Prospects for detecting oxygen, water, and chlorophyll on an exo-Earth

Significance

One of NASA’s most important long-term goals is to detect and characterize terrestrial exoplanets, and to search their spectra for signs of life. This overarching goal is currently driving concepts for a future high-contrast flagship mission. We determine the fidelity with which such a mission would need to measure an exo-Earth’s spectrum to detect oxygen, water, and chlorophyll. Our results suggest that a well-designed space mission could detect O₂ and H₂O in a nearby Earth twin, but that it would need to be significantly more sensitive (or very lucky) to see chlorophyll. We suggest designing the instrument with an eye toward oxygen, and perhaps looking for chlorophyll around one or a few exceptional targets.

Abstract

The goal of finding and characterizing nearby Earth-like planets is driving many NASA high-contrast flagship mission concepts, the latest of which is known as the Advanced Technology Large-Aperture Space Telescope (ATLAST). In this article, we calculate the optimal spectral resolution R = λ/δλ and minimum signal-to-noise ratio per spectral bin (SNR), two central design requirements for a high-contrast space mission, to detect signatures of water, oxygen, and chlorophyll on an Earth twin. We first develop a minimally parametric model and demonstrate its ability to fit synthetic and observed Earth spectra; this allows us to measure the statistical evidence for each component’s presence. We find that water is the easiest to detect, requiring a resolution R ≳ 20, while the optimal resolution for oxygen is likely to be closer to R = 150, somewhat higher than the canonical value in the literature. At these resolutions, detecting oxygen will require approximately two times the SNR as water. Chlorophyll requires approximately six times the SNR as oxygen for an Earth twin, only falling to oxygen-like levels of detectability for a low cloud cover and/or a large vegetation covering fraction. This suggests designing a mission for sensitivity to oxygen and adopting a multitiered observing strategy, first targeting water, then oxygen on the more favorable planets, and finally chlorophyll on only the most promising worlds.

While indirect methods have now discovered several thousand exoplanets (1–4), most of these are currently inaccessible to characterization. Direct imaging offers the ability to observe an exoplanet in either thermal or reflected light, and provides a window into the structure and composition of its atmosphere. Ultimately, one of NASA’s goals is to find and characterize terrestrial exoplanets around nearby stars and to search for molecules and biosignatures. The Terrestrial Planet Finder (e.g. refs. 5 and 6) was one mission concept with this goal in mind, while the Advanced Technology Large-Aperture Space Telescope (ATLAST, ref. 7) represents a more recent proposal. Such a mission would target at least the optical wavelength range from ∼0.5 μm to ∼1 μm to look for spectral indications of molecular oxygen (O₂), ozone (O₃), and water (H₂O). These molecules are the most prominent absorbers in this spectral range, and are all critical species for terrestrial life.

Several studies have looked at the prospects for detecting biosignatures on an Earth twin (8–10), or for learning about an exo-Earth’s surface from phase variations in its colors (11–14). Of course, there is no unique exo-Earth spectrum: The composition of Earth’s atmosphere, including its oxygen abundance, has changed enormously throughout life’s existence (15). Furthermore, features that are biosignatures in Earth’s spectrum may not necessarily be so in a terrestrial exoplanet. For instance, diatomic oxygen can, under some circumstances, also be produced abiotically (16). More speculatively, chlorophyll shows a strong increase in its albedo around 0.7 μm (the “red edge”), which could be detected on an exo-Earth (17, 18). Such an argument relies on the uniqueness of the chlorophyll family of molecules as the basis for photosynthesis (19).

Many of the papers referenced above have run detailed model atmosphere calculations. Our goal here is different. We seek to construct the simplest model that can adequately reproduce a terrestrial planet’s spectrum, and to use it to derive statistically rigorous criteria to claim detections of molecular species. Using a model with few free parameters increases the statistical significance with which the most interesting parameters (like the H₂O or O₂ column) may be estimated. We make as few assumptions as possible about the (highly uncertain) performance of a future high-contrast space mission. Rather than working from an instrument to detectability, we turn the problem around, and attempt to quantify the optimal design and minimum performance needed to reach NASA’s terrestrial planet characterization goals.

