Detrend survey transiting light curves algorithm (DSTL)

Mon. Not. R. Astron. Soc. 000, 1 5 (2002) Printed 19 November 2010 (MN LATEX style file v2.2) Detrend survey transiting light curves algorithm (DSTL) D. Mislis 1, S. Hodgkin 1, J. Birkby 1 1 Institute of Astronomy, Madingley Road, Cambridge CB3 0HA, UK Accepted??. Received??; in original form?? ABSTRACT We introduce Distill algorithm (DSTL) for correcting transiting survey The algorithm is searching for correlations between all light curves of the sample and creates the best comparison stars for reduction. Statistical studies in real data, shows that DSTL is able to improve further more, already corrected light curves from systematic features. On the other hand, the algorithm could be applied in raw light curves from any transiting survey. For our test we have used a sample of 12000 light curves from the WTS (WFCAM Transit Survey) infrared survey. WTS is using the infrared 3.8m UKIRT telescope in Hawaii. DSTL improves the rms of our sample by a factor of 5 mmag and also reduces the number of false transits detections. Key words: Extrasolar planets transits survey algorithm. 1 INTRODUCTION Since 2000 many teams are searching for transiting exoplanets using ground based telescopes, such as like Super- WAP, HatNet, TrES etc. The photometric accuracy which needed for exoplanet detection is higher that 1 % and very often, ground based data are suffering not only from general systematics as airmass and seeing, but for trends and flux jumps. Kovács et al. (2005) and Tamuz et al. (2005) gave some solutions for de-trending these features with TFA (Kovács et al. 2005) and SysRem (Tamuz et al. 2005) respectively. TFA is creating a light curve base using light curves with the smallest rms and searching systematics trends in all light curves from this base. On the other hand, SysRem is searching for systematics in the full light curve sample and corrects common features in all Both algorithms are searching for general trends in the data sample and that is why some features, which do not appear in many light curves, remain in the sample. In this paper we present the Distill algorithm (DSTL) and using it, we study the case in which our sample, except general systematic trends, suffers by features which are not appear in all For testing our algorithm we used infrared data from WTS survey and RoPACS (Rocky Planets Around Cool Stars - Lodieu et al. (2009)) project. WTS is an infrared survey searching for transiting exoplanets around late type stars (K & M type stars) using the 3.8m UKIRT telescope in Hawaii. WTS is using 4 fields close to the galactic plane monitoring 12000 stars per chip. The magnitude range is 13 < m < 22 in J-band. In order to test DSTL we have used stars, only from one CCD (12000 in total). E-mail: misldim@ast.cam.ac.uk 2 THE PROBLEM The data we have used are not raw For data processing we have used the CASU pipeline (Irwin et al. 2004). CASU after the bias and flat fielding corrections, fits an airmass and a seeing polynomial function, in order to remove systematic effects. In our examples, is obvious that our data do not include systematic patterns. The problem is that, many times there are trends which are not systematics ( jumps ) and some times are similar with transit events. These features appear only in some of the light curves ( 0.2 2%) in our sample. He have searched for correlations in 12000 light curves and we found that there is a linear distribution of correlation between magnitudes. Figure 1 shows the results from our test in which bright stars are higher correlated (linear fit). This kind of correlation is irrelevant from any general systematic effects like airmass and seeing because there are already removed. One explanation for these correlations are hot pixels, cosmic rays etc., and to avoid all these causes, we create the correlation diagram of the star s chip positions. Figure 2, shows the same test as Figure 1 but instead of magnitudes we have used the chip s x and y coordinates of each star to calculate the separation between them. Correlation is randomly distributed in this diagram (Figure 2), meaning that there are no evidence for position correlation. 3 THE ALGORITHM Before we start to explain the algorithm, we assume that it is almost impossible to have in the same field (some thousands stars), two or more transits with exactly the same period c 2002 RAS

