11institutetext: Université Claude Bernard Lyon 1 & CNRS, Institute Lumière
Matière, 69622 Villeurbanne, France 22institutetext: Université de
Montpellier, CNRS, LUPM, 34095 Montpellier, France 33institutetext: Université
de Toulouse CNRS, IRAP, 14 av. Belin, 31400 Toulouse, France 44institutetext:
Science Division, Directorate of Science, European Space Research and
Technology Centre (ESA/ESTEC), Keplerlaan 1, 2201 AZ, Noordwijk, The
Netherlands 55institutetext: Université Grenoble Alpes & CNRS, IPAG, 38000
Grenoble, France 66institutetext: Konkoly Observatory, HUN-REN Research Centre
for Astronomy and Earth Sciences (CSFK, MTA Centre of Excellence), Konkoly-
Thege Miklós út 15-17, 1121 Budapest, Hungary 77institutetext: Max Planck
Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany
88institutetext: Department of Chemistry, University of New Brunswick,
Fredericton, NB, Canada E3B 5A3 99institutetext: Department of Physics,
University of New Brunswick, Fredericton, NB, Canada E3B 5A3

# Correlations between laboratory line lists for FeH, CrH, and NiH and M-star
spectra collected with ESPaDOnS and SPIRou††thanks: Our line lists are
available in electronic format only. They can be obtained from the CDS via
anonymous ftp to http://cdsarc.cds.unistra.fr/ or via
https://cdsarc.cds.unistra.fr/

P. Crozet 11 J. Morin 22 A. J. Ross 11 S. Bellotti, 3344 J. F. Donati 33 P.
Fouqué 33 C. Moutou 33 P. Petit 33 A. Carmona 55 A. Kóspál, 6677 A. G. Adam 88
D. W. Tokaryk 99

(Received 18/07/2023 Accepted 19/09/2023 )

###### Abstract

Context. Molecular bands of metal oxides and hydrides dominate the optical and
near-infrared spectra of M dwarfs. High-resolution spectra of these bands have
immense potential for determining many properties of these stars, such as
effective temperature, surface gravity, elemental abundances, radial velocity,
or surface magnetic fields. Techniques are being developed to do this but
remain limited by the current availability and accuracy of molecular data and
spectral line lists.

Aims. This paper reports metal monohydride line lists selected from near-
infrared and visible laboratory data to show that specific bands in several
electronic transitions can be used to identify CrH, NiH, and FeH in M stars
and to determine radial velocities from Doppler shifts. The possibility of
measuring magnetic fields is also investigated for FeH and CrH.

Methods. We used systematic cross-correlation analysis between unpolarised
spectra from a selection of M stars and state-specific laboratory line lists.
These lists were generated from a combination of existing data and new
laboratory laser-excitation spectra recorded at Doppler-limited resolution, in
zero-field conditions or in magnetic fields up to 0.6 tesla.

Results. We show that transitions at visible wavelengths in FeH and NiH,
usually neglected in the analysis of the spectra of M-type stars, do in fact
contribute to the spectra, and we demonstrate the influence of magnetic
sensitivity on selected transitions in CrH and FeH.

Conclusions. Although the new line lists focus on transitions recorded at
temperatures significantly lower than those of stellar objects, they remain
pertinent because they cover some band-head regions of high spectral density.
FeH bands can provide a useful supplement to atomic lines for the analysis of
high-resolution optical and near-infrared spectra of M dwarfs. We demonstrate
the influence of a magnetic field on CrH signatures around 862 nm.

