CHARACTERIZING THE ATMOSPHERES OF TRANSITING PLANETS WITH A DEDICATED SPACE TELESCOPE

We classified the planetary atmospheres according to equilibrium temperatures and sizes into three classes of atmospheric temperatures—"Hot" (800–2000 K), "Warm" (350–800 K), and "Habitable" (250–350 K)—and three types of planetary sizes—Jupiter-like, Neptune-like, and super-Earth (see Table 1). Planets with "Cold" temperatures (200 K or below) are not studied in this paper.

Super-Earths are expected to be between 1 and 10 M_⊕; in this paper we assume a 5 Earth-mass body for our calculations, with a radius of 1.6–1.8 R_⊕ (Grasset et al. 2009). By comparing Earth's cross-section σ_⊕ = π · R²_⊕ to those of the super-Earth, Neptune-like, and Jupiter-like planets, we obtain

$$\begin{equation} \sigma _{{\rm SE}} \sim 3 \, \sigma _\oplus ; \qquad \sigma _{N} \sim 25 \, \sigma _\oplus ; \qquad \sigma _{J} \sim 100 \sigma _\oplus. \end{equation} \tag{ 1 }$$

For transit and combined-light observations (transiting and non-transiting planets), the important parameter is the ratio between the planetary and stellar cross-sections, κ, obtainable by measuring the transit depth:

$$\begin{equation} \kappa = \sigma _p/\sigma _* . \end{equation} \tag{ 2 }$$

This parameter changes significantly for different planet/star types. In Table 2, we give σ_* for a few key stellar types, along with the cross-section ratio value κ for the three planetary types considered in this paper, expressed as a factor of κ_Jupiter (κ_Jup. ∼ 100σ_⊕/σ_☉). A Jupiter-sized planet orbiting a Sun-like star and a super-Earth orbiting an M4.5-dwarf will both have a similar cross-section ratio κ ∼ κ_Jup., observable with small, ground-based telescopes.

A primary transit occurs when a planet passes in front of its parent star with respect to our line of sight. By subtracting the "in-transit" stellar flux from the "out-of-transit," we can measure directly the parameter κ as described in Equation (2), and hence the planetary radius in units of stellar radii. If we repeat the observation of κ at different wavelengths, we can infer the presence or absence of an atmosphere as well as retrieve the main atmospheric components (Seager & Sasselov 2000; Brown et al. 2001). The spectral absorption of the planetary atmosphere, while in transit, is measured from the transmission spectrum obtained. For key examples of planetary cases, we use synthetic models fitting the existing observations or we extrapolate from our knowledge of the planets in the solar system. The models were calculated with the line-by-line radiative transfer code described in Tinetti et al. (2007a, 2011a), with updated line lists from Barber et al. (2006), Yurchenko et al. (2011), Rothman et al. (2010), and Tashkun & Perevalov (2011). For feasibility studies, we also adopt a more heuristic estimate of the atmospheric contribution rather than these detailed simulations. In particular, the amount of light passing through the atmosphere of the planet will cross a small annulus,

$$\begin{equation} \frac{2 R_p \pi \Delta z}{\pi {R_\star }^2} = \frac{2 R_p \Delta z}{{R_\star }^2}, \end{equation} \tag{ 3 }$$

where R_p is the radius of the planet, R_⋆ is the radius of the star, and Δz is the height of the atmosphere. From observations, Δz = nH, where typically n ∼ 5, depending on the spectral resolution and wavelength. H is the scale height defined by

$$\begin{equation} H = \frac{k\,T}{\mu g}, \end{equation} \tag{ 4 }$$

where k is the Boltzmann constant, g is the gravity acceleration, and μ is the mean molecular mass of the atmosphere.