Terrestrial Planet Spectra

We begin with a crude, but roughly correct, approximation of a terrestrial planet spectrum in reflection. Our goal is to capture the main spectral features of Earth in a context where we can easily modify the cloud, surface, and atmospheric compositions, allowing us to validate the statistical approach we present in this paper.

We assume a (wavelength-dependent) surface albedo α_λ, a cloud albedo c_λ, a cloud fraction f_c, an optical depth to Rayleigh scattering ${\mathrm{ℛ}}_{\lambda }$ (assumed to be small), and absorption cross sections σ_s[λ] for chemical species s in Earth’s atmosphere. The wavelength-dependent optical depth for a species s is the product of its cross section σ_s[λ] and its column density N_s, so that τ_λ, the full atmosphere’s optical depth, is

$${\tau }_{\lambda }={\displaystyle \sum _s{\sigma }_s\left[\lambda \right]N_s},$$ [1]

where the sum over s includes the molecules O₂, O₃, and H₂O.

We approximate all Rayleigh scattering as occurring through half the available atmosphere, as illustrated in Fig. 1. While O₂ is relatively well mixed up to the stratosphere, most O₃ is above, and most water below, the tropopause (20). We therefore assume that all scattered photons pass through the entire O₃ column twice, while photons Rayleigh scattered by O₂ and N₂, as well as those scattered by clouds, pass through less than half the water vapor column. We find that assuming these photons to pass through 20% of the H₂O column reproduces the approximate strength of the water features in more detailed models (21).

Fig. 1.

Illustration of the scattering approximation described by Eq. 2; we approximate all Rayleigh scattering as occurring below half of the available atmosphere. We assume that all photons pass through the stratospheric O₃ layer twice, while photons scattered by clouds and Rayeigh scattered by atmospheric O₂ and N₂ pass through less than half the water vapor column.

Our full approximation to the reflected flux density becomes

$$\frac{F_{\text{refl}}}{F_{\mathrm{\star }}}\approx \frac{{\mathrm{ℛ}}_{\lambda }}{2}{f}_c\exp \left[-2{\tau }_{\text{top}}\right]+\left(1-\frac{{\mathrm{ℛ}}_{\lambda }}{2}\right)f_c{c}_{\lambda }\exp \left[-2{\tau }_{\text{mid}}\right]+{\mathrm{ℛ}}_{\lambda }\left(1-f_c\right)\text{exp}\left[-2{\tau }_{\text{mid}}\right]+\left(1-{\mathrm{ℛ}}_{\lambda }\right)\left(1-f_c\right){\alpha }_{\lambda }\exp \left[-2{\tau }_{\text{full}}\right],$$ [2]

where $F_{\mathrm{\star }}$ is the incident (solar, http://rredc.nrel.gov/solar/spectra/am0/) flux on the planetary atmosphere, and F_refl is the reflected flux. The first term approximates Rayleigh scattering above the clouds, the second term accounts for scattering by the clouds themselves, the third term is Rayleigh scattering above the surface, and the last term is scattering by the surface (we have dropped all terms with ${\mathrm{ℛ}}_{\lambda }^2$). The three optical depths, through 1/4, 1/2, and all of the atmosphere, are given by

$${\tau }_{\text{top}}={\sigma }_{\text{O}3}{N}_{\text{O}3}+{\sigma }_{\text{O}2}{N}_{\text{O}2}/4+{\sigma }_{\text{H}2\text{O}}{N}_{\text{H}2\text{O}}/10,$$ [3]

$${\tau }_{\text{mid}}={\sigma }_{\text{O}3}{N}_{\text{O}3}+{\sigma }_{\text{O}2}{N}_{\text{O}2}/2+{\sigma }_{\text{H}2\text{O}}{N}_{\text{H}2\text{O}}/5,$$ [4]

$${\tau }_{\text{full}}={\sigma }_{\text{O}3}{N}_{\text{O}3}+{\sigma }_{\text{O}2}{N}_{\text{O}2}+{\sigma }_{\text{H}2\text{O}}{N}_{\text{H}2\text{O}}.$$ [5]