###### Key Words.:

Stars : M-type stars; Stars: magnetic field ; Molecular data ; Radial
velocities; cross-correlation analysis

##  1 Introduction

The extended study of cool stellar objects, and concurrent discoveries of
exoplanets, has led to a demand for more reference data of diatomic molecules
seen in stellar atmospheres, species that can also be formed in plasma and
flame environments in the laboratory. Accurate line lists, that include as
many relevant species and transitions as possible, are essential for
generating synthetic spectra to improve determinations of stellar properties,
such as temperature, Doppler shifts, stellar magnetic fields, and rotation,
either from direct comparison or from cross-correlation (CC) calculations.
Precise and complete line lists – including molecules – for M dwarfs will be
particularly valuable if such data can explain the diverse behaviour of
several subsets of spectral lines, with key applications for velocimetry and
magnetometry (e.g. Klein et al., 2021; Bellotti et al., 2022). We consider
here some molecular transitions expected to be sensitive to magnetic fields,
aiming to identify and characterise those likely to have sharp and deep
features that should be well suited for such diagnostics via CC calculations.
Our laboratory work on FeH, NiH, and CrH falls in the visible and near-
infrared regions; we present comparisons with data from ESPaDOnS (Echelle
SpectroPolarimetric Device for the Observation of Stars; Donati 2003), which
operates in the optical region 0.37–1.05 $\upmu$m, its twin instrument Narval
(Aurière, 2003) at the Pic du Midi, and SPIRou (SpectroPolarimètre InfraRouge;
Donati et al. 2020) in the near-infrared (0.95–2.5 $\upmu$m). These
spectropolarimetric data have already been analysed in the context of stellar
magnetism and radial velocity (RV) determinations (Donati et al., 2008; Morin
et al., 2008, 2010; Cristofari et al., 2023; Carmona et al., 2023; Bellotti et
al., 2023).

Cross-correlation is a powerful tool that has been successfully applied in a
variety of scientific fields, from signal processing and wireless
communications to quantum physics. In the context of stellar astrophysics,
Doppler shifts supply one correlation function linking stellar spectra with
laboratory-measured ‘masks’, consisting of reference collections of atomic or
molecular transitions. Information can be extracted at several levels,
starting with whether the species is present. Spectral details then lead to
estimates of temperature (at thermal equilibrium or otherwise), RV, magnetic
field characteristics, surface gravity (through pressure broadening of
spectral lines), and relative chemical abundances. Precise RV determinations
have been used to detect exoplanets around stars for more than 2 decades,
following evidence from Mayor & Queloz (1995) of an extra-solar planet around
a Sun-like star. Their CC approach was introduced for cool dwarfs of spectral
type FGK that feature mostly atomic lines and a well-defined continuum. Moving
towards cooler M dwarfs, atomic transitions become fewer and weaker, and
molecular bands emerge. Molecular line lists are notoriously less precise than
atomic ones, and purely synthetic masks can be insufficiently accurate to give
precise RVs. Different approaches have been proposed to compensate for these
issues. Optical developments and new algorithms to describe the instrumental
response of the High Accuracy Radial velocity Planet Searcher (HARPS)
spectrometer have resulted in precise RVs via ‘template matching’, effectively
averaging many spectra of the object of interest (Anglada-Escudé & Butler,
2012). An alternative ‘line-by-line’ approach, employed for example in papers
by Dumusque, X. (2018), Lafarga et al. (2020), and Artigau et al. (2022),
determines RVs from individual features, then recognises and excludes outliers
prior to averaging the outcomes. Molecular templates have also proven helpful
in probing exoplanetary atmospheres. Pioneering work by Snellen et al. (2010)
extracted evidence for strong winds on exoplanet HD209458b from RV results
derived from CC functions with resolved CO lines around 2.3 $\upmu$m. The
review by Birkby (2018) illustrates the importance of information from high-
resolution (ground-based) instruments for the detection and characterisation
of exoplanets and their atmospheres, and highlights the power of the CC
approach.

