ebook img

Planck early results: first assessment of the High Frequency Instrument in-flight performance PDF

7.2 MB·English
Save to my drive
Quick download
Download
Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.

Preview Planck early results: first assessment of the High Frequency Instrument in-flight performance

Astronomy & Astrophysics manuscript no. Planck2011-1.5_astroph (cid:13)c ESO 2012 November 26, 2012 Planck early results: first assessment of the High Frequency Instrument in-flight performance Planck HFI Core Team: P. A. R. Ade47, N. Aghanim25, R. Ansari39, M. Arnaud35, M. Ashdown33,54, J. Aumont25, A. J. Banday52,5,41, M. Bartelmann51,41, J. G. Bartlett1,31, E. Battaner57, K. Benabed26, A. Benoît26, J.-P. Bernard52,5, M. Bersanelli15,20, R. Bhatia17, J. J. Bock31,6, J. R. Bond3, J. Borrill40,49, F. R. Bouchet26, F. Boulanger25, T. Bradshaw45, E. Bréelle1, M. Bucher1, P. Camus38, J.-F. Cardoso36,1,26, A. Catalano1,34, A. Challinor55,33,7, A. Chamballu23, J. Charra25,†, M.Charra25,R.-R.Chary24,C.Chiang11,S.Church50,D.L.Clements23,S.Colombi26,F.Couchot39,A.Coulais34,C.Cressiot1, B. P. Crill31,43, M. Crook45, P. de Bernardis14, J. Delabrouille1, J.-M. Delouis26, F.-X. Désert22, K. Dolag41, H. Dole25, O. Doré31,6, M. Douspis25, G. Efstathiou55, P. Eng25, C. Filliard39, O. Forni52,5, P. Fosalba27, J.-J. Fourmond25, K. Ganga1,24, M. Giard52,5, D. Girard38, Y. Giraud-Héraud1, R. Gispert25,†, K. M. Górski31,59, S. Gratton33,55, M. Griffin47, G. Guyot21, J. Haissinski39, D. Harrison55,33, G. Helou6, S. Henrot-Versillé39, C. Hernández-Monteagudo41, S. R. Hildebrandt6,38,30, 1 R. Hills56, E. Hivon26, M. Hobson54, W. A. Holmes31, K. M. Huffenberger58, A. H. Jaffe23, W. C. Jones11, J. Kaplan1, 1 R. Kneissl16,2, L. Knox12, G. Lagache25, J.-M. Lamarre34,(cid:63), P. Lami25, A. E. Lange24,†, A. Lasenby54,33, A. Lavabre39, 0 C. R. Lawrence31, B. Leriche25, C. Leroy25,52,5, Y. Longval25, J. F. Macías-Pérez38, T. Maciaszek4, C. J. MacTavish33, 2 B. Maffei32, N. Mandolesi19, R. Mann46, B. Mansoux39, S. Masi14, T. Matsumura6, P. McGehee24, J.-B. Melin8, C. Mercier25, n M.-A. Miville-Deschênes25,3, A. Moneti26, L. Montier52,5, D. Mortlock23, A. Murphy42, F. Nati14, C. B. Netterfield10, a H. U. Nørgaard-Nielsen9, C. North47, F. Noviello25, D. Novikov23, S. Osborne50, C. Paine31, F. Pajot25, G. Patanchon1, J T.Peacocke42,T.J.Pearson6,24,O.Perdereau39,L.Perotto38,F.Piacentini14,M.Piat1,S.Plaszczynski39,E.Pointecouteau52,5, 1 R. Pons52,5, N. Ponthieu25, G. Prézeau6,31, S. Prunet26, J.-L. Puget25, W. T. Reach53, C. Renault38, I. Ristorcelli52,5, 1 G. Rocha31,6, C. Rosset1, G. Roudier1, M. Rowan-Robinson23, B. Rusholme24, D. Santos38, G. Savini44, B. M. Schaefer51, P. Shellard7, L. Spencer47, J.-L. Starck35,8, P. Stassi38, V. Stolyarov54, R. Stompor1, R. Sudiwala47, R. Sunyaev41,48, ] M J.-F.Sygnet26,J.A.Tauber17,C.Thum29,J.-P.Torre25,F.Touze39,M.Tristram39,F.VanLeeuwen55,L.Vibert25,D.Vibert37, L. A. Wade31, B. D. Wandelt26,13, S. D. M. White41, H. Wiesemeyer28, A. Woodcraft47, V. Yurchenko42, D. Yvon8, and I A. Zacchei18 . h p (Affiliations can be found after the references) - o November 26, 2012 r t s a Abstract [ ThePlanck HighFrequencyInstrument(HFI)isdesignedtomeasurethetemperatureandpolarizationanisotropiesoftheCosmic 1 Microwave Background and galactic foregrounds in six wide bands centered at 100, 143, 217, 353, 545 and 857GHz at an angular v resolutionof10(cid:48) (100GHz),7(cid:48) (143GHz),and5(cid:48) (217GHzandhigher).HFIhasbeenoperatingflawlesslysincelaunchon14May 9 2009. The bolometers cooled to 100mK as planned. The settings of the readout electronics, such as the bolometer bias current, 3 that optimize HFI’s noise performance on orbit are nearly the same as the ones chosen during ground testing. Observations of 0 Mars, Jupiter, and Saturn verified both the optical system and the time response of the detection chains. The optical beams are 2 closetopredictionsfromphysicalopticsmodeling.Thetimeresponseofthedetectionchainsisclosetopre-launchmeasurements. 1. The detectors suffer from an unexpected high flux of cosmic rays related to low solar activity. Due to the redundancy of Planck’s 0 observationstrategy,theremovalofafewpercentofdatacontaminatedbyglitchesdoesnotsignificantlyaffectthesensitivity.The 1 cosmicraysheatupthebolometerplateandthemodulationonperiodsofdaystomonthsoftheheatloadcreatesacommondriftof 1 allbolometersignalswhichdonotaffectthescientificcapabilities.Onlythehighenergycosmicrayshowersinduceinhomogeneous : heating which is a probable source of low frequency noise. The removal of systematic effects in the time ordered data provides v a signal with an average level of noise less than 70% of our goal values in the 0.6–2.5Hz range. This is slightly higher than the i pre-launchmeasurementsbutbetterthanpredictedintheearlyphasesoftheproject.Thisisattributedtothelowlevelofphoton X noise resulting from an optimized optical and thermal design. r a Key words. Methods: data analysis – Cosmology: observations 1. Introduction is the third-generation space mission to measure the anisotropy of the cosmic microwave background (CMB). Planck1 (Tauberetal.2010a;PlanckCollaboration2011a) It observes the sky in nine frequency bands covering 30– (cid:63) Corresponding author: J.-M. Lamarre, jean-michel. [email protected]. ticular the lead countries France and Italy), with contributions 1 Planck (http://www.esa.int/Planck) is a project of the fromNASA(USA)andtelescopereflectorsprovidedbyacollab- European Space Agency (ESA) with instruments provided by orationbetweenESAandascientificconsortiumledandfunded two scientific consortia funded by ESA member states (in par- by Denmark. 