We use the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) spectral library (22) for our surface albedos excepting water, an approximation based on ref. 23 for oceans (including a substantial correction for specular reflection at blue wavelengths), ref. 24 for water cloud albedos, and ref. 25 for the cross sections of O₂, H₂O, and O₃. We assume the surface to be 70% water, 10% sand, 10% vegetation, 5% dry grass, and 5% snow, consistent with estimates from data taken by the Moderate Resolution Imaging Spectroradiometer (MODIS) satellite (26) and tabulated in ref. 11. We take our normalization of the Rayleigh scattering optical depths for Earth’s atmosphere from ref. 27. We take a 50% cloud coverage, noting that its main effects are to obscure spectral features from the surface and dilute the water features (cloud albedos are gray to an excellent approximation, while photons must still travel through at least ∼1/2 the atmosphere). The effective albedo of clouds is ∼60–65% across the wavelength range, washing out surface spectral features by a factor ≫1 when the clouds are optically thick.

We create mock spectra by smoothing the output of Eq. 2 to an adopted spectral resolution using a Gaussian line spread function,

$$\text{LSF}\left[\lambda /{\lambda }_0\right]\propto \exp \left[-\left(4\ln 2\right)R^2{\left(\frac{\lambda }{{\lambda }_0}-1\right)}^2\right],$$ [6]

where R is the (dimensionless) instrumental resolution, the full width at half maximum of the Gaussian. We assume that these spectra are well sampled [i.e., at the Nyquist rate or better, δλ ≲ λ/(2R)]. Binning the spectra, in contrast, would be equivalent to convolving with a boxcar line spread function and sampling at the boxcar’s full width. Such undersampling makes spectral reconstruction dependent on excellent knowledge of the line spread function and even on the centers chosen (often arbitrarily) for the wavelength bins.

Finally, we convert our units into flux density f_ν, proportional to photons per logarithmic wavelength bin. The resulting flux density is approximately constant (within a factor of ∼1.5) across our wavelength range: an upturn in albedo from Rayleigh scattering at ≲0.5 μm compensates for a sharp fall in stellar intensity. Supporting Information provides additional details. We further assume that noise, whether from speckle residuals, background photon noise, read noise, or some other source, is also a constant across the wavelength range, so that the signal-to-noise ratio per λ/R bin (SNR) is nearly independent of wavelength (apart from the centers of spectral lines/features, where the signal drops).

Fig. 2 shows noiseless mock spectra of an Earth twin at full phase for a variety of spectral resolutions. For spectral resolutions R ≲ 20, the prominent 0.76-μm O₂ absorption feature becomes almost completely blended with neighboring water features, making the spectrum flat. The ozone band centered at λ ∼ 0.59 μm is both broad and shallow, making it difficult to see at any spectral resolution. Water features, on the other hand, remain conspicuous down to R ∼ 20.

Fig. 2.

Comparison of our spectrum of an Earth twin convolved to a given spectral resolution with a Gaussian line spread function. The prominent O₂ absorption feature at 0.76 μm becomes completely blended with neighboring water features for R ≲ 20, while the O₃ feature is wide and shallow, and very difficult to see.

A Minimally Parametric Model

We assume that the spectrum of a hypothetical terrestrial exoplanet will be modeled using a known stellar spectrum, absorption spectra of possible atmospheric constituents, and Rayleigh scattering. Unfortunately, a space mission capable of achieving contrasts of 10⁻¹⁰ will be unlikely to have perfect spectrophotometric calibration of a faint exoplanet. Surface materials have spectral albedos that vary across the visible wavelength range, although most plausible surface materials, including soils, snow, and water, lack sharp spectral features from ∼0.5 μm to 1 μm. We therefore combine the unknown spectrophotometric calibration and surface albedos into a free multiplicative low-order polynomial. We make one exception: the “red edge” of chlorophyll at ∼0.72 μm, which we approximate using a softened Heaviside function,

$$H\left[\lambda \right]={\left(1+\exp \left[80\left(0.72-\lambda /\mathrm{\mu }\text{m}\right)\right]\right)}^{-1},$$ [7]

with the center and width chosen to match the feature in vegetation in the ASTER libraries.