Absorption spectra from cool stellar objects display rovibrational and/or
electronic bands of small molecules (mostly diatomic oxides and hydrides, and
water) as well as strong atomic features, providing further insight into
chemistry and conditions. There is some bias induced by the intrinsic strength
of the optical transitions, with the lighter Group II and first-row transition
metal diatomics dominating the picture. Their numerous molecular signatures,
particularly in the near-infrared (Y, J, H, and K bands) allow the
identification of species in photospheres with certainty, thanks to precise
molecular line lists, typically with $\Delta\uplambda$/$\uplambda\leq 2\times
10^{-7}$, widely distributed in rotational quantum numbers. Because many of
the species stable above 1000 K are open-shell fragments of chemically stable
laboratory precursors, many of them are sensitive to magnetic fields. Magnetic
response depends on the changes in quantum numbers (rotation and electronic)
associated with a given spectral line, and this results in some transitions
being effectively insensitive to the magnetic field whilst others show
pronounced Zeeman effects. It is helpful to select the appropriate subset of
reference lines to infer the influence of magnetic fields, assuming the
relevant Landé factors are known. Attempts to model the Landé factors for
transition metal monohydride radicals, either from laboratory work (Harker et
al., 2013; Crozet et al., 2014) or from solar and stellar spectra (Afram et
al., 2008; Shulyak et al., 2010), show that they are not trivial to predict.

Of course, there are limitations and complications. Contributions from
different systems frequently overlap one another: TiO bands (McKemmish et al.,
2019) stretch across the visible and near-infrared spectrum, and electronic
bands of atmospheric oxygen overlap part of the A-X system of CrH at 764 nm.
Whenever possible, it is preferable to work in a spectral range with a single
dominant contribution, such as FeH around 1 micron (Wende et al., 2010). It is
also true that Landé factors have been measured for few of the molecules of
interest except at very low temperatures, notably from molecular beam
experiments conducted in Steimle’s group (Virgo et al., 2005; Chen et al.,
2006, 2007; Harrison et al., 2008; Qin et al., 2012) for TiO, TiH, CrH, and
CaH, for example. Work is in progress in Lyon and in Fredericton, at the
University of New Brunswick (UNB), to supply this information for selected
transition metal hydrides, using high-resolution laser spectroscopic
techniques.

We collated metal monohydride (MH) transition wavenumbers from our own
laboratory work and from literature sources to target reasonably narrow
spectral windows across the near-infrared and visible regions. We then used
them to identify MH transitions in some M-star spectra recorded at telescopes
at Pic du Midi (Bernard Lyot Telescope) and on Maunakea (Canada-France-Hawaii
Telescope), and to extract RVs via CC calculations. The values from the
molecular data are found to match values derived from atomic masks, even
though it is sometimes difficult to recognise spectral features at a glance.
The band-heads of the A ${}^{6}\Sigma^{+}$ \- X ${}^{6}\Sigma^{+}$ system of
CrH and F ${}^{4}\Delta$ \- X${}^{4}\Delta$ system of FeH emerge clearly in
the stellar spectra we have selected, but NiH contributions do not. They are
spread across the visible region and overlap with strong contributions from
TiO. Even though individual lines cannot be identified, we find that NiH is
present in some sources. It seems to be a genuine result because a ‘deuterium
test’, following Pavlenko et al. 2008 and performing the same calculation
using a mask constructed for NiD (not expected to be present), gives a
negative outcome. CH, SiH, and NH radicals are already included in the widely
used Vienna Atomic Line Database (VALD) (Ryabchikova et al., 2015), but only
one metal hydride, MgH, is found
there111https://www.astro.uu.se/valdwiki/Molecules. We make a case for adding
a few more. Sources such as MoLList (Bernath, 2020) and ExoMol (Tennyson et
al., 2020) offer more extensive, high-temperature line lists for FeH and CrH,
but not all entries match experimental precision. This contribution is
intended as a supplement and not a replacement, since the focus of our work is
on defining selective diagnostic transitions.

In the following, we give a description of the CC approach used here, to be
applied with narrow-band spectral masks, and then discuss some optical
transitions suitable as molecular templates in the investigation of spectra
from some M-dwarf stars, recorded on the ESPaDOnS, Narval, and SPIRou
spectropolarimeters. We use CC to show that these systems retrieve RVs with
degraded signal-to-noise ratios (S/Ns) for magnetically active objects. We use
CrH to illustrate that the density of the spectrum in the presence of a
magnetic field is such that very few sharp, deep features remain in the mask.
The RV determined in this way is closer to reference data, but the statistical
uncertainty remains large.