2 D. Mislis Figure 1. Magnitude versus correlation. A liner fit shows that bright stars are higher correlated. Figure 3. Correlation diagram versus magnitude for a single light curve (19e-2-00100 ). The horizontal line at R T,B = 0.2 shows the correlation cut that we have used. Light curves above the 0.2 threshold (2.5σ), belong to the target family. Figure 2. Star separation versus correlation. There is no correlation pattern. and epoch. DSTL is based in this assumption. We split the algorithm on 3 steps. 3.1 Step 1: Define the target family We assume M light curves and for each light curve f(i) we can write f(i) : {i = 1, 2, 3,..., n}, (1) where f(i) is the flux and n is the total number of data points. First, we create two kind of lists and each list contains the same number of stars. Let s call the first list target list (TL) and the second Base list (BL). The algorithm select the first light curve from the TL. We are going to explain the algorithm for just one light curve of the TL but the procedure is similar for all the other light curves in the TL. TL s first light curve is 19e-2-00100. We calculate the correlation between the target light curve (19e-2-00100 ) and all the light curves from the BL using the equation R T,B = 1 n 1 n i=1 (T i T )(B i B) SD T SD B, (2) where T i and T are the target light curve and the mean value respectively. Also B i and B are the base light curve and the mean value. Finally, SD T and SD B are the standard deviation of target and base light curve respectively. At the end, we calculate M correlation numbers in total and we create the correlation plot of the 19e-2-00100 light curve. Figure 3 shows this correlation plot. We call target family light curves (FTL) all light curves in the base list, which show correlation higher than 2.5σ (R T,B > 0.2). FLT contains light curves with different magnitudes. In our example the family contains 223 light curves ( 1.86 % of the full sample). If the target light curve does not include any systematics, we expect the mean correlation to be equal to zero (R T,B = 0.0) and Figure 3 shows exactly this scenario. 3.2 Step 2: Remove the trends FTL includes light curves with different magnitudes and because of that, we can not simply remove the family from the target. If there is a jump, because the different magnitudes, the mag of the jump is different for each family light curve. To solve this problem we normalize and zero average all the family Then, we subtract the first family light curve from our target calling the new light curve NT. The rms of the NT (RMS 2) is smaller than the rms of the target light curve (RMS 1). We continue to subtract the first family light curve from the NT again and again, until the RMS 2 becomes larger that RMS 1. Then we continue the same procedure using all the FTL. Mathematically, we need to minimize the equation below { RMSk 2 = MIN 1 n } n (NT i F T L i,j NT ) 2 i=1 j k,(3) where NT is the mean of the target, F T L i,j is the j th target light curve, and k is the number of loops per FTL. Using this technique, we avoid double correlations. For each per target-base light curve there are two correlation numbers, the target-base R T,B and the base-target R B,T as well. If we minimize Eq. 3, we skip to create double binary or transits

Detrend survey transiting light curves algorithm (DSTL) 3 Figure 4. The mag reduction of shake algorithm. mag is function of the period and the duration of the transit. For a typical hot Jupiter the mag is 1-10 %. When the algorithm stops minimizing Eq. 3, then the current NT i is our pre-final target light curve (PFL). 3.3 Step 3: Fit & Shake In this step, the algorithm fits a low-degree polynomial in order to remove a long term variability P F L(t) = a + b t + c t 2 + d t 3, (4) where a, b, c & d are fitting parameters and t the time in Julian date. As final step DSTL applies the shake algorithm. In this step we are using only the flux column from the PFL file (NP F L 1) and we create a second light curve by replacing the first data point of thr P F L with the last one (NP F L 2). Using the same trick we replace the last data point of the PFL, with the first one and we create a third light curve (NP F L 3). In principal, we have now three light curves, with the same number of points, the same real events but with different noise pattern. NP F L 1,i = P F L 1,2,3,...,n (5) NP F L 2,i = P F L n,1,2,...,n 1 (6) NP F L 3,i = P F L 2,3,4,...,n,1 (7) The final light curve is the average of these three new NF L i = (NP F L 1,i + NP F L 2,i + NP F L 3,i)/3, (8) where NF L i is the final light curve. The shake algorithm is optional and give good results if the target light curve has many data points. For example, if the PFL, has only one point during the transit, the depth of the transit is reduced by a factor of three after shaking. The reduced transit depth is a function of the time resolution of the light curve, the period and the duration of the transit. The best way to handle shake is to fit in the phase folded, because the phase folded light curve has many more data points than the normal light curve during the transit. Figure 4 shows the reduced mag of the depth over the period and duration, after shaking. Finally, Figure 5 is a map diagram of DSTL s steps. Figure 5. DSTL steps diagram. 4 EXAMPLES & RESULTS 4.1 Statistical results To test DSTL, we have used the 19h field of WTS infrared transit survey and 12000 light curves for one CCD chip. All light curves have passed through CASU reduction pipeline which removes all systematics effects such airmass and seeing. After applying DSTL in our sample, the rms of all light curves have been reduced by a factor of 5 mmag (Fig. 6). The reason we create DSTL is to clean transiting light curves. To test how good is DSTL, we run a transit detection algorithm (Aigrain & Irwin 2004) in 9000 light curves of our sample before and after DSTL. This test shows, that the detection signals before DSTL are stronger than the same signals after DSTL. That means, (a) the detection limit decreasing and we can search for transits around fainter objects and (b) the number of fake alarms has been reduced and DSTL could be used to improve light curves for transiting surveys. The results of the previous test are plotting in Figure 7 and the difference of the detection signals (before and after) are sim 1.5 σ. 4.2 DSTL & non-systematics features The light curve 19e-2-00100 is a very clear case of what DSTL does. The family of the target light curve, contains 223 light curves with correlation 0.2 to 0.7 (Figure 3). Figure 8, on the other hand, shows the raw and the reduced light curve after 6 integrations. At the first light curve (top) there is one small jump around frame 500 and a bigger

