3-D climate simulations for the detectability of Proxima Centauri b
Daniele Galuzzo, Chiara Cagnazzo, Francesco Berrilli, Federico Fierli, Luca Giovannelli
aa r X i v : . [ a s t r o - ph . E P ] F e b Draft version February 8, 2021
Typeset using L A TEX twocolumn style in AASTeX63
Daniele Galuzzo, Chiara Cagnazzo, Francesco Berrilli, Federico Fierli, and Luca Giovannelli Department of Physics, University of Rome Tor Vergata, Via della Ricerca Scientifica, 1, I-00133, Rome, Italy Institute of Marine Sciences (ISMAR), National Research Council (CNR), Via del Fosso del Cavaliere, 100, I-00133, Rome, Italy Institute of Atmospheric and Climate Sciences (ISAC), National Research Council (CNR), Via del Fosso del Cavaliere, 100, I-00133,Rome, Italy (Received April 16, 2019; Accepted January 15, 2021)
Submitted to ApJABSTRACTThe discovery of a planet orbiting around Proxima Centauri, the closest star to the Sun, opensnew avenues for the remote observations of the atmosphere and surface of an exoplanet, Proxima b.To date, three-dimensional (3D) General Circulation Models (GCMs) are the best available tools toinvestigate the properties of the exo-atmospheres, waiting for the next generation of space and ground-based telescopes. In this work, we use the PlanetSimulator (PlaSim), an intermediate complexity3D GCM, a flexible and fast model, suited to handle all the orbital and physical parameters of aplanet and to study the dynamics of its atmosphere. Assuming an Earth-like atmosphere and a 1:1spin/orbit configuration (tidal locking), our simulations of Proxima b are consistent with a day-sideopen ocean planet with a superrotating atmosphere. Moreover, because of the limited representationof the radiative transfer in PlaSim, we compute the spectrum of the exoplanet with an offline RadiativeTransfer Code with a spectral resolution of 1 nm. This spectrum is used to derive the thermal phasecurves for different orbital inclination angles. In combination with instrumental detection sensitivities,the different thermal phase curves are used to evaluate observation conditions at ground level (e.g.,ELT) or in space (e.g., JWST). We estimated the exposure time to detect Proxima b (assumingan Earth-like atmosphere) thermal phase curve in the FIR with JWST with signal-to-noise ratio ≃
1. Under the hypothesis of total noise dominated by shot noise, neglecting other possible extracontribution producing a noise floor, the exposure time is equal to 5 hours for each orbital epoch.
Keywords: planets and satellites: atmospheres — planets and satellites: terrestrial planets — stars:individual (Proxima Centauri) — techniques: photometric INTRODUCTIONA planet in the habitable zone of Proxima Cen-tauri was detected in Anglada-Escud´e et al. (2016)and confirmed recently in Damasso et al. (2020) andSu´arez Mascare˜no et al. (2020). The planet, known asProxima b, has not been observed as a transiting planet(Davenport et al. 2016; Kipping et al. 2017; Liu et al.2018; Blank et al. 2018; Feliz et al. 2019; Jenkins et al.2019) and the estimated geometric probability of a tran-sit is about 1.5%, (Anglada-Escud´e et al. 2016). As a
Corresponding author: Luca [email protected] consequence, constraints can exclusively be set on theorbit semi-major axis and on the planet’s revolution pe-riod, leaving mass, radius, and density of the planet tobe assumed.Such an indeterminacy on the physical parameters aswell as on the chemical composition of a possible at-mosphere or ocean/land distribution, makes every hy-pothesis on the climate of Proxima b extremely specu-lative. Nevertheless, thanks to the proximity of Proximab, remote observations of its atmosphere and its surfacewill be possible in the next decade (see e.g. Kuhn et al.2018).Nevertheless, some authors started assessing the Prox-ima b observation feasibility with current or forthcomingtelescopes, investigating the possible detection limits.
Galuzzo et al.
Turbet et al. (2016) used a 3D General CirculationModel (GCM), derived from LMDZ (Hourdin et al.2006) and assuming an Earth-like atmosphere to com-pute synthetic emission spectra of the planet, proposedfor the first time to observe Proxima b with the JamesWebb Space Telescope (JWST), either with direct imag-ing or with thermal phase curves. Kreidberg & Loeb(2016), using an analytic toy climate model to pre-sume the planet thermal phase curve, estimated inmore details the JWST noise, and how the infraredthermal phase curve could be used to reveal the pres-ence of an atmosphere on Proxima b. Lovis et al.(2017) proposed a theoretical setup in which Prox-ima b could be observed with a 8-m class telescopethrough a high resolution high contrast technique. Re-sults similar to Turbet et al. (2016) were obtained byBoutle et al. (2017) using the Met Office Unified Model(Walters et al. 2017), which has a higher spectral res-olution than LMDZ. In this work, we propose a newset-up of simulations for the Proxima b atmosphere per-formed with an intermediate complexity, flexible andfast 3D GCM model integrated with an offline 1D Ra-diative Transfer Code (RTC). Specifically, the 3D GCMis a modified version of the Planet Simulator (PlaSim,Fraedrich et al. 2005a) developed at University of Ham-burg and based on the Reading multi-level spectralSimple Global Circulation Model (SGCM) describedby Hoskins & Simmons (1975). This model, developedto maximize the compatibility with the comprehensiveEuropean Centre Hamburg (ECHAM) GCM, has beenapplied and tested in different research fields, including:climate change and variability studies (Lunkeit et al.1998, Bordi et al. 2007 and Bordi et al. 2015), atmo-spheric dynamics and thermodynamics theoretical stud-ies (P´erez-Mu˜nuzuri et al. 2005, Seiffert et al. 2007,Kunz et al. 2009, Schmittner et al. 2011, Bordi et al.2012a and Fraedrich 2012), sensitivities studies forEarth climate (Fraedrich et al. 2005b, Romanova et al.2006, Lucarini et al. 2010a, Bordi et al. 2012b,Bathiany et al. 2012 and Knietzsch et al. 2015),simulations of Solar System planetary atmosphere(Grieger et al. 2004, Segschneider et al. 2005 andStenzel et al. 2007) and simulations of plane-tary atmosphere in general (Lucarini et al. 2010b,Lucarini et al. 2013, Pascale et al. 2013, Boschi et al.2013, Linsenmeier et al. 2015, G´omez-Leal et al. 2018and G´omez-Leal et al. 2019). PlaSim is a fast and flex-ible model, adaptable to extensively alter planetaryparameters, but, at the same time, it takes into accountas many processes occurring on Earth’s atmosphere aspossible. However, PlaSim only provides the integratedplanetary atmosphere radiation within three bands, two for the shortwave radiation and one for the longwaveradiation. Thus, to explore the planet emission spec-tra and to derive thermal phase curves, we combine theRTC uvspec to PlaSim. uvspec is included in the libRad-Tran library (Emde et al. 2016) and uses the
DIScreteOrdinate Radiative Transfer (DISORT) solver, reviewedby Stamnes et al. (1988) and Tsay et al. (2000). In thiswork, uvspec is used in an offline configuration, i.e. it isnot directly implemented within the PlaSim code, butit runs on PlaSim outputs: the atmospheric state (e.g.trace gas profiles, temperature and pressure profiles,surface properties and eventually cloud liquid watercontent, cloud droplet size) obtained by the PlaSim 3Dsimulation is given as input to uvspec for each atmo-spheric vertical column. Our approach, in particularthe offline radiative transfer calculations, provides ro-bust results which are in line with those obtained withmore complex models. Furthermore, libRadTran modelallows us to have an accurate representation of theatmospheric emission spectra, useful to estimate thesignal-to-noise ratio and evaluate the detection limitsof broadband planetary emission for different orbitalconfigurations.This article is structured as follows. In Section 2 wepresent the known properties and parameters of theProxima system. In Section 3 we describe the interac-tions between PlaSim and uvspec and we discuss theassumptions and parameterizations used in our simula-tion. In Section 4 the dynamical properties of an Earth-like atmosphere for Proxima b are reported, assumingits minimum mass as the planet mass. In Section 5, weevaluate the importance of planetary atmosphere andclimate when assessing the observational limits throughthe use of thermal phase curves technique. Finally, inSection 6 we report our conclusions. INPUTS FOR THE SIMULATION OF PROXIMACENTAURI SYSTEM2.1.
