Using Dimers to Measure Biosignatures and Atmospheric Pressure for Terrestrial Exoplanets
aa r X i v : . [ a s t r o - ph . E P ] D ec Using Dimers to Measure Biosignatures and Atmospheric Pressure forTerrestrial Exoplanets
Amit Misra , , Box 351580, UWSeattle, WA 98195-1580Phone: 206-616-4549Fax: 206-685-0403 [email protected] andVictoria Meadows , , , Mark Claire , , & Dave Crisp , ABSTRACT
We present a new method to probe atmospheric pressure on Earthlike planets using(O -O ) dimers in the near-infrared. We also show that dimer features could be the mostreadily detectable biosignatures for Earthlike atmospheres, and may even be detectablein transit transmission with the James Webb Space Telescope (JWST). The absorptionby dimers changes more rapidly with pressure and density than that of monomers, andcan therefore provide additional information about atmospheric pressures. By compar-ing the absorption strengths of rotational and vibrational features to the absorptionstrengths of dimer features, we show that in some cases it may be possible to estimatethe pressure at the reflecting surface of a planet. This method is demonstrated by us-ing the O A band and the 1.06 µ m dimer feature, either in transmission or reflectedspectra. It works best for planets around M dwarfs with atmospheric pressures be-tween 0.1 and 10 bars, and for O volume mixing ratios above 50% of Earth’s presentday level. Furthermore, unlike observations of Rayleigh scattering, this method can Univ. of Washington Astronomy Dept., Seattle, Washington, USA NAI Virtual Planetary Laboratory, Seattle, Washington, USA Univ. of Washington Astrobiology Program, Seattle, Washington, USA Dept. of Earth and Environmental Sciences, University of St Andrews, Fife, Scotland Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, USA Blue Marble Space Institute of Science, Seattle, WA, USA µ m, and is therefore potentially applicable, al-though challenging, to near-term planet characterization missions such as JWST. Wehave also performed detectability studies for JWST transit transmission spectroscopyand find that the 1.06 µ m and 1.27 µ m dimer features could be detectable (SNR > monomer and dimer features in di-rect imaging reflected spectra and find that signal-to-noise ratios greater than 10 at aspectral resolving power of R=100 would be required. Subject headings:
Remote Sensing, Extrasolar terrestrial planets, Habitability, Radia-tive transfer
1. Introduction
Atmospheric pressure is a fundamental parameter for characterizing the environment and hab-itability of an extrasolar planet. Water’s stability on a planetary surface as a liquid depends on boththe surface temperature and pressure. While the freezing point of water is not strongly dependenton pressure, pressure does affect water’s boiling point and sublimation. Thus, a reliable estimateof the surface pressure is an important part of the measurement suite required to determine thehabitability of an exoplanet.Despite the importance of atmospheric pressure, current proposed methods for measuringpressure using remote-sensing techniques that could be applicable to exoplanet atmospheres arechallenging. The existing techniques include the use of Rayleigh scattering (Kasting et al. 2010)or the widths of individual absorption lines (Kaplan et al. 1964; Gray 1966) or absorption bands(Ignatiev et al. 2009; Chamberlain et al. 2006; Spiga et al. 2007; Chamberlain et al. 2013). Thepresence and location of a blue Rayleigh scattering tail in a spectrum can provide information aboutthe existence and pressure of an atmosphere. However, strong blue absorbers in the atmosphere(e.g. O , SO , NO and many others) or surface features can mask this tail (Crow et al. 2011).Furthermore, the Rayleigh scattering tail is most prominent shortward of 0.6 µ m, below the shortwavelength cutoff of the James Webb Space Telescope (JWST) (Gardner et al. 2006). Lastly,planets around M dwarfs are likely to be the first to be characterized (Deming et al. 2009), and Mdwarfs have relatively less visible-flux to Rayleigh scatter than solar-type stars. The Rayleigh tailwould be more difficult to detect and characterize for planets orbiting stars of this stellar class.It is also possible to use the widths of absorption features to estimate pressure. Pressureincreases the widths of vibration rotation lines of gases. This method has been successful for theEarth using high-resolution spectra of the O A band (Barton and Scott 1986; Mitchell and O’Brien1987; Crisp et al. 2012), for Mars using CO features near 2 µ m (Gray 1966; Chamberlain et al. 3 –2006; Forget et al. 2007; Spiga et al. 2007) and the cloud tops of Venus using the 1.6 µ m CO band(Ignatiev et al. 2009). This method provides unambiguous results when the spectral resolution issufficiently high to resolve the profiles of individual spectral lines. It can also be used at lowerspectral resolution, but requires prior knowledge of the mixing ratio of the absorbing gas.Here we explore the feasibility of a new method to directly measure the pressure of an Earth-like atmosphere that combines the absorption features of dimers with those of monomer vibration-rotation bands to yield estimates of the atmospheric pressures even when the mixing ratio of themonomer is uncertain. Previous pressure estimates using dimer absorption have been made forthe cloud tops of Earth, but these techniques have required prior knowledge of the gas mixingratio profile (Acarreta et al. 2004). Dimers are bound or quasi-bound states between two moleculesdriven together by molecular interactions. For example, the O -O or O dimer consists of twoO molecules temporarily bound to each other by Van der Waals forces. This dimer has its ownrotational and vibrational modes, and produces spectral features distinct from its constituent O monomers. Additionally, absorption from dimer molecules is more sensitive to pressure than thatof monomers. The optical depth (how much absorption occurs) for dimers and monomers can beexpressed by the following equations: dτ monomer = σρdl = σP/T dl (1) dτ dimer = kρ dl = kP /T dl (2)where dτ monomer and dτ dimer are the monomer and dimer differential optical depths, σ is themonomer cross section, ρ is the number density of the gas, k is the dimer cross section, P isthe pressure, T is the temperature, and dl is the path length. While the monomer (e.g. O )optical depth is directly proportional to pressure, the optical depth of the dimer (e.g. O -O )is dependent on the square of the density (and hence square of the pressure). This differencein pressure dependence allows us to estimate atmospheric pressure by comparing the dimer andmonomer absorption featuresFor an oxygen-rich, Earth-like atmosphere, the best combination of bands to use for pressuredetermination at near infrared wavelengths ( > µ m) would be the (O ) A band at 0.76 µ m, andthe 1.06 µ m O dimer band. The 0.76 µ m O A band is the strongest O feature in the visible-near-infrared spectral region, and is found in a relatively clean region of the spectrum betweentwo water vapor bands. We have chosen the dimer feature at 1.06 µ m as the likely best option,due to its combination of band strength and its location in a relatively uncluttered region of theplanetary spectrum. Other O features overlap with water features (dimer feature between 5.5 and7 µ m) or O vibration-rotation bands (0.63 µ m, 0.76 µ m and 1.27 µ m dimer features) or are weakerthan the 1.06 µ m dimer feature (0.477 µ m and 0.57 µ m dimer features). Nevertheless, some otherfeatures, in particular the strong 1.27 µ m feature, could be used if the 1.06 µ m dimer feature is notdetectable.In the proposed technique, the O µ m (monomer) band is used to provide an estimate of theatmospheric concentration of O , and combined with the O µ m (dimer) band to constrain the 4 –atmospheric pressure. This method can be used with either transmission spectroscopy, or directly-detected reflection or emission spectra, and serves as a complement to pressure determinationtechniques such as Rayleigh scattering, which only work in the visible. Although the proof ofconcept is shown here with oxygen, this technique is not limited to the oxygen dimer in an Earth-likeatmosphere in the visible to near-infrared. The same technique is applicable to pairs of monomerand dimer absorption features across a wider range of planetary atmospheric composition andspectral wavelength range.
