Detecting Atmospheric Molecules of Temperate Terrestrial Exoplanets using High-Resolution Spectroscopy in the Mid Infrared Domain
DDraft version February 8, 2021
Typeset using L A TEX preprint2 style in AASTeX63
Detecting Atmospheric Molecules of Temperate Terrestrial Exoplanets usingHigh-Resolution Spectroscopy in the Mid Infrared Domain
Yuka Fujii
1, 2 and Taro Matsuo National Astronomical Observatory of Japan Earth-Life Science Institute, Tokyo Institute of Technology Nagoya University (Accepted January 28, 2021)
ABSTRACTMotivated by the development of high-dispersion spectrographs in the mid-infrared(MIR) range, we study their application to the atmospheric characterization of nearbynon-transiting temperate terrestrial planets around M-type stars. We examine thedetectability of CO , H O, N O, and O in high-resolution planetary thermal emissionspectra at 12-18 µ m assuming an Earth-like profile and a simplified thermal structure.The molecular line width of such planets can be comparable to or broader than theDoppler shift due to the planetary orbital motion. Given the likely difficulty in knowingthe high-resolution MIR spectrum of the host star with sufficient accuracy, we proposeto observe the target system at two quadrature phases and extract the differentialspectra as the planetary signal. In this case, the signals can be substantially suppressedcompared with the case where the host star spectrum is perfectly known, as some partsof the spectral features do not remain in the differential spectra. Despite this self-subtraction, the CO and H O features of nearby ( (cid:46) and N O in a 1 barEarth-like atmosphere, this method would be sensitive when the mixing ratio is 1-10 ppm. The detectability of molecules except O is not significantly improved when thespectral resolution is higher than R (cid:38) , Keywords: planets and satellites: atmospheres — planets and satellites: terrestrialplanets — astrobiology INTRODUCTION
Corresponding author: Yuka [email protected]
Spectroscopy of Earth-sized planets aroundthe so-called habitable zones (HZs; e.g., Kast-ing et al. 1993) is one of the key near-future tar-gets in astronomical observations. Several ap- a r X i v : . [ a s t r o - ph . E P ] F e b proaches have been put forward so far. The firstmajor approach is direct (high-contrast) imag-ing. Since the late 20th century, space-baseddirect imaging possibilities—with coronagraphsin the visible and near-infrared domains, or us-ing nulling interferometers in the mid-infrared(MIR) domain—have been examined and wereencapsulated in the proposed missions like TPF-C, TPF-I, and Darwin (e.g., Levine et al. 2009;Beichman et al. 1999; L´eger et al. 1996). Thesestudies are inherited by the ongoing discussionsfor the future space missions for direct imagingof scattered light of Earth-sized planets (e.g.,Starshade with Roman Space Telescope, LU-VOIR, HabEx, LIFE).In the meanwhile, the successful atmosphericcharacterization of Hot Jupiters through trans-mission spectroscopy, eclipse spectroscopy, anddetection of phase variations has encouragedits application to smaller Earth-sized planetsaround late-type stars—this is the second ap-praoch (see a review by Deming & Seager 2017,and references therein). It has actually beenapplied to the Hubble Space Telescope (HST)observations of TRAPPIST-1 planets (Gillonet al. 2016, 2017), the Earth-sized transitingplanets around the habitable zone of an M8-type star, while only the upper limit of atmo-spheric features have been obtained (de Witet al. 2018; Zhang et al. 2018). The upcom-ing James Webb Space Telescope (JWST) willbe used for more sensitive transit spectroscopyof smaller planets in a wider wavelength range(Beichman et al. 2014; Greene et al. 2016).The high-dispersion spectrographs on the next-generation ground-based telescopes (i.e., ex-tremely large telescopes) may also be used fortransit transmission spectroscopy to identify theatmospheric features of Earth-sized exoplanetsburied in a number of telluric absorption lines(e.g., Snellen et al. 2013).The third approach to study potentially hab-itable exoplanets is to combine high-contrast imaging and high-resolution spectroscopy withthese next-generation ground-based telescopes(e.g., Snellen et al. 2015). Such observa-tions using ground-based telescopes are plannedmainly in the near-infrared wavelengths, so asto avoid thermal background that is inevitablefor ground-based observations at longer wave-lengths, while achieving the spatial resolutionnecessary for high-contrast imaging.Lastly, the atmospheric features of potentiallyhabitable planets may be identified in the com-bined spectrum of the star and the planet inthe MIR range, without a planetary transit ora starlight-suppressing instrument (e.g., Kreid-berg & Loeb 2016; Snellen et al. 2017). Indeed,the planet-to-star flux ratio of potentially hab-itable planets is significantly improved in theMIR domain ( ∼ a few tens of parts-per-millionor larger) compared with that in the shorter vis-ible domain ( ∼ − or less) as shown in the up-per panel of Figure 1, and it is not unrealisticto detect planetary signal in the combined spec-tra. Approximately estimating the wavelength-dependence of the signal-to-noise ratio for theplanet signal per wavelength resolution elementby N p ∆ λ/ √N (cid:63) ∆ λ = (cid:112) N p C ∆ λ = (cid:112) N p Cλ/ R ( N p and N (cid:63) are the photon spectrum of theplanet and the star, respectively, ∆ λ is thewavelength width of the resolution element, C is the planet-to-star flux ratio, i.e., C ≡ N p / N (cid:63) ,and R is the fixed spectral resolution), the MIRdomain, specifically around 13-100 µ m, is mostuseful (the lower panel of Figure 1). The uniqueadvantages of this MIR approach are that (1)unlike high-contrast technique it does not re-quire specialized instruments to occult stellarflux, and that (2) unlike transmission or eclipsespectroscopy it can be applied to both transitingand non-transiting planets. The latter is criticalto increase the number of targets, as the tran-sit probability of habitable-zone planets is up toabout 5%. IR HR for HZ planets p h o t o n c o un t p e r r e s o l u t i o n e l e m e n t ( a r b i t r a r y un i t ) p l a n e t - t o - s t a r f l u x r a t i o ( = c o n t r a s t ) wavelength [ m]0.00.20.40.60.81.0 S / N p e r r e s o l u t i o n e l e m e n t ( a r b i t r a r y un i t ) Figure 1.
