their atmospheres.

We also assessed the detectability of (anti-)biomarker molecules in habitable-
zone terrestrial planets with transmission spectroscopy. For this, planets
orbiting M-dwarfs are the most feasible candidates, with favorable transit
depths and short orbital periods. The most promising planetary system for this
is TRAPPIST-1, which is a 7-planet system around an M8V host star at 12.5 pc
distance from the solar system, with up to four of its planets in the present-
day habitable zone [141]. However, as reported in [90], CO is best detected in
the H-band in transmission of habitable zone planets, requiring $\sim$100
transits. $CO_{2}$ may be detectable in the bluest part of the K-band
($\sim$2.1 µm), but also here Currie et al [90] argue for H-band being a
better option.

We also studied whether $PH_{3}$ may be detectable in the K-band, assuming a
$CO_{2}$-dominated atmosphere. This is motivated by the claimed $PH_{3}$
detection in Venus, where it was interpreted as a potential biomarker [147].
For TRAPPIST-1b we found that $PH_{3}$ is only detectable (in 40 nights) when
increasing the $PH_{3}$ abundances by a hundredfold when compared to the value
of 10 ppb reported in Greaves et al [147], making this an unlikely scenario,
although according to [340] $PH_{3}$ could enter a runaway buildup and reach
such abundances.

Figure 18: A comparison of the spectral response of the Ca II K, H$\alpha$,
and Ca II 8542 Å lines to changes in solar activity, demonstrating the
sensitivity of the Ca II K line over the other chromospherically active lines.
First panel: An SDO/AIA [192] observation of the Sun at 2017-09-06T12:10:00 in
the 1700 Å continuum showing one of the largest solar flares of the last solar
cycle ($\approx 10^{32}$ erg). An enlarged view of the same image is shown on
the lower left side of this figure. Second-fourth panel: Flare spectrum in
blue, quiet Sun spectrum in orange, and a scaled flare spectrum with a 1% fill
factor in green for each of the three aforementioned lines. The line core of
the Ca II K line is reacting much more strongly to the flare than the line
cores of the H$\alpha$ line and the lines of the Ca infrared triplet.

###  7.5 Protoplanetary Disks

As discussed in Section 6, various science cases are of interest to the
protoplanetary disk community in the K-band, such as the characterization of
young stellar objects via emission lines from the inner disk and weak
photospheric features or measuring the magnetic field strengths of T Tauri
stars via Zeeman splitting (e.g., Johns-Krull 168, and references therein).
Some of the most transformative science cases, which the K-band uniquely
enables, concern the role of the angular momentum loss in protoplanetary disks
via molecular winds and the characterization of embedded protostars and their
accretion disks in different environments (see Sect. 6). These studies are
highly relevant in defining the timescales for accretion and disk dispersal
during the early evolution and, more in general, for planet formation, as
protoplanetary disks are the birthplaces of exoplanetary systems.

##  8 Exoplanet Science cases in the U-band

Currently, the ANDES baseline design extends to 4000 Å, but with the goal of
extending the spectral coverage to 3500 Å, covering the U-band. The U-band
strongly benefits the core exoplanet science case of characterizing
atmospheres and detecting biosignatures for habitable-zone exoplanets and
makes several additional exoplanet science cases possible to study.

The core exoplanet science case of studying habitable-zone exoplanets relies
on the different planetary and stellar rest frames, moving at different radial
velocities, to tell planetary and stellar absorption and emission signatures
apart (see for example [48, 39]). The atmospheres of hot Jupiters are
successfully studied using this technique. However, the difference between the
planetary and stellar rest frame velocity is much smaller for temperate
planets, pushing the planetary and stellar signatures in time-series of
spectra closer together, see Fig.1. If the surface of the host star could be
expected not to change during ANDES observations, this would be unproblematic.
However, especially the low-mass stars that ANDES will target for temperate-
planet observations display stellar activity features even at old ages, which
manifest themselves as changing spots and faculae as well as multitudes of
small and sometimes also larger flares [34, 376, 151, 281]. In fact, a recent
analysis of spectral lines in low-mass stars showed that most of those lines
show at least a minor response to changes in stellar activity [186]. For ANDES
this means that stellar activity changes can be expected to produce a non-
negligible signal in the stellar rest frame, which needs to be quantified and
separated from the planetary signal in the adjacent planetary rest frame.

The most sensitive tracers of stellar activity accessible to ANDES are the Ca
II H and K lines at 3933 and 3968 Å, i.e. in the ANDES U-band. We illustrate
this in Fig.18 by comparing the spectral response of the Ca II K, H$\alpha$,
and Ca II 8542 Å lines to a solar flare with an energy of $\approx 10^{32}$
erg as observed by the Swedish 1-m Solar Telescope [SST, 320] and described in
[283], with quiet Sun observations from [284]. The former is an average taken
over an area of approximately 2x2 arcseconds inside of the lower brightened
area marked in the first panel of the figure. Additionally, a scaled flare
response is generated using the NESSI code [282] where the same profile is
assumed to take up 1% of the solar area, in this case the Ca II K line is the
only line where a response is clearly visible. We note that in the stellar
context, where one would observe the spectrum of the full stellar disk, this
would correspond to a rather weak flare. Average observed flare energies of
cool stars tend to be an order of magnitude more energetic [e.g. 218, 281],
however the ratios between the three aforementioned lines are expected to stay
largely the same.

In the stellar context, several studies have shown that the sensitivity of Ca
II H&K to even small activity changes cannot be matched by other
chromospherically sensitive lines such as H$\alpha$, Ca IRT or the Na D lines
[232, 99, 129]. Additionally, it has been shown that these lines are uniquely
suitable for deriving the filling-factor and distribution of different types
of active regions [83]. Having strictly simultaneous access to CaII H&K data
with ANDES will strongly help isolate planetary absorption features and
benefit the core exoplanetary science case.

In addition, the U-band will enable additional exoplanet science cases:

Due to Rayleigh scattering, clear exoplanet atmospheres will produce an upward
slope towards the blue end of the spectrum. Techniques like the chromatic
Rossiter-McLaughlin effect [98] or chromatic Doppler Tomography [117] can be
used to test for such blue skies with data from the ANDES U-band. The presence
of clear skies can be used as a consistency check for the interpretation of
biosignature detections; most biosignatures should not produce a detectable
signal in cases of cloudy/hazy skies.

