arXiv:1004.0738v1 [astro-ph.SR] 5 Apr 2010 srn ah./AN / Nachr. Astron. eeu aast uhlwrpooercnielvl,and levels, noise homo- photometric very lower a much to cycle set, leads duty data which geneous high be instrument, very same can a the sky with with the years and in to field months single for exter- A monitored of Earth. minimization from a to influences La- lead nal the will around which orbit L2 Lissajous point a grange cycle. in diurnal situated the be and will PLATO disturbances atmospheric of lack mai the is exo-planets detecting or asteroseismology for stars (2009) Catala in found be (2010). can Claudi and mission PLATO the the descrip or detailed of system A planets. tion a detected to the of of key age density the and the mass be as will such characteristics host-stars pinpoint the of stud Asteroseismology follow-up ground-based ies. facilitate to exo- photometry pre study ultra-high sion using to stars is bright around mission PLATO systems planetary the of objective main The Introduction 1 ⋆ orsodn uhr -al [email protected] e-mail: author: Corresponding h oiaint ot pc oaqiepooer of photometry acquire to space to go to motivation The fdfeetpooercagrtm,teslcino h o the of selection the tha algorithms, questions photometric main different The of uncertain sources. noise pointing natural the important field, all stellar in the by images optics, CCD telescope end-to- of an made time-series created photometric observations We simulates the Consortium. which Payload of PLATO the course simulati of the study realistic in through sources tackled noise various ex be concer of best aspects analysis can Many statistical studies. performance follow-up full detailed a for host-stars provide enough their to of is asteroseismology mission PLATO to and exo-planets of words Key later 2010 online Nov Published 11 accepted 2010, May 30 Received 5 4 3 2 1 .Zima W. Mission PLATO the of study photometr sessment CCD precision ultra-high space-based – Modelling Simulator CCD End-to-End PLATO The oeta 00 oldaf rgtrta m than brighter dwarfs cool mag 20000 stellar than conc the more multi-telescope of proposed function the that a showed as simulations light-curves of budget noise ferhlk x-lntr ytm sn h rni meth transit the using systems exo-planetary earth-like of h LT aelt iso rjc sanx eeainESA generation next a is project mission satellite PLATO The eateto srpyis MP nvriyo Nijmegen, of University IMAP, Astrophysics, of Department Univers France Curie, Marie et Universit´e Pierre UMR8109, LESIA, ntttd srpyiu td ´ohsqed ’Universi l’ G´eophysique de de et Astrophysique d’ Institut nttu o yi gAtooi ahsUiestt yMu Ny Universitet, Aarhus Astronomi, og Fysik for Instituut nttu orSernud,KU evn Celestijnenlaa Leuven, K.U. Sterrenkunde, voor Instituut 999 1 ,⋆ o 8 8 9 20)/ (2006) 793 – 789 88, No. , .Arentoft T. , dtra oe ntuto o authors for instruction – notes Editorial 2 .D Ridder De J. , DOI V 1 .Salmon S. , 1 ihapeiinbte hn2 p/ hc sesnilf essential is which ppm/h 27 than better precision a with =11 nly ci- laestDOI! set please - - ooeeu otaeto ae npeeitn codes pre-existing on created based we tool Mission, software PLATO homogeneous for a study simulator assessment a such the of need for perfor- the in- to the Due and on instrument. natural the impact of an important mance have most that the sources for noise designed optical account strumental is to the It way in instrument. a space-based stars in a of by photometry acquired CCD range of simulation tic space of performance observations. overall simulations based the study numerical to sources, suited ideally noise com- are the the to of Due ma- interplay budget. the noise plex overall remains the noise must of photon electronics contributor that jor the ensure of to limits minimized the be to of due construction and technical spacecraft the instrumental the to be due The are can photons. which data sources more on noise effect collecting relative by whose minimized noise, shot photon o sourc is noise quality natural the unavoidable on main The impact observations. their the estimate quantified to be studies must detailed and in remain Neverthe- sources spectra. noise power many still in less, aliasing daily of avoidance the yo h aelt o tiueCnrlSse AS jitter [ACS] System Control Attitude (or satellite the of ty od. p fPAOcnflltedfie cetfi olo measuring of goal scientific defined the fulfil can PLATO of ept tcldsg,tealwbejte mltd,adteexpe the and amplitude, jitter allowable the design, ptical eeadesdwt hssmltrwr h os properti noise the were simulator this with addressed were t 0D 01Lue,Belgium Leuven, 3001 200D, n LTSmi otaeto eiae oterealis- the to dedicated tool software a is PLATOSim sn lr-ihpeiinpooer.Temi olo the of goal main The photometry. precision ultra-high using n fteepce bevtos h ope nepa of interplay complex The observations. expected the of ons igtedsg rd-f fasaebsdisrmn n it and instrument space-based a of trade-off design the ning 3 iuefrdfeetprmtrcniin.Terslso o of results The conditions. parameter different for nitude ´ eL`g,Ale u6Aˆt 7B40 Li`ege, Belgium B-4000 Aoˆut, 17 6 Li`ege, All´ee du t´e de .Catala C. , -lntr ytm rudsasta r rgtadclose and bright are that stars around systems o-planetary ldn elsi oeso h C n t lcrnc,the electronics, its and CCD the of models realistic cluding uhsmltosa nipnal ato h assessment the of part indispensable an simulations such kgd yn 2,DK-8000 520, Bygn. nkegade OBx91,60 LNjee,TeNetherlands The Nijmegen, GL 6500 9010, Box PO omcVso aelt rjc eiae otedetection the to dedicated project satellite Vision Cosmic teDnsDdrt bevtied ai,915Meudon, 92195 Paris, de Observatoire Diderot, it´e Denis n C iuainsfwr-ol ubdPLATOSim, dubbed software-tool, simulation CCD end 4 .Kjeldsen H. ,

