EFFECT OF UV RADIATION ON THE SPECTRAL FINGERPRINTS OF EARTH-LIKE PLANETS ORBITING M STARS

M dwarfs span nearly three orders of magnitude in luminosity and remain active for much longer timescales than earlier stellar types. As main-sequence stars age, their UV flux levels decrease even as their bolometric luminosity increases. Understanding the UV flux incident on a planetary atmosphere is critical to understanding and interpreting future observations of atmospheric constituents, including biosignatures.

Current stellar models are unable to model the UV region from M dwarfs self-consistently for three main reasons. First, complex magnetic fields responsible for heating the chromosphere are thought to drive much of the UV activity and have thus far been ignored in stellar models. Second, the models are missing opacities in the UV. Third, the models are semi-empirical, with no energy conservation to balance magnetic heating with radiative losses. These problems are being addressed by current work, and models will be available in the future to test against M dwarf UV observations.

We generate stellar input models for the entire M dwarf spectral class (M0 to M9) to explore the boundaries of the UV environment of an exoplanet orbiting a main-sequence star. We create two sets of models based on the extreme limits of stellar activity. For the purposes of this paper, "active" stellar models are constructed to represent the most active M dwarf measurements, and "inactive" semi-empirical models without chromospheres are constructed to represent the lowest theoretical UV flux field. We compare these limiting-case models with six well-observed M dwarfs that show significant chromospheric flux (see Figure 1) despite being traditionally classified as quiescent stars owing to the presence of Hα in absorption (France et al. 2013). A few M dwarfs observed with GALEX in the near-ultraviolet (near-UV; 1750–2750 Å) show near-photospheric continuum level fluxes (as computed with PHOENIX models) and can be classified as inactive even though the exact UV flux level has not been measured yet. For example, Gl 445 and Gl 682 have roughly 90% of the observed NUV flux density predicted by PHOENIX model photospheres (Shkolnik & Barman 2014). More observations are needed to determine the ultimate lower limit of UV flux emitted by old and/or late M dwarfs. To compare our calculations for inactive star models with published work, we use theoretical photosphere PHOENIX models as a lower bound (Allard 2014).

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The chromospheric far-ultraviolet (far-UV) flux from M, L, and T dwarfs (i.e., very low mass stars and brown dwarfs), while crucial for determining the potential habitability of any planets around them, is very poorly characterized through direct observations. Given their common chromospheric origin, Hα, Lyα, Ca ii H and K, and Mg ii H and K emission lines have all been used as proxies for FUV activity. However, many of these lines are inaccessible to M dwarfs because they are at shorter wavelengths, where these stars are intrinsically less luminous. For M dwarfs, Hα emission, in particular, has been studied extensively and to date has the most robust data set for each M dwarf spectral type compared with the other lines considered above (West et al. 2004, 2011). In addition, Jones & West (2015) shows that Hα fluxes correlate with NUV fluxes from GALEX. Therefore, we use Hα to estimate the FUV emission for our active stellar grid by scaling the known FUV and Hα emission from the active M3.5 star AD Leo (see Equation (1) and Figure 2). Very active, early M dwarfs (M0–M5) are known to saturate in the Hα emission around log $({L}_{{{\rm{H}}}_{\alpha }}/{L}_{\mathrm{bol}})=-3.75$ (Hawley et al. 1996; West et al. 2004; Reiners & Basri 2008).

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West et al. (2004) tabulate the log(mean ${L}_{{{\rm{H}}}_{\alpha }}/{L}_{\mathrm{bol}}$) versus spectral type from M0 to L0 from observations of 1910 active M dwarfs. We parameterize the data from West et al. (2004) to derive a relationship of UV to mean Hα emission for each spectral subtype in the M dwarf class (see Figure 2 and Equation (1)):

$$\begin{eqnarray}\mathrm{log}({L}_{{{\rm{H}}}_{\alpha }*}/{L}_{\mathrm{bol}*}) & = & -3.62\;\mathrm{for}\ {\rm{M}}0-{\rm{M}}4\\ \mathrm{log}({L}_{{{\rm{H}}}_{\alpha }*}/{L}_{\mathrm{bol}*}) & = & -0.32\times (M)-2.07\\ \ \mathrm{where}\ M & = & 5,6,7\ \mathrm{for}\ {\rm{M}}5,\ {\rm{M}}6,\ {\rm{M}}7\\ \mathrm{log}({{\rm{L}}}_{{{\rm{H}}}_{\alpha }*}/{{\rm{L}}}_{\mathrm{bol}*}) & = & -4.25\ \mathrm{for}\ {\rm{M}}8-{\rm{M}}9.\end{eqnarray} \tag{ 1 }$$

We use the Hα/UV scaling of AD Leo, which has both a well-characterized UV spectrum and Hα emission measurement as a calibration data point to set the scale. AD Leo, an M3.5 eV star, has log(${L}_{{{\rm{H}}}_{\alpha }}/{L}_{\mathrm{bol}}$) = −3.51 (Walkowicz & Hawley 2009) and has been well observed in the UV (see Segura et al. 2005 for AD Leo IUE spectrum and Linsky et al. 2013 for reconstructed Lyα flux). The M dwarf active spectrum is then given by

$$\begin{eqnarray}{F}_{\mathrm{FUV}*} & = & {F}_{\mathrm{FUV}\ \mathrm{AD}\ \mathrm{Leo}}\times {(\displaystyle \frac{{T}_{\mathrm{eff}\ *}}{{T}_{\mathrm{eff}\ \mathrm{AD}\ \mathrm{Leo}}})}^{4}\\ & & \times \displaystyle \frac{\mathrm{log}({L}_{{{\rm{H}}}_{\alpha }*}/{L}_{\mathrm{bol}*})}{\mathrm{log}({L}_{{{\rm{H}}}_{\alpha }\mathrm{ADLeo}}/{L}_{\mathrm{bolADLeo}})}.\end{eqnarray} \tag{ 2 }$$

Our stellar temperature grid (Figure 3) covers the full M dwarf spectral range, with the stellar parameters for active and inactive models given in Table 1. For the active star models, we scale the UV flux in the wavelength range 1000–3000 Å from AD Leo's observed UV spectrum to the other spectral types according to Equation (2). For each active model star on our grid we concatenated a solar-metallicity, unreddened synthetic PHOENIX spectrum, which only considers photospheric emission (Allard 2014), from 3000 to 45450 Å to the scaled observations from the IUE archive for AD Leo from 1000 to 3000 Å combined with the reconstructed Lyα from Linsky et al. (2013) for the region 1210–1222 Å.⁷ Note that young active stars are highly variable, especially in the UV. AD Leo is the most active and well-characterized M dwarf. Our active models therefore represent the extreme high end of activity for each stellar type from an active flare star. For comparison, the inactive semi-empirical models include no chromospheric emission. The continuum originating from the photosphere is taken from a PHOENIX model with the same stellar parameters as the corresponding active star from 1000–45450 Å. Thus, these models provide only a lower limit to the stellar UV flux. More observations are needed to determine the true lower limit of inactive M dwarfs in the UV.

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Table 1.  Stellar Properties for Active and Inactive Models

Star	Teff (K)	Mass (${M}_{\odot }$)	Radius (${R}_{\odot }$)
M0	3800	0.60	0.62
M1	3600	0.49	0.49
M2	3400	0.44	0.44
M3	3200	0.36	0.39
M4	3100	0.2	0.36
M5	2800	0.14	0.2
M6	2600	0.10	0.15
M7	2500	0.09	0.12
M8	2400	0.08	0.11
M9	2300	0.075	0.08

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The models represent the extreme limits of the UV radiation environment for an exoplanet using a flare star for the upper bound and a photosphere-only model for the lower bound in the UV. Figure 1 shows that the UV flux region between those two limits spans over 10 orders of magnitude in the FUV. We use the observations of six M dwarfs from the MUSCLES program to probe the region in between our active and inactive models. The MUSCLES stars have been traditionally classified as "quiescent" because they do not present Hα in emission.

The six M dwarfs were observed by two UV spectrographs (COS and STIS) on HST (France et al. 2013). We joined these HST measurements⁸ with the star's corresponding PHOENIX models at 2800 Å after adjusting the HST flux levels to the level a planet would receive at the 1 AU equivalent in the habitable zone. The input parameters for the PHOENIX models are the observed star's T_eff, [Fe/H], log g, and the rotation velocity, v sin i, as summarized in Table 2 and described for each star based on the most recent observations in the Appendix. When observations of v sin i were not available, we used instead the peak of the observed distribution for 56 M dwarfs (Jenkins et al. 2009).

Table 2.  Stellar Properties for MUSCLES Model Stellar Spectra

MUSCLES	Teff (K)	Radius (${R}_{\odot }$)	[Fe/H]	log g	Age (Gyr)	v sin i
Stars						(km s−1)
GJ 832	3620	0.48	−0.12	4.70	⋯	3
GJ 667C	3350	0.348	−0.55	5.00	$\gt 2$	3
GJ 1214	3250	0.211	+0.05	4.99	6 ± 3	<1
GJ 436	3416	0.455	+0.04	4.83	6.5–9.9	< 1
GJ 581	3498	0.299	−0.10	4.96	7–11	2.1
GJ 876	3129	0.3761	+0.19	4.89	0.1–5	1.38

Note. For GJ 832 and GJ 667C there is no v sin i measurement. We assumed a v sin i = 3.0 corresponding to the peak of the distribution (Jenkins et al. 2009) when generating a PHOENIX model. See text for references.

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The MUSCLES database interpolates the region between 1760 and 2100 Å because the noise in the observations was large in that region since those wavelengths were covered by the lowest-sensitivity part of the STIS G230L bandpass. In order to not bias the results too high or too low, the MUSCLES team used the average flux in the 2100–2200 Å region to interpolate the 1760–2100 Å region. Follow-up observations to the MUSCLES program with a new HST Treasury program aim to probe the 1760–2100 Å region of the spectrum with higher sensitivity. We used the MUSCLES database and interpolation as given. Because this region of the UV is important for O₃ production, uncertainty of this interpolation could influence our atmospheric results.

Input active stellar spectra and MUSCLES spectra are shown in Figure 3 (inactive models are not shown).

We use EXO-P (Kaltenegger & Sasselov 2010), a coupled 1D radiative-convective atmosphere code developed for rocky exoplanets. The code incorporates a 1D climate (Kasting & Ackerman 1986; Pavlov et al. 2000; Haqq-Misra et al. 2008), 1D photochemistry (Pavlov & Kasting 2002; Segura et al. 2005, 2007) and 1D radiative transfer model (Traub & Stier 1976; Kaltenegger & Traub 2009) to calculate the model spectrum of an Earth-like exoplanet orbiting host M dwarfs in the habitable zone.

EXO-P is a model that simulates both the effects of stellar radiation on a planetary environment and the planet's outgoing spectrum. We model an altitude range that extends upward to 60 km with 100 height layers. We use a geometrical model in which the average 1D global atmospheric model profile is generated using a plane-parallel atmosphere, treating the planet as a Lambertian sphere, and setting the stellar zenith angle to 60° to represent the average incoming stellar flux on the dayside of the planet (see also Schindler & Kasting 2000). The temperature in each layer is calculated from the difference between the incoming and outgoing flux and the heat capacity of the atmosphere in each layer. If the lapse rate of a given layer is larger than the adiabatic lapse rate, it is adjusted to the adiabatic rate until the atmosphere reaches equilibrium. We use a two-stream approximation (see Toon et al. 1989), which includes multiple scattering by atmospheric gases, in the visible/near-IR (NIR) to calculate the short-wave fluxes. Four-term, correlated-k coefficients parameterize the absorption by O₃, H₂O, O₂, and CH₄ (Pavlov et al. 2000). In the thermal IR region, a rapid radiative transfer model calculates the long-wave fluxes. Clouds are not explicitly calculated. The effects of clouds on the temperature versus pressure profile are included by adjusting the surface albedo of the Earth–Sun system to have a surface temperature of 288 K (see Kasting et al. 1984; Pavlov et al. 2000; Segura et al. 2003, 2005). The photochemistry code, originally developed by Kasting et al. (1985), solves for 55 chemical species linked by 220 reactions using a reverse-Euler method (see Segura et al. 2010, and references therein). The photochemical model is stationary, and convergence is achieved when the following criteria are fulfilled: the production and loss rates of chemical species are balanced, which results in a steady state for the chemical concentrations, and the initial boundary conditions, such as surface mixing ratios or surface fluxes, are met.

The radiative transfer model used to compute planetary spectra is based on a model originally developed for trace gas retrieval in Earth's atmospheric spectra (Traub & Stier 1976) and further developed for exoplanet transmission and emergent spectra (Kaltenegger et al. 2007, 2013; Kaltenegger & Traub 2009; Kaltenegger 2010; Kaltenegger & Sasselov 2010). In this paper, we model Earth's reflected and thermal emission spectra using 21 of the most spectroscopically significant molecules (H₂O, O₃, O₂, CH₄, CO₂, OH, CH₃Cl, NO₂, N₂O, HNO₃, CO, H₂S, SO₂, H₂O₂, NO, ClO, HOCl, HO₂, H₂CO, N₂O₅, and HCl). We use a Lambert sphere as an approximation for the disk-integrated planet in our model. The surface of our model planet corresponds to Earth's current surface of 70% ocean, 2% coast, and 28% land. The land surface consists of 30% grass, 30% trees, 9% granite, 9% basalt, 15% snow, and 7% sand. Surface reflectivities are taken from the USGS Digital Spectral Library⁹ and the ASTER Spectral Library¹⁰ (following Kaltenegger et al. 2007).

Clouds have a strong impact on the detectability of atmospheric species. For the spectra shown in Figures 7–9, we assume a 60% global cloud cover with cloud layers analogous to Earth (40% water clouds at 1 km, 40% water clouds at 6 km, and 20% ice clouds at 12 km, following Kaltenegger et al. 2007). In the visible to NIR, clouds increase the reflectivity of an Earth-like planet substantially and therefore increase the equivalent widths of all observable features, even though clouds block access to some of the lower atmosphere. In the IR, clouds slightly decrease the overall emitted flux of an Earth-like planet because they radiate at lower temperatures and therefore decrease the equivalent widths of all observable absorption features, even though they can increase the relative depth of a spectral feature as a result of lowering the continuum temperature of the planet. For a comparison of scenarios with Earth-analog clouds to those of clear sky spectra see Rugheimer et al. (2013).

Using 34 layers, we calculate the spectrum at high spectral resolution with several points per line width. The line shapes and widths are computed using Doppler and pressure broadening on a line-by-line basis for each layer in the model atmosphere. The overall high-resolution spectrum is calculated with 0.1 cm⁻¹ wavenumber steps. The figures are shown smoothed to a resolving power of 150 in the IR and 800 in the visible using a triangular smoothing kernel. The spectra may be binned further for comparison with proposed future spectroscopy missions designed to characterize Earth-like planets. We previously validated EXO-P from the visible to the IR using data from ground and space (Kaltenegger et al. 2007; Kaltenegger & Traub 2009; Rugheimer et al. 2013).

To examine the effects of the varying UV flux of M dwarfs on an Earth-like atmosphere and its observable spectral features, we use the temperature grid of stellar models ranging from M9 to M0 (T_eff = 3800–2300 K) for active and inactive models, along with the six M dwarfs with well-characterized UV fluxes from HST (see Section 2.2). We simulated an Earth-like planet with the same mass as Earth at the 1 AU equivalent orbital distance, defined by the wavelength integrated stellar flux received on top of the planet's atmosphere being equivalent to 1 AU in our solar system, calculated by $1\;{\mathrm{AU}}_{\mathrm{eq}}=\mathrm{AU}\times \sqrt{{(R/{R}_{\odot })}^{2}\times {({T}_{\mathrm{eff}}/{T}_{\mathrm{eff}\ \odot })}^{4}}$.

The biogenic (produced by living organisms) fluxes were held fixed in the models in accordance with the fluxes that reproduce the modern mixing ratios in the Earth–Sun case, except for the cooler M dwarfs, where CH₄ and N₂O were given a fixed mixing ratio of $1.0\times {10}^{-3}$ and $1.5\times {10}^{-2}$, respectively (following Segura et al. 2003, 2005). The surface fluxes for the long-lived gases H₂, CH₄, N₂O, CO, and CH₃Cl were calculated such that the Earth around the Sun yields a ${T}_{\mathrm{surf}}$ = 288 K for surface mixing ratios: cH₂ = $5.5\times {10}^{-7}$, cCH₄ = $1.6\times {10}^{-6}$, cCO₂ = $3.5\times {10}^{-4}$, cN₂O = $3.0\times {10}^{-7}$, cCO = $9.0\times {10}^{-8}$, and cCH₃Cl = $5.0\times {10}^{-10}$ (see Rugheimer et al. 2013). The corresponding input surface fluxes to the atmosphere are $-1.9\times {10}^{12}$ g H₂ yr⁻¹, $5.3\times {10}^{14}$ g CH₄ yr⁻¹, $7.9\times {10}^{12}$ g N₂O yr⁻¹, $1.8\times {10}^{15}$ g CO yr⁻¹, and $4.3\times {10}^{12}$ g CH₃Cl yr⁻¹. The N₂ mixing ratio is set to be a "fill gas" such that the total surface pressure is 1 bar. These boundary conditions were used for M0–M5 active grid stars, M0–M3 inactive grid stars, and all MUSCLES stars.

For M6–M9 active grid stars and for M4–M9 inactive grid stars, the boundary condition for CH₄ is changed to a fixed mixing ratio once the UV environment of the host star drops below a certain level because CO, H₂, and CH₄ do not converge according to the criteria described in Section 2.2 assuming a modern Earth biological flux (see also Segura et al. 2005). In reality, the thermodynamical cost for microbes producing CH₄ would become unprofitable as temperatures would initially rise owing to the increased greenhouse effect, causing the microbes to operate less efficiently. This type of biological feedback is not included in the models. CH₄ is produced biotically by methanogens and other organisms and abiotically through hydrothermal vent systems. In the modern atmosphere there is a significant anthropogenic source of CH₄ from natural gas, livestock, and rice paddies. Upper limits of abiotic fluxes of methane can be estimated for terrestrial planets following Guzmán-Marmolejo et al. (2014). An estimate of Earth biotic methane is about 30 times the abiotic flux (see discussion in Segura et al. 2005), and thus a range of methane fluxes may be maintained on a terrestrial planet via methanogenesis in addition to abiotic methane production.

Therefore, we set the mixing ratio of CH₄ to $1\times {10}^{-3}$, corresponding to a value of the last stable run with an Earth-like biological CH₄ flux for an active M5 star for planets around host stars that show this "runaway" behavior. Given these boundary conditions, the methane flux necessary to sustain a $1\times {10}^{-3}$ mixing ratio of methane is $5.65\times {10}^{14}$ g yr⁻¹ (equal to our present Earth methane flux) for the planet around the hottest M dwarf (T_eff = 3800 K), either active or inactive, $1.16\times {10}^{14}$ g yr⁻¹ (20.5% of the Earth value) for the planet around the coolest (T_eff = 2300 K) active star, and $5.87\times {10}^{12}$ g yr⁻¹ (1% of the Earth value) for the coolest inactive M dwarf of our sample.

For the less active stars, we set the deposition velocity (rate at which they are deposited to the surface) for H₂ and CO to $2.4\times {10}^{-4}$ cm s⁻¹ and $1.2\times {10}^{-4}$ cm s⁻¹, respectively (see also Kharecha et al. 2005; Segura et al. 2005). Rauer et al. (2011) used a deposition velocity for H₂ of $7.7\times {10}^{-4}$ cm s⁻¹. This number was obtained after calibrating the model to reproduce the H₂ atmospheric abundance measured for present Earth. In our case, the deposition values for H₂ and CO correspond to maximum air–sea transfer rates estimated using the "piston velocity" approach (Broecker 1982; Kharecha et al. 2005). Since a larger H₂ deposition velocity implies consumption by bacteria, we use the abiological value in Kharecha et al. (2005).

We followed a similar procedure for constraining the N₂O concentrations for M6–M9 inactive stars. We set the mixing ratio of N₂O to $1.5\times {10}^{-2}$, corresponding to values of the last stable run with Earth-like biological fluxes, to prevent unphysical buildup of N₂O. N₂O is emitted primarily by (de)nitrifying bacteria with anthropogenic sources from fertilizers in agriculture, biomass burning, industry, and livestock and is a relatively minor constituent of the modern atmosphere at around 320 parts per billion (ppb), compared to the preindustrial concentration of 270 ppb (Forster et al. 2007).

We used modern Earth fluxes for all of the MUSCLES stars without any "runaway" buildup of reduced gases. The CH₄ and N₂O fluxes are given in Table 3.

Table 3.  CH₄ and N₂O Fluxes and Mixing Ratios and O₃ Column Depths

	Surface	Flux (g yr−1)	% Earth	Surface	Flux (g yr−1)	% Earth	O3 Column
	Mixing	CH4	CH4 flux	Mixing	N2O	N2O flux	Depth
	Ratio CH4			Ratio N2O			(cm−2)
Active
M0 A	330 ppm	$5.65\times {10}^{14}$	100%	0.70 ppm	$7.99\times {10}^{12}$	100%	$4.1\times {10}^{18}$
M1 A	370 ppm	$5.65\times {10}^{14}$	100%	0.70 ppm	$7.99\times {10}^{12}$	100%	$4.0\times {10}^{18}$
M2 A	450 ppm	$5.65\times {10}^{14}$	100%	0.76 ppm	$7.99\times {10}^{12}$	100%	$3.8\times {10}^{18}$
M3 A	570 ppm	$5.65\times {10}^{14}$	100%	0.82 ppm	$7.99\times {10}^{12}$	100%	$3.6\times {10}^{18}$
M4 A	910 ppm	$5.65\times {10}^{14}$	100%	0.93 ppm	$7.99\times {10}^{12}$	100%	$3.5\times {10}^{18}$
M5 A	1000 ppm	$5.65\times {10}^{14}$	100%	0.98 ppm	$7.99\times {10}^{12}$	100%	$2.6\times {10}^{18}$
M6 A	1000 ppm	$2.90\times {10}^{14}$	51.8%	1.7 ppm	$7.99\times {10}^{12}$	100%	$3.1\times {10}^{18}$
M7 A	1000 ppm	$1.28\times {10}^{14}$	22.7%	3.0 ppm	$7.99\times {10}^{12}$	100%	$2.4\times {10}^{18}$
M8 A	1000 ppm	$1.36\times {10}^{14}$	24.0%	3.1 ppm	$7.99\times {10}^{12}$	100%	$2.5\times {10}^{18}$
M9 A	1000 ppm	$1.20\times {10}^{14}$	21.2%	3.5 ppm	$7.99\times {10}^{12}$	100%	$2.3\times {10}^{18}$
Inactive
M0 I	490 ppm	$5.65\times {10}^{14}$	100%	34 ppm	$7.99\times {10}^{12}$	100%	$1.7\times {10}^{18}$
M1 I	580 ppm	$5.65\times {10}^{14}$	100%	64 ppm	$7.99\times {10}^{12}$	100%	$1.5\times {10}^{18}$
M2 I	650 ppm	$5.65\times {10}^{14}$	100%	120 ppm	$7.99\times {10}^{12}$	100%	$1.4\times {10}^{18}$
M3 I	1000 ppm	$5.65\times {10}^{14}$	100%	360 ppm	$7.99\times {10}^{12}$	100%	$1.3\times {10}^{18}$
M4 I	1000 ppm	$4.15\times {10}^{14}$	73.5%	670 ppm	$7.99\times {10}^{12}$	100%	$1.0\times {10}^{18}$
M5 I	1000 ppm	$1.23\times {10}^{14}$	21.8%	15000 ppm	$7.99\times {10}^{12}$	100%	$4.5\times {10}^{17}$
M6 I	1000 ppm	$2.42\times {10}^{13}$	4.3%	15000 ppm	$4.04\times {10}^{11}$	5.1%	$1.4\times {10}^{17}$
M7 I	1000 ppm	$1.67\times {10}^{13}$	3.0%	15000 ppm	$4.96\times {10}^{10}$	0.6%	$6.1\times {10}^{16}$
M8 I	1000 ppm	$1.34\times {10}^{13}$	2.4%	15000 ppm	$5.72\times {10}^{9}$	0.07%	$2.6\times {10}^{16}$
M9 I	1000 ppm	$5.87\times {10}^{12}$	1.0%	15000 ppm	$3.17\times {10}^{9}$	0.04%	$1.1\times {10}^{16}$
MUSCLES
GJ 832	550 ppm	$5.65\times {10}^{14}$	100%	15 ppm	$7.99\times {10}^{12}$	100%	$1.6\times {10}^{18}$
GJ 667C	330 ppm	$5.65\times {10}^{14}$	100%	0.7 ppm	$7.99\times {10}^{12}$	100%	$7.0\times {10}^{18}$
GJ 1214	1600 ppm	$5.65\times {10}^{14}$	100%	1.1 ppm	$7.99\times {10}^{12}$	100%	$2.3\times {10}^{18}$
GJ 436	1600 ppm	$5.65\times {10}^{14}$	100%	4.3 ppm	$7.99\times {10}^{12}$	100%	$1.1\times {10}^{18}$
GJ 581	1400 ppm	$5.65\times {10}^{14}$	100%	2.9 ppm	$7.99\times {10}^{12}$	100%	$1.2\times {10}^{18}$
GJ 876	3400 ppm	$5.65\times {10}^{14}$	100%	6.9 ppm	$7.99\times {10}^{12}$	100%	$8.8\times {10}^{17}$

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All of our simulations used a fixed mixing ratio of 355 ppm for CO₂, 21% O₂, and a fixed upper boundary of 10⁻⁴ bar (∼60 km). In the 1D climate model, a surface albedo of 0.2 is fixed for all simulations, corresponding to the surface albedo that reproduces Earth's average temperature of 288 K for the Earth/Sun case. The planetary Bond albedo (surface + atmosphere) is calculated by the 1D climate code.

Lyα is the brightest line in the UV spectra for cool stars and accounts for a significant portion of the overall UV flux. However, the intrinsic Lyα flux must be reconstructed to account for interstellar absorption by neutral hydrogen (see Wood et al. 2005; Linsky et al. 2013). For the observed MUSCLES stars, the Lyα line flux is 13%–33% the total UV flux excluding Lyα. GJ 1214 has no observed Lyα and only an upper limit that is 0.5% of the total UV flux (France et al. 2013). In our active models, Lyα ranges from 2% to 17% of the total UV flux based on observations of AD Leo. In the inactive models (i.e., no chromosphere) Lyα is negligible compared with total UV flux.

We ran two sensitivity tests of the photochemistry of Earth-like planets to the amount of Lyα flux from their host star. First, we increased the Lyα by a factor of 10³, 10⁶, 10⁹, 10¹², and 10¹⁵ above the M0 inactive model, corresponding to flux levels of $2.7\times {10}^{-8}$, $2.7\times {10}^{-5}$, $2.7\times {10}^{-2}$, $2.7\times {10}^{1}$, $2.7\times {10}^{4}$ ergs cm⁻² s⁻¹, respectively. The highest Lyα value considered is 84× higher than that of the M0 active model and 180× higher than the highest observed Lyα flux in the MUSCLES stellar sample. As seen in Figure 6 (top), increasing the Lyα flux has only a small effect on the photochemistry until the most extreme case considered, where it primarily photolyzes N₂O and CH₄. We run our models to around 60 km, corresponding to a pressure of $1\times {10}^{-4}$ bars. The effect of Lyα will be more pronounced at pressures lower than this, as Miguel et al. (2015) has shown for mini-Neptune atmospheres.

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GJ 1214 is the only MUSCLES star to not have a directly detected Lyα flux. An upper limit was placed at $2.4\times {10}^{-15}$ ergs cm⁻² s⁻¹. We artificially set the Lyα flux to be 10⁻², 10⁻¹, 10¹, 10², and 10³ times this upper limit. We tested values both above and below the upper limit to see how sensitive an Earth-like planet atmosphere is to changes in Lyα flux when the rest of the NUV radiation field is still much higher than the inactive model in the previous sensitivity test. As shown in Figure 6 (bottom), the largest changes are seen in the CH₄ and to a smaller extent in stratospheric H₂O concentrations. O₃ and N₂O remain relatively constant through the five order of magnitude change in Lyα flux.

Figures 4 and 6 show that it is important to characterize the entire UV spectrum, including the NUV and the base level flux between emission lines, to understand future observations of extrasolar planet atmospheres. Lyα is one of the most important lines to characterize.

Figure 7 shows the reflected visible and NIR spectra from 0.4 to 2 μm of Earth-like planets around the M dwarf grid of active, inactive, and MUSCLES stars, using the SED of the host star. We assume Earth-analog cloud cover. The high-resolution spectra calculated with 0.1 cm⁻¹ steps have been smoothed to a resolving power of 800 using a triangular smoothing kernel to show the individual features more clearly. The Earth–Sun spectrum is shown for comparison as a dashed black line.

Owing to the increased stellar flux at shorter wavelengths for a G-type star, Rayleigh scattering is much more pronounced for FGK stars, which greatly increases the flux from 0.4 to 0.8 μm for an Earth-like planet around a hotter star. Since M dwarfs have stronger NIR emission, the 1–2 μm flux is larger around Earth-like planets orbiting M dwarfs than for the Earth–Sun equivalent. The most notable features in the visible/NIR spectra are O₃ at 0.6 μm (the Chappuis band), O₂ at 0.76 μm, H₂O at 0.95 μm, and CH₄ at 0.6, 0.7, 0.8, 0.9, 1.0, and 1.7 μm. Note that shallow spectral features like the visible O₃ feature would require a very high signal-to-noise ratio (S/N) to be detected.

Figure 8 shows details for one of the most notable feature in the visible, the O₂ A band at 0.76 μm in both the relative flux as planet-to-star contrast ratio (left) and the reflected emergent flux for a 60% cloud cover model for M0–M9 model stars (top middle) and for the six MUSCLES stars (top right). Note that the detectability of the O₂ feature in reflected light is similar for active and inactive models since the stellar flux at 0.76 μm is activity independent. The relative flux shows an equivalently deep feature for each case owing to a constant mixing ratio of 21%. However, the oxygen feature in absolute flux (Figure 8, upper middle panel) becomes increasingly difficult to detect for the later stellar types. For the latest M stellar types modeled here, the detection of the O₂ feature requires a very high S/N to detect even if the planet has an active photosynthetic biosphere like Earth (see Figure 7). If one assumes a blackbody radiation Planck function, rather than a realistic stellar model, when calculating the shape of the reflected light curve, the reduction in the feature's depth on moving to later stellar types (i.e., going from blue to red lines in Figure 8, second and third columns) is less pronounced. The O₂ feature is pronounced for all MUSCLES stars since none of those stars have a low enough T_eff for the O₂ feature to be diminished by the SED. GJ 876 is the coolest MUSCLES star, with T_eff = 3129 K, and in our models the O₂ feature becomes most obscured for stars with T_eff = 2300–2600 K.

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CH₄ also has several features of interest in the visible/NIR range at 0.6, 0.7, 0.8, 0.9, 1.0, and 1.7 μm (see Figure 9). The CH₄ feature is deeper for less active and cooler M dwarfs. In particular, the CH₄ features at 0.8, 0.9, and 1.0 μm become much more pronounced for the cooler M dwarfs and for some of the MUSCLES stars, such as GJ 876.

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H₂O has several features in the visible/NIR at 0.95, 1.14, 1.41, 1.86 μm. These features are deeper for cooler and less active stars.

Clouds increase reflectivity but can also decrease the depth of all observable features compared to the clear sky case. It will be difficult, therefore, to remotely determine the absolute abundance of a molecule without a well-characterized temperature versus pressure distribution and cloud profile.

Figure 10 shows the thermal emission spectra from 4 to 20 μm of Earth-like planets with Earth-analog cloud cover around the M dwarf grid of active, inactive, and MUSCLES stars using the stellar SED. The high-resolution spectra have been smoothed to a resolving power of 150 using a triangular smoothing kernel to show the resolution expected by JWST. The Earth–Sun IR spectrum is shown for comparison as a dashed black line. Figure 11 shows the individual component gas contributions of the dominant gases (H₂O, CH₄, CO₂, CH₃Cl, O₃, and N₂O) to the final IR planetary spectrum for an M9 active and inactive stellar model.

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The depth of the O₃ feature at 9.6 μm decreases for planets orbiting cooler and less active M dwarfs, as expected owing to lower O₃ abundances for lower UV incident flux and also to the decreased temperature difference between the O₃-emitting layer (around 40 km) and the surface temperature, which is larger for the earlier M dwarfs, as seen in Figure 4.

The CH₄ feature at 7.7 μm decreases in depth for planets orbiting cooler M dwarfs, despite increasing CH₄ abundances making it difficult to remotely determine the CH₄ abundance without a well-characterized temperature versus pressure profile. Note that the 7.7 μm feature is partially obscured by the wings of the H₂O feature at 5–8 μm.

The N₂O features are the most striking addition in the inactive models with low UV flux. N₂O has features at 7.75 (overlapping with the CH₄ feature), 8.5, 10.65, and 16.9 μm (see Figure 11) that become deeper with decreasing UV flux. In the active M0–M9 stellar models we do not see any strong N₂O features, although it does contribute to the depth of the 7.7 CH₄ feature. For the inactive M5–M9 models we see a strong N₂O feature at 10.65 μm and wide absorption from 14–19 μm owing to the strong buildup of N₂O in low UV environments assuming an Earth-like biological surface flux of $7.99\times {10}^{12}$ g yr⁻¹ (see Sections 2 and 3). However, even for modest mixing ratios of 15–34 ppm in GJ 832 and the M0 inactive models, respectively, we see a strong N₂O feature at 16.9 μm. These concentrations are not much higher than the model mixing ratios calculated for the other MUSCLES stars and the later active M dwarf models. N₂O has been considered to be a strong biosignature (see, e.g., Segura et al. 2005; Seager et al. 2012) and will be easier to detect around M dwarfs—especially inactive ones—than around FGK stars.

The CO₂ absorption feature at 15 μm does not have a central emission peak, usually seen in F and G stars, owing to the more isothermal stratospheres of planets around all M dwarfs.

The depth of the H₂O feature at 5–8 μm decreases for later M dwarfs despite increasing stratospheric H₂O concentrations.

Clouds reduce the continuum level and the depth of all of the observable features compared to the clear sky case. Therefore, it will be difficult to remotely determine absolute abundances without a well-characterized temperature versus pressure distribution and cloud profile.

Observability of Biosignatures: detecting the combination of O₂ or O₃ and a reducing gas like CH₄ in emergent spectra and in secondary eclipse measurements requires either observations in the IR between 7 and 10 μm that include the 7.7 μm CH₄ and 9.6 μm O₃ features, or observations in the visible to NIR between 0.7 and 3 μm that include the 0.76 μm O₂ and 2.4 μm CH₄ features in the observed spectral range. The strengths of absorption features (see Figures 7 and 11 for visible/NIR and IR, respectively) depend on the effective temperature of the host star and its UV flux and vary significantly between stellar types (see Figures 7–11).

In the IR, CH₄ at 7.7 μm is more easily detected at low resolution for earlier grid stars (M0–M4) than for later grid stars (M5–M9) in the active models.

The 9.6 μm O₃ feature is deepest in earlier and/or more active M dwarfs, where there are more UV photons. For M5–M9 inactive models, O₃ is not detectable in low resolution at 9.6 μm owing to the extremely low UV flux for these models. The narrow O₂ feature in the visible at 0.72 μm becomes weaker for cooler M dwarfs even though the mixing ratio of O₂ remains fixed in our simulations at 21%. This is a consequence of the faint SEDs at shorter wavelengths for both active and inactive late M stellar models.

For the modern Earth, N₂O and CH₃Cl do not contribute substantially to the spectrum owing to their low mixing ratios and will likely be undetectable by the first low-resolution and photon-limited exoplanet atmosphere characterization missions (Selsis 2000; Kaltenegger et al. 2007). However, both N₂O and CH₃Cl reach detectable levels in the IR spectra for our models of cooler and less active stars owing to low photolysis rates, even though N₂O has many absorption features in the IR (see Figure 11).

N₂O is considered a strong biosignature because there are no significant abiotic sources (Des Marais et al. 2002). One MUSCLES star, GJ 832, has a noticeable N₂O feature at 17 μm, with 15 ppm for a modern Earth-like flux. This case is interesting because GJ 832 has the highest total FUV flux at wavelengths where N₂O is photolyzed (1000–2400 Å). We find that the high Lyα flux of GJ 832 promotes the destruction of O₃, producing more O(¹D), which then reacts with N₂ to form N₂O.

For planets orbiting inactive M5–M9 star models we observe a sharp increase in N₂O concentrations as a consequence of few available UV photons. N₂O features dominate the spectrum for these late, inactive M dwarfs and can be detected in the IR at 4–5 μm, 8–11 μm, and 16–19 μm (see Figure 11). In an atmosphere dominated by N₂O, such strong absorption throughout the IR could obscure the 7.7 μm CH₄ feature. It is unknown whether a strong buildup of biotic N₂O would be physically possible around stars with little or no chromospheric flux. Given the existence of a few GALEX stars with little excess chromospheric NUV flux (Shkolnik & Barman 2014) and only an upper limit established for the Lyα flux from GJ 1214, a small fraction of M dwarfs could exhibit low UV fluxes. However, the MUSCLES data set shows that all six observed M dwarfs have sufficient UV flux to photolyze N₂O and to prevent "runaway" N₂O buildup.

CH₃Cl contributes to our IR spectrum from 13 to 14 μm in the short-wavelength wing of the CO₂ and N₂O features and could also be detectable, depending on the CO₂ and N₂O concentrations present (see Figure 11).

For clear sky models, the vegetation red edge (VRE) surface feature is detectable in low-resolution spectra owing to the order-of-magnitude-increased VRE reflectance between 0.7 and 0.75 μm for all M grid stars assuming that the exoplanets of these host stars have similar plant life (see Rugheimer et al. 2013 for FGK stars). Clouds partly obscure this feature compared to the clear sky case, although the increase in flux can be seen at 0.7 μm in Figure 7, which includes Earth-like clouds. Owing to the shift in available photons to longer wavelengths for M dwarfs, a different photosynthesis biochemistry could have evolved, resulting in a different but potentially observable vegetation signature (Kiang et al. 2007).

Observability of Spectral Features: note that we have not added noise to these model spectra in order to be useful as input models for a wide variety of instrument simulators for both secondary eclipse and direct detection simulations. Different instrument simulators for JWST (see, e.g., Deming et al. 2009; Kaltenegger & Traub 2009) explore the capability of JWST's MIRI and NIRspec instruments to characterize extrasolar Earth-like planets for nearby and luminous host stars. Several groups are providing realistic instrument simulators that can be used to determine the detectability of these absorption features. Future ground- and space-based telescopes are being designed to characterize exoplanets as small as Earth-like planets and will provide opportunities to observe atmospheric features, especially for super-Earths with radii up to twice Earth's radius and therefore four times the flux and planet-to-star contrast ratio levels for Earth-size planets, as shown in Figure 12.

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In addition to measuring the size of the planet, future observations will occur at different phases throughout the planet's orbit. The maximum observable planetary flux in the visible spectrum scales with the illuminated fraction of the planet that is visible to the observer. At quadrature, representing an average viewing geometry, the contrast ratios presented in Figure 12 will be a factor of ∼2 lower in the visible. In the IR, the maximum flux remains constant throughout the planet's orbit, assuming a similar temperature on the planet's dayside and nightside.