Upper panel: A schematic figure of thephoton count per wavelength resolution element as-suming a black body planet spectrum with 288 K(i.e. N p ∆ λ ; red dashed) and the planet-to-star fluxratio assuming a black body spectrum mimicking amid-M host star (i.e. C ; blue solid). The wave-length dependence of the planet-to-star flux ratiodoes not depend on the spectral types of the staras long as the stellar spectrum can be approximatedby Rayleigh-Jeans law. Lower panel: Signal-to-noise ratio per wavelength resolution element as afunction of wavelength, estimated by the productof the planet photon count and the planet-to-starflux ratio. Along this line, Kreidberg & Loeb (2016)proposed low-resolution spectroscopy of Prox-ima Centauri systems to try to detect 9.6 µ mO features originated from the atmosphere ofProxima Centauri b, the nearest non-transitingpotentially habitable planets (Anglada-Escud´eet al. 2016).Snellen et al. (2017) proposed that medium-resolution spectroscopy (MRS) in the MIRrange can be used to identify high-frequency fea-tures due to planetary atmospheric molecules inthe combined spectra, and they estimated thatCO features of Proxima Centauri b would bedetected after 5 days of observations with MRSmode of JWST/MIRI. Although these are en- couraging possibilities, such observations relyon the precise knowledge of the stellar spec-trum as well as the sensitivity of the detectorelements.While the above studies have in mind theupcoming JWST that have only low-resolutionand medium-resolution capabilities in the MIR,technologies for high-dispersion spectrograph inthe MIR have been recently developed for futurecryogenic space telescopes, including SPICA(e.g., Sarugaku et al. 2012). The technolo-gies are expected to largely reduce the size ofthe MIR spectrograph and enhance its through-put. In the further future, Origins SpaceTelescope (OST) is also contemplating high-resolution spectrograph with a larger aperture(Sakon et al. 2018). With high-resolution spec-troscopy ( R ∼ , § § ATMOSPHERIC FEATURES IN MIRHIGH-RESOLUTION SPECTRAIn this section, we model high-resolution plan-etary spectra of an Earth-like planet and dis-cuss the characteristics of the spectral featuresof molecules of interest. These modeled spec-tra will be used as input for the detectabilityanalyses in Section 3.2.1.
Model Atmosphere
Our model atmosphere is based on Earth’satmosphere except for the temperature profile.We consider four molecules that are present inEarth’s atmosphere and are radiatively activein the mid infrared range: CO , H O, N O,and O . The vertical profiles of the mixingratios of these molecules are taken from the“US standard” model and are shown in the leftpanel of Figure 2. The surface temperature isset at 288 K, again referring to the “US stan-dard” model. The vertical temperature profileis, however, replaced by a simplified one com-prised of a troposphere with a constant lapserate (Γ = g/C p where g is the gravity and C p is the specific heat capacity) and an isother-mal stratosphere. The removal of stratosphericthermal inversion is motivated by the fact thatO , even if it exists, does not lead to a strongthermal inversion under the irradiation of M- mix ratio p r e ss u r e [ b a r ] CO H ON OO
150 200 250 300 temperature [K]
Figure 2.
The assumed vertical profiles of themixing ratios of the molecules considered (left) andtemperature (right). The mixing ratio of moleculesare based on “US standard” model. The tempera-ture profile is determined by the dry adiabatic lapserate (9.8 K/km) in the lower atmospheres below0.1 bar, above which an isothermal profile is as-sumed.description symbol valuesurface pressure P surf T surf
288 Ktropopause P tp g tropospheric lapse rate Γ(= g/C p ) 9.8 K/km Table 1.
Assumptions for atmospheric profiles. type stars due to the reduced near-UV flux.The effects of the atmospheric profile on the de-tectability of molecules are discussed in Section5.3.1. For simplicity, the effects of clouds areignored.The surface pressure is fixed at 1 bar, and thetropopause is set at 0.1 bar. This tropopausepressure is consistent with the observations ofSolar system planets (e.g., Robinson & Catling2014) and 3D climate simulations for habitableplanets around M-type stars (e.g., Fujii et al.2017).Given a vertical profile, the top-of-atmosphereoutgoing radiance at wavelength λ and the co- IR HR for HZ planets µ , L ( λ, µ ), is computedby L ( λ, µ ) = (cid:90) B ( T ; λ ) exp( − τ /µ ) dτ /µ (1) τ ≡ (cid:90) ∞ z k [ T ( z ) , P ( z )] x ( z ) n ( z ) dz (2)= (cid:90) p k [ T ( P ) , P ] x ( P ) dPµ atm g (3)assuming a no-scattering atmosphere.The cross sections of molecules are based onHITRAN2016 (Gordon et al. 2017) and the linesare broadened by the Voigt functions using thealgorithm of Zaghloul & Ali (2011) with the par-tition functions adopted from HAPI program(Kochanov et al. 2016). We impose the cut-off of the line wings at 100 cm − apart fromthe line centers. We do not include the con-tinuum absorption (e.g., H O continuum), as itdoes not significantly affect the detectability ofhigh-resolution features.For the efficient evaluation of equation (1) at alarge number of the wavelength grid points, weemployed GPU computation through PyCUDA.The integral in equation (3) is performed with50 equi-distributed points in log P space andthat in equation (1) with 50 equi-distributedpoints in log τ space (from 10 − to 10 ), usingthe trapezoidal rule.Thermal emission spectrum is calculated withthe opacities of all four molecules included. Inaddition, we also calculate the spectra with theopacity of only one molecule turned on, in orderto discuss the spectral characteristics and de-tectability of individual molecules in isolation.To obtain the total thermal emission from theplanet, equation (1) needs to be integrated overthe planetary disk. With several trials, we findthat the disk-averaged radiance that integratesequation (1) over different µ with the weight ofthe projected area is close to the radiance at µ = 0 .
6. Thus, we represent the disk-averagedradiance by the radiance with µ = 0 .
6. Doppler broadening due to planet rotation is not in-cluded; HZ planets around M-type stars arelikely to be tidally locked, which means the ro-tational velocity of ∼ ∼ − µ m,is sufficiently smaller than the wavelength reso-lution elements considered in this paper.2.2. Model Spectra and Their Characteristics
Figure 3 presents the major features in high-resolution spectra ( R = 30 , has the prominent rotational-vibrationalfeatures around 15 µ m associated with the fun-damental bending mode ( ν ). The strongestlines on the P- and R-branches are separatedby ∼ . µ m, corresponding to the rotationalenergy ∼ . − , well resolved with R =30 , O has rotationallines that broadly spread in the MIR range. The17 µ m N O band is mainly due to the bendingmode ( ν ) and has a structure similar to the15 µ m CO band. Among these, CO largelycontribute to shaping the overall shape of theall-included spectrum, although the minor fea-tures due to H O and N O can also be seen.Compared to these bands, the famous 9.7 µ mO band with the overlapping fundamental vi-bration modes (symmetric ν and asymmetric ν ) is densely populated with lines. A weaker O band exists around 14.5 µ m, corresponding tothe bending mode, which also features clusteredlines in a narrow bandpass. The latter is largelymasked by CO in Earth’s thermal emissionspectra. We find that this band start to kickin when CO is smaller than ∼ -poor atmosphere exist? It is possible, asCO abundance in general depends on the car-bon cycles, as well as how much the planet ac-
12 13 14 15 16 17 180510
All
12 13 14 15 16 17 180510 CO H O r a d i a n c e [ W / m / m / s r ] N O O wavelength [ m] O wavelength [ m] Figure 3.