Proxima Centauri stellar spectral irradiance
Proxima Centauri is the Solar System neareststar with a distance of 4 . ± .
001 light-years(Gaia Collaboration et al. 2018). It is a red dwarf ofspectral type M5.5e (Bessell 1991), with estimated ra-dius and mass R ⋆ = 0 . ± . R ⊙ and M ⋆ =0 . ± . M ⊙ (Anglada-Escud´e et al. 2016), re-spectively. The effective temperature estimated byRibas et al. (2017) is T eff⋆ = 2980 ±
80 K. Proxima Cen-tauri peak of emission is in the Near-Infrared region andthe spectral energy distribution is largely different froma G-type, Sun-like star. A comparison between Sun andProxima Centauri spectral energy distributions is shownin Figure 1, where the star fluxes are evaluated at the -D simulations for Proxima b detectability ±
44 W m − .This value is similar to that of Boutle et al. (2017) andDel Genio et al. (2019), equal to 881 . − , while itturns out to be about 8% less than the irradiance pro-posed by Turbet et al. (2016), as already discussed byBoutle et al. (2017). Recently, observations of Proximab compatible with super-flare occurrence, probably pro-duced by magneto-convective processes similar to thoseobserved on a small scale in our sun, have been reported(Howard et al. 2018). We know that in the solar case themagnetic activity of the star causes variations in irradi-ance. Small variations ( ≃ . ≃ − Proxima b planetary parameters
Proxima Centauri b, has been detected using the ra-dial velocity method. The measured revolution periodis 11.186 Earth days, with the orbit semi-major axisequal to 0.0485 AU. Because of the proximity to thehost star, the planet should be captured in a 3:2 or 1:1spin-orbit resonance, depending on the orbit eccentric-ity e , as described by Ribas et al. (2016). A thresh-old value of e < .
35 was set from the observations byAnglada-Escud´e et al. (2016). In this work, we considera planet captured in synchronous rotation (tidal lock-ing) on a circular orbit ( e = 0) with an obliquity (ax-ial tilt) equal to zero. Such configuration causes theplanet to have a permanent day-side and night-side,with a fixed sub-stellar point which always receives thesame amount of stellar radiation. The principal physi-cal and orbital parameters used in this work for Prox-ima b are summarized in Table 1. They indicate theexact values introduced in our models and, for this rea-son, the relative uncertainties of these parameters arenot reported in this table. In order to establish ra-dius ( r p ) and gravity acceleration ( g p ) at the surface,we assume that the planet, for the edge-on orbital con-figuration, has a spherical shape with the same meandensity of the Earth. The radius corresponding to theminimum mass is r p = 1 . R ⊕ . In Section 4 wepresent a detailed climatological analysis for the edge-on configuration, thus assuming the planet minimummass (1 . M ⊕ ) as its mass. However, we perform sev-eral climate simulations with adjusted radius and massvalues to correctly estimate the thermal phase curve ofProxima b. For smaller values of the orbital plane incli-nation angle ι , the planet increases in mass, and thus inradius. This has a significant effect on both the emis-sion and reflected spectra of the planet. In particular,consequences on reflected light were extensively studiedby Kane et al. (2017). To estimate the mass and ra-dius changes for different orbital plane inclinations, weassume a simple mass-radius relation (see Swift et al.2012; Kane & Gelino 2012; Kane et al. 2017), and inparticular the one assumed by Turbet et al. (2016) forProxima b, r p ∝ ( M/ sin ι ) . . Although orbit incli-nation, true mass and radius are unknown, the planethas ∼
84% probability to be in the terrestrial regime(Kane et al. 2017). In particular, a density transitionand a planet composition dominated by volatile ma-terials in non-terrestrial regime can be expected for amass > . M ⊕ , corresponding to an orbit inclination ι < ◦ (Kane et al. 2017). Thus, we exclude the range ι < ◦ from our analysis. Furthermore, the recent dis-covery of Proxima c (Damasso et al. 2020) may help infurther constraining Proxima b planetary parameters.Kervella et al. (2020) combine spectroscopic orbital pa- Galuzzo et al.
500 1000 1500 2000 2500 wavelength [nm] S pe c t r a l f l u x den s i t y [ W m - n m - ] Figure 1.
Sun (black curve, http://kurucz.harvard.edu/) and Proxima Centauri (red curve, Meadows et al. 2018) spectralirradiances as measured and evaluated at the top of the atmosphere of Earth and Proxima b, respectively. rameters from HARPS and UVES with the astrometricproper motion anomaly (PMa) from HIPPARCOS andGaia DR2, constraining Proxima c orbital inclination totwo symmetric possible values, having the same sin ι :152 ±
14 deg for a prograde orbit(90 ◦ ≤ ι ≤ ◦ ) and28 ±
14 deg for a retrograde orbit(0 ◦ ≤ ι ≤ ◦ ). As-suming the coplanarity of the orbits of the two planets,the mass of Proxima b is then 2 . +1 . − . M ⊕ , likely posingthe planet in the terrestrial regime. PLASIM AND LIBRADTRAN SETTINGSPlaSim is a model derived from the Earth SystemModels (ESM) and its default configuration is set toreproduce the Earth climate. Consequently, the im-plemented parameterizations for the radiative transfercalculation within the atmosphere are based on the in-coming solar radiation, and, in particular, on the TotalSolar Irradiance (TSI) value, which is ≃ − (e.g. Kopp 2018). Nonetheless, in order to study the at-mosphere of Proxima b taking into account the differentspectral energy distribution of Proxima Centauri, theparameterizations have to be modified. In particular,the stellar contribution in PlaSim simulations is param-eterized by three quantities defined at the planet TOA:the total stellar irradiance S in W m − , the normalizedfraction of S in the ultraviolet and visible (UV-VIS)spectral region, E , and the normalized fraction of S in the near infrared (NIR) spectral region, E . Thesetwo spectral regions are considered in our model as the shortwave radiation. Although the output quantity pro-vided by PlaSim are the integrated flux along all theshortwave range, the calculations in the source code areperformed considering the separation between the twomentioned broadbands and the physical processes oc-curring within each one of them. Specifically: in theUV-VIS band, defined for wavelengths λ < . µ m,pure cloud scattering, ozone absorption and Rayleighscattering are taken into account without water vaporabsorption, whereas in the NIR band, defined for wave-lengths λ > . µ m, cloud scattering and absorptionand water vapor absorption are considered. Followingthis parameterization with a given stellar spectral irra-diance I ( λ, T ) in W m − nm − , the resulting total irra-diance in W m − can be obtained as S = Z ∞ I ( λ, T ) dλ, (1)and consequently, the normalized energy flux fractionsin the two spectral regions described above can be com-puted as E = R λ τ I ( λ, T ) dλS , (2)and E = 1 − E , (3)where λ τ = 0 . µ m.The normalized flux fractions derived from the Prox-ima Centauri spectrum in Figure 1 are E = 0 .