2 The Planck HFI core team: Planck early results: first assessment of the HFI in-flight performance 857GHz with high sensitivity and angular resolution from the sky at roughly 1rpm. They offer a very low cross- 31(cid:48) to 5(cid:48). The Low Frequency Instrument (LFI; Mandolesi sectiontocosmicraysthatprovestobeessentialinthis etal.2010;Bersanellietal.2010;Mennellaetal.2011)cov- environment and with this sensitivity. ers the 30, 44, and 70GHz bands with amplifiers cooled to – A space qualified 100mK dilution cooler (Benoît et al. 20K.TheHighFrequencyInstrument(HFI;Lamarreetal. 1997)associatedwithahighprecisiontemperaturecon- 2010; Planck HFI Core Team 2011a) covers the 100, 143, trol system. 217, 353, 545, and 857GHz bands with bolometers cooled – An active cooler for 4K (Bradshaw & Orlowska 1997) to0.1K.Polarizationismeasuredinallbutthehighesttwo using vibration controlled mechanical compressors to bands (Leahy et al. 2010; Rosset et al. 2010). A combina- preventexcessivewarmingofthe100mKstageandmin- tion of radiative cooling and three mechanical coolers pro- imize parasitic effects on bolometers. vides the temperatures needed for the detectors and optics – AC biased readout electronics that extend high sensi- (PlanckCollaboration2011b).Twodataprocessingcentres tivity to very slow signals (Gaertner et al. 1997). (DPCs)checkandcalibratethedataandmakemapsofthe – A thermo-optical design consisting, for each optical sky (Planck HFI Core Team 2011b; Zacchei et al. 2011). channel,ofthreecorrugatedhornsandasetofcompact Planck’s sensitivity, angular resolution, and frequency cov- reflective filters and lenses at cryogenic temperatures erage make it a powerful instrument for galactic and ex- (Church et al. 1996). These include high throughput tragalactic astrophysics as well as cosmology. Early astro- (multimoded)corrugatedhornsforthe545and857GHz physicsresultsaregiveninPlanckCollaboration(2011h–x). channels (Murphy et al. 2002). Thegoalofthispaperistodescribethein-flightperfor- manceoftheHFIinspaceandafterthechallenginglaunch The angular resolution was chosen to extend the mea- conditions. It does not attempt to duplicate the content of surement of the small scale features in the CMB, while the Planck pre-launch status papers (Lamarre et al. 2010; keeping the level of stray light to extremely low levels. At Pajot et al. 2010), but rather presents the operational sta- the same time, at this sensitivity, the measurement and tus from an instrumental viewpoint. These results propa- removal of foregrounds requires a large number of bands gate to scientific products through the data processing re- extending on both sides of the foreground minimum. This ported in the companion paper (Planck HFI Core Team is achieved with the six bands of the HFI (Table 1) and 2011b)whichdescribestheinstrumentalpropertiesasthey the three bands of the Low Frequency Instrument (LFI; appearinthemapsusedbythe“Planck earlyresults” com- Mennella et al. 2011). panionpapers.ThispaperfocusesontheabilityoftheHFI The instrument uses a ∼ 20K sorption cooler com- to measure intensity without any description of its perfor- mon to the HFI and the LFI (Planck Collaboration 2011b; mance in measuring polarization, which will be reported Bhandari et al. 2000, 2004). The HFI focal plane unit later. (FPU) is integrated inside the mechanical structure of the Section 2 summarizes the instrument design. Section 3 LFI, on axis of the focal plane of a common telescope focuses on early in-flight operations, the verification phase (Tauber et al. 2010a). and the setting of the parameters that have to be tuned in The ability to achieve background limited sensitivity flight.Section4addressesthemeasurementofthebeamson was demonstrated by the ARCHEOPS balloon-borne ex- planets and the disentangling of time response effects from periment (Benoît et al. 2003a,b), an adaptation of the HFI thebeamshape.Italsopresentsthebestcurrentknowledge designedforoperationintheenvironmentofastratospheric of the physical beams resulting from this work. The effec- balloon. Similarly, the method of polarimetry employed by tive beam obtained after data processing are to be found the HFI was demonstrated by the Boomerang experiment in Planck HFI Core Team (2011b). Sections 5, 6 and 7 are (Montroy et al. 2006; Piacentini et al. 2006; Jones et al. dedicated to noise, systematic effects and instrument sta- 2006). The HFI itself was extensively tested on the ground bility respectively. A summary of the HFI in-flight perfor- duringthecalibrationcampaigns(Pajotetal.2010)atIAS mance and a comparison with pre-launch expectations are in Orsay and CSL at Liège. However, the fully integrated presented in section 8. instrument was never characterized in an operational envi- ronment like that of the second Earth-Sun Lagrange point (L2).Inadditiontothermalandgravitationalenvironmen- 2. The HFI instrument tal conditions, the spectrum and flux of cosmic rays at L2 is vastly different than that during the pre-flight testing. 2.1. Design Finally, due to the operational constraints of the cryogenic receiver,theendtoendopticalassemblycouldnotbetested The High Frequency Instrument (HFI) was proposed to on the ground with the focal plane instruments. ESA in response to the announcement of opportunity for The instrument design and development are described instrumentsforthePlanckmissionin1995.Itisdesignedto in Lamarre et al. (2010). The calibration of the instrument measure the sky in six bands (Tab. 1) with bolometer sen- is described in Pajot et al. (2010). The overall thermal and sitivity close to the fundamental limit set by photon noise. cryogenic design and the Planck payload performance are The lower four frequency bands include the measurement criticalaspectsofthemission.Detailedsystem-levelaspects of the polarization. This sensitivity is obtained through a are described in Planck Collaboration (2011a) and Planck combination of technological breakthroughs in each of the Collaboration (2011b). critical components needed for bolometric detection: – Spider web bolometers (Bock et al. 1995; Holmes et al. 2.2. Spectral transmission 2008)andpolarizationsensitivebolometers(Jonesetal. 