High-resolution ( R = 30 , ∼
100 km/s). quires and retains carbon. Planets which devel-ops higher weathering rate may turn into CO -poor worlds (e.g., Nakayama et al. 2019). In theabsence of CO features, 14.5 µ m O band maybe more useful than the 9.7 µ m band, due tothe better intrinsic detectability (Fig. 1); seemore discussions in Section 4.2.Here we highlight a characteristics of thesehigh-resolution features—the relative width ofthe lines. As indicated in the right panel of Fig- ure 3, the broad lines extend beyond the wave-length resolution (5 × − µ m at 15 µ m) andthe width of the Doppler shift ( ∼ µ m at15 µ m; horizontal bars). This is partly due tothe intrinsic broadening of the lines. The halfwidth of the Lorentz profile (collisional broad-ening), which is important at pressures higherthan ∼ .
01 bar, is approximately constant in wavenumber for a given set of pressure and tem-perature, i.e., the width relative to the wave-
IR HR for HZ planets Table 2.
Assumptions for the host star and theplanetary orbit.description M5 star M8 starstar radius ( R (cid:63) ) 0.14 R (cid:12) R (cid:12) star temperature ( T (cid:63) ) 3000 K 2500 Kplanet/star flux ratio a ∼
70 ppm ∼
200 ppmplanet orbital radius 0.0485 au 0.0146 auplanet orbital period 11.26 days 2.27 daysplanet orbital velocity 46.83 km/s 69.70 km/s a Evaluated at 15 µ m, assuming a black bodyspectrum with 288 K for the planet spectrum. length is wider at longer wavelengths. At 1 barand 288 K, it is approximately 0.1 cm − , cor-responding to 0.002 µ m. The line shape alsodepends on the abundance of the molecule andthe vertical temperature gradient. Lines be-come broad if the opacity is so large that theatmosphere becomes optically thick at the farwings; this happens for CO and H O with ourmodel atmosphere. The broad lines have no-table influence on the analysis, as we will see inthe next section. DETECTABILITYIn this section, we examine the detectabilityof MIR molecular features of temperate Earth-sized planets presented in Section 2, assuminga high-dispersion spectrograph mounted on acryogenic telescope. We try to identify molec-ular features in the combined spectrum of thehost star and the planet. The assumptions formock observations and noise estimate are givenin Section 3.1, which is followed by the descrip-tion of our analysis procedures in Section 3.2.The resultant constraints on the contrast andthe orbital inclination are discussed in Section3.3. 3.1.
Mock observation
Targets
The prime target of this study is temper-ate rocky planets around M-type stars, becausethose around earlier-type stars have too largeplanet-to-star flux ratio for planetary signals tobe detectable in a reasonable amount of time.We initially considered three types of host star:early-, mid- and late-M stars. However, the typ-ical planet-to-star flux ratio with early-M starsis smaller than 10 ppm, making it extremelychallenging to detect planetary features. There-fore, we focus on mid-M and late-M stars.Our fiducial model assumes an M5 or M8 starat 5 parsecs. The assumed host star and plan-etary parameters are summarized in Table 2.Additionally, the case study for Proxima Cen-tauri b is also presented, where the host starproperties are the same as those of M5 star inTable 2, the distance is set to 1.3 parsecs, andthe planetary radius is assumed to be 1.1 Earthradius (e.g., Snellen et al. 2017).The inclination of the planetary orbit, whichcontrols the amplitude of the planetary line-of-sight velocity, is fixed at 60 ◦ .The host star spectra are taken from the BT-Settl model (Allard et al. 2012) with the corre-sponding effective temperatures, while assum-ing log g = 5 . .
0. This is anupdate from the previous studies on the de-tectability of spectral features of Proxima Cen-tauri b where the black-body spectrum is as-sumed (Snellen et al. 2017; Kreidberg & Loeb2016). 3.1.2.
Configuration
Figure 4 illustrates the observational configu-ration. We assume that the mock observationsare carried out when the planet is near φ = 90 ◦ and near φ = 270 ◦ , where φ is the orbital lon-gitude (Figure 4). This is because the orbitalinclination would be constrained best when thedata cover the orbital phases where the radialvelocity changes the most.For a planet around a M5 (M8) star, mockobservations are continued for 1 (0.25) day cen-tered at φ = 90 ◦ and for another 1 (0.25) daycentered at φ = 270 ◦ , which cover approxi-mately 32 ◦ (40 ◦ ) on each side. These two ca-dences are repeated until the parameters areconstrained, and the total integration time isrecorded. Figure 4.
Observational configuration showing thegeometrical parameters. The data near φ = 90 ◦ and φ = 270 ◦ are used in this study. Instruments and observationalconfigurations
Mock observations are carried out with a high-resolution spectrograph at 12-18 µ m with theresolving power of R = 30 , R ∼ , µ m) (e.g., Kaneda et al. 2018) andby the expected resolution of OST/MISC (e.g.,Sakon et al. 2018). The dependences on the Figure 5.
Schematic figures showing the signals tobe detected. Analysis (A) (left) utilizes the high-frequency features of the spectra extracted by sub-tracting the moving average from the spectrum,while Analysis (B) (right) utilizes the difference ofthe Doppler shifted spectra from the average spec-tra. spectral resolution and the bandpass are exam-ined in Section 4.The total throughput including the quan-tum efficiency of the detector is assumed tobe 0.2. We note that the throughput of theoptical system of existing high-resolution spec-trographs installed on ground-based telescopeshave reached approximately 60% (e.g., Ikedaet al. 2016, 2018), and the throughput of fu-
IR HR for HZ planets description symbol valuespectral resolution R D ξ d R p R ⊕ (= 6 . × m)exposure time τ exp Table 3.
Fiducial values for observational param-eters. The scaling of the required integration timeby these parameters are given in equation (13). ture instruments could be higher than what weassume here. It is trivial to scale our results bythroughput; see Section 3.3.1.We collect data every 1800 sec (i.e., exposuretime is assumed to be 1800 sec). Due to thechange of the planetary radial velocity, the plan-etary spectrum is Doppler shifted relative to thehost star spectrum on the detector plane. Overthe course of the planetary orbital motion, theplanetary spectrum moves beyond the resolu-tion elements unless the orbital inclination isclose to zero (i.e., face-on orbit), as the radialvelocity amplitudes shown in Table 2 (and theassumed orbital inclination of 60 ◦ ) are largerthan the velocity corresponding to the resolu-tion element, c/ R ∼
10 km/s. )3.1.4.