Our model for a terrestrial planet’s reflection spectrum takes the form

$$F_{\lambda }\approx F_{\lambda ,\mathrm{\star }}\left({\displaystyle \sum _i{a}_i{\lambda }^i}\right)(\left(1+bH\left[\lambda \right]\right)\exp \left[-{\displaystyle \sum _{s}2{\sigma }_s\left[\lambda \right]N_s}\right]+\frac{c}{{\lambda }^4}\exp \left[-{\displaystyle \sum _s{\sigma }_s\left[\lambda \right]N_s}\right]),$$ [8]

where σ_s[λ] is the (known) cross section of a molecular species s, N_s is its column density (making σ_s[λ]N_s the optical depth of each pass through the atmosphere), and the first term, a polynomial, accounts for uncertainties in the surface (and cloud) albedo and spectrophotometric calibration. We crudely include Rayleigh scattering with a term c/λ⁴, making the approximation that all Rayleigh scattering occurs beneath half the atmosphere. Photons scattered off the surface pass through the atmosphere twice, accounting for the factor of 2 in the first sum over species s. We caution against interpreting the Rayleigh-like term too literally; it also combines with the polynomial term to add flexibility to account for the unknown surface albedo. The vegetation parameter b, which we can either fix to be zero or allow to float, approximates the addition of an arbitrary vegetation covering fraction. We compute Eq. 8 at very high spectral resolution and then convolve it with the line spread function (Eq. 6).

We fit Eq. 8 to our mock terrestrial planet spectra, varying its parameters to minimize

$${\chi }^2={\displaystyle \sum _{\lambda }\frac{{\left(F_{\lambda ,\text{obs}}-F_{\lambda ,\text{model}}\right)}^2}{{\sigma }_{\lambda }^2}},$$ [9]

where σ_λ is the measurement error at λ. We fit as many as eight free parameters: a column density N_s ≥ 0 for each of O₂, O₃, and H₂O, a normalization c of Rayleigh scattering, three polynomial coefficients a_i (for a free quadratic), and a chlorophyll strength b. By fixing one (or more) of the N_s to be zero, the minimum value of χ² will generally increase as the model loses flexibility; the magnitude of the increase is a measure of the evidence for that species’ presence (N_s > 0).

We test our minimally parametric model, Eq. 8, against three reference spectra: the output of Eq. 2, a full radiative transfer model from the Virtual Planet Laboratory (VPL) (21), and an Earthshine spectrum spliced together from visible and near-infrared observations (28, 29). Fig. 3 Top shows these fits at a spectral resolution R = 150; the thick, dashed, colored lines are the reference spectra, while the thin black lines are the fits using Eq. 8. Eq. 8 has difficulty reproducing the exact shape of the deep water features. If we extend the model by confining the water vapor to a fraction f of the atmosphere (adding one additional free parameter, for a new total of nine), the fits improve significantly (thin magenta curves).

Fig. 3.

(Top) The best-fitting minimally parametric model (Eq. 8, black curves) to Eq. 2 (red dashed curve), a VPL model (21) (R11, blue dashed curve), and a spliced Earthshine spectrum (28, 29) (W02+T06, green dashed curve). The magenta curves add one additional parameter to Eq. 8, the fraction of the atmosphere containing water vapor, and provide a much better fit to the deep water features. (Middle) The fit of our minimally parametric model (MPM, Eq. 8, blue curve) to one realization of Gaussian noise with SNR = 8 (black histogram). (Bottom) The fit in Middle decomposed by terms, at R = 1,000. We caution against interpreting the Rayleigh term (∝ λ⁻⁴) too literally, as this term ends up including much of the spectral variation in albedo.