##  2 Cross-correlation functions

The CC method described by Tonry & Davis (1979) and by Queloz (1995) seeks the
optimum match between a stellar spectrum and a reference mask, when the mask
is Doppler-shifted by small steps of RV. We took sampling steps of 0.5 km s-1
in our calculations. The correlation curve should ideally be a flat baseline
with a single sharp peak. The mask can be either a simulated model-star stick-
spectrum or a fully calibrated line list obtained in the laboratory.

Two strategies emerged for the intensity of the reference mask: the elements
of the stick spectrum can either be weighted, assuming relative intensities
are known, or given a uniform influence (binary mask). Pepe et al. (2002)
showed that significant improvement in the S/N of the correlation curve can be
achieved with proper weighting, but intensity data are not always available.
We investigated the performance of weighted and binary masks on a subset of
data for FeH where lines were well resolved, and found very little difference
in the S/N, or the RV result. A more sophisticated approach would incorporate
weighting according to the S/N of the stellar spectrum. We have not done this,
as our tests are performed over small spectral regions, but this strategy
would have to be implemented were CC functions to be calculated over a very
wide domain, with different line parameters and S/Ns.

If the correlation calculation gives a successful outcome, the peak is fitted
to a Gaussian function, yielding a RV in the heliocentric rest frame (assuming
the barycentric correction has already been applied to the telescope input
data). A S/N can be obtained by taking the amplitude of the correlation curve
lying outside the correlation peak as noise. We developed procedures to do
this in Igor pro software (Wavemetrics Inc).

##  3 Telescope spectropolarimetric data and laboratory line lists

###  3.1 Stellar spectra from ESPaDOnS, Narval, and SPIRou

Because of our interest in the Zeeman effect in MH molecular radicals, we
selected data for some M-type dwarfs that span a wide range of magnetic
activity, including several stars that are known to host very strong magnetic
fields as test cases. Spectra recorded on ESPaDOnS and its twin instrument
Narval came from the PolarBase (Petit et al., 2014) data archive of stellar
spectropolarimetric observations. Spectra from SPIRou were measured as part of
the SPIRou Legacy Survey222https://SPIRou-legacy.irap.omp.eu described by
Donati et al. (2020), and processed as part of the follow-up SPICE
programme333SPICE: SPIRou Legacy Survey - Consolidation and Enhancement, with
observation time 2022-2024. SPIRou wavelength-calibrated telluric-corrected
spectra and polarimetry data products were obtained using the APERO pipeline
(Cook et al., 2022) installed at the SPIRou Data Centre hosted at the
Laboratoire d’Astrophysique de Marseille. The spectrum for GJ 873 (EV Lac) is
a template constructed by averaging 706 spectra recorded between 24 May 2018
and 13 March 2022, with a S/N ¿ 72. The template for GJ 388 (AD Leo) averaged
348 spectra recorded between 24 May 2018 and 3 November 2020, with S/N ¿ 86.
The template for GJ 411 averaged 947 spectra taken between 26 April 2018 and
12 May 2023. Table 1 lists some reference average magnetic field strengths,
¡B¿, established from Zeeman-broadening and intensification analysis (Shulyak
et al., 2017; Cristofari et al., 2023), of (mostly) Ti i, Fe i, and FeH
signatures.

Table 1: Identification of the cool stars chosen for this study, their average
magnetic field, ¡B¿, and their RVs with respect to the heliocentric rest
frame. Uncertainties are indicated in parentheses, in units of last digit. ¡B¿
values are taken from publications by Reiners et al. (2022)a, Kochukhov
(2021)b, Shulyak et al. (2017)c, and from Cristofari et al. (2023)d. RV values
come from supplementary data associated with work by Lafarga et al. (2020).

