ArielRad: the Ariel Radiometric Model
Lorenzo V. Mugnai, Enzo Pascale, Billy Edwards, Andreas Papageorgiou, Subhajit Sarkar
NNoname manuscript No. (will be inserted by the editor)
ArielRad: the
Ariel
Radiometric Model
Lorenzo V. Mugnai · Enzo Pascale · Billy Edwards · Andreas Papageorgiou · Subhajit Sarkar
Received: date / Accepted: date
Abstract
ArielRad, the
Ariel radiometric model, is a simulator developed toaddress the challenges in optimising the space mission science payload and todemonstrate its compliance with the performance requirements.
Ariel , the At-mospheric Remote-Sensing Infrared Exoplanet Large-survey, has been selectedby ESA as the M4 mission in the Cosmic Vision programme and, during its 4years primary operation, will provide the first unbiased spectroscopic surveyof a large and diverse sample of transiting exoplanet atmospheres. To allowfor an accurate study of the mission, ArielRad uses a physically motivatednoise model to estimate contributions arising from stationary processes, andincludes margins for correlated and time-dependent noise sources. We showthat the measurement uncertainties are dominated by the photon statistic,and that an observing programme with about 1000 exoplanetary targets canbe completed during the primary mission lifetime.
Keywords
Ariel · exoplanet · simulated science In the past 20 years more than 4000 exoplanets have been detected using spaceand ground based surveys, and many more are expected to be discovered in
This work has been supported by ASI grant n. 2018.22.HH.O.L. V. Mugnai · E.PascaleDipartimento di Fisica, La Sapienza Universit`a di Roma, Piazzale Aldo Moro 2, 00185 Roma,Italy E-mail: [email protected]. EdwardsDepartment of Physics and Astronomy, University College London, Gower Street, London,WC1E 6BT, UKA. Papageorgiou · S. SarkarSchool of Physics and Astronomy, Cardiff University, Queens Buildings, The Parade, Cardiff,CF24 3AA, UK a r X i v : . [ a s t r o - ph . I M ] S e p Lorenzo V. Mugnai et al. the coming years thanks to space missions such as
TESS (Ricker et al., 2016),
CHEOPS (Cessa et al., 2017),
PLATO (Rauer et al., 2014) and
GAIA (GaiaCollaboration et al., 2016), and to ground instrumentation such as
HARPS (Mayor et al., 2003),
HATnet (Bakos, 2018),
WASP (Pollacco et al., 2006),
KELT (Pepper et al., 2018),
OGLE (Udalski et al., 2015),
NGTS (Wheatleyet al., 2013) and many others.Planets have been found to be ubiquitous in our Galaxy, have been de-tected around almost every type of star and Cassan et al. (2012) infer thaton average every star in our Galaxy hosts one planetary companion. The ex-oplanets detected thus-far show a diversity in their masses, sizes, orbits, and,presumably, physical and chemical conditions unseen among the planets in ourown Solar System.However, the essential nature of these exoplanets remains elusive. We havelittle idea whether the planet chemistry is linked to the formation environmentor whether the type of host star drives the physics and chemistry of the planetsbirth, and evolution (Tinetti et al., 2018).Atmospheric spectroscopy holds the key to unlock the mysteries of thechemical and physical conditions of these alien worlds as well as their forma-tion and evolutionary histories. Multi-band photometry and spectroscopy oftransiting exoplanets (Seager and Sasselov, 2000) is currently one of the mosteffective observational techniques for revealing the chemistry and thermody-namics of exoplanet atmospheres (Charbonneau et al., 2005; Tinetti et al.,2007; Sing et al., 2016; Madhusudhan et al., 2012; Huitson et al., 2012; Krei-dberg et al., 2014). Photometric and spectroscopic light-curves of transitingexoplanets provide a measurement of the transmission (transit) or emission(eclipse) spectrum of an exo-atmosphere, and can be used to reveal chemicalconstituents, as well as the pressure and temperature profile, using retrievaltechniques originally developed for the study of the Earth and Solar Systemplanets, and adapted to the new field of investigation (Irwin et al., 2008; Lineet al., 2013; Waldmann et al., 2015; Gandhi and Madhusudhan, 2017, e.g.).Existing astronomical instrumentation has allowed to study spectroscop-ically a few tens of exoplanets, selected among those that are more easilyobservable based on their sizes and temperatures, and over a limited spectralrange (e.g. Sing et al., 2016; Tsiaras et al., 2018). A significantly larger popu-lation study is now required in order to decipher the secrets of the exoplanetsand their diversity.The Atmospheric Remote-Sensing Infrared Exoplanet Large-survey,
Ariel ,has been selected by ESA as the next medium class mission of the CosmicVision programme to spectroscopically characterise the atmospheres of a largeand diverse sample of exoplanets.