2. Methods
In this paper we generated transit transmission and direct imaging reflected spectra for cloudand aerosol-free Earthlike exoplanets. The models we have used to do this are described below.
When an extrasolar planet transits or occults its host star, the planetary atmosphere is backlitand some of the star’s light traverses the planet’s atmosphere on limb trajectories. This transmittedlight can be used to characterize the planet’s atmosphere (Seager and Sasselov 2000; Brown 2001;Hubbard et al. 2001). This has been done for a number of Jupiter- and Neptune-sized planets(e.g. Charbonneau et al. (2002); Vidal-Madjar et al. (2003); Pont et al. (2008)) and the super-Earth/mini-Neptune GJ1214b (e.g. Bean et al. (2010))The transmission spectroscopy model used here is based on SMART (Spectral Mapping At-mospheric Radiative Transfer) (Meadows and Crisp 1996; Crisp 1997), which is a spectrum resolv-ing (line-by-line), multi-stream, multiple scattering radiative transfer model. We have modifiedSMART to generate transit transmission spectra by combining the monochromatic absorption andscattering opacities for each atmospheric layer calculated by SMART with the limb path lengthsinherent in a transit transmission event. The transmission model included gas absorption, Rayleighscattering, interaction-induced absorption, extinction from clouds and aerosols, refraction and limbdarkening. Because multiple scattering was not included in the transit transmission component ofthe model, we have considered only cloud and aerosol-free atmospheres for this work.
An important characteristic of the transit transmission spectroscopy model is the inclusion ofrefraction. As described in Garc´ıa Mu˜noz et al. (2012), refraction sets a fundamental limit on therange of pressures that can be probed during a transit, independent of absorption and scattering. 5 –Light refracts as it passes through an atmosphere, with a larger refraction angle as higher pressuresand densities are probed. For every planet-star system there will be a maximum tangent pressure inthe planet’s atmosphere that can be probed, because at greater pressures the light will be refractedby too large of an angle to be able to reach a distant observer during the transit.For each tangent height in each atmosphere, we calculated the total angle of refraction fora beam of light emitted from the host star using a modified version of the method described inAuer and Standish (2000). Their method was developed for calculating refraction for astronomicalobservations on the Earth given a tangent altitude, apparent zenith angle and an atmosphericdensity profile. We calculated the angle of refraction over a range of zenith angles to determine ifa path exists to connect the host star to a distant observer via the planetary atmosphere. Transittransmission spectroscopy cannot probe the tangent altitudes at which no such path exists.The radius of the star, planet-star distance and composition of the planet’s atmosphere deter-mine the maximum tangent pressure. The radius of the star and planet-star distance control theapparent angular size of the star from the planet’s perspective. The larger the angular size, thegreater the range of pressures that can be probed. For an Earth-analog orbiting a Sun-like star theangular size of the star is ∼ ◦ while for an Earth-analog orbiting an M5 dwarf and receiving thesame total flux, the angular size of the star is ∼ ◦ . Therefore, transit transmission spectroscopycan probe higher pressures, i.e. see deeper into the atmosphere, for the planet orbiting an M dwarf.Figure 1 shows this effect by comparing all possible paths at one tangent height for a planet aroundan M dwarf and a planet around a Sun-like star, with each planet receiving the same total flux.The composition of the atmosphere determines the refractivity (index of refraction - 1) of theatmosphere. Atmospheres with greater refractivities will have lower maximum tangent pressures.The refractivity at STP (standard temperature and pressure) can vary from ∼ to slightly less than half the refractivity of air for H , when considering onlythe common bulk atmospheric gases in the solar system. Therefore, in general it will be possibleto probe higher pressures for an H atmosphere than a CO or air atmosphere. The reflected spectra were generated using the standard version of SMART, which can includemultiple scattering from clouds and aerosols. However, to maintain consistency with the transmis-sion spectrum model, clouds were not included in this study. The reflected spectra were generatedassuming a surface with a constant albedo of 0.16, which is the average albedo of the cloud-freeEarth (Pierrehumbert 2010). We also assumed the surface is a Lambertian scatterer. Other surfacetypes could have introduced an error into any quantitative estimates in this paper, unless explicitlyincluded in a retrieval attempt. Figure 2 shows the wavelength-dependence of a variety of sur-face types from the ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer)spectral library (Baldridge et al. 2009) and the USGS (United States Geological Survey) digital 6 –spectral library (Clark et al. 2007). Surface albedos are nearly constant in the bands consideredhere, though, for example, snow fluctuates by ∼
20% within the 1.06 µ m dimer band. We modeled atest case with SMART with the snow surface to determine the error different surfaces can introduce.We found a difference of 15% between the seawater and snow cases when measuring the equivalentwidth (defined in Section 2.4) of the 1.06 µ m dimer band. This difference was significantly less thanthe difference in measured equivalent widths for the cases considered in this paper. Therefore, wehave considered any discrepancies due to variations in surface albedo to be minimal for the presentwork. The cloud-free model atmospheres were generated by a one-dimensional (altitude) photochem-ical code with an extensive history in early Earth (Zerkle et al. 2012), modern Earth (Catling et al.2010) and exoplanet (Domagal-Goldman et al. 2011) research. The planetary radius and surfacegravity used were the radius of the Earth (6371 km) and surface gravity of the Earth (9.87 m/s ).The vertical grid consists of 200 plane-parallel layers that are each 0.5km thick in altitude, inwhich radiative transfer, atmospheric transport, and photochemical production and loss are solvedsimultaneously, subject to upper (stellar flux, atmospheric escape) and lower (volcanos and biol-ogy) boundary conditions. The model calculates the mixing ratios of each species in each layer bysolving the coupled mass-continuity/flux equations with the reverse Euler method (appropriate forstiff systems) and a variable time-stepping algorithm. Dimer concentrations were computed usingestimations from quantum mechanical calculations. First, we fit the temperature dependence ofthe equilibrium constant for O -dimer formation using the following equations: Kp = ( p ( O ) / ( pO ) ) /atm − (3) Kp ( T ) = 2428 ∗ T ( − . (4)where p(O ) and pO are the dimer and monomer partial pressures and T is the temperature(Uhlik et al. 1993). The dimer mixing ratio was then computed as: p ( O ) = Kp ( T ) ∗ ( pO ) ∗ P (5)where P is the pressure in atmospheres. The choice of quantum parameters in our fit of equation4 ensures that our calculation is a lower limit to the dimer concentrations, an assumption whichmatches modern atmospheric data well (Slanina et al. 1994).The model atmospheres used in this study started with boundary conditions that reproduceEarth’s modern atmospheric chemistry. We then replaced the solar spectrum with the M dwarfspectrum described in 2.3.3 and decreased the surface albedo to 0.16 to account for cloud-freeconditions. This “modified Earth around an M dwarf” model was then perturbed to examine 7 –changes to both total pressure and oxygen concentrations. Total atmospheric pressures of 0.1, 0.5,1.0, 3.0, 5.0 and 10.0 bar were examined. At each of these total pressures, lower boundary conditionson O mixing ratios were set at 0.1, 0.5, 1.0 and 2.0 times Earths present level. This correspondsto oxygen mixing ratios from 2% to 42%, which is roughly the range of oxygen concentrationsexperienced throughout the past 2.5 Gyr of Earths history (Kump 2008). Boundary conditions forall other species were held fixed at modern values. Figure 3 shows the pressure-temperature profileand volume mixing ratio profiles for the 1.0 times the present atmospheric level (PAL) O casesfor spectrally active gases in the wavelength region examined here. Stable steady-state solutionswere analyzed in all but the three cases with the highest O surface partial pressures. For thosethree cases, we extrapolated from our converged results at lower O mixing ratios by increasingO concentrations, scaling the dimer concentrations with the square of the O mixing ratio, andkeeping all other gas mixing ratios constant.For all tests