Signal and noise
The total photoelectron count that the de-tector receives is the summation of the plan-etary light ( N p ), stellar light ( N (cid:63) ), zodiacallight ( N zodi ), thermal background of the tele-scope ( N tele ), and the dark current ( N dark ). Weassume that the contribution from the zodicallight and the dark current are perfectly sub-tracted through a post-processing. This leaves N total = N (cid:63) + N p alone as a signal.The shot noise from all of these factors con-tributes to the observational noise, although theshot noise due to the planetary flux is negligi-ble compared to that from the stellar flux. Anadditional factor that is taken into account is the read noise. The systematic noises such asa fringe of the detector are assumed to be per-fectly removed; the effect of systematic noise isdiscussed in Section 5.2.2. These assumptionsimply the Gaussian random noise with the fol-lowing standard deviation for j -th wavelengthelement at wavelength λ j : σ ,j = N star , j (1 + ξb j ( T (cid:63) )) + N zodi , j + N tele , j + N dark , j + σ (4)where σ represents the read noise, b ( T ) is theBose factor, and ξ is the total throughput.The Bose factor, b ( T ), is to take account ofthe sub-Poissonian nature of the photon countstatistics at hν (cid:28) kT (e.g., Boyd 1982): b j ( T ) = 1exp (cid:16) hcλ j kT (cid:17) − λ ∼ µ m) of M-typestars ( ∼ b ∼ .
7. Multiplied by thethroughput ( ξ = 0 . Planet/star spectra — The photoelectron countsof the planet and the host star per exposure aresimply: N p ( λ ) = F L p ( λ ) · πR (cid:18) d (cid:19) (6) N (cid:63) ( λ ) = F L (cid:63) ( λ ) · πR (cid:63) (cid:18) d (cid:19) (7) F ≡ π (cid:18) D (cid:19) ξτ exp λ R (8)0 target distance [pc]10 p h o t o n c o un t s / s e c / D = 6.5 m mid-M (10 m)late-M (10 m)mid-M (20 m)late-M (20 m)zodi Figure 6.
Photon count of the zodiacal light(black) and the starlight (colors) at wavelength10 µ m (solid line) and at 20 µ m (dashed line),per exposure time (1800 sec) per wavelength res-olution element ( λ/ R ). These numbers can alsobe compared with dark current (360 e − /exposure)read noise, 14 × e − /exposure. where L p and L (cid:63) represent the radiance of theplanet and star, respectively, while R p and R (cid:63) represent the radius of the planet and the star,respectively. The meanings of other parame-ters are summarized in Table 3 together withour fiducial values. Here F is used to denotethe common factor related to the observationalconfiguration. Zodiacal light — The zodiacal flux of the SolarSystem is set to 15 MJy/sr (Glasse et al. 2015)and is assumed to be constant over the observ-ing wavelength range. The zodiacal light inthe target system is not included in our simu-lation because it is much fainter than the othersources. Thus, N zodi = F f zodi · π ( θ aperture ) (9)where f zodi is the zodiacal flux per wavelengthper steradian (rather than per frequency as rep-resented in Jansky per steradian) and θ aperture denotes the aperture radius. The aperture ra-dius should be determined by the balance be-tween the shot noise of the thermal background and the systematic noise (Matsuo et al. 2018).Based on the analytical formulation on the rela-tion between the aperture radius and systematicnoise (Itoh et al. 2017), the aperture radius is setto 1.85 arcsecond, corresponding to 4 times thediffraction limit at 15 µ m such that the system-atic noise is reduced down to 100 ppm under acondition that the pointing jitter of the OriginsSpace Telescope is 22 milli-arcsecond (RMS),corresponding to approximately 0.05 λ/D at 15 µ m (Leisawitz et al. 2018). Telescope background — The thermal light andstray light from a telescope assembly also con-tributes to the background light. For the JWSTMIRI, the telescope background can be ap-proximately fitted by a combination of severalblackbody radiations with temperatures rang-ing from 50 to 70 K (Glasse et al. 2015). Whenthe telescope is cooled down to below 10 K, asplanned for SPICA and OST, and the telescopebackground becomes negligible at < µ m. Dark current — The dark current is assumed tobe 0.2 e − s − based on the performance of theSi:As detector for the JWST MIRI (Rieke et al.2015), but this never becomes of relative impor-tance in our study. Read noise — The read noise is assumed to be14 e − /read assuming the Fowler-eight sampling(Rieke et al. 2015). The loss time due to thereadout is not considered in the paper. Eachresolution element is sampled by 4 pixels. Withthese assumptions, read noise never becomesdominant for the exposure time of 1800 sec. Wenote that 1800 sec is longer than the typical val-ues for JWST. The reduction in the exposuretime can lead to a significant contribution fromread noise. 3.2. Analysis
Because the planetary signal is a tiny por-tion in the total spectrum, it is critical to sub-tract the stellar spectra precisely from the to-
IR HR for HZ planets
Analysis (A): with a well-modeled stellarspectrum
In the first analysis, we follow the procedureof Snellen et al. (2017), assuming that the finestructure of the stellar spectrum can be mod-eled precisely. Even with this assumption, wecannot separate the host star and the planetspectra from observations alone, so we take thefollowing steps:1. The model stellar spectrum is fitted to thedata (that is the combined spectrum ofthe star and the planet), by varying the
13 14 15 16 17wavelength [ m]10 s p e c t r a ( a r b i t r a r y s c a l e ) mid-M late-M Figure 7.
