A survey of exoplanet phase curves with Ariel
Benjamin Charnay, Joao M. Mendonça, Laura Kreidberg, Nicolas B. Cowan, Jake Taylor, Taylor J. Bell, Olivier Demangeon, Billy Edwards, Carole A. Haswell, Giuseppe Morello, Lorenzo V. Mugnai, Enzo Pascale, Giovanna Tinetti, Pascal Tremblin, Robert T. Zellem
NNoname manuscript No. (will be inserted by the editor)
A survey of exoplanet phase curves with Ariel
Benjamin Charnay · Jo˜ao M. Mendon¸ca · Laura Kreidberg · Nicolas B. Cowan · Jake Taylor · Taylor J. Bell · OlivierDemangeon · Billy Edwards · Carole A.Haswell · Giuseppe Morello · LorenzoV. Mugnai · Enzo Pascale · GiovannaTinetti · Pascal Tremblin · Robert T.Zellem
Received: date / Accepted: dateB. CharnayLESIA, Observatoire de Paris, Universit´e PSL, CNRS, Sorbonne Universit´e, Universit´e deParis, 5 place Jules Janssen, 92195 Meudon, France.E-mail: [email protected]. M. Mendon¸caNational Space Institute, Technical University of Denmark, DenmarkL. KreidbergMax Planck Institute for Astronomy, Heidelberg, GermanyN. B. CowanDepartment of Earth & Planetary Sciences, Department of Physics, McGill University,Montr´eal, CanadaJ. TaylorDepartment of Physics (Atmospheric, Oceanic and Planetary Physics), University of Oxford,UKT. J. BellDepartment of Physics, McGill University, 3600 rue University, Montr´eal, QC H3A 2T8,CanadaO. DemangeonInstituto de Astrof´ısica e Ciˆencias do Espa¸co, Universidade do Porto, Porto, PortugalB. EdwardsDepartment of Physics and Astronomy, University College London, London, UKCarole A. HaswellSchool of Physical Sciences, The Open University, Walton Hall, Milton Keynes, MK17 8TT,UKG. MorelloAIM, CEA, CNRS, Universit´e Paris-Saclay, Universit´e Paris Diderot, Sorbonne Paris Cit´e,Gif-sur-Yvette, FranceL. V. MugnaiDipartimento di Fisica, La Sapienza Universit`a di Roma, P.le A. Moro 2, 00185 Roma, ItalyE. PascaleDipartimento di Fisica, La Sapienza Universit`a di Roma, P.le A. Moro 2, 00185 Roma, ItalyG. TinettiDepartment of Physics and Astronomy, University College London, London, UK a r X i v : . [ a s t r o - ph . E P ] F e b Benjamin Charnay et al.
Abstract
The ESA-Ariel mission will include a tier dedicated to exoplanet phasecurves corresponding to ∼
10% of the science time. We present here the currentobserving strategy for studying exoplanet phase curves with Ariel. We define sci-ence questions, requirements and a list of potential targets. We also estimate theprecision of phase curve reconstruction and atmospheric retrieval using simulatedphase curves. Based on this work, we found that full-orbit phase variations for 35-40 exoplanets could be observed during the 3.5-yr mission. This statistical samplewould provide key constraints on atmospheric dynamics, composition, thermalstructure and clouds of warm exoplanets, complementary to the scientific yieldfrom spectroscopic transits/eclipses measurements.
Keywords
Exoplanets · Ariel space mission · Atmospheres · Phase curves
The ESA-Ariel mission [1] due for launch in 2029, will conduct a survey of ∼ µ m. Datawill be collected by 3 instruments: FGS (3 photometric channels: VIS-Phot, FGS-1 and FGS-2, from 0.5 to 1.1 µ m), NIRSpec (1.1-1.95 µ m and R ∼
10) and AIRS(two channels: AIRS-CH0 for 1.95-3.9 µ m with R=100-200; AIRS-CH1 for 3.9-7.8 µ m with R=30-60). Ariel’s observational strategy is based on a 4-Tier approach.Tier 1 (Reconnaissance survey) will consist of a general transit survey at lowspectral resolution (photometric bands) of ∼ ∼
500 planets (transits and eclipsesat R ∼
100 for AIRS-CH0 and R ∼
30 for AIRS-CH1). Tier 3 (Benchmark planets)will consist of a detailed analysis of ∼
50 planets amongst the best targets (transitsand eclipses at R ∼
200 for AIRS-CH0 and R ∼
60 for AIRS-CH1). Finally, Tier 4will correspond mostly of phase curve observations. Over Ariel’s 3.5-yr mission,roughly 10% of the science time will be dedicated to phase curves.The principle of phase curve observations is to measure the radiation reflectedor emitted by an exoplanet throughout its orbit around its star. Planets are in-herently three-dimensional objects, and only by observing their phase variationscan we obtain a complete picture of the global atmospheric chemistry and cli-mate. Ariel has several advantages compared to other space missions for studyingphase curves. Firstly, Ariel’s spectral bands cover most of the thermal emission ofwarm/hot planets allowing accurate estimates of atmospheric heat redistribution
P. TremblinUniversit´e Paris-Saclay, UVSQ, CNRS, CEA, Maison de la Simulation, 91191, Gif-sur-Yvette,FranceR. ZellemJet Propulsion Laboratory, California Institute of Technology, Pasadena, USA survey of exoplanet phase curves with Ariel 3 and Bond albedo. Secondly, simultaneous observations with the different Ariel’schannels may enable us to disentangle reflected light from thermal emission forfavourable cases. Finally, phase curves are very time consuming so the forthcom-ing Jame Webb Space Telescope (JWST) will probably only observed one to threedozen exoplanet phase curves as explained in the next section. Conversely, Arielprovides a unique opportunity to perform a statistical survey of exoplanet spec-troscopic phase curves.We present here the plan defined by the Ariel Phase Curve Working Groupto measure thermal phase curves of 35-40 exoplanets. We start in Section 2 witha brief review of phase curves to highlight their interest, lessons from past mea-surements and expectations for the coming decade with JWST. In Section 3, weoutline five science questions to be investigated with Ariel phase curves. We de-scribe the target list and the observational strategy in Section 4. We then discussthe effect of systematic error and the expected precision for atmospheric retrievalbased on simulated phase curves from a 3D model (Section 5). We finish with asummary and conclusions in Section 6.