23, and -D simulations for Proxima b detectability Table 1.
Proxima b Keplerian and planetary parameters assumed inPlaSim simulations.Proxima Centauri b: derived and assumed quantities.Parameter Symbol ValueOrbital period P 11.186 Earth days † Orbit eccentricity e p ‡ Orbit semi-major axis a † Obliquity α ‡ Minimum mass M min . M ⊕ † Mean density ρ p = ρ ⊕ . − ‡ Radius r p . R ⊕ ‡ Surface gravitational acceleration g p . − ‡ Rotation rate ω p . × − rad s − ‡ Note — † Measured or derived value by Anglada-Escud´e et al. (2016); ‡ Assumed value for the simulation. Radius and surfacegravitational acceleration refer to the edge-on configuration. E = 0 .
77, respectively and are modified in the PlaSimsource code accordingly.The longwave radiation parameterization in PlaSimincludes CO , ozone, water vapor and clouds. Thescheme uses one only spectral band, with broadbandemissivity and transmissivity calculations based onManabe & M¨oller (1961) and Sasamori (1968) for aclear sky atmosphere and vertical discretization basedon Chou et al. (2002). This means that, as well as inthe shortwave case, the radiation emitted by the planetis given as an integrated quantity along all the longwavespectral range, also known as the outgoing longwaveradiation (OLR, Petty 2006).Since our aim is to study Earth-like planets, we use asimple approach and we assume an Earth-like atmo-sphere. The initial surface pressure is assumed equal to1000 hPa. Moreover, an ozone layer is maintained witha prescribed vertical profile parameterized by Green(1964), in order to reproduce the Earth’s one, withthe exception that, because of the completely differentinsolation pattern between Proxima b and the Earth,we neglect the typical ozone seasonality, keeping itsvertical and meridional distribution constant over time.For an active star, as Proxima Centauri is, the impactof the stellar UV variation on the ozone vertical distri-bution should be considered. Due to surface magneticstructures, the stellar UV variability can be describedby [FUV-MUV] color index variation during the activ-ity cycle (e.g., Lovric et al. 2017, Criscuoli et al. 2018,Berrilli et al. 2020). However, for simplicity, in thiswork we hypothesize a constant stellar flux (i.e. no stel-lar variability), postponing to a future work a detailedstudy of the connection between stellar UV activity and planetary ozone distribution.Of importance, due to its spectral properties, the albedoof sea-ice is significantly reduced around an M star withrespect to a G star like the Sun (Joshi & Haberle 2012;Shields et al. 2013; Turbet et al. 2016; Boutle et al.2017; Del Genio et al. 2019 among others). In orderto take this into account, in PlaSim the maximum valueof broad band albedo over sea ice has been set to 0.27,based on the calculation of Turbet et al. (2016). Inthe PlaSIM code, the sea ice albedo parameterizationdepends on the temperature, following the formula: R S = min ( R maxS , . . . − T i ). Where T i is thetemperature over sea-ice and the prescribed maximumsea ice background albedo R maxS , originally set to adefault value of 0.7 for the Earth, has been set to 0.27in this study.The carbon dioxide concentration is maintained fixed to360 ppm during the simulation. This is chosen in orderto compare our results with the works of Turbet et al.(2016), Boutle et al. (2017) and Del Genio et al. (2019)in which similar parameters were used. Water vaporconcentration is directly computed by PlaSim in a spe-cific module, using pressure and temperature fields inorder to determine its properties for each time-step.The planet is initialized as an aquaplanet, i.e. a planetwith a surface entirely covered by an ocean. This choiceis motivated by two considerations. Firstly, Tian & Ida2015 showed that, in the habitable zones around Mdwarfs, there are two favored types of planets withEarth-like mass which are aquaplanet and desert plan-ets with orders of magnitude less surface water than onEarth. Secondly, land mass distribution alters both dy-namics and thermodynamics in different ways depend- Galuzzo et al. ing on the orography and the surface properties, such asalbedo and soil type. Since any land mass distributionintroduced in the model would be completely arbitrary,the most straightforward choice is to totally neglect landmasses. Furthermore, although Del Genio et al. (2019)showed that ocean dynamics could play a relevant roleon tidally-locked planet climate, in this work we simu-late a thermodynamic slab ocean of 50 meters depth,where the horizontal and vertical mixing are neglected.The advantage of using a slab ocean instead of a fullocean (i.e. an ocean for which the 3D Navier-Stokesequations are numerically solved as well as for the at-mosphere) is that it allows the climatic system to reacha steady state in less than a few decades, returning afast numerical simulation which enables sensitivity eval-uation to parameter variations.In order to obtain the effect of the synchronous rotationof the planet, we modify the PlaSim radiation modulesource code, to fix the position of the star in the planetsky at each simulation timestep. We run the Proximab climate equilibrium simulation for a period of 110Earth years with a temporal resolution of 45 minutes,that is the default timestep of the model. The outputtemporal resolution is 1 Earth day. Because of the spu-rious variability of the system introduced by the initialnon-equilibrium spin-up of the simulation, a specificperiod at the beginning of the simulation is discarded.This is chosen following the stabilization of the surfacetemperature variability, i.e. when no long-term trendsare found, and the mean surface temperature reach asteady state. We find that this system stabilization oc-curs after 10 years from the beginning of the simulation.Model outputs are gridded on a 128 ×
64 longitude-latitude grid, with 20 vertical pressure levels, from 1000hPa to 50 hPa, setting the sub-stellar point above theequator, at 180 ◦ E of longitude.As discussed above, PlaSim returns integrated fluxes inboth shortwave and longwave spectral ranges. However,integrated fluxes are not sufficient for our purposes.Given that our aim is to determine whether Proxima bcan be detected by analyzing its thermal emission withinspecific bands from current or future telescopes observa-tions, we evaluate the planet thermal infrared emissionin narrower spectral bands compared to PlaSim outputs.In order to perform the radiative transfer calculation onthe atmosphere of Proxima b, obtaining high resolutionsynthetic emission spectrum, we use the uvspec modeland the DISORT method. In particular, given the spec-trally resolved stellar irradiance at planet TOA andthe vertical profiles of the planetary atmosphere con-stituents, DISORT solves the 1D plane-parallel radiativetransfer equation, returning radiances, irradiances, and actinic fluxes as outputs. In this work, we use the spec-tral irradiance of Proxima Centauri shown in Figure 1 asstellar input for DISORT, whereas atmospheric verticalprofiles are extracted from PlaSim simulation, consider-ing the atmospheric columns above each grid-box. Weindicate these columns as grid-columns . Specifically,the extracted profiles within a grid-column are: i) at-mospheric pressure, ii) temperature, iii) air density, iv) ozone, v) water vapor concentration and vi) carbondioxide concentration. Furthermore, our implementa-tion takes into account the cloud properties such as theliquid water content, the cloud droplet effective radiusand the total optical depth. The output from uvspec arethen used to estimate the line-by-line emission spectraof the simulated planetary atmosphere, with a spectralresolution of 1 nm, for each time-step and each grid-column from which we reconstruct thermal emissionfrom planet TOA. Because of the imposed planetaryaxial and orbital symmetry, the year-to-year variabil-ity of the different atmospheric constituents (includingwater vapour and clouds), estimated as the standarddeviation of the yearly time series over 100 Earth years,in the three regions is very small, as shown in Figure 2for the temperature profile only. This small atmosphericvariability allows us to assume stationary vertical pro-files. This means that we can use the mean verticalprofiles within each grid-column, as representative forthe entire period of simulation. PROXIMA CENTAURI B CLIMATE4.1.