Ariel will largely focus on warm and hotexoplanets, taking advantage from their well mixed atmospheres that showminimal condensation and sequestration of high atomic weight metals such asC, O, N, S, Si. The
Ariel science payload uses a 1-m class telescope to feed amulti-band photometer and spectrometers covering the wavelength range from0.5 µ m to 7.8 µ m, to sample both the peak thermal emission of the exoplanet rielRad: the Ariel
Radiometric Model 3 atmospheres, and the spectral signature of all major atmospheric gases (e.g.H O, CO, CO , NH , CH , HCN, H S, TiO, VO) and condensed species.The
Ariel payload design is investigated using detailed simulations of theastrophysical detection, that take into account mission design parameters suchas flight duration and sky availability, and payload and astrophysical uncer-tainties. Margins are used on each estimate to ensure all performance predic-tions are derived under reasonably conservative assumptions.In this work we describe ArielRad, the
Ariel radiometric model simula-tor used to assess the payload science performance and to demonstrate itscompliance with the science requirements. ArielRad is the third simulationtool developed to assess the mission performance and follows ExoSim (Sarkaret al., 2020), and the
Ariel
ESA Radiometric Model (AERM), developed bythe Space Agency (Puig et al., 2015) to support the flow down of science re-quirements to instrument requirements the radiometric model during the
Ariel phase/A study (Tinetti et al., 2018).ExoSim is a end-to-end, time-domain simulator of
Ariel observations. Itevaluates photometric and spectroscopic light curves implementing a detaileddescription of the instrument design, source of uncertainties, and systematicsof instrument and astrophysical origin. As such, the simulated observationsproduced by ExoSim are similar to those expected with
Ariel and require afull data reduction pipeline to detrend the observations and reconstruct theplanet spectrum. ExoSim has been fully validated using noise modelling as wellas real measurements obtained with Hubble Space Telescope. ExoSim simu-lations allow us to study effects of spatially and temporally correlated noiseprocesses such as the photometric uncertainties arising from the jitter of theline of sight, or from the activity of the host star. However, ExoSim analyses arecomputationally intensive and it is currently impractical to conduct studies onmore than a few targets, until a fully automated data reduction pipeline is de-veloped and validated in the next phase of the project. AERM overcomes thislimitation implementing a simplified approach based on a radiometric mod-elling of the detection and of the uncertainties. These simplifications mean itis capable of assessing the confidence limit on the detection of emission andtransmission spectra of hundreds of exoplanet targets. AERM implements anoise model calibrated using ExoSim estimates and delivers compatible esti-mates on test targets. However, the noise model implemented in AERM is atwo parameters model that falls short in capturing the complexity of the
Ariel payload design. Consequently, AERM provides an overly pessimistic predictionon some targets which makes this simulator unsuitable in assessing instrumentdesign solutions.ArielRad has been written to derive payload requirements from sciencerequirements through detailed error budgeting, to validate the compliance ofthe payload design with the science requirements, and to optimise the payloaddesign evaluating instrument design solutions over a proposed target list com-prising about 1000 exoplanets. ArielRad overcomes the limitations of AERMby implementing a detailed payload model, similar to that used by ExoSim,capable of describing all major instrument components. ExoSim computing
Lorenzo V. Mugnai et al. limitations are overcome in ArielRad by implementing radiometric estimatesof the uncertainties of the detection. Noise contributions that need to be es-timated in the time domain, such as the photometric noise arising from thejitter of the line-of-sight, are imported in ArielRad from pre-computed Ex-oSim estimates. ArielRad is used to create and maintain the top level payloadperformance error budgets, allowing a balanced allocation of resources acrossthe payload.In this work we describe ArielRad, the models implemented, their valida-tion, and provide examples of how ArielRad can be used to support the
Ariel mission development, leaving to a future work a detailed assessment of the
Ariel mission performance. Ariel instrument design and observational strategy
The
Ariel payload design is briefly described in this section with more detailsavailable in Tinetti et al. (2016); Tinetti et al. (2018); Pascale et al. (2018),and in the
Ariel
Assessment Study Reports . The telescope is an off-axis0 . m Cassegrain with an elliptical primary mirror, that provides diffractionlimited performance at wavelengths longer than 3 µm ; there is no need forimaging capabilities and the telescope is cooled to less than 70 K . A refocusingmechanism actuates the secondary mirror to correct possible misalignments,that can occur at launch and during thermalisation.The flux collected by the primary aperture feeds two separated instrumentmodules. A dichroic mirror splits the light into two beams, one at wavelengthsshorter than 1 . µm and the second at wavelengths between 1 . µm and7 . µm . The first beam is fed to an instrument module containing three pho-tometers (VISPhot, 0 . µm − . µm ; FGS-1, 0 . µm − . µm ; FGS-2, 0 . µm − . µm ) and a slit-less prism spectrometer (NIRSpec, 1 . µm − . µm ) withspectral resolving power >
15. The two photometers, FGS1 and FGS2, oper-ate as Fine Guidance Sensors (FGS), providing both photometric and pointinginformation for the attitude and orbital control system (AOCS). The secondinstrument module, fed by the longer wavelength beam, hosts the
Ariel
In-frared Spectrometer (AIRS), which consists of two prism-dispersed channels:Channel 0 (CH0) covering the 1 . µm − . µm band with a spectral resolvingpower larger than 100, and Channel 1 (CH1) covering the 3 . µm − . µm bandwith a spectral resolving power larger than 30. The spectrometers have fieldstops (slits) at an intermediate image plane, that are wider than the telescopePoint Spread Function (PSF) and are used to limit the stray-light and thediffuse emission from reaching the focal plane.During its four years primary mission, Ariel will observe ∼ https://arielmission.space/ariel-publications/.rielRad: the Ariel
Radiometric Model 5
Table 1
Summary of the science addressed in each tier.
Tier Name ObservationalStrategy Science case
Tier 1: Recon-naissance sur-vey Low Spectral Res-olution observationof ∼ ∼ – What fraction of planets are covered byclouds? – What fraction of small planets have stillretained H/He? – Classification through colour-colour dia-grams – Constraining/removing degeneracies inthe interpretation of mass-radius diagrams – Albedo, bulk temperature and energy bal-ance for sub-sampleTier 2: Deepsurvey Higher SpectralResolution ob-servations of asub-sample in theVIS-IR – Main atmospheric component for smallplanets – Chemical abundances of trace gases – Atmospheric thermal structure (verti-cal/horizontal) – Cloud characterisation – Elemental compositionTier 3: Bench-mark planets Very best planets,re-observed multi-ple times with alltechniques – Very detailed knowledge of the planetarychemistry dynamics – Weather, spatial and temporal variability
Tab. 1 with the first tier (Tier 1) being a low spectral resolution reconnaissancesurvey of ∼ ∼
50% of the planets from Tier 1, are studied with a higher spectralresolution, merging the data collected in two juxtaposed spectral bins. Tier2 analysis searches for potential correlations between atmospheric chemistryand basic parameters such as planetary size, density, temperature, stellar typeand metallicity. It allows investigations of chemical abundances, cloud char-acterisation and elemental composition. Finally, ∼
10% of Tier 1 planets arere-observed multiple times in Tier 3, and the data are analysed using thefull spectral resolution provided by the payload to gain detailed knowledge ofthe planetary chemistry dynamics and temporal variability of the exoplanetatmospheres.
ArielRad is a radiometric simulator of the
Ariel payload, it is implemented inPython and it is maintained by the
Ariel
Consortium. The software packagecomes with an exhaustive documentation and the primary inputs are containedin a XML configuration file describing the payload, an XML configuration filedescribing the mission parameters, and a CSV or spreadsheet table containing
Lorenzo V. Mugnai et al.
