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Principal component analysis to correct data systematics. Case study: K2 light curves

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Abstract

Instrumental data are affected by systematic effects that dominate the errors and can be relevant when searching for small signals. This is the case of the K2 mission, a follow up of the Kepler mission, that, after a failure on two reaction wheels, has lost its stability properties rising strongly the systematics in the light curves and reducing its photometric precision. In this work, we have developed a general method to remove time related systematics from a set of light curves, that has been applied to K2 data. The method uses the Principal Component Analysis to retrieve the correlation between the light curves due to the systematics and to remove its effect without knowing any information other than the data itself. We have applied the method to all the K2 campaigns available at the Mikulski Archive for Space Telescopes, and we have tested the effectiveness of the procedure and its capability in preserving the astrophysical signal on a few transits and on eclipsing binaries. One product of this work is the identification of stable sources along the ecliptic plane that can be used as photometric calibrators for the upcoming Atmospheric Remote-sensing Exoplanet Large-survey mission.

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References

  1. Aigrain, S., Hodgkin S.T., Irwin, M.J., Lewis, J.R., Roberts, S.J.: Precise time series photometry for the Kepler-2.0 mission. MNRAS 447, 2880–2893 (2015). https://doi.org/10.1093/mnras/stu2638. 1412.6304

    Article  ADS  Google Scholar 

  2. Aigrain, S., Parviainen, H., Pope, B.J.S.: K2SC: flexible systematics correction and detrending of K2 light curves using Gaussian process regression. MNRAS 459, 2408–2419 (2016). https://doi.org/10.1093/mnras/stw706. 1603.09167

    Article  ADS  Google Scholar 

  3. Armstrong, D.J., Kirk, J., Lam, K.W.F., McCormac, J., Walker, S.R., Brown, D.J.A., Osborn, H.P., Pollacco, D.L., Spake, J.: K2 Variable Catalogue: Variable stars and eclipsing binaries in K2 campaigns 1 and 0. A & A 579, A19 (2015). https://doi.org/10.1051/0004-6361/201525889. 1502.04004

    Article  ADS  Google Scholar 

  4. Bohlin, R.C., Landolt, A.U.: The CALSPEC Stars P177D and P330E. AJ 149(4), 122 (2015). https://doi.org/10.1088/0004-6256/149/4/122. 1502.01754

    Article  ADS  Google Scholar 

  5. Borucki, W.J., Koch, D., Basri, G., Batalha, N., Brown, T., Caldwell, D., Caldwell, J., Christensen-Dalsgaard, J., Cochran, W.D., DeVore, E., Dunham, E.W., Dupree, A.K., Gautier, T.N., Geary, J.C., Gilliland, R., Gould, A., Howell, S.B., Jenkins, J.M., Kondo, Y., Latham, D.W., Marcy, G.W., Meibom, S., Kjeldsen, H., Lissauer, J.J., Monet, D.G., Morrison, D., Sasselov, D., Tarter, J., Boss, A., Brownlee, D., Owen, T., Buzasi, D., Charbonneau, D., Doyle, L., Fortney, J., Ford, E.B., Holman, M.J., Seager, S., Steffen, J.H., Welsh, W.F., Rowe, J., Anderson, H., Buchhave, L., Ciardi, D., Walkowicz, L., Sherry, W., Horch, E., Isaacson, H., Everett, M.E., Fischer, D., Torres, G., Johnson, J.A., Endl, M., MacQueen, P., Bryson, S.T., Dotson, J., Haas, M., Kolodziejczak, J., Van Cleve, J., Chandrasekaran, H., Twicken, J.D., Quintana, E.V., Clarke, B.D., Allen, C., Li, J., Wu, H., Tenenbaum, P., Verner, E., Bruhweiler, F., Barnes, J., Prsa, A.: Kepler Planet-Detection mission: Introduction and first results. Science 327, 977 (2010). https://doi.org/10.1126/science.1185402