c c 06WLYVHVra mH&C.Ka,Weinheim KGaA, Co. & GmbH Verlag WILEY-VCH 2006 06WLYVHVra mH&C.Ka,Weinheim KGaA, Co. & GmbH Verlag WILEY-VCH 2006 2 , and ru ,Danmark C, Arhus ˚ .Aerts C. o h as- the for y 1 , rtestudy the or 5 ,and ), cted es ur e s - f 790 W. Zima et al.: The PLATO End-to-End CCD Simulator

Fig. 2 Simulated images at sub-pixel scale of a stellar field using PSFs at different distances from the optical axis (left panel: 0◦, middle panel: 6.5◦, right panel: 14.1◦). Note the grid-like structure at the image background which arises from the lower intra-pixel sensitivity. Image generated with PLATOSim. Fig. 1 Screenshot of PLATOSim. On the left panels, pa- rameters for the simulations can be set. The right panel shows a simulated image which contains several visible computed assuming orthogonal projection which is a good noise features such as saturation smearing (bright vertical approximation for a relatively small FoV. spikes of stars) and frame-transfer trails (vertical lines). We call the pixels that represent the real pixels of the CCD normal pixels. In a sub-image, each normal pixel is represented by typically up to 128x128 sub-pixels. These that had been developedfor the Eddingtonand MONS space sub-pixels assure a realistic modelling of intra-pixel sensi- missions (Arentoft et al. 2004; De Ridder et al. 2006). tivity variations of the CCD and of the ACS jitter movement PLATOSim has been coded in C++ and features a graphical which is equivalent to a few percent of a normal pixel. Only user interface (see Fig. 1) based on Qt4. The contributions at the very end of the CCD modelling, the sub-pixels are of the different noise sources are described through mathe- re-binned to the normal pixel scale. After this first step of matical models and use a large number of parametrised in- modelling, a noise-free image is created, containing the lo- puts and numerical pre-computed input data like PSFs, jitter cations and the fluxes of all stars in the field-of-view. time-series, and sky background brightness. The next step of the image simulation takes into account Several improvements have been applied to the simu- the physical noise sources of the CCD, the jitter movements lator compared to the pre-existing version. These concern of the spacecraft, and the instrumental optics. We model the mainly a significant increase in computationalspeed, a more global sensitivity variations (flat field) of the CCD by as- realistic treatment of jitter, and the inclusion of two different suming a 1/f spatial power spectrum which resembles that of photometric algorithms and statistical tools to estimate the a typical CCD (De Ridder et al. 2006). Additionally, at sub- noise properties of the data. The graphical interface permits pixel level sensitivity variations that have white-noise char- in an easy way to test several different instrument set-ups acteristics are introduced. The lower sensitivity between sin- by modifying the parameters for the simulations. gle pixels is also modelled at sub-pixel level. Due to various external forces such as the solar wind 2 Modelling of CCD observations and the magnetic field, and internal disturbances such as the reaction wheel noise and structural and thermal flexibility, The modelling of the synthetic CCD image is carried out the pointing of the satellite undergoes steady perturbations. in several steps which are described in the following. The This jitter has to be kept as small as possible due to its dete- first step is to define the field-of-view (FoV) of one CCD. riorating effect on the observations by increasing the noise Important parameters here are the size of the CCD in terms of the measured light-curves. We used a jitter time-series of the number of pixels, the pixel-scale on the focal plane, that has been modelled specifically for PLATO and vali- and the positions and magnitudes of the stars. PLATO will dated using data from two space crafts, ISO and CoRoT, consist of a large numberof small telescopes, each with four where pointing error history is available. The CCD image is CCDs in the focal plane. As a simplification, we only sim- created by summing up sub-exposures with their individual ulate the observations acquired by a single CCD and ex- shift of the FoV, which is in the order of a few sub-pixels. trapolate its properties on the complete system by assuming The image is further degraded by the telescope optics that all telescopes behave in a similar way. Moreover, due to which are characterised by the PSF. We used mono-chromatic computational limitations, not the complete CCD but only PSFs that have been pre-computed for three different opti- a sub-image of typically 200x200 pixels is simulated. On cal designs and different distances to the optical axis (see such an image, all stars are assumed to have the same effec- Fig. 2) for a wavelength range between 400 and 1000 nm. tive temperature and the same point spread function (PSF). White light PSFs were integrated over the effective wave- Different distances from the optical axis can be simulated by length range of PLATO taking into account its wavelength using corresponding PSFs that were pre-computed for dif- dependent transmission and quantum efficiency. The result- ferent distances. The positions of the stars on the CCD are ing image is constructed by convolution in Fourier space.