presented here, we assumed Earth-like temperature and water vapor profiles,precluding the need for costly climate simulations. More specifically, we took the modern Earthtemperature profile as a function of altitude, and computed the corresponding pressure levels as-suming hydrostatic equilibrium. This simplification provides a useful baseline, but limits the rangeof validity of these results somewhat because the gas absorption cross sections and number densitiesdepend on these atmospheric properties. The impact of this assumption is assessed in Section 3.4.For pressure/temperature regions corresponding to Earth’s mesosphere, we adopted a temperatureof 180 K which likely overestimates the temperature in these regions. Dimer absorption preferen-tially occurs in higher pressure regions and so is insensitive to assumed conditions in the tenuousupper atmosphere. Our model grid was capped at 100km altitude ensuring optically thin conditionsfor nearly all species, and made allowances for CO and N photolysis above the upper boundary.We used the modern measured eddy-diffusion profile to simulate convective motion for all atmo-spheres regardless of pressure. While this simplification would affect the prediction of trace gasconcentrations, all species analyzed here are either well-mixed (CO , O , N ) or short-lived (dimers)so are not sensitive to changes in turbulent mixing. We used the HITRAN 2008 database line lists (Rothman et al. 2009) to generate opacitiesin SMART. The dimer absorption cross sections for O were taken from Greenblatt et al. (1990);Mat´e et al. (1999). In this paper we have assumed that the planet orbits an M5V star, or an M dwarf with stellarradius of 0.20 R ⊙ and a luminosity of 0.0022 L ⊙ (Kaltenegger and Traub 2009). The planet was 8 –placed at a distance of 0.047 AU, so that the total integrated incoming stellar flux was equal to thetotal flux the Earth receives from the Sun today. An M5 dwarf was chosen for these tests becausethere is a high probability that the terrestrial planets which will be the most easily characterizedin the near future will be orbiting this class of star (Deming et al. 2009). Additionally, transittransmission spectroscopy can probe pressures up to the ∼ ∼ µ m dimer feature is very weak, evenat 200% PAL O . Thus, using Earth-like atmospheres around an M dwarf instead of around theSun provides a better demonstration of the pressure-dependence of dimer features.To simulate the spectrum of the star, we used a Phoenix NextGen synthetic spectrum (Hauschildt et al.1999) for all wavelengths greater than ∼
300 nm. For the shorter wavelengths we used the UV spec-trum of AD Leo (Segura et al. 2005). The Phoenix spectrum was normalized so that the totalintegrated flux was equal to 1373 W/m , which is the integrated flux the Earth receives fromthe Sun. The AD Leo spectrum from Segura et al. (2005) was left unchanged, as it was alreadynormalized to equal the amount of flux a planet near the inner edge of the habitable zone wouldreceive. We have used a spectral resolving power of 100 to provide relevance to the James WebbSpace Telescope (JWST), which will provide new opportunities for characterizing the atmospheresof transiting exoplanets (Lafreniere et al. 2013). Once the JWST is launched, the Near-InfraredSpectrograph (NIRSPEC) will provide spectra with a spectral resolving power (R= λ ∆ λ ) of ≃ µ m in single prism mode (K¨ohler et al. 2005). We examine the effect of varyingthe spectral resolution in Sections 3.6 and 4.3. To make a quantitative estimate of absorption strengths we measured equivalent widths forthe reflected spectra and measured parts per million (ppm) differences in flux for the transmissionspectra. Equivalent widths were calculated using the following equation: W = Z (1 − F λ /F ) dλ (6)where W is the equivalent width, F λ is the flux at each wavelength λ , and F is the continuum fluxat each wavelength. To obtain the equivalent widths, we first measured the area of the spectralband below the continuum. For each absorption band, we define the continuum by hand. For theO A band, the continuum was assumed to be linear with wavelength, and for the 1.06 µ m featurethe continuum was assumed to be constant with wavelength because in several of the cases the 9 –continuum at the longer wavelengths was difficult to define due to H O absorption. The equivalentwidth is the width, in units of wavelength, of a rectangle measured from the continuum to thelevel of zero flux with the same total area as the spectral band. We could not use this type ofmeasurement for the transmission spectra because of the difficulty in defining the zero flux level.Therefore, we quantified the absorption strengths for the transmission spectra by measuring thechange in flux from the continuum to the point of greatest absorption within a band.
We performed detectability studies (Kaltenegger and Traub 2009; Deming et al. 2009; Belu et al.2011; Rauer et al. 2011) for the model spectra, assuming the exoplanet-star system is at a distanceof 5 pc. We calculated the expected signal-to-noise ratio (SNR star ) using the JWST Exposure TimeCalculator (ETC) . The JWST ETC includes background noise from sky, dark, thermal and zodi-acal sources along with read-out noise and photon noise. The estimates provided are expected to bewithin 20% of the mission requirements. We note that for all the cases considered, the noise is dom-inated by photon noise. We do not include noise from detector intrapixel variations (Deming et al.2009), but in principle calibration time could be devoted to mapping the pixels, as has been donewith Spitzer Space Telescope Infrared Array Camera (Carey et al. 2012). We also note that noiselevels within ∼
20% of the photon noise limit have been obtained for transit transmission spec-tra with HST in spatial scan mode, wherein the target star is trailed during each exposure bytelescope motion perpendicular to the direction of dispersion (Deming et al. 2013; Wakeford et al.2013). Spatial scan mode is being considered for JWST, and so assuming photon-limited noise inour calculations, while optimistic, provides a reasonable estimate of the detectability of absorptionfeatures (Drake Deming, private communication, October 13, 2013).We assumed that every possible transit is observed in JWST’s 5 year mission lifetime, ignoringdecreases in integration time due to non-zero impact parameters (where the planet does not traversethe center of the stellar disk and therefore has a lower transit duration) and limits on visibilitybased on the ecliptic latitude of the exoplanet (see Belu et al. (2011)). For the Earth-Sun analog,this corresponds to a total integration time of ∼ seconds, and for the Earth-M5V analog,an integration time of ∼ seconds. We normalize the Solar spectrum (using the Phoenix G2Vmodel available on the site) to a Johnson V magnitude of 3.32 and the M5V spectrum to 2.1*10 − erg cm − s − ˚A − at 1 µ m.At each wavelength within an absorption band we measured the signal as the magnitude of thedifference from the continuum flux. The noise is expressed in parts per million (ppm, 10 /SNR star )at each wavelength. The final SNR of the transit transmission spectrum is the square root of thesum of the squares of the SNR at each wavelength in the absorption band divided by √
2, which is http://jwstetc.stsci.edu
10 –included because the transit transmission spectrum must be calibrated against the out of transitspectrum of the star.We also performed detectability studies for the direct imaging reflected spectra that couldbe relevant to proposed direct imaging planet detection and characterization missions. For thesecalculations, we did not use an instrument simulator because the exact specifications for thesemissions are not currently defined. For each absorption band, we calculated two SNRs, one fordetecting the spectral feature (SNR D ) and one for measuring the flux at the center of the band toa precision of 3 σ (SNR P ). We calculated two SNRs because obtaining information about pressurefrom a spectral feature requires more than detection; it also requires a quantitative estimate of thestrength of that spectral feature. To calculate SNR D , we divided the reflected flux by the stellarflux, defined a continuum and calculated the signal as the difference between the continuum andthe normalized reflected flux. We assumed the noise is constant over the entire absorption band,and then calculated the noise level required to detect the spectral feature with a SNR band of 3 in theabsorption band. The final SNR D is the mean of the continuum reflected flux level divided by thecalculated noise. To calculate SNR P , we selected the wavelength within the band with the lowestradiance. We set the value of a second noise level as the lowest radiance divided by 3. SNR P is thecontinuum flux level divided by the noise required to obtain a SNR of 3 at the lowest radiance inthe absorption band.