Thermal phase curves of a short-period planet constrain its atmospheric circula- tion—specifically the transport of energy from the day to night hemisphere of asynchronously-rotating planet (for a recent review, see [2]). The combination ofthermal eclipse depths and phase amplitudes allows one to estimate a planet’slarge-scale energy budget: how much incident flux is absorbed, and where it movesbefore being re-radiated to space. In other words, thermal phase curves enable theconstruction of simple Trenberth diagrams for exoplanets [3]. Phase variations canalso be inverted to produce a longitudinal map of the planet [4]. There are nowexcellent publicly-available codes to perform these inversions numerically [5] andanalytically [6].Planets on eccentric orbits present different challenges and opportunities [7].They exhibit eccentricity seasons and hence do not have a static temperature mapand cannot be mapped via phase variations. On the other hand, the time-variableincident flux allows us to break the degeneracy between advective and radiativetimescales that plagues circular phase curves [8,9]. This opportunity has beenleveraged for most of the nearby eccentric hot Jupiters [10–13].2.1 Review of Previous Phase Curve MeasurementsPhase curves have so far been published for more than two dozen planets, andobservations are in hand, but not yet published, for about two dozen more. Thevast majority of these phase curves were obtained with the Spitzer Space Telescope [14], primarily as part of the post-cryogenic “warm” mission. Multi-epoch phasecurves and/or phase curves of non-transiting planets are fraught with astrophysicaland detector degeneracy and hence have been less useful [15–17]. On the otherhand, the out-of-eclipse baseline can constrain the phase variations of short-periodplanets [18].
Benjamin Charnay et al.
Due to its Earth-trailing orbit, Spitzer was capable of uniterrupted monitoringof an entire planetary orbit. Indeed, continuous Spitzer phase curves of transiting(and eclipsing) planets have been the most useful, starting with the continuous,half-orbit observations [19]. Full-orbit continuous phase observations [20] offer alook at all of the longitudes on the planet, as well as providing two eclipses withwhich to remove first-order detector and astrophysical noise (the in-eclipse systemflux should be the same at the start and the end of the observations).More recently, a few near-infrared phase curves have been measured with theHubble Space Telescope (HST) [21–23]. HST phase curves have two advantages:1) the NIR coincides with the peak dayside emission of many hot Jupiters, and 2)HST enables spectroscopic phase curves. HST has offered us a glimpse of what ex-oplanet characterization will be like in the era of JWST, but HST’s low Earth orbitmakes it impossible to obtain continuous measurements throughout a planet’s or-bit. Full-orbit phase curves are therefore stitched together, which requires a modelof the telescope and detector systematics, which can lead to increased astrophysicaluncertainty [21,24,5,25–27].Lastly, optical phase curves have been observed for a handful of planets withKepler and TESS. For the hottest planets, these phase curves still primarily probethermal emission from the planet, while for cooler planets they probe reflectedstarlight [28]. In cases where the temperature of the planet can be established withthermal measurements, it has been possible to measure not only the geometricalbedo of an exoplanet but also to map the albedo across the dayside of theplanet with an optical phase curve [29]. A planet’s reflected light can also bedisentangled from its thermal emission with polarimetric phase measurements,but these measurements have so far proven exceedingly difficult and rare [30–32].2.2 Trends from Past MeasurementsThe past decade of exoplanet phase curve measurements has revealed a few in-triguing trends and some notable exceptions. First of all, it has been observed thatthe day-to-night temperature contrast increases with equilibrium temperature [33,34], likely due to the shorter radiative relaxation timescale of hotter atmospheres[35]. However, the strong temperature dependence of the radiative timescale hasmade it difficult to tease out the variations in wind speed [36–38].Phase curve measurements have also uncovered trends in albedo: the Bondalbedos inferred from Spitzer thermal phase measurements are significantly greaterthan the geometric albedos inferred from Kepler optical eclipse measurements [34],a dichotomy known as the “Albedo Problem” [39]. One hypothesis is that mosthot Jupiters are dark at optical wavelengths but reflective in the near-infrared [34];this can be tested with NIR spectroscopic or —ideally— polarimetric observations.More recently, it was shown that the Bond albedo inferred from thermal phasecurves is negatively correlated with planetary mass [40]. If corroborated, this trendcould be due to metallicity or surface gravity, but the details remain to be worked out.The nightside flux of a synchronously rotating exoplanet is a direct measure ofheat transport: any power radiated from the nightside must have been conveyedthere from the dayside. Two recent studies have noted that the nightside effectivetemperatures of hot Jupiters are remarkably uniform at ∼ survey of exoplanet phase curves with Ariel 5 of their equilibrium temperature, T eq , or dayside effective temperature, T day [26,41], possibly due to optically thick nightside clouds. The ultra-hot Jupiters, on theother hand, exhibit an increase in nightside temperature (and larger phase offsets[40]), likely due to hydrogen dissociation and recombination [42,38,43].The broad trends observed among exoplanets have occasionally been bucked byindividual planets. Most thermal phase curves peak before the eclipse, indicative ofeastward winds, as predicted by global circulation models [35]. The hotspot offsetof HAT-P-7b as seen in the optical with Kepler, however, seems to change directionover time [44], while the Spitzer phase curve of CoRoT-2b exhibits a significantwestward offset [45]. Likewise, while most hot Jupiters appear to have opticalgeometric albedos of a few percent [46], Kepler-7b is about an order of magnitudemore reflective [29]. Lastly, while nightside temperatures generally seem to be aweak function of equilibrium temperature, the hot Jupiter WASP-43b has beenreported to have a very low nightside temperature [21], at odds with other hotJupiters with similar equilibrium temperatures. If taken at face value, the aboveoddballs suggest that planetary age (CoRoT-2b), gravity (Kepler-7b), and orbitalperiod (WASP-43b) significantly affect the large-scale absorption and transport ofenergy on hot Jupiters. Indeed, comparing phase curves of exoplanets with similarbulk properties is a promising approach to establish the fundamental parametersgoverning planetary climates [47].2.3 What to expect from JWSTWe know of four phase curve observations planned for Early Release Science orGuaranteed Time Observations: WASP-43b (MIRI/LRS ERS and NIRSpec/BOTSGTO) , WASP-121b and TOI-193.01 (NIRISS/SOSS GTO). It is safe to say thatJWST spectroscopic phase curves will be even more informative than the handfulof HST phase curves due to the much greater collecting area and spectral coverage.It remains to be seen how many additional phase curve measurements will beobserved as part of JWST General Observer (GO) programs. One can obtain apessimistic estimate from the Hubble Space Telescope, which, like JWST, enjoysenormous proposal pressure from a wide variety of astronomers. The first HSTphase curve was observed in 2013 and published the following year [21]. Since thatlandmark paper, Hubble phase curves have been obtained and published at a rateof about one per year. The allocation of JWST guaranteed time observations, onthe other hand, bodes well for phase curves: three planets will benefit from fullorbit phase measurements as part of GTO. So one could optimistically expectthat JWST will observe complete phase curves for approximately three planetsper year for the duration of the mission. Given its expected duration of 5–10years, we therefore estimate that between 7 and 30 full orbit phase curves will beacquired by JWST over the course of the mission. We may reasonably expect thelion’s share of those to be for planets with orbital periods shorter than one day, the cutoff between small and medium proposals. Regarding planets with longerorbital periods, it would make sense to point JWST at temperate and terrestrialplanets since it is the only space telescope able to meaningfully characterize theiratmospheres and climate [48]. Backup ERS targets are WASP-103b and KELT-16b Benjamin Charnay et al.