Thermodynamic properties of Proxima batmosphere
The planet surface temperature is largely used as aclimatological proxy to estimate the habitability con-ditions on a planet (Kasting et al. 1993) or to studythe fluctuations between different multiple steady statesof its climate (Lucarini et al. 2013). Using the plane-tary parameters and atmospheric composition discussedin Section 2.2, the resulting mean surface temperaturefield from our PlaSim simulation shows an insolation-symmetric pattern with temperatures below the waterfreezing temperature T ice on the night-side of the planetsurface, and an open ocean on most of the day-side. Sur-face maximum temperature is located to the east of thesub-stellar point. This is likely due to the superrotatingatmosphere and will be discussed in more details laterin this section. Surface temperature ranges from a min- The actinic flux is the radiant quantity used to calculate differ-ent photodissociation rates. It represents the total number ofphotons, or radiation, incident at a point (Madronich 1987). -D simulations for Proxima b detectability
160 180 200 220 240 260 280
Temperature [K] H e i gh t [ k m ]
50 100 200 300 400 600 800 1000 P r e ss u r e [ h P a ] Anti-stellar point a)
160 180 200 220 240 260 280
Temperature [K] H e i gh t [ k m ]
50 100 200 300 400 600 800 1000 P r e ss u r e [ h P a ] Equatorial dusk point b)
160 180 200 220 240 260 280
Temperature [K] H e i gh t [ k m ]
50 100 200 300 400 600 800 1000 P r e ss u r e [ h P a ] Sub-stellar point c)
160 180 200 220 240 260 280
Temperature [K] H e i gh t [ k m ]
50 100 200 300 400 600 800 1000 P r e ss u r e [ h P a ] Equatorial dawn point d)
160 180 200 220 240 260 280
Temperature [K] H e i gh t [ k m ]
50 100 200 300 400 600 800 1000 P r e ss u r e [ h P a ] North Pole e)
160 180 200 220 240 260 280
Temperature [K] H e i gh t [ k m ]
50 100 200 300 400 600 800 1000 P r e ss u r e [ h P a ] South Pole f) Figure 2.
Temperature mean vertical profiles (black curve) and relative ± σ deviation from mean profile (gray-shaded area)for six grid-column of PlaSim simulation, relative to different regions of Proxima b: a) anti-stellar point; b) equator dusk point; c) sub-stellar point; d) equator dawn point; e) North Pole; f )
South Pole. On the x -axis the value of temperature is reported,while on two y -axis the height and isobar level are reported, respectively. The different height of planet TOA in sub-stellarregion, depends on planet thermal structure. The 1 σ deviation is evaluated on the entire period of simulation (100 Earth years)and the relative maximum deviation for each panel is: a) ± .
78 K at surface; b) ± .
32 K at surface, c) ± .
36 K at 11.5 km; d) ± .
60 K at surface; e) ± .
88 K at surface; f ) ± .
87 K at surface. imum value of 160 K to a maximum value of 295 K.These values are smaller compared to those reportedby Turbet et al. (2016) for similar simulation settings,that were 200 K and 300 K, respectively, but compara-ble to those shown by Boutle et al. (2017). Moreover,our surface temperature maximum on the day-side iscomparable with that found by Del Genio et al. (2019),whereas surface temperature minimum is about 20 Khigher. Furthermore, our results regarding the planetsurface region where
T > T ice are in line with that ob-tained by all the three aforementioned studies for sim-ilar simulation settings. Given the comparable resultsobtained using either intermediate complexity models(PlaSim in our study) or the more sophisticated GCMs(as reported in previous literature), such simplified mod-els may represent an innovative and promising tool forfuture climate studies, especially to simulate future ex-oplanetary observations.Thermodynamic processes determine the amount ofinfrared radiation emitted by the planet towards spaceand consequently they can be used to set observationallimits. One of the main absorbers in an Earth-like at-mosphere is water, both as vapor and liquid (i.e. inthe clouds). In our simulation, the atmospheric liquid water content in clouds ( w L ) is lower than Earth, witha maximum of 1 . × − kg m − located in the firstlayer above the planet surface in the day-side and witha dry night-side. For reference, the maximum valueof cloud liquid water content on Earth has been evalu-ated by Hu et al. (2007) to be around 5 . × − kg m − .4.2. Atmospheric dynamics
The planetary surface temperature pattern reportedin Figure 3, causes a convective structure in the day-side which brings the surface air masses to ascend upto 15 km. This convective flow is consistent with theplanet’s mean global circulation shown in Figure 4. Inthis figure, the mass stream function ψ is superimposedto the zonally averaged zonal wind. ψ is defined as inCeppi & Hartmann (2013): ψ = − πr p g p Z p [¯ v ] cos θ dp ′ (4)where g p is the gravitational acceleration, [¯ v ] is the zonalmean of the meridional wind, θ is the latitude and p isthe pressure level. The mass stream function indicatesthe meridional flows on Proxima b and the formation Galuzzo et al.
Figure 3. Mean surface temperature . The tidal-locking of the planet produces the symmetrical pattern of ProximaCentauri b surface temperature: higher temperatures in the region of the sub-stellar point, with the presence of an open ocean( T ice = 273 . K ) and colder temperatures in the night-side of the planet. Planet rotation is assumed clockwise in the simulation.This map is shown as it would be for a planet with anticlockwise (prograde) rotation, for easy comparison with previous works.See e.g. the position of the cold points in Fig.2 of Boutle et al. 2017 and Fig. 6 of Turbet et al. 2016. of a Hadley cell-like circulation which surrounds the en-tire planet from equator to poles. The cell presents aclockwise branch in the northern hemisphere (solid linesin Figure 4) and an anticlockwise counterpart, in thesouthern hemisphere (dashed lines in Figure 4). Thisglobal circulation is in agreement with results from sim-ilar studies reported in the literature (e.g., Turbet et al.2016; Boutle et al. 2017; Komacek & Abbot 2019) for aplanet rotation period of the order of one tenth of theEarth’s one.This implies that the planetary atmosphere dynamics,triggered by the constant insolation on the day-side, isdriven by the interaction of the meridional circulationwith the Coriolis force due to the planet rotation. Thisresults in an equatorial symmetric jet stream at 300 hPa(Figure 4).Furthermore, this tidally-locked rocky planet, exhibitsa superrotating atmosphere. This result is comparableto previous results (e.g., Joshi et al. 1997, Heng & Vogt2011, Edson et al. 2011, Wordsworth et al. 2011Showman et al. 2013, Merlis et al. 2013). Superrotationis a condition whereby the atmospheric axial angularmomentum is locally greater than the surface axial an-gular momentum. The specific equatorial angular mo-mentum of the planet is M = ωr p and it only dependson the planet radius and rotation rate, whereas the at-mosphere’s axial angular momentum M a also depends on the zonal wind and it can be expressed as M a = r p cos θ ( ωr p cos θ + u ) , (5)where θ is the latitude.Assuming that the atmospheric angular momentum isequal to the planet equatorial angular momentum, M a = M , (6)a zonal wind threshold value can be derived as a functionof θ : u m = ωr p sin θ cos θ . (7)Hence, u m represents the threshold value for whichthe atmosphere would be co-rotating with the planetsurface at the equator. In Figure 5 the threshold value u m and zonal mean zonal wind at different pressure lev-els for Proxima b are shown for global, night-side andday-side averages. The equatorial superrotation condi-tion is satisfied in the region between 30 ◦ S − ◦ N withthe exception of the first atmospheric layer which rep-resents the planet surface. Such an exception seems tosuggest that the aforementioned surface displacement ofthe warm region from the sub-stellar point is not due tosuperrotation. However, this result is biased by the factthat the zonal mean of zonal wind is evaluated by globalaverages. Nevertheless, when performing the same anal-ysis considering the night-side and the day-side sepa-rately, the superrotation condition is satisfied also at -D simulations for Proxima b detectability Figure 4.