From the scale height expression (4), it is clear that the hotter and lighter the atmosphere is, the easier it is to observe with this technique. Also, dense objects such as telluric bodies will have a higher value for g and consequently a more compact atmosphere. For example, hot Jupiters have high temperatures, low mean molecular mass of the atmosphere (μ ∼ 2 amu for hydrogen-rich atmospheres), and relatively low density. Their scale height can easily reach 500 km. By contrast, Earth's temperature is colder (∼280 K), μ is ∼28 amu, and the bulk composition is denser. As a result, the scale height is compacted to ∼8 km.

As explained in Section 2.1, here we are interested in three main classes of planets: gas giants, Neptune-like planets, and super-Earths. While gas giants and Neptunes are optimal targets for primary transit observations, in general super-Earths are the least favorable unless they transit an M star and host a relatively hot and light atmosphere (see Table 3). For this reason, in the most general case, super-Earths should be observed with the secondary eclipse technique, as described in the next section.

A complementary technique to the primary transit is the so-called secondary eclipse. This method relies on the possibility of observing the star alone when the planet is passing behind it, so we can effectively subtract the stellar contribution from the star+planet system. In practice, we measure the flux emitted and/or reflected by the planet in units of stellar flux,

$$\begin{equation} F_{\rm II} (\lambda) = {\left(\frac{R_p}{R_\star } \right)}^2 \frac{F_p(\lambda) }{F_\star (\lambda)} = \kappa \, \frac{F_p(\lambda) }{F_\star (\lambda)}, \end{equation} \tag{ 5 }$$

where F_p and F_⋆ are the planetary and stellar spectra and κ is as defined in Section 2.1. It is clear from this equation that both the relative size of the planet/star (the parameter κ) and the relative temperature are key parameters for secondary eclipse measurements. Here we use synthetic models to represent key examples of exoplanets (Tinetti et al. 2010b). The emitted/reflected spectra were generated with the line-by-line radiative transfer codes described in Tinetti et al. (2005, 2006), with updated line lists from Barber et al. (2006), Yurchenko et al. (2011), and Rothman et al. (2010). For these key cases, the stellar spectra are either observed or modeled (Kurucz 1995). In Figure 1 we show how F_II(λ) changes for a given planet as a function of star type. In this example, we chose a super-Earth with an Earth-like atmosphere orbiting a selection of known M-dwarfs: clearly, late M stars offer the best planet/star contrast.

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Infrared observations.

For feasibility studies in the IR, we approximate the planetary and stellar spectra in Equation (5) with two Planck curves at temperatures T_p and T_⋆, with T_p being the day-side temperature of the planet. While this approximation is not accurate enough to model specific examples, it is helpful when estimating the general case:

$$\begin{equation} F_{\rm II} (\lambda) \sim \kappa \, \frac{B_p(\lambda, T_p) }{B_\star (\lambda, T_\star)} . \end{equation} \tag{ 6 }$$

In Figure 2, we show the Planck curves for a few bodies at different temperatures. The planet-to-star flux contrast will clearly be higher for hot planets. Note that in the IR temperate planets at ∼300 K can be observed only at wavelengths longer than 5 μm, as they emit a negligible amount of flux at λ ⩽ 5 μm (Figure 2).

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Optical observations.

For observations in the optical, we need to estimate the reflected light from the planet. Equation (5) becomes

$$\begin{equation} F_{\rm II} (\lambda) = {\left(\frac{R_p}{R_\star } \right)}^2 \frac{F_p(\lambda) }{F_\star (\lambda)} = \kappa \, A \, \zeta \, \frac{R_*^2}{a^2} \, \frac{F_\star (\lambda) }{F_\star (\lambda)} = \kappa \, A \, \zeta \, \frac{R_*^2}{a^2} , \end{equation} \tag{ 7 }$$

where A is the planetary albedo, ζ is the observed fraction of the planet illuminated, and a is the semimajor axis. The closer the planet is to its stellar companion and the higher its albedo, the larger the contrast in the optical will be. For planets colder than ∼1200 K, the reflected light component is predominant in the optical wavelength range (λ < 0.8 μm). For hotter planets, both Equations (6) and (7) will have a contribution (emission and reflection).

Planet phase variations and eclipse mapping.

Phase variations are important to understanding a planet's atmospheric dynamics and the redistribution of absorbed stellar energy from their irradiated day side to the night side. These observations can only be conducted from space since the typical timescale of these phase variations largely exceeds that of one observing night. Phase variations are very insightful both at reflected and thermal wavebands. In the infrared case, these kinds of observations are critical for constraining the General Circulation Models (GCMs) of exoplanets, and of hot gaseous planets in particular. For instance, the infrared 8 μm Spitzer observations of the exoplanet HD 189733b have shown the night side of this hot Jupiter to be only ∼300 K cooler than its day side (Knutson et al. 2007a), suggesting an efficient redistribution of the absorbed stellar energy. In addition, toward the optical wavelength regime, an increasing contribution from reflected light is expected (Snellen et al. 2009; Borucki et al. 2009).

A great advantage of a dedicated exoplanet mission would be the potential for long campaigns: staring at a known planetary system for a sizable fraction of an orbit (Knutson et al. 2007a, 2009b, 2009a) or for an entire orbit (Snellen et al. 2009; Borucki et al. 2009), or—provided the flux calibration is accurate enough—using multi-epoch observations to obtain a more sparsely sampled phase curve (Cowan et al. 2007; Crossfield et al. 2010). At thermal wavelengths this may only be interesting for short-period planets, where the diurnal temperature contrast is high. Additionally, non-transiting planets open up interesting possibilities for studying seasons (e.g., Gaidos & Williams 2004). Furthermore, the simultaneous multi-band coverage would make it possible to simultaneously probe the longitudinal temperature distribution as a function of pressure, which would be a very helpful constraint for GCMs.

The potential for using phase variations to study non-transiting systems should also be noted (Selsis et al. 2011). Non-transiting systems will be closer on average than their transiting counterparts. The challenge is stellar and telescope stability over the orbital time of a planet. For planets on circular orbits, thermal phases have limited value because of the inherent degeneracies of inverting phase variations (Cowan & Agol 2008), but for eccentric planets, phase variations will be much richer (Langton & Laughlin 2008; Lewis et al. 2010; Iro & Deming 2010; Cowan & Agol 2011). As one considers increasingly long-period planets (warm rather than hot) even more of them will be on eccentric orbits because of the weaker tidal influence of the host star.

For the brightest targets, eclipses can also be used as powerful tools to spatially resolve the emission properties of planets. During ingress and egress, partial occultation effectively maps the photospheric emission region of the object being eclipsed (Williams et al. 2006; Rauscher et al. 2007; Agol et al. 2010). Key constraints can be placed on three-dimensional atmospheric models through repeated infrared measurements. In this paper, we will focus on the feasibility of primary transits and secondary eclipses. A more detailed and thorough study of the observability of phase variations and eclipse mapping will be the topic of future publications.

The primary and secondary transit techniques are complementary. Transmission spectra in the infrared, from primary transits, are more sensitive to atomic and molecular abundances, but less to temperature gradients. By comparison, emission spectroscopy allows for detection of molecular species as well as constraining the bulk temperature and vertical thermal gradient of the planet. Additionally, during the primary transit we can sound the terminator, whereas during the secondary eclipse we can observe the planetary day side.

In Table 3, we present ratios of signal values from primary transit and secondary eclipse observations for the key examples of the planetary classes (see Table 1). Given that long integration times require the co-adding of multiple transit observations, for the primary case, any systematic difference in the stellar flux could hamper results. For example, spot redistributions over the stellar surface could potentially alter the depth of the transit, and could be a cause for concern for late-type stars since, on average, they can be quite active. In the case of M-type star super-Earths, though, we rely mostly on secondary eclipse observations which are quite immune from effects related to stellar activity, as the planetary signal follows directly from the depth of the occultation without the need to model the stellar surface.

In this section, we focus our attention on M-class stars and their HZs. The main reasons to consider them are the following:

• 1.  
  Among the stars in the solar neighborhood, 90% are M-type (e.g., Perryman & ESA 1997).
• 2.  
  The relatively small size of M stars (typically between 0.08 and 0.5 R_☉) allows us to probe planetary sizes down to a few Earth masses (see Equation (5)).
• 3.  
  The low effective temperature of the star (2900 <T_eff < 3900 K) places the HZ region closer the star than would be the case for a hotter star. An HZ planet will hence have a short orbital period (see Figure 4) and a larger number of transit events will be observable within a given time interval than would be the case for a planet in the HZ of a hotter (K, G, or F) star.
• 4.  
  M stars are brightest in the IR (i.e., more photons impinging onto the detector), where temperate exoplanets are easier to observe (see Figure 2).

The combination of these effects brings the prospect of characterizing terrestrial planets in the HZs of main-sequence stars within current technology capabilities. By contrast, it is currently impractical to use the transit technique to observe the atmosphere of terrestrial planets in the HZs of more massive stars, as the orbital periods in these cases would be very long (e.g., more than 100 days for a K-type star and 300 for a G-type star). In addition, M-dwarf spectra differ significantly from blackbody radiation curves in the visible and near-infrared parts of the spectrum, but in the mid-infrared, which is considered for our HZ targets, the molecular absorptions are less important.

2.5.1. M-star Population

At the time of this writing, over 25% of stars in the Sun's near neighborhood were believed to be missing from star surveys (such as the catalog by Lépine & Gaidos 2011), in part because bright M stars in the infrared are quite faint in the visible, due to a combination of temperature and the presence of molecular and atomic species absorbing in this spectral region. For instance, an M3V star with V = 12.30 mag corresponds to K = 7.53 mag, and an M5V star with V = 15.01 mag corresponds to K = 8.40 mag (Delfosse et al. 2000). For this reason, in this paper we use K magnitude rather than V magnitude to classify the luminosity of M stars. The most complete catalog of late-type nearby stars available today is the Lépine & Gaidos (2011) catalog, which includes nearly 9000 M-dwarfs with magnitude J <10. According to the authors, the catalog represents ∼75% of the estimated ∼11, 900 M-dwarfs with J < 10 expected to populate the entire sky.

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An evaluation of the number of M stars in a magnitude-limited sample can also be derived from the analysis of the 100 nearest RECONS star systems (RECONS 2011). Their distribution in distance shows clearly that, while the M1–4V star sample is evenly distributed within 6.7 pc, the M5–8V sample is significantly incomplete beyond 4–5 pc (see Figure 3). This analysis supports the hypothesis that a significant number of stars are still missing in catalogs in the very close solar neighborhood; there needs to be a major effort in the next years in this direction.

Independent estimates of the M star population in the solar neighborhood were provided by G. Micela (2011, private communication) through color–color diagrams applied to the Two Micron All Sky Survey (2MASS) catalog. This selection might have some contamination from two different sources: (1) distant giant stars may overlap with the nearby very early M type, where the main sequence and giant models are still close together and (2) stars of early spectral type could contaminate the dwarf M-star regime only if highly reddened by intervening dust.

NASA's WISE might help to remove the contamination by providing a survey in four additional IR channels (Wright et al. 2010).

The Gaia mission, in its all-sky astrometric survey, will deliver direct parallax estimates and spectrophotometry for nearby main-sequence stars down to R ∼ 20. At the magnitude limit of the survey, distances to relatively bright M stars out to 20–30 pc will be known with 0.1%–1% precision (depending on spectral sub-type). This will constitute an improvement of up to over a factor of 100 with respect to the typical 25%–30% uncertainties in the distance reported for low-mass stars identified as nearby based on proper motion and color selections (e.g., Lépine & Gaidos 2011). Starting with early data releases around mid-mission, Gaia's extremely precise distance estimates, and thus absolute luminosities, to nearby late-type stars will allow us to significantly improve standard stellar evolution models at the bottom of the main sequence. For transiting planet systems, updated values of the masses and radii of the host stars will be of critical importance. Model predictions for the radii of M-dwarfs show typical discrepancies of ∼15% with respect to observations, and, as shown by the GJ 1214b example (Charbonneau et al. 2009), limits in the knowledge of the stellar properties significantly hamper the understanding of the relevant physical characteristics (density, and thus internal structure and composition) of the detected planets. Meanwhile, to account for the possibility of errors in current measurements, we provide a variety of stellar temperatures and calculated corresponding star radii with our results. The radii were calculated using isochrones of old (∼5 Gyr) low-mass stars (Baraffe et al. 1998) and observational constraints (Delfosse et al. 2000). For comparison, based on the simple radius–temperature–luminosity relation considerations, we can infer that estimates of stellar radii, when Gaia parallaxes known to <1% will become available for nearby red stars, will carry much reduced uncertainties, on the order of 1%–3%. Indeed, the precision in the M-dwarf effective temperature estimates from spectroscopy or photometric calibrations (currently, 3%–5% at best) will then become the limiting factor in the knowledge of this fundamental quantity.

2.5.2. Planetary Periods

Figure 4 shows periods and transit durations for HZ super-Earths orbiting a range of M stars. These values clearly depend on orbital distances that are computed by fixing the planet temperature and stellar type. We define the radiation in and out of the planet (in Watts):

$$\begin{eqnarray} {\rm Rad}_{{\rm in}} &=&\pi R_{pl}^2 L_* f(1-A) \end{eqnarray} \tag{ 8 }$$

$$\begin{eqnarray} {\rm Rad}_{{\rm out}} &=&4\pi R_{pl}^2 \sigma T_{pl}^4,\quad \end{eqnarray} \tag{ 9 }$$

where the planetary albedo is A = 0.3, and a small greenhouse effect contribution of = 0.7 is assumed. The distance of the HZ for each M star type was estimated by considering an average surface temperature for the planet T_pl = 287 K. More specifically, we started with the bolometric luminosity of the star at a distance a (semimajor axis): L_* = (4πR²_*σT⁴_*)/(4πa²). By equating the radiation in and out of the planet, we obtain an expression for the planetary effective temperature:

$$\begin{equation} T_{{\rm pl}} = T_{*} \left({\sqrt{\frac{\left(1 - A \right)}{\epsilon }} \frac{R_*}{2 a}}\right)^{{1}/{2}}. \end{equation} \tag{ 10 }$$

By imposing T_pl = 287 K and assuming different values for the stellar temperature, 2900 K < T_* < 3900 K, we rearrange this equation to calculate the semimajor axis a and the planetary period $P = 2\pi \sqrt{(a^3/{\it GM})}$. For the other cases presented in this paper, period and transit durations were obtained either using similar calculations, or from observations. For the transit duration t_t we assume a circular, edge-on orbit. From Seager & Mellen-Ornelas (2003) we obtain

$$\begin{equation} t_{t} = \frac{P R_*}{\pi a} \sqrt{\left(1 + \frac{R_{pl}}{R_*} \right)^2 - b^2} . \end{equation} \tag{ 11 }$$

For the general case the impact parameter b was set to zero, unless otherwise specified, so that Equation (11) simplifies to

$$\begin{equation} t_{t} = \frac{P}{\pi } \left(\frac{R_* + R_{pl}}{a} \right). \end{equation} \tag{ 12 }$$

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The integration time needed to observe specific targets depends on the following:

• 1.  
  The parent star: spectral class, type, magnitude in a specified spectral region.
• 2.  
  The contrast between the parent star and the companion planet in the observed spectral interval: this can be estimated from known observed or simulated objects.
• 3.  
  The observational requirements: spectral region, resolution, and signal-to-noise ratio (S/N).
• 4.  
  The telescope characteristics: primary mirror diameter, overall transmission, coverage, and sensitivity of the detectors.
• 5.  
  The focal plane array characteristics during observation: the number of pixels used per spectral resolution element, readout time, quantum efficiency, full well capacity (FWC), saturation threshold, dark current, and readout noise.

We consider then the flux of photons from the planet. This flux (given in photons/s/m² in the whole spectral interval) is converted into electrons/pixel/s/"resolution element" within the defined spectral region using the following expression:

$$\begin{equation} F_{e^-} = \frac{F_{\gamma }\cdot A \cdot {\rm transmission} \cdot {\rm QE}}{Res \cdot N_{px/{\rm Res}}}, \end{equation} \tag{ 13 }$$

where $F_{e^-}$ and F_γ are, respectively, the electron and photon fluxes, A is the telescope mirror surface area, QE is the quantum efficiency, Res is the number of spectral elements in the band (resolution), and N_px/Res is the number of pixels per resolution element. From here on, F will only refer to the electron flux: $F_{e^-}$. The transmission is the overall fraction of energy that reaches the detector (before conversion to electrons). It includes the telescope and instrument (optical) transmission.

Using these values, the time required for one detector pixel readout is computed:

$$\begin{equation} t_{{\rm ro}} = \frac{{\rm FWC} \cdot {\rm saturation}}{F_{\star }+F_{pl}+{\rm DC}}, \end{equation} \tag{ 14 }$$

where ``ro'' stands for read out, FWC for full well capacity, DC for dark current, and saturation is a fraction of the FWC. Usually, a saturation at 70% of the FWC is taken into account, that is, the limit of electrons that can be accumulated in a single exposure.

The number of readouts required is then computed using the following formula:

$$\begin{equation} N_{{\rm ro}}=({\rm S/N})^2 \cdot \frac{F_{\star }+F_{{\rm pl}}+{\rm DC}+({\rm RON}^2 / t_{{\rm ro}})}{F_{{\rm pl}}^2 \cdot t_{{\rm ro}} \cdot N_{px/{\rm Res}}}, \end{equation} \tag{ 15 }$$

where S/N is the signal-to-noise ratio within the defined spectral band and RON is the detector readout noise. For the secondary eclipse case, F_pl is the flux emitted or reflected by the planet, while for the primary transit case (explained in Section 2.2), F_pl corresponds to the amount of flux (written as a negative) absorbed by the planet's atmosphere,

$$\begin{equation} F_{{\rm pl}} = - \frac{\pi {R_{{\rm pl}}}^2}{\pi {R_{\star }}^2} \left(\left(1+\frac{nH^2}{R_{{\rm pl}}}\right) - 1\right) = -\frac{2 n H R_{{\rm pl}}}{{R_\star }^2}, \end{equation} \tag{ 16 }$$

where n is an atmospheric absorption factor.

With these values, the total integration time is computed by multiplying the duration of a detector pixel readout by the number of readouts required.

The planet/star flux contrast ratio and the star brightness are the obvious main factors affecting integration times. To estimate the contrast, we have considered observed spectra and simulated synthetic spectra of stellar and planetary atmospheres (Sections 2.1–2.5).

2.6.1. Instrument Detector and Validation

Our simulations do not include the effects of stellar variability on transit observations. Kepler is reaching 200 ppm minute⁻¹ on a V = 11 mag star and 40 ppm minute⁻¹ on a V = 7 mag star. The most up-to-date information about variability comes from the studies of Basri et al. (2010, 2011) based on the analysis of 100,000 stars (first release of 43 days of Kepler data). For timescales between 3 and 16 days, the authors showed that 57% of the G stars are active and tend to be more active than the Sun (up to twice the activity level is typical). This fraction increases to 87% of the K- and M-dwarfs (Figure 4 of Basri et al. 2010). The peak of the histogram of amplitude distribution is centered at 2 mmag. Scatter plots from Basri et al. show that for K and M stars the dominant source of scatter is variability, not Poisson noise. The bulk of the periodicities are found at periods larger than 10 days, with amplitudes ranging from 1–10 mmag. Ciardi et al. (2011) found that 80% of the M-dwarfs have dispersion less than 500 ppm over a period of 12 hr, while G-dwarfs are the most stable group down to 40 ppm.

It is important to note here that photometric variability is significantly lower in the near-infrared than in the Kepler band (Agol et al. 2010; Knutson et al. 2011) because of the lower contrast between spots and the stellar photosphere at larger wavelengths. For instance, Agol et al. (2010) measured that the infrared flux variations in the case of the active K star HD 189733 are about 20% of the optical variations. This is in agreement with the theoretical estimates by Ballerini et al. (2011).

Most importantly, all the timescales related to stellar activity patterns are very different from the timescales associated with single transit observations (a few hours), and thus can easily be removed. CoRoT-7 b provides a good example. The activity modulations are of the order of 2% and yet CoRoT managed to find a transit with a depth of 0.03%. This was made possible by the continuous monitoring provided by CoRoT and the different timescale compared with the transit signal that allowed for the removal of the activity effects and the discovery of variations smaller than the overall modulation by a factor of 70. The same situation has been encountered in the list of 1200 Kepler candidates announced recently, in which stellar activity modulations and transit events have been disentangled, often with the former being far greater than the latter.

In conclusion, the overall (random) photometric jitter of the star should not be a crucial factor with the right strategy to adequately correct for modulations caused by spot variations. Time series can be used as an "activity monitor" by the visible part of the spectrum. As mentioned in Section 2.4, systematic differences in the stellar flux could hamper multiple transit combinations. However, where primary transit observations are subject to these effects, secondary eclipse observations are preferred as they are immune to them.

Upper limits on eclipse variability have been reported by Agol et al. (2010) and Knutson et al. (2011). We do not know the nature of this variability, but the chance of observing multiple spectra rather than photometric bands might be helpful in exploring the potential sources of atmospheric variability (thermal changes? chemical changes? clouds/hazes?) for the most favorable targets. In the case of faint targets, for which co-adding eclipse observations is necessary, only spatially/temporally averaged information will be available. From the experience with the planets in our own solar system, this information, although more limited, is expected to still be very significant.

The integration times required to study HZ super-Earths (given in Table 12) show that characterization of these targets is possible provided they orbit late-type dwarfs. While bright targets are preferred, as they provide a higher photon signal, our results cover a range of magnitudes from K = 5 to K = 9. In parallel, the M-type population found in the RECONS catalog (RECONS 2011), which lists 100 stars up to 6.6 pc in the Sun's local neighborhood, is mostly formed of bright targets with a significant fraction having magnitudes between K = 4 and K = 6 (see Figure 3). However, extrapolation from the catalog up to magnitude K = 9 yields a much larger stellar population that can be studied for super-Earths. Thus, combining the feasibility of studying targets up to K = 9, while keeping a preference for brighter sources, and the greater amount of fainter stars up to mag K = 9 creates a common area ideal for super-Earth observations centered around the K = 7–8 magnitude region. A mission that aims to characterize HZ super-Earths should have detectors optimized for this magnitude range.

Throughout this paper we have considered an instrumental transmission value of 0.7. In practical applications, many factors can reduce this transmission value. While most of the cases presented allow for slightly longer observations, the most challenging category of HZ super-Earths will require high instrumental transmission values to remain feasible. Instrument designs with high levels of transmission, such as Fourier transform spectrographs, can be considered a possibility for the characterization of these most challenging targets.

We presented here idealized cases where systematic errors (such as detector time constants, pointing jitter, re-acquisition errors, temperature fluctuations, etc.) were not accounted for. Instrumental settings for our results from the visible to the infrared were based on available technology and can be considered realistic. With these considerations, the results presented in this paper highlight that in the coming years HZ super-Earths are realistically within reach. In future work, we will update our models as information on the systematic effects of specific instruments becomes available.

In addition to the numbers presented throughout the paper for a 1.4 m telescope, we provide here two supplementary sets of results for a 1.2 m telescope. We detail in Table 13 the parameters adopted for the two cases. The results are displayed in the following way: Number of transits: Case 1 (Case 2).

See Table 14 for results.

See Table 15 for results.

See Table 16 for results.