Fig. 1
Simulator work flow. The simulation starts with two input files: a payload configura-tion file and a candidate planet list. ArielRad propagates the target host star signal thoughtthe payload, then evaluates the noise. Finally, the simulator estimates the transit or eclipseobservation and the resultant SNR. a list of target exoplanetary systems with their parameters. An instrumentindependent version of the radiometric simulator called ExoRad is publiclyavailable on GitHub .The simulator evaluates the payload science performance by estimating theexpected experimental uncertainties on measured exoplanet atmospheric spec-tra in emission and transmission. Each simulation starts with the generationof the source signal from the star. The signal is then propagated through theinstrument to the detector focal planes (assuming no field stars), accountingfor the transmission of each optical component and the dispersion of the prismspectrometers.Uncertainty estimates account for detector noise (readout noise and gainnoise, the latter arising from variations in acquisition electronic chain), darkcurrent, photon noise from the star, the zodiacal background and includesinstrument emission, and jitter noise. Margins are included to account foruncertainties in the current noise estimates and instrument performances. Thesimulation continues by estimating the planet atmospheric signal and thus theSNR of the detection when observing the target in transit or eclipse. Everycandidate target observation is considered to last 2 . T . This strategy allows the collection of data both inand out of transit for the light curve fit and the transit depth estimation.This parameter can be configured by the user as well as all other parametersdescribed later. The data is then binned according to the tier resolution, aswill be done in Ariel data analysis. Tier 1 uses a low resolution spectroscopy(4 spectral resolution elements covering 1 . − . µm ); Tier 2 has spectralresolution R ∼
10 for 1 . < λ < . µm , R ∼
50 for 1 . < λ < . µm and R ∼
15 for 3 . < λ < . µm ; Tier 3 uses the full R , that means R = 100 ,
30 for AIRS-CH0 and AIRS-CH1 respectively, and for NIRSpec, asthe requirement is
R >
15, we use R = 20. Finally, ArielRad estimates thenumber of observations required to achieve a desired SNR for each planet (e.g.SNR = 7) and from this the total observing time required on target. Thisprocess is summarised graphically in Fig. 1) and each stage described in detailin the following sections. https://github.com/ExObsSim/ExoRad2-publicrielRad: the Ariel
Radiometric Model 7 S ( λ k ) = 1 λ k − λ k − R (cid:63) D (cid:90) λ k λ k − S P h ( λ ) dλ (1)where λ k = (cid:0) (cid:1) k λ min is a logarithmic spaced wavelength grid, deter-mined starting from the sample spectral resolution of 6000 and the minimumwavelength λ min . This binning reduces the spectral resolution of the inputspectra for computational efficiency, while preserving the total power. R (cid:63) isthe target star radius, D is the distance and S ph the input Phoenix spectrum.The units of S ( λ k ) are those of a spectral energy density. ArielRad includes contributions from the Zodiacal background, and instrumentthermal emission.The Zodiacal background emission is modelled using a modified version ofthe JWST-MIRI Zodiacal model (Glasse et al., 2010), scaled according to thetarget position in the sky and the Zodi model of Kelsall et al. (1998): I zodi ( λ ) = A · . − · BB ( λ, K ) + B · . − · BB ( λ, K ) (2)where BB is the Planck law, and A and B are the fitted coefficients. Typically, A and B evaluate to ∼ . ∼ ∼ . A = B = 2 . I inst , is estimated by modelling each of theoptical element as a Planck law at the element operating temperature andmodified by a wavelength dependent emissivity. All the reflective surfaces aremade in aluminium, and we conservatively assume a 3% emissivity. Same emis-sivity is assumed for the refractive components. All optical elements are pas-sively cooled to 60K. Because of the almost isothermal Ariel design, the totalinstrument emission from optics is computed from the emission of one com-ponent, multiplied by the number of optical components along the light path.The exception is the contribution of the detector box, I Inner , as the fluxis not coming from the instrument field of view (FoV) but instead directlyirradiates the pixels from all directions. This contribution is referred to as the“Inner Sanctum” and it is estimated as the radiation emitted from a black bodycavity at the detector operating temperature (i.e. unit emissivity is assumed).
Lorenzo V. Mugnai et al. m ]0.10.20.30.40.5 () Q E () VISPhotFGS1 FGS2 NIRSpec AIRS-CH0 AIRS-CH1
Photon Conversion Efficiency
Fig. 2
Total photon conversion efficiency, Φ Y ( λ ) QE Y ( λ ), as used in ArielRad. Φ Y ( λ ), where Y is one of VISPhot, FGS1,FGS2, NIRSpec, AIRS-CH0 or AIRS-CH1, is obtained by simulating the lightpath from the telescope to the detectors through the optics. The detectorquantum efficiency QE Y ( λ ) is also dependent on wavelength and defined foreach channel. The photon conversion efficiency (PCE) is the product betweentransmission and quantum efficiency and it is shown in Fig. 2. The lower PCEobserved in VISPhot and FGS1 with respect to FGS2 and NIRSpec is causedby a lower detector QE at short wavelengths, while a similar PCE reductionat AIRS wavelengths is mainly a consequence of the refractive materials usedin the mid-infrared. The Point Spread Functions (PSF) are estimated as afunction of the wavelength using external software and included, allowing forwavelength interpolations.3.3 Signal modelThe Point Response Function (PRF) is the PSF, normalised to unit volumeand convolved with the pixel response, which is assumed to be a top-hat func-tion, H pix ( x, y ). The effects of a non-flat pixel response function are onlyrelevant for pointing jitter. As discussed later, this effect is estimated withExoSim and imported in ArielRad as an additional noise contribution (see sec3.4.3). Hence, P RF ( x l , y m , λ ) = (cid:90) (cid:90) P SF ( x, y, λ ) H pix ( x l − x, y m − y ) dxdy (3) rielRad: the Ariel
Radiometric Model 9 where l and m are detector pixel indices, and (cid:80) l,m P RF ( x l , y m , λ ) = 1.For each photometric channel, the signal of the target star T is modelledas the sum of the signals sampled by all detector pixels within an ellipticalaperture, the size of which depends on the PRF. Hence, this is estimated as S T,phot ( λ s ) = A tel (cid:88) x l ,y m ∈ A p P RF ( x l , y m , λ s ) (cid:90) QE Y ( λ ) Φ Y ( λ ) S ( λ ) λhc dλ (4)where λ s is the central wavelength of the photometric band (e.g. 0 .