Zonally averaged zonal wind (colored contours) and mass stream function (black contour lines). Hadley cell-likestructure in the atmosphere of Proxima Centauri b, driven by the constant insolation in the day-side. Colors represent thezonal mean of the zonal wind, where positive values are for easterlies winds (from west to the east) and negative values arefor westerlies winds (from east to the west). The black lines show the mass stream function: the solid lines denote clockwisecirculation ( ψ > ψ < ψ in 10 kg s − units. The mass stream function gives the extent of the Hadley cell-like circulation which, in the caseof Proxima Centauri b, extends horizontally from the equator to poles, and vertically above 150 hPa. the planet surface, but only in day-side, as shown inFigure 5c and discussed by Showman & Guillot (2002)and Showman & Polvani (2011). This result suggeststhat the east shift in surface temperature maximum isindeed due to the superrotating atmosphere. This alsoclearly demonstrates that, in case of tidally-locked plan-ets, the average evaluations over the entire planet sur-face could lead to substantial misinterpretations of keyclimatic features and thus we strongly support the anal-ysis of both hemispheres, separately. Moreover, the ad-vantage of using 3D over 1D or 2D models is evident. Infact, these latter models cannot simulate the full dynam-ical structure of an atmosphere, which is only possiblein 3D models. DETECTABILITY OF PLANETARYATMOSPHERE EMISSIONS FROM SPACE ANDGROUND-BASED OBSERVATIONSProxima b has not yet been observed with directimaging. This is due to the angular separation of37 milliarcseconds between the planet and the hoststar (Anglada-Escud´e et al. 2016) and the planet-to-starcontrast in different spectral regions. Lovis et al. (2017)explored the possibility to observe Proxima b in the visible coupling SPHERE and ESPRESSO at VLT, toreach a contrast of 10 − . Turbet et al. (2016) showedthe opportunity to exploit higher planet-to-star contrast(10 − ) at 10 µ m using JWST as well as the advantagesthat will be offered by ELT at 1 µ m with a contrast(10 − ) using high-resolution spectroscopy. Observationsin the thermal IR wavelengths provide distinctive in-formation to constrain planet atmospheric properties.However, given that the spatial resolution depends onwavelength in diffraction limited instruments, the IR di-rect imaging is limited to exoplanets with larger semi-major axis respect to the same technique applied in theoptical spectral region. ELT will provide a significantimprovement, nevertheless, due to its diffraction limit,direct imaging for Proxima b, even for a 39 m aper-ture, is limited in wavelength up to 3 µ m (Turbet et al.2016). Thus, a possible strategy to overcome this limi-tation is to characterize the planet’s atmosphere and cli-mate studying the thermal phase curve (e.g. Selsis et al.2011, Cowan et al. 2012 and Maurin et al. 2012). Weuse PlaSim and the offline RTC to identify the spec-tral regions more sensitive to contrast variations dur-ing the orbital period. We evaluate this effect firstlyfor the OLR, applying the uvspec model to PlaSim out-0 Galuzzo et al. -50 0 50
Latitude [deg] -10-505101520253035 Z ona l w i nd [ m s - ] Global a) -50 0 50 Latitude [deg] -10-505101520253035
Nightside b) U m U U
800 hPa U
550 hPa U
300 hPa U
50 hPa -50 0 50
Latitude [deg] -10-505101520253035
Dayside c) Figure 5. Atmospheric superrotation . Angular momentum conserving wind u m (black curve) and zonal mean zonal wind(colored dashed lines) as a function of latitude θ ( x -axis), for planet a) global mean, b) night-side mean and c) day-side mean.Each zonal mean wind curve represents the x component of the wind ( y -axis) at different pressure levels, namely 1000 hPa(blue-dashed curve), 800 hPa (red-dashed curve), 550 hPa (yellow-dashed curve), 300 hPa (purple-dashed curve) and 50 hPa(green-dashed curve). The blue horizontal line represents the zero mean of the zonal wind. If a colored curve is above the solidblack curve for a given latitude range, the condition u > u m is satisfied, and the relative atmospheric layer is in an equatorialsuperrotation state in that latitude range. puts. Typically, the peak of emission of an Earth-likeplanet in the habitable zone is expected to be in themid-IR region around 10-20 µ m. Hence, we investigatethe thermal phase curves in specific spectral bands, us-ing Boutle et al. 2017 approach, to evaluate the planetdetectability with space or ground-based instruments.5.1. Planetary spectra and thermal phase curves
To evaluate spectral properties of the planetary at-mosphere, we follow the method described in Section 3.Planetary spectral thermal fluxes at the TOA for differ-ent planet regions, are shown in Figure 6. Because ofthe synchronous rotation, the planet thermal flux hasa strong dependence from longitude and latitude, withthe peak of emission at λ ≈ µ m. The uvspec mod-ule applied to the PlaSim outputs returns 8192 thermalspectra, one for each latitude/longitude grid-column ofthe simulation (i.e. 64 ×
128 spectra). In Figure 6, onlyfour of these spectra are shown as reference: the ther-mal spectra as seen from the planet TOA above the sub-stellar and anti-stellar points and above the warm andcold points. The carbon dioxide absorption/emissionfeature can be seen at λ ≈ µ m (i.e. ˜ ν ≈
600 cm − )in all panels and it is clear how its emission tempera-ture remains the same in each region, being ∼
200 K.In particular, on the planet night-side, the carbon diox- ide signature is clearly visible being the feature with themaximum peak of emission.The planet emission spectra is used to derive the ther-mal phase curve. The expected flux from Proxima bis obtained integrating the thermal emission over thewhole surface of the planet taking into account the dis-tance and the position angle. Since the exact geome-try of the planet-star system is not currently known weconsider several possible inclinations of the orbital planewith respect to an observer on Earth. For this purpose,we use the visibility function V ( θ, φ, t, θ ) =max { sin( θ ) sin( θ ) cos [ φ − φ ( t )] +cos( θ ) cos( θ ) , } (8)described by Cowan et al. (2013), to obtain the visibleregion of the planet as a function of the orbital pa-rameters at given orbital time. The visibility function V , depends on 4 parameters: i) the planet longitude φ ∈ (0 , π ]; ii) the planet co-latitude θ ∈ (0 , π ); iii) the sub-observer longitude φ ∈ (0 , π ]; and iv) the sub-observer co-latitude θ ∈ (0 , π ).The sub-observer longitude is a function of the orbitaltime t and it can be linked to the phase angle ξ (seeFigure 8a), via the relationship ξ = Ω t, where Ω is the -D simulations for Proxima b detectability
5 6.5 8 10 15 20 50 051015 R ad i an c e [ W m - µ m - ] Anti-stellar point wavenumber [(cm -1 ) -1 ]
5 6.5 8 10 15 20 50 051015 R ad i an c e [ W m - µ m - ] Cold point wavenumber [(cm -1 ) -1 ]
5 6.5 8 10 15 20 50 wavelength [ µ m] R ad i an c e [ W m - µ m - ] Sub-stellar point wavelength [ µ m] R ad i an c e [ W m - µ m - ] Warm point