Ozone, which is a possible biosignature in exoplanet atmospheres [239],
produces a broad absorption band that intensifies sharply towards near-
ultraviolet wavelengths. In the ANDES U-band, the wavelength region shorter
than 3900 Å is the most relevant one for this. Since ozone does not produce
sharp absorption features here but rather a broad absorption band, a possible
detection method with ANDES is the chromatic Rossiter-McLaughlin effect or
chromatic Doppler Tomography.

Lava worlds, i.e., hot rocky exoplanets, may produce absorption in the CaII
H&K lines themselves. The expected mechanism is exospheres absorbing at these
wavelengths, for example, due to sputtered species arising from the rocky
surface, or material degassed from a magma ocean[187]. So far, searches for
this effect have mainly focused on 55 Cnc e, but have not yet been successful
[302]. ANDES U-band spectra would efficiently probe this scenario.

##  9 Additional Exoplanet Science Cases

###  9.1 Radial Velocity Mass Measurements

Figure 19:  Left panel: shows the distribution of known exoplanets with masses
measured via RV, along with some of the solar system’s planets. The dotted and
thick lines show the detection limits assuming 1 m/s and 10 cm/s precision for
solar and M2-type stars, respectively. Right panel: shows the mass-radius
diagram of known low-mass planets with masses and radii measured with
uncertainties lower than 33%. The dotted and thick squares show the regions of
the parameter-space accessible assuming 1 m s-1 and 10 cm s-1 precision,
respectively.

One of the scientific objectives of ANDES is to detect and characterize
exoplanets by measuring their induced radial velocity signals. ANDES will
achieve a minimum radial velocity precision of 1 m s-1, with a goal of 10 cm
s-1. A precision of 1 m s-1 is sufficient to detect the signals of super-
Earths and mini-Neptunes orbiting Sun-like stars and Earth-mass planets
orbiting the habitable zone of low-mass stars [9]. Reaching the goal of 10 cm
s-1 would make it capable of detecting the signals created by Earth-mass
planets orbiting in the habitable zones of Sun-like stars or Mars-like planets
orbiting around low-mass stars [277].

Figure 19, left panel, shows the expected detection limits of ANDES for the
case of a G2-type star (1 M⊙) and an M2-type star (0.3 M⊙). With 1 m s-1
precision, ANDES will be able to detect planets at the low end of the mass
distribution of known exoplanets. A precision of 10 cm s-1 would make it
capable of investigating a still unexplored region of the parameter space.

It is known that by improving the determination of the masses of the
exoplanets, it is possible to constrain their interior structure and formation
history [206]. Currently, the precision of the masses of many transiting
exoplanets is limited by the RV precision of the data, which is limited by the
apparent brightness of the host stars. Paired with the massive collecting area
of the ELT, ANDES will be able to measure the masses of transiting exoplanets
with enough precision to constrain their interior structure, even those
orbiting faint stars. It will be capable of measuring the masses of Earth-like
exoplanet candidates detected by space missions such as PLATO [295], which are
expected to be located in systems at a moderate distance to the Sun. ANDES
will be able to confirm candidate signals of Earth-like exoplanets detected by
ground-based surveys such as the Terra Hunting Experiment [347] by exploiting
its superior data quality. It will also be capable of characterizing the
population of low-mass exoplanets of the solar neighborhood, even those
orbiting very faint stars.

With a precision of 1 m s-1, ANDES will be able to fully populate the current
low-mass regime by studying fainter targets. Scaling from the capabilities of
ESPRESSO@VLT [277], ANDES@ELT will be able to reach 1 m s-1 precision in
solar-type stars up to $V=15$ mag and in M-dwarfs up to $V=16$ mag777According
to the SN relationships presented in [277], and scaling by the collected area
of the ELT. . This difference already provides more than 200 known candidate
systems in which ESPRESSO cannot achieve a precision of 1 m s-1, including 24
systems hosting Earth-size planets888Based on data of the Nasa exoplanet
archive; 2023/09/28. With a precision of 10 cm s-1, ANDES would be able to
explore an empty region of the parameter space up to magnitude $V=10$ mag for
solar-type stars and $V=10.8$ mag for M-dwarfs (Figure 19, right panel).
Currently, there are 28 known systems for which ANDES would be the only
instrument that could achieve a precision of 10 cm s-1.

###  9.2 Stellar pulsations

The physical properties of the exoplanets’ host stars are fundamental to
understanding their nature, origin, and evolution. To start with, planetary
radii derived from transit observations are expressed in terms of the host
star radius, while planetary masses derived from radial velocity measurements
depend on the host star’s mass. In addition to mass and radius, the abundance
of C, O, and rock-forming elements like Mg, Si, and Fe determines the
mineralogy, structure, geodynamics, and potential habitability of rocky-like
planets. Furthermore, models of planet formation have inferred that the
frequency of certain types of planets does show a dependence on the host
star’s metallicity and mass. Also, planetary periods and eccentricities might
be related to the presence of heavy elements in the stellar host.

This is especially critical for M dwarfs [e.g. 222]. First, they are faint in
the optical, so high signal-to-noise spectra tend to be limited by telescope
size. Furthermore, the temperatures of M dwarf atmospheres are cool enough to
form diatomic and triatomic molecules that create thousands of spectral lines
that are poorly known and, moreover, many of them blend with each other.
Therefore, many of the spectral lines traditionally used in the spectral
analysis of solar-type stars are blended or not present, while the spectral
synthesis of M dwarfs suffers from the incomplete knowledge of many molecular
data as well as from the accuracy of the atmospheric models used.

Asteroseismology, which makes use of the radial and non-radial pulsations of
stars permeating throughout the stellar atmosphere, is a powerful tool to
provide independent constraints on the fundamental parameters of the stars
along with the internal structure. Asteroseismology is based on comparing of
patterns of observed oscillation frequencies with theoretical predictions
based on stellar evolution models. Many applications of asteroseismology of
relevance to exoplanet host stars have been reported. For example, using 29
months of Kepler data, [124] yield the radius of Kepler-10 b with an
unprecedented uncertainty of only 125 km. The authors also confirm that
Kepler-10 was (at that moment) the oldest known rocky-planet-harbouring system
(10.41 Gyr). If the planet transits, asteroseismology gives the orbital
eccentricity [e.g., Kepler-419 91]. Furthermore, the stellar rotation axis
derived from asteroseismology can be combined with the inclination of the
planetary orbit plane to yield the host star’s obliquity directly [e.g. Kepler
56; the first spin-orbit misalignment in a multiplanet system, 166]. See [165]
for more examples and a recent review.