Star | Instrument | ¡B¿ | RV |
---|---|---|---|---
|  | Tesla | km s-1 |
GJ 411 | SPIRou | ¡0.02a | -85.02 (2) |
GJ 1002 | ESPaDOnS | 0.08b | -40.12(2) |
GJ 49 | Narval | 0.08((2)c | -6.30 (2) |
GJ 406 (CN Leo) | ESPaDOnS | 0.345(20)d | +19.28 (2) |
GJ 388 (AD Leo) | SPIRou | 0.303(6)d | +12.29 (2) |
GJ 873 (EV Lac) | SPIRou | 0.453(7)d | +0.35 (3) |
GJ 412B (WX UMa) | ESPaDOnS | 0.73(3)c | +69.16(2) |

###  3.2 Laboratory line lists

#### FeH data in the visible.

Most of the high-resolution spectroscopy of FeH in the visible region was
performed by the J.M. Brown group in Oxford in the 1990s, reacting Fe(CO)5
with atomic hydrogen (Fletcher et al., 1990; Carter et al., 1993; Goodridge et
al., 1997; Wilson & Brown, 2001a, b). Several electronic transitions are
known, as illustrated in Fig. 1, originating from the electronic ground state,
and from low-lying sextet states. Strong transitions were observed from the
lowest (metastable) sextet state, a ${}^{6}\Delta$, which was populated under
their laboratory conditions. $\Delta\Omega$ =-1 and 0 transitions in the e
${}^{6}\Pi$ \- a ${}^{6}\Delta$ system around 535 - 540 nm (Goodridge et al.,
1997; Wilson et al., 2001; Wilson & Brown, 2001a), $\Delta\Omega$ = 0 and +1
transitions in the g ${}^{6}\Phi$ \- a ${}^{6}\Delta$ system near 493 nm
(Carter & Brown, 1994) have been reported in the literature. We took
information on the origin (0-0) bands of both systems to create masks for CC
calculations. The e ${}^{6}\Pi$ \- A ${}^{4}\Pi$ transition at 510 nm
indicated with dash-dot line in Fig. 1 is formally spin-forbidden and weak. It
has not been included in the compilation for CC, but will provide a route to
experimental determination of Landé factors for the low-lying A ${}^{4}\Pi$
state in future work.

Figure 1: Some quartet and sextet electronic states of FeH, following Wilson &
Brown (2001a). Arrows denote observations as excitation or fluorescence. Solid
lines show the energy of the lowest spin-orbit component for observed
electronic levels. Faint, broken lines indicate calculated (but currently
unreported) levels from Langhoff & Bauschlicher (1990).

#### FeH data in the near-infrared.

Two quartet systems are well-known contributors to spectra of cool stellar
objects and sunspots. The F ${{}^{4}\Delta}$ \- X ${}^{4}\Delta$ ‘Wing-Ford’
band near 0.99 $\upmu$m studied in detail for example by Wende et al. (2010)
and by Shulyak et al. (2019) is accessible to ESPaDOnS, Narval and SPIRou,
although it falls right at the edge of SPIRou’s spectral response. The E
${{}^{4}\Pi}$ \- A ${}^{4}\Pi$ bands around 1.6 $\upmu$m investigated by
Wallace et al. (2000)) and E ${{}^{4}\Pi}$ \- X ${}^{4}\Delta$ bands around
1.35 $\upmu$m are much better placed for the optics of the SPIRou instrument.
We took line lists from the Kitt Peak National Solar Observatory (NSO)
database (Balfour et al., 2004; Hargreaves et al., 2010) to apply the CC
method to the spectra of some M stars recorded by SPIRou.

#### CrH data.

The origin (0-0) band of the A ${}^{6}\Sigma^{+}$ \- X ${}^{6}\Sigma^{+}$
system of chromium monohydride near 862 nm is a marker proposed by Kirkpatrick
et al. (1999) and by Burrows et al. (2002) for L-type brown dwarfs. Slightly
weaker, the (1-0) band near 764 nm is conveniently placed for laboratory
studies, but it overlaps with the atmospheric A-band of O2, and is therefore
less useful for astrophysical purposes. The A-X (0-1) CrH band at 996.9 nm
mentioned by Reiners et al. (2007) is also quite strong, but lies beneath the
even stronger (0-0) Wing-Ford band of FeH. Still further to the infrared, in
the J-band around $\sim 1.2\leavevmode\nobreak\ \upmu$m, weaker bands of FeH
and CrH again appear together, although the CrH band-head falls in a sparser
region of FeH, according to simulations by Dulick et al. (2003).