2003) which can reach the photon noise limit with suf- The spectral calibration is described in Pajot et al. (2010) ficient bandwidth to enable scanning great circles on and consists of pre-launch data, in the passband and The Planck HFI core team: Planck early results: first assessment of the HFI in-flight performance 3 Table 1. The HFI receivers. P stands for polarisation sensitive bolometers. Channel 100P 143P 143 217P 217 353P 353 545 857 Central frequency (GHz) 100 143 143 217 217 353 353 545 857 Bandwidth (%) 33 32 30 29 33 29 28 31 30 Number of bolometers 8 8 4 8 4 8 4 4 4 These numbers were very close to the planned operat- ing point. As the whole system worked nominally, margins on the cooling chain for interface temperatures and heat lift are large. The Planck active cooling chain was one of the great technological challenges of this mission and is fully successful. A full description of the performance of the cryogenic chain and its system aspects can be found in Planck Collaboration (2011b). The parameters of the operating points of the 4K, 1.4K and 100mK stages are summarised in Table 2. The temperature stability of the regulated stages has a direct impact on the scientific performance of the HFI. These stabilities are discussed in detail in Planck Collaboration(2011b).Theirimpactonthepowerreceived by the detectors is given in Sect. 3.3.1. Figure1. HFI spectral transmission 3.2. Calibration and performance verification phase 3.2.1. Overview around, combined with component level data to determine theoutofbandrejectionoveranextendedfrequencyrange The calibration and performance verification (CPV) phase (radio–UV). Analysis of the in-flight data shows that the oftheHFIconsistedofactivitiesduringtheinitialcooldown contribution of CO rotational transitions to the HFI mea- to 100mK and during a period of about six weeks before surements is important. An evaluation of this contribution the start of the survey. The cooldown phase is summarized for the J = 1 → 0 (100 and 143 GHz), J = 2 → 1 (217 in Sect. 3.1. The pre-launch value of the 4He-JT cooler op- GHz) and J = 3 → 2 (353 GHz) transitions of CO is pre- erating frequency was used (see Sect. 3.2.2). Activities re- sented in Planck HFI Core Team (2011b). lated to the optimization of the detection chain settings were performed firstduring the cooldown ofthe JFET am- plifiers, and again when the bolometers were at their oper- 3. Early HFI operation ating temperature. Most of the operating conditions were pre-determined during the ground calibration. The main 3.1. HFI Cool down and cryogenic operating point unknown was the in-flight background on the detectors. The detection chain settings are presented in Sect. 3.2.3. The Planck satellite cooldown is described in Planck Other CPV activities performed are: Collaboration (2011b). The first two weeks after launch were used for passive – determination of the detection chain time response un- outgassing, which ended on 2 June 2009. During this pe- der the flight background riod,gaswascirculatedthroughthe4He-JTcoolerandthe – determinationofthedetectionchainchannel-to-channel dilution cooler to prevent clogging by condensable gases. crosstalk under the flight background The sorption cooler thermal interface with HFI reached a – characterization of the bolometer response to the 4K temperature of 17.2K on 13 June. The 4He-JT cooler was and 1.4K optical stages, and to the bolometer plate only operated at its nominal stroke amplitude of 3.5mm temperature variations on 24 June to leave time for the LFI to carry out a spe- – checkingtheimmunityoftheinstrumenttothesatellite cificcalibrationwiththeirreferenceloadsaround20K.The transponder operating temperature was reached on 27 June, with the – optimization of the numerical compression parameters thermal interface with the focal plane unit at 4.37K. for the actual sky signal and high energy particle glitch The dilution cooler cold head reached 93mK on 3 July rate 2009. Taking into account the specific LFI calibration re- – variousring-to-ringslewangles(1.(cid:48)7,2.(cid:48)0[nominal],2.(cid:48)5) quirement that slowed down the cooldown, the system be- – checkingtheeffectof thescananglewith respecttothe havedasexpectedwithinafewdays,accordingtothether- Sun mal models adjusted to the full system cryogenic tests in – checking the effect of the satellite spin rate around its the summer 2008 at CSL (Liège). nominal value of 1rpm. The regulated operating temperature point of the 4K stage was set at 4.8K for the 4K feed horns on the FPU. On5August2009,anunexpectedshutdownofthe4He- The other stages were set to 1.395K for the so called JTcoolerwastriggeredbyitscurrentregulatorunit(CRU). 