Millimagnitude Accuracy Photometry of Extra solar Planets Transits using Small Telescopes S. Kozłowski 1, 2, A. Szary 1, M. Zub 1, G. Melikidze 1, K. Maciesiak 1, J. A. Gil 1 1 Institute of Astronomy University of Zielona Góra, Lubuska 2, 65 265 Zielona Góra, Poland 2 Jodrell Bank Observatory, Macclesfield, Cheshire SK11 9DL, United Kingdom e mail: simkoz@astro.ia.uz.zgora.pl Abstract Nowadays, the extra solar planets observations are possible for universities, or even amateur observatories equipped with a small telescope with a CCD detector. Up to date many extra solar planets have been found (Henry et al. 1999, Udalski et al. 2002, 2003, Alonso et al. 2004), which movement on their orbits causes from time to time a small decrease of the central star s brightness. A planet s transit may be detected with millimagnitude accuracy thanks to an appropriate data analysis. Using the astronomical equipment donated by the Alexander von Humboldt Foundation we managed to detect two transits of the planet orbiting HD 209458, measuring the 1.77% brightness decrease with up to the 0.19% accuracy. Moreover, our observations were done at the ground level, on the suburban area of a middle size university town. Introduction Throughout the world university observatories are usually equipped with small telescopes and CCD detectors. With such equipment it is possible to observe transits of extra solar planets. Up till now a few extra solar planets have been found with orbits inclinations of nearly 90 degrees to the line of sight. Such positioning results in a partial eclipse of the star by the planet, which in turn is seen as a decrease in the brightness of the star (Borucki et al. 1985). The planet moving around HD 209458 was thoroughly investigated by several groups of scientists (e.g. Brown et al. 2001). Its period equals 3.52 days. Computing consecutive transits is relatively easy, thus observing this planet is a good test of both: the equipment and the system of data reduction. Basing on a single CCD exposure, after reduction (dark current subtraction, flat field correction), the brightness of a star of 6 9 magnitude can be measured with the accuracy of 0.01 0.02 magnitude. Such accuracy is not satisfactory as the star s brightness decrease caused by a transit of the planet orbiting HD 209458 is on the level of 0.017 magnitudes. To extract from the noise the brightness decrease it is necessary to maximise the accuracy by means of a sophisticated observational data analysis.
Equipment To measure the brightness of HD 209458 we used a Meade LX200GPS SMT telescope of the Schmidt Cassegrain type with the diameter D = 355.6 mm (14 ), and the focal length equal f = 3556 mm (140 ), which gives the power ratio f/10. A CCD SBIG detector of the type ST 8XE together with UBVRI filters was placed at the telescopes focus. All the optical surfaces were covered with an anti reflexive layer of UHTC (Ultra High Transmitting Coating), thanks to which more than 94% of light reaching the correction plate concentrates at the focus. The telescope steering is fully computerised and operates both: in the Windows (software: Sky Map, Meade Autostar) and Linux (software: Xephem, Xmtel) environments. The accuracy of tracking is not very good, which makes longer, narrow field expositions nearly impossible. The worst tracking accuracy in the case of azimuthally mounting without an auto guider is 0.2 /s. The CCD detector we used, model ST 8XE SBIG, comprises two CCD chips. The auto guider chip (TI TC 237) gives 657 x 495 pixels, and the measuring chip 1530 x 1020 pixels (Kodak KAF 1602E). A pixel dimension is 9 x 9 µm, which gives the chip dimension of 13.8 x 9.2 mm. The chip response is linear up to 43000 ADU, which, with the amplification of 2.3 e /ADU, gives the depth of the potential well of about 100000 e (without anti blooming). The dynamical range for this detector is about 74 db. The dark current is 1e /pixel/sec at 0C. The exposure times are from 0.12 s to 1 h, and the time of image reading is about 3.7 sec. The read noise does not exceed 15 e. The range of quantum efficiency is about 200 1000 nm, with the maximum for the wavelength of about 600 nm (68%). The research grade UBVRI SBIG filters were used. The transmittance ranges for particular filters are equal to those of Bessel s filters (Bessel 1990). The transmission maxima for particular filters are respectively: U (367 nm, 68%), B (431 nm, 71%), V (523 nm, 86%), R (594 nm, 83%) and I (778 nm, 92%). An additional micro focuser was also employed to boost the focusing precision. For the above described configuration 0.55 of the sky is reflected in one pixel, which for the CCD detector employed gives the field of view of 14.0' x 9.3'. Observations The observations of HD 209458 star brightness were done during two transits of the planet on 3rd August and 10/11th August 2004. On 3rd August 463 exposures were taken, from those 430 well focused were included into our analysis. On 10/11th August from 1260 exposures only 1209 were taken into account. On the rejected exposures the stars were shifted/blurred (PSF ellipses, arcs). The observations were done using the LX200GPS SMT 14 telescope, CCD SBIG ST 8XE detector, and V filter. Exposure time for single exposure was equal 10 sec. With this kind of exposure time, there was at the maximum 18000 ADU for a pixel for HD 209458 and 5000 ADU for the comparison star GSC2.2 N002201115158. Seeing during the observation time was in the range of 2.4 2.8 (FWHM). The CCD detector was operated automatically with, alternatively, a 10 sec exposure and 5 sec gap (reading). The telescope was operated by SkyMap Pro 8 software, and CCD camera by CCDOPS.
Analysis The brightness of HD 209458 star is V = 7.65 magnitude and the star is located at: RA: 22h 03m 10.8s, Dec: +18 o 53' 04. As the comparison star was chosen the brightest star in this field of view GSC2.2 N002201115158 with V = 11.16 magnitude and coordinates RA: 22h 03m 07.5s, Dec: +18 o 51' 35. During observations seeing was 2.4 2.8 (the star radius (FWHM) in an exposure < 3 pixels). In photometry as a standard it is taken that the aperture radius is 1.5 times bigger than FWHM (Full Width at Half Maximum) of the star. In our case accepting such measuring aperture would omit long PSF tails (Point Spread Function), due to this fact part of the light would not be measured. In our observations we put the measuring aperture radius equal 20 pixels, thus yielding PSF values at the noise level. At the distance of about 35 pixels from our comparison star there was another star, so the internal background radius was set at 44 pixels, and the external at 54 pixels. Preliminary image reduction was done using IMARITH programme. Automatic scripts based on IRAF package were written, both for searching the stars in the picture (DAOFIND), and for measuring the number of counts (APPHOT). The number of counts within our aperture for HD 209458 was about 560000, and about 22000 for the comparison star. The photon noise for these values was equal, respectively 750 and 150 counts. The uncertainty of measurements resulting from the photon noise is given by the formula = 100 N %, (1) where N is a number of counts from the star. The uncertainties due to photon noise are equal respectively 0.13% and 0.67%. The star brightness in particular exposures differ due to the atmospheric scintillation. In our case, for 10 sec exposures, these errors are, respectively 1.2 and 1.8%. These errors measurements were done on basis of 300 observations of the same star brightness. The standard deviation was computed outside the transit dip. Two main measurement errors result from the above described causes, and the remaining (e.g. reading noise) are of no real importance (less than 10% of the total error), and we will disregard them. The total error is a square root of the sum of squares of single errors and in our case it is 2.3% which represents the change in brightness of about 0.023 magnitudes. The decrease of HD 209458 brightness caused by the extrasolar planet s transit is about 1.7 %, thus it cannot be easily noticed in a single, 10 sec exposure. To increase the measurements accuracy, single observations were summed by 20 and 80, respectively, and the sum was taken as a single observation. It can be seen, that in such case the measurement errors are considerably diminished. For observations summed by 20 the error is 0.26% (0.19% scintillations; Fig. 1), and for observations summed by 80 0.19% (0.12% scintillations; Fig. 2). In order to estimate the uncertainties we measured the number of counts from our stars in each exposure, and we sum the measured values. The photon noise is calculated according to (1) and the scintillation noise according to: sc = A1.75 D 2/3 2 t, (2)