Stellar oscillations appear all across the Hertzsprung-Russell diagram.
Theoretical studies [305, 306] predict that low-mass M-dwarf stars have the
potential to pulsate. These studies predict short periodicities ranging from
20 minutes up to 3 hours and empirically estimated amplitudes of just a few
$\mu$mag or a few tens of cm s-1. So far, the analysis of HARPS data has shown
that no signals below 0.5 m s-1 can be detected with a confidence level better
than 90% on M dwarfs [see 32]. Nonetheless, [32] report some power excess for
the two most long-term stable M dwarfs in their sample, one of them with a 2
hours period and an amplitude as low as 0.36 m s-1, compatible with the
theoretical prediction for low-radial, low-order g-modes. [33] acquired more
observations for the pulsating candidate but could not confirm the
oscillations.

The better sensitivity and precision offered by ANDES will allow a better
sampling of the predicted short periods and reduce the noise level, thus
increasing the chances of detecting the stellar pulsations in M stars for the
very first time. Since the stellar pulsation signatures are like a fingerprint
of the star, the combination of optical and near-infrared spectra will allow a
complete characterization of the pulsation modes and strengths and, therefore,
a more detailed analysis of the internal structure and physics of M-stars.
Based on the results by [32], and considering the lower limit for the expected
pulsation frequencies (3 hours), we estimate that 50 measurements per star
should be enough for the detection of these modes with an SNR of 5. Assuming a
total integration time per target of 180 seconds and setting a V magnitude
limit of 11, we estimate that a sample of 30–65 M-dwarfs can be targeted in
100–200 hours.

It is also worth noticing the stellar atmospheric studies that can be done at
high-resolution with ANDES, which is important for assessing if metallicity
correlations are present at the stellar/sub-stellar boundary. For this work,
the near-infrared band is particularly useful. For example, [309] used the
equivalent width of the Na I can Ca I triplet and the H20-K2 index in the
K-band of high-resolution spectra for calculating stellar basic parameters and
metallicities. This technique has been widely extended to provide calibrations
and near-infrared indexes to characterize large samples of M dwarfs. In this
way, we can move forward with modeling the atmospheres where the transition
from a hydrogen-fusing object to a dusty object is difficult to model
accurately.

###  9.3 RM planet characterization/Obliquity measurements

Spectra taken before, during, and after transit can be used to probe not only
the constituents of and physical conditions in extrasolar planet atmospheres
but also to measure the projection of the spin-orbit angle on the sky plane,
i.e., the projected obliquity of the host star. When a transiting planet hides
a portion of the stellar disk, the corresponding radial-velocity component is
diminished in the disk-integrated stellar spectrum, leading to line-profile
distortions known as the Rossiter–McLaughlin (RM) effect (see [3] and
references therein). While the Sun’s obliquity is low ($\sim 7^{\circ}$
relative to the ecliptic) this is not necessarily true for extrasolar planet
systems. See, for example, the TEPCAT
catalogue999https://www.astro.keele.ac.uk/jkt/tepcat/ for an up-to-date
listing. Spin-orbit misalignment can be created during the epoch of planet
formation as well as later during the main-sequence lifetime of the system.
Therefore, the degree of alignment between the stellar spin and orbital spin
contains important information about the system’s past history. Unfortunately,
no RM measurements have been conducted for Earth-sized planets orbiting solar-
like stars as these are out of reach of current instruments 101010The RM
effect in the Trappist system has been measured. Asteroseismic measurements
have led to inclination measurements of solar-like stars with Earth-sized
planets in two systems (Kepler-50 and Kepler-65). This leaves a major gap in
our knowledge. ANDES will be able to determine the obliquities of just such
systems. There is an additional advantage for transiting Earth-mass planets on
long-period orbits around solar-like stars. Their RM amplitude is larger - of
the order of 30 cm s-1 \- relative to the radial velocity reflex semi-
amplitude, 9 cm s-1 for Earth [135]. The signal occurs also on a timescale of
a few hours and not months or years. Therefore, confirming such a transiting
planet from a transit survey might be more readily achievable through
measurements of the RM effect. Although the host stars’ projected obliquity
will be known, no mass estimate of the planet is gained.

In summary, the RM effect can be observed and analyzed for ”free” if
transmission spectroscopy is conducted in a transiting exoplanet system. The
quantity measured, projected stellar obliquity, is unknown for the types of
systems ANDES will target. For other classes of exoplanet systems spin-orbit
misalignments have defied theoretical expectations and have been proven useful
in understanding the histories of these systems. In addition, for low-mass
planets on long-period orbits, confirmation of transiting exoplanet candidates
through the RM effect will be more readily achievable than via traditional
radial velocity measurements obtained throughout the orbit.

###  9.4 The Chromatic Rossiter-Mclaughlin effect

The Chromatic Rossiter-Mclaughlin (CRM) effect can be exploited to gain
additional atmospheric information on exoplanet atmospheres from high-
resolution spectra which normally are best accessible through analysis of
additional low-resolution spectra [e.g., 333, 109, 316, 44, 118]. Its
measurement principle relies on the amplitude of the RM effect at different
wavelengths and depends on the square of the star-to-planet radius ratio at
the respective wavelength. Determining the amplitudes in the different
wavelength regions allows us to measure the apparent star-to-planet radii
ratios over the complete wavelength range of high-resolution echelle spectra.
By measuring the CRM, we will obtain access to low-res features (e.g.,
Rayleigh scattering, clouds) that probe different atmospheric pressure ranges
and are inaccessible to high-res transmission spectroscopy [380].