3. Results3.1. Transit Transmission Spectra
We have generated transit transmission spectra and direct imaging spectra for atmosphereswith O concentrations of 10%, 50%, 100% and 200% of the PAL and pressures of 0.1, 0.5, 1,3, 5 and 10 bars. Figure 4 shows the resulting transit transmission spectra for 100% PAL O .Transmission spectra of atmospheres with pressures ≥ concentration because refraction limits to depth of penetration to < concentrations of 10%,50% and 200% PAL. The 1.06 µ m dimer feature is very weak at all pressures for O concentrationsat 10% PAL and weak for 50% PAL O , while it is very strong for pressures above 0.1 bars at 200%PAL O . Figure 8 shows the reflected spectra for modern O mixing ratios in atmospheres with a rangeof total pressure from 0.1 to 10 bars. The 0.5 and 5.0 bar cases are omitted from the plots to 11 –increase clarity, but are still included in the equivalent width and SNR calculations. The 1.06 µ mdimer feature is extremely weak for the present-day atmosphere, but in contrast to its behavior inthe transmission spectra, it is a very prominent feature for the 3, 5 and 10 bar atmospheres.Figures 9, 10 and 11 show the reflected spectra at pressures between 0.1 and 10 bars for 10%,50%, and 200% PAL of O , respectively. In the 10% PAL case, the O dimer feature at 1.06 µ m isvery weak because the total amount of O is very low, even for a 10 bar atmosphere. The 1.06 µ mdimer feature is stronger in the 3, 5 and 10 bar cases for atmospheres with 50% PAL O . Finallyfor the 200% O atmospheres, the 1.06 µ m dimer feature is one of the strongest spectral features,even in the 1 bar atmosphere. Figure 12 shows the flux change for the transmission spectra and equivalent widths for reflectedspectra at different pressures and O concentrations for the O A band and the 1.06 µ m dimerfeature. For a given O concentration the transit transmission flux differences for the O A bandare roughly constant for pressures ≥ µ m dimer feature fluxdifferences increase slightly with pressure but are also constant for pressures ≥ concentration. The dimer feature does not appear in transmission for cases with 10% PAL O .For the direct imaging (reflected) spectra, both the O A band and 1.06 µ m dimer featureequivalent widths increase with pressure and increased O concentrations. However, the dimerfeature equivalent widths are much more sensitive to pressure. At higher pressures the dimerfeature is strong except for cases with 10% PAL O , in which the 1.06 µ m dimer feature is tooweak to quantify.Figures 13-15 show the relationships between the quantitative absorption measurements de-scribed above and atmospheric quantities including the O mixing ratio and the O partial pressureat the surface. The ppm flux difference measured in transit transmission for the O A band couldbe used to constrain the O mixing ratio, as shown in Figure 13B. The O partial pressure at thesurface can be estimated using the ratio between the 1.06 µ m dimer and O A band absorptionmeasurements. These ratios are shown in Figure 13a using ppm flux differences, and in Figure14 using equivalent widths. The O mixing ratio and O partial pressure at the surface can becombined to provide a unique estimate of the surface pressure of the planet. A more detaileddescription of the pressure measurement technique is given in Section 4.1. To quantify the errors introduced by assuming the modern day temperature profile, we gen-erated spectra to test the sensitivity of our models to changes in the temperature profile and in 12 –changes to the water vapor profiles. We compared our 1.0 bar, 1.0x PAL O spectra to a spectrumgenerated using the same volume mixing ratio profiles but with an isothermal atmosphere at 250K. We also compared our 1.0 bar, 1.0x PAL O transit transmission spectrum to spectra generatedwith atmospheres with 0.1 and 10.0 times the H O levels. We perform a similar comparison for the1.0 bar, 2.0x PAL O reflected spectrum.Figure 16 shows the sensitivity of the spectra to the temperature profile, with our Earth-like profile and an isothermal approximation profile compared. Both the transit transmission andreflected spectra show little sensitivity to the temperature profile. The 1.06 µ m dimer band alsoshows little sensitivity to the temperature profile, despite the dependence of the dimer opticaldepth on the square of the temperature because the isothermal temperature profile approximatesthe average temeprature of the troposphere, where the majority of dimer absorption occurs.Figures 17, 18 and 19 show the results for the H O sensitivity tests. The O A band equivalentwidths and ppm flux differences are not strongly affected by changes in the H O profiles. However,changes in the H O mixing ratios affect the continuum flux in the wings of the 1.06 micron dimerfeature, complicating measurements of the equivalent width of this feature. For the transit trans-mission spectra, the change in the total ppm flux difference (across the entire band) is less than20% between the 0.1 and 10.0x H O cases. For the reflected spectra, the change in the equivalentwidth of the 1.06 µ m dimer feature is less than 20%. For the reflected spectra, the equivalentwidths can be much greater than that for the 1.0 bar, 2.0x O case. For these greater equivalentwidths, the effect of increasing or decreasing H O levels will diminish as the difference from thecontinuum flux (affected by H O) and the flux within the absorption band will increase.
Table 1 shows the SNRs for observations by JWST for the O A band, 1.06 µ m feature andthe 1.27 µ m feature for the range of pressures and O concentrations considered here for an Earthanalog at a distance of 5 pc. The SNR are calculated assuming that every transit of an Earth analogorbiting an M5V star is observed over JWST’s 5 year mission lifetime. In transit transmission, theO A band SNRs are no greater than 1.1. The 1.06 µ m dimer feature is detectable at a SNR of > cases. The 1.27 µ m feature is the most detectable O feature in thiswavelength range, with SNRs greater than 5 for many of the 1.0x PAL O cases and greater than7 for many of the 2.0x PAL O cases. JWST will not be able to detect O species for Earth-likeexoplanets in secondary eclipse in the visible and near-infrared, as shown by the secondary eclipseSNR levels. Even for the highest pressure cases, the SNRs are no greater than ∼ A band, 1.06 µ m bandand the 1.27 µ m feature for the range of pressures and O concentrations considered here for thedirect imaging reflected spectra at R=100. The SNRs in Table 2 would be relevant to a directimaging characterization mission. While these SNRs were calculated for an Earth analog orbiting 13 –an M5V star, the results should be independent of stellar spectral type because we divided out thestellar flux in our calculations. The O A band, 1.06 µ m dimer feature and 1.27 µ m feature aredetectable at an average SNR D of 14, 9 and 14, respectively, for the cases when the features arestrong enough to identify in the model spectra. The average required SNR P to use the features forpressure estimation are 11, 31 and 34. We examined the effect of spectral resolving power on the detectability of spectral features bygenerating transit transmission spectra for the 1.0 bar, 1.0x PAL O case with spectral resolvingpowers of 500, 200, 100, 80, 60, 40, 30 and 20. Figure 20 shows the spectra for each of these cases.We also measured the SNR of each feature at each resolving power. The SNRs were calculatedassuming a noise profile equivalent to the JWST NIRSPEC noise profile, but with the noise levelat each wavelength divided by (100/R) , so that the noise at each wavelength decreased as theresolving power decreased. Figure 21 shows how the total SNR in each absorption band changeswith resolving power. In general, the SNRs drop off rapidly as resolving power decreases for R < case at resolvingpowers of 500, 200, 100, 80, 60, 40, 30 and 20, as shown in Figure 22. Figures 23 and 24 show howthe SNR for detection and precision vary with resolving power for the O A band, 1.06 µ m dimerfeature and the 1.27 µ m feature. The SNR required to detect each feature increases as resolvingpower decreases. At R=20, the SNRs are not shown because no spectral features could be identified,and at R=30 only the O A band was identified. The SNR required to quantify the flux at thecenter of each spectral feature decreases as resolving power decreases, because the lowest radiancelevel increases as the spectral resolving power decreases.