where is a constant depending on the observation site, A airmass, D telescope diameter in cm, t integration time. A thorough analysis of the measurement errors is accessible at: http://astro.corlan.net/gcx/html/node8.html Fitting models to observational data Using analytical equations describing the dip in the light curve during a transit given by Mandel & Agol (2002) we fitted two models to our data (summed by 20). First model was called model with uniform surface brightness of a star and the second one was limb darkening model, which describes an event in a right way. By fitting the model with uniform surface brightness of a star we obtained the following parameters: Ratio of the radius of the planet to radius of the star p = 0.125 ± 0.071, what corresponds to 1.56% ± 0.51% of decrease of the brightness of the star. Transit time was equal to 2.89h. Fitting the limb darkening model we obtained the following results: p = 0.120 ± 0.034 and the decrease of the brightness of the star: 1.77% ± 0.26% (decrease of the brightness in this model does not follow relation of the square ratio of radius of the planet to radius of the star). Time of the event was 2.99h. Other parameters for the limb darkening model were: u 1 = 0.372, u 2 = 0.348 (more details in paper by Mandel & Agol 2002). Summary The aim of our research was not deriving physical parameters of the planet orbiting the star HD 209458 (you can find them in many papers, e.g. Brown et al. 2001). Our main goal was to show that using small telescope one could perform professional observations. Parameters derived in our investigation stay in agreement with those found by the group using the HST. Comparison of results obtained by the HST (Brown et al. 2001) and ours is shown in Table 1. Similar results were obtained by other observatories equipped with small telescopes. Bruce L. Gary from the USA, using 10 Meade LX200 and CCD detector SBIG ST8 E + filter V found decrease of brightness of the star by about 1.55% ± 0.22% and the transit time 2.4h. Another transit of this planet was observed by Osamu Ohshima from Japan, who used 4 telescope equipped with CCD detector SBIG ST9 XE and found dip in the light curve as 1.6% and transit time 2.96h. Our Astronomical Observatory is going to undertake observations of other extra solar planets in collaboration with international group of observers transitsearch.org. Information on the next observation of extra solar planets will be available on the website: http://astro.ia.uz.zgora.pl. We thank for helpful comments to Łukasz Wyrzykowski (Warsaw Astronomical Observatory), prof. Andrzej Udalski (Warsaw Astronomical Observatory) and prof. Jerzy Kreiner (Mt. Suhora Astronomical Observatory). Conclusions The observations of HD 209458 presented in this paper were done at the ground level, on the suburban area of a middle size university town. Soon our telescope will be mounted under the dome
of the newly built astronomical observatory of the University of Zielona Gora. Then, the accuracy of extra solar planets transits photometry will increase, although even now it is sufficient to join the world programme of extra solar planets search by transits detection: transitsearch.org. Bibliography Alonso et al. (2004), ApJ., 613, 153 Borucki et al. (1985), ApJ., 291, 852 854 Brown et al. (2001), ApJ., 552, 699 Henry et al. (1999), IAU telegramme 7307 Alonso et al. (2004), ApJ., 613, 153 Udalski et al. (2002), Acta Astron., 52, 317. Udalski et al. (2003), Acta Astron., 53, 133. Table 1. Comparison of the results derived using the HST (Brown et al. 2001) with our results. brightness dip [%] transit time [h] p u 1 u 2 HST 1,64 ± 0,000087 3,07 0,122 ± 0,050 0,292 0,348 OAUZ 1,77 ± 0,26 2,99 0,120 ± 0,034 0,372 0,348
Fig. 1. Observations of two extra solar planet transits. Filled circles represent the sum of 20 observations of 3 August 2004, empty circles show summed in the same way observations from 10/11 August 2004. Decrease in the star s brightness of about 1.70 % can be seen, observational errors during the first night were at the level of 0.45% (changeable weather during observations) observational errors during the second night are at about 0.26%.