MIR spectra based on BT-Settl model(Allard et al. 2012). scaling of the spectrum as well as the stel-lar parameters.2. The best-fit stellar spectrum is subtractedfrom the data.3. The residual spectrum is corrected by sub-tracting its moving-average.4. The model planet spectrum, which is alsocorrected through the moving-averagesubtraction (the bottom panel of Figure5), is fitted to the corrected residual spec-tra.In Step 1, we use the input BT-Settl modeland fit for the absolute scale. The best-fit scaleis slightly larger than the input stellar model,due to the contribution from the planet spec-trum. In other words, some fraction of the plan-etary spectrum is subtracted in Step 2. This re-sults in a trend in the residual spectrum, whichis corrected in Step 3.Finally in Step 4, the high-frequency featuresare fitted by the model planet spectrum. Forsimplicity, our fitting model is the same as theinput model, similar to Snellen et al. (2017), andwe consider two fitting parameters: the planet-to-star contrast C and the orbital inclination I .The parameter estimate is based on the poste-2rior probability, P ( c, i |{N i ( t k ) } ): P ( C, I |{N res ,jk } ) = L ( {N res ,jk }| C, I )Π( C )Π( I )(10)The N res ,jk represents the corrected residualspectra at j -th wavelength elements and k -thobservation epoch. The likelihood is simply: L ( {N res ,jk | c, i ) ∝ exp (cid:18) − χ (cid:19) (11) χ ≡ (cid:88) { j,k } (cid:32) N obsres ,jk − C N theoryres ,jk ( I ) σ j,k (cid:33) . (12)We assume a flat prior for contrast C between0 and 10, and a flat prior for the orbital incli-nation I between 0 to 90 degree; Π( C ) = const. and Π( I ) = const. This means that the pos-terior probability is simply equivalent to thelikelihood function. The posterior probabilityis normalized so that the total is unity. The 1 σ ,2 σ , and 3 σ contours of the posterior probabilityare close to those of ∆ χ measure (e.g., Snellenet al. 2017), with a slight difference due to thenon-linear I -dependence of the model.3.2.2. Analysis (B): with unknown stellarspectrum
In the second analysis, we do not assume thatthe stellar spectrum is known a priori. Instead,we consider the time average of the combinedspectra of the star and the planet and assumethat the stellar spectrum is fully included in thisaveraged spectrum, which is valid if the stel-lar spectrum is stable in time. On the otherhand, the spectral features of the planet shouldremain in the average-subtracted residual spec-trum, due to the Doppler shift caused by itsorbital motion.The analysis procedure is as follows:1. The average of the spectra at differentplanetary orbital phases is obtained.2. The average spectrum is subtracted fromthe spectrum at different orbital phases. 3. The model planet spectrum, which is alsoDoppler-shifted and average-subtracted(the bottom panel of Figure 5), is fittedto the set of residual spectra.The parameter estimate in Step 3 is performedin the same way as Analysis (A) (equations (10)-(12)).Figure 5 illustrates the signal that can be usedin this analysis. The average of the spectrum at φ = 90 ◦ and that at φ = 270 ◦ is shown in theblack line in the upper panel, and the average-subtracted spectra are shown in the lower panel.During this subtraction process, some portionsof the planetary spectral features are cancelledout, reducing the signal level. This effect is sub-stantial in the case of MIR observations of po-tentially habitable planets whose strongest linesare broader than the Doppler shift (Figure 3).The situation is different from the typical high-resolution spectroscopy of hot Jupiters at theshorter wavelengths, where the lines are nar-rower and the Doppler-shift is larger. In sucha case, the Doppler shift moves the line beyondtheir intrinsic width and the average-subtractedspectra are more similar to the original spec-trum.3.2.3. Notes on cross-correlation analysis
High-resolution spectroscopy of hot-Jupitersystems have been routinely analyzed throughcross-correlation function (Snellen et al. 2010;Brogi et al. 2013). While this technique is use-ful for detecting high-frequency features, its sta-tistical treatment and the uncertainties in theestimated model parameters are not straight-forward (e.g., Brogi et al. 2017). On the otherhand, fitting observed data with theoreticalmodels by minimizing the sum of squared resid-uals offers a more plain interpretation (Snellenet al. 2017). Thus, in this paper, we employ thelatter method. 3.3.
Results
IR HR for HZ planets Figure 8.
The 1 σ (solid lines), 2 σ (dashed lines), and 3 σ (dotted lines) confidence intervals for planetsaround a mid-M star (upper panels) and a late-M star (lower panels), based on analysis (A), i.e., when thestellar spectrum is precisely determined. Both the mock data and the fitting model are based on the modelthermal emission spectra presented in Figure 3. The constraints from two integration times are presentedfor some cases, in order to show how the constraints are developed as the integration time becomes longer.The blue colors imply that the presence of the molecule is detected (i.e., the C = 0 is rejected by 3 σ ) andthe inclination is not well constrained, while the red colors imply that both the contrast and inclination areconstrained. The corresponding signal-to-noise ratios of the host star spectrum per wavelength resolutionelement (SN) are also reported. Figures 8 and 9 summarize the results ofAnalysis (A) and Analysis (B), respectively,performed on the thermal emission spectrawith all molecules included and with individ-ual molecules in isolation (Figure 3). The solid,dashed, and dotted lines present the 1 σ , 2 σ , and3 σ constraints in the contrast-inclination plane(i.e., 68.27%, 95.45%, and 99.73% probability),after the indicated integration time. The cor-responding average signal-to-noise ratio (SN) ofthe host star spectra per wavelength resolutionelement is also presented.As expected, detecting any molecule is eas-ier for planets around late-M stars than aroundmid-M stars due to the larger planet-to-star fluxratio and, for analysis (B), to the larger radialvelocity amplitude. In the model consideredhere, the total observation time required for a M5-star system is by a few times larger thana M8-star system, or 3 times smaller signal-to-noise ratio of the host star.When the host star spectrum is accuratelyknown and corrected (Analysis (A); Figure 8),the spectral features of an Earth-like atmo-sphere at 5 prsecs away can be detected within afew days of total observation time, even aroundmid-M systems (the leftmost column). Com-pared to this optimistic scenario, Analysis (B)requires approximately 4 times longer obser-vations to detect the spectral features of thesame target, or doubled signal-to-noise ratio ofthe host star flux. This is because of the self-subtraction discussed in Section 3.2.2.For comparison, we also perform the sameanalysis assuming only one of the molecules asopacity source (the lower five panels of Figure4 Figure 9.
Same as Figure 8, but the mock data are now analyzed by analysis (B). . In addition, for Analysis (B), the contrastand the inclination angle tend to degenerate forpure CO or pure H O atmospheres. This is be-cause when a small orbital inclination (i.e., closeto face-on) is assumed, the Doppler shift of theplanetary spectrum is small and the amplitudeof the differential spectrum (the lower panel ofFigure 5) is also small, which is then compen-sated by a large contrast. Note that the or-bital inclination is poorly constrained even withAnalysis (A) for pure CO or pure H O atmo-spheres, due to the broad nature of the spectrallines.Compared to these two molecules, the self-subtraction is not substantial for O because theO bands are densely populated by narrow lines,and the detectability through Analysis (B) issimilar to that of Analysis (A). Furthermore,the orbital inclination is well constrained assoon as the contrast is constrained to non-zero.N O features are also relatively good at con- straining the inclination, despite its relativelyweak features.In the spectrum with all the molecules in-cluded, the features of each molecule tend tobe more muted than the features of individualmolecules in isolation, due to the line overlaps.However, the spectrum become more rich in fea-tures, and the constraints on the contrast is asgood as for the pure-CO or pure-H O cases.Furthermore, the overlaps of the spectral fea-tures of individual molecules break the degen-eracy between the contrast and inclination forAnalysis (B), significantly improving the con-straints on the orbital inclination compared tothe pure-CO or pure-H O cases. As a result,both the contrast and the orbital inclination canbe reasonably constrained within ∼ Scaling and the application to the knowntargets
IR HR for HZ planets τ esp , , is propor-tional to: τ esp , ∝ (cid:18) R p R ⊕ (cid:19) − (cid:18) d (cid:19) (cid:18) D (cid:19) − (cid:18) ξ . (cid:19) − (13)In particular, the observations of the nearestpossible target, Proxima Centauri b, at the dis-tance of 1.3 pc and with the estimated radiusof ∼ . R ⊕ , would only require ∼ D =2 . ξ = 0 . ∼
14 days of total integration time. DEPENDENCE OF DETECTABILITYON SPECTRAL RESOLUTION,MOLECULAR ABUNDANCE, ANDBANDPASSIn the assessment in Section 3, we have madeseveral assumptions for the specifications of thespectrographs and the atmospheric profile. Inthis section, we discuss the effects of varyingthese assumptions on the detectability of themolecules.4.1.