4. Discussion
The 1.06 µ m dimer feature is prominent in transit transmission for atmospheres with ≥ and surface pressures ≥ ≥
50% PAL O and surface pressure ≥ A band and therefore the dimer feature can be used to constrain pressure. Here we discuss how todo this for the cases investigated here. 14 –
Figure 12 confirms that dimer absorption features are more strongly dependent on pressurethan monomer features. Therefore dimer features can be combined with monomer features todetermine pressure, even if the mixing ratio of the absorbing gas is not known. With only transittransmission spectroscopy, it is impossible to probe pressures over ∼ mixing ratio and set a lower bound for pressure.In reflected spectra, it is possible to determine the surface partial pressure of O and set a lowerbound for pressure using the 1.06 µ m dimer feature as an on/off pressure gauge. With both atransit transmission spectrum and a reflected spectrum, it should be possible to determine totalatmospheric surface pressure for an Earth-like exoplanet. Transmission spectroscopy provides only a lower bound on the atmospheric pressure becauserefraction provides a fundamental limit to which pressures can be probed using this technique. Forthe spectra presented here, a lower limit of ∼ concentration a unique estimate of the pressure can be retrieved from the ratio betweenthe ppm flux differences of the 1.06 µ m dimer feature and the O A band. Figure 13a shows therelationship between this ratio and the total amount of O above 0.9 bars, which is the highestpressure that can be probed in this particular case. There is a clear trend between this ratio andthe amount of O in the atmosphere. When combined with an O mixing ratio this relationshipcan provide a quantitative estimate of a lower level of the surface or cloud-top pressure.The O mixing ratio can be estimated from the flux difference of the O A band in transmission.Figure 13B shows the relationship between the O mixing ratio (which is constant throughout theatmosphere) and the O A band flux difference. For pressure ≥ flux difference isroughly constant for a given O concentration, meaning that a measurement of the O A band fluxdifference should correlate with the O mixing ratio. Reflected spectra alone can provide an estimate of the surface partial pressure of O by exam-ination of the ratio of the 1.06 µ m dimer equivalent width and the O A band equivalent width.Figure 14 shows the relationship between this ratio and the surface partial pressure of O . Thestrength of the 1.06 µ m dimer feature could also be used as an on/off gauge to set a lower boundfor pressure. Determining total atmospheric pressure with only a reflected spectrum is difficult dueto degeneracies between the O concentration and total atmospheric pressure, as shown in Figure15. For large equivalent widths of the dimer feature, the pressure will certainly be above 1 bar. 15 –However, it is difficult to differentiate between atmospheres with the same O surface partial pres-sure. Nevertheless, it appears that it is possible to set a lower limit on pressure by measuring the1.06 µ m dimer feature equivalent width. For example, a 1.06 µ m dimer feature equivalent widthgreater than ∼
10 nm would imply a surface pressure > If both a transit transmission spectrum and a reflected spectrum are available, it should bepossible to directly measure the total atmospheric surface pressure in the absence of clouds. Transittransmission spectroscopy can provide an estimate of the O mixing ratio as described previously.A reflected spectrum can theoretically probe to the reflecting surface and therefore can be usedto constrain the O partial pressure at the surface. By combining the O mixing ratio and O partial pressure we can determine the total pressure at the reflecting surface, which could either bea reflective cloud layer or the physical surface of the planet. The methods described here could be used in the near future by the JWST NIRSPEC instru-ment, which will potentially be able to characterize transiting planets between 0.6 and 5.0 µ m.The O A band will likely not be detectable for a nearby Earth-analog with JWST. Although thisfeature is strong in the spectrum, the sensitivity of NIRSPEC is poor at shorter wavelengths. The1.06 µ m dimer feature is detectable at the 3 σ level in transit transmission for cases with 2.0x PALO and high surface pressures. Thus, the detection of the 1.06 µ m dimer feature would imply a sur-face or cloud-top pressure greater than or equal to 1.0 bars. For cases in which the 1.06 µ m dimerfeature is not detectable, the 1.27 µ m feature could be used to constrain the pressure. This featureis not as strongly dependent on pressure as the 1.06 µ m dimer feature, but it is more detectable inall cases explored here.TPF, Darwin or a similar direct imaging mission will be required to characterize the reflectedspectra of nearby Earth analogs in the visible and near-infrared. The SNR values for secondaryeclipse using JWST are all less than 1, so JWST will not be able to characterize the reflectedspectra of Earth-analogs in secondary eclipse. Table 2 shows the necessary SNRs to detect andcharacterize spectral features for a direct imaging planet characterization mission. While the SNRswere calculated for an Earth analog orbiting an M5V star, the results should be largely independentof spectral type because we have divided the reflected flux by the stellar flux in our calculations.The required SNR values suggest that a SNR of >
10 would be necessary to detect and quantify theO A band, 1.06 µ m dimer feature and 1.27 µ m feature for a true Earth analog. However, becausecontinuum brightness changes with pressure, a different SNR criteria would be necessary for higherpressure atmospheres. For example, the continuum brightness near the O A band is three times 16 –lower for the 10.0 bar cases than it is for the 0.1 bar cases. For most cases, a SNR of > µ m dimer feature.Clouds and aerosols will also affect the detectability of absorption features. In transit transmis-sion, clouds can effectively mask the highest pressures of the atmospheres at which dimer absorptionis most prominent. However, in partially cloudy atmospheres some of the paths will probe pres-sures as high as the maximum tangent pressure, and thus the planetary transmission spectrumcould show evidence of dimer absorption. Furthermore, absorption in the 1.27 µ m dimer band canbe detected with SNR > ≥ monomer absorption incloudy atmospheres when compared to cloud-free cases (Evans et al. 2011), though the effect ofcloud albedo on the detectability of dimer absorption features has not been heretofore examined.Therefore, while clouds will impact the detectability of dimer features, using dimers to determinepressure and as biosignatures may still be feasible for cloudy atmospheres. Figures 21 shows the SNRs for spectral features at varying resolving powers for transit trans-mission spectra of a 1.0 bar, 1.0x PAL O atmosphere. The SNRs for each band are greatest atthe highest resolving powers, and then gradually decrease until R ∼