    Article  ADS  Google Scholar 

  6. Christiansen, J.L., Vanderburg, A., Burt, J., Fulton, B.J., Batygin, K., Benneke, B., Brewer, J.M., Charbonneau, D., Ciardi, D.R., Collier-Cameron, A., Coughlin, J.L., Crossfield, I.J.M., Dressing, C., Greene, T.P., Howard, A.W., Latham, D.W., Molinari, E., Mortier, A., Mullally, F., Pepe, F., Rice, K., Sinukoff, E., Sozzetti, A., Thompson, S.E., Udry, S., Vogt, S.S., Barman, T.S., Batalha, N.E., Bouchy, F., Buchhave, L.A., Butler, R.P., Cosentino, R., Dupuy, T.J., Ehrenreich, D., Fiorenzano, A., Hansen, B.M.S., Henning, T., Hirsch, L., Holden, B.P., Isaacson, H.T., Johnson, J.A., Knutson, H.A., Kosiarek, M., López-Morales, M., Lovis, C., Malavolta, L., Mayor, M., Micela, G., Motalebi, F., Petigura, E., Phillips, D.F., Piotto, G., Rogers, L.A., Sasselov, D., Schlieder, J.E., Ségransan, D., Watson, C.A., Weiss, L.M.: Threeś company: an additional non-transiting super-earth in the bright hd 3167 system, and masses for all three planets. AJ 154, 122 (2017). https://doi.org/10.3847/1538-3881/aa832d. 1706.01892

    Article  ADS  Google Scholar 

  7. Clem, J.L., Landolt, A.U.: Faint UBVRI standard star fields. AJ 146(4), 88 (2013). https://doi.org/10.1088/0004-6256/146/4/88

    Article  ADS  Google Scholar 

  8. Clem, J.L., Landolt, A.U.: Faint UBVRI Standard Star Fields at + 50 deg Declination. AJ 152(4), 91 (2016). https://doi.org/10.3847/0004-6256/152/4/91

    Article  ADS  Google Scholar 

  9. Crossfield, I.J.M., Petigura, E., Schlieder, J.E., Howard, A.W., Fulton, B.J., Aller, K.M., Ciardi, D.R., Lépine, S., Barclay, T., de Pater, I., de Kleer, K., Quintana, E.V., Christiansen, J.L., Schlafly, E., Kaltenegger, L., Crepp, J.R., Henning, T., Obermeier, C., Deacon, N., Weiss, L.M., Isaacson, H.T., Hansen, B.M.S., Liu, M.C., Greene, T., Howell, S.B., Barman, T., Mordasini, C.: A nearby M Star with three transiting super-earths discovered by K2. ApJ 804, 10 (2015). https://doi.org/10.1088/0004-637X/804/1/10. 1501.03798

    Article  ADS  Google Scholar 

  10. Deming, D., Knutson, H., Kammer, J., Fulton, B.J., Ingalls, J., Carey, S., Burrows, A., Fortney, J.J., Todorov, K., Agol, E., Cowan, N., Desert, J.M., Fraine, J, Langton, J, Morley, C, Showman, AP: Spitzer secondary eclipses of the dense, modestly-irradiated, giant exoplanet HAT-P-20b using pixel-level decorrelation. ApJ 805, 132 (2015). https://doi.org/10.1088/0004-637X/805/2/132. 1411.7404

    Article  ADS  Google Scholar 

  11. Howell, SB, Sobeck, C, Haas, M, Still, M, Barclay, T, Mullally, F, Troeltzsch, J, Aigrain, S, Bryson, ST, Caldwell, D, Chaplin, WJ, Cochran, WD, Huber, D, Marcy, GW, Miglio, A, Najita, JR, Smith, M, Twicken, JD, Fortney, JJ: The K2 mission: characterization and early results. PASP 126, 398 (2014). https://doi.org/10.1086/676406. 1402.5163

    Article  ADS  Google Scholar 

  12. Huang, CX, Penev, K, Hartman, JD, Bakos, G.A.́, Bhatti, W, Domsa, I, de Val-Borro, M: High-precision photometry for K2 Campaign 1. MNRAS 454, 4159–4171 (2015). https://doi.org/10.1093/mnras/stv2257. 1507.07578

    Article  ADS  Google Scholar 

  13. Landolt AU: UBVRI photometric standard stars around the Sky at -50 deg declination. AJ 133, 2502–2523 (2007). https://doi.org/10.1086/518000. 0704.3034

    Article  ADS  Google Scholar 

  14. Landolt, AU: UBVRI photometric standard stars around the celestial equator: Updates and additions. AJ 137, 4186–4269 (2009). https://doi.org/10.1088/0004-6256/137/5/4186. 0904.0638

    Article  ADS  Google Scholar 

  15. Landolt, A.U.: UBVRI Photometric Standard Stars Around the Sky at + 50 deg Declination. AJ 146(5), 131 (2013). https://doi.org/10.1088/0004-6256/146/5/131