We have defined five science questions to investigate with Ariel phase curves. Theyare focused on the coupling between atmospheric dynamics, chemical composition,thermal structure and clouds. Our objective is to answer these questions using astatistical sample of phase curves, covering a large parameter space.
SQ1: Which parameters control atmospheric heat redistribution?
Phase curve measurements will allow us to determine atmospheric heat redistri-bution as a function of stellar irradiation, planetary radius, metallicity and ec-centricity. Measuring dayside/nightside emission and phase offsets from the sub-stellar point of the phase curve peak for a large range of planetary parameterswould provide information about the circulation regime, the atmospheric radia-tive timescales, wind speeds and the effect of nightside clouds.
SQ2: How do atmospheric composition & thermal structure change fromdayside to nightside? We expect significant variations in the chemical composition as a function of lon-gitude for strongly irradiated planets due to thermochemistry and molecular dis-sociation. Atmospheric circulation should smooth out these variations, producingchemical disequilibrium. In addition, longitudinal/vertical temperature variationsare expected, with stratospheric thermal inversion on the dayside of some hotJupiters due to absorption of incoming stellar flux at low pressure.
SQ3: What is the atmospheric composition of low-mass planets?
A major question for Ariel is to understand the atmospheric composition or theatmospheric metallicity of low-mass planets. 3D climate models predict that theday-to-night heat redistribution decreases with atmospheric metallicity due to areduction of the atmospheric radiative timescale [49,50]. Consequently, low-massplanets with high atmospheric metallicity should have high-amplitude phase curves(see Fig. 1). Phase curves can thus be used to measure independently of transitspectroscopy atmospheric metallicity. Finally, they can reveal the presence of anatmosphere on a rocky planet through the inferred heat redistribution (e.g. [51]).
SQ4: What is the albedo of exoplanets?
Most exoplanets are at least partially cloudy. A major questions is to under-stand the nature of these aerosols. Are they condensate clouds or photochemicalhazes? The albedo of exoplanets is related to the optical properties and cover ofclouds/hazes. Transitions in the values of the albedo are expected due to the dis-appearance of some clouds with temperature, as for the L-T transition for browndwarfs [28]. Measuring the albedo would help to determine the nature of theseaerosols. The wavelength-integrated albedo is also a fundamental parameter forthe thermal balance of planets.
SQ5: How do thermal structure and aerosols vary in time?
Atmospheric variability could be caused by shear instability and shocks, varia-tion in cloud cover, or magnetic interactions [52,28,53]. Given that brown dwarfswith the same size, composition, and temperature as hot Jupiters have long beenknown to exhibit weather, it will come as no surprise if hot Jupiters are variable, survey of exoplanet phase curves with Ariel 7
Phase (°) −50050100150200250300350 F p / F * ( pp m ) Phase (°) −50050100150200250300350 F p / F * ( pp m ) Phase (°) −50050100150200250300350 F p / F * ( pp m ) Phase (°) −50050100150200250300350 F p / F * ( pp m ) H O (no cloud)
Fig. 1
Simulated phase curve of GJ 1214b for one orbit with AIRS-CH1 (3.9-7.8 micron) andfor different atmospheric compositions. The red line is the GCM flux variations [50], blue pointsare simulated Ariel observations and the light blue curve is a sinusoidal fit. The correspondingSNR for the amplitude is: 0.38, 1.63, 4.9 and 7.5 for the solar metallicity, 10 × solar metallic-ity, 100 × solar metallicity and pure water case respectively. Without heat redistribution, theSNR would reach 11.1. The thermal phase curve is easily detected for high-metallicity cases( ≥ × solar). too. It would be useful to measure the magnitude and timescale of such variabil-ity. 3D cloud-free simulations suggest variations of the order of just 1% for thephase curve amplitude over timescales of a few days to a few weeks [54]. The pres-ence of clouds may lead to a higher photometric variability (e.g. a few percent forthe phase curve amplitude), as suggested by some 3D simulations [55] and browndwarfs observations [56]. Science Questions Observations Required precisionSQ1 Atmospheric heat transport photometric 10% for amplitude and 5 ◦ for offsetSQ2 Variations of composition spectroscopic 0.5 dex for molecular abundancesSQ3 Low-mass planets photometric 0.5 dex for the metallicitySQ4 Albedo photometric 0.1 for geometric and Bond albedoSQ5 Time variability photometric 2% for amplitude and 3 ◦ for offset Table 1
Science questions and requirements for Ariel phase curves.
General requirements for the science questions (SQs):
Table 1 shows the type of observations (photometric or spectroscopic phase curves)and the required precision for each science question. For most of them, the required precision is equivalent to 10% on the maximal amplitude (i.e. the case with no heatredistribution) of the phase curve. According to Fig. 2, a precision of 0.5 dex on themetallicity corresponds to 10% of precision on the maximal amplitude. For SQ5,we chose a required precision of 2% for the amplitude (SNR > Benjamin Charnay et al.