60 or 80, at which the SNRs de-crease strongly. This dramatic decrease with resolving power occurs because at the lowest resolvingpowers, the absorption bands are indistinguishable from the continuum. Additionally, the highestflux levels in the continuum cannot be resolved at lower spectral resolving powers, decreasing thetotal signal. This effect can be seen most easily for the spectra with R=20, in which no absorptionfeatures can be identified.Figures 23 and 24 show the SNRs for the direct imaging reflected spectra. In contrast to Figure21, these two figures show the required SNR to detect and characterize an absorption band, not theSNR that could be obtained with JWST. The required SNR to detect spectral features increases asresolving power decreases. However, this effect would be mitigated because the expected noise ateach wavelength should decrease as resolving power decreases. The SNR required to quantify eachabsorption band decreases as resolving power decreases because the lowest radiance level increases.At R <
40, however, spectral features are very difficult to identify, making these resolving powersunsuitable for detecting and characterizing O -related absorption features. 17 – Dimer Biosignatures
In addition to their utility as pressure probes, the 1.06 µ m dimer feature and 1.27 µ m featurecould potentially be detectable biosignatures for nearby Earth-like planets. The O A band haslong been considered the most viable O biosignature, but it is unlikely to be the most detectablebiosignature for an Earth-like planet in transit transmission. As initially described in (Pall´e et al.2009), lunar eclipse observations show that the 1.06 µ m and 1.27 µ m dimer features are more de-tectable than O monomer features like the A band, which is corroborated by our model spectra anddetectability calculations. The 1.27 µ m O feature has been examined as a potential biosignaturefor ground-based telescopes by Kawahara et al. (2012), but to our knowledge detectability studiesof neither the 1.06 µ m dimer feature nor the 1.27 µ m feature have been undertaken for JWST. Ourresults show that the 1.27 µ m feature would be detectable with a SNR of 5 for a cloud-free Earth-analog at 5 pc. Therefore, we conclude that O features, especially the 1.06 µ m dimer feature andthe 1.27 µ m feature, could be detectable biosignatures for oxygenic photosynthesis with JWST. Clouds and aerosols will make estimating pressure using dimer features more difficult. A directimaging observation of a partially cloud-covered planet will be able to probe to the surface for afraction of the paths, such that the dimer feature will be weaker than for a cloud-free planet. Cloudand aerosol extinction can also be wavelength dependent, which may complicate using equivalentwidths or ppm flux differences to determine pressure. Nevertheless dimer features can still providea lower bound for pressure if clouds and aerosols cannot be explicitly included in the retrievalmethod.Higher H O or CO abundances in an atmosphere could also make this method more chal-lenging. Higher H O abundances will make it more difficult to define a continuum for the 1.06 µ mdimer feature, as shown in Figures 18 and 19. However, as discussed in Section 3.4, the magnitudeof this error should typically be less than 20% for most cases in which the 1.06 µ m dimer featurecould be detectable. CO has an absorption feature near 1.06 µ m (Segura et al. 2007), which couldmake using the 1.06 µ m dimer feature difficult. This could be overcome by modeling out absorptionfrom H O and CO or by using other dimer features to supplement information from the 1.06 µ mdimer feature, such as the 1.27 µ m dimer feature.Lastly, not knowing the mixing ratio of O will make estimating pressure difficult when onlya reflected spectrum is available. This is similar to the problem in using the absorption widthsof rotation-vibration features to constrain pressure. However, the 1.06 µ m dimer feature is moresensitive to pressure than a monomer feature, and therefore can provide a better estimate of pressurethan a monomer feature alone. Furthermore, monomer features cannot be used as an on/off pressuregauge, while dimer features can. 18 –
5. Conclusions
Spectrally resolved observations of O dimer absorption can be combined with observationsof the absorption by O vibration-rotation bands to provide independent constraints on the O concentration and the surface or cloud-top pressure in oxygenated atmospheres for planets aroundM dwarfs, and with low levels of CO . Even if a precise estimate for the pressure is not possible,the presence of dimer absorption is indicative of pressures greater than ≃ ≃ concentrations ≥ > partial pressure at the surface is > µ m dimer feature and the 1.27 µ m O feature for anEarth analog orbiting an M dwarf in transit transmission. Thus, while not all the techniquesdescribed here will be applicable to JWST observations, a lower bound on pressure could be setfor an exoplanet using an O dimer feature. Furthermore, we showed that a direct imaging missionoperating in the visible and near-infrared like TPF would require a spectral resolving power ofR >
40, and preferably higher. At R=100, a SNR of >
30 would be required to not only detect O related absorption features, but to also provide an estimate of an exoplanet’s atmospheric pressure. Acknowledgments
We thank Drake Deming for helpful dscussions on the detectability calculations, and the twoanonymous reviewers for their thorough and helpful reviews that greatly improved the paper.This work was performed by the NASA Astrobiology Institute’s Virtual Planetary Laboratory,supported by the National Aeronautics and Space Administration through the NASA AstrobiologyInstitute under Cooperative Agreement solicitation NNH05ZDA001C. This work has also been sup-ported by a generous fellowship from the ARCS Seattle chapter and funding from the Astrobiologyprogram at the University of Washington under an NSF IGERT award.Some of the work described here was conducted at the Jet Propulsion Laboratory, CaliforniaInstitute of Technology, under contract with NASA.This research has made use of NASA’s Astrophysics Data System. 19 –
Author Disclosure Statement
No competing financial interests exist.