4 D. Mislis Figure 6. Top: rms diagram. The rms before DSTL (red circles) is larger that rms after after DSTL (blue squares) by a factor of 5 mmag. Bottom: The rms after (RMS 2 ) over rms before (RMS 1 ) ration versus magnitude. All light curves of our sample belongs below 1.0. Figure 8. The 19e-2-00100 light curve before (top) and after (bottom) DSTL. rms values are RMS 1 = 0.11 and RMS 2 = 0.048 for the first and second light curve respectively. 4.3 Shake & transiting depths Light curve 19h-3-14922 is a eclipsing binary system. This light curve shows no jumps or other trends, but it is a nice example of shake algorithm. The shake algorithm does not reduce the depth of the eclipse but improves the total rms of the light curve. At the top panel of Figure 9, we show the phase folded light curve before and after DSTL (red circles and blue squares respectively). The RMS 2 is smaller than RMS 1 (RMS 1 = 0.0685, RMS 2 = 0.0656) and the final light curve has been improved. The bottom panel of Figure 9 shows the residuals of the two light curves above. Figure 7. Transit detection signal before versus after DSTL. The detection signal decreases or remains the same in the worse case after DSTL. jump at the end of the light curve. The high correlations of Figure 3, suggest that these features are not unique in our sample, but only few light curves are suffering by them. At the second light curve (bottom), the first jump has been removed completely and the second has been reduced. The 4.4 DSTL versus TFA & SysRem The final question which have to answer in this point is : Why we do not use other algorithms like TFA or SysRem? Figure 3 answers this question. In Figure 3, as we mention before, the mean correlation average is zero. There are many light curves with positive correlation and equal number of light curves with negative correlation. Because the uncorrelated sample is 98.1 %, TFA or SysRem fail to remove jumps which appear only in very few To prove that, we run both TFA and SysRem in our raw light curve

Detrend survey transiting light curves algorithm (DSTL) 5 Figure 9. Top: The 19h-3-14922 light curve before (red circles) and after (blue squares) DSTL.Bottom: Residuals from the two Figure 10. RMS 2 vs RMS 1. Top: The dash line is the DSTL fit and dash-dotted line is the TFA fit. Bottom: Similar, the dash line refers to DSTL and dash-dotted line to SysRem. The difference between DSTL and TFA or SysRem is 1.55 mmag sample. As a result, we found that the RMS 2 using DSTL is much smaller that the RMS 2 using TFA or SysRem. In Figure 10, both plots (top and bottom) show the RMS 2 versus RMS 1. The dash line is DSTL and dotted-dash lines are TFA and SysRem respectively. After DSTL the RMS 2 has been improved more than the other two algorithms. 5 CONCLUSIONS We have presented the Distill algorithm (DSTL) for detrending transiting Our algorithm is based on correlation and not on the common systematic errors, but the correlation method is more general because includes systematic effects already. DSTL can be used in raw data or already reduced data, after applying known algorithms such TFA or SysRem. Our analysis shows that the light curves from a photometric survey is possible to suffer by nonsystematics features. In this situation, known algorithms do not succeed to clean the data. For our tests we have used 12000 light curves from the WTS infrared transiting survey and using DSTL, we managed to improve our light curves by 5 mmag and the transits detection signals by 1.5 σ. ACKNOWLEDGMENTS We thank Garbor Kovacs and Brigitta Sipocz for helpful suggestions. REFERENCES Aigrain, S., Irwin, M., MNRAS, 350, 331 Irwin, M., J. Lewis, J., Hodgkin, S., Bunclark, P., Evans, D., McMahon, R., Emerson, J., P., Stewart, M., Beard, S., 2004, SPIE, 5493, 411 2009, MNRAS, 397, 258L Kovács, G., Bakos, G., Noyes, R., W., MNRAS, 356, 557 Lodieu N., Burningham B., Hambly N. C., Pinfield D. J., 2009, MNRAS, 397, 258L Tamuz, O., Mazeh, T., Zucker, S., MNRAS, 356, 1466 This paper has been typeset from a TEX/ L A TEX file prepared by the author.