1.4K stage, 100.4mK for the regulated dilution plate, and Despite investigations into this event, its origin is still un- 103mK for the bolometer regulated plate. explained. A procedure for a quick restart was developed 4 The Planck HFI core team: Planck early results: first assessment of the HFI in-flight performance Table 2. Main operation and interface parameters of the cooling chain Interface Sorption cooler-4He-JT cooler (4K gas pre-cooling temperature) 17.2 K Interface 4He-JT cooler-dilution cooler (dilution gas pre-cooling temperature) 4.37 K Interface 1.4K cooler-dilution gas precooling 1.34 K Temperature of dilution plate (after regulation) 100.4 mK Temperature of bolometer plate (after regulation) 103 mK Temperature of 1.4K plate (after regulation) 1.395 K Temperature of 4K plate (after regulation) 4.80 K Dilution plate PID power 24.3–30.7 nW Bolometer plate PID power 5.1–7.4 nW 1.4K PID power 270 µW 4K PID power 1.7 mW 4He-JT cooler stroke amplitude 3450 µm Dilution cooler 4He flow rate 16.19–16.65 µmole/s Dilution cooler 3He flow rate 5.92–6.00 µmole/s Present survey life time (started 6 August 2009) 29.4 months and implemented in case the problem recurred, but it has highersignal-to-noiseratio,weusetheresponsivitytoopti- not. Six days were required to re-cool the instrument to its mizethebiascurrents(Catalanoetal.2010).Theoptimum operating point. The two-week first light survey (FLS) fol- in-flight bias current values correspond to the pre-launch lowed this recovery, starting on 15 August 2009. The FLS estimates within 5%. Therefore the pre-launch settings, for allowedassessmentofthequalityoftheinstrumentsettings, which extensive ground characterizations were performed, readiness of the data processing chain, and satellite scan- were kept (Fig. 2). In a similar way, the lock-in phase was ning before the start of science operations. The complete explored and optimized, and again the pre-launch settings instrument and satellite settings were validated and kept, were kept. andscienceoperationsbegan.Allactivitiesperformeddur- The optical background power on the bolometers is on ing the CPV phase confirmed the pre-launch estimates of thelowendofourratherconservativerangeofpredictions, theinstrumentsettingsandoperatingmode.Wewilldetail even lower than expected from the ground measurements. in the following paragraphs the most significant ones. This is attributed to a low telescope temperature and no detectable contamination of the telescope surface by dust during launch. This should result in a level of photon noise 3.2.2. 4He-JT cooler operating frequency setting lower than initially expected and an improved sensitivity. The 4He-JT cooler operating frequency was set to the nominal value of 40.08Hz determined during ground tests. 3.2.4. Numerical data-compression tuning Oncethecryochainstabilized,thein-flightbehaviourofthe coolerwasfoundtobeverysimilartothatobservedduring Theoutputofthereadoutelectronicunit(REU)consistsof groundtests.Thelinesobservedinthesignalduetoknown onenumberforeachofthe72sciencechannelsforeachhalf- electromagneticinterference(EMI)fromthe4He-JTcooler period of modulation (Lamarre et al. 2010). This number, drive electronics have the same very narrow width. The S , is the exact sum of the 40 16-bit ADC signal values REU long term evolution of the 4He-JT cooler parasitic lines is obtained within the given half-period. The data processor discussed in Sect. 6. unit (DPU) performs a lossy quantization of S . REU First, 254 S values corresponding to about 1.4s of REU observation for each detector, covering a strip of sky about 3.2.3. Detection chain parameters setting 8◦ long, are processed. These 254 values are called a com- pression slice.Themean<S >ofthedatawithineach The JFET preamplifiers are operated at the temperature REU compression slice is computed, and data are demodulated whichminimizestheirnoise.Thissettingwascheckedwhen using this mean: the bolometers were still warm (above 100K) during the cooldown, since the bolometer Johnson noise was then S =(S −<S >)∗(−1)i (1) much lower than the JFET noise. Optimum noise perfor- demod,i REU,i REU manceoftheJFETswasfoundcloseat130K,inagreement where 1 < i < 254 is the running index within the com- with the ground calibration. pression slice. After ground calibration, the only parameters of the Then the mean < S > of the demodulated data demod REU remaining to optimize in-flight were the bolometer S is computed and subtracted. The resulting data demod,i bias current and the phase of the lock-in detection, which slice is quantized according to a step Q fixed per detector: slightlydependsonthebolometerimpedance.Fig.2shows the bolometer responses for a set of bias current values S =round((S −<S >)/Q) (2) DPU,i demod,i demod measured while Planck was scanning the sky. For this se- quence, the satellite rotation axis was fixed. For each bias This is the lossy part of the algorithm: the required com- value, the total detection chain noise was computed after pression factor, obtained through the tuning of the quan- subtraction of the sky signal. Ground measurements have tization step Q, adds some extra noise to the data. For shown that the minimum NEP and the maximum respon- σ/Q = 2, where σ is the standard deviation of Gaussian sivity bias currents differ by less than 1%. Because of its white noise, the quantization adds 1% to the noise (Pajot The Planck HFI core team: Planck early results: first assessment of the HFI in-flight performance 5 Figure2. Optimization of the bolometer bias currents. Vertical lines indicate the final bias value setting. These values are shifted with respect to the maximum because a dynamic response correction has been taken into account. A bias value of 100digits corresponds approximately to 0.1nA. et al. 2010; Pratt 1978). In flight, the value of σ was deter- while scanning through the galactic center in September minedattheendoftheCPVphaseaftersubtractionofthe 2009 triggered the load limitation mechanism (compres- signal from the timeline. sion error) and up to 80000 samples were lost for each of Thetwomeans<S >and<S >computedas the 857GHz band bolometers. Therefore a new value of REU demod 32-bit words are sent through the telemetry, together with Q = σ/2 was set for those bolometers from 21 December theS values.AvariablelengthencodingoftheS 2009 onward, reducing the number of samples lost to less DPU,i DPU,i values is performed on board, and the inverse decoding is than200duringthefollowingscanthroughthegalacticcen- applied on ground. This provides a lossless transmission of ter in March 2010. An illustration of a compression error thequantizedvalues.Aloadlimitationmechanisminhibits loss is shown in Fig. 4. Thanks to the redundancy of the the data transmission, first at the compression slice level Planck scan strategy and the irregular distribution of the (compressionerrors),andsecondattheringlevel(Lamarre few remaining compression errors, no pixels are missing in et al. 2010). the maps of the high signal-to-noise ratio galactic center regions. Periodic checks of the noise value σ are done for For a given Q value, the load on each channel depends each channel, but no deviation requiring a change in the on the dynamic range of the signal above the level of the quantization step Q has been encountered so far. noise. This dynamic range is largest for the high frequency bolometers because of the galactic signal. The large rate of glitches due to high energy particle interactions also contributes to the load of each channel. Optimal use of 3.2.5. Instrument readiness at the end of the CPV phase the bandpass available for the downlink (75kbs−1 average for HFI science) was obtained by using initially a value Theoverallreadinessoftheinstrumentwasassessedduring of Q = σ/2.5 for all bolometer signals, therefore includ- the FLS. This end-to-end test was completely successful, ing a margin with respect to the requirement of σ/Q = 2. fromboththeinstrumentsettingandthesatellitescanning The load on each HFI channel is shown and compared to points of view. The part of the sky covered during the FLS simulated data in Fig. 3. The increase of signal gradients was included in the first all sky survey. 6 The Planck HFI core team: Planck early results: first assessment of the HFI in-flight performance 6 Table 3. Relative response deviation (in %) from linearity data for the CMB dipole, the galactic center (GC) and planets. simulation Saturation (Sat.) occurs for the Jupiter measurements at high frequency. Dipole GC Mars Saturn Jupiter e 5 100 GHz 3.8 10−4 0.001 0.01 0.13 0.8 mpl 143 GHz 10−3 0.0017 0.02 0.18 1.0 a of bits/s 231573 GGHHzz 68.41100−−44 00..000037 00..0056 00..583 34..25 ber 545 GHz <10−4 0.01 0.08 0.8 Sat. m u 857 GHz <10−4 0.1 0.06 0.8 Sat. n 4 100 143 217 353 545857 thermos stages is discussed in Planck Collaboration (2011b). The optical coupling of the HFI bolometers to each cryogenic 3 stage is shown in the left panels of Figs. 5 and 6 and in 0 20 40 60 Fig. 7. (The fact that the 100mK couplings all agree with channel pre-launch measurements shows that no bolometers were Figure3. Load measured for each HFI channel on 16 July damaged during launch.) These couplings are used to cal- 2010. Simulated data for the same patch of the sky are culate the effect of the fluctuations of each cryogenic stage shown for bolometers. Channels #54 and higher corrre- on the bolometer signals. The right panels of Figs. 5 and spond to the fine thermometers on the optical stages of 6 show the power spectral density (PSD) of the respective the instruments, plus a fixed resistor (#60) and a capaci- thermometersscaledbytheopticalcouplingfactorsforthe tor (#61) on the bolometer plate. most extreme bolometers. The scaled PSDs of the thermal fluctuations of the 4K and 1.4K stages are below the line corresponding to 30% of the total noise of the correspond- 2.0 106 Limits of the compression slice ing bolometer for all frequencies above the spacecraft spin DPU demodulated signal BC=25 frequency. Compression error The bolometer plate thermometers have a large cos- DU)1.8 106 mic particle hit rate (Planck Collaboration 2011b) be- A cause of the large size of their sensors compared to that e ( of the bolometers. Cosmic ray hits detection and removal d plitu1.6 106 donotallowustoreachthethermometernominalsensitiv- m ity, therefore they cannot be used to remove the effect of A bolometerplatetemperaturefluctuationsonthebolometer signal. Instead, the data processing pipeline (Planck HFI 1.4 106 Core Team 2011b) uses blind bolometers located on the bolometer plate. The bolometer noise components are dis- cussed in Sect. 6. 2010/03/20 20:20:56 1.2 106 0 100 200 300 400 Sample number 3.3.2. Linearity Figure4. Example of loss in one compression slice of data The way a bolometer transforms absorbed optical power on bolometer 857-1. Note the large signal-to-noise ratio into a voltage is not a linear process because both the con- while scanning through the galactic center. ductance between the bolometer and the heat sink, and the bolometer impedance have a non-linear dependence on the temperature (see e.g. Catalano (2008); Sudiwala et al. 3.3. Response (2000)). 