We say that Eq. 8 becomes inadequate when its best fit χ² exceeds the number of degrees of freedom by the same amount required to detect an atmospheric feature (Δχ² ∼ 10, as we derive in False Positives and Significance Thresholds). In other words, this is the point at which the information missing in Eq. 8 might be enough to detect an additional feature of the planet’s spectrum. According to this criterion, at R = 150, Eq. 8 provides a satisfactory fit to Eq. 2 for SNR ≲ 45, and to the VPL model and the spliced Earthshine spectrum for SNR ≲ 10. Adding one additional parameter, the fraction of the atmosphere free of water, enables the model to fit the VPL and the Earthshine spectra up to SNR ∼ 20 at R = 150. In all cases, our neglect of nongray surface albedos and detailed radiative transfer appears to be unimportant except at very high SNR.

Fig. 3 Middle shows the fit of Eq. 8 (blue curve) to Eq. 2 (red curve) at R = 150 for one realization of Gaussian noise with SNR = 8 (black histogram). The noisy spectrum is sampled at $R\sqrt{8\ln 2}\approx 2.35R$, the inverse SD of the line spread function; the signal-to-noise ratio per spectral measurement is then $\left(1/\sqrt{2.35}\approx 0.65\right)\times \text{SNR}$. Fig. 3 Bottom shows the best-fit spectrum, the blue curve from Fig. 3 Middle, decomposed by the individual terms in Eq. 8. We have smoothed the spectra to R = 1000 for illustration purposes. The polynomial fit (red curve) is redder than the solar spectrum, while including the “Rayleigh term” gives a spectrum bluer than solar. In practice, the Rayleigh term does not accurately measure the optical depth to Rayleigh scattering. It is strongly covariant with the free polynomial, and enables Eq. 8 to fit broad spectral variations in cloud and surface albedos.

False Positives and Significance Thresholds

In this section, we return to our approximation to a terrestrial planet’s reflection spectrum (Eq. 2). We quantify the significance of a possible detection of water, oxygen, and/or ozone in its atmosphere, using the improvement in the χ² parameter with the addition of a molecular absorption template to Eq. 8 (as a free parameter) to measure the evidence for that species’ presence. To set the minimum χ² needed to claim a detection, we create a series of mock atmospheres using Eq. 2, but without a given species. We then measure the distribution of differences in χ² with and without constraining that species’ N_s to zero in Eq. 8. This is the distribution of χ² improvements under the null hypothesis, and it allows us to set thresholds for a given false positive probability.

Fig. 4 shows the results of this test for our Earth analog with 50% cloud cover, first setting the O₂ column to zero, and then setting both O₂ and O₃ to zero. We perform the same test on our desert world assuming a 30% cloud cover, and finally with H₂O on a dry exoplanet with a surface composed of 100% sand and rock. In the cases of O₂ and H₂O, the addition of an (unwarranted) extra degree of freedom produces a distribution of improvement in χ² values that matches $\left({\chi }_1^2+\delta \right)/2$, one-half the χ² distribution with one degree of freedom plus a Dirac delta function (this is because of the nonnegativity constraint on the column densities: half of the distribution is a delta function at zero). The distribution in the case of two missing atmospheric components, O₂ and O₃, is not quite a linear combination of ${\chi }_1^2$ and ${\chi }_2^2$, the χ² distributions with one and two degrees of freedom, particularly in the tail. Ozone’s ∼0.6-μm band is a broad and shallow spectral feature that can combine with the Rayleigh term and polynomial term in Eq. 8 to reproduce a wider range of spectral shapes.

Fig. 4.