It comes with several disadvantages, chiefly only planetary atmospheres in
wavelength regions where stellar lines are present can be probed. Because the
signal in the stellar lines is analyzed, the Signal-to-Noise ratio (SNR) is
reduced relative to the case of standard low-resolution observations. Some
advantages make an analysis of the CRM in particular systems desirable. The
same spectrum as the high-resolution atmospheric study can be used; no
additional observations are required. Therefore, narrow and broad spectral
features are measured simultaneously. Its dependence on astrophysical stellar
noise differs from that of low-resolution observations. For faster-rotating
stars, its SNR decreases linearly with planet radius instead of the square of
this quantity, potentially offsetting some of the disadvantages in specific
systems [e.g., 3].

###  9.5 Stellar science cases addressed by exoplanet observations

Questions such as the nature of the stellar dynamo and stellar surface
features are actively investigated in ANDES’ working group 2 (see respective
White Paper). Observations of exoplanet transits yield additional information
about the host star that can be used to address those stellar science goals
and do not necessarily require separate observations. Instead, relevant
stellar observables can be extracted from the same observational data
collected for exoplanet transmission or emission spectra.

One example is the differential rotation of cool stars with convective
envelopes, which is an important parameter in stellar dynamo studies. In cases
where the exoplanetary orbit is even only slightly misaligned with the stellar
rotation axis, transit observations sample different latitudes on the host
star. The collected spectra can be used to reconstruct the spectrum of the
occulted patch of the stellar surface [66], yielding sensitive measurements of
stellar differential rotation and stellar limb darkening [e.g. 220, 87, 68,
104, 299] or stellar granulation [74].

Another illustration pertains to the spectral line profile linked to the
granulation pattern, which, in turn, significantly relies on the stellar
fundamental parameters. Each spectral line has unique finger-prints in the
spectrum that depend on line strength, depth, shift, width, and asymmetry
across the granulation pattern depending on their height of formation and
sensitivity to the atmospheric conditions [11]. In this context, it is
possible to measure and characterize the granulation pattern of the hosting
star performing (spatially-) resolved spectroscopy during planet transits
[106, 105, 107, 72, 108].

Other examples of stellar science cases being addressed by exoplanet
observations with ANDES are starspot properties encoded in spot occultations
during transits [e.g. 58] or more generally stellar magnetic field [e.g. 67],
short-term stellar variability [e.g. 345], and serendipitous observations of
stellar flares, particularly in the case of M dwarf stars for which ANDES will
be crucial in terms of shaping the behavior of the complex observed
atmospheres [e.g. 128, 253] and determine the impact of flares on the chemical
composition of transmission spectra [181].

##  10 Solar System Science with ANDES

###  10.1 Doppler velocimetry technique in planetary atmospheres

The Doppler effect measurement has been previously used to derive wind
estimates in the atmospheres of Venus [211, 145], Mars [212], Jupiter [144,
330] or Saturn [213].

The technique consists in measuring the Doppler shift of solar lines reflected
by the planetary disk [136] and using it to directly derive the zonal wind
across a large range of latitudes and local times, in the dayside. The Doppler
velocimetry method, used in the previously referred works, takes advantage of
the backscattered solar radiation at the planetary atmosphere. Doppler wind
speeds can be retrieved from observing stellar lines (e.g., Fraunhofer lines)
at very high spectral resolution. This method was previously applied for
determining radial velocities of stars [16] and in asteroseismology [231].

The technique was also used in recent planetary measurements in the visible
range [78]. The measurements of the wind velocities in planetary atmospheres
are retrieved using an adaptaded form of the absolute accelerometry (AA)
technique (Connes, 1985), applied to high-resolution spectra obtained at the
Very Large Telescope (ESO). Its applicability to planetary atmospheric winds
retrieval has also been demonstrated for the case of Venus [211, 145], Mars
[212], Jupiter [144, 330], Saturn [213] and even for Titan atmosphere’s
dynamical studies in the scope of an exploratory study [209, 210].

The method is based on an optimum correlation between a measured spectrum and
a reference spectrum. A detailed analysis of the particular method used for
outer planets has been made by Civeit et al [78]. Instead of determining the
Doppler shifts on individual lines the AA technique takes the ensemble of
lines and achieves a statistical precision in the velocity determination which
varies inversely with the spectral line density of the source. Hence,
observations at solar wavelengths with a high resolution spectrometer are
particularly suited to this technique, since the solar spectrum scattered off
by the planetary atmospheres carries the signatures of some 4000 Fraunhofer
solar absorption lines in the wavelength domain we use, yielding a theoretical
precision of a few m$s^{-1}$. In a Titan’s atmosphere dynamical study, as a
consequence of the observations’ geometry and of the moon’s rotation, the line
of sight Doppler shift at each pixel on the image of the planetary disk is
affected by the combination of the relative orbital motion, the planetary
motion and the cloud particles’ motion.

In the AA technique the velocity information is extracted from the variation
of the spectral intensity in a given measurement relative to an idealized
spectral intensity, which can be an average of many observations, or even a
model. Let us denote I ($\lambda$) and $I_{0}$($\lambda$) respectively the
Doppler-shifted (measured) and the idealized spectral intensities of the
target at a given wavelength. Then, assuming Doppler shifts smaller than the
typical line width, combining the first order expansion $I_{0}$ \- I $\simeq$
$\delta$$\lambda$$\partial$$I_{0}$/$\partial$$\lambda$ and $\delta$$V_{m}$/c =
$\delta$$\lambda$/$\lambda$, yields -$\delta$$V_{m}$($\lambda$)/c =
(I-$I_{0}$)/($\lambda$$\partial$$I_{0}$$/$$\partial$$\lambda$), where
$\delta$$V_{m}$ is the measured velocity signal projected on the line of
sight. Computing a weighted average over a given spectral domain yields

$\Delta V=\frac{\int{\frac{\delta V_{m}}{\sigma^{2}(\delta
V_{m})}}d\lambda}{\int{\frac{1}{\sigma^{2}(\delta V_{m})}}d\lambda}$ (1)

where $\sigma^{2}$($\delta$Vm($\lambda$)) is the variance of the velocity
measurement at wavelength $\lambda$ . The rule for optimum weighting is that
each weight be proportional to the inverse square of the RMS error. Under the
assumption of pure photon noise $\sigma^{2}$(I($\lambda$)) = I ($\lambda$)
with:

$-\frac{\Delta
V}{c}=\frac{\int{(I(\lambda)-I_{0}(\lambda))}M(\lambda)d\lambda}{\int{\lambda\frac{\partial
I_{0}}{\partial\lambda}}M(\lambda)d\lambda}$ (2)

Where M($\lambda$) = ($\lambda$/I)$\partial$I0/$\partial$$\lambda$ is called
the mask function [80]. The mask function can be interpreted as a weighting
function which amplifies the differences between the reference and the shifted
spectrum within absorption lines, and nullifies them where the spectrum is
flat. The technique takes into consideration the whole spectrum, independently
of individual spectral lines, and taking the variance it can be shown that the
standard deviation is inversely proportional to the packing of lines in the
spectrum. The constant Doppler shift arising from the relative motion of the
planet and the observer, and systematic shifts from instrumental effects, are
eliminated by considering the differential measurements between a spectrum
taken at a given point of the disk and the reference spectrum, taken at the
center of the disk where the phase angle is null, which are both observed
almost simultaneously.