3.3.1. Variation of the signal with background and with the The characterization of the linearity of the HFI detec- bolometer plate temperature tors has a direct impact on the calibration of the instru- ment: strong non-linearity takes place during the galaxy The optical background on the bolometers originates from crossing for high frequency bolometers and during planet the sky, the telescope, and from the HFI itself. The oper- crossings. An accurate absolute calibration is also neces- ating point of the bolometers is constrained by this total sary for the CMB dipole. Finally, the energy scale of large opticalbackground,andthefluctuationsofthisbackground glitchescanbecorrected.Thestaticresponsehasbeenchar- have a direct impact on the stability of the HFI measure- acterized during ground calibration showing a small devia- ments. tionfromlinearityaroundatenthofonepercentforfainter The power spectral density of each contribution to the sources (few hundreds of attowatts) and around a few per- backgroundiscomparedto30%ofthetotalnoisemeasured cent for brighter sources like planets (Pajot et al. 2010). in-flight (NEP column of Table 6). This specification cor- ThestaticresponsemeasuredduringtheCPVphaseagrees 1 responds to a quadratic contribution smaller than 5% on with the ground estimate to better than 1%. Nevertheless, the total noise. the use of the static non-linearity determination does not Thein-flighttemperaturestabilityoftheHFIcryogenic represent the true bolometric non-linear behaviour when The Planck HFI core team: Planck early results: first assessment of the HFI in-flight performance 7 Figure5.Left:couplingcoefficientsofthe4Kstage.Right:scaledpowerspectraldensity(PSD)ofthe4Kstagethermal fluctuations for the 100-1a and 353-5a-7a bolometers. Figure6.Left:couplingcoefficientsofthe1.4Kstage.Thethermalemissioninhighfrequencybandsbecomestoosmall to be measured. Right: scaled PSD of the 1.4K stage thermal fluctuations for the 100-1a and 353-5a-7a bolometers. times the gain (depending on the amplitude of the signal) and convolving it with the temporal transfer function nor- malized to 1 at the lowest frequency, is valid in the case of small signals. However this is not the case for bright point sources for which the estimate of non-linearity using the static response may be incorrect by up to 40% in the ex- treme case of Jupiter. For these sources we use a model to correct the static results. The use of fainter planets like Mars to characterize the beams minimizes this effect. Table 3 gives the deviation from linearity for various sources at the center of the beam for the bolometers at each frequency. 3.4. Electrical crosstalk on HFI detectors Figure7. Bolometer signal coupling coefficients to the The electrical coupling of the signal of one bolometer into 100mK bolometer plate. the readout chain of another, or electrical crosstalk, was measured to be less than −60dB for all pairs of chan- nels during ground-based tests (Pajot et al. 2010). We per- scanningthroughbrightpointsourceslikeplanets.Thelin- formed two tests in flight to verify this result, described earization of the response done by multiplying the signal below. 8 The Planck HFI core team: Planck early results: first assessment of the HFI in-flight performance results suggest that the CPV test has measured electrical crosstalk in current which is unrelated to the scientific sig- nal. 3.4.2. Measurements using glitches We used high energy glitches in one channel to study the impactonthesignalofsurroundingchannels.Thousandsof glitch events are collected for one channel, and the signals of all other channels for the same time period are stacked. The crosstalk in volts for individual glitches is defined as: cV =∆V /∆V (4) ij j i where V is the glitch amplitude in volts in the channel hit i by a cosmic ray, and V the response amplitude of another j channel j. Then, for a pair of channels i and j, the global voltage crosstalk coefficient is CV =median(cV) (5) ij ij For SWB channels, in contrast with the CPV previous results,noevidenceofcrosstalkisseen,withanupperlimit of −100dB. There are outliers in galactic channels because of incorrect glitch flagging. A second analysis using planet crossing data instead of glitches gave the same results. Concerning the coupling between PSB pairs, we see crosstalkaround−60dB,inagreementwiththeCPVtests; however, this is likely an upper limit because it includes the effects of coincident cosmic ray glitches which produce a similar effect but are not crosstalk. 4. Beams and time response 4.1. Measurement of Time Response 4.1.1. Introduction The time response of HFI describes the shift, in amplitude Figure8.Top:ElectricalcrosstalkmatrixC 54x54forall and phase, between the optical signal incident to each de- ij bolometers, coefficients are in dB. Bottom: Distribution of tector and the output of the readout electronics. The re- electrical crosstalk coefficients in dB. sponse can be approximated by a linear complex trans- fer function in the frequency domain. The signal band of HFI extends from the spin frequency of the spacecraft 3.4.1. CPV crosstalk measurements (f (cid:39) 16.7mHz) to a cutoff defined by the angular size spin of the beam (14–70Hz; see Table 4 from Lamarre et al. DuringtheCPVphase,weswitchedoffeachreadoutchan- (2010)). For the channels at 100, 143, 217, and 353GHz, nel one at a time for ten minutes, and observed the impact the dipole calibration normalizes the time response at the onallotherchannels.Foreachbolometerwecollectedabout spinfrequency.Toproperlymeasuretheskysignalatsmall 660minutes of data. scales,thetimeresponsemustbecharacterizedtohighpre- The crosstalk coefficient between channels i and j is cision across the entire signal band, spanning four decades expressed as: from 16.7mHz to ∼100Hz. C =∆V˜ /∆V˜, (3) The time response of bolometers typically is nearly flat ij j i over a signal band from zero frequency to a frequency de- whereV˜ andV˜ arethechanneliandj voltages,corrected fined by the bolometer’s thermal time constant, and then i j for thermal drift. The crosstalk matrix and a histogram of drops sharply at higher frequencies. For the HFI bolome- crosstalklevelsareshowninFig.8.Thecrosstalkismostly ters, the thermal frequency is 20–50Hz (Lamarre et al. confined to nearest neighbours in the belt, channels whose 2010;Holmesetal.2008),asnotedinLamarreetal.