Distributions of the improvements in χ² by adding an additional degree of freedom represented by a species not present in a model atmosphere; the vertical axis is the probability density per logarithmic χ², allowing the curves to be integrated by eye. The O₂ and H₂O fits are consistent with ${\chi }_1^2/2$, half of the χ² distribution with one degree of freedom (the factor of 1/2 arising because column densities must be nonnegative); the O₂+O₃ fits disagree somewhat with the relevant linear combination of ${\chi }_1^2$ and ${\chi }_2^2$ (the χ² distribution with two degrees of freedom) in the tails. We use the ${\chi }_1^2/2$ distribution to set Δχ² detection thresholds for O₂ and H₂O.

In the case of O₂ and H₂O, we use $\left({\chi }_1^2+\delta \right)/2$, 1/2 the χ² distribution with one degree of freedom plus a Dirac delta function, to establish our false positive thresholds. This distribution has 99.9% of its integrated probability below Δχ² = 9.6, and 99.99% below Δχ² = 13.8; we adopt these as our thresholds for a 10⁻³ and 10⁻⁴ false positive rate, respectively. With two molecular species, the thresholds for a 10⁻³ and 10⁻⁴ false positive rate would become 11.8 and 16.3, respectively, if they were described by the ${\chi }_1^2/2+{\chi }_2^2/4+\delta /4$ distribution. The actual distributions for the combination of O₂ and O₃, the red and green histograms in Fig. 4, have longer tails. The χ² values containing 99.9% and 99.99% of these distributions are not 11.8 and 16.3, but rather 14 and 19 for the Earth twin, and 12.4 and 17.5 for the desert world.

We also note that the addition of a second free parameter to describe H₂O, which significantly improves the fits in Fig. 3 Top, changes the relevant χ² distribution to ${\chi }_1^2/4+{\chi }_2^2/4+\delta /2$ (both parameters are subject to nonnegativity constraints). The additional parameter thus modifies the χ² thresholds to 11.4 and 16 for false positive probabilities of 10⁻³ and 10⁻⁴, respectively, illustrating the drawback of fitting a more complex model than necessary.

Detecting Components of the Atmosphere and Surface

We now turn to the probability of detecting an atmospheric constituent given our mock spectra, our eight-parameter fitting routine, and an adopted false positive threshold (which we take to be either 10⁻³ or 10⁻⁴). These detection probabilities depend on the spectral resolution and noise level, so that the probability for each species resides in a 2D space.

We consider three paths through the space of resolution and noise level. In a best-case scenario, read noise is negligible, and the instrumental resolution may be arbitrarily high with no noise penalty. The variance per bin then scales as R⁻¹, and SNR as R^−1/2. We consider the worst-case scenario to be a read-noise-limited instrument that simply varies the dispersion, holding everything else fixed; the SNR in this case scales as R⁻¹. Finally, we consider an intermediate case in which SNR scales as R^−3/4. We normalize all of these paths at R = 50. Table 1 summarizes our results, which we discuss in detail in Oxygen and Ozone, Water, and The Red Edge of Chlorophyll.

Table 1.

Approximate optimal resolutions and minimum SNRs

Species	$\tilde{R}$	$\mathrm{SN}{\mathrm{R}}_{\tilde{R}}^{\ast }$	$\mathrm{SN}{\mathrm{R}}_{150}^{\ast }$
H2O	40	7.5	3.3
O2	150	6	6
Chlorophyll	20	120	40

^*A 90% detection probability for 10⁻³ false positive rate.

Oxygen and Ozone.

Fig. 5 Left shows our results for the case of atmospheric O₂. Given a SNR of 10 at R = 50, the optimal resolution for an O₂ detection varies from ∼70 to many hundreds, with a value of R ∼ 150 for our intermediate noise case. Supporting Information contains a mostly analytic derivation of these approximate resolutions. At R = 150, we would need SNR ≳ 6 for a likely detection; this corresponds to SNR ∼ 10 at R = 50 in our best-case noise scaling.

Fig. 5.