ANDES’s combined high spectral and spatial resolutions in IFU mode will allow
us to push the Doppler velocimetry technique at unprecedented levels to derive
wind maps at very high spatial resolution. This is, however, at the cost of
being able to close the Adaptive Optics loop, which requires targeting
planetary objects with a relatively small angular size, such as Titan. The
typical angular diameter of Titan is 0.8”. With a diffraction limit (at 2
$\lambda$/D, 0.75 $\mu$m) of ANDES at about 8 mas, we expect to reach a
typical horizontal resolution of 50 km $\times$ 50 km. Using the radial
velocity photon noise limits [298]111111We used the online tool
http://www.astro.physik.uni-goettingen.de/research/rvprecision/, we evaluate
that a 1 hour integration time is sufficient to reach a 2 m s-1 precision per
element of resolution for Titan. However, this approach neglects the effect of
instrument stability, stellar activity, calibration, and others that can
significantly increase noise level [144] and deserve to be quantified in
detail.

Interestingly, Titan has a forest of strong CH4 lines from the visible (as
seen in previous ESPRESSO observations of Titan; Turbet et al., in
preparation) to the infrared [62]; these lines could be used to improve
further the SNR of wind measurements (in addition to using stellar lines), as
well as to extend wind measurements at altitudes above the haze layer.
However, doing so requires an experimental effort to accurately constrain CH4
line parameters in the visible (see an example in Campargue et al 63).

Moreover, high-resolution spectroscopy presents a unique opportunity to
observe a planetary target with a CH4-rich atmosphere, from which CH4 optical
proprieties can be studied and retrieve related isotopic ratios. It also
showcases the use of a close planetary target to test new methods for chemical
retrieval of minor atmospheric compounds (some of them with relevant
astrobiological interest as shown in R. Silva et al., in revision in Planetary
and Space Science), in preparation for upcoming studies of cold terrestrial
exoplanet atmospheres.

###  10.2 Probing tenuous planetary atmospheres

ANDES high spectral resolution and sensitivity will make it a powerful
instrument to study tenuous planetary atmospheres, where due to the low
pressures ($\mu$bar to nbar range), line profiles are defined by thermal
broadening, yielding intrinsic FWHM of $\sim$0.01 cm-1 at 2 $\mu$m. Such
atmospheres include the sublimation-driven atmospheres of Pluto, Triton and
Io, the latter including also a volcanic contribution. A common feature is the
existence of an orbital pressure cycle, related to changing heliocentric
distance and/or subsolar latitude. On Pluto and Triton, the pressure seasonal
cycle is best monitored through stellar occultations [e.g., 329], but infrared
spectroscopy can also contribute by measuring the N2 ice temperature [241],
which determines the total pressure. Moreover, CH4 and CO are present at the
surface and in the atmosphere. In particular, Pluto’s northern latitudes are
covered by methane deposits, which are a major source of atmospheric methane
[37]. But how such deposits will react as this region will reach Northern
Solstice by 2029 is unknown and global climate model predictions can be tested
against temporally-sampled and spatially-resolved (if the AO loop can be
closed on a 0.1” target) observations with ANDES. VLT/CRIRES observations
[191] have demonstrated the possibility to monitor Pluto’s atmospheric methane
from ground-based IR spectroscopy but the ability to map it on Pluto’s and
Triton’s disks will be unique to ANDES.

Other Transneptunian objects (TNOs) such as Quaoar, Gongdong, Makemake, and
Eris are known to have volatile-covered surfaces [N2, CH4, see review in 18],
and recent JWST observations have shown that CO2 and CO are also common on the
surfaces of Kuiper Belt objects [55]. This is generally consistent with
volatile escape models [e.g. 56, 382] that show that large KBO are able to
retain their volatiles over the age of the solar system. This leaves the
possibility that other TNOs besides Pluto and Triton may exhibit atmospheres
at least along some parts of their orbits. From an observational perspective,
the target object should be warm enough when observed – typically, a 21 K
(resp. 29 K) N2 (resp. CH4) atmosphere is at the transition between
collisional and ballistic – and global atmospheres are more promising for
detection than atmospheres restricted to the subsolar region. Stellar
occultations (e.g. Ortiz et al [267] for Makemake) provide complementary
searches for atmospheres, but by nature can constrain them only near the
terminator, a priori not the most favourable region.

Although most of the knowledge of Io’s nanobar-class atmosphere – see review
in de Pater et al [94] – is based on UV and sub-mm observations, it is also
accessible to near-IR spectroscopy, with the spatially-resolved detection of
SO2 gas at 4 $\mu$m in sunlight and of SO emission at 1.7 $\mu$m in Jupiter
eclipse. The latter has been known for over 20 years but its interpretation
remains uncertain. The most plausible scenario [95] is that it represents
emission of hot SO gas directly ejected from volcanic vents at a high
quenching temperature. However, studies of the correlation between this
emission and the distribution of hot spots have given contradictory results,
and the overall spectral shape (so far restricted to the disk-average spectrum
due to S/N limitations) is still defying modelling. ANDES observations
combining both high spectral and high spatial resolution should shed light on
the origin of this emission. Finally, plume atmospheres, such as Enceladus’,
recently observed by JWST [365], and Europa’s elusive one [364], may also be
explored with ANDES. Although the major gas H2O (and CO2) will be inaccessible
from the ground, other species diagnostic of sub-surface ocean chemical
conditions, e.g. CO, CH4, C2H6, CH3OH, may be searched for.