500 750 1000 1250 1500 1750 2000 2250 2500
Teff(K) P h a s e - c u r v e r e l a t i v e a m p li t u d e met=1xsolarmet=10xsolarmet=100xsolarmet=1000xsolar Fig. 2
Relative phase curve amplitude in AIRS-CH1 (3.9-7.8 micron) as a function of metal-licity and effective temperature from a grid of 2D ATMO models [57]. Simulations performedwith the radius, rotation and stellar type of GJ436b. to-noise ratio (SNR) higher than 10 (i.e. detection at 10 sigma) for the fitting of photometric phase curves, assuming no heat redistribution and no offset. Forspectroscopic phase curves, we consider that the requirement is to reach SNR > ∼
50) in each of 10 orbital phasebins. – rocky planets with planetary radii lower than 1.8 R ⊕ – sub-Neptunes with planetary radii between 1.8 and 3.5 R ⊕ – Neptunes with planetary radii between 3.5 and 7 R ⊕ – Giants with planetary radii larger than 7 R ⊕ We limited the sample to planets with orbital periods of less than 5 days. Weclassified them by the SNR of the maximal phase curve amplitude (no heat redis-tribution). The SNR is computed accumulating a whole number of orbits up to10 days at Tier 1 resolution for rocky/sub-Neptunes, observing one orbit at Tier survey of exoplanet phase curves with Ariel 9
SN R = F planck ( T p ) F planck ( T s ) (cid:18) R p R s (cid:19) × σ (1)where T p is the planet equilibrium temperature with no heat redistribution assum-ing a Bond albedo of A B =0.3 ( T p < A B =0.1 ( T p > T s is the startemperature, R p and R s are the planet and star radii. These parameters are givenin the Ariel target list [58]. σ h is the noise for a 1-hour observation and obtainedwith the Ariel Radiometric Model ( Ariel-RAD ) [59]. We used the maximal valueof SNR between the different Ariel’s spectral bands (Tier 1 resolution).By computing the error on the estimation of the amplitude of the phase curveassumed to be a pure sine, the SNR for a full orbit (with P the orbital period inhours and P (cid:29) SN R orbit = 0 . × SN R × (cid:112) P/ >
10, which corre-sponds to a 10-sigma detection of the phase curve, for the conditions given abovefor each planet category. We also limit the number of giant planets to 20. With allthese conditions, we get 44 planets (see the bottom panel in Fig. 3) including: – – –
15 Neptunes –
20 giantsAll planets in this sample reach SNR >
10 for photometric (Tier 1 resolution) ther-mal phase curves, which is the requirement for SQ1 (heat redistribution), 3 (thecomposition of low-mass planets and exo-Neptunes) and 4 (albedo). All giant plan-ets fulfill the conditions for spectroscopic phase curves (i.e. SNR >
10 in 10% of theorbital period at Tier 2 resolution, SQ2) and for variability (SQ5). Six Neptunesreach SNR > Jup , equilibrium temperature from 600 to 2200 K, and expected atmosphericmetallicity from 1 to 300 × solar. 15 planets from our sample are already known,including 1 rocky planet, 2 sub-Neptunes, 2 Neptunes, 10 giant planets (see Table2). We found that a total of 136 giant planets from the Ariel target list reachthe conditions for spectroscopic phase curves (see the top panel Fig. 3). Theyinclude 83 already known giant planets, most of them coming from the WASP,HAT-P and KELT transit surveys. This implies a lot of choice for the selectionof giant planets. Our remaining targets targets are simulated discoveries from theTransiting Exoplanet Survey Satellite (TESS). TESS is surveying nearby stars fortransiting planets with near-complete sky-coverage [60]. TESS has delivered over1000 planet candidates in its first year (Guerrero et al., submitted). Some of these may be exceptional targets for phase curve observations, including several new hotNeptunes with short orbital periods and high equilibrium temperatures (i.e. LTT9779b, HD 219666b, TOI 132b, and TOI 824b). TESS is currently on track todetect over 2000 planets around bright nearby stars, providing the large statisticalsample needed for Ariel. Planet Radius [R
Earth ] P l a n e t P e r i o d [ d a y s ] Phase-curve targets (R=Tier 1, SNR>10 for 10 days or 1 full orbit) P l a n e t a r y T e m p e r a t u r e [ K ] Planet Radius [R
Earth ] P l a n e t P e r i o d [ d a y s ] Phase-curve targets (R=Tier 1, SNR>10 for 10 days or 1 full orbit) P l a n e t a r y T e m p e r a t u r e [ K ] Fig. 3
Targets for phase curves as a function of planetary radius, planet period and temper-ature (color bar). Vertical dashed lines represent the radius limits of the 4 categories: rockyplanets, sub-Neptunes, Neptunes and giants planets. The top panel shows all targets reachingthe conditions for phase curves. The bottom panel is limited to the 20 best giant planets. to a maximal error of 0.1 on the eccentricity, e (the uncertainty on the eclipsetime is 2 eP/π ). The study of variability (SQ5) with multi-epoch phase curves willbe limited to one or two planets (e.g. HD 189733b) with 3 phase curves (i.e. 3orbits). The observations of all planets from our target list, including 2 planetswith multi-epoch phase curves; would take ∼
175 days of observing time, or ∼ survey of exoplanet phase curves with Ariel 11Planet Period Orbits SNR SNR Thermal/Reflected(days) (thermal emission) (reflected light) (FGS)GJ 1214 b 1.58 1 11.0 0.3 0.0K2-266b 0.66 4 11.1 1.5 0.055 Cnc e 0.74 4 10.3 0.3 0.7GJ 436b 2.64 1 15.2 0.9 0.0GJ 3470b 3.34 1 10.4 0.6 0.0HD 189733b 2.22 1 or 3 205.2 3.0 0.04HD 209458b 3.52 1 or 3 168.1 2.3 0.2XO-6b 3.77 1 107.6 3.5 0.9WASP-77Ab 1.36 1 106.1 3.5 0.3KELT-7b 2.73 1 105.3 2.8 1.0WASP-74b 2.14 1 97.6 3.4 0.8XO-3b 3.19 1 95.1 3.5 1.0WASP-82b 2.71 1 78.8 3.0 1.3WASP-14b 2.24 1 75.1 2.3 0.7KELT-14b 1.71 1 71.1 3.9 0.8 Table 2
Known planets from the phase curve target list with the number of orbits requiredto reach SNR >
10 (3 orbits are indicated for multi-epoch phase curves) and the SNR at Tier1 resolution for thermal and reflected light phase curves. For thermal emission, we give thehighest value of SNR between the different photometric channels, assuming a Bond albedoof A B =0.3 ( T p < A B =0.1 ( T p > µ m (the 3 FGS channels), assuming a geometric albedoequal to the Bond albedo. The last column is the ratio of the flux from thermal emission to theflux from reflected light integrated from 0.5 to 1.1 µ m. Horizontal lines separate sub-Neptunes,Neptunes and giant planets. Note that with our limit at 1.8 R Earth , 55 Cnc e is listed as asub-Neptune but it is likely a rocky planet. of Ariel science time. Removing 1 sub-Neptune, 5 giants and keeping only oneplanet with multi-epoch phase curves, the observing time goes down to 10% ofAriel science time, compatible with the current mission time dedicated to Tier4. We can, therefore, expect that the final target list for Ariel phase curves willinclude 35-40 exoplanets and will represent a statistical sample for gas planets. Itis worth mentioning that the observation of phase curves also provide transits andeclipses. In the current observing plan for Ariel, a single transit or eclipse takes 2.5times the transit duration. For our phase curve observing plan, the equivalent of28% of the observation time is dedicated to transits or eclipses. This high fractionsignificantly reduces the cost of phase curves. It comes from the fact that we aretargeting short period planets (P < ∼ µ m). Reflected light dominates only for HD189733band HD209458b as well as warm Neptunes and sub-Neptunes. Figure 4 shows the fraction of the total flux (thermal emission+reflected light) covered by the differentARIEL’s instruments (FGS, NIRSpec and AIRS). Reflected light dominates forFGS only for effective temperatures lower than 1700K for a G star and 1500K foran M star. Therefore, the thermal emission will represent a non-negligible fractionof the flux measured with FGS for most of hot Jupiters, even if we limit the measurements to VIS-Phot (0.5-0.6 µ m). However, the contribution of reflectedlight is almost negligible in NIRSpec and AIRS channels for these planets. Itwould be possible to extrapolate the thermal flux at short wavelength (i.g. inFGS channels) to extract the reflected light. This method has been applied tosimulated Ariel eclipse observations [61]. According to this study, the geometricalbedo could be measured with a precision of ± ∼