Probability of detecting of O₂ (Left) and H₂O (Right) on an Earth twin as a function of spectral resolution and SNR. All curves are normalized to a common SNR at R = 50, SNR = 10 for O₂ and SNR = 5 for H₂O. The curves are scaled to either reproduce the read-noise-limited case (burgundy line) in which SNR scales as R⁻¹, the perfect background-limited case (blue line) in which SNR scales as R^−1/2, or an intermediate case (orange line). The solid lines indicate a false-alarm probability of 10⁻³, while the dot-dashed lines have a false-alarm probability of 10⁻⁴. (Left) The optimal resolution in the intermediate case is R ∼ 150, with a corresponding minimum SNR of ∼5. (Right) The optimal resolution in the intermediate case is R ∼ 40, where the minimum SNR is ∼6. This is a factor of ∼2 lower than the scaled SNR needed to detect O₂ in the same Earth twin.

UV photons from the star will convert diatomic oxygen into ozone, so we may also ask if it would be easier to detect atmospheric oxygen in our model by simultaneously searching for both O₂ and O₃. In the case of an Earth twin, the answer is no: The extra degree of freedom increases the Δχ² threshold, and the depth of the ozone feature is insufficient to compensate (see Fig. 3). The ozone feature is also broad (Δλ/λ ∼ 0.1) and occurs just redward of a major upturn in albedo from Rayleigh scattering, making it somewhat degenerate with spectrophotometric uncertainties. This is reflected in significance thresholds somewhat higher than for the relevant χ² distributions (as shown in Fig. 4).

While fitting for both O₂ and O₃ does not improve the detection probabilities for an Earth twin, it could help for a terrestrial planet with a significantly higher ozone column. This could arise either from a higher UV flux (from an F-star, for example), from a significantly lower concentration of molecules and ions to catalyze ozone’s decomposition, or both. However, as noted earlier, any analysis simultaneously searching for O₂ and O₃ would need to set a higher significance threshold to account for ozone’s ability to mimic a variable spectral albedo.

Water.

Water has a series of deep absorption features from the red end of the visible into the near-infrared, with a variety of effective widths, making it easier to detect than diatomic oxygen. As Fig. 2 suggests, water absorption remains conspicuous in the spectrum down to spectral resolutions of R ∼ 20. At still lower resolutions, water absorption becomes more difficult to separate from variations in the surface albedo or errors in the spectrophotometric calibration.

Fig. 5 Right shows the probability of a high-significance H₂O detection for an Earth twin, with all of the same assumptions used in the O₂ panel (Fig. 5 Left), but half of the fiducial SNR. For the case intermediate between the optimal and pessimal noise scalings, the optimal spectral resolution for H₂O detection is R ∼ 40. This is a factor of several lower than for O₂ and reflects the broader widths of the features.

The Red Edge of Chlorophyll.

Chlorophyll on Earth has a sharp rise in reflectivity around 0.7 μm, the “red edge.” An analogous feature could be detectable on an exo-Earth, with the (large) caveat that photosynthetic extraterrestrial life may use a different family of pigment molecules than their terrestrial analogs, and the understanding that any claimed detection would be extremely controversial.

We approximate the albedo of vegetation as a softened Heaviside step function (Eq. 7), which provides a reasonable match in the wavelength range from ∼0.5 μm to 1 μm. Although the jump is very strong in pure vegetation, with the albedo increasing from ∼5% to ∼50%, it is much weaker in an integrated Earth spectrum. This is due both to the small fraction of surface area covered by vegetation (∼10%) and to the fact that much of this area is covered by optically thick clouds. We optimistically use the same Δχ² thresholds as for O₂ and H₂O to indicate a detection.

The “red edge” of vegetation does not require a high spectral resolution to identify; assuming our intermediate noise scaling, a value R ∼ 20 is optimal. Chlorophyll is, however, exceedingly difficult to detect with significance in an Earth twin. To facilitate a comparison with O₂, we explore chlorophyll’s detectability as a function of SNR, the vegetation covering fraction, and the cloud fraction, at a fiducial R of 150 (implicitly assuming a mission optimized to detect O₂).