Effects of Spectral Resolution
First, we discuss the dependence on the spec-tral resolution of the spectrograph. Let us rep-resent the signal by the total area of the shadedregion shown in Figure 5, namely the integra-tion of the absolute value of the differentialspectrum both in Analysis (A) and (B); ForAnalysis (A), the differential spectrum corre-sponds to the difference between the originalspectrum and the moving average, while forAnalysis (B) it is the difference between the
Figure 10.
The total areas of the filled region inFigure 5, one of the diagnostics of the signal, asa function of the spectral resolution, using Analy-sis (A) (left) or Analysis (B) (right). The fiducialatmospheric profile is assumed.
Figure 11. σ constraints in the contrast-inclination plane based on the observations of Prox-ima Centauri b with CO features using varyingspectral resolution, after 2 days (left) or 7 days(right) of integration. spectrum at a certain orbital phase and thetime-averaged spectrum.Figure 10 shows the signals defined above forAnalysis (A) and (B) as a function of the spec-tral resolution. Black line shows the case ofthe spectrum with all four molecules included(the bottom panel of Figure 3), while otherlines show the cases for the spectra of individualmolecules. As expected, the signal level mono-tonically increases as the spectral resolution in-creases. However, it is mostly saturated above6 R (cid:38) ,
000 except O , in both analysis (A) and(B). This is partly because the interval of thestrongest lines are ∼ . − . µ m and these linesstart to be resolved with R (cid:38) R (cid:38) , R (cid:38) , λ ∼ µ m), R (cid:38) , , wherethe narrow lines are densely populated. Thus,detection O benefits from the increased spec-tral resolution beyond R ∼ , R ∼ , R ∼ , Choice of the bandapss
Our fiducial bandpass is set to 12-18 µ m, based on the planned specification ofSPICA/SMI and OST/MISC. In this rangeof wavelengths, several other molecules haveprominent absorption bands, in addition to themolecules studied in this manuscript. They in-cludes NH , SO , and NO and they may alsobe useful for characterizing the surface environ-ment of potentially habitable planets.Although there is no planed high-resolutionspectrograph that goes beyond this bandpass, it would be worth considering the impact of thealternative choice of bandpass for future instru-mental designs. In the following, we briefly dis-cuss how the extension of the bandpass wouldaffect the prospects.If the bandpass is extended toward shorterwavelengths, a feature of particular interestwould be O µ m band (the bottom panel ofFigure 3). The peak line strength of this bandis approximately one order of magnitude largerthan the 14.5 µ m band and, combined with thefact that the shorter wavelength is in the Wien’sregime of the Planck function, the feature rela-tive to the continuum is deeper. However, thereduced planet-to-star contrast (Figure 1) doesnot make this band easy to detect. We findthat detection of O µ m O band would re-quire approximately 1.7 times longer integrationtime (or 75% photon noise) than the detectionof 14 µ m O band, in the absence of CO (notshown). In the presence of CO larger than 1ppm, 9.7 µ m band would be the only detectableband. The detectability of O µ m would beimproved for planets with higher surface tem-perature. The features at even shorter wave-lengths is even less likely to be detectable withthis method due to the small planet-to-star con-trast.At the wavelengths longer than 18 µ m, thereare few vibrational modes of simple molecules.However, the rotational lines of H O extend be-yond 18 µ m and adding longer wavelengths im-proves the detectability of H O. Using 12-24 µ mbandpass, the integration time required for thedetection of H O from the H O-only spectrum(the second panel of Figure 3) would be reducedto approximately 60%.4.3.
Molecular abundances that can be mostsensitively probed
The detectability also depends on the actualabundance of the molecules. While in trans-mission spectroscopy the detectability of certainmolecules generally increases as the abundance
IR HR for HZ planets Figure 12.
Same as Figure 10 but with varyingmixing ratio of CO . increases (ignoring the effects of clouds), this isnot the case for the high-resolution method con-sidered in this paper. It is true that the signalwould not be detected if the abundance is toosmall. However, larger abundances does not al-ways lead to the improved detectability, becausesome of the features start to saturate. For ex-ample, with the assumed Earth-like abundanceof CO ( ∼
330 ppm) the strongest lines of CO around 15 µ m are saturated (i.e., the spectrumis flattened) and do not significantly contributeto the signal. With larger abundance, the flat-tened region only increases, although the fea-tures associated with smaller opacities kick in.Thus, there is the optimal range of molecularabundance.To see such a dependence of detectability ofCO and N O, we created model spectrum withvarying mixing ratio assuming a 1-bar atmo-sphere with vertically uniform mixing ratio ofeach molecule. For each model spectrum, werepeated the analysis of Section 4.1 to see thedependence of the “signal” as a function of thespectral resolution. The result is shown in Fig-ure 12. The signal level is maximized whenthe mixing ratio is 1-10 ppm. A similar trendwas found for N O, with the signal level beingmaximized for 1-10 ppm. Therefore, this tech-nique is sensitive to relatively small amount ofmolecules. This would be rather complemen- tary to scattered-light observations where largerabundance of these molecules would be probed;see Section 5.1. DISCUSSION5.1.
Potential Targets and Synergy with othertechniques
The prime targets of the method studied inthis manuscript would be potentially habitableplanets around mid- to late-M stars within5 parsecs. The fact that this method does notrequire planetary transits is a significant advan-tage over transmission or eclipse spectroscopy,given the low transit probability ( ∼ ∼ µ m wouldbe larger than the abundance probed by thehigh-resolution technique (Section 4.3), thus thecombination would constrain a wide range of at-mospheric properties.The targets of MIR high-resolution techniqueare also complementary to the prime targetsfor transmission and eclipse spectroscopy. Themain scope of OST is currently to character-ize potentially habitable planets through tran-sit spectroscopy by achieving ultrahigh stabil-ity (see the technical report of OST). Thereare pros and cons for transit spectroscopy andfor the technique studied in this paper. Whilethe former may require less total observationtime for certain biosignature molecules (pro-vided that the noise floor could be down to a fewppm) than the latter, it has to visit the target50 times for TRAPPIST-1 planets (Tremblayet al. 2020) and more for less favorable targets,likely spanning 1 year or longer. The numberof visits of the high-resolution method studiedin this manuscript can be much smaller becauseof the longer observation time per visit. In ad-dition, the transmission spectroscopy could behampered by high-altitude thin clouds, whichdoes not significantly affect the high-resolutiontechnique. Thus, combining both techniqueswould expand our capability of investigating po-tentially habitable worlds.5.2. Effects of other noise
Time variability of stellar spectra
The major concern of this method is the vari-ability of high-resolution stellar spectra. Asidefrom sporadic flares, stars generally exhibit pho-tometric and spectroscopic variabilities mainlydue to starspots. Given that the signal fromthe planet is a tiny fraction of the stellar spec-
Table 4.