10 giant planets fromTier 3. In addition, inhomogeneous cloud and temperature distributions lead todifferences in the shape of phase curves (i.e. the offset) between thermal emissionand reflected light. This could also help to distinguish thermal emission fromreflected light. Additional modeling work will be needed on this aspect.Only giant planets from the phase curve target list are expected to reach a SNRsufficient to detect reflected light and to measure the geometric albedo (see Ta-ble2). For these planets and assuming that the reflected light can be distinguishedfrom the thermal emission (as explained above), the geometric albedo would bemeasured with a precision of around ± ± ∼ ∼
30 ppm in 1 hour for bright solar-like stars(mag(V) < ◦ , which is the current plan) will be observed for 1-3 years,cumulating a few hundred orbits for short-period planets around bright stars. PLATO phase curves of reflected light should achieve a much higher precision thanthe other space telescopes mentioned above. Since there will be many giant planets(136 with the current list) reaching the requirements for Ariel phase curves, we planto choose those which will benefit from a precise visible phase curve observed byTESS, CHEOPS or PLATO. This would be a strong synergy, combining visible survey of exoplanet phase curves with Ariel 13 and infrared phase curves from these telescopes, together with accurate stellarcharacterization.
Effective temperature (K) F r a c t i o n o f t o t a l f l u x Fraction of total flux from thermal emission and reflected light (star=Sun, albedo=0.1)
AIRSNIRSpecFGS
Effective temperature (K) F r a c t i o n o f t o t a l f l u x Fraction of total flux from thermal emission and reflected light (star=GJ1214, albedo=0.1)
AIRSNIRSpecFGS
Fig. 4
Fraction of the total flux (thermal emission+reflected light) covered by the differentARIEL’s instruments (FGS, NIRSpec and AIRS). Solid lines show the thermal emission anddashed lines show the reflected flux as a function of the planetary effective temperature. Thecalculation is done assuming a Bond albedo and a geometric albedo of 0.1, for a Sun-like star(left panel) and for an M star as GJ1214b (right panel).
We used theoretical models to evaluate Ariel’s potential performance for phasecurve observations of a hot Jupiter planet. We test our theoretical tools on theplanet WASP-43b and assume that the atmosphere is either cloud-free or cov-ered by clouds on the night side. We simulated Ariel phase curves based on 3Datmospheric model results and used simulated spectra to explore our retrievalframework on Ariel observations.5.1 Phase curves calculated from a global circulation modelGlobal Circulation Models (GCMs) are powerful tools that self-consistently simu-late 3D atmospheric temperature distributions and here can predict thermal phasecurves. Using a 3D GCM,
THOR , we have simulated the phase curves of WASP-43b[64] with a clear atmosphere. WASP-43b has twice the mass of Jupiter, orbits itsparent star in 19.2 hours with a semi-major axis of 0.0153 AU [65] and an esti-mated equilibrium temperature of 1440 K [66]. The parent star is a K7 star of 0.73M
Sun . THOR is a flexible GCM that can calculate phase curves and is based on adynamical core that solves the non-hydrostatic compressible Euler equations on an icosahedral grid [67]. To represent the radiative processes in the GCM simulations,we used a two-band formulation calibrated to reproduce the results from morecomplex codes on WASP-43b [68].The multi-wavelength phase curves are obtained from post-processing the 3Dsimulated atmosphere with a more sophisticated radiative transfer model [68]. The spectra include cross-sections of the main absorbers in the infrared - EXOMOL:H O [69], CH [70], NH [71], HCN [72], H S [73]; HITEMP [74]: CO , CO; HI-TRAN [75]: C H . The Na and K resonance lines are also added [76] and H -H H -He CIA [77]. We assumed that the atmosphere has solar abundances. As shownin [9], the HST-WFC3 spectrum [21] of the dayside in WASP-43b is compatiblewith a clear atmosphere with solar abundances. Our THOR simulation includes achemical relaxation method fully coupled with the 3D dynamics for 4 differentchemical species [78]: H O, CH , CO and CO . This implementation allows us tostudy chemical disequilibrium in the atmosphere due to atmospheric transport,which we use later to explore the potential of our retrieval framework to finddepartures from chemical equilibrium in future Ariel observations of WASP-43b.Other molecules in the atmosphere are assumed to be in chemical equilibrium,and their concentrations are calculated with the FastChem model [79]. The stellarspectrum was obtained from the
PHOENIX model ([80], [81]).The disc averaged planet spectrum is calculated at each orbital phase by pro-jecting the outgoing intensity for each geographical location of the observed hemi-sphere. In Fig. 5, we show the theoretical phase curves simulated with
THOR . Thedifferent lines show the planet spectra for each orbital phase: the red lines repre-sent the hotter dayside of the atmosphere and blue the colder nightside. The leftpanel in Fig. 5 corresponds to the WASP-43b simulation with a clear atmosphere.We also show the impact of a grey cloud deck on the night side of the planet in theright panel of Fig. 5. The cloud distribution and optical properties are parameter-ized (see [68] for further details). Clouds block most of the radiative flux from thedeep hot layers in the planet, which reduces the observed infrared flux for orbitalphases near the primary transit [68] and reduces the spectral features. Therefore,clouds can limit atmospheric retrieval for spectroscopic phase curves. In contrast,clouds generally make the detection of photometric phase curves easier. As shownfor WASP-43b (see Fig. 4), nightside clouds tend to increase the amplitude of ther-mal phase curves (see [82]. In addition, dayside clouds can increase the amplitudeof phase curves of reflected light and also of thermal phase curves for absorbingclouds. In this last case, the effect of clouds may remain limited compared to thatof the atmospheric metallicity (see Fig. 1 and [50]).