55, 0 . . µm for VISPhot, FGS1 and FGS2 respectively). A tel is the telescopeeffective collecting area. A p is an elliptical aperture used for aperture photom-etry. Typical aperture sizes are chosen to encircle either 83.8% or 91.0% ofthe energy in the PSF as ExoSim models indicate a reduction of jitter noiseto negligible levels compared to other noise sources for these aperture sizes(Sarkar and Pascale, 2015). The aperture, A p , is defined over x,y pixels withcoordinate indices l, m .The case of a spectroscopic channel is similar and the signal sampled bythe detector is estimated as S T,spec ( λ s ) = A tel (cid:88) x l ,y m ∈ A s P RF ( x l , y m ) QE Y ( λ ) Φ Y ( λ ) S ( y m ) λhc ∆λ m (5)where A s is now a rectangular box aperture of the size of the spectral bin alongthe y-axis, assumed to be parallel to the dispersion direction. Apertures arespaced such as to obtain the desired spectral binning R , which is 20, 100, 30for NIRSpec, AIRS-CH0 and AIRS-CH1 respectively. ∆λ m is the wavelengthinterval sampled by the pixel at coordinate y m , and λ s is the wavelength atthe centre of the spectral bin sampled by the spectrometer, defined as λ s = 12 ( λ j + λ j +1 ) (6)where λ j is the wavelength at the bin edge defined by the recursive relation λ j +1 = λ j (cid:18) R (cid:19) (7)and the focal plane wavelength solution maps pixel coordinates to wavelength( λ j +1 , λ j → y i +1 , y i ).For the Zodiacal light contribution, the effect is proportional to the pixelsolid angle, Ω = (cid:16) ∆ pix f eff (cid:17) , where ∆ pix is the pixel size and f eff is the effectivefocal length. For the photometers and the slit-less NIRSpec spectrometer thiscontribution is given by S zodi,phot ( λ s ) = A tel Ω (cid:90) QE Y ( λ ) Φ Y ( λ ) I zodi ( λ ) λhc dλ (8)However, the AIRS instrument includes a field stop that being wider thanthe input PSF has no effects on a point source target, but acts as a slit for diffuse radiation. Therefore, Zodiacal light must be modelled differently forAIRS channels. ArielRad simulates the signal incoming to the detector asthe convolution between the Zodiacal light and the field stop/slit. If the slitwidth expressed in number of pixels at the focal plane is L , and the spectralresolving power computed at a certain λ is R ( λ ), the detector receives diffuseradiation over the wavelength range (cid:16) λ j − Lλ R ( λ ) , λ j + Lλ R ( λ ) (cid:17) , and not overthe full range of wavelengths accepted by the filter, so S zodi,spec ( λ s ) = A tel Ω (cid:90) λ c + Lλ R ( λ λ c − Lλ R ( λ QE Y ( λ ) Φ Y ( λ ) I zodi ( y m ) λhc ∆λ m (9)where λ is 1 .
95 and 3 . µm and R ( λ ) is R (1 .
95) = 100 and R (3 .
90) = 30for AIRS-CH0 and AIRS-CH1 respectively.ArielRad models the diffuse light coming from instrument emission by sub-stituting I zodi ( λ ) with n(cid:15)I instr ( λ ) in Eq. 8 and 9, where we are assuming thatall the n optical elements (lenses, mirrors, etc.) have the same emissivity, (cid:15) .If the components are modelled with different emissivity, (cid:80) ni =1 (cid:15) i I instr ( λ ) isused instead.The Inner Sanctum contribution is the same for all detector focal planes,as it originates from the emission of their enclosures, and it is proportional tothe pixel surface: S Inner ( λ s ) = ∆ pix ( π − Ω ) (cid:90) QE Y ( λ ) I Inner ( λ ) λhc dλ (10)Diffuse backgrounds add a DC offset in the measured stellar signal. Ariel-Rad assumes that these are removed using standard techniques, e.g. aperturephotometry, and only their (uncorrelated) contribution to the noise budget isconsidered later in this work.The resultant total signal in one spectral bin is the sum of all the previouscontributions S Y ( λ s ) = S T,Y ( λ s ) + S zodi,Y ( λ s ) + S instr,Y ( λ s ) + S Inner ( λ s ) (11)where in our notation Y can be one of VISPhot, FGS1, FGS2, NIRSpec,AIRS-CH0 or AIRS-CH1. S Y ( λ s ) has units of counts (electrons) per second.3.4 Noise modelArielRad simulates the noise for each spectral bin from the signal estimate. Ina real instrument, noise sources act at every stage of the detection chain andcan be stationary and non-stationary. ArielRad estimates the contributions ofnoise components that are stationary random processes, such as Poisson noiseand detector noise. It also includes Jitter noise (provided from an ExoSimsimulation), margins for other noise contributions, and a noise floor. Fig. 3shows a noise tree including all the noise sources considered. rielRad: the Ariel
Radiometric Model 11
Fig. 3
Noise tree diagram listing all noise contributors considered in Eq. 12. The PoissonNoise term depends on signals collected by the telescope (in yellow the target and theZodiacal background photon noise), and on signals of instrument origin (in blue, photonnoise from instrument and inner sanctum self emission). The detector noise contributorsare from dark current, gain and read noise. The Jitter noise term is discussed separatelyfrom the rest of the noise terms as it is imported as a model from ExoSim simulations. Thepayload noise floor prevents noise from integrating down indefinitely.