Nearby systems that are found to harborEarth-sized planets around habitable zones. Stellarparameters are based on Gaidos et al. (2014).Star name d Spectral type T (cid:63) Proxima Cen 1.3 pc M7 2883 KRoss 128 3.4 pc M5 3145 KGliese 1061 3.7 pc M6? 3000 K?Luyten’s 3.8 pc M4 3317 KTeegarden’s 3.9 pc M7 2700 KGJ 682 5.1 pc M5 3190 K trum, such variability potentially cases seriousproblem in the analysis.There is a growing amount of modeling ef-forts for the temperatures and covering frac-tions of star spots/faculae of mid- to late-Mstars based on observations. One piece of ev-idence comes from Doppler imaging. Dopplerimaging of mid- to late-M stars (Morin et al.2008; Barnes et al. 2015, 2017) estimates thataround a few % of the surface is covered withspots that are assumed to be cooler than otherarea by 200-400 K. Recently, characterization ofTRAPPIST-1, an M8 star harboring transitingtemperate Earth-sized planets, has attractedattention. The light curve of TRAPPIST-1observed by Kepler/K2 (0.43-0.89 µ m) shows ∼
1% peak-to-peak variation amplitude, whichmay be explained by rotating dark spots or fac-ulae. In contrast, the variability of
Spitzer at 4.5 µ m do not show a clear variability and is at leastsmaller than the photometric precision, which islimited to the order of 0.1% owing to the shotnoise and instrumental systematic noise. Morriset al. (2018) find that the combination of theselight curves at different wavelengths can be ex-plained by the existence of several very smallfaculae with > µ m with this model seems to berandom with an amplitude of about 100 ppm.This prediction is encouraging because this is IR HR for HZ planets > Kepler/K2 vari-ability of TRAPPIST-1. In reality, stars exhibitthe diversity in their surface magnetic activitiesand the resultant spots/faculae, and thereforeit is critical to characterize individual stars be-fore characterizing the planets. With the launchof JWST that achieves higher precision than
Spitzer thanks to its larger aperture and bet-ter attitude control, our understanding of vari-abilities of the stellar MIR spectra will be de-veloped and the techniques to cope with thesevariability will be advanced. For example, si-multaneous light-curve observations at differentwavelengths will allow us to better model thespots, as demonstrated by Morris et al. (2018).Such practice will further enhance the feasibilityof the method presented in this manuscript.5.2.2.
Systematic Noise
We did not explicitly deal with the impactof the unknown instrumental systematic errors.Because this technique utilizes high-frequencyfeatures of the spectrum, the uncertainties inthe absolute flux or the low-frequency modula-tion of the continuum, even if it is substantial,will not affect our results after applying somecorrections (e.g., high-pass filter; Snellen et al.2017).In contrast, residual flat-fielding, spectralfringe patterns, and telescope pointing jittersform artificial absorption and emission lines(i.e., high-frequency systematic noise) in the ob-served spectrum. Such artificial high-frequencypatterns will be problematic for both the anal-yses (A) and (B). The high-frequency noise willcontribute to the total noise floor because ofits random distribution along the wavelength.Since the high-frequency systematic noise is in-dependent of the shot noise, the total noisemay be expressed by (cid:113) σ ,j + σ ,j , where σ photon ,j is defined by equation (4) and σ sys ,j de-notes the high-frequency systematic noise at the j -th spectral element. Given that the noise re-quired for detection is order of 100 ppm, it isnecessary that the instrument systematic noiseis less than this level. If the systematic noise is ∼
30 ppm or less, the systematic noise will notaffect our estimate much. Conversely, if it iscomparable to the photon noise, a substantiallylarger integration time will be required in orderto reduce the photon noise further. We notethat the high-resolution spectroscopy observesthe shift of the planetary Doppler signal on thedetector, which could mitigate an impact of thepatterns fixed to the detector (owing to relativesensitivity variations between adjacent spectralchannels).5.3.
Variety of Planet Thermal EmissionSpectrum
Stratospheric Thermal Inversion Figure 13.
Left: high-resolution ( R = 30 , that are same as Earth’s “US standard” profile. Right: Parameter constraints basedon the left panel, assuming a late-M host star at 5 parsec. This section discusses the variety of high-resolution thermal emission spectra, and howthey affect the parameter estimate.Our fiducial model atmosphere has a rela-tively cool stratosphere, approximately 150 K.A higher stratospheric temperature results inshallower spectral features, increasing the re-quired integration time for detection.If the planet has thermal inversion in the up-per atmosphere (like the ozone layer of Earth),thermal spectra may exhibit emission lines.These lines can be sharp, because the pressurein the upper atmosphere (where the emissionline are formed) is low and the line width is rel-atively narrow. This can relax the degeneracybetween the contrast and the orbital inclinationwhich would otherwise be present, like our fidu-cial cases for CO and H O.As a demonstration, Figure 13 is the mod-eled thermal emission spectrum that assumesan Earth-like temperature profile with a strato-spheric thermal inversion as well as an Earth-like CO vertical profile. Note the narrow emis-sion lines within 14-16 µ m. The analysis (B)performed on this spectrum yields the con-straints shown in the right panel of Figure 13,assuming a late-M host star. While the totalintegration time required for detection is longerthan our fiducial case due to the reduced linedepths (corresponding to the warmer upper at-mosphere), the degeneracy between the contrastand the inclination is less severe. 5.3.2. Horizontal temperature gradient
We did not include the horizontal tempera-ture gradient of the planet. In reality, it canbe substantial near the surface, depending onthe heat re-distribution efficiency of the atmo-sphere and/or ocean. The horizontal tempera-ture gradient would result in the time variationof the disk-averaged thermal emission as theplanet rotates (e.g., Knutson et al. 2007). Whilethis itself can be used to characterize planet at-mosphere, such variations may complicate theanalysis of high-resolution spectroscopy. For-tunately, the effect of the horizontal tempera-ture gradient will be mitigated if the data atthe same phase angle are stacked and analyzed.Our analysis assumes observations near 90 de-grees and 270 degrees (i.e., the same phase an-gle) so the impact will be limited unless thereis an extreme asymmetry between the easternand western hemispheres.5.3.3.