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The sky backgroundof each sub-image is assumed to be stars have constant intrinsic magnitude. In a few simula- uniformly lit by the zodiacal light and background objects tions, low-amplitude stellar variability has been introduced like unresolved stars and galaxies. Through photon noise, to test the effect of crowding on the detectability of pulsa- the sky background increases the noise of the stellar photo- tions. metric measurements. Values for the sky background are in- The following questions have been tackled during the terpolated from tabulated data from Wehrli (1985)and Lein- assessment study of PLATO: ert et al. (1998). The PLATO CCDs will be working in frame-transfer – How many stars are affected by crowdingof other sources mode to read out the image. This read-out mode causes due to confusion during photometry dependent on the 2 the flux of all stars to be spread along the columns of the number of stars per deg . Due to the large pixel size of CCD and introduces an additional noise source by increas- 15 arcsec/pixel, confusion, i.e. the presence of the target ing the background flux. Although we are only simulating star plus at least one fainter (or brighter) star in the pho- sub-images of the CCD with PLATOSim, for the determi- tometry mask, is a serious problem for stars fainter than nation of this structure the stars on the complete CCD are mV = 11. taken into account. As it will be done for the PLATO CCDs, – To which extent does confusion influence the detection we save this trailing structure and use it to correct for during of variable stars? To explore this question we calculated data reduction. how much the photon noise of a target may be elevated In the further steps, the simulated sub-image is re-binned due to confusionbefore a pulsation amplitude of 10 ppm to normal pixel scale and the photon noise is computed for fails to be statistically significant detectable during a 3- each pixel. For pixels, where the flux exceeds the full well year run. Different scenarios, where half or all of the capacity (=saturation), the flux is smeared along the readout polluting sources pulsate with the same amplitude were direction. Finally, charge-transfer efficiency degradation,read- explored. out noise, and digital saturation are computed and the image – How do different photometric algorithms - simple aper- is written as a FITS-file to the disk. The series of FITS files ture and weighted mask photometry - perform in terms can be further analysed and reduced with standard scientific of the noise budget? Each time-series of simulated frames software. The right panel of Fig. 1 shows the example of an has been analysed with both photometric algorithms. image that has been simulated with PLATOSim. – What is the effect of ACS jitter on the noise budget? We also implemented two photometric algorithms in Simulations with and without considering jitter with an PLATOSim, simple aperture and weighted mask photome- rms of 0.2 arcsec have been compared. try, to acquire photometric measurements of all stars on the – Which optical design performs best? The PSFs of three simulated CCD in an efficient way and to compute statis- different proposed optical designs and different distances tics to determine their noise levels. Both algorithms take to the optical axis were compared. into account the sub-pixel position of the stars and the the- – How many stars are observable for PLATO at specific oretical shape of the PSF to define the photometry mask noise levels? This is essential to decide if the selected which includes between 60 and 95% of the stellar flux. We baseline design of PLATO is compliant with the mission were able to demonstrate that aperture photometry produces requirements. lower noise for brightertargets where pollutiondue to crowd- ing in dense fields does not pose a problem. In contrast, weighted mask photometry performs generally better for 3.1 Results fainter stars in a crowded field due to its smaller size of the mask. Our findings can be summarized as follows.