Figure 6. Infrared emission spectra . Infrared emission spectra at Proxima b TOA, as a function of wavelength λ (bottomx-axis) and wavenumber ˜ ν (top x-axis) are obtained with uvspec , above different regions of the planet: a) the anti-stellar point(0 ◦ N , ◦ E); b) the cold point (66 ◦ N , ◦ E); c) the sub-stellar point (0 ◦ N , ◦ E) and d) the warm point (1 ◦ N , ◦ E).Dashed lines represent the ideal black body emission from Planck’s law curves relative to the black body temperatures from100 K to 300 K, with 10 K separation. The radiative effect of the atmospheric component can be seen on the curves and inparticular, the carbon dioxide signature, around λ = 15 µ m (˜ ν = 666 cm − ), the ozone signature, around λ = 9.6 µ m (˜ ν = 1040cm − ) and the water vapor signatures at λ < µ m (˜ ν > − ). planet orbital angular velocity (i.e. the revolution rate).Since we assumed a tidally-locked planet, the revolu-tion period is equal to the rotation period and Ω = ω .The sub-observer co-latitude instead, corresponds to theplanet orbital plane inclination ι , with respect to the ob-server.Finally, by performing the substitution θ → ι , theplanet thermal emission F p ( ξ, ι ) is given by: F p ( ξ, ι ) = Z π Z π I ( θ, φ ) V ( θ, φ, ξ, ι ) dθdφ, (9)where I ( θ, φ ) is the planet integrated thermal flux ina selected spectral range λ ≤ λ ≤ λ , for each lati-tude/longitude box of the simulation.The integrated flux from Proxima Centauri, F ⋆ , is con-sidered constant with time for any wavelength range.This means that we are neglecting any possible influ-ence of the stellar variability. We define the planet/starcontrast Φ( ξ, ι ): Φ( ξ, ι ) = F p ( ξ, ι ) F ⋆ , (10)where F p is the planet atmospheric emission. Both F p and F ⋆ are evaluated in the same spectral range. In particular, we are interested in the amplitude A ( ι ) ofthe planet thermal phase curve defined as A ( ι ) ≡ Φ max ( ξ, ι ) − Φ min ( ξ, ι ) , (11)since the amplitude modulation of the phase curve isthe measurable quantity for unresolved exoplanetarysystems. Furthermore, A ( ι ) must be compared to theachievable photometric precision, which crucially de-pends on the photons available in the considered spectralrange. The ratio between these two quantities identifiesthe most suitable band for the observations.In Figure 8b, the planet thermal phase curve com-puted in the OLR spectral range (3 µ m ≤ λ ≤ µ m)is shown for different orbital plane inclinations.Although we evaluated the thermal phase curves forseveral inclination angles 0 ◦ ≤ ι ≤ ◦ , here we showonly the results obtained for ι ≤ ◦ , because the sys-tem symmetry produces completely specular curves for ι > ◦ . The presence of atmosphere and its role inheat advection produces a not perfectly symmetric phasecurve.2 Galuzzo et al.
Figure 7. Proxima b orbit.
The figure represents Proxima b on its circular orbit around the host star. Because of the 1:1spin/orbit resonance, an outside observer can explore all sides of the planet in a single revolution. Surface color represents theamount of OLR emission: red regions represent the emission maximum, whereas the dark blue regions represent the emissionminimum. π /2 π π /2 2 π π /2 π π /2 2 π Phase angle [rad] F P / F ⋆ [ pp m ] i = 22.5°i = 45°i = 67.5°i = 90° Figure 8. Planet phase curves.
Planet/Star contrast in the OLR region (3 µ m ≤ λ ≤ µ m), during two complete orbitsof Proxima b around the host star. Each curve represents a different inclination angle of the planet orbital plane with respectto the observer. The black curve represents the thermal emission for an edge-on geometry, i.e. the case of a transiting planet.For this reason, the value of Φ( ξ,
90) drops to zero at ξ = 2 π (secondary eclipse). Also, the small effect due to primary eclipseis visible at ξ = π . -D simulations for Proxima b detectability Proxima b detectability from space observatories
Future detection of Proxima b thermal emission isevaluated considering the technical specification of theJames Webb Space Telescope (JWST), specifically thecase of the imaging mode of the Mid-Infrared Instrument(MIRI, Wells et al. 2015). The photometric bands of theMIRI imager (MIRIM, Bouchet et al. 2015) are consid-ered and we compute the amplitude of the phase curve,fixing the orbital inclination angle to 90 ◦ . Given theProxima Centauri spectrum, the photometric precisionachievable in each band is also computed, expressed interms of the minimum detectable amplitude A ( N )0 . Thisis calculated assuming photon noise limited observationsand it will be extensively described later in this section.In Table 2 these quantities are compared and the ratiobetween the two amplitudes is found to be maximum inthe MIRI F2100W passband filter, corresponding to thespectral band 18 . µ m ≤ λ ≤ . µ m.In Table 3 the maximum values of Φ( ξ, ι ), Φ max and the relative amplitude A , evaluated in the abovementioned spectral band, are reported as a functionof the system inclination. The geometric probabil-ity of transit for Proxima b is very small ( ∼ . . µ m (Jenkins et al. 2019). Thus,the effect of a transit is excluded from subsequent anal-ysis. The ι = 90 ◦ case has to be intended as an almostedge-on configuration with no-transit. The amplitude A is expected to decrease with inclination, consideringthat day-side becomes partially visible along the full or-bit. Nevertheless, this decrease is compensated by theincrease of the planet mass and, in turns, its radius(Turbet et al. 2016). The amplitude A results in thiscase almost constant with respect to the orbital inclina-tion. Our results are also in line with Kane et al. (2017)results regarding the planet/star contrast.In order to derive the detectability limits of Proxima busing the JWST, the signal-to-noise ratio on the MIRIMdetector is computed for the passband filter F2100W.Assuming a photon noise limited observation, two dif-ferent methods are used to evaluate the photometric pre-cision. In both cases we consider an exposure time τ = 5hours, which is a small fraction of the planet orbital pe-riod ( τ ∗ < P/ con-sists of several short exposures ( ∼ . https://jwst.etc.stsci.edu/ Proxima Centauri is a bright source, so an individualexposure of 1.2 s almost exploits the full dynamic rangeof the camera, thus the readout noise is not a limitingfactor for the observations. The readout time for theSUB128 subarry is 0.119 s, therefore the duty cycle is ∼
90% and 5.5 hours are needed for a 5 hours exposuretime.Our first method consists in computing the number ofphotons, within the assigned spectral band, collected bythe instrument, as per Yang et al. (2013): N = ε π A T τ (cid:18) R ⋆ D (cid:19) Z λ λ F ⋆ ( λ ) E ( λ ) dλ, (12)where A T is the telescope collecting area, τ is the expo-sure time, R ⋆ is the star radius, D is the star-observerdistance, F ⋆ ( λ ) is the stellar spectral energy distribu-tion and E = hc/λ is the energy of a photon for a givenwavelength λ . In the case of JWST, the primary mirroreffective collecting area is A T = 25 m (Gardner et al.2006). Furthermore, we also consider the factor ε inorder to take the MIRIM filter efficiency into account,which is 25% for the F2100W filter .The instrument photometric precision is estimatedconsidering a photon shot noise limited observation, ob-taining P P N = 5 . σ levelis equal to twice the computed photometric precision: A ( N )0 = 10 . A ( N )0 .The second method we use to evaluate the pho-tometric precision of JWST exploits the ETC. TheJWST ETC estimates the infrared background us-ing a model including many celestial sources, e.g. ,zodiacal light, interstellar medium, and cosmic in-frared background (Reach et al. 1997; Kelsall et al.1998; Krick et al. 2012), in addition to telescope ther-mal and scattered light. Moreover, it achieves accu-rate calculation of signal-to-noise ratio, considering theMIRIM instrumental characteristics and the filter re-sponse functions. Using JWST ETC, we obtain a photo-metric precision P P
ET C = 7 . A ( ET C )0 = 15 . https://jwst-docs.stsci.edu/display/JTI/MIRI+Filters+and+Dispersers Galuzzo et al.