The variance of each spectral bin is modelled as
V AR [ S Y ( λ s )] = (1 + χ Y ) V AR P [ S Y ( λ s )] ∆t int + (Poisson noise term)+ V AR D [ S Y ( λ s )] ∆t int + (Detector noise term)+ V AR J [ S Y ( λ s )] ∆t int + (Jitter noise term)+ [ p S T,Y ( λ s )] (Payload noise floor)(12)where all quantities except p are estimated at a 1 hr integration time and atlonger time scales are assumed to decrease as the inverse of ∆t int , the integra-tion time in hours. Time scales longer than 1 hr are expected to be above thecorrelation time scale of coloured noise processes considered. χ Y is a marginadded to include noise sources that cannot be simulated with ArielRad, such ascorrelated noise, time-dependent effects, and unknown unknowns. Typically, χ = 0 . Hubble /WFC3 and
Spitzer /IRAC ( ∼ The
Payload noise floor , p , models low frequencies instabilities (e.g. Brow-nian or pink noise processes) that prevents noise to integrate down indefinitelywith time. Following Greene et al. (2016), we use p = 20 ppm of the incomingsignal S T,Y ( λ s ). See also Beichman et al. (2014); Molli`ere et al. (2017) for anexample of this approach. The Poisson noise term includes all the photon noise contributions: targetsource, zodiacal background, inner sanctum and instrument emission. Hence,the Poisson variance at 1 hr time scale is
V AR P [ S Y ( λ s )] = 1 hr3600 s 1 η n + 1)5 n ( n + 1) S Y ( λ s ) (13)The factor 3600 s normalises the variance at 1 hr time scale and the parameter η (cid:46) n consecutive non-destructive reads (NDRs) during each exposure, Eq. 13 is multiplied by n +1)5 n ( n +1) as discussed in Rauscher et al. (2007) (MULTIACCUM readout strategy, seetheir Equation 1). This is appropriate as the number of group elements is 1 inthe Ariel baseline payload design. The minimum value of n is 2, i.e. correlateddouble sampling (CDS) required to remove the detector KTC noise; n +1)5 n ( n +1) evaluates to 1 when n = 2. NDRs are read at a constant cadence and n dependsfrom the detector saturation time T sat = f W D · W DS
Y,max (14)where
W D is the detector well depth, f W D is the fraction of well depth used(e.g. f W D = 0 .
75, Berta et al., 2012), and S Y,max is the largest pixel signal inthe channel Y , that is estimated by ArielRad, but is not explicitly discussedhere for the sake of conciseness. V AR P [ S Y ( λ s )] has units of s − hr. The detector noise variance can be divided in three terms, read noise, gain noiseand dark current. The dark current signal depends on the detector pixel darkcurrent, I dark , and on the number of pixels, N pix , included in the photometricapertures A p or A s defined earlier, with S dark curr = N pix I dark . The detectornoise variance at 1 hr is V AR D [ S Y ( λ s )] = 1 hr3600 s 12( n − n ( n + 1) N pix σ rd,Y η T sat ++ σ gain,Y S Y ( λ s )++ 1 hr3600 s 1 η n + 1)5 n ( n + 1) S dark curr (15) rielRad: the Ariel
Radiometric Model 13 where σ rd,Y is the noise variance on each individual NDR and has no units.Following Rauscher et al. (2007), the factor n − n ( n +1) accounts for a line fit tothe NDR ramp in one exposure, and decreases as n increases.The gain noise , σ gain,Y in units of √ hr, accounts for instabilities of the elec-tronic acquisition chain (amplifiers, digitisers, etc.), assumed post-processing,i.e. after common modes are removed using housekeeping information. With T sat in units of seconds, V AR D [ S Y ( λ s )] has units of s − hr. Pointing drifts and jitter of the line-of-sight (LoS) manifest themselves in theobserved data product via two mechanisms: 1) the drifting of the spectrumalong the spectral dispersion axis of the detector; 2) the drift of the spec-trum along the cross-dispersion (spatial) direction. The effect of jitter on theobserved time series is the introduction of noise, characterised by the power-spectrum of the telescope pointing (usually not stationary). It is correlated intime, as the power-spectrum is not constant in frequency. The amplitude ofthe resultant photometric scatter depends on the amount of spectral/spatialdisplacement of the spectrum, the monochromatic PSF of the instruments,the detector pixel response function (intra-pixel response) and the amplitudeof the inter-pixel variations (i.e. QE variations across the focal plane detec-tor array). Modelling the complexity of the jitter noise effect is beyond thecapabilities of a radiometric model, therefore ArielRad imports jitter noisemodels from ExoSim simulations that provides variance vs wavelength at atimescale of 1 hr, i.e.
V AR J ([ S Y ( λ s )] in Eq. 12. At longer timescales, jitternoise is to good approximation time uncorrelated and can be therefore scaledat any desired observing time longer than 1 hr. As ArielRad is a radiometric model of the
Ariel payload performance, it can-not simulate non-stationary noise processes, or processes that require a moresophisticated simulation strategy, i.e. time-domain. One example of the latteris the already discussed pointing jitter, that is accounted for in ArielRad usingexternal modelling with ExoSim.Detector persistence is an additional potential systematic that cannot bemodelled with ArielRad, but
HST observations have shown that it can beeffectively corrected in data analysis (Zhou et al., 2017). Further, this effectis expected to be negligible in
Ariel observations compared to
HST as Ariel stares continuously at a target from an L2 orbit ensuring that detectors reacha steady state in a relatively short amount of time (few minutes at most).Detector non-linear behaviour is well characterised in detector testing ac-tivities before launch and during commissioning. Coupled with a stable line-of-sight provided by the AOCS at the sub-pixel level, detectors pixels sample thesame optical power level during an observation, therefore dwarfing, relatively R e l a t i v e N o i s e [ h ] GJ 1214 m ]10 R e l a t i v e N o i s e [ h ] HD 209458 total noisephoton noisedark current noiseread noisezodiacal backgroundgain noisejitter noisenoise floor
Fig. 4
ArielRad noise budget example of the
Ariel payload at 1 hr integration time, usingTier 3 binning. Two targets are considered: GJ 1214, a faint target for the
Ariel mission, andHD 209458, a typical bright target. The total noise estimate is in black and includes a 20%margin in excess of the target photon noise (green). Also shown are the detector dark currentand read noise (purple and yellow, respectively), photon noise from the zodiacal background(blue), gain noise (brown), and pointing jitter noise (gray). A noise floor is indicated by thehorizontal dashed line. The pointing jitter noise model is estimated using ExoSim (Sarkarand Pascale, 2015) simulations with identical payload parametrization. Gain noise is assumedto be equal to 40 ppm √ hr. Photon noise from instrument and inner sanctum emission areomitted because are negligibly small and out of the scale of the diagram. . The Ariel payloadmodel used in this budget is that at the mid of phase B1, it includes a noise floor of 20ppmand identical detector median dark current noise across all channels, that might result in anoverestimate of up to a factor of 3 in all channels, but CH1. to other sources of experimental uncertainties, this type of systematic that isalso known to be amendable (de Jong, 2006).Throughput variations can be caused by thermoelastic deformations thatcan also induce temporal variations in the shape of the PSF. To minimisethis effect, the
Ariel payload design uses aluminium structures, including thetelescope mirrors. Along with the thermal stability enjoyed by spacecraft in L2orbits, this prevents driving any significant thermal gradient on the payloadstructure and subsystems. It is therefore expected by design that thermoelasticthroughput variations during
Ariel observations will be significantly below anydetection limit.