– About 80% of all stars with mV ≤ 12 in the sparse 3 Simulation study for the PLATO and medium field, which are representativefor the major assessment phase part of the PLATO FoV, are not affected significantly by crowding from close-by sources. We made an extensive set of simulations to test the perfor- – Due to the smaller size of the masks, weighted mask mance of the photometric observations of PLATO for dif- photometry is less sensitive due to crowding than aper- ferent set-ups of the telescope optics and the CCD in dif- ture photometry. ferent positions in the sky. For these simulations, we used a – Stars that are affected by crowdingfrom close-by sources catalogue of the proposed FoV of PLATO containing stars also show a larger increase in noise due to ACS jitter. with mV ≤ 15 (M. Barbieri, priv. comm.). Three differ- – Aperture photometry generally delivers lower noise for ent sub-fields with spatial stellar densities that account for mV ≤ 11, whereas weighted mask photometry per- each about a third of the FoV were studied in detail (named forms better for mV ≥ 12 for simulations with and sparse, medium, and dense field). We computed time-series without jitter. of typically 200 images and applied different photometric – All three proposed optical designs perform similar with algorithms for all stars on the CCD and assuming that the respect to crowding and the noise budget.

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10000 100 observed noise theoretical photon noise 27 ppm/hour 80.0 ppm/hour 80 1000

60

100 40 Occurence [%] Noise level(ppm/hour)

20 10

0 7 8 9 10 11 12 13 14 15 5 6 7 8 9 10 11 12 13 Input magnitude Magnitude Fig. 3 Expected noise level in ppm/h for observations Fig. 4 Results of simulations to test the detectability of with 40 telescopes using realistic noise modelling without a stellar oscillation signal with an amplitude of 10 ppm jitter in the sub-field and a PSF at the optical axis. Each red through confusion with neighbouring (pulsating) stars. The cross represents the noise of a star using aperture photome- different coloured bars show the situation for the follow- try. The dark blue line is the median of the noise in bins of ing assumptions (the target star is assumed to pulsate with 0.5 mag. The theoretical photon noise is indicated as green an amplitude of 10 ppm): Red bars: Only the target star is line. Measurements that fall below this value are affected by pulsating with an amplitude of 10 ppm. The other stars in smearing from saturated stars. The two relevant noise levels the photometry mask only contribute noise through photon for PLATO at 27 and 80 ppm/h are marked. It can be seen noise. Green bars: 50% of the polluting stellar sources in that the limit for a precision of 27 ppm/h is at approximately the photometry mask pulsate with an amplitude of 10 ppm mV = 11. Towards faint magnitudes, the noise increases in a broad frequency range. Blue bars: All polluting stellar rapidly due to the confusion issue. sources in the photometry mask pulsate with an amplitude of 10 ppm in a broad frequency range. Above mV = 12, no pulsations with an amplitude of 10 ppm can be detected. These simulations were done for a medium dense field and – Applying photometry by using a mask derived from a aPSFat6◦ from the optical axis. slightly inaccurately modelled PSF delivers no signifi- cant signal-to-noise degradation if the used PSF deviates by a few degrees from the optical axis from the intrinsic – 52000 (goal 80000) dwarfs/sub-giants at 54 ppm/h PSF or if the stellar colour is not accurately known. and later 27 ppm/h – ACS jitter significantly increases the measured noise of the stars at all magnitudes. The increase is more pro- nouncedin the dense field and for the near-edgePSFs. A 4 Future outlook subsequent jitter correction for photometry will be nec- essary to reach the required specifications of PLATO. The ESA Science Program Committee has decided in its Such an approachhas been provensuccessful for CoRoT meeting on Feb. 17/18, 2010 that the PLATO mission pro- (De Oliveira Fialho et al. 2007, Drummond et al. 2006). ceeds to a Phase B definition study which will end in June, – The number of detectable pulsating stars, assuming pul- 2011. A modification of the current design of the mission, sation amplitudes of 10 ppm in a broad frequencyrange, to enable compliance with the mission requirements regard- decreases when more neighbouring stars add noise to ing especially the mass budget and schedule is necessary. the target star due to confusion and/or variability. Still, Therefore,in the new design for PLATO, the number of tele- confusion is very limited except for stars in the densest scopes will be reduced, the telescope optics will be modified fields and for mV ≥ 12. (fewer lenses), the FoV will be increased and the observa- – The importantmagnitude range for asteroseismology be- tion of brighter stars is anticipated. These modifications will tween mV = 4 to 11 is only weakly affected by confu- require more simulations to fine-tune the mission design and sion. ensure that the scientific requirements will be met. – Star counts reveal that with 40 refractivetelescopes (most) Acknowledgements. The research leading to these results has re- scientific requirements can be fulfilled. ceived funding from the European Research Council under the Eu- – 21000 (goal 20000) dwarfs/sub-giants at 27 ppm/h ropean Community’s Seventh Framework Programme (FP7/2007– m 8 – 13500 (goal 1000) dwarfs/sub-giants with V ≤ 2013)/ERC grant agreement n◦227224 (PROSPERITY), as well at 27 ppm/h as from the Research Council of K.U. Leuven grant agreement – 316000(goal 200000)dwarfs/sub-giants with mV ≥ GOA/2008/04. WZ thanks R´eza Samadi for fruitful discussions 8 at 80 ppm/h and important scientific input to this work.

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