Fig. 6 shows our results. For an Earth twin, O₂ requires twice the SNR needed for H₂O, while chlorophyll, even if the pigment is known, requires a SNR approximately six times higher than O₂. At these levels, our assumption that the spectrum can be modeled with a total disregard for the details of the surface albedo begins to break down. In order for chlorophyll to become as easy to detect as oxygen, we must either assume a vegetation covering fraction of at least 30% with a light cloud cover, or a cloud-free Earth. The former scenario would have roughly half of Earth’s cloud coverage and would see all land covered in greenery. The cloud-free Earth twin has a lower mean albedo, making it harder to achieve a given SNR. It is also difficult to imagine chlorophyll, part of a photosynthetic cycle based on water, occurring on a cloud-free world.

Fig. 6.

Detectability of H₂O, O₂, and the red edge of chlorophyll for three terrestrial planets, assuming R = 150 (i.e., a mission optimized to detect O₂) and a false alarm probability of 10⁻³. For an Earth twin, with 50% cloud coverage and 10% vegetation coverage, chlorophyll requires approximately six times as much SNR as O₂. Only under optimistic assumptions about cloud and vegetation cover (and the universality of chlorophyll) does the molecular family approach O₂ in detectability.

While a future mission will undoubtedly search for chlorophyll on nearby terrestrial planets, we argue that a high-contrast mission should be designed to achieve the easier and better-defined goals of oxygen and water detection. A plausible observing strategy would attempt to achieve the requisite SNR for O₂ and H₂O around nearby stars, and then spend an enormous amount of time attempting to reach the SNR needed to detect chlorophyll around the very best target(s).

Conclusions

In this paper, we have constructed a minimally parametric model to recover the components of a terrestrial planet’s atmosphere as observed by a future high-contrast space mission. We find that we can reproduce the spectrum of an Earth twin to a very high accuracy even when completely neglecting the surface albedo, apart from an overall multiplicative term quadratic in wavelength. Such a term also includes uncertainties in the spectrophotometric calibration, which are likely to be significant.

We have focused our analysis on the optical and very near-infrared spectrum. A solar-type star is brightest at these wavelengths, giving the maximum photon flux. Diatomic oxygen and water have very prominent absorption features from ∼0.6 μm to 1 μm, while likely surface materials like rock, sand, and water have nearly featureless spectral albedos. By targeting shorter wavelengths, we also have the advantage of a finer diffraction-limited resolution.

We find that a future space mission will be likely to detect water on an Earth twin with a spectral resolution of R ≳ 40 and a SNR per bin of ≳ 7. Such a mission will have a much more difficult time detecting atmospheric oxygen, and is unlikely to improve its sensitivity by searching for O₂ and O₃ simultaneously, at least at visible wavelengths (ozone has a strong absorption edge in the near-UV, at ∼0.3 μm). For a mission targeting only O₂, we find an optimal resolution of R ∼ 150 for our intermediate noise scaling case, and a minimum SNR of ∼6 at R = 150. This is approximately three times the resolution of an instrument optimized to see water, and a factor of ∼2 more challenging than water as measured by the scaled SNR.

Finally, we show that the “red edge” of chlorophyll absorption at λ ∼ 0.7 μm will be extremely difficult to detect, unless the cloud cover is much lower and/or the vegetation fraction is much higher than on Earth. Assuming extraterrestrial chlorophyll to have the same optical properties as the terrestrial pigments, and assuming Earth-like cloud and vegetation coverings, detecting chlorophyll will require a SNR approximately six times higher than for diatomic oxygen, equivalent to a SNR ≳ 100 at R ∼ 20. The detectability only approaches that of O₂ if the cloud covering is zero, or if cloud cover is light and a much larger surface fraction, ∼30%, is covered in vegetation.

Based on our findings, we argue that a future mission should be designed toward the well-defined goal of sensitivity to O₂ and H₂O around the best candidate terrestrial exoplanets, perhaps even with two dispersing elements to achieve both R ∼ 40 and R ∼ 150. Extensive (and expensive) follow-up of the very best targets, preferably with O₂ and H₂O detections, might then be used to search for the red edge of chlorophyll.