    Article  ADS  Google Scholar 

  16. Landolt, AU, Uomoto, AK: Optical multicolor photometry of spectrophotometric standard stars. AJ 133(3), 768–790 (2007). https://doi.org/10.1086/510485. 0704.3030

    Article  ADS  Google Scholar 

  17. Luger, R, Agol, E, Kruse, E, Barnes, R, Becker, A, Foreman-Mackey, D, Deming, D: EVEREST: pixel level decorrelation of K2 light curves. AJ 152, 100 (2016). https://doi.org/10.3847/0004-6256/152/4/100, 1607.00524

    Article  ADS  Google Scholar 

  18. Lund, MN, Handberg, R, Davies, GR, Chaplin, WJ, Jones, CD: K2P2 - A photometry pipeline for the K2 mission. ApJ 806, 30 (2015). https://doi.org/10.1088/0004-637X/806/1/30, 1504.05199

    Article  ADS  Google Scholar 

  19. Raschka, S., Mirjalili, V.: Python machine learning, 2nd edn. Packt Publishing, Birmingham (2017)

    Google Scholar 

  20. Smith, JC, Stumpe, MC, Van Cleve, JE, Jenkins, JM, Barclay, TS, Fanelli, MN, Girouard, FR, Kolodziejczak, JJ, McCauliff, SD, Morris, RL, Twicken, JD: Kepler presearch data conditioning II - A Bayesian approach to systematic error correction. PASP 124, 1000 (2012). https://doi.org/10.1086/667697, 1203.1383

    Article  ADS  Google Scholar 

  21. Stetson, PB: Homogeneous photometry for star clusters and resolved galaxies. II. Photometric Standard Stars. PASP 112 (773), 925–931 (2000). https://doi.org/10.1086/316595, astro-ph/0004144

    Article  ADS  Google Scholar 

  22. Stumpe, M.C., Smith, J.C., Catanzarite, J.H., Van Cleve, J.E., Jenkins, J.M., Twicken, J.D., Girouard, F.R.: Multiscale systematic error correction via wavelet-based bandsplitting in kepler data. PASP 126, 100 (2014). 10.1086/674989

    Article  ADS  Google Scholar 

  23. Thatte, A, Deroo, P, Swain, MR: Selective principal component extraction and reconstruction: A novel method for ground based exoplanet spectroscopy. A&A 523, A35 (2010). https://doi.org/10.1051/0004-6361/201015148, 1009.2473