ArielRad outputs the noise integrated over 1 hr of observation relative to thetarget signal: σ Y, hr ( λ s ) = (cid:112) (1 + χ Y ) V AR P + V AR D + V AR J S T,Y ( λ s ) (16) rielRad: the Ariel
Radiometric Model 15
The units are hr / . The relative noise achieved during one observation is σ Y,∆t ( λ s ) = σ Y, hr ( λ s ) ∆t int + p (17)where ∆t int is the observing time in hours, and the payload noise floor p is added in quadrature to prevent the noise to integrate down indefinitely asdiscussed earlier.The payload (relative) noise budget is shown in Fig. 4 for a typical brighttarget star (HD 209458) and for a faint target star (GJ 1214). These stars arerepresentative of respectively the bright and faint flux limits of the payloaddesign requirements. The noise budget has been estimated at 1 hr integrationassuming that detectors are analysed in CDS samples, i.e. n = 2. The budgetis sampled at Tier 3 resolution and it allows comparison of noise contributionsto the total noise in any individual Ariel channel. A comparison of sensitivityamong channels for any given target needs to take into account the differentspectral binning used that is higher in CH0 ( R = 100) compared to NIRSpec( R = 20) and CH1 ( R = 30). A strong increase with wavelength is seen inthe read and dark current noise components as a consequence of a decreasingstellar SED toward the red.As it is evident from the noise budget, the Ariel payload design reachesphoton noise limited performances, allowing observations of even dimmer tar-gets.
In a transit or eclipse observation, the observable is the wavelength-dependentcontrast-ratio that is the difference between the flux incoming from the extra-solar system star plus planet when the planet is moving in front (transit) orbehind (secondary transit, i.e. eclipse) the star and when it is not: CR ( λ ) = S OOT ( λ ) − S IT ( λ ) S OOT ( λ ) (18)where the labels OOT and IT identify signals measured respectively out oftransit and in transit.For a primary transit the contrast ratio is evaluated from the comparisonbetween the SED of the star S (cid:63) ( λ ) plus that of the planet S p ( λ ), S OOT ( λ ) = S (cid:63) ( λ ) + S p ( λ ), and the SED measured during the transit, that up to the firstorder depends on the radii ratio (Mandel and Agol, 2002; Seager and Mall´en-Ornelas, 2002). ArielRad simulates the contrast ratio in each spectral binfor the primary transit, considering also the portion of the star light passingthrough the planet atmosphere, as described in Seager and Sasselov (2000)and Brown (2001): CR tot ( λ ) = (cid:18) R p R (cid:63) (cid:19) + 2 ∆z ( λ ) R p R (cid:63) (19) where R p and R (cid:63) are the planet and star radii respectively and ∆z ( λ ) is theatmospheric height. Because the interest is on the detection of the exoplantatmosphere, the “signal” is just the rightmost quantity (Louie et al., 2018;Zellem et al., 2019) in the expression above, i.e. CR ( λ ) = 2 ∆z ( λ ) R p R (cid:63) (20)The atmospheric height is proportional to the scale height H = k B T /µg where k B is the Boltzmann constant, T is the temperature of the atmosphere, µ is themean molecular weight and g is the gravitational acceleration. The wavelengthdependent constant of proportionality can be provided by atmospheric modelsor, following Tinetti et al. (2013), set to 5 independently from the wavelengthfor a simple, yet representative performance estimate.For the eclipse case, the contrast ratio is simply CR ( λ ) = S p ( λ ) /S (cid:63) ( λ )(Charbonneau et al., 2005; Deming et al., 2005), and the planetary SED ispart due to the planet thermal emission, S em ( λ ), and part due to the reflectedstar light, A l ( λ ). Thus, CR ( λ ) = S em ( λ ) + A l ( λ ) S (cid:63) ( λ ) (21)The simulator estimates the contrast ratio in each spectral bin modelling theplanet emission as a Black Body at the planet temperature, and computes thereflected light component according to Charbonneau et al. (1999) as A l ( λ ) = α ( λ ) (cid:16) R p a (cid:17) S (cid:63) ( λ ) where α ( λ ) is the geometric albedo and a is the semi-majororbital axis.ArielRad can estimate these contrast-ratios considering the observation of S IT lasting the time between the first and last contact, T , and S OOT lasting γ T , with γ = 1 .
5, topically, from current
Ariel science requirements. UsingEq. 17 and 18, the noise variance estimate on a contrast ratio measurement is
V AR ( CR Y , λ s ) = σ Y, hr ( λ s ) (cid:20) γ (cid:21) T + p (22)and the Signal-to-Noise Ratio in each spectral bin is SN R Y ( λ s ) = CR Y ( λ s ) (cid:112) V AR ( CR Y , λ s ) (23)where we can substitute CR ( λ s ) with the estimated contrast ratio for transit oreclipse observations. The label Y indicates that quantities are integrated overthe photometric band or spectral bin of interest. Therefore ArielRad estimatesthree sets of SNR, one for each of the three Ariel tier discussed in Section 2.The SNR achieved in multiple, N obs observations of the same target extra-solar system is assumed to scale as √ N obs , under the assumption that dis-turbances originate from stochastic processes that are uncorrelated over thetime scale separating two observations, and longer. If this were not the case, rielRad: the Ariel
Radiometric Model 17 it would be more appropriate to assume that the noise floor is not reduced byaveraging multiple observations. However, there is currently no evidence sup-porting this as
Hubble /WFC3 and
Spitzer /IRAC observations have not yetreached a noise floor (Zellem et al., 2019) .