Table 2.
Amplitude of the phase curve A (90 ◦ ), minimum de-tectable amplitude A ( N )0 (24 hours integration time) and ratiobetween them for the photometric bands of JWST/MIRIM.MIRIM filter A (90 ◦ ) ( ppm ) A ( N )0 ( ppm ) A (90 ◦ ) /A ( N )0 F560W 0.06 1.6 0.04F770W 2.4 1.7 1.4F1000W 8.3 2.4 3.5F1130W 15.0 5.2 2.9F1280W 13.6 3.4 4.0F1500W 4.0 3.8 1.1F1800W 24.7 4.9 5.0F2100W 34.3 4.7 7.3F2550W 14.0 9.9 1.4
Table 3.
Planet/star thermalemission maximum contrast Φ max and amplitude A for different or-bital inclination angle ι (MIRI im-ager F2100W). ι Φ max ( ppm ) A ( ppm )22 . ◦
364 21.145 ◦
271 23.467 . ◦
245 32.790 ◦
240 34.3 inclination angle. In particular, we compare A ( N )0 as afunction of τ and A as a function of ι . A semi-empiricalequation for A ( ι ) is obtained by fitting with a cubicfunction the four points resulting from our simulationand reported in Table 3. From this figure, we can alsoestablish for which exposure time the instrumental pho-tometric precision A ( N )0 is sufficient for the detectionof signature of the planet of amplitude A ( ι ∗ ), given itsdependency on the inclination. For instance, in the caseshown in Figure 10a, an exposure time of ∼ ◦ and 42 ◦ . The amplitudeof the phase curve for those inclination is expectedto be between ∼
15 ppm and ∼
30 ppm in the band18 . ÷ . µ m. 5.3. Proxima b detectability from ground-basedobservatories
In the previous section, the JWST photometric accu-racy in the case of Proxima b observations has been com-puted. Such an approach can in principle be applied tosimilar observations performed from ground-based ob-servatories. However, for ground-based infrared observa-tions, mainly at mid-IR wavelengths (e.g. Berrilli et al.1987, 1989, 1992), the background is large when com-pared to the emission of stellar sources. Further, thisbackground emission is very sensitive to the telescopethermal and scattered light (at 10 microns the telescopeemissivity can dominate over sky emission) and atmo-spheric status can fluctuate rather fast in time and inspace.Here, we compare estimated 1 σ detection for bothJWST-MIRIM and the mid-infrared imager and spec-trograph METIS (Brandl et al. 2014) which will beinstalled at the Extremely Large Telescope (ELT)(Gilmozzi & Spyromilio 2007). ELT will be the largest -D simulations for Proxima b detectability F P / F ⋆ [ pp m ] ι = 22.5°0 5 10 15 20230260290 F P / F ⋆ [ pp m ] ι = 45°0 5 10 15 20 Time [Earth days] F P / F ⋆ [ pp m ] ι = 67.5° 0 5 10 15 20320350380 F P / F ⋆ [ pp m ] ι = 22.5°0 5 10 15 20230260290 F P / F ⋆ [ pp m ] ι = 45°0 5 10 15 20 Time [Earth days] F P / F ⋆ [ pp m ] ι = 67.5° Figure 9. Five hours exposure time detection limits.
The planet/star contrast (y-axis) in the spectral band 18 . ÷ . µ mas a function of time for a sample of three possible planet orbital plane inclination angles. Gray area represent the minimumdetectable amplitude of the phase curve at 1- σ level for Proxima b (5 hours exposure time) obtained considering the photonnumber: a) derived from the stellar flux following Yang et al. (2013) (left) and b) the Exposure Time Calculator (ETC) ofJWST, with MIRIM settings (right). Orbital plane inclination [deg] A ( ι ) [ pp m ] a) JWST A( ι )A ( τ ) Exposure time [hours] A [ pp m ] Orbital plane inclination [deg] A ( ι ) [ pp m ] b) ELT A( ι )A ( τ ) Exposure time [hours] A [ pp m ] Figure 10. Proxima b atmosphere detection comparison.
Comparison between JWST-MIRIM (18 . ÷ . µ m), panela, and ELT-METIS (8 . ÷ . µ m), panel b, for 1 σ detection of broadband Proxima b atmospheric emission. The black curvesrepresent the semi-empirical thermal phase curve amplitude A as a function of the planet orbital plane inclination angle ι . Valuesof this function below ι = 15 ◦ are not shown since they are outside the validity range of our model. Star symbols representsample values of the amplitude A for the fixed inclination angles reported in Table 3. The blue curves represent the minimumdetectable amplitude A as a function of exposure time, evaluated as in Yang et al. (2013). The green horizontal line indicatesthe values of A relative to an exposure time of 1 hour in both panels. optical/NIR telescope in the world with a primary mir-ror of 39 meters diameter. The technical characteris-tics of the ELT METIS needed to perform our eval-uation have been obtained from Brandl et al. (2014),Brandl et al. (2016), and Brandl et al. (2018). An at-tempt to estimate the performance of ELT METISthrough a sensitivity model introducing a variety ofsources is presented in Kendrew et al. (2010). However,in this work, we do not make assumptions about the noise introduced by the instrument and the Earth at-mosphere by limiting the analysis to only photometricshot noise. In order to estimate the photometric preci-sion of METIS we assume a primary mirror collectingarea for ELT A ELT = 978 m and a 10% efficiency.The amplitude A ( ι ) is computed for the N band(8 . ÷ . µ m, see also Table 4) and it is shown as blackstar symbols in Figure 10. The values of A ( ι ) are smallercompared to those evaluated by JWST-MIRIM, this is6 Galuzzo et al.
Table 4.
Effective wavelengths, full width half maxima, zero-magnitudefluxes for the ESO infrared passbands used in this work, taken fromvan der Bliek et al. 1996. We also report the corresponding amplitude ofthe phase curve A (90 ◦ ), minimum detectable amplitude A ( N )0 (1 hour in-tegration time) and ratio between them for the same photometric bands.Filter λ eff. FWHM F λ ( m λ = 0) A (90 ◦ ) A ( N )0 A (90 ◦ ) /A ( N )0 µ m µ m Wm − nm − ppm ppmL’ 3.771 0.580 5 . × − . × − , × − Q , × − mainly due to the different spectral intervals used. Con-sidering a 1 hour exposure time for ELT-METIS, a min-imum detectable amplitude A = 1 . M , N and Q , tomaximize the planet contribution. These bands, withthe relative zeropoint magnitude fluxes, are describedin van der Bliek et al. (1996) and summarized in Table4. We compute the color indices M − N and N − Q forthe Proxima system as a function of the planet phaseangle. We define the color variation as∆( X − Y ) = ( X − Y ) − ( X − Y ) , (13)where X and Y are respectively M and N or N and Q and ( X − Y ) is the mean value over the orbital period.In Figure 11, we evaluate the color index variation forfour different Proxima b orbital plane inclinations. Ifthe planet had a face-on orbit inclination, there wouldbe no color index variation, in contrast, approaching theedge-on inclination the color index variation increases.For Proxima Centauri System, the M − N and N − Q color variations are of the order of 8 ppm and 18 ppm, re-spectively, for an orbital plane inclination angle of 45 ◦ .Although these values are at the edge of the capabili- ties of METIS, the color variation technique could opendetection possibilities for the next generation ground-based large aperture telescopes. CONCLUSIONSIn this work we propose and use a method to studythe climate of a terrestrial exoplanet with an Earth-likeatmosphere and we evaluate its detectability by pho-tometry in the thermal IR bands. A fast and flexible3D GCM (PlaSim) is used and modified in order to re-produce the atmosphere and the climate of the planet.Moreover, a robust RTC is run offline in order to de-termine the radiative properties of such an atmosphere.Intermediate complexity 3D GCMs have the potential toinclude more details compared to 1D atmospheric mod-els, retaining enough computational speed to allow forparameter space exploration.Our main conclusions are as follows:1.