(2010) wiring is physically close. The measured crosstalk level is and Pajot et al. (2010), however, the time response of HFI in good agreement with ground measurements, typically is not flat at very low frequencies, but exhibits a low fre- <−70dB,andthusmeetstherequirement.Afewofthepo- quency excess response (LFER). larizationsensitivebolometerpairsshowacrosstalkaround We define the optical beam as the instantaneous direc- −60dB. tional response to a point source. Any sky signal is con- In the next section we see that crosstalk measurement volved with this function, which is completely determined from glitches shows a much lower level of crosstalk. These by the optical systems of HFI and Planck. The Planck HFI core team: Planck early results: first assessment of the HFI in-flight performance 9 Since Planck is rotating at a nearly constant rate and 1.2 around the same direction, the data are the convolution of 1.0 the signal with both the beam and the time response of e HFI. We separate the two effects and deconvolve the time ud0.8 responsefromthetimeordereddata.Thisdeconvolutionre- gnit0.6 a sults in a flat signal response, but necessarily amplifies any M0.4 components of the system noise that are not rolled off by 0.2 the bolometric response. This amplified noise is supressed 0.0 by a low-pass filter (Planck HFI Core Team 2011b). 3 2 4.1.2. TF10 model 1 e s a 0 The main ingredients of the time response are: (i) heat h P -1 propagationwithinthebolometer;(ii)signalmodulationat -2 afrequencyoff =90.188Hzperformedbyreversingthe mod -3 bolometer bias current; (iii) the effect of parasitic capaci- -4 tancealongthehighimpedancewiringbetweenthebolome- 0 20 40 60 80 100 Frequency(Hz) ter and the first electronics stage (JFETs); (iv) band-pass filtering, to reject the low frequency and high frequency Figure9. The amplitude and phase (in radians) of the whitenoiseintheelectronics;(v)signalaveragingandsam- three components of the TF10 model of the time response. pling; and (vi) demodulation. The solid blue line is H (f), the dotted green line shows bolo Because of the complexity of this sequence, a phe- H (f) and the dashed red line shows H . The solid filter res nomenological approach was chosen to build the time re- black line is H (f), the product of the three components. 10 sponse model. The time response is written as the product The vertical dotted black line shows the signal frequency of three factors: wherethebeamofa217GHzchannelcutsthesignalpower by half. H (f)=H ×H ×H (6) 10 bolo res filter Schematically, the first factor takes into account step (i), the second factor describes a resonance effect that re- sultsfromthecombinationofsteps(ii)and(iii),whilethe 4.1.3. Fitting the TF10 Model to Ground Data purpose of H is to account for step (iv). filter Toobtainthe10×52parametervalues,weusedthreesets Detailed analysis and measurements of heat propaga- of pre-launch measurements. (i) The bolometer response tion within the bolometer have shown that H is given bolo wasmeasuredat10differentfrequenciesbyilluminatingall by the algebraic sum of three single pole low pass filters. 52 bolometers with a chopped light source. (ii) Other mea- Explicitly: surements were done using carbon fibers as light sources; H = (cid:88) ai (7) the latter were alternately turned on and off at a variable bolo 1+j2πfτi frequency. (iii) The bolometer bias currents were periodi- i=1,3 callysteppedupandloweredbyasmallamount.Byadding with 6 parameters (a1,a2,a3,τ1,τ2,τ3). asquarewavetotheDCcurrent,temperaturestepsarein- duced, simulating turning on and off a light source (the 1+p (2πf)2 H = 7 (8) analysis of these data requires bolometer modelling). res 1−p (2πf)2+jp (2πf) 8 9 Noneofthesemeasurementswasabsolutelynormalized; all compared the relative response to inputs of various fre- with 3 free parameters (p ,p ,p ), 7 8 9 quencies. While measurement (i) only provided the ampli- 1−(f/F )2 tude of the time response, measurements (ii) and (iii) pro- H = mod (9) filter 1−p (2πf)2+j(f/F )2 vided both the amplitude and the phase. Note that for the 10 filter phase analysis, because of the lack of precise knowledge of withonefreeparameter(p10).Atotalof10freeparameters the time origin t0 of the light/current pulses, a fourth fac- describethismodel,asindicatedbyitsname.SeeFig.9for torexp(j2π∆t f)isintroducedintheexpressionofH (f), 0 10 anillustrationofthethreecomponentsofthetimeresponse where the additional parameter ∆t represents the uncer- 0 model TF10 for a typical 217 GHz channel. tainty in time. The parameter Ffilter characterizes the rejection filter Amongthethreesetsofmeasurements,thecarbonfiber widthandiskeptfixedto6Hzinthefittingprocess.Besides setcoveredthelargestfrequencyrange.Thusitwasthebest thefactthatthisphenomenologicalmodelisphysicallymo- for building the transfer function model described above tivated, this parameterization: andforinvestigatingitsmainfeatures.However,itinvolves uncertainties that could be resolved only with a very de- – ensures causality tailed simulation of the set-up, therefore it was not used to – satisfies H(−f)=H∗(f) calculate the final set of parameter values. The final values – goes to 1 when f goes to zero (because we define a + 1 werecalculatedfromdatasets(i)and(iii),whosefrequency a +a =1), while it goes to 0 when f goes to infinity 2 3 ranges are complementary, 2–140Hz and 0.0167–10Hz, re- – includes enough parameters to provide the necessary spectively. Since no absolute normalization was available, flexibilitytofitthetimeresponsedataofall52bolome- the two datasets were matched in the overlap frequency ters. range. 