ArielRad has been validated by comparing its estimates to those of ExoSimand AERM introduced in Section 1.As ExoSim has been extensively validated against real astrophysical obser-vations (Sarkar et al., 2020), the comparison between ArielRad and ExoSimestimates are the most interesting to investigate. For this, we chose to comparethe predictions made of T sat (Eq. 14). A consistent result between EsoSim andArielRad on this parameter implies that ArielRad captures the complexity ofthe payload design as thoroughly as ExoSim does, and validates the imple-mentation of the radiometric algorithms. The comparison is therefore doneimplementing the same baseline Ariel model in the two simulators, and T sat isevaluated for the three target stars GJ 1214 (M4.5, mag K (cid:39) . K (cid:39) .
3) and HD 219134 (K3V, mag K (cid:39) .
3) that cover a rangein brightness and temperature representative of potential
Ariel targets (e.g.Edwards et al., 2019). The comparison is given in Table 2 For the visible pho-tometer and the infrared spectrometer; it is found that the two models agreeto better than 5% on all targets.
Table 2
Comparison between T sat estimates with ExoSim and ArielRad.GJ 1214 HD 209458 HD 219134Channel Percent variationVISPhot -0.8 -0.5 -0.4AIRS-CH0 -2.9 1.0 1.2AIRS-CH1 4.4 2.5 2.8 The comparison between ArielRad and AERM provides validation of theSNR calculations summarised by Eq. 23, that means a validation of all cal-culations implemented concerning the estimate of the exoplanet atmosphericsignatures observable during a transit or an eclipse and uncertainties. Puiget al. (2015), and reference therein, detail the algorithms implemented byAERM, that estimates the noise during 1 s of integration as σ Y,T otal = (cid:113) [ S T,Y ( λ s ) + S zodi,Y ( λ s )] · (1 + χ Y ) + N min,Y ( λ s ) (24)The main difference with the ArielRad implementations is the N min ( λ s ) termthat combines the noise variance in a spectral bin or photometric band fromdetector dark current and instrument emissions. For the photometric channels, N min,Y ( λ s ) is set to 400 s − . For the prism spectrometers, N min,Y ( λ s ) ∝ λ s , Fig. 5
Comparison between ArielRad and AERM SNR estimates in one transit ( left ) andone eclipse ( right ) observation of a sample of 2500 candidate exoplanet atmospheres. Eachdatapoint is the average SNR across the NIRSpec (green), AIRC-CH0 (red) and AIRS-CH1(blue) bands, binned at the
Ariel tier 3 spectral resolution. Trend lines are shown with slopeand intercept given in the text annotation in each panel. A black dotted line with unity slopeis shown. While estimates for CH0 and CH1 are in good agreement among both models,AERM provides SNR estimates in NIRSpec that systematically and unrealistically largerthan ArielRad. This is due to a limitation in the AERM algorithms implemented and it isfurther discussed in Section 4. and it is set to 17 s − µ m − ,20 s − µ m − , and 5 s − µ m − at the blue end ofNIRSpec, AIRS-CH0 and AIRS-CH1, respectively. There is no provision forother noise sources in AERM, including detector readout and gain noise, norpointing jitter. These effects are accounted for in the term χ Y that is set to 0.2for the photometers and NIRSpec, and to 0.3 for both AIRS channels. AERMfurther assume a photon conversion efficiency that, in each photometric orspectroscopic channel is wavelength independent. For this validation exercise,the ArielRad input configuration is adapted to match that in AERM, in termsof photon conversion efficiency, and matching dark currents to the equivalent N min,Y ( λ s ). Furthermore, the parameters in Eq. 13 are chosen such that n =2 (i.e. AERM assumes CDS), η = 1 (i.e. AERM assumes 100% samplingefficiency) and the photon noise margin parameter χ are set to those in use inAERM. V AR D , V AR J , and p are set to zero in Eq. 12. With this, AERMand ArielRad implement effectively the same instrument model, and are runto evaluate the SNR achieved on one transit or one eclipse over 2500 candidate Ariel targets (Edwards et al., 2019). Figure 5 shows the comparison of the twomodel estimates of the average SNR over spectral bins in each spectrometer.We find that, on average, the SNR estimates agree to better than 2 or 3% forAIRS channels. For NIRSpec we find that on average ArielRad predicts SNRthat are up to 8% smaller than AERM’s predictions. A further investigationhas revealed the root cause of this discrepancy in the way AERM estimatesthe signals: while ArielRad integrates SEDs over wavelengths in a spectralbin, AERM uses the SED estimated at the blue end of each spectral bin.This always implies that signal in AERM are systematically larger resulting rielRad: the
Ariel
Radiometric Model 19 is smaller uncertainties. The effect is more evident in NIRSpec because thelarger spectral bin width (R = 10, as impleneted in ESArad) compared toAIRS channels (R=100 and R = 30 in CH0 and CH1, respectively).
ArielRad has been developed to support the
Ariel phase B study, leading toMission Adoption by ESA in the Autumn 2020. ArielRad allows to evaluate thepayload science performance over a large target list of thousands of potentialexoplanetary targets and to assess the compliance of the payload design withthe science requirements briefly discussed in Section 2, with a more detaileddiscussion in Tinetti et al. (2018) and in the
Ariel yellow book . ArielRad isthe main tool used to assess the Ariel payload design solutions and providesa guide to optimise the payload to achieve requirements, and to maximise the
Ariel science return beyond requirements, when possible.The observed diversity of exoplanets can only be investigate by surveyinga large parameter space in planetary radii and masses, thermodynamic con-ditions, chemical properties and host star types.