Proxima b climate simulation.
The recently dis-covered planet Proxima b is used as a case study,assuming a 1:1 gravitational resonance. A surfacetemperature distribution consistent with an openocean day-side, and a cold and dry night-side isreported. This is in line with Boutle et al. (2017)and Del Genio et al. (2019). The permanent day-side heating is partially distributed in the night-side by the slow atmospheric circulation. Thus, inthe night-side, energy is irradiated towards spacein the form of IR radiation in a very efficient radia-tive cooling process. Consistent with other find-ings, e.g. Selsis et al. (2011), Showman & Polvani(2011), Cowan et al. (2012) and Showman et al.(2013), it has been found that the warmest place ofthe planet surface is not located at the sub-stellarpoint, but it stands eastwards to that region. Thismay be due to the atmospheric superrotation asso- -D simulations for Proxima b detectability -5 0 5 ∆ (M - N) [ppm] -10-50510 ∆ ( N - Q ) [ pp m ] i = 22.5° a) -5 0 5 ∆ (M - N) [ppm] -10-50510 ∆ ( N - Q ) [ pp m ] i = 45° b) -5 0 5 ∆ (M - N) [ppm] -10-50510 ∆ ( N - Q ) [ pp m ] i = 67.5° c) -5 0 5 ∆ (M - N) [ppm] -10-50510 ∆ ( N - Q ) [ pp m ] i = 90° d) T i m e [ d ] Figure 11. Color-color scatter plot . The color variation of the Proxima Centauri/Planet b system during one full orbit forfour different orbital plane inclination angles, respectively 22 . ◦ , 45 ◦ , 67 . ◦ , and 90 ◦ . The color variation is obtained evaluatingthe magnitude of the system in three different bands reported in Table 4. ciated with the planet rotation rate. The simula-tions presented here, performed with an interme-diate complexity model integrated with an offlineRTC, are in agreement with model runs made withmore sophisticated GCMs on one hand and on theother hand they allow to compute the exoplanetspectrum with a resolution of 1 nm. Consider-ing the very limited computational effort, inter-mediate complexity models with offline RTC rep-resent a suitable tool to perform different sensitiv-ity studies and, at the same time, to accuratelyestimate the emitted and reflected planet radia-tions.2. Detection via thermal phase curve.
Photometricmeasurements of the planet thermal emission withforthcoming instruments will be more easily ex-ploited choosing the appropriate spectral band.This choice is not straightforward since, in eachspectral band, it depends on the trade-off amongthe planet-to-star contrast, the amplitude of thethermal phase curve and the available photons,which affect the achievable photometric precision.In the case of cold planets, the contrast betweenthe IR flux of the planet and that of the star ishigher for λ > µ m. This is usually the spec-tral region where the amplitude of the thermalphase curve of a planet in the habitable zone isdetectable with broad band photometry. How-ever, as reported in the literature, the presence of an atmosphere mitigates the amplitude of thermalphase curve given the role of circulation in heat re-distribution (see Turbet et al. 2016; Boutle et al.2017 for a more extensive description). This im-plies that, in similar conditions, the thermal phasecurve modulation is smaller for a planet with at-mosphere compared to a planet without it. Conse-quently, this affects the possible detection of sucha planet, that is more favorable in case of the ab-sence of an atmosphere. Therefore, a fast modelto compute the emitted IR spectrum of an exo-planet, including the effects of its atmosphere, isneeded to choose the most effective spectral bandin thermal phase curve observations.3. Detection limits for JWST and ELT.
To under-stand the feasibility of a photometric detection ofProxima b, we evaluate the prospected limit of de-tection for the MIRIM instrument on board of theJames Webb Space Telescope. Analyzing the in-frared planet/star contrast for the F2100W filterof MIRIM ( λ = 21 µ m), we find that the ampli-tude of the planet thermal phase curve increasesby more than one order of magnitude comparedto the same parameter computed for the case ofthe OLR. Taking into account the collecting areaof JWST, MIRIM filter efficiency and an exposuretime of 5 hours, we evaluate a photometric pre-cision of 5 . Galuzzo et al. culator, obtaining, for the same exposure time, aphotometric precision of 7 . >
15 ppm all over the planet orbitalplane inclination range 15 ◦ > ι > ◦ , and there-fore detectable at the level S/N ≃ ∼ ≃
1. In this case the N band is considered, where theachievable photometric precision is 0 .
85 ppm, andthe amplitude of Proxima b thermal phase curveis > ◦ > ι > ◦ .However, we have to note that in the case ofJWST/MIRI this estimate is based on the as-sumption that total noise derives from shot noise,telescope thermal and scattered light, and fromother celestial sources, e.g. , zodiacal light, inter-stellar medium, and cosmic infrared background(Reach et al. 1997; Kelsall et al. 1998; Krick et al.2012) as computed using the JWST ETC. Thisestimate does not take into account any possibleextra contribution that can potentially affect thenoise floor. However the final performance of MIRIinstrument will be fully evaluated only after theJWST commissioning, and this lead us to focusthe analysis on photon-noise dominated observa-tions. Nevertheless we briefly discuss here the ex-pected performance of MIRI. Based on the per-formance of Spitzer, the noise floor for MIRI wasestimated by Greene et al. (2016) to be ∼
50 ppm.Fauchez et al. (2019) revised the noise floor valueto a more optimistic ∼
25 ppm at 1 σ confidencelevel, that would allow a detection for an orbitalplane inclination angle & Detection via color variations.
Finally, we con-sider an alternative method to detect exoplanetsby analyzing the color variation of an exoplan-etary system in the infrared bands due to thepresence of an orbiting planet. Color variation isvery sensitive to the orbital inclination and to theplanet temperature gradient between day-side and night-side. For a non-face-on orbit, the more theplanet’s hemispherical temperature difference is,the greater the color variation will be during theorbital period. For the case study of this work,the color index variation M − N correlates withthe variation N − Q . This correlation reflects thesymmetry of the system under consideration. Suchanalyses can be very helpful to independently con-firm the presence of non-transiting exoplanets an-alyzing the periodic color shift of a star.To date, because of the lack of observations in the midinfrared region with sufficient photometric precision,characterization of the atmosphere of non-transiting ter-restrial exoplanets is very challenging. To foster in-frared broad band photometric observations of exoplan-etary systems, an improvement in photometric precision( <
10 ppm), at wavelengths above the 10 µ m is neededfor the next generation telescopes. At the same time,the atmospheric models can pave the way for futuremeasurement campaigns giving for instance the orderof magnitude of the expected flux on telescopes, settingthe observational limits and the required precision forthe detection. ∼ solare) and from theAtmospheric and Climate Sciences Institute (ISAC) ofthe Italian National Research Counsil (CNR) withinthe Joint Research PhD Program in Astronomy, Astro-physics and Space Science between the universities ofRoma Tor Vergata, Roma Sapienza and INAF. We arealso grateful to professors Nicolas Iro, Valerio Lucarini,Edilbert Kirk and Brunella Nisini for technical assis-tance and support. Thanks to Ilaria Giovannelli andAngela Stabile for proofreading the article. The authorsthank the anonymous reviewer for her/his valuable helpin improving the manuscript. Software:
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