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24 –Pressure fO Transit Transmission Secondary EclipseBars PAL O A band O -O µ m O µ m O A band O -O µ m O µ m0.1 0.1 0.2 0.0 0.0 5.2e-04 0.0e+00 2.7e-030.1 0.5 0.5 0.0 0.9 1.2e-03 0.0e+00 3.4e-030.1 1.0 0.6 0.0 1.2 1.7e-03 0.0e+00 4.2e-030.1 2.0 0.8 0.0 1.5 2.4e-03 0.0e+00 5.5e-030.5 0.1 0.5 0.0 1.1 2.3e-03 0.0e+00 5.5e-030.5 0.5 0.8 0.0 2.5 5.0e-03 0.0e+00 1.2e-020.5 1.0 1.1 1.2 3.7 6.7e-03 0.0e+00 1.8e-020.5 2.0 1.1 2.3 5.1 8.5e-03 1.2e-02 2.7e-021.0 0.1 0.5 0.0 1.6 4.1e-03 0.0e+00 9.5e-031.0 0.5 0.8 0.5 3.9 7.8e-03 0.0e+00 2.6e-021.0 1.0 1.1 1.5 5.2 9.4e-03 1.3e-02 3.9e-021.0 2.0 1.1 3.4 7.5 1.1e-02 3.5e-02 6.3e-023.0 0.1 0.5 0.0 1.2 7.3e-03 0.0e+00 3.2e-023.0 0.5 0.8 0.6 3.5 1.0e-02 2.1e-02 8.4e-023.0 1.0 1.1 1.5 5.0 1.1e-02 6.2e-02 9.9e-023.0 2.0 1.1 3.5 7.2 1.2e-02 1.5e-01 1.2e-015.0 0.1 0.5 0.0 1.1 7.5e-03 0.0e+00 5.8e-025.0 0.5 0.8 0.6 3.3 9.6e-03 4.3e-02 1.1e-015.0 1.0 1.1 1.4 4.9 1.1e-02 1.2e-01 9.4e-025.0 2.0 1.1 3.3 7.2 1.2e-02 2.1e-01 1.1e-0110.0 0.1 0.5 0.0 1.1 5.9e-03 0.0e+00 9.2e-0210.0 0.5 0.8 0.7 3.4 7.8e-03 9.3e-02 6.1e-0210.0 1.0 1.1 1.4 5.0 8.6e-03 1.7e-01 6.1e-0210.0 2.0 1.1 3.4 7.4 9.0e-03 2.1e-01 5.0e-02Table 1: SNRs for the O A band, the 1.06 µ m dimer feature and the 1.27 µ m feature for all thecases considered in both transit transmission and secondary eclipse. The calculations were donefor an Earth analog orbiting an M5V star at a distance of 5 pc. The total integration time wasassumed to be 10 s, equal to the total amount of time spent in transit for this case over JWST’s5 year mission lifetime. The 1.06 µ m dimer feature and the 1.27 µ m feature could be detectable,allowing a lower limit for atmospheric pressure to be set. 25 –Pressure fO O A band 1.06 µ m dimer 1.27 µ m featureBars PAL SNR D SNR P SNR D SNR P SNR D SNR P >
100 3.1 - - - -0.1 0.5 50.0 3.2 - - >
100 3.00.1 1.0 35.0 5.4 - - >
100 5.10.1 2.0 24.4 3.4 - - 89.8 3.10.5 0.1 25.1 3.4 - - >
100 3.10.5 0.5 11.4 3.9 - - 38.8 3.20.5 1.0 8.6 7.3 - - 23.8 5.60.5 2.0 6.8 5.0 30.9 3.2 14.3 3.71.0 0.1 13.4 3.8 - - 62.0 3.11.0 0.5 7.1 4.8 - - 16.4 3.61.0 1.0 5.8 9.1 29.0 5.4 9.9 6.91.0 2.0 5.0 6.1 9.6 3.7 5.9 5.43.0 0.1 6.2 5.3 - - 12.8 3.83.0 0.5 4.4 6.9 16.5 3.4 4.3 7.23.0 1.0 3.9 13.2 4.9 8.1 2.9 26.73.0 2.0 3.5 9.4 1.9 18.9 1.7 > > >
100 1.3 > > >
100 1.2 > >
100 1.0 > D ) and to obtain precision of 3 σ in the center of the band (SNR P )for the O A band, the 1.06 µ m dimer feature and the 1.27 µ m feature at pressures ranging from0.1 to 10.0 bars and O concentrations ranging from 0.1 to 2.0 times PAL O for direct imagingreflected spectra. 26 –Fig. 1.— Comparison of the effect of refraction on (a) an exoplanet around an M dwarf and (b) aplanet around a Sun-like star with both planets receiving the same total flux. The dashed circlesare the planetary atmospheres. The solid lines represent different refracted paths through theatmosphere, and the dashed lines are the hypothetical paths to a distant observer observing theplanet in transit transmission. Only paths that lie exactly on that dashed line will be observed. Forthe M dwarf case, there will be a path connecting the star to the observer through the atmosphereat this particular tangent height. However, there is no path in the Sun-like star case. This meansthat a transit transmission spectrum of the planet around the M dwarf can theoretically probehigher pressures of the atmosphere than in the Sun-like star case. 27 – A l b e d o Fig. 2.— Wavelength-dependent albedos for a variety of surfaces. The shaded regions correspondto O monomer and dimer bands. For any absorption band, as long as the albedo does not varywidely within the band’s wavelength range it should be possible to measure an accurate equivalentwidth for each feature. The maximum variation within a band is no more than ∼ -7 -6 -5 -4 -3 -2 -1 Volume Mixing Ratio10 -8 -7 -6 -5 -4 -3 -2 -1 P r e ss u r e ( b a r s ) TOA Pressure=3.5e-080.1 bars180 200 220 240 260 280 300Temperature (K) 10 -7 -6 -5 -4 -3 -2 -1 Volume Mixing RatioTOA Pressure=1.8e-070.5 bars180 200 220 240 260 280 300Temperature (K) 10 -7 -6 -5 -4 -3 -2 -1 Volume Mixing RatioTOA Pressure=3.6e-071.0 bars180 200 220 240 260 280 300Temperature (K)10 -7 -6 -5 -4 -3 -2 -1 Volume Mixing Ratio10 -8 -7 -6 -5 -4 -3 -2 -1 P r e ss u r e ( b a r s ) TOA Pressure=1.1e-063.0 bars180 200 220 240 260 280 300Temperature (K) 10 -7 -6 -5 -4 -3 -2 -1 Volume Mixing RatioTOA Pressure=1.8e-065.0 bars180 200 220 240 260 280 300Temperature (K) 10 -7 -6 -5 -4 -3 -2 -1 Volume Mixing RatioTOA Pressure=4.4e-0610.0 bars180 200 220 240 260 280 300Temperature (K) H OO O CO T Fig. 3.— Pressure-temperature profiles and volume mixing ratio profiles for all pressures at 1.0xPAL O . The black dashed lines represent the surface pressures and top of atmosphere pressures.We use the modern Earth temperature-altitude profile in all cases and calculate the pressuresassuming hydrostatic equilibrium. The remainder of the atmosphere is N for all cases. 28 – (cid:0) m) (cid:1) (cid:2) (cid:3) (cid:4) (cid:5) (cid:6) (cid:7) (cid:8) D i ff e r e n c e f r o m s t e ll a r f l u x ( pp m ) O Aband 1.06 (cid:9) mdimer0.69 (cid:10) mO (cid:11) mfeature a (cid:12) m)0.20950.21000.21050.21100.21150.21200.21250.2130 P e r c e n t a b s o r p t i o n O Aband 1.06 (cid:13) mdimer0.69 (cid:14) mO (cid:15) mfeature b Fig. 4.— Transmission spectra of an Earth-like atmosphere with different total atmospheric pres-sures. (a)
Difference in flux from the stellar flux. (b)
Percent of stellar flux absorbed by theatmosphere. The 1.06 µ m dimer feature is strong only in the spectra corresponding to atmosphericpressures greater than ∼ ≥ ∼ (cid:16) m) (cid:17) (cid:18) (cid:19) (cid:20) (cid:21) (cid:22) (cid:23) (cid:24) D i ff e r e n c e f r o m s t e ll a r f l u x ( pp m ) O Aband 1.06 (cid:25) mdimer0.69 (cid:26) mO (cid:27) mfeature a (cid:28) m)0.20950.21000.21050.21100.21150.21200.21250.2130 P e r c e n t a b s o r p t i o n O Aband 1.06 (cid:29) mdimer0.69 (cid:30) mO (cid:31) mfeature b Fig. 5.— Same as Figure 4 but for 10% of the present day level of O . The dimer features do notappear at all because the O concentration is too low. 29 – m) ! " $ % & ’ ( D i ff e r e n c e f r o m s t e ll a r f l u x ( pp m ) O Aband 1.06 ) mdimer0.69 * mO + mfeature a , m)0.20950.21000.21050.21100.21150.21200.21250.2130 P e r c e n t a b s o r p t i o n O Aband 1.06 - mdimer0.69 . mO / mfeature b Fig. 6.— Same as Figure 4 but for 50% of the present day level of O . The 1.06 µ m dimer featureis very weak, and is still weak for the highest surface pressure atmospheres. m) D i ff e r e n c e f r o m s t e ll a r f l u x ( pp m ) O Aband 1.06 mdimer0.69 : mO ; mfeature a < m)0.20950.21000.21050.21100.21150.21200.21250.2130 P e r c e n t a b s o r p t i o n O Aband 1.06 = mdimer0.69 > mO ? mfeature b Fig. 7.— Same as Figure 4 but for 200% of the present day level of O . The 1.06 µ m dimer featureis very strong in every case except for the 0.1 bar atmosphere. 30 – P l a n e t a r y A l b e d o @ mdimerO Abanddimer0.63 A m 1.27 B mfeature0.69 C mO Fig. 8.— Reflected spectra for Earth-like atmospheres with 100% PAL O but with different totalatmospheric pressures. In the reflected spectrum there is no fundamental limit to which pressurescan be probed in an atmosphere. Assuming a cloud-free case, it is possible to probe the surfacelayers of the atmosphere. The 1.06 µ m dimer feature is fairly weak in the present day Earth’satmosphere, but it is a very strong feature in atmospheres with greater pressures. The 1.27 µ mfeature is very strong in most of the spectra. P l a n e t a r y A l b e d o D mdimerO Abanddimer0.63 E m 1.27 F mfeature0.69 G mO Fig. 9.— Same as Figure 8 but for an O concentration of 10% PAL. For this amount of O , the1.06 µ m dimer feature is very weak. However, the 1.27 µ m feature is still quite strong. 31 – P l a n e t a r y A l b e d o H mdimerO Abanddimer0.63 I m 1.27 J mfeature0.69 K mO Fig. 10.— Same as Figure 8 but for an O concentration of 50% PAL. The 1.06 µ m dimer featureis strong at pressures ≥ P l a n e t a r y A l b e d o L mdimerO Abanddimer0.63 M m 1.27 N mfeature0.69 O mO Fig. 11.— Same as Figure 8 but for an O concentration of 200% PAL. The dimer features aremuch stronger with more O in the atmosphere, as expected. 32 – P a r t s p e r m illi o n ( pp m ) d i ff e r e n c e Transmission E q u i v a l e n t W i d t h ( n m ) ReflectedO A bandO dimer a b Fig. 12.— (a)