###  10.3 Isotopic ratios in comets

Isotopic ratios represent a powerful tracer of the origin of planetary bodies,
especially for small bodies, that suffered less chemical evolution during
their lifetime, compared to planets. The comets are among the most primitive
materials in the solar system and can provide unique constraints on the
composition of the pre-solar nebula. Their main advantage for measuring their
chemical composition is the presence of a coma with species (molecules,
radicals, ions, and atoms) in gas phase. It permits a detailed chemical
analysis of the cometary ices by means of spectroscopy. In the spectral range
covered by ANDES many emission lines due to different radicals can be
observed. The main source of information – that implies a high signal-to-noise
ratio – coming from these emission lines is the isotopic ratios.

The two main isotopic ratios that can be measured in the spectral range
covered by ANDES are 12C/13C and 14N/15N that can be measured in the following
species: CN (for both ratios, in the U band), NH2 (for nitrogen, in the V
band), C2 (in the B band), CO+ (for carbon, in the B band) and N${}_{2}^{+}$
(in the U band). These last two species are not always detected in the inner
coma. The results obtained so far, mainly with 8-m class telescopes [377, 225,
311, 312, 324, 266, 313] indicate a 12C/13C ratio similar to the terrestrial
value of 89 (but with large errorbars) for C2, CN and CO+ (only one
measurement in this ion, rarely observed in the inner coma) and a significant
enrichment of 15N compared to 14N in both CN and NH2 radicals compared to
terrestrial value (by a factor of about 2) and solar bulk [234] and Jupiter
ammonia [125] (by a factor of about 3), only one lower limit being so far
obtained for the 14N/15N ratio for N2 with ground-based observations.

The significant improvement in the signal-to-noise ratio expected with ANDES
at ELT, compared to UVES at VLT (the main spectrograph used so far for these
observations) opens very interesting possibilities, both for comets belonging
to our solar system and interstellar comets expected to be observed in the
near future. A significant reduction of the errorbars is expected, leading to
more constraints on the origin of the comets (e.g. according to their
dynamical type) and first measurements in interstellar comets – never done so
far – will provide unique insight in extrasolar planetary systems.

##  11 Synergies with other instruments

As a next-generation instrument, ANDES will be preceded by a suite of ground-
and space-based facilities for exoplanet science, namely the ELTs, JWST,
PLATO, ARIEL, ALMA and SKAO, and will be a vital stepping stone on the way to
the study of Earth analogues with the possible future great observatories
under study like the Habitable Worlds Observatory (HabWorlds) and the Large
Interferometer For Exoplanets (LIFE). It therefore plays a crucial role in
further advancing our knowledge of exoplanet atmospheres through synergy and
complementarity with other instruments, some of which we discuss below.

###  11.1 Ground-based

ANDES will follow on the exoplanet characterization efforts of the first
generation of spectroscopic workhorses for the ELT, i.e. METIS [289], HARMONI
[164], and MICADO [353]. For exoplanet atmospheric characterization at high
spectral resolution, each has its own niche, complementary to ANDES.

MICADO offers single slit ($0.016^{\prime\prime}\times 3^{\prime\prime}$)
mode, AO-assisted, high contrast spectroscopy at $R<20,000$ for non-
instantaneous wavelengths between $0.84-2.46\mu$m. At similar wavelengths,
HARMONI hosts an AO-assisted, image slicer IFU, with a high contrast mode
covering the H & K band (non-simultaneously) at $R=18,000$, with excellent
spatial sampling (spaxel size) of 3.88 mas. Both have the potential to search
for the reflected light spectra of nearby and widely-separated exoplanets.
HARMONI’s IFU in particular could observe Proxima b (separation $<37$ mas),
though the design of its focal plane mask and apodizer may require some
modification from its current design or use non-standard observing modes to
enable this (Vaughan et al. submitted). Thanks to its $R=100,000$ resolution,
the ANDES infrared IFU avoids the issue of stellar PSF saturation that
necessitates the HARMONI focal plane mask. Thus, ANDES will be able to observe
reflected light spectra of exoplanet atmospheres at much higher spectral
resolution, leading to not only tighter abundance constraints, but more
comprehensive chemical analyses of rocky exoplanets, thanks to its increased
sensitivity to weaker lines from less abundant species in these wavelength
regimes, including the key biosignature species oxygen.

METIS will offer an IFU in the L & M bands ($3-5\mu$m) at $R=100,000$. It is
the perfect complement to ANDES. METIS will be primarily sensitive to the
thermal emission of temperate rocky worlds, providing detailed analyses of
their composition and thermal structure [46]. Combined, ANDES and METIS will
obtain a holistic, detailed view of these planets across the full optical-NIR
regime, probing both reflected and thermal emission resulting in measurements
of the planetary albedo, its heat budget and ultimately establishing the main
parameters of its global climate. METIS and ANDES will also use their high
spectral resolution to probe the exact shape of spectral lines in the
atmospheres of gas giants, providing complementary wavelength information that
has the potential to examine dynamic and chemical effects, particularly in
disequilibrium, at different altitude/pressure levels in greater detail than
ever before.

ANDES will also have significant synergies with METIS regarding proto-
planetary disk science. METIS will be able to image and spectrally map the
inner dusty disk structure, it will study the excitation and dynamics of CO
fundamental emission in the inner gaseous disk, and it will allow a study of
the gas chemistry in the hot region of the disk through observations of key
species such as $H_{2}$, H2O, and organic molecules. On the other hand, ANDES
will provide dynamical information and full characterization in terms of
physical parameters of the atomic component of the inner gas, it will study
the accretion process and provide measurements of the magnetic field, and it
will understand the influence of jets in the star-disk interaction.

In addition, observations of molecular lines at higher energies with respect
to those covered by METIS will give important information for a correct
interpretation of the excitation mechanism. The science performed by ANDES in
the field of proto-planetary disks will be, therefore, highly complementary to
that of METIS and the combination of observations from the two instruments
will allow a complete picture of the inner disk region and its interaction
with the still accreting star.