Full Exploration of Parameter Space
Although in this paper we attempted to con-strain the contrast and inclination by fitting themock data by specific model spectra, in real-ity, the spectral shape of the planet thermalemission also has to be constrained. In otherwords, the distribution of the molecules as wellas the temperature structure should be fittingparameters as well, and the dimension of theparameter space is large. It is also possiblethat the constraints on certain parameters can
IR HR for HZ planets
Significance of mid-infraredhigh-resolution spectroscopy forcharacterization of potentially habitableplanets
Because our analysis (A) follows the proce-dure of Snellen et al. (2017), we compare ourresults with their estimate. Their modeled CO features in the medium-resolution spectra is de-tected (by nearly 4 σ ) after the photon noisebecomes ∼
50 ppm. Using the same bandpass(13.2-15.8 µ m) and a similar temperature pro-file (left panel of Figure 13), our analysis (A)of high-resolution spectra was able to detectthe CO features when the photon noise is ∼
100 ppm. This is likely a consequence of abouttwo times sharper features at high-resolutionspectra, as well as the minor features that aresmoothed in the medium resolution spectra.Note that it is not trivial to compare ourestimate for the integration time to the inte-gration time estimated in Snellen et al. (2017)for JWST/MIRI. This is because the noise ofJWST/MIRI, especially beyond 12 µ m, is notdominated by the photon noise of the star.Other noise, including the thermal backgroundof the telescope, zodiacal light (with the largeraperture size), and/or the readout noise (dueto the short exposure time assumed) suppressesS/N per exposure by 2-3 times compared tothe idealized case. This leads to the substan-tial difference in the integration time requiredto achieve a certain precision. Thus, it is crit-ical to suppress the background noise in order to be able to detect atmospheric molecules ofnearby mid-M and late-M stars in a reasonableamount of time. SUMMARYIn this paper, we study the use of anMIR high-resolution spectrograph mounted ona cryogenic telescope for characterizing non-transiting temperate terrestrial planets orbit-ing M-type stars. We modeled high-resolutionthermal emission spectra of an Earth-like at-mosphere with CO , H O, N O, and O assum-ing a simplified temperature profile composedof an dry adiabatic troposphere and an isother-mal stratosphere. We show that the MIR spec-tral features of Earth-like atmospheres can bebroader than the width of the Doppler shift, de-pending on the atmospheric structure.In order to reasonably identify the tiny plane-tary features in the combined spectra of the starand the planet, it is critical to subtract the stel-lar contribution precisely, as low-mass stars areparticularly rich in spectral features in the MIR.For non-transiting planets, the stellar spectrumcannot be determined observationally as we al-ways observe the star and planet together. Con-sidering this possible difficulty, we proposed toobserve the target at around φ = 90 ◦ and at φ = 270 ◦ and that the differential spectra arefitted by the model. This process can reduce thesignal because some fraction of broad lines areself-subtracted. This effect is substantial exceptfor O , increasing the total integration requiredfor detection by several times.Nevertheless, the spectral features ( R =30 , µ m would allow us to constrain the contrast andthe orbital inclination within ∼ wouldbe inferred in ∼ R (cid:38) ,
000 do not result in significant improve-ment except for O whose absorption bands aredensely populated with narrow lines. However,the constraints on the inclination would benefitfrom the higher spectral resolution. We also findthat this method is most sensitive to relativelysmall amount of CO and N O (1-10 ppm for a1-bar Earth-like atmosphere), where the higherabundance does not lead to better detectability.In this study, we did not include the stellarvariability and systematic noise in our simula-tion. Because the photon noise required for thedetection of these features is 100 ppm or larger,the stellar variability and systematic noise must be suppressed to these levels in order to detectthe planetary features. The expected stellarvariability in the mid-infrared wavelength rangebased on the previous photometric observationsof TRAPPIST-1 with Spitzer is comparable orless than 100 ppm, which will not affect thismethod. Suppression of the noise sources otherthan the shot noise from the stellar flux (e.g.,thermal background) is critical in reducing therequired integration time and making the obser-vations realistic.ACKNOWLEDGMENTSWe thank Teruyuki Hirano for helpful dis-cussions on high-resolution spectroscopy andKlaus Pontoppidan for the information aboutthe instrumental noise of JWST. YF is sup-ported by Grand-in-Aid from MEXT of Japan,No. 18K13601. TM is supported by Grand-in-Aid from MEXT of Japan, No. 19H00700.REFERENCES
Allard, F., Homeier, D., & Freytag, B. 2012,Philosophical Transactions of the Royal Societyof London Series A, 370, 2765Anglada-Escud´e, G., Amado, P. J., Barnes, J.,et al. 2016, Nature, 536, 437Barnes, J. R., Jeffers, S. V., Haswell, C. A., et al.2017, MNRAS, 471, 811Barnes, J. R., Jeffers, S. V., Jones, H. R. A., et al.2015, ApJ, 812, 42Beichman, C., Benneke, B., Knutson, H., et al.2014, PASP, 126, 1134Beichman, C. A., Woolf, N. J., & Lindensmith,C. A. 1999, The Terrestrial Planet Finder(TPF) : a NASA Origins Program to search forhabitable planetsBoyd, R. W. 1982, Infrared Physics, 22, 157Brogi, M., Line, M., Bean, J., D´esert, J. M., &Schwarz, H. 2017, ApJL, 839, L2Brogi, M., Snellen, I. A. G., de Kok, R. J., et al.2013, ApJ, 767, 27de Wit, J., Wakeford, H. R., Lewis, N. K., et al.2018, Nature Astronomy, 2, 214 Deming, L. D., & Seager, S. 2017, Journal ofGeophysical Research (Planets), 122, 53Fujii, Y., Del Genio, A. D., & Amundsen, D. S.2017, ApJ, 848, 100Fujii, Y., Angerhausen, D., Deitrick, R., et al.2018, Astrobiology, 18, 739Gaidos, E., Mann, A. W., L´epine, S., et al. 2014,MNRAS, 443, 2561Gillon, M., Jehin, E., Lederer, S. M., et al. 2016,Nature, 533, 221Gillon, M., Triaud, A. H. M. J., Demory, B.-O.,et al. 2017, Nature, 542, 456Glasse, A., Rieke, G. H., Bauwens, E., et al. 2015,PASP, 127, 686Gordon, I. E., Rothman, L. S., Hill, C., et al.2017, JQSRT, 203, 3Greene, T. P., Line, M. R., Montero, C., et al.2016, ApJ, 817, 17Ikeda, Y., Kobayashi, N., Kondo, S., et al. 2016,in Society of Photo-Optical InstrumentationEngineers (SPIE) Conference Series, Vol. 9908,Ground-based and Airborne Instrumentationfor Astronomy VI, 99085Z
IR HR for HZ planets23