10 The Planck HFI core team: Planck early results: first assessment of the HFI in-flight performance The fitting of the analytic expression given above to the merged data was done in the range between 16.7mHz 11 amtaatawirnohantgaesyeadidsmapsttAAnensaif1a(nsusnir2gmnlcvgtrl0lraeditaiecislhttHelbtauprhcueseeenzhlrecerram.eertnvrtsaiishTaaubsat)deaistl.hne,n1uiitdedgevi.iσend1snea5mt3btgtam2iaoae,eclnaps.laofiicnodanlTdatpwrd<selechrac,ilrhomhceurh6detaoalnaehcautvr×tkusitesceneee.mae1rgdatdlst0eis,hmt−uroχbhewis42cebyai.5/hanet2DlrTiegpcetvnhcohlshiaaonpFidelnswv-oueefladnmepfietririssansgisoeearhetodanardutfteimnc,sbhpoledebuue1bfia0mtstussbeiseldoarayeorniidtdvbnswraceptoiwaoqtcpalnisasehuironmysotoasnehepsetoisddeecet-f, normalized signal normalized signal 000000000000000000..................00112233445566778899 (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0) 00 00..0055 00..11 00..1155 00..22 analyticalexpressionofthesteps(ii)to(vi)ofsection4.1.2. ttiimmee ((ss)) Based on a closer analysis of the electronics stages, this Figure10. Comparison of the impulse response of chan- model is more physically motivated than the 10-parameter nel 143-2a (red curve) and a template made from stack- model. It requires only 8 parameters and provides better ing glitch events (black curve). Noise begins to dominate results near the modulation frequency. Nevertheless the further in the timeline. The ringing observed at the mod- model has not been used in the current data release. It ulation frequency is generated by the electronics rejection is only used as a benchmark, to check possible systematic filter. effects in the current release. Most of the effects of the dif- ference between the models disappear when the data are low-pass filtered. planetamplitudeisparameterizedwithadisktemperature rather than a single amplitude: 4.1.4. Fitting TF10 to Flight Data Ω (t) A(t)=T p , (11) TheplanetsMars,Jupiter,andSaturnarebright,compact disk Ω b sources that are suitable for measuring the beam and pro- vide a near-delta-function stimulus to the system that can where Tdisk is the whole-disk temperature of the planet, beusedtoconstrainthetimeresponse.Duringthefirstsky Ωp is the solid angle of the planet, which can vary signifi- survey,Planck observedMarstwiceandJupiterandSaturn cantly during the observation, and Ωb is the solid angle of once (Planck HFI Core Team 2011b). During a planet ob- the beam. Ωp is computed using Horizons, which is pro- servation, the spacecraft scans in its usual observing mode grammed with Planck’s orbit. (Planck Collaboration 2011a), shifting the spin axis in 2(cid:48) The free parameters of the fit are the six parameters steps along a cycloidal path on the sky. Since planets are of the time response corresponding to Hbolo, the two com- closetotheeclipticplane,thecoverageinthecross-scandi- ponents of the centroid of the beam x0, the mean FWHM rection is not as fine as in the scan direction. In the case of θFWHM,theellipticity(cid:15),theellipseorientationangleψ,and Jupiter and Saturn, each channel observes the planet once the planetary disk temperature Tdisk. The four parameters per rotation for a period of approximately 6 hours (9 peri- describing the electronics are somewhat degenerate with ods of stationary pointing, or "rings"). Because Mars has the bolometer part of the time response, and we fix them alargepropermotion,thefirstobservationlasted12hours at the ground-based values. (or 18 rings). Becauseofthelargenonlinearresponseandhighlynon- We use the forward-sense time domain approach Gaussian beams at 545 and 857GHz, we do not perform (Huffenbergeretal.2010)tosimultaneouslyfitforGaussian fits to the planet data at these frequencies. Instead we rely beam parameters and TF10 time response parameters. A on pre-launch fits for the time response. custom processing pipeline avoids filtering the data. We By taking the Fourier transform of the time response extract the raw bolometer signal and demodulate it using function derived on planets, one obtains the system re- theparitybit.Weusetheflagscreatedbythetimeordered sponse to a Dirac impulse. This response can be compared information(TOI)processingpipelinetoexcludedatasam- totheglitchesgeneratedbycosmicraysthatdepositenergy ples contaminated by cosmic rays, and we additionally flag in the sensor grids. alldatasampleswherethenonlineargaincorrectionismore The glitches detected by HFI are sampled with time than0.1%.WeuseHorizons2emphemeridestocomputethe steps1/(2Fmod).However,theglitchescanbesuperresolved pointing of each horn relative to the planet center. in time by normalizing, phasing, and stacking single glitch Thetimedomainsignalfromtheplanetismodeledasan events (Crill et al. 2003). This gives glitch templates for elliptical Gaussian convolved with the TF10 time response each channel (Alexandre Sauvé, private communication) as follows: that are effectively sampled at a much higher frequency. Figure 10 shows the comparison between a superre- d(t)=H (cid:63)A(t)G[x(t);x ,(cid:15),θ ,ψ] (10) solvedglitchtemplateandthecorrespondingcalculatedre- 10 0 FWHM sponse. There is good agreement in general, but there are wheretheGaussianopticalbeammodelGisparameterized discrepancies at high frequency (f >100Hz). The physical as in Eqs. 9–11 of Huffenberger et al. (2010), except the modelfortheelectronicstransferfunctionsbrieflydescribed at the end of section 4.1.3 suppresses this discrepancy at 2 ssd.jpl.nasa.gov/?horizons high frequency.

See more

The list of books you might like

Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.