Kuzmychov & Berdyugina (2013) noted that CrH could provide a very sensitive
diagnostic for magnetic field, with the degeneracy of rotational levels
splitting very quickly in the presence of very modest magnetic fields. The
Zeeman/Paschen-Back effect in the electronic ground state has been studied and
modelled in the laboratory (Corkery et al., 1991; Lipus et al., 1991), but the
excited states are much more challenging, with very strong perturbations
making the spectra very irregular even in zero-field conditions, as noted by
several authors, notably Ram et al. (1993), Bauschlicher et al. (2001), and
Chowdhury et al. (2006).

The best available CrH atlas, from Burrows et al. (2002) combines constants
derived from unperturbed transitions with ab initio results (including
transition dipole moments) and covers the electronic spectrum of CrH from 0.67
to 1.0 $\upmu$m. This atlas is part of the Bernath (2020) MoLLIST database. It
has been adopted on the ExoMol website developed by Tennyson et al. (2020),
and can be used to generate a synthetic spectrum at any desired temperature or
resolution. This work nevertheless fails to reproduce the true positions of
many spectral features, with ‘observed’ minus ‘atlas’ wavenumbers sometimes in
excess of 1 cm-1; this was reported as a handicap for applications in stellar
spectroscopy by Pavlenko (2005) and Reiners et al. (2007). Focusing on the 0-0
band-head regions, the Lyon group re-recorded laser excitation spectra of CrH
produced in a discharge source in order to fine-tune the reference line list.
An ‘effective parameter’ fit with the PGOPHER program from Western (2017) can
reproduce our transitions with rotational quantum number N${}^{\prime}\leq 15$
with an rms deviation ¡ 0.025 cm-1, assuming an interaction between a single
vibrational level of a ${{}^{4}\Sigma^{+}}$ state and v=0 of A
${{}^{6}\Sigma^{+}}$. Figure 2 illustrates the situation, with the upper
traces corresponding to the PGOPHER and Atlas models, and the lower trace a
small part (11598–11612 cm-1) of a laboratory laser-excitation spectrum at
Doppler resolution. We also recorded the R-head of the (0-0) band of the A-X
system of CrH when forming the molecule between permanent magnets, and
established that PGOPHER reproduces the observed Paschen-Back splittings
properly for fields up to 0.5 tesla. A PGOPHER data file is available in
electronic format from the CDS, as supplementary material.

Figure 2: R-head region of the 0-0 band of 52CrH A-X, at arbitrary scale.
Shown in red is our fit, N’ $<$ 15\. In blue is the calculated absorption
cross-sections from the ExoMol software (Tennyson et al., 2020) based on the
data from Burrows et al. (2002); the full intensity scale for the strongest
line shown is 8 $\times$ 10-15 cm2/molecule. A laboratory spectrum is shown in
black. Dashed green lines indicate significant improvements in our model.

Although a few inaccurate transition wavenumbers will not prevent CrH from
being recognised in a spectrum, they will be critical for magnetic field
diagnostics near the band origin, where the lowest rotational lines produce
the best-resolved magnetic components, and the most distinctive patterns in
Stokes-V signals.

#### NiH data.

The low-lying coupled states of NiH have been studied by Fourier-transform
resolved laser-induced fluorescence, with a view to understanding the
rovibronic structure of this relatively simple system (just three electronic
states are close in energy, each with a single unpaired electron (Gray et al.,
1991; Abbasi et al., 2018; Havalyova et al., 2021). The transitions measured
during this project now form a stand-alone low-temperature line list, and we
used this for the CC calculations here. The original dataset from Vallon et
al. (2009) has since been extended further to the blue (Ross et al., 2012;
Harker et al., 2013); the corresponding data for 58NiH are available on the
ExoMol database444https://www.exomol.com. Ross et al. (2012) and Harker et al.
(2013) also recorded and analysed Zeeman patterns for many but not all of
these transