# MIRECLE: Science Yield for a Mid-IR Explorer-Class Mission to Study Non-
Transiting Rocky Planets Orbiting the Nearest M-Stars Using Planetary Infrared
Excess

Avi M. Mandell NASA Goddard Space Flight Center, 8800 Greenbelt Rd, Greenbelt,
MD 20771, USA  GSFC Sellers Exoplanet Environments Collaboration  Jacob
Lustig-Yaeger Johns Hopkins University Applied Physics Laboratory, Laurel, MD
20723, USA  NASA NExSS Virtual Planetary Laboratory, Box 351580, University of
Washington, Seattle, Washington 98195, USA  Kevin B. Stevenson Johns Hopkins
University Applied Physics Laboratory, Laurel, MD 20723, USA  Johns Hopkins
University, 3400 N. Charles St, Baltimore, MD 21218, USA  Johannes Staguhn
NASA Goddard Space Flight Center, 8800 Greenbelt Rd, Greenbelt, MD 20771, USA
Johns Hopkins University, 3400 N. Charles St, Baltimore, MD 21218, USA

###### Abstract

Recent investigations have demonstrated the potential for utilizing a new
observational and data analysis technique for studying the atmospheres of non-
transiting exoplanets with combined light that relies on acquiring
simultaneous, broad-wavelength spectra and resolving planetary infrared
emission from the stellar spectrum through simultaneous fitting of the stellar
and planetary spectral signatures. This new data analysis technique, called
Planetary Infrared Excess (PIE), holds the potential to open up the
opportunity for measuring MIR phase curves of non-transiting rocky planets
around the nearest stars with a relatively modest telescope aperture. We
present simulations of the performance and science yield for a mission and
instrument concept that we call the MIR Exoplanet CLimate Explorer (MIRECLE),
a concept for a moderately-sized cryogenic telescope with broad wavelength
coverage ($1-18\;\mu$m) and a low-resolution ($R\sim 50$) spectrograph
designed for the simultaneous wavelength coverage and extreme flux measurement
precision necessary to detect the emission from cool rocky planets with PIE.
We present exploratory simulations of the potential science yield for PIE
measurements of the nearby planet Proxima Cen b, showing the potential to
measure the composition and structure of an Earth-like atmosphere with a
relatively modest observing time. We also present overall science yields for
several mission architecture and performance metrics, and discuss the
technical performance requirements and potential telescope and instrument
technologies that could meet these requirements.

Interdisciplinary astronomy(804)

##  1 Introduction

Cool stars provide an advantage in detecting and characterizing smaller
planets, since the fractional planet signal is larger in both primary transit
and emission/reflection measurements compared with larger stars. Additionally,
the demographics of planet occurrence reveal that the number of small planets
per star increases for cooler stars (Dressing & Charbonneau, 2015), and since
the overall stellar number density increases with decreasing stellar mass (75%
of nearby stars are M dwarfs), cool stars dominate the population of nearby
stars with small planets. Even more tantalizing is the fact that rocky planets
in the habitable zones (HZ) of cool stars have relatively short orbital
periods (4 - 30 days), making them amenable to repeated primary transit and
secondary eclipse measurements, as well as phase-resolved measurements of the
planetary flux.

Transit observations place constraints on the atmospheric conditions at the
planet’s terminator, and are effective in obtaining a first assessment of the
bulk characteristics of the atmosphere. Unfortunately, the size of atmospheric
spectral features is inversely proportional to the square of the stellar
radius and proportional to the planet radius and atmospheric scale height;
therefore, due to the cool and dense nature of the atmospheres expected for
habitable zone rocky planets, the atmospheric scale height will be quite
small. The absorption signature of molecular constituents imprinted on the
starlight from a transiting habitable Earth-like planet around an M dwarf
would be on the order of 5 - 30 parts per million (ppm) even for the very
coolest stars, potentially requiring 10s - 100s of repeated visits with the
James Webb Space Telescope (JWST) to detect H2O or other signs of habitability
in the atmosphere of TRAPPIST-1e, one of the best transiting temperate
terrestrial planets around M-dwarfs for follow-up characterization discovered
to date (Morley et al., 2017; Wunderlich et al., 2019; Fauchez et al., 2019;
Lustig-Yaeger et al., 2019; Suissa et al., 2020; Komacek et al., 2020).

Exoplanets can also be characterized using thermal emission. While the signal-
to-noise ratio (SNR) for primary transit observations tends to increase
towards shorter optical wavelengths where the star is brightest, the SNR for
thermal emission increases towards longer infrared wavelengths due to the
combined effect of weaker emission from the star and stronger emission from
the planet. The SNR peaks in the mid-infrared (MIR) for planets in the HZ. For
TRAPPIST-1e, the planet-to-star flux contrast ratio is estimated to be $<$ 2
ppm below 7 $\upmu$m, $\sim$25 ppm at 10 $\upmu$m, and $\sim$150 ppm at 20
$\upmu$m (Mullally et al., 2019). However, the SNR for thermal emission
measurements is still dependent on the measured brightness of the planet,
leading to requirements for numerous secondary eclipse measurements in order
to detect the emission from even the most optimal transiting planets in the HZ
with JWST (Piette et al., 2022).

To increase SNR and decrease observing time, we either need a larger
collecting area or a brighter target. Stevenson (2020, henceforth S20)
explored the second option, presenting a method for characterizing the thermal
emission from non-transiting planets called the Planetary Infrared Excess
(PIE) technique. PIE relies on simultaneous wavelength coverage of spectral
regions covering both the planet’s infrared flux (longer wavelengths) as well
as spectral regions heavily dominated by the star (shorter wavelengths). S20
showed that, based on certain simplifying assumptions and sufficient
wavelength coverage and measurement precision, the flux from the planet could
be extracted from the star by mutually fitting for the thermal flux of both
the star and planet. S20 performed blackbody simulations of the PIE technique
for measurements of the canonical nearby non-transiting rocky exoplanet
Proxima Centauri b (Anglada-Escudé et al., 2016) with both JWST and a 2-m MIR
telescope, finding that JWST is unlikely to be able to constrain the planet’s
surface temperature or radius due to insufficient wavelength coverage beyond
13 $\upmu$m. Conversely, for a 2-m aperture with 3–20 $\upmu$m wavelength
coverage and 100 hours of integration time, S20 was able to constrain the
simulated planet’s temperature to within $\pm$15 K and its radius to within
$\pm$0.1 Earth radii.

Building on the work from S20, Lustig-Yaeger et al. (2021, henceforth LY21)
utilized realistic planetary atmosphere models to demonstrate that the PIE
technique applied to measurements of the hot Jupiter WASP-43b. Of importance
to this work, LY21 found that sampling the Wien edge of the planet spectrum
provides the best temperature constraint, while sampling the Rayleigh–Jeans
tail provides the best radius constraint, and having both the Wien edge and
Rayleigh–Jeans tail drastically reduces the degeneracy between these two
planet parameters.

In this paper we extend the work of S20 to examine the instrument and mission
requirements for utilizing the PIE technique to characterize the atmospheres
of the nearest cool rocky and Neptune-like non-transiting planets around
M-dwarf stars, and determine the sample of known planets that could be
characterized with different potential aperture sizes. In Section 3 we use
simulated atmospheric retrievals for PCb to examine the impact of various
instrument and mission parameters on the ability to characterize the
atmospheric properties of the planet using the PIE technique. In Section 4 we
scale the results for PCb to examine the total yield of thermal emission
measurements of small cool planets that could be achieved in a reasonable
mission lifetime with a stand-alone MIR exoplanet characterization mission
concept such as the Mid-IR Exoplanet CLimate Explorer (MIRECLE) concept
proposed in Staguhn et al. (2019). In Section 5 we review the technical
readiness of the key observatory and instrument sub-systems needed to achieve
the performance requirements, and in Section 6 we conclude with a discussion
of outstanding issues and future work.

##  2 Motivation

As stated above, we are severely limited by photon noise for thermal emission
measurements of transiting HZ rocky planets; however, the opportunities for
characterizing HZ rocky planets increase dramatically when non-transiting
planets are included as potential targets. In the top of Figure 1 we plot the
emission spectroscopy metric (ESM) from Kempton et al. (2018) for known
transiting and non-transiting planets with derived inclination-dependent
masses ($M~{}\text{sin}~{}i$) less than 6 MEarth within 20 parsecs. Assuming
an Earth-like composition (32.5% Fe and 67.5% MgSiO3), 6 MEarth roughly
corresponds to 1.6 REarth, which is a reasonable upper limit in size for
terrestrial planets (Rogers, 2015). The ESM provides a relative metric for
comparing the expected SNR for a measurement of a specific planet’s thermal
emission assuming a fixed observation time, and is determined by the radius
and effective temperatures of both the star and planet, the distance to the
star, and the reference wavelength of the observation. The traditional ESM
assumes a reference wavelength of 7.5 $\upmu$m and uses a scaling factor that
produces a value of 10 for the well-known planet GJ 1132b, which is the best
known sub-Neptune-mass transiting planet for emission measurements. It is
clear that the addition of non-transiting planets could add a significant
number of new targets equivalent to GJ 1132b in their potential for
characterization, but even in this scenario, no planet with T${}_{eq}<350$ has
an ESM value $>6$; this is due to the fact that the bulk of their thermal
emission is emitted at wavelengths longer than 10 $\upmu$m. In the bottom of
Figure 1 we plot the ESM metric but with a reference wavelength of 15
$\upmu$m. There are now many targets with ESM $>10$, with equilibrium
temperatures extending down to 220K.

Figure 1: Emission spectroscopy metric (ESM) from Kempton et al. (2018) for
all known planets with $M~{}\text{sin}~{}i$ less than 6 ME. Top: ESM as
traditionally defined at 7.5 $\upmu$m. Bottom: Same metric but defined at 15
$\upmu$m. Transiting planets are marked in orange. Due to the impact of
apparent magnitude, the best non-transiting planets have higher ESM, with many
low-temperature planets having an ESM at 15 $\upmu$m above the nominal
threshold of 10 due to the improved blackbody planet-to-star flux ratio. The
two best targets with T${}_{eq}<300$K in the Exo.MAST database, Proxima Cen b
and GJ 3323 b, are noted.

This large number of high-quality targets for the population of non-transiting
warm and temperate rocky planets around nearby stars could be investigated at
wavelengths beyond 10 $\upmu$m, but would require instrumentation optimized
for leveraging the PIE technique at long wavelengths. However, in contrast to
secondary eclipse measurements, PIE measurements of time-integrated thermal
emission would not be limited in SNR by the duration of the in-eclipse
measurement period – enabling the potential for a relatively small telescope
to detect the planetary infrared excess of smaller and cooler planets using
long and continuous integration times.

S20 focused on the potential of the PIE technique for constraining the
planetary radius and brightness temperature of a non-transiting planet, but
PIE spectroscopy in the 8 - 20 $\upmu$m wavelength range would also sample a
number of prominent atmospheric absorption features indicative of habitability
and/or biology such as H2O, CH4, CO2, O3, NH3, N2O, and SO2. Emission
measurements of these atmospheric constituents would provide strong
constraints on whether a planet is a wet, Earth-like planet, a dry, Venus-like
planet with a dense CO2 atmosphere, or a Mars-like planet with a thin CO2
atmosphere. The strong ozone band at 9.6 $\upmu$m allows for the inference of
the presence of molecular oxygen in the atmosphere, which is a powerful
biosignature when combined with other out-of-equilibrium molecular species
(such as CH4 and/or N2O; Schwieterman et al., 2018; Thompson et al., 2022).

Furthermore, long continous integration times enabled by a dedicated mission
would also be able to obtain phase-resolved thermal emission measurements
(i.e. phase curves). Extending from a single time-integrated thermal emission
spectrum to phase-dependent spectroscopy measurements can provide additional
constraints on a wealth of atmospheric properties of terrestrial M-dwarf
planets. Phase curves can be used to more firmly distinguish between planets
with and without substantial atmospheres (e.g. Maurin et al., 2012; Kreidberg
et al., 2019), and subsequently identify the presence of hemispheric-wide
clouds (Yang et al., 2013). For planets with an atmosphere, phase-resolved
thermal emission measurements allow for detailed mapping of a planet’s
atmospheric composition and thermal structure, which is critical towards
assessing habitability. Phase curves can also constrain the planet’s rotation
rate — the morphology of thermal phase curves can differentiate synchronous
rotators with radial or super-rotating winds (Carone et al., 2018) from those
in spin-orbit resonances (Wang et al., 2014), and can distinguish runaway and
non-runaway greenhouse climate states (Kopparapu et al., 2017).

##  3 Simulated Atmospheric Retrievals of Proxima Cen b

The effectiveness of the PIE method is driven by the ability to independently
constrain the stellar and planetary contributions to the spectral energy
distribution; therefore the key observational factors are the simultaneous
wavelength range covered by the instrument and the SNR of the data at
different wavelengths. In order to define the requirements needed to
adequately constrain the atmospheric characteristics of temperate rocky
planets with a MIRECLE mission, we have conducted atmospheric retrievals on
simulated observations of Proxima Cen b, the archetype for the population of
non-transiting temperate terrestrial and sub-Neptune planets around the
nearest M-stars.

Proxima Cen b, or PCb, is a planet in the habitable zone of Proxima Centauri,
the closest star to our solar system at a distance of 1.3 pc. It was first
detected by Anglada-Escudé et al. (2016) using RV measurements and
subsequently confirmed by Suárez Mascareño et al. (2020), with a measured
$M\sin(i)$ of 1.27 ME. With an orbital period of 11.2 days and a semimajor
axis of 0.049 AU, the planet receives a stellar flux of $0.65-0.7\times$
Earth’s insolation (SE) and has a zero-albedo equilibrium temperature
corresponding to $\sim 270$ K (Turbet et al., 2016). Subsequent to the
detection of PCb, several other planet candidates have been tentatively
detected in the same system: one similar-mass candidate at a much longer
orbital period of 5.21 yr (Damasso et al., 2020) and a second much lower-mass
candidate with a period of 5.1 days (Faria et al., 2022); however, to date
neither candidate has been confirmed. Additionally, a detection of a dust belt
around Proxima Cen based on ALMA images was announced by Anglada et al.
(2017), but the signal was later determined to be due to an extreme flare
event (MacGregor et al., 2018) and no further evidence of dust in the system
has been detected.

Based on the close proximity of the target and the potential habitability of
the planet, we use PCb as our fiducial target for our proof-of-concept
retrieval simulations. To date, essentially nothing is known about the
presence and composition of an atmosphere on PCb; however, for the purpose of
developing observing techniques and analysis methods capable of assessing the
planet’s atmospheric characteristics, habitability, and biosignatures, we
adopt the common fiducial assumption that the planet is Earth-like in
atmospheric composition. Since PCb was discovered by RV and it has not been
found to transit (Jenkins et al., 2019), the unknown inclination and planet
radius as well as the uncertainty in planet mass mean that the planet could
either have a fully rocky composition, a significant ice component, or a H/He
envelope (although the latter has been shown to be only 10% likely; Bixel &
Apai (2017)). Critically, if PCb is assumed to have formed with a low fraction
of H/He, atmospheric loss processes could present a substantial threat to the
retention of atmospheres over long timescales and the planet may be airless
(Barnes et al., 2016; Dong et al., 2017; Garcia-Sage et al., 2017; Zahnle &
Catling, 2017). On the other hand, the large inherent uncertainties in
interior composition propagate into uncertainty in the outgassing rate from
the interior (e.g., Noack et al., 2021), a process that can serve to produce
and sustain a secondary atmosphere. Thus the possibility that PCb is a
terrestrial planet with an atmosphere cannot be ruled out, and climate and
photochemical models of PCb under the assumption of relatively Earth-like
atmospheric conditions show that the planet could maintain habitable surface
temperatures with stable surface oceans (Turbet et al., 2016; Meadows et al.,
2018; Del Genio et al., 2019; Galuzzo et al., 2021). However, it is clear that
with the potential additional planet candidates and the impact of continual
flaring from the host star, the assumptions underlying these initial
simulations may need to be modified in the future - but only observations of
PCb can provide definitive answers on the presence and nature of its
atmosphere. We further discuss these issues in §6.

In the following subsection §3.1 we describe the retrieval model, and then
present retrieval results in §3.2.

###  3.1 Retrieval Model

We use the Spectral Mapping Atmospheric Radiative Transfer Exoplanet Retrieval
(smarter) model to infer physical parameters from synthetic observed spectra
(Lustig-Yaeger, 2020; Lustig-Yaeger et al., 2022; Lustig-Yaeger et al. 2022b,
in prep). At the core of the forward model, smarter uses the Spectral Mapping
Atmospheric Radiative Transfer code (smart; Meadows & Crisp, 1996) to perform
line-by-line, multi-stream, multi-scattering radiative transfer calculations
in a plane-parallel 1D atmosphere. smart has been used extensively to simulate
the emission, reflection, and transmission spectra of solar system planet
atmospheres (e.g., Meadows & Crisp, 1996; Robinson et al., 2010, 2011; Arney
et al., 2014; Schwieterman et al., 2015) and exoplanet atmospheres (e.g.,
Segura et al., 2005; Schwieterman et al., 2016; Meadows et al., 2018;
Lincowski et al., 2018).

We limit our descriptions of smart here to the relevant components for
modeling the thermal emission of an Earth-like planet from approximately
$1-20$ $\upmu$m. As such, we consider atmospheres composed of CO2, O3, H2O,
CH4, N2O, and N2. We use the HITRAN2016 (Gordon et al., 2017) line list to
calculate molecular rotational-vibrational absorption coefficients for input
into smart using the Line-By-Line ABsorption Coefficient model (lblabc;
Meadows & Crisp, 1996). We use a nominal Earth composite surface albedo from
Meadows et al. (2018), which results in a surface emissivity of approximately
0.996 throughout the MIR. All radiative transfer calculations with smart were
performed using 8 streams (4 upward and 4 downward; defined at Gaussian
points), and Gaussian quadrature integration was used to produce top-of-
atmosphere (TOA) thermal emission spectra.

We adapted a relatively standard exoplanet thermal emission retrieval modeling
approach to work with the PIE technique similar to the methods used by LY21 to
explore the potential for PIE with JWST. The key difference between standard
secondary eclipse thermal emission modeling and PIE modeling is that PIE
requires joint modeling of planetary and stellar parameters. For PIE, the
wavelength-dependent observable flux from the exoplanetary system ($F_{\rm
sys}$) is modeled as

$F_{\rm sys}=F_{\rm s}+F_{\rm p}$ (1)

where $F_{\rm s}$ is the flux from the star and $F_{\rm p}$ is the flux from
the planet, and both are distance-scaled to the observer at/near Earth. As
discussed in LY21, many additional factors can be added to Equation 1 to
account for additional flux sources that may be unresolved in the field, such
as exozodiacal emissions; however, we neglect these in this work to focus
exclusively on the first-order planet-star effects. Our stellar flux model
uses Phoenix stellar grids (Allard et al., 2003, 2007, 2012) accessed via the
pysynphot code (STScI Development Team, 2013) and linearly interpolated in
effective temperature $T_{\rm eff}$, surface gravity $\mathrm{log}(g)$, and
metallicity $\mathrm{log}([M/H])$. In addition, we scale the stellar spectrum
using the stellar radius $R_{\rm s}$ and the distance $d$, although only
$R_{\rm s}$ is used as a free parameter because $d$ is well known for the
Proxima Centauri system, so it is held fixed.

For the planetary flux model, the smarter forward model assumes evenly mixed
volume mixing ratios (VMRs) for the molecules composing the atmosphere. The
forward model uses an adiabatic equation of state parameterization for the
vertical temperature profile,

$T(P)=\begin{cases}T_{0}\left(\frac{P}{P_{0}}\right)^{\alpha(\gamma-1)/\gamma},~{}\mathrm{for}~{}P\geq
P_{1}\\\
T_{0}\left(\frac{P_{1}}{P_{0}}\right)^{\alpha(\gamma-1)/\gamma},~{}\mathrm{for}~{}P<P_{1}\end{cases}$
(2)

where $T(P)$ is the temperature as a function of pressure $P$, $T_{0}$ is the
reference/surface temperature, $P_{0}$ is the reference/surface pressure,
$\gamma$ is the ratio of specific heats, $\alpha$ is used to modify the dry
adiabat due to, for example, latent heat release or non-constant specific
heats (Catling & Kasting, 2017; Tolento & Robinson, 2019). Since
$\gamma=c_{p}/c_{v}$, it could be calculated in terms of the gases composing
the bulk atmospheric volume rather than treated as a free parameter in the
retrieval. However, bulk atmospheric compositions for high mean molecular
weight atmospheres are not trivially constrained by retrievals (Barstow et
al., 2020), so we directly fit for $\gamma$ as a free parameter independent of
the retrieved gas VMRs. Similarly, although reparameterizing Equation 2 to
combine $\gamma$ and $\alpha$ into a single parameter may be a sensible choice
for reducing the dimensionality of the retrieval posterior sampling problem,
we elected to keep both physical parameters and marginalize over their
degeneracy to more easily track how the retrieval constrains them
individually.

For pressures lower than $P_{1}$ (nominally the tropopause pressure), an
isothermal profile is assumed, fixed to the value of the profile at $P_{1}$.
Thus, Equation 2 results in five free retrieval parameters that together
describe the vertical TP profile. We note that this TP profile is not capable
of producing temperature inversions, such as the stratospheric inversion in
Earth’s atmosphere, and is therefore limited. However, as we will show, it is
capable of fitting the spectrum of, and retrieving unbiased information about,
an Earth-like exoplanet’s atmosphere using the spectral resolution and
precision considered for MIRECLE.

Given this 1D description of the planetary atmosphere, along with the
aforementioned gas optical properties and surface emissivity information,
smart simulates top-of-atmosphere planetary emission spectra, as previously
described, which are added to the stellar flux as shown in Equation 1.

Figure 2: Simulated stellar and planetary flux for the Proxima Cen system. The
left axis shows the relative fluxes of the two sources; the right axis shows
the planet-to-star flux ratio. The planetary spectrum peaks at ${\sim}10.4$
$\upmu$m, the stellar spectrum peaks at ${\sim}1$ $\upmu$m, and $F_{p}/F_{s}$
steadily rises towards longer wavelengths.

To produce a plausible observed spectrum of PCb for our retrieval experiments,
we used a 1D Earth-like atmospheric model from Meadows et al. (2018) (see
their Figure 8) as our fiducial “truth”. This 1D thermal structure and
composition is vertically resolved as a function of altitude, and therefore
contains realistic vertical composition gradients, such as a stratospheric O3
bulge and a H2O profile that increases in abundance from the tropopause down
to the surface. These additional vertically-resolved atmospheric inputs were
then provided to smart to produce a high resolution emission spectrum for PCb
to use as the synthetic data for our simulated observations.

Figure 2 shows the high-resolution simulated stellar and planetary spectra for
reference, prior to degrading them appropriately for use as our simulated
observations. The reflected component of the planetary flux declines following
the stellar spectrum out to between 3 and 4 $\upmu$m where the thermal
component begins to sharply rise on the Wein tail of the planet’s thermal
blackbody. The reflected planet flux contributes ${<}0.1$ ppm to the total
system flux at all wavelengths considered and is henceforth neglected.

We used the GSFC Planetary Spectrum Generator (PSG; Villanueva et al. (2018))
to produce noise estimates for the PIE observations of PCb under various
different assumptions for the MIRECLE telescope and instrument performance.
The PSG noise estimation module includes uncertainty contributions from both
the astrophysical scene as well as the instrument and telescope. Specifically,
PSG includes photon noise for both the observed object (in this case, star and
planet) as well as the astrophysical background flux from the Solar System
zodiacal background. It also includes noise contributions from the thermal
background of the telescope and the noise produced by the instrument
detectors.

Figure 3: Noise contributions for an observation of PCb as a function of
wavelength for the 2-m and 0.5-m telescope sizes, assuming the additional
parameters listed in Table 1. Observations with a 2-m telescope are photon-
noise dominated through the wavelength range, while the 0.5-m telescope
quickly becomes dominated by the zodiacal background and detector noise. The
positions of 5 ppm and 10 ppm noise floors are indicated by dotted lines.

PSG utilizes planetary parameters from the NExSci Exoplanet Database. We
varied the wavelength range and aperture size based on our assumed mission
parameters, and set the instrument aperture size to match $2\times$FWHM at the
longest wavelength, in order to avoid significant flux loses. Since Proxima
Cen has a very high ecliptic latitude, we use the minimum value for the Solar
System zodiacal light background of 23.3 magV per arcsec2, based on the PSG
parameterization of the zodiacal flux computed by combining data from Kwon et
al. (2004) and Leinert et al. (1998). These values and additional parameters
for the telescope throughput, primary mirror temperature and emissivity are
listed in Table 1. In Figure 3 we plot the noise contributions from the
various sources of noise for an observation of PCb, assuming a 2-m aperture
versus a 0.5-m aperture. For the 2-m telescope, the photon noise from the star
dominates at all wavelengths, and never rises above 9 ppm. However, for a
0.5-m aperture, the sky background and detector dark current become
increasingly important past 10 $\upmu$m. For more distant targets or smaller
apertures, observations will eventually be background- and detector-limited,
leading to longer exposure times to reach the desired SNR.

Table 1: PSG Parameters for Proxima Cen Noise Calculations Parameter | Value
---|---
Stellar temperature | 3050 K
Stellar radius | 0.14 Rsun
Stellar distance | 1.3 pc
Zodiacal background | 23.3 magV per arcsec2
Primary mirror diameter | (2 / 1 / 0.5) meters
Total throughput | 50%
Telescope temperature | 35 K
Detector dark current | 100 e-/s
Detector read noise | 16 e-
Spectral range | (1 / 2.5) - (16.7 / 18) $\upmu$m
Spectral resolution | 50
Spectral aperture size |  $2\times$FWHM at LW cut-off
Total integration time | 100 hours

We run our atmospheric retrievals using the emcee Markov Chain Monte Carlo
(MCMC) Python package to draw samples from the posterior distribution
(Foreman-Mackey et al., 2013). We defined the log-posterior probability
function as the sum of a $\chi^{2}$ log-likelihood function and the log-prior
probability. We selected uninformative flat priors for the planetary
parameters and Gaussian (and truncated Gaussian) priors for the stellar
parameters conditioned using current estimates from the literature for Proxima
Cen. The upper and lower prior bounds on the TP profile parameters $\gamma$
and $\alpha$ correspond, respectively, to a range between 2-10 degrees of
freedom for primary molecular constituent of the atmosphere (which is unknown
a priori and not guaranteed to be constrained from the spectrum) and an
empirical range found within Solar System atmospheres based on the ratio of
the true convective lapse rate to the dry adiabatic lapse rate (Catling &
Kasting, 2017). Table 2 lists the parameter priors in the third column. We
used 30 walkers per dimension, with 14 dimensions unless otherwise stated,
yielding a total of 420 walkers in our nominal retrievals.

We initialized the walkers in a Gaussian ball with mean and standard deviation
defined by the results of running a preliminary non-linear least-squares fit
to the data using scipy.optimize.curve_fit. Beginning the MCMC near the
maximum a posteriori state with the walkers distributed in accordance to an
approximation to the 1D marginal posterior distribution allows the MCMC to
rapidly burn-in, needing only to identify deviations from Gaussianity and the
multi-dimensional parameter covariances. We used emcee to draw samples from
the posterior until the length of the chain is equal to approximately
$50\times$ the integrated auto-correlation length of the chain—a common
convergence heuristic. While each retrieval runs for a different amount of
time, primarily dictated by the wavelength range, for an average forward model
evaluation time of 1 minute the full MCMC retrieval running on 25 cores
typically takes approximately one month to converge.

###  3.2 Retrieval Results

For our fiducial retrieval experiment (Case 1) we considered a 2-m diameter
mirror with simultaneous wavelength coverage from $1-18$ $\upmu$m and a 5 ppm
noise floor. Figure 4 shows a corner plot with the retrieved posterior
distributions for our fiducial noise case. The upper right quadrant of Figure
4 displays the distribution of planet spectra that were derived from samples
from the posterior distribution, which shows the prominent 15 $\upmu$m CO2
band, the 9.6 $\upmu$m O3 band, and the location of other bands which are
difficult to discern by eye. Only a subset of the retrieved planetary and
stellar parameters are shown for clarity and to highlight the most important
parameters; this includes the evenly mixed VMRs of CO2, O3, H2O, CH4, and N2O,
the solid body planet radius $R_{0}$, the surface temperature $T_{0}$, and the
surface pressure $P_{0}$. Additional

Table 2: Retrieved constraints on planetary parameters using the PIE technique
with MIRECLE

|  |  | Case 1 | Case 2 | Case 3 | Case 4 | Case 5 | Case 6 | Case 7 | Case 8 | Case 9
---|---|---|---|---|---|---|---|---|---|---|---
| Wavelengths ($\upmu$m): | 1-18 | 1-18 | 1-18 | 1-18 | 1-18 | 1-16.7 | 2.5-18 | 5-12 | 5-12
| Diameter (m): | 2 | 2 | 2 | 1 | 0.5 | 2 | 2 | 6.5 | 6.5
| Noise Floor (ppm): | 5 | 0 | 10 | 5 | 5 | 5 | 5 | 5 | 20
| Int. Time (hrs): | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 12.6aaAn integration time of 12.6 hours for a 6.5-meter aperture is equivalent to 100 hours with a 2-m aperture, thereby preserving the photon-noise contribution. | 12.6aaAn integration time of 12.6 hours for a 6.5-meter aperture is equivalent to 100 hours with a 2-m aperture, thereby preserving the photon-noise contribution.
Parameters | Defaults | Priors | Retrieved Constraints (Median${}^{+1\sigma}_{-1\sigma}$)
CO2 [VMR] |  $-3.55$bbThese are approximate (column averaged) values to be used as a reference since the simulated data were generated using vertically resolved profiles from (Meadows et al., 2018). | $\mathcal{U}(-12,0)$ | $-3.10^{+0.81}_{-0.59}$ | $-3.40^{+0.46}_{-0.32}$ | $-3.12^{+0.83}_{-0.86}$ | $-3.00^{+0.83}_{-0.87}$ | $-3.4^{+1.4}_{-1.4}$ | $-3.12^{+0.73}_{-0.80}$ | $-3.03^{+0.78}_{-0.72}$ | $-6.1^{+3.6}_{-4.0}$ | $-6.2^{+4.3}_{-3.9}$
O3 [VMR] |  $-5.70$bbThese are approximate (column averaged) values to be used as a reference since the simulated data were generated using vertically resolved profiles from (Meadows et al., 2018). | $\mathcal{U}(-12,0)$ | $-6.9^{+1.2}_{-2.5}$ | $-6.71^{+0.46}_{-0.29}$ | $-7.8^{+2.0}_{-2.8}$ | $-7.4^{+1.6}_{-3.0}$ | $-7.9^{+2.4}_{-2.8}$ | $-7.3^{+1.4}_{-2.8}$ | $-7.1^{+1.4}_{-3.2}$ | $-7.6^{+2.0}_{-3.0}$ | $-7.0^{+4.3}_{-3.3}$
H2O [VMR] |  $-3.44$bbThese are approximate (column averaged) values to be used as a reference since the simulated data were generated using vertically resolved profiles from (Meadows et al., 2018). | $\mathcal{U}(-12,0)$ | $-2.7^{+1.0}_{-1.0}$ | $-2.97^{+0.62}_{-0.48}$ | $-4.0^{+2.0}_{-4.5}$ | $-3.4^{+1.7}_{-4.1}$ | $-4.8^{+2.6}_{-4.1}$ | $-3.3^{+1.4}_{-3.1}$ | $-2.8^{+1.2}_{-1.5}$ | $-5.6^{+3.6}_{-4.0}$ | $-5.7^{+3.9}_{-4.1}$
CH4 [VMR] |  $-6.76$bbThese are approximate (column averaged) values to be used as a reference since the simulated data were generated using vertically resolved profiles from (Meadows et al., 2018). | $\mathcal{U}(-12,0)$ | $-7.5^{+3.3}_{-3.2}$ | $-7.1^{+2.0}_{-3.1}$ | $-6.7^{+3.7}_{-3.5}$ | $-6.9^{+3.2}_{-3.4}$ | $-6.8^{+3.7}_{-3.3}$ | $-7.3^{+3.0}_{-3.2}$ | $-6.7^{+2.8}_{-3.6}$ | $-7.3^{+3.2}_{-3.2}$ | $-6.3^{+4.2}_{-3.9}$
N2O [VMR] |  $-7.12$bbThese are approximate (column averaged) values to be used as a reference since the simulated data were generated using vertically resolved profiles from (Meadows et al., 2018). | $\mathcal{U}(-12,0)$ | $-8.0^{+2.1}_{-2.7}$ | $-7.0^{+0.9}_{-2.6}$ | $-7.6^{+2.2}_{-2.9}$ | $-7.9^{+2.2}_{-2.8}$ | $-8.0^{+2.9}_{-2.7}$ | $-8.0^{+2.1}_{-2.6}$ | $-8.5^{+2.3}_{-2.4}$ | $-8.1^{+2.9}_{-2.7}$ | $-6.9^{+4.4}_{-3.5}$
$R_{p}$ [R⊕] | $1.074$ | $\mathcal{U}(0.7,1.5)$ | $1.01^{+0.19}_{-0.14}$ | $1.031^{+0.078}_{-0.070}$ | $0.91^{+0.29}_{-0.13}$ | $0.96^{+0.21}_{-0.14}$ | $0.93^{+0.23}_{-0.14}$ | $1.06^{+0.20}_{-0.18}$ | $0.98^{+0.23}_{-0.14}$ | $1.06^{+0.29}_{-0.24}$ | $1.06^{+0.29}_{-0.26}$
$P_{0}$ [log(Pa)] | $5.0$ | $\mathcal{U}(4,6)$ | $4.73^{+0.37}_{-0.50}$ | $4.89^{+0.18}_{-0.27}$ | $4.62^{+0.53}_{-0.44}$ | $4.58^{+0.53}_{-0.41}$ | $4.62^{+0.65}_{-0.44}$ | $4.67^{+0.45}_{-0.47}$ | $4.64^{+0.44}_{-0.46}$ | $4.62^{+0.68}_{-0.45}$ | $4.93^{+0.67}_{-0.62}$
$P_{1}$ [log(Pa)] | $4.34$ | $\mathcal{U}(1.34,5.34)$ | $4.08^{+0.44}_{-0.50}$ | $4.40^{+0.21}_{-0.31}$ | $3.95^{+0.57}_{-0.54}$ | $3.94^{+0.56}_{-0.60}$ | $3.81^{+0.75}_{-1.15}$ | $3.98^{+0.52}_{-0.51}$ | $4.02^{+0.48}_{-0.49}$ | $3.5^{+1.2}_{-1.4}$ | $3.5^{+1.3}_{-1.5}$
$T_{0}$ [K] | $288.0$ | $\mathcal{U}(100,400)$ | $293^{+22}_{-21}$ | $290.6^{+9.5}_{-9.0}$ | $304^{+27}_{-33}$ | $296^{+24}_{-24}$ | $299^{+28}_{-27}$ | $285^{+25}_{-20}$ | $294^{+23}_{-25}$ | $287^{+38}_{-29}$ | $269^{+59}_{-77}$
$\gamma$ |  $1.45$bbThese are approximate (column averaged) values to be used as a reference since the simulated data were generated using vertically resolved profiles from (Meadows et al., 2018). | $\mathcal{U}(1.2,2.0)$ | $1.44^{+0.34}_{-0.19}$ | $1.45^{+0.30}_{-0.18}$ | $1.44^{+0.33}_{-0.19}$ | $1.42^{+0.38}_{-0.18}$ | $1.46^{+0.35}_{-0.20}$ | $1.41^{+0.36}_{-0.17}$ | $1.45^{+0.30}_{-0.20}$ | $1.55^{+0.33}_{-0.27}$ | $1.56^{+0.31}_{-0.25}$
$\alpha$ |  $0.6$bbThese are approximate (column averaged) values to be used as a reference since the simulated data were generated using vertically resolved profiles from (Meadows et al., 2018). | $\mathcal{U}(0.4,0.9)$ | $0.57^{+0.20}_{-0.13}$ | $0.73^{+0.12}_{-0.09}$ | $0.57^{+0.21}_{-0.12}$ | $0.58^{+0.20}_{-0.13}$ | $0.59^{+0.20}_{-0.14}$ | $0.57^{+0.19}_{-0.13}$ | $0.57^{+0.20}_{-0.13}$ | $0.65^{+0.16}_{-0.17}$ | $0.66^{+0.16}_{-0.19}$

Note. — $\mathcal{U}$ denotes a uniform prior probability distribution
described in terms of the lower and upper bounds.

parameters and their $\pm 1\sigma$ posterior constraints are listed in Table 2
under Case 1. The VMRs of CO2 and H2O are constrained to better than an order
of magnitude ($<1$ dex), O3 and N2O have strongly peaked posteriors with
slight tails extending towards low abundances, and the CH4 constraint is most
consistent with an upper limit. There is a curving degeneracy (negative
correlation) seen between the surface temperature and planet radius, which is
consistent with the PIE retrieval findings from S20 and LY21, and underscores
a key challenge that the PIE technique faces for non-transiting planets that
do not have well constrained radii. Put simply, an increase in planetary flux
across the entire wavelength range could be the result of an increase in the
planet radius or an increase in the planet surface temperature; hence the
degeneracy. The surface pressure $P_{0}$ is anticorrelated with the molecular
VMRs because an increase in the surface pressure at fixed VMR increases the
optical depth. With multiple resolved bands in the spectrum, $P_{0}$ can be
constrained.

Figure 4: Corner plot showing the 1D and 2D marginalized posterior
distributions (histograms and contours) for a subset of the retrieved
parameters from our fiducial synthetic MIRECLE data. The 1D marginals along
the diagonal show the true vertical atmospheric profiles as a function of
pressure, from which the synthetic data was generated. The upper right inset
shows the median retrieved spectrum sampled from the posterior with envelopes
showing the $\pm 1\sigma$ and $\pm 3\sigma$ credible intervals. These PIE
observations are sufficient to retrieve robust constraints on the VMRs of
numerous critical atmospheric gases and the surface temperature.

##### Noise Floor

In our second retrieval experiment we studied how the presence and value of a
spectroscopic noise floor affects the atmospheric constraints that can be
inferred for PCb using the PIE technique. To complement the Case 1 retrieval
that used a 5 ppm noise floor, we repeated the aforementioned experiment using
data with no noise floor (Case 2) and data with a 10 ppm noise floor (Case 3).
The $\pm 1\sigma$ posterior constraints for Case 2 and Case 3 are listed in
Table 2 for reference. The spectroscopic precision of these cases are shown as
a function of wavelength in the lower left panel of Figure 5. The 1D marginal
posterior distributions for the primary atmospheric parameters are compared in
the upper row of subpanels in Figure 5, and the 2D covariance between the
surface temperature and planet radius is shown in the lower right panel of
Figure 5. As expected, the use of a detector without a noise floor enables
observations at the photon limit, which provides the best constraints on the
atmosphere. The 5 ppm noise floor case still enables robust constraints on the
VMRs of CO2, H2O, and O3. The 10 ppm noise floor case shows significantly
degraded sensitivity to the O3 and H2O VMRs, but it is still able to place
constraints on the CO2 abundance and the surface temperature. This comparison
also helps to illuminate the nature of the radius-temperature degeneracy,
since the photon limited observations are still subject to the same curving
negative correlation, but generally show accurate 1D marginals. This indicates
that precise observations help to provide unique constraints on each
parameter, despite the degeneracy. This is consistent with the fact that
temperature and radius are not perfectly degenerate: temperature induces a
wavelength-dependent observable (as a blackbody), while the radius is a purely
gray effect (modulo the photospheric radius correction discussed in Fortney et
al. (2019), which is not considered in this work).

Figure 5: Results for retrievals on spectra with varying noise floors. Top
Panels: 1D marginalized posterior distributions (histograms) for the five gas
abundances under consideration (in $\log_{10}$ VMR) and the median retrieved
TP profiles with $1\sigma$ envelopes relative to the true atmospheric profiles
(black lines) that were assumed for the input data. Lower Left: Spectroscopic
precision ($1\sigma$ errors) as a function of wavelength for the three noise
floor cases considered. Lower Right: 2D marginalized posterior distributions
showing the covariance between surface temperature and planet radius.

##### Aperture Size

In our next retrieval experiment we kept the noise floor fixed at 5 ppm and
examined the effect of aperture size. A larger aperture size results in both a
higher SNR for the same integration time as well as a lower astrophysical
background level, since the PSF at a specific wavelength would be smaller and
therefore the sky aperture could be smaller as well; this effect can be seen
in Figure 3. We generated synthetic observations assuming a primary mirror
diameter of 1 meter (Case 4) and 0.5 meters (Case 5) to compare with our
previous results using a 2-m primary mirror diameter (Case 1). For each
aperture size we kept the exposure time fixed at 100 hours. The posterior
constraints for Case 4 and Case 5 are provided in Table 2. Figure 6 compares a
subset of the retrieval results. Although the surface temperature ($T_{0}$)
and pressure ($P_{0}$) constraints are not significantly improved for the 2m
compared to the 0.5-m and 1-m (approximately $1.3\times$ and $1.1\times$ more
constrained at $1\sigma$, respectively), the higher quality data enable
$2.0\times$ and $1.2\times$ tighter constraints on the tropopause pressure
($P_{1}$) at $1\sigma$, respectively. This is also revealed by the tighter
constraints on the retrieved TP profile shown in the rightmost panel of Figure
6. In a 100-hour observations, the 0.5-m telescope would be limited to only
detecting the surface/brightness temperature and the presence of CO2. The 2-m
telescope may be required to provide a robust H2O detection, which is critical
for assessing habitability. The smaller aperture 1-m and 0.5-m telescopes only
approach the 5 ppm noise floor at the very shortest wavelengths (in 100 hours)
and as a result, provide comparable constraints on the stellar parameters
using the PIE technique, despite these telescope’s divergent capabilities at
constraining PCb’s atmospheric conditions using the data from longer
wavelengths.

Figure 6: Posterior constraints resulting from retrievals on spectra obtained
with different primary mirror diameters for the MIRECLE concept. Results using
2-m (Case 1), 1-m (Case 4), and 0.5-m (Case 5) primary aperture sizes are
shown in purple, dark green, and light green, respectively. The rightmost
panel shows the median retrieved TP profiles and $1\sigma$ envelopes for each
case.  Figure 7: Posterior constraints resulting from retrievals on spectra
obtained with a 2-m MIRECLE concept (purple), compared to results using the
JWST MIRI LRS wavelength range with a MIRECLE-like 5 ppm noise floor (orange),
and using JWST MIRI LRS but assuming a 20 ppm noise floor based on MIRI
performance expectations. The rightmost panel shows the median retrieved TP
profiles and $1\sigma$ envelopes for each case. Although MIRECLE requires
longer exposure times, the combination of broader wavelength coverage and high
instrument sensitivity is necessary to enable atmospheric characterization of
PCb with PIE.

##### Wavelength Range

In our final retrieval experiment we held the spectroscopic precision
(approximately) fixed near a 5 ppm noise floor and varied the wavelength range
of the contiguous bandpass to compare different detector capabilities and to
perform a comparison with JWST. We investigated five cases: (1) our nominal
MIRECLE concept with full wavelength coverage between $1-18$ $\upmu$m (Case
1), (2) a MIRECLE concept with a longwave cutoff at 16.7 $\upmu$m (Case 6;
$1-16.7$ $\upmu$m), a MIRECLE concept with a shortwave cutoff at 2.5 $\upmu$m
(Case 7; $2.5-18$ $\upmu$m), (4) observations using the same wavelength
coverage as JWST’s MIRI LRS ($5-12$ $\upmu$m, Kendrew et al., 2015) but using
a MIRECLE-like noise floor of 5 ppm (Case 8), and finally JWST’s MIRI LRS but
assuming a 20 ppm noise floor based on optimistic MIRI performance
expectations (Case 9). For our MIRECLE concepts we used an exposure time of
100 hrs. For MIRI LRS we used an exposure time of 12.6 hrs, which results in a
similar number of photon counts to the MIRECLE concepts. The $\pm 1\sigma$
posterior constraints for all of the cases are provided in Table 2.

The loss of a small portion of the wavelength range at the red end of the
spectrum (Case 6) and at the blue end (Case 7) yields planetary constraints
that are only marginally worse compared to the full $1-18$ $\upmu$m range
(Case 1), with one notable exception. The H2O constraint swells by a factor of
$2.3\times$ for Case 6, indicating that the water absorption seen in Figure 4
at wavelengths longer than the 15 $\upmu$m CO2 band (between about $16-18$
$\upmu$m) contributes significantly to the H2O abundance
retrieval—particularly for ruling out low H2O abundances.

Figure 7 compares the retrieval results for the MIRI LRS cases (Case 8 and
Case 9) with our fiducial MIRECLE concept (Case 1). Despite the prominence of
CO2 bands in the IR, the MIRI LRS wavelength range misses the 4.3 $\upmu$m
band and all but the shortwave wings of the 15 $\upmu$m band. As a result,
MIRI LRS is only weakly sensitive to atmospheric CO2 in our simulations, as
demonstrated in Cases 8 and 9. While MIRI LRS with an unrealistic 5 ppm noise
floor shows some sensitivity to the 9.6 $\upmu$m O3 band, the increase in
background noise with wavelength in the MIRI LRS bandpass makes the abundance
constraint quite limited. With a 20 ppm noise floor the MIRI LRS sensitivity
to O3 is lost altogether. On the shortwave end, the spectral coverage between
$1-5$ $\upmu$m enables MIRECLE to retrieve ${\sim}20\times$ more precise
stellar parameters than using the PIE technique with MIRI LRS.

In considering the three MIRECLE cases (1, 6, and 7) with 5 ppm noise floors,
we see a marginal increase in the retrieved uncertainties on the planet radius
and temperature with decreasing wavelength range. The uncertainties grow
noticeably for Case 8, however, where the wavelength range drops to 5 – 12
$\upmu$m. The larger uncertainties for Case 8 are to be expected based on
results from LY21.

We also note that although it may seem that a better comparison would be to
have MIRI LRS observe for 100 hours, the longer exposure time would yield
negligible gains because the noise floor is already reached in the 12.6 hour
integration, so additional integration time would only push up against that
floor. Furthermore, MIRI LRS is expected to fully saturate on observations of
Proxima Centauri between approximately $5-6$ $\upmu$m (Glasse et al., 2015;
Kreidberg & Loeb, 2016), which would further decrease the precision of stellar
and planetary retrievals using the PIE technique compared to our simulations
that neglected saturation.

Figure 8: Posterior constraints on stellar parameters expressed as deviation
from the input value in parts-per-million (ppm) from PIE retrievals using
different simulated datasets. The nominal 2-m MIRECLE concept covering $1-18$
$\upmu$m (Case 1) is in purple, a MIRECLE concept covering $1-16.7$ $\upmu$m
(Case 6) is in light green, a MIRECLE concept covering $2.5-18$ $\upmu$m (Case
7) is in light orange, and a MIRECLE concept with the JWST MIRI LRS wavelength
range of $5-12$ $\upmu$m (Case 8) is in dark orange.

Figure 8 shows the retrieved constraints on the stellar effective temperature
$T_{\rm eff}$, stellar surface gravity $\log(g)$, and stellar radius $R_{s}$
for the cases discussed in this section with different wavelength ranges. Each
parameter is shown in ppm deviation from the assumed input value. In general,
the constraints on the stellar parameters scale as one would expect. The
broadest wavelength range, highest precision observations (Case 1) provide the
tightest constraints. Spectra that maintain the same shortwave cutoff, but do
not extend as far into the MIR (Case 6) provide effectively the same
constraint due to the NIR peak of the stellar blackbody curve. Spectra that do
not cover as much of the NIR (Case 7 and Case 8) do not provide as tight of
constraints on the stellar parameters.

However, the stellar parameters are exceedingly well constrained in all cases
and reveal a caveat of our simple stellar model parameterization. Since we
assumed that the star was a static source over the entire duration of our
simulated long-exposure observations, and we sampled our observations from our
simple stellar model, we were able to infer exactly what we put in. While this
helps to demonstrate that the combined stellar and planetary spectra are
separable, realistic observations will have numerous sources of variability
that operate on different timescales and dominate at different wavelengths.
Moreover, existing stellar models need not be good fits to such high SNR
observations. More work is needed to study the effect of more realistic
stellar sources and the cost-benefit analysis of including more sophisticated
stellar spectral models in PIE retrievals. We note that the PIE technique only
requires the stellar parameters to be retrieved in so far as they control the
stellar spectrum and allow it to be fit precisely enough to reveal the planet
spectrum in the residuals. If increasing the sophistication of the stellar
model with more parameters causes the precision on the stellar parameters to
degrade via degeneracies between various stellar parameters, the PIE technique
can tolerate this. If additional stellar parameters prove degenerate with the
planet parameters, then it may become more difficult to separate the planetary
and stellar spectra, and uncertainty may propagate into the planetary
inference. Similarly, if stellar models fail to fit the stellar component of
the combined light spectra at wavelengths where the planet spectrum is
recoverable with PIE (e.g., due to missing stellar opacities or contributions
from photospheric heterogeneity or variability), then this is likely to bias
the retrieved planet parameters. Thus, the accuracy of stellar spectral models
at NIR and MIR wavelengths is critical to the success of PIE, particularly for
small terrestrial exoplanets. We discuss avenues for future progress on these
issues in §7.

##  4 Target Sample Demographics

While PCb is one of the most promising potentially rocky planets in the
habitable zone of a nearby star, Figure 1 demonstrates that there are a large
number of high-quality targets discovered around nearby stars by RV surveys
that a PIE survey mission would be able to characterize. In order to determine
the planetary demographics of a potential MIRECLE mission yield, we utilized
the Exo.MAST catalog (Mullally et al., 2019) to construct an initial target
list based on the results from §3 and realistic assumptions about the mission
lifetime.

We first calculated the exposure time for every planet known around a star
within 20 pc, based on scaling the nominal observing time needed to
characterize PCb for different aperture sizes (100 hours for 2- and 1-m
apertures, 400 hours for a 0.5-m aperture in order to push down to the 5 ppm
noise floor). We used 15 $\upmu$m as a reference wavelength for these
calculations, and scaled the planetary signal based on the planetary
equilibrium temperature and the stellar photon noise based on the star’s
effective temperature and K-band magnitude. We used the values in Exo.MAST
from the NExSci Exoplanet Archive; we note that the values for planet radius
for non-transiting planets in the archive are calculated using the mass-radius
relationship from Chen & Kipping (2017).

We then adjusted the SNR values to include the noise contribution from the
Solar System zodiacal background. Using iterative noise calculations from PSG,
we determined that a 2-m telescope is background-limited for K $>8.8$, while
the background-limited regime is K $>7.25$ for a 1-m and K $>5.7$ for a 0.5-m.
For potential targets dimmer than the background-limited magnitude, we scaled
the SNR based on a background-limited noise assumption rather than a photon-
limited assumption.

We also identified all of the multi-planet systems where multiple planets
could be expected to produce similar thermal fluxes at 15 $\upmu$m and removed
them from the target sample. Since the PIE technique does not remove the
signal from additional astrophysical sources in the scene, several planets
with similar flux levels could lead to confusion and difficulty in retrieving
the atmospheric characteristics of a single planet. Factors such as the
orbital period could be used to disentangle the signals, but for this study we
removed planetary systems with multiple planets where the difference in
expected thermal flux between the planets at 15 $\upmu$m is expected to be
less than a factor of 10. The one notable exception to this removal is Proxima
Cen, where a third planet candidate interior to PCb was recently announced
(see §3); however, since all of these calculations were performed prior to the
announcement, and the candidate has not yet been confirmed, we kept PCb in our
target list.

We then performed cuts in the potential target list by defining a mission goal
of examining the transition in planetary properties from rocky planets
($M_{p}<6M_{E}$) to Neptune-like planets ($M_{p}<20M_{E}$), and planets with
potential surface water conditions ($T_{p}<400K$) versus warmer planets
($400K<T_{p}<700K$). This regime is also similar to the inner Solar System
conditions, and also where JWST will be more limited due to the 13 $\upmu$m
wavelength cut-off and the limitations for longer-duration phase curves.

Finally, we defined two separate assumptions for a primary survey strategy:

  * •

A time-integrated thermal emission reconnaissance survey, where the time-
average thermal emission spectrum for a planet would be measured based on
expectations for SNR calculated from the stellar and planetary parameters

  * •

A four-quadrant hemisphere mapping survey, where the minimum observing time is
equivalent to the orbital period, and the target SNR needs to be achieved in
1/4 of the total time on-source so variations in phase-dependent emission
could be detected

In both cases we limit the total observing time to a maximum of 18 months by
varying the maximum exposure time, in order to achieve a prime mission period
of 2 years with a 75% duty cycle. We address the results of both of these
reference mission simulations below.

###  4.1 Yields From A Time-Integrated Thermal Emission Survey

In this scenario, we calculate the total observing time for each target that
would be needed to detect an emission spectrum by binning up all the
observations, assuming an atmospheric temperature equivalent to the planetary
equilibrium temperature.

Our results are summarized in Figure 9, and the full lists of potential
targets for each mission scenario are listed in the Appendix. We find that
with 18 months of exposure time, a 2-m telescope could obtain spectra for 37
planets, a 1-m telescope could observe 36 planets, and a 0.5-m telescope could
examine 20 planets. The planet temperatures range from 250K to 690K, and
inclination-dependent planet masses range from 1.27 ME to 20 ME for all
mission sizes; the main difference is the total number of planets
characterized and the exposure time required for each planet. The 2-m and 1-m
telescope sizes could gather spectra for almost every planet in less than 600
hours, while the 0.5-m telescope would require longer exposure times.

We also conclude that the 2-meter telescope is essentially target-limited in
terms of time-integrated thermal emission measurements; even with an exposure
time that is 1/4 of the original exposure time (essentially achieving the same
sensitivity as a 1-m telescope), the total number of observable planets only
rises by 2; all other known targets require significantly long exposure times
due to stellar radii or distance. However, if we accept this penalty in SNR,
the total required observing time for integrated emission measurements of 39
planets would be only 8 months instead of 18.

Figure 9: Distribution of planet equilibrium temperatures, minimum masses,
K-band magnitudes of the host stars, and total exposure times for a survey of
time-integrated emission measurements. The orange bars denote potentially
rocky planets ($M_{p}<6M_{E}$). Top: 2-meter aperture, Middle: 1-m, Bottom:
0.5-m.

###  4.2 Yields From A Thermal Phase Curve Survey

In this scenario, we calculate the total observing time for each target that
would be needed to achieve a four-quadrant phase-resolved measurement -
essentially obtaining integrated spectra for the day-side, night-side and two
transitional hemispheres, assuming an atmospheric temperature equivalent to
the planetary equilibrium temperature.

Our results are summarized in Figure 10. In total, we determined that phase
curves for 24 planets could be measured to the same precision as PCb in 18
months with a 2-meter telescope; this number drops to 20 planets for a 1-m
telescope and 10 planets for a 0.5-m telescope. There is a similar
distribution of planet properties, but the exposure time per planet is
naturally much longer. In particular, for the 0.5-m telescope, only 3 Neptune-
class planets can be observed with exposure times of less than 25 days, while
the 1-m and 2-m telescopes have 3-4 terrestrial planets that could be measured
with total exposure times less than 25 days.

We also examined how the numbers change if the required exposure time for the
2-meter aperture is decreased by 4$\times$, to achieve the same precision as a
1-m aperture (Figure 11). We find that for phase curves, the numbers increase
significantly; the 18-month total exposure time limit was the limiting factor,
and now more planets can be observed. In this scenario, we could observe phase
curves for 33 planets in 18 months, and most of them would have total exposure
times less than 30 days.

As stated above, these yield numbers are only a rough estimate of the actual
potential mission yield. In particular, we excluded targets with more than one
planet in the system with a similar thermal flux signal; in principle, this
requirement could be relaxed by utilizing sophisticated fitting routines to
determine the contribution from each planet. However, we also used a estimate
for the zodiacal dust contribution based on the value for PCb, which is at a
high ecliptic latitude; this will increase somewhat for low ecliptic
latitudes, though we can design the observing schedule to minimize the
contribution in the line of sight by pointing directly away from the Sun.
Additional work on including individual target properties is necessary to
determine an exact target list and further improve science yield estimates.

Figure 10: Distribution of planet equilibrium temperatures, minimum masses,
K-band magnitudes of the host stars, and total exposure times for a survey of
phase curve measurements. The orange bars denote potentially rocky planets
($M_{p}<6M_{E}$). Top: 2-meter aperture, middle: 1-m, bottom: 0.5-m Figure 11:
Same as the top of Figure 10 but with a reference exposure time of 25 hours
instead of 100 hours, matching the S/N per target of a 1-m telescope. The
number of planets observed increases significantly, demonstrating that the
18-month total exposure time limit is the limited factor in this scenario.

##  5 Technology Requirements and Readiness

As we demonstrate above, the practical limit on the measurement precision
achievable with the PIE technique for bright nearby stars is dependent on the
total simultaneous wavelength coverage, the contribution from astrophysical
and instrument noise sources at long wavelengths, and the absolute noise floor
achievable after integrating over the full exposure time. For a specific
wavelength and noise performance, the overall mission science yield is then
dependent primarily on the aperture size and overall throughput, since the
total collecting area also affects the amount of astrophysical background and
therefore the background-limiting target magnitude. With these factors in
mind, we now address the readiness of the telescope and instrument
technologies best positioned to achieve the MIRECLE performance requirements.

###  5.1 Telescope

The overall MIRECLE observatory would require a cooled telescope and optics,
in order to limit the thermal background in the MIR. However, since the
telescope serves only as a point-source light bucket with no need to image the
unresolved star or surrounding FOV and is limited to IR wavelengths,
relatively relaxed requirements for the primary mirror performance are
acceptable. The primary driving requirements on the observatory would be a
relatively cold primary mirror and optics ($T_{obs}\leq 35$K)

To meet the observatory temperature requirement, a combination of radiative
and mechanical cooling could be employed, similar to the Spitzer and JWST
architectures. MIRECLE would most likely need to operate in either an Earth-
trailing orbit like Spitzer, an orbit at the Sun-Earth L2 similar to JWST, or
some other orbital configuration that maximizes time away from the Earth’s
thermal radiation. Using a telescope barrel and sunshields, Spitzer’s inner
sunshield surface was able to reach 28K (Van Dyk et al., 2021); assuming the
proper orbit and pointing strategy, optimized radiative cooling designs could
be expected to achieve $30-35$K as an equilibrium temperature (i.e.
equilibrium between energy radiated versus parasitic heating due to the
spacecraft and stray radiation from either the Sun, Earth, or Moon).

###  5.2 Instrument

The MIRECLE instrument would be a spectrometer using fixed dispersive elements
(prism, grating and/or grism) to capture the full wavelength range (1 - 18
$\upmu$m maximum, 2.5 - 16.7 $\upmu$m minimum) simultaneously, and a focal-
plane array and electronics that can achieve a flux measurement
stability/repeatability of $\leq 5$ ppm over 100 - 600 hours after post-
processing to remove known systematics. The wavelength and flux measurement
stability requirements on the detector array would be the most challenging
aspect, and will most likely only be possible through a combination of a
stable and well-characterized detector array and electronics, and a real-time
calibration system that continually provides a stable illumination to re-
calibrate the detector gain and offset over the length of the observation and
allow for highly effective removal of systematic trends.

These instrument and detector characteristics can potentially be met using
existing technologies. Roellig et al. (2020) examined the readiness and
development paths of various detector technologies for a similar science case
for the Origins Space Telescope, focusing on three technology options: Si:As
impurity band conduction (IBC) arrays, HgCdTe arrays, and transition edge
superconductor (TES) bolometer arrays. A laboratory experiment that
incorporates the types of instrument control and calibration features
described above has been built and is currently being tested at NASA/Goddard
Space Flight Center (Staguhn et al., 2019). In Sections 5.2.1 \- 5.2.3 we
discuss potential detector technologies, their current demonstrated
performance and availability, and the obstacles that need to be addressed to
meet MIRECLE requirements, and we examine the design considerations for a
continuous calibration system in Section 5.2.4.

####  5.2.1 Impurity Band Conduction Detectors

Si:As impurity band conduction (IBC) detectors have served as a core detector
technology for a number of space-based MIR instruments. In particular, the
Spitzer IRAC instrument utilized Si:As detectors to achieve ground-breaking
space-based NIR and MIR photometric exoplanet measurements, and the JWST/MIRI
instrument uses similar arrays. The IRAC detectors achieved excellent
sensitivity and stability of $\sim$35 ppm (e.g. Tamburo et al., 2018), and the
MIRI detectors are expected to achieve similar or moderately improved
stability (Bright et al., 2016). Upcoming transit and phase curve observations
with JWST/MIRI will push the limits of the noise performance, and on-orbit
calibration and post-processing are expected to measure and mitigate the
instrument instabilities to some level and reveal what can be corrected in the
presence of drifts in the instrument and in the astrophysical sources (Greene
et al., 2016).

However, limiting factors in stability for IBC detectors are currently not
sufficiently understood to determine whether they could achieve 5 ppm over
long-duration measurements. The intrinsic stability of existing Si:As detector
systems may be driven by fundamental detector materials properties, the
current cryogenic detector readout circuitry (which is not optimized for
operation at cryogenic temperatures), or other instabilities in the system.
Therefore, a detailed study of instabilities in MIR detectors would be needed
to determine where technology investments will be most effective.

The main obstacle for the future use of IBC detectors will be the commercial
availability of these detectors. At this time, commercial suppliers for these
detectors that previously fabricated the arrays for such missions as Spitzer,
WISE, and JWST (Raytheon and DRS) have discontinued fabrication efforts in
this wavelength range. This is also a result of lack of need of these
technologies for applications for the Department of Defense. While large
contracts could be used to re-start the development and production of these
detectors, this would be associated with significant cost.

####  5.2.2 HgCdTe Detectors

HgCdTe detector array technology has matured dramatically over the years, and
high-performance devices with a cutoff wavelength of 5 $\upmu$m have been used
for JWST and WISE, while the Roman Space Telescope will be using 2.5 $\upmu$m
cutoff HgCdTe devices. With large-format arrays, high well-depths, and
relatively high operating temperatures, these devices have become the
workhorse of space-based NIR astronomy. However, the performance of longer
cutoff devices had been limited by larger tunneling dark currents, and the
softer material of these arrays (due to increased mercury content) can lead to
an increased likelihood of forming defects/dislocations that contribute to
trap-assisted dark currents (Carmody et al., 2003).

Longer-wavelength HgCdTe arrays are now being developed by University of
Rochester (UR) infrared detector group and Teledyne Imaging Systems (TIS) in
support of the NEO Surveyor mission concept, with long-wavelength cut-offs of
10.5 (McMurtry et al., 2016), 13 (Cabrera et al., 2019), and now 15 $\upmu$m
(Cabrera et al., 2020) now being demonstrated. These devices employed a
proprietary design to mitigate quantum tunneling dark currents, and yielded
three devices with excellent read noise ($\sim 30e^{-}$), QE $\geq 80\%$ in
the 6 - 12 $\upmu$m wavelength range (without anti-reflective coating), and
reduced expected tunneling dark current behavior. One of those three devices
tested by Cabrera et al. (2020) has a cutoff wavelength of 16.7 $\upmu$m at a
temperature of 30 K and is bonded to a HAWAII-1RG multiplexer (MUX). The
characterization of this device showed that the performance was limited by
tunneling dark currents when a modest amount of reverse bias is applied to
increase the pixel well depth. These results are very encouraging since the
tunneling dark currents showed an improvement in the TIS proprietary design of
this device by several orders of magnitude, and motivated our long-wavelength
sensitivity analysis in §3.

Additionally, this was the first attempt in producing these devices; with
further enhancement to the device design, the tunneling currents may be
conceivably mitigated further. Another option for avoiding tunneling dark
currents for future devices would be to bond these devices to a MUX based on a
capacitive trans-impedance amplifier (CTIA) structure that can provide large
well depths while operating at lower biases where the contribution from
tunneling currents are minimal. The HAWAII MUX was chosen by UR for the 15
$\upmu$m devices due to their lower power dissipation relative to CTIA
structure MUXes. Temperature-controlled operation at 25 K would also minimize
the dark current in the current devices, while maintaining the highest level
of operability. Space qualified readout of these detectors will be straight-
forward, since the electronics developed for JWST would be sufficient and
provide a high-TRL entry level point.

####  5.2.3 Transition Edge Sensors (TES)

TES detectors have been measured to produce white, flat, and featureless noise
spectra down to $\sim$10 mHz or below. Compared with semiconducting bolometers
or kinetic inductance detectors (KIDs), TES have demonstrated superior
stability on timescales of several minutes. Even when 1/f noise is detectable,
it is attributed to the SQUID MUX readout rather than the TES device itself,
and therefore can be removed as a common mode feature (since each SQUID MUX
reads out several detectors). Staguhn et al. (2019) examined the stability of
TES arrays in the laboratory, showing that the power spectrum of their
detectors shows a signal between 1 Hz and several tens of seconds that is
almost flat, while at times greater than $\sim$ 1 minute there is a slight
upturn in the noise. However, the increase in noise is moderate, in particular
significantly shallower than 1/f, i.e. the noise increase vs time is more
modest than it would be in the 1/f case.

The physics of TES detectors themselves is well understood, so the performance
of those devices can be reliably designed. TESs are also flexible in terms of
readout technologies: The devices can directly be read out with relatively low
bandwidth (a few MHz) time domain digital warm electronics. Achievable
multiplexing factors for time domain readout systems would not be an issue,
since the number of TES pixels required for a MIR spectrometer as described
here is modest ($<1000$). Alternatively, microwave multiplexers have been
developed at NIST Boulder, which could be used for GHZ frequency domain
readout systems that are used for other superconducting detector technologies
such as MKIDs.

The most significant instrument design challenge for TES and KID detectors is
the required sub-Kelvin operating temperatures necessary to reach optimal
sensitivity. For the expected temperatures of $\sim$100 mK, inclusion of
adiabatic demagnetization refrigeration (ADR) along with the required
cryogenic cooling to reach the ADR operating temperature of approximately 4K
is necessary. Several mission concepts, most notably the Hitomi mission
(Shirron et al., 2018), have developed this technology to high TRL, but the
requirements on the instrument design are substantial.

####  5.2.4 Continuous Calibration

For dimmer targets or phase-curve measurements requiring a stability of many
hours to reach the required shot-noise uncertainty, the need for continuous
calibration of the detector response becomes essential. Staguhn et al. (2019)
describes such a calibration system that uses a black body source as a
reference signal that is simultaneously observed with the exoplanet by the
detectors in the spectrometer. A similar calibrator has been used on the
JWST/MIRI instrument for instrument testing (Wright et al., 2015), but is not
designed for use in flight.

By turning the tungsten filament on and off (or otherwise modulating the
signal) the gain of the detector can effectively be measured at each on/off
transition; modulating on the order of once per minute is sufficient to
monitor the gain. There is no penalty on the achieved sensitivity of the
measurement, since the black body signal power is chosen to be sufficiently
small as not to increase the photon noise budget materially due to the
significant photon noise from the bright stellar hosts. Implementation of this
calibration scheme will be an important step in providing the required long
term stability of the spectrometer used in MIRECLE.

##  6 Mission-Level Science Impact

We have demonstrated that with the appropriate simultaneous wavelength
coverage and measurement precision, a modestly-sized space telescope could
detect and analyze the atmospheres of non-transiting planets around the
nearest M-stars, including Proxima Cen b. We have also reviewed the
technological readiness of the instrumentation needed to achieve the required
performance, identifying several potential detector technologies that may be
able to meet requirements. Below we discuss the overall potential science
returns from the MIRECLE survey science described above, as well as additional
science beyond the PIE survey of planets with $M~{}\text{sin}~{}i<20$ that
could be accomplished with MIRECLE. Finally, we address the question of
complementarity between the capabilities of MIRECLE and those of upcoming
exoplanet-related space-based observatories.

###  6.1 Primary Survey Science Yield

One of the primary science questions that MIRECLE would answer is the
distribution of a rocky planets having tenuous, clear, or cloudy atmospheres.
Planets orbiting in the habitable zones (HZs) of M dwarf stars have relatively
short orbital periods (5 – 40 days) and receive higher levels of UV flux than
planets in the HZs of G stars. Extreme UV flux can enhance atmospheric escape
to the point of yielding only a tenuous atmosphere. M dwarfs tend to be most
active shortly after formation ($<$ 1 Gyr), thus potentially impacting planets
that formed in-situ. Planets that have migrated into the HZ after 1 Gyr are
more likely to retain appreciable atmospheres. Additionally, the secondary
atmospheres of impacted (e.g., in-situ formation) planets could be replenished
from infalling cometary material. Understanding what fraction of temperate
terrestrial planets with short orbital periods have substantial atmospheres
can provide information on the formation and migration of these systems and
place our Earth into a broader context.

Similarly, a PIE survey of planets from 1.3 - 20 Earth masses would directly
explore the super-Earth/sub-Neptune boundary. At orbital periods less than 50
days, planets below 1.6 Earth radii are thought to be predominantly rocky
(Rogers, 2015), but it’s not known if they formed that size or were once
larger and subsequently lost their primordial atmospheres. The Kepler
observatory has shown us that there is a gap in the occurrence rate of planets
between 1.5 and 2.0 Earth radii (e.g., Fulton et al., 2017; Petigura et al.,
2022). This paucity of planets supports the idea that a sub-population of
close-in sub-Neptune planets undergo a relatively quick process of atmospheric
mass loss that leaves them with a rocky core measuring up to 1.6 Earth radii
and potentially a thin, high-mean-molecular-weight atmosphere (i.e., super
Earths). A large characterization survey of super-Earth and sub-Neptune size
planets would confirm theoretical predictions of the formation and evolution
of super-Earths and sub-Neptunes.

###  6.2 Additional Potential MIRECLE Science

Beyond studies of rocky and Neptune-like worlds using PIE, MIRECLE would also
have the capability to bridge the gap between the Hot Jupiters being studied
with current and near-term missions and the giant planets in our own Solar
System. For giant planets with hydrogen-dominated atmospheres ($\gtrsim 10$
Earth masses), missions such as JWST and ARIEL will mostly target warm planets
($>600$ K) in thermal emission. This will leave a gap in our understanding
between these objects and the solar system giant planets ($<200$ K). Mid-IR
spectroscopic phase curves of Jupiter and Saturn exoplanetary analogs would
enable transformational science in the chemistry and structure of temperate
giant planets around K and M. In these cooler atmospheres, the abundances of
CH4 and NH3 probe metallicity, non-equilibrium chemistry, and the strength of
vertical mixing (Zahnle & Marley, 2014). MIRECLE could probe the rich
photochemistry expected for these atmospheres, via production of HCN, C2H2,
and C2H4 from methane, as is seen in Jupiter beyond 5 $\upmu$m.

MIRECLE could also advance our understanding of the physics and chemistry of
clouds and hazes, which are currently a major source of uncertainty in models
of exoplanet atmospheres. Since most clouds appear only as Rayleigh or gray
scatterers in the optical and near-IR, we have poor constraints on the
composition of clouds that are inferred in hot Jupiter atmospheres. A number
of cloud species expected to impact the spectra of these planets have known
features in the mid-IR (e.g., Wakeford & Sing, 2015). Examples include: Al2O3
(12 $\upmu$m), CaTiO3 (13 $\upmu$m, 22 $\upmu$m), and MgXSiOY (8 – 22
$\upmu$m). The population of giant exoplanets that could be probed in thermal
emission (down to $\sim$250 K) will be cool enough to, for the first time,
serve as a bridge between the extrasolar planet population and our own solar
system, and enable the unique identification of aerosols that impact the
transmission spectra of hot exoplanets as well.

MIRECLE would also enable high-precision MIR time series spectroscopy of brown
dwarf atmospheres. Brown dwarfs are self-luminous bodies that form like stars,
but are more similar in temperature to warm and hot Jupiters. As a result,
most brown dwarfs have atmospheres that are near-solar in composition;
however, there are numerous examples of brown dwarfs with metal-rich and
metal-poor atmospheres (e.g., inner galactic disk and halo galaxies,
respectively). Unlike hot Jupiters, brown dwarfs provide an isolated
laboratory to investigate condensate cloud formation, pressure-temperature
profiles, chemistry, non-equilibrium processes, and three-dimensional time-
dependent weather. For example, long-baseline, multi-epoch observations with
MIRECLE would reveal the source of previously-observed variability (e.g.,
short-lived clouds vs. long-lived features at different latitudes).

###  6.3 MIRECLE Complementarity with Existing and Planned MIR Space Missions

There are already two existing or approved space observatories with NIR/MIR
capabilities that are expected to dramatically expand the characterization of
transiting exoplanets spanning a wide range of stellar and planetary
properties, and we consider their complementarity to MIRECLE. The recently
launched JWST is expected to be a transformative tool for transiting exoplanet
characterization due to the large collecting area (equivalent to a 5.7-meter
circular aperture) and a combined wavelength coverage from 0.6 to 28 $\upmu$m
across all the instruments. The Atmospheric Remote-sensing Infrared Exoplanet
Large-survey (ARIEL) mission, selected by ESA for launch in 2028, will focus
on systematically characterizing a sample of transiting exoplanets using
simultaneous measurements of visible/NIR photometry (0.5 - 1.1 $\upmu$m) and
low-resolution NIR/MIR spectroscopy (1.1 - 7.8 $\upmu$m).

Both missions will significantly advance our understanding of the diversity of
exoplanet atmospheres through transmission, eclipse, and phase curve
measurements of transiting planets (Greene et al., 2016). However, they will
be hampered in their ability to study the non-transiting temperate terrestrial
planet population around the nearest stars – primarily because neither
telescope will have the simultaneous wavelength coverage across the NIR and
MIR necessary to effectively perform PIE measurements for small and cool
planets.

JWST includes multiple NIR instruments, and the MIRI instrument includes a
low-resolution spectroscopy mode (LRS) that extends from 5 to $\sim$13
$\upmu$m with a spectral resolving power of $R=100$. MIRI also includes a mid-
resolution spectroscopy mode (MRS) which has four different bands spanning 5 -
28 $\upmu$m and several resolving power settings, but this mode uses an image
slicer design that makes high-precision time series measurements extremely
challenging. LY21 demonstrated that combining observations with the NIR
instruments and MIRI-LRS would allow for emission spectroscopy measurements of
hot Jupiters with the PIE technique. However, the NIR and MIR instruments
cannot be used to observe the same FOV simultaneously, requiring the stitching
of different data sets together to fully constrain the stellar and planetary
emission. While the absolute flux uncertainty expected for JWST measurements
is not especially detrimental (as shown by LY21), the asynchronous nature of
the measurements would introduce a number of challenges for extracting small-
amplitude signals, and we do not examine this option further. Alternatively,
using only the MIRI-LRS instrument alone cannot achieve sufficient constraints
on the MIR flux of PCb due to the inability to constrain the stellar
contribution to the measured MIR flux (as we show in Figure 7).

Similar restrictions in simultaneous wavelength coverage limit the
capabilities for PIE measurements with the ARIEL mission. ARIEL includes a
NIR/MIR spectrograph (AIRS) with R=30–200 as well as simultaneous photometry
at shorter wavelengths. However, with only a few photometric measurements at
short wavelengths and a spectrograph that only extends out to 8 $\upmu$m,
ARIEL would be similarly unable to measure thermal emission for non-transiting
temperate planets.

##  7 Future Work

Thus far, the PIE technique has shown considerable promise when it comes to
characterizing the atmospheres of rocky worlds orbiting nearby M-dwarf stars,
such as Proxima Cen b. However, untangling the diverse array of complicating
astrophysical and instrumental factors will be critical in ensuring that
robust planetary information can be inferred using the PIE technique on non-
transiting systems.

Beyond successfully implementing the technique on broadband spectroscopic data
of large and hot planets with JWST observations (e.g., HAT-P-26b, WASP-17b,
etc.), additional model validation work is also needed to evaluate and improve
the robustness of our stellar modeling strategies. The impact of inaccurate
spectral opacities and stellar variability on the morphology and temporal
variation in the stellar SED is a primary issue that must be addressed, since
the stellar flux at MIR wavelengths must be removed accurately without biasing
planetary parameters. Multi-wavelength observations spanning X-ray to visible
wavelengths have shown the ubiquity of stellar variability and flaring in
M-stars (e.g. MacGregor et al., 2018), and the impact of stellar variability
on exoplanet transmission spectroscopy has been well documented (Rackham et
al., 2018; Barclay et al., 2021).

However, due to a lack of spaceborne MIR spectroscopic capabilities since the
end of the Cold Spitzer mission, no broadband MIR spectra of M-stars that are
both high-SNR and free of telluric absorption exist, making the assessment of
opacity linelists and the impact of stellar flares impossible. Fortunately,
upcoming observations of M-stars with JWST will help significantly in
improving our confidence in stellar models in both the spectral and temporal
dimensions. Data from approved exoplanet observations, either for systems with
no hot planets or for periods where a planet is eclipsed by the star, can be
used for initial model validation and variability studies, and new moderate-
resolution observations with the MRS mode of MIRI (5 – 28 $\upmu$m) could
provide high-quality ground truth for validating and improving stellar line
lists. Multiple stellar model grids are now available for M-star stellar
temperatures, and model grid intercomparison can be used to determine
differences and potential areas of future model improvement.

Similarly, the contribution from additional known or even unknown planets in
multi-planet systems needs to be addressed. In theory, RV measurements should
detect and constrain the orbital periods and eccentricities of any planets
sufficiently large and close to the parent star to produce an appreciable
thermal signal; however, as demonstrated by the recent tentative detection of
Proxima Cen d, small planets are hard to detect through RV measurements but
can produce a large thermal signal if they are hot enough. While multiple
planetary signals may provide an opportunity for a “joint” constraint on the
combined thermal flux and atmospheric absorption, the goal would be to gain
constraints on each planet separately by fitting for the variation in thermal
flux over the orbital period of each planet. Uninterrupted simultaneous
measurements of the emission from both the star and planet over days and even
weeks should provide sufficient leverage to differentiate stellar, planetary,
and instrumental flux variations - but this would clearly be impacted by
uncertainties in the ephemerides for each planet. More algorithmic
development, as well as demonstrations with existing telescopes using well-
characterized planetary systems, is necessary to validate these data
processing strategies.

There are several other factors that may lead to large uncertainties in the
the final constraints that can be obtained for a particular planet. The
unknown orbital inclination of non-transiting planets means that phase-
dependent variations in thermal flux from a planet cannot be directly
translated into longitudinal temperature constraints, as is done for
transiting planets (e.g. Knutson et al., 2007). Orbital inclinations for the
nearest M-star systems may be measured in the future through direct imaging or
astrometry, but there may also be additional ways to constrain inclination of
unresolved systems. The contribution from unknown exozodical dust could also
contribute flux at MIR wavelengths, and if the temperature of the dust is
similar to that of the planet, it would produce a degeneracy that would be
hard to break. However, dynamical modeling of the dust in systems with known
planets could put constraints on the potential dust distribution and therefore
the likelihood of signal confusion.

Answering these and other related questions will be the focus of future work
as they require increasingly more sophisticated stellar and planetary models.
By leveraging the broad and interdisciplinary expertise of the astrophysics,
astrobiology, and instrumentation communities, we can continue advancing the
PIE technique as a means to study the vast population of nearby, non-
transiting exoplanets and their atmospheres.

##  8 Conclusion

In this paper, we have examined the potential science yield for a stand-alone
mission (MIRECLE) to characterize the population of cool, non-transiting
terrestrial and sub-Neptune planets around the nearest M-dwarf stars using
simultaneous NIR/MIR spectroscopy and the Planetary Infrared Excess (PIE)
technique to extract the planet’s emission spectrum (Stevenson, 2020; Lustig-
Yaeger et al., 2021). We first simulated observations of the nearest planet to
Earth, Proxima Cen b, under the assumption that the planet has an Earth-like
atmospheric composition and structure. We explored the impact of the aperture
size, simultaneous wavelength range, and absolute noise floor on the ability
to constrain the composition and temperature of the atmosphere. We then used
the reference exposure times derived for Prox Cen b and the list of all nearby
planets from the Exo.MAST database to calculate a potential planet
characterization yield under two separate scenarios: a survey of planets using
a time-integrated emission spectrum to constrain the temperature, radius and
bulk composition of the planets, and a deeper exploration of the atmosphere
and/or surface properties of nearby temperate rocky and sub-Neptune planets
using thermal phase curves.

Our results above clearly indicate that, under standard assumptions for
astrophysical and instrument noise contributions, a 2-year mission with a
2-meter aperture and simultaneous wavelength coverage from $1-18\;\mu$m can
effectively minimize the planet temperature/radius degeneracy and detect
multiple atmospheric absorption features for Proxima Cen b and more than 36
other planets with $M_{p}<20\;M_{E}$ and $T_{eq}<700$K, including 13
potentially rocky planets with $M_{p}<6\;M_{E}$ and $T_{eq}<600$K – as long as
a noise floor of 5 ppm or better and total integration times of at least 25
days can be achieved. If phase curves are prioritized instead, 28 planets
could be examined, including 9 potentially rocky planets. Diminishing the
aperture size to 0.5 meters decreases the number of available targets and the
exposure times, but still allows for thermal emission spectroscopy of 20
planets.

With the publication of the Astro2020 Decadal Survey Report (National
Academies of Sciences, Engineering, and Medicine, 2021), initial preparation
is beginning for both the Explorer-class mission proposal opportunities as
well as the new Probe-class mission opportunities – one of which will be a
Far-IR Probe that could incorporate the MIRECLE instrumentation and science
cases. Now that JWST is beginning its science operations, it is time to look
towards the next generation of exoplanet characterization missions. We predict
that the MIRECLE science case and instrumentation requirements needed for the
study of non-transiting planets using the PIE technique will be a key part of
these future mission portfolios.

This material is based in part upon work performed as part of the CHAMPs
(Consortium on Habitability and Atmospheres of M-dwarf Planets) team,
supported by the National Aeronautics and Space Administration (NASA) under
Grant No. 80NSSC21K0905 issued through the Interdisciplinary Consortia for
Astrobiology Research (ICAR) program. Funding was also provided through the
NASA Goddard SEEC (Sellers Exoplanet Environments Collaboration) team, which
is funded in part by the NASA Planetary Science Division’s Internal Scientist
Funding Model, and by NASA ROSES grants 17-APRA17-0126 and 18-SAT18-0024. We
also thank T. Barclay, D. Fixsen, D. Koll, E. Sharp, and G. Villanueva for
valuable conversations and suggestions on the analysis and the manuscript.

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##  Appendix A Target Lists for Integrated Emission Spectroscopy and Phase
Curve Spectroscopy

Each of the target lists are organized based on increasing aperture - all the
targets that are amenable to measurements with a 0.5-meter aperture would also
be included in the targets for a 1-meter and 2-meter apertures. The horizontal
lines indicate the breakpoints between 0.5, 1, and 2 meters.

Table 3: Stellar and planetary parameters for targets amenable to integrated emission spectroscopy with the three different aperture sizes (0.5, 1.0, and 2.0 meters).  Name | Dist | Kmag | Teff | $M~{}\text{sin}~{}i$ | Teq | Orb. Period | ESM-15$\upmu$m
---|---|---|---|---|---|---|---
| (pc) |  | (K) | (ME) | (K) | (days) |
Proxima Cen b | 1.3 | 4.4 | 3050 | 1.3 | 250 | 11.2 | 46.5
GJ 96 b | 11.9 | 5.6 | 3785 | 19.7 | 258 | 73.9 | 23.8
GJ 687 b | 4.6 | 4.5 | 3413 | 17.2 | 264 | 38.1 | 79.1
Ross 128 b | 3.4 | 5.7 | 3192 | 1.4 | 309 | 9.9 | 22.8
GJ 251 b | 5.6 | 5.3 | 3451 | 4.0 | 349 | 14.2 | 27.5
Gl 686 b | 8.2 | 5.6 | 3656 | 6.6 | 383 | 15.5 | 37.5
GJ 411 b | 5.7 | 3.5 | 3601 | 2.7 | 386 | 12.9 | 43.3
HD 102365 b | 9.3 | 3.5 | 5630 | 15.9 | 390 | 122.1 | 36.9
GJ 338 B b | 6.3 | 4.1 | 4005 | 10.3 | 392 | 24.4 | 63.2
HD 211970 b | 13.1 | 5.7 | 4127 | 13.0 | 397 | 25.2 | 43.5
GJ 15 A b | 3.6 | 4.0 | 3607 | 3.0 | 400 | 11.4 | 45.5
GJ 720 A b | 15.6 | 6.1 | 3837 | 13.6 | 401 | 19.5 | 44.2
GJ 1265 b | 10.2 | 8.1 | 3236 | 7.4 | 422 | 3.7 | 95.3
GJ 480 b | 14.2 | 6.7 | 3381 | 13.2 | 424 | 9.6 | 61.3
Gl 49 b | 9.8 | 5.4 | 3805 | 5.6 | 436 | 13.9 | 30.9
CD Cet b | 8.6 | 7.8 | 3130 | 4.0 | 458 | 2.3 | 82.1
GJ 536 b | 10.4 | 5.7 | 3685 | 5.4 | 487 | 8.7 | 33.2
GJ 674 b | 4.6 | 4.9 | 3600 | 11.1 | 527 | 4.7 | 278.3
HD 177565 b | 16.9 | 4.5 | 5627 | 15.1 | 539 | 44.5 | 42.1
HD 190007 b | 12.7 | 4.8 | 4610 | 16.5 | 651 | 11.7 | 108.6
HD 180617 b | 5.9 | 4.7 | 3534 | 12.2 | 202 | 105.9 | 13.4
GJ 229 A c | 5.8 | 4.2 | 3913 | 7.3 | 220 | 122.0 | 11.9
GJ 3323 b | 5.4 | 6.7 | 3159 | 2.0 | 291 | 5.4 | 41.3
GJ 422 b | 12.7 | 7.0 | 3323 | 11.1 | 293 | 20.1 | 26.9
GJ 625 b | 6.5 | 5.8 | 3499 | 2.8 | 336 | 14.6 | 17.3
GJ 685 b | 14.3 | 6.1 | 3816 | 9.0 | 369 | 24.2 | 22.9
LSPM J2116+0234 b | 17.6 | 7.3 | 3475 | 13.3 | 371 | 14.4 | 37.8
LTT 1445 A b | 6.9 | 6.5 | 3337 | 2.2 | 436 | 5.4 | 26.0
GJ 3082 b | 16.6 | 7.0 | 3910 | 8.2 | 460 | 11.9 | 29.7
HD 238090 b | 15.2 | 6.1 | 3933 | 6.9 | 469 | 13.7 | 26.8
GJ 393 b | 7.0 | 5.3 | 3579 | 1.7 | 487 | 7.0 | 15.5
GJ 1151 b | 8.0 | 7.6 | 3114 | 2.5 | 510 | 2.0 | 46.0
GJ 3779 b | 13.7 | 8.0 | 3324 | 8.0 | 526 | 3.0 | 77.0
GJ 1214 b | 14.6 | 8.8 | 3250 | 8.2 | 588 | 1.6 | 120.1
GJ 3942 b | 16.9 | 6.3 | 3867 | 7.1 | 591 | 6.9 | 34.2
HD 154088 b | 18.3 | 4.8 | 5374 | 6.6 | 690 | 18.6 | 23.5
HIP 38594 b | 17.8 | 6.2 | 4086 | 8.1 | 309 | 60.7 | 8.6

Table 4: Stellar and planetary parameters for targets amenable to spectroscopic phase curves with the three different aperture sizes (0.5, 1.0, and 2.0 meters).  Name | Dist | Kmag | Teff | $M~{}\text{sin}~{}i$ | Teq | Orb. Period | ESM-15$\upmu$m
---|---|---|---|---|---|---|---
| (pc) |  | (K) | (ME) | (K) | (days) |
Proxima Cen b | 1.3 | 4.4 | 3050 | 1.3 | 250 | 11.2 | 46.5
Gl 686 b | 8.2 | 5.6 | 3656 | 6.6 | 383 | 15.5 | 37.5
GJ 411 b | 5.7 | 3.5 | 3601 | 2.7 | 386 | 12.9 | 43.3
GJ 338 B b | 6.3 | 4.1 | 4005 | 10.3 | 392 | 24.4 | 63.2
HD 211970 b | 13.1 | 5.7 | 4127 | 13.0 | 397 | 25.2 | 43.5
GJ 15 A b | 3.6 | 4.0 | 3607 | 3.0 | 400 | 11.4 | 45.5
GJ 536 b | 10.4 | 5.7 | 3685 | 5.4 | 487 | 8.7 | 33.2
GJ 674 b | 4.6 | 4.9 | 3600 | 11.1 | 527 | 4.7 | 278.3
HD 177565 b | 16.9 | 4.5 | 5627 | 15.1 | 539 | 44.5 | 42.1
HD 190007 b | 12.7 | 4.8 | 4610 | 16.5 | 651 | 11.7 | 108.6
GJ 687 b | 4.6 | 4.5 | 3413 | 17.2 | 264 | 38.1 | 79.1
GJ 3323 b | 5.4 | 6.7 | 3159 | 2.0 | 291 | 5.4 | 41.3
GJ 251 b | 5.6 | 5.3 | 3451 | 4.0 | 349 | 14.2 | 27.5
GJ 720 A b | 15.6 | 6.1 | 3837 | 13.6 | 401 | 19.5 | 44.2
GJ 480 b | 14.2 | 6.7 | 3381 | 13.2 | 424 | 9.6 | 61.3
LTT 1445 A b | 6.9 | 6.5 | 3337 | 2.2 | 436 | 5.4 | 26.0
Gl 49 b | 9.8 | 5.4 | 3805 | 5.6 | 436 | 13.9 | 30.9
GJ 3082 b | 16.6 | 7.0 | 3910 | 8.2 | 460 | 11.9 | 29.7
HD 238090 b | 15.2 | 6.1 | 3933 | 6.9 | 469 | 13.7 | 26.8
GJ 3942 b | 16.9 | 6.3 | 3867 | 7.1 | 591 | 6.9 | 34.2
HD 154088 b | 18.3 | 4.8 | 5374 | 6.6 | 690 | 18.6 | 23.5
GJ 96 b | 11.9 | 5.6 | 3785 | 19.7 | 258 | 73.9 | 23.8
GJ 422 b | 12.7 | 7.0 | 3323 | 11.1 | 293 | 20.1 | 26.9
Ross 128 b | 3.4 | 5.7 | 3192 | 1.4 | 309 | 9.9 | 22.8
GJ 625 b | 6.5 | 5.8 | 3499 | 2.8 | 336 | 14.6 | 17.3
GJ 685 b | 14.3 | 6.1 | 3816 | 9.0 | 369 | 24.2 | 22.9
LSPM J2116+0234 b | 17.6 | 7.3 | 3475 | 13.3 | 371 | 14.4 | 37.8
GJ 1265 b | 10.2 | 8.1 | 3236 | 7.4 | 422 | 3.7 | 95.3
CD Cet b | 8.6 | 7.8 | 3130 | 4.0 | 458 | 2.3 | 82.1
GJ 393 b | 7.0 | 5.3 | 3579 | 1.7 | 487 | 7.0 | 15.5
GJ 1151 b | 8.0 | 7.6 | 3114 | 2.5 | 510 | 2.0 | 46.0
GJ 3779 b | 13.7 | 8.0 | 3324 | 8.0 | 526 | 3.0 | 77.0
GJ 1214 b | 14.6 | 8.8 | 3250 | 8.2 | 588 | 1.6 | 120.1