###  11.2 Space-based

JWST [134], which is already a reality, and ARIEL [349], with a foreseen
launch in 2029, are both expected to be operational within a similar time
frame (early 2030’s) as ANDES. Their combined observations are expected to
yield crucial synergies, enabling the exploration of a wide parameter space of
exoplanet atmospheres. JWST is a more powerful observatory than ARIEL for
single observations, but ARIEL holds a great advantage which is that it covers
the entire spectral region from 0.5 to 8 microns simultaneously and that it is
a dedicated mission for exoplanet population statistics. Both missions
together will measure global planetary atmospheric parameters, including
temperature-pressure profiles, cloud coverage, and bulk molecular abundances
of more than 1000 planets [113]. These space-based observations offer very
complementary information as they can access parts of the electromagnetic
spectrum that are inaccessible to ground-based observatories due to absorption
and scattering in Earth’s atmosphere.

High contrast imaging instruments at ELT will examine a volume-limited
population of young, non-transiting exoplanets formed with the same initial
composition as the ARIEL and JWST sample but at considerably colder
temperatures (beyond 100 AU). On the other hand, high-dispersion spectroscopy
instruments are tailored to study the atmospheres of exoplanets overlapping
with ARIEL’s sample and those accesible to JWST.

With a resolving power of $R>100,000$, ELTs can resolve atomic and molecular
bands in exoplanet spectra into hundreds or thousands of individual lines.
These signals can be combined for detection, offering astrophysical
information over small wavelength scales that JWST or ARIEL won’t be able to
obtain. In particular ANDES will measure planet metallicities [161, 64, 381],
inhomogeneities and dynamics in the planetary atmosphere through time-resolved
transmission measurements [114], individual lines that can be used as tracers
to understand evaporation and atmospheric evolution processes [379, 260],
planetary albedos through the detection of reflected light at different
wavelengths [233] and detailed information about the properties of stellar
active regions, augmenting JWST and ARIEL’s capability to mitigate stellar
activity-induced noise in retrieved transmission spectra [291, 41]. More
importantly, the high resolution spectroscopic observations can be combined
with the bulk compositions, T-P profiles, and thermal inversions derived from
ARIEL and JWST data in a single analysis framework [52]. These combined
analysis of high and low dispersal data analysis will provide a holistic
picture of planetary atmospheres.

Finally, ANDES radial velocity measurements can be used to determine accurate
planet masses for small planets or faint host stars, which might be crucial
for some of the best earth-sized targets PLATO [295] might find, and also to
provide information on planetary rotation and high-altitude wind speeds for
the most favorable targets. Accurate mass measurements are necessary to
interpret the atmospheric characterization data, whether it is to understand
the lack of an atmosphere or to perform retrievals on molecular features [19,
69].

##  12 Conclusions

In this work we have presented detailed simulations of some of the ground-
breaking exoplanet (and solar system) science that will be attainable with
ANDES at the ELT. ANDEs will feature a seeing-limited spectrograph with a
minimum spectral resolution of $R=100,000$, covering simultaneously the
wavelength range of 0.5–1.8 µm, and with the goal for an extended coverage
into the U and the K bands. It will also feature an AO-assisted mode with an
IFU covering simultaneously the Y, J, and H bands.

The main objective of the ANDES project is to characterize the atmosphere of
rocky planets in the habitable zone, mostly around M-dwarf stars. This is
particularly relevant as the characterization of these accessible and abundant
planets is crucial to understanding their habitability and determining if they
could support life. ANDES will also focus on the detection of reflected light
from the planetary atmosphere, allowing to explore their structure,
composition, and surface conditions. This will provide an unprecedented
detailed understanding beyond basic parameters such as mass, radius, and bulk
composition. A golden sample of at least five nearby non-transiting earth-
sized habitable zone planets will be accessible to ANDES for atmospheric
characterization and search for biomarkers within a few nights. This would be
a major scientific milestone for exoplanets and astrobiology, an objective
that no other currently approved astronomical facility will be able to reach.

Furthermore, ANDES will also be dedicated to studying the initial conditions
under which planets form and the physical mechanisms that lead to the
different observed planet types populations and system architectures. This
involves investigating the composition and spatial distribution of atomic and
molecular gas in the inner regions of young circumstellar disks, which is
needed for a better understanding of the initial formation and later evolution
of planetary systems.

Since ANDES will be operational at the same time as NASA’s JWST and ESA’s
ARIEL missions, it will provide enormous synergies in the characterization of
planetary atmospheres at high and low spectral resolution. This will open a
true golden era for full comprehensive understanding of the diversity of
exoplanet atmospheres and how they form and evolve.

Acknowledgments

EP and HP acknowledge financial support from the Spanish Ministry of Science
and Innovation (MICINN) project PID2021-125627OB-C32 and PGC2018-098153-B-C31.
JIGH and ASM acknowledge financial support from the Spanish Ministry of
Science and Innovation (MICINN) project PID2020-117493GB-I00. FD thanks Hayley
Beltz for valuable support with the WASP-76 b ANDES simulations. JLB
acknowledges funding from the European Research Council (ERC) under the
European Union’s Horizon 2020 research and innovation program under grant
agreement No 805445. BLCM acknowledges continuous grants from the Brazilian
funding agencies CNPq and Print/CAPES/UFRN. This study was financed in part by
the Coordenaçao de Aperfeiçoamento de Pessoal de Nivel Superior - Brasil
(CAPES) - Finance Code 001

##  Appendix A ANDES AO-assisted performance modelling

###  A.1 ANDES AO expected performance

The current ANDES-SCAO design includes a modulated pyramid WFS sensor inspired
on the HARMONI-SCAO in what respect to the main system parameters (wavelength
range, number of sub-apertures, and control strategy). We obtained a first
estimation of the achievable contrast, starting from the end-to-end AO
simulations from [43] performed for HARMONI-SCAO, and adding error
contributions that had been neglected so far. In particular, we summed up to
the HARMONI-SCAO wavefront residuals the effects of: 1) $SP$: static
petalling; 2) $DP$: dynamic petalling; 3) $J$: residual PSF jitter. As
petalling error we refer here to the differential piston between the 6
segments of ELT-M4. Then, we accumulated 2000 instantaneous PSFs
(corresponding to 4s of integration) obtained from these residuals and we
computed the contrast achieved by the SCAO system. This approach provides an
optimistic estimation of the performance because the mentioned errors will
impact the AO loop itself, increasing the AO residuals. Here, we are
neglecting this aspect that will be taken into account in the near future with
dedicated end-to-end simulations.

