneau et al.; 2005, ApJ, 626, 523 Deming et al.; 2005, Nature, 434, 740 Deming et al.; 2006, ApJ, 644, 560D Mayor & Queloz; 1995, Nat, 378, 355 Sackett; 1998, astro-ph/ Sozetti et al.; 2004, ApJ, 616L, 167S Udry et al.; 2007, A&A, 469L, 43U Winn, Holman & Roussanova; 2007, ApJ, 657, 1098W Wolszczan & Frail; 1992, Nat, 355, 145W 7 Abbreviations 2MASS COROT ESA FIR FWHM HD NASA NIR NOT PSF PSST RA STARE SNR SWIR TPF TrES 2 Micron All Sky Survey COnvection, ROtation and planetary Transits European Space Agency Far InfraRed Full Width at Half Maximum Henry Draper (Catalogue) National Aeronautics and Space Administration Near InfraRed Nordic Optical Telescope Point Spread Function Planet Search Survey Telescope Right Ascension Stellar Astrophysics and Research on Exoplanets Signal-to-Noise Ratio Short Wave Infrared Region Terrestial Planet Finder Trans-Atlantic Exoplanet Survey 25