Ariel is designed to providethe first large survey of the atmospheres of about 1000 diverse planets andArielRad is the tool used to craft a target list that is compliant with this sci-ence mandate. Edwards et al. (2019) used ArielRad simulations to provide apreliminary mission reference sample (MRS) of 1000 planets. While the MRSis expected to evolve during the next phases of the project until launch in2028, the ArielRad performance analysis demonstrates that the atmospheresof planets in the MRS can be characterised with a
SN R >
Ariel noise budget (Figure 4) on individual targets. The analysis can beextended to provide a comprehensive description of the payload performanceover all targets in the MRS to show how
Ariel achieves a photon noise limitedperformance on all targets, as shown in Figure 6. The MRS of Edwards et al.(2019) is used. It lists both exoplanets already discovered and expected TESSyields. At AIRS wavelengths ( λ s > . µ m) photon noise is the dominantsource of uncertainty, dwarfing all other noise contributions. At shorter wave-length, photon noise is less important for a small, but significant number oftargets, with detector gain noise playing a larger role in the noise budget. Theseare largely TESS targets around M-type (cold) host stars, demonstrating thepower of the Ariel
IR bands for these type of targets.The
Ariel telescope isdiffraction limited at a wavelength of 3 µ m and significant optical aberrationsdegrade the image quality at shorter wavelengths. However, Ariel works asa light bucket, and image quality is not relevant to achieve its performancerequirements. This aspect is also investigated in Figure 6 where the analysisis done for both a diffraction limited instrument and using estimates of aber-rated PSF from engineering optical modelling, corresponding to a wave front https://sci.esa.int/s/8zPrb9w.0 Lorenzo V. Mugnai et al. m ]1.01.52.02.53.03.54.0 N o i s e t o t a l + X s t a r P h o t o n N o i s e Real planets
Diffraction limited PSFAberrated PSF 0.500.60 0.80 1.10 1.95 3.90 7.80Wavelength [ m ] TESS yield forecast planets
Fig. 6
Total noise to photon noise ratio in one hour integration for all
Ariel
MRS targets.Solid and dashed lines mark median values across all targets evaluated for diffraction limited(red) and aberrated (blue) optics. Blue area represents the dispersion of 95% of simulatedplanets for the aberrated optics configuration. As the MRS contains exoplanets alreadydiscovered as well as expected TESS yields, these are separated respectively in the left andright panels. As discussed in the text, the apparent excess noise above photon noise atvisible-nearIR wavelengths is due to the presence of cold M-type stellar targets, that aremore numerous among TESS targets, and the assumed gain noise contribution. For thesetype of targets, observations in the nearIR-midIR are more sensitive showing the power of
Ariel ’s IR bands that are always shot noise limited. error of 250 nm RMS at the VISPhot, FGS1, FGS2 and NIRSpec focal planes,and 280 nm RMS at the AIRS focal planes. The differences are negligible andit can be noted from the figure that an aberrated PSF behaves slightly betterthan a diffraction limited PSF, despite the former requires a larger numberof pixel in each photometric or spectral bin aperture. However, because theaberrated PSF dilutes the signal more, pixels take longer to saturate, thereare fewer exposure in a given observing time, hence read noise has overall asmaller impact.ArielRad uncertainties estimates support the the science community tooptimise the science of
Ariel . For instance Changeat et al. (2019) used Ariel-Rad estimates to investigate the capability of
Ariel in retrieving pressure-dependent chemical profiles from predictions of observed atmospheric spectra.Science analyses using ArielRad performance estimates are ongoing, includeaspects related to atmospheric retrieval, phase curve detection, transit timingvariations, etc., and will be reported in
Ariel phase B study report later in2020 ahead of Mission Adoption: the
Ariel ”Red Book”.
In this work we have discussed the algorithmic implementation of ArielRad,the
Ariel radiometric simulator, used for the optimisation of the payload de-sign and to evaluate the science performance of the ESA M4 space mission. rielRad: the
Ariel
Radiometric Model 21
ArielRad accounts for all relevant sources of uncertainties on the detection ofexoplanetary atmospheres with
Ariel , that are: photon noise (of astrophysicalorigin and from the instrument self emission), detector noise and electronicnoise, and jitter noise. All other potential systematic of instrument origin areexpected to be made negligible by a careful instrument design as detailed byTinetti et al. (2018) and further discussed in the
Ariel
Yellow Book.ArielRad has been extensively validated against two alternative models,ExoSim and AERM, always showing excellent agreement at a few percentlevel across all
Ariel bands.
Ariel will perform the first statistical survey of the atmospheres of a largeand diverse sample, observing about 1000 exoplanets during its life time, asdiscussed in Edwards et al. (2019) with the help of ArielRad. For all exoplanetobservations, the photon noise of their host stars is the dominant source ofuncertainties, as revealed by an ArielRad assessment.ArielRad performance estimates, in the form of noise vs wavelength achievedon a given set of exoplanetary targets, are a product distributed upon request.As the phase-B continues, the payload design is optimised in an iterative pro-cess that aims at building the most performant space mission within the en-velope provided. An advancement in payload design does not however implythe need to modify the algorithmic implementation of ArielRad thanks to itsparametric description of the payload model. As a consequence, the simulatoritself is planned to be released at the freeze-out of the payload design, to occurafter mission adoption.
Acknowledgements
We thank G. Pilbratt (ESA-ESTEC) for comments that greatly im-proved the development of ArielRad.
Appendices
Acronyms and symbols
References
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Table 4
Table 3 ( continued )Symbol meaning S Inner detector box signal in spectroscopic channels S Y total incoming signal in photometric or spectroscopic channels S instr,Y instrument signal in photometric or spectroscopic channels V AR () total variance
V AR P () Poisson noise contribution to the variance V AR D () Detector noise contribution to the variance V AR J () Jitter noise contribution to the variance ∆t int integration time expressed in hours χ Y margin added to Poisson noise N pix number of pixel included in spectral bin I dark detector dark current n number of Non Destructive Reads T sat detector saturation time W D pixel well depth f WD coefficient describing the fraction of pixel well depth σ rd pixel read noise CR contrast ratio S OOT flux observed out-of-transit S IT flux observed in-transit S P flux from the planet S (cid:63) flux from the star ∆z atmosphere height R p planetary radius S em flux from the planet thermal emission A l fraction of starlight reflected by the planet α geometrical albedo a semi-major axis in planet orbit N min minimum noise considered in the channel in ESA radiometric model for Ariel
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