The contrast is considered as the ratio between the radial profile and the
peak of the PSF. For the contrasts reported in Section 4, we considered: AO
reference star $I\leq 8$; median seeing conditions ($0.71asec$, ”$L_{0}=50m$);
$DP=50nm$ RMS and $J=100nm$ RMS, accounting for vibration and wind shake
residuals. About $SP$, we envisioned two possible scenarios: high piston - M4
is delivered to the instrument with $SP=200nm$ RMS and SCAO system is not able
to correct for this static error that persists during the observation; low
piston - $SP=25nm$ thanks to a good phasing performed by ELT before the
handover to ANDES, or thanks to the SCAO capability to correct the petalling
error down to this level.

The low piston scenario will also enable the use of a coronagraph. The
simulations show that even a classic Lyot coronagraph will provide a contrast
gain $\geq 10$ in the region around $20mas$ at $1600nm$, reaching values
$<1.0\cdot 10^{-3}$.

###  A.2 Planet observations simulations

We have simulated ANDES-SCAO observations of known exoplanets to explore the
target sample that can be probed in this mode. We base the simulation on the
stellar and planetary data available in the “Planetary Systems Composite Data”
table121212https://exoplanetarchive.ipac.caltech.edu/cgi-bin/TblView/nph-
tblView?app=ExoTbls&config=PSCompPars in the NASA Exoplanet
Archive131313https://exoplanetarchive.ipac.caltech.edu/index.html. We note
that a small subset of the systems must include some quantities required for
the simulation. Instead of excluding these systems, we choose to replace these
missing values either with sensible default values or with values based on the
rest of the quantities.

  * •

For stars, some stellar radius, mass, or effective temperature estimates need
to be included. We set the missing effective temperatures to 5000 K, and then
we fill in the missing mass and radius values using either mass-radius or
temperature-mass-radius relations.

  * •

For planets, the estimates for some of the orbital parameters, radii, or
masses are missing. We default the missing eccentricities, arguments of
periastron, and inclinations to $0,90^{\circ}$, and $90^{\circ}$,
respectively. Next, we calculate the missing semi-major axes using the
planet’s orbital period and stellar mass (and assume circular orbits).
Finally, for planets with either a mass or radius estimate but not both, we
set the missing value to match Jupiter’s if the existing value indicates the
planet to be Jupiter-sized.

We first calculate the maximum projected planet-star distance for each planet
based on the planet’s orbital parameters (semi-major axis, inclination,
eccentricity, and argument of periastron), after which we use the maximum
projected distance and the distance to the system to calculate the planet’s
maximum angular separation from its host star. Next, we calculate the planet-
star radius and area ratios based on the planet and star radii, and then the
planetary equilibrium temperature based on the stellar effective temperature
and the planet’s semi-major axis.

The planet-star flux ratios are calculated as a sum of the planet’s reflected
and emitted light, $F_{\mathrm{r}}$ and $F_{\mathrm{e}}$, respectively,
relative to the flux from its host star,

$f=\frac{F_{\mathrm{r}}+F_{\mathrm{e}}}{F_{\star}}.$ (3)

The reflected flux ratio is calculated using the maximum projected planet-star
distance, assuming an earth-like albedo of 0.3 and a phase angle of $\pi$/2.
In contrast, the emitted flux ratio is calculated using the planet-star area
ratio, planet equilibrium temperature, and the star’s effective temperature,
approximating both the planet and the star as black bodies.

We calculate the number of photons received by a resolution element per second
as a function of magnitude using a first-order polynomial in log10(photons/s)
fitted to photons/s estimates created by the ANDES ETC v1.1 for a compact
source.

We use the ETC to calculate the S/N ratios (SNRs) for two magnitudes (5 and
10) with a 6000 s exposure time for each passband. The number of photons/s is
obtained as SNR2 / 6000, after which a polynomial is fit to the two
$\log_{10}$(photons/s) estimates as a function of AB magnitude.141414We also
tested that the logarithm of the number of photons per second obtained using
the ETC is linear in AB magnitude, as it should. We set the exposure time to
6000 s, the sky background to 30 counts, the telescope and optics temperature
to 200 K, and the read-out noise and dark current to 0 to ensure that $\approx
100\%$ of the noise comes from photon noise. We convert the V, J, H, and K
mags into the AB magnitude
system151515https://en.wikipedia.org/wiki/AB_magnitude to calculate the number
of photons received by a resolution element for each star. We first convert
the magnitude into a flux density using PyAstronomy.magToFluxDensity_bessel98.
The method calculates the flux density in Jy, which we then convert to AB
magnitude as

$m_{\mathrm{AB}}=-2.5\log_{10}\left(\frac{f_{\nu}}{3621~{}\mathrm{Jy}}\right)$
(4)

After this, the AB magnitude can be used with the photons/second model to
estimate the number of photons arriving at a resolution element in a given
time.

We use the contrast curves for the low (750, 1000, 1600, 2200 nm) and high
(1000, 1600, 2200 nm) piston scenarios discussed above and provided by Anne-
Laure Cheffot and Enrico Pinna (priv. Comm.). The final SNR is calculated
following Lovis et al [200] and Snellen et al [332], as

$\mathrm{SNR}=f\sqrt{t_{\mathrm{e}}F_{\star}n_{\mathrm{l}}K},$ (5)

and the time to a given SNR as

$T_{\mathrm{SNR}}=\frac{\mathrm{SNR}^{2}}{f^{2}F_{\star}n_{\mathrm{l}}K},$ (6)

where $f$ is the planet-star flux ratio, $t_{\mathrm{e}}$ is the exposure
time, $F_{\star}$ is the flux from the star, $n_{\mathrm{l}}$ the number of
lines (assumed here arbitrarily to be 1000, which is a typical number for
other ground-based spectrographs), and K is 1/contrast. The SNR considers only
photon noise and ignores other white noise sources (readout) and systematics
(in particular telluric and stellar lines are assumed to be perfectly
removed).

Figure 20:  Same as Figure 7, but here the contrast curves assume a low-piston
scenario and no coronagraph.

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