Fig. 5
Emission plus reflected light at different orbital phases obtained with
THOR . The circularcolor map shows the color for different orbital phases. The primary transit occurs at orbitalphase 0 ◦ (blue) and the secondary eclipse at 180 ◦ (red). The two panels show the phase curvevalues for a simulation with clear sky (left panel) and a cloudy night side (right panel). survey of exoplanet phase curves with Ariel 15 − . We considered two sub-cases: one with an overlapbetween visits of 10% in orbital phase, and the other with a 25% overlap.3. A pessimistic case, same as case (2) above except with an additional lineartrend for each visit, also drawn from a normal distribution with mean 0 andstandard deviation 10 − .The amplitude of the systematic noise was inspired by long-duration Spitzerand Hubble observations, which show long-term systematic trends and offsets thatare still poorly explained (e.g. [84]). Spitzer and Hubble’s data also show additionalnoise from intrapixel sensitivity variations and charge trapping ([85], [86], [87]),but Ariel observations are less likely to be affected by these noise sources thanksto the stability requirements and uninterrupted pointing.For each case (optimistic, realistic, pessimistic), the simulated phase curvesfor WASP-43b with clouds based on the THOR results are shown in Fig. 6. Wegenerated 500 instances of each phase curve with randomly generated photon shotnoise calculated with
Ariel-Rad [59] and the assumed instrument systematic noisemodel. We calculated the broadband phase curve from AIRS Channel 0 (1.95 -3.9 microns). The time resolution of the simulated light curves was 0.01 times theorbital period of the planet.We fit a single sinusoid as our nominal phase variation model. We also per-formed a fit with a double sinusoid model that also included the first harmonic;however, the inferred amplitude of the harmonic was consistent with zero, so wefocus here on results from the single sinusoid case.
We show the inferred sinusoid amplitudes and offsets for each case in Table 3.For case (1), the optimistic phase curve with continuous phase coverage and noinstrument systematics, we detected the phase curve amplitude at high confidence(52 sigma for WASP-43b) and measured the phase offset to an accuracy of 2-3 degrees. This precision is more than sufficient to achieve the science goals for phase curve observations. For example, the measured phase curve will constrain theatmospheric metallicity to better than 0.5 dex and enable a search for variabilitydue to weather.
WASP-43b Amplitude (ppm) Hotspot offset (degrees)1. Optimistic 1560 +/- 30 4.2 +/- 1.02a. Realistic (10% overlap) 1560 +/- 30 4.3 +/- 2.12b. Realistic (25% overlap) 1560 +/- 30 3.9 +/- 1.83a. Pessimistic (10% overlap) 990 +/- 250 5.9 +/- 3.53b. Pessimistic (25% overlap) 1520 +/- 150 4.6 +/- 3.2
Table 3
Accuracy of retrieved phase curve amplitude and hotspot offset for different scenariosof systematic noise.
Fig. 6
Simulated phase curves for WASP-43b for different assumptions about instrumentperformance. The optimistic case is a continuous stare with no instrument systematics, therealistic case is a phase curve split into 10-hour stares with 10% overlap in phase coverage withrandomly drawn offsets between each visit, and the pessimistic case adds a randomly drawnlinear trend to each 10-hour visit.