    Article  ADS  Google Scholar 

  24. Tinetti, G., Drossart, P., Eccleston, P., Hartogh, P., Heske, A., Leconte, J., Micela, G., Ollivier, M., Pilbratt, G., Puig, L., Turrini, D., Vandenbussche, B., Wolkenberg, P., Beaulieu, J.P., Buchave, L.A., Ferus, M., Griffin, M., Guedel, M., Justtanont, K., Lagage, P.O., Machado, P., Malaguti, G., Min, M., Norgaard-Nielsen, H.U., Rataj, M., Ray, T., Ribas, I., Swain, M., Szabo, R., Werner, S., Barstow, J., Burleigh, M., Cho, J., du Foresto, V.C., Coustenis, A., Decin, L., Encrenaz, T., Galand, M., Gillon, M., Helled, R., Morales, J.C., Muñoz, A G, Moneti, A., Pagano, I., Pascale, E., Piccioni, G., Pinfield, D., Sarkar, S., Selsis, F., Tennyson, J., Triaud, A., Venot, O., Waldmann, I., Waltham, D., Wright, G., Amiaux, J., Auguères, J L, Berthé, M, Bezawada, N., Bishop, G., Bowles, N., Coffey, D., Colomé, J, Crook, M., Crouzet, P.E., Da Peppo, V., Sanz, I.E., Focardi, M., Frericks, M., Hunt, T., Kohley, R., Middleton, K., Morgante, G., Ottensamer, R., Pace, E., Pearson, C., Stamper, R., Symonds, K., Rengel, M., Renotte, E., Ade, P., Affer, L., Alard, C., Allard, N., Altieri, F., André, Y, Arena, C., Argyriou, I., Aylward, A., Baccani, C., Bakos, G., Banaszkiewicz, M., Barlow, M., Batista, V., Bellucci, G., Benatti, S., Bernardi, P., Bézard, B, Blecka, M., Bolmont, E., Bonfond, B., Bonito, R., Bonomo, A.S., Brucato, J.R., Brun, A.S., Bryson, I., Bujwan, W., Casewell, S., Charnay, B., Pestellini, C.C., Chen, G., Ciaravella, A., Claudi, R., Clédassou, R, Damasso, M., Damiano, M., Danielski, C., Deroo, P., Di Giorgio, A.M., Dominik, C., Doublier, V., Doyle, S., Doyon, R., Drummond, B., Duong, B., Eales, S., Edwards, B., Farina, M., Flaccomio, E., Fletcher, L., Forget, F., Fossey, S., Fränz, M, Fujii, Y., García-Piquer, Á, Gear, W., Geoffray, H., Gérard, J C, Gesa, L., Gomez, H., Graczyk, R., Griffith, C., Grodent, D., Guarcello, M.G., Gustin, J., Hamano, K., Hargrave, P., Hello, Y., Heng, K., Herrero, E., Hornstrup, A., Hubert, B., Ida, S., Ikoma, M., Iro, N., Irwin, P., Jarchow, C., Jaubert, J., Jones, H., Julien, Q., Kameda, S., Kerschbaum, F., Kervella, P., Koskinen, T., Krijger, M., Krupp, N., Lafarga, M., Landini, F., Lellouch, E., Leto, G., Luntzer, A., Rank-Lüftinger, T, Maggio, A., Maldonado, J., Maillard, J.P., Mall, U., Marquette, J.B., Mathis, S., Maxted, P., Matsuo, T., Medvedev, A., Miguel, Y., Minier, V., Morello, G., Mura, A., Narita, N., Nascimbeni, V., Nguyen Tong, N., Noce, V., Oliva, F., Palle, E., Palmer, P., Pancrazzi, M., Papageorgiou, A., Parmentier, V., Perger, M., Petralia, A., Pezzuto, S., Pierrehumbert, R., Pillitteri, I., Piotto, G., Pisano, G., Prisinzano, L., Radioti, A., Réess, J M, Rezac, L., Rocchetto, M., Rosich, A., Sanna, N., Santerne, A., Savini, G., Scandariato, G., Sicardy, B., Sierra, C., Sindoni, G., Skup, K, Snellen, I, Sobiecki, M, Soret, L, Sozzetti, A, Stiepen, A, Strugarek, A, Taylor, J, Taylor, W, Terenzi, L, Tessenyi, M, Tsiaras, A, Tucker, C, Valencia, D, Vasisht, G, Vazan, A, Vilardell, F, Vinatier, S, Viti, S, Waters, R, Wawer, P, Wawrzaszek, A, Whitworth, A, Yung, YL, Yurchenko, SN, Osorio, MRZ, Zellem, R, Zingales, T, Zwart, F: A chemical survey of exoplanets with ARIEL. Exp Astron 46(1), 135–209 (2018). https://doi.org/10.1007/s10686-018-9598-x

    Article  ADS  Google Scholar 

  25. Vanderburg, A, Johnson, JA: A technique for extracting highly precise photometry for the two-wheeled kepler mission. PASP 126, 948 (2014). https://doi.org/10.1086/678764, 1408.3853

    Article  ADS  Google Scholar 

  26. Vanderburg, A, Bieryla, A, Duev, DA, Jensen-Clem, R, Latham, DW, Mayo, AW, Baranec, C, Berlind, P, Kulkarni S, Law NM, Nieberding MN, Riddle R, Salama M: Two small planets transiting HD 3167. ApJ 829, L9 (2016). https://doi.org/10.3847/2041-8205/829/1/L9, 1607.05248

    Article  ADS  Google Scholar 

  27. Zellem RT, Griffith CA, Deroo P, Swain MR, Waldmann IP: The ground-based H-, K-, and L-band absolute emission spectra of HD 209458b. ApJ 796(1), 48 (2014). https://doi.org/10.1088/0004-637X/796/1/48, 1409.8187

    Article  ADS  Google Scholar 

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Acknowledgements

We acknowledge the support of the ARIEL ASI-INAF agreement n. 2018-22-HH.0

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  1. INAF-Osservatorio Astronomico di Palermo, Piazza del Parlamento 1, 90134, Palermo, Italy

    A. Petralia & G. Micela

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Petralia, A., Micela, G. Principal component analysis to correct data systematics. Case study: K2 light curves. Exp Astron 49, 97–114 (2020). https://doi.org/10.1007/s10686-020-09656-x

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