Flux differences (in ppm) for transit transmission spectra and (b) equivalent widths(in nm) for reflected spectra for the O A band and the 1.06 µ m dimer feature at various pressuresand O concentrations. In transmission, for the Earth-like planet orbiting an M5V star consideredhere, only the top 0.9 bars can be probed, meaning the dimer and A band equivalent widths areroughly constant with pressure above 1.0 bars for a given O concentration. In comparison to thereflected spectra, the dimer equivalent widths are extremely sensitive to pressure. 33 – P T o t a l b a r s o f O a t s u r f a c e a f O b Fig. 13.— This plot shows how one could determine a lower limit on the surface or cloud-toppressure using only a transmission spectrum. (a) O partial pressure at maximum tangent pressurevs. the ratio of the dimer feature and O A band flux difference ratio. The ratio can be used todetermine the O partial pressure. (b) fO (or O mixing ratio) vs A band flux difference. The Aband flux difference is roughly constant for a given O mixing ratio. 34 – Q B a r s o f O Fig. 14.— Plot of total atmospheric O vs the ratio of the 1.06 µ m dimer feature equivalent widthto the O A band equivalent width for the reflected spectrum. There is a trend between this ratioand the total amount of O . This could be used as a way to estimate the pressure if a transmissionspectrum is not available. E q u i v a l e n t W i d t h ( A b a n d ) Fig. 15.— Atmospheric pressure as a function of the dimer and A band equivalent widths in thereflected spectrum. It will be possible to set a lower bound on the pressure with only the O Aband equivalent width and the 1.06 µ m dimer equivalent width. 35 – D i ff e r e n c e f r o m S t e ll a r F l u x ( m ) a P l a n e t a r y A l b e d o b P l a n e t / S t e ll a r F l u x Fig. 16.— ( a ) Transit transmission spectra for the Earth (blue) and an isothermal atmosphere at250K with the same pressure-composition profiles (green). ( b ) Reflected spectra for an Earth analogwith 2.0x PAL O (blue) and an isothermal atmosphere at 250K with the same pressure-compositionprofiles (green). In both cases, the spectra for the calculated temperature-pressure profile and theisothermal profile are very similar, showing that the spectra are not strongly dependent on thetemperature profile. R S T U V W X D i ff e r e n c e f r o m s t e ll a r f l u x ( pp m ) O A band 1.06 Y m dimer 1.27 Z mfeature O1.0xH O10.0xH O Fig. 17.— Transit transmission spectra of a 1.0 bar, 1.0x PAL O Earth analog with H O concen-trations varying from 0.1 to 10.0x PAL H O. While H O absorbs near the wings of the O A bandthe ppm flux difference and the SNR do not change greatly as the H O concentration changes. Thecontinuum near the 1.06 µ m dimer feature is strongly affected by the increases in H O. However,the magnitude of the change in the ppm flux difference over the entire band and the SNR is lessthan 20% when comparing the 1.0x PAL H O case to either the 0.1 or 10.0x H O cases. 36 – [ \ ] ^ _ ‘ a D i ff e r e n c e f r o m s t e ll a r f l u x ( pp m ) O1.0xH O10.0xH O Fig. 18.— The 1.06 µ m dimer feature in transit transmission with different amounts of H O. Thespectra have been artificially offset for ease of viewing. The black dashed lines are spectra that donot include any O dimer absorption and are included to help show the continuum flux level. Thetotal ppm flux difference and SNR for the dimer band vary by less than 20% with respect to the1.0xH O case. b P l a n e t a r y A l b e d o O1.0xH O10.0xH O P l a n e t / S t e ll a r F l u x c Fig. 19.— The 1.06 µ m dimer feature in the direct beam reflected spectra with varying amounts ofH O for an Earth analog with a 1.0 bar, 2.0x PAL O atmosphere. There is an artificial offset forease of viewing, and the black dashed lines are spectra that do not include any O dimer absorption.As in transit transmission, the SNR of the dimer feature varies by less than 20% with respect to the1.0x H O case. Additionally, the SNRs for higher pressure cases should be less affected by changesin H O concentrations because of greater absorption within the dimer band. 37 – d e f g h i D i ff e r e n c e f r o m s t e ll a r f l u x ( pp m ) R=500R=200R=100R=80R=60R=40R=30R=20 1.06 j m dimerO A band 1.27 k m feature Fig. 20.— Transit transmission spectra for the 1.0 bar, 1.0x PAL O case at various spectralresolving powers. The wavelengths for the O A band, the 1.06 µ m dimer band, and the 1.27 µ mband are highlighted. An artificial offset has been added to the spectra for ease of viewing. At thelowest resolving powers, it is difficult to identify spectral features. S N R i n a b s o r p t i o n b a n d O A band1.06 l m dimer1.27 m m feature Fig. 21.— SNRs of absorption features for the spectra shown in Figure 20. The SNRs decreaseas resolving power decreases because the absorption bands can no longer be resolved from thecontinuum. For R=30 and R=20 it is very difficult to identify any of the O spectral features. 38 – P l a n e t a r y A l b e d o R=500R=200R=100R=80R=60R=40R=30R=20 1.06 n m dimerO A band 1.27 o m feature Fig. 22.— Direct imaging reflected spectra generated at spectral resolving powers from 500 to 20.The y-axis is the planetary albedo with an arbitrary offset added for ease of viewing. The O Aband, 1.06 µ m dimer feature and 1.27 µ m feature are highlighted. At resolving powers of R=30and R=20 it is difficult to identify any O absorption features. S N R r e q u i r e d f o r d e t e c t i o n O A band1.06 p m dimer feature1.27 q m feature Fig. 23.— SNRs needed to detect the O A band, 1.06 µ m dimer feature and the 1.27 µ m featurefor direct imaging reflected spectra. As resolving power decreases, the required SNR to detect eachfeature increases because the continuum level decreases, resulting in a lower overall signal in theabsorption band. Furthermore, at the lowest resolutions the absorption bands cannot be resolved.Thus, this decreases the measurable signal even more, leading to an increase in the required SNR. 39 – S N R O A band1.06 r m dimer feature1.27 s m feature Fig. 24.— SNRs required to quantify the flux within 3 σ in the center of the absorption band (definedas the lowest flux level) for the O A band, 1.06 µ m dimer feature and the 1.27 µ m feature. TheSNR required for this level of precision decreases as resolving power decreases because the flux isaveraged over fewer wavelength bins, leading to an increase in the lowest flux. This decrease inrequired resolving power occurs for all three absorption features, though the trend is most apparentfor the O2