For case (2), the light curve with three visits with constant offsets betweenthem, we find that we can recover the phase curve amplitude almost as well as forcase (1). The estimated sinusoid amplitudes are consistent, and the precision onthe hotspot offset increases by a factor of two. survey of exoplanet phase curves with Ariel 17
The more pessimistic case (3) gives consistent results with the other two cases;however, the precision is noticeably worse. The phase curve amplitude is detectedat 10 sigma confidence, but only if the visits overlap by 25% in phase coverage.We conclude that depending on the phase curve amplitude and overlap in phasecoverage, the pessimistic noise scenario may not allow us to achieve our sciencegoals.The ideal scenario is that Ariel observes phase curves continuously. If thisis not possible, multi-epoch phase curves are a viable alternative. The optimalstrategy depends on the instrument noise performance. If the detector is stableand has minimal trends in time (change in flux less than 1e-3 over 24 hours), thephase curve can be split into visits with just 10% overlap in phase coverage withno negative impact on science goals. By contrast, if linear systematic trends arepresent, at least 25% overlap in phase coverage is required to measure the phasecurve amplitude and offset at sufficient precision, and it may only be possiblefor larger amplitude phase curves. The science will still be possible for the mostpessimistic case, but the number of observable phase curves will decrease due tothe large overlap in phase coverage that is required.Ariel’s instrument systematics should be carefully assessed early on in themission to determine the optimal strategy for phase curve observations.5.3 Retrieval of spectroscopic phase curvesTo better understand the capability of Ariel to reveal the global climate behaviourof planets, we performed 1D spectral retrievals on the disc average flux of WASP-43b produced by
THOR . We chose to perform retrievals with a phase angle step of60 ◦ . The error on the observations was estimated using Ariel-Rad for an integra-tion time of 1 hour.We used the radiative transfer and retrieval framework
NEMESIS [88,89] toperform 1D spectral retrievals. We use the correlated-k approach to model ourspectra [90,91], which has been shown to be effective and accurate when comparedto using the line-by-line or cross-section approaches [92]. The line lists used in theretrieval are those used to calculate
THOR ’s phase curves, however,
NEMESIS uses amore recently developed line list for H O [93].We model the atmosphere with a uniformly mixed vertical chemical structureand a temperature profile following the description of [94] and [95]. Fig. 7 showsthe retrieved temperature profiles for the cloud-free WASP-43b simulation. Thetemperature retrieval shows that we can generally retrieve the gradient of theprofile within one sigma and the vertical shape of the profile within two sigma,apart from at a phase angle of 300 ◦ which is slightly outside of 2 sigma at thelowest pressures.In this retrieval exercise, we also test if we can distinguish between atmospheresin equilibrium and disequilibrium. The disequilibrium profiles are obtained from THOR simulations with solar metallicity and C/O. As seen in Fig. 8, we find that our retrieved chemical abundances are within one sigma of the input value, withthe tightest constraints being on the water abundance. The water abundance inour simulation is 3.6 × − , compatible with HST constraints of 0 . − × − [96]. We show that for H O and CO it is not possible to distinguish between thedisequilibrium and equilibrium case, but it is possible for CO and CH , with
500 1000 1500 2000 2500 3000
Temperature [K] P r e ss u r e [ b a r ] THOR TPRetrieved TP 500 1000 1500 2000 2500 3000
Temperature [K] P r e ss u r e [ b a r ] THOR TPRetrieved TP 500 1000 1500 2000 2500 3000
Temperature [K] P r e ss u r e [ b a r ] THOR TPRetrieved TP500 1000 1500 2000 2500 3000
Temperature [K] P r e ss u r e [ b a r ] THOR TPRetrieved TP 500 1000 1500 2000 2500 3000
Temperature [K] P r e ss u r e [ b a r ] THOR TPRetrieved TP 500 1000 1500 2000 2500 3000
Temperature [K] P r e ss u r e [ b a r ] THOR TPRetrieved TP
Fig. 7
Retrieved temperature structures for the cloud free WASP-43b numerical experiment.We present the median, 1-sigma and 2-sigma intervals in decreasing opacity of purple, and thetemperature structure from
THOR is presented in black. the greatest difference being for CH . It may however only be possible to put anupper limit on CH and CO due to their low abundance which results in less of animpact on the observed spectrum. H O abundance is retrieved with a precision of 3dex for 1 hour observations. For 3 hour observations (6 different phases for WASP-43b), H O abundance is retrieved with a precision of 3 dex. The global mean H Oabundance is retrieved with a precision of around 60% over the full orbit. Thisprecision is sufficient to address the SQ2 for spectroscopic phase curves. We seefrom the chemistry retrieval that the error bars for CO are large for a phase angleof 180 degrees, this is due to the isothermal nature of the temperature-pressureprofile in the region of the atmosphere to which we are sensitive to (i.e., around0.1 bar), hence the features would appear muted and have a greater uncertainty.We perform the same retrieval exercise for an atmosphere that is cloudy. The3D cloudy atmosphere was built from the simulations in [68] and shown in Fig.5. To model the cloud in our retrieval framework we consider 3 extra param-eters: the opacity of the cloud, the fractional scale height, and the cloud basepressure. We also assume that the cloud is non-scattering and grey in nature.We recognise that considering the scattering properties of the cloud could helpto improve the retrieved atmospheric properties [97]. The retrieved abundancesin Fig. 9 demonstrate that we are able to detect and constrain the abundanceof H O with comparable precision to the cloud free scenario. We find that the other molecules are trickier to constrain due to the muted features introduced bythe cloud. The retrieved thermal profiles in Fig. 10 demonstrate the inability torecover the shape of the thermal structure for the cloudy atmosphere. The shapeof the thermal structure calculated using
THOR is not able to be captured by aGuillot-style parameterisation, given that the former is a state-of-the-art thermal survey of exoplanet phase curves with Ariel 19 l o g ( V M R ) H O DisequilibriumEquilibrium 0 100 200 300121086420 CH DisequilibriumEquilibrium0 100 200 300Phase angle ( )121086420 l o g ( V M R ) CO DisequilibriumEquilibrium 0 100 200 300Phase angle ( )121086420 CO DisequilibriumEquilibrium
Fig. 8
Retrieved abundances (VMR) and associated uncertainty for the cloud-free WASP-43b simulations. They are shown by the vertical lines for each molecule. The horizontal solidand dashed lines are the disequilibrium and equilibrium abundances respectively, the valuesare taken to be around ∼ ◦ and phase 180 ◦ correspond to the transit and the eclipse respectively. Syntheticobservations use disequilibrium chemistry. structure parameterisations used in exoplanet emission retrievals. In other words,we demonstrate that observations from future instruments will require a morecomplex vertical temperature parameterisation for cloudy atmospheres. Phase curves of thermal emission and reflected light are a powerful technic to char-acterize exoplanetary atmospheres. They provide insights into the atmosphericdynamics and longitudinal variations of the thermal structure, the chemical com-position and clouds. In the next decade, JWST will likely observe a dozen planetswith phase curves, preferentially smaller and cooler planets than Ariel can effi-ciently observe.
We defined 5 science questions: 1) heat redistribution, 2) longitudinal compo-sition & temperature variations, 3) atmospheric composition of low-mass planets,4) albedo & clouds and 5) time variability, to investigate with phase curves. Theyare focused on the coupling between atmospheric dynamics, chemical composition,thermal structure, and clouds. For most of these science questions, the requirement l o g ( V M R ) H O DisequilibriumEquilibrium 0 60 120 180 240 300 360121086420 CH DisequilibriumEquilibrium0 60 120 180 240 300 360
Phase angle ( ) l o g ( V M R ) CO DisequilibriumEquilibrium 0 60 120 180 240 300 360
Phase angle ( ) CO DisequilibriumEquilibrium
Fig. 9
Retrieved abundances (VMR) and associated uncertainty for the cloudy WASP-43bsimulations. They are shown by the vertical lines for each molecule. The horizontal solid anddashed lines are the disequilibrium and equilibrium abundances respectively, the values aretaken to be around ∼ ◦ and phase 180 ◦ correspond to the transit and the eclipse respectively. Syntheticobservations use disequilibrium chemistry. is to reach a SNR >
10, i.e. detection at 10 sigma of photometric phase curves (atTier 1 resolution), assuming no heat redistribution.We constructed a list of 44 potential targets for phase curves from the Arielgeneral target list. These planets fulfill the requirements for the science questionsand were divided into four size categories (rocky, sub-Neptunes, Neptunes andgiants). Based on this potential target list, we expect that 35-40 exoplanets couldbe observed if 10% of Ariel science time were dedicated to phase curves. Accordingto this study, Neptune-size and giant planets are excellent targets for Ariel. Theycomprise ∼
80% of planets in the target list. However, our observing plan onlypartially answers SQ4 (albedo & clouds), mostly based on reflected light. For giantplanets (for which there is a multitude of good targets), an ideal strategy wouldbe to choose those which will benefit from a precise visible phase curve observedby TESS, CHEOPS or PLATO. In particular, there would be a strong synergy bycombining the hundreds of PLATO visible phase curves with Ariel infrared phase curves.The study of the effect of systematics shows that multi-epoch observationsreduce the precision of phase-curve reconstruction. That performance degrada-tion is drastic when a linear trend is present in the instrumental systematic ef-fects.We therefore recommend performing continuous observations, starting before survey of exoplanet phase curves with Ariel 21
500 1000 1500 2000 2500 3000
Temperature [K] P r e ss u r e [ b a r ] THOR TPRetrieved TP
500 1000 1500 2000 2500 3000
Temperature [K] P r e ss u r e [ b a r ] THOR TPRetrieved TP
500 1000 1500 2000 2500 3000
Temperature [K] P r e ss u r e [ b a r ] THOR TPRetrieved TP
500 1000 1500 2000 2500 3000
Temperature [K] P r e ss u r e [ b a r ] THOR TPRetrieved TP
500 1000 1500 2000 2500 3000
Temperature [K] P r e ss u r e [ b a r ] THOR TPRetrieved TP
500 1000 1500 2000 2500 3000
Temperature [K] P r e ss u r e [ b a r ] THOR TPRetrieved TP
Fig. 10
Retrieved temperature structures for the cloudy WASP-43b numerical experiment.We present the median, 1-sigma and 2-sigma intervals in decreasing opacity of purple, and thetemperature structure from
THOR is presented in black. an eclipse and ending after the following eclipse. We also recommend to carefullyassessing Ariel’s instrument systematic effects early on in the mission.Dependingon their nature, we could consider multi-epoch phase curves, filling gaps in theobserving scheduling.The atmospheric retrieval of a simulated spectroscopic phase curves of cloud-free WASP-43b allows to measure the abundance of water within 0.5 dex for a 3-hobservation. Combining measurements over the whole orbit, the mean abundanceis retrieved with a 60% precision. In addition, the spectroscopic phase curve ofWASP-43b allows distinguishing chemical equilibrium and disequilibrium thanksto CH and CO variations. It is important to note that all the giant planets onour target list have a SNR for a full phase curve similar to or higher than WASP-43b. This would imply a precision for atmospheric retrieval generally better thanour simulated case for WASP-43b.To conclude, the Ariel mission is a unique opportunity to perform a statis-tical survey of exoplanet phase curves, mostly warm/hot gaseous planets. Theseobservations will be complemented by Ariel transit/eclipse spectroscopy and bymeasurements from other telescopes (e.g. TESS, CHEOPS, PLATO, JWST andELTs). Together, they will provide insights into the global climate of these planetsas well as a context for the interpretation of all Ariel observations. Acknowledgements
B.C. acknowledges financial support from CNES. J.M.M. work on Arielis supported by PRODEX grant (PEA: 4000127377). T.J.B. acknowledges support from theMcGill Space Institute Graduate Fellowship, the Natural Sciences and Engineering ResearchCouncil of Canada’s Postgraduate Scholarships-Doctoral Fellowship, and from the Fonds derecherche du Qu´ebec – Nature et technologies through the Centre de recherche en astrophysique2 Benjamin Charnay et al.du Qu´ebec. L.V.M. and E.P. were funded by the ASI grant n. 2018.22.HH.O. C.A. Haswell’swork on Ariel is supported by STFC under grant ST/T00178X/1 P ) is given by: F ( t ) = F max F star × (cos(2 πt/P ) + 1)2 (3)Phase curve data can be fitted with a cosine function f ( t ) = A × cos(2 πt/P ) + B .For P (cid:29) A is: δA = (cid:114) P σ (4)where σ is the noise (in ppm) in the given spectral or photometric band for a 1-hour observation of the host star and obtained with Ariel-Rad, and P is expressedin hours. With A = F max F star , the SNR of the full phase curve is: SN R orbit = AδA = 0 . × SN R × (cid:112) P/ SN R = F max F star σ is the SNR for a 1-hour observation at full phase givenin equation (1).7.2 Comparison to Spitzer data of LHS 3844bWe compared our expressions (4) and (5) to the analysis of the Spitzer phasecurves of LHS 3844b [51]. In this study, the planet-to-star flux variation is binnedover 25 equally spaced intervals over the orbital period with 1-sigma uncertaintiesof ∼
50 ppm. The peak-to-trough amplitude of the phase variation is 350 ±
40 ppmfrom MCMC fitting. This corresponds to a SNR of ∼
9. Applying formula (4) and(5), we find an uncertainty of the peak-to-trough amplitude of ∼
30 ppm and aSNR of 12. We note that our basic fitting tends to underestimate the uncertaintyon the amplitude of the phase curve since it assumes a perfect sine wave and doesnot take into account the transit and the eclipse. In addition, our formula givesthe statistical uncertainty, so there would naturally be some deviation comparedto a given dataset. Finally, the uncertainty on the peak-to-trough sine amplitudefor real LHS 3844b data is higher than predicted by the idealized model because itwas simultaneously fit with an instrument systematic noise model. The instrumentsystematics for Ariel are expected to be much less severe than for Spitzer, so theAriel uncertainties are expected to match those calculated with Equation (4).
Using noise estimations from Ariel-Rad, we predict a SNR of ∼
13 with Ariel forthe same observing duration ( ∼ µ m)as Spitzer. The SNR is consistent with our previous estimation and it would risesup to 17 with AIRS-CH1. We conclude that our metric compares favourably withprevious Spitzer observations and analysis of LHS 3844b. survey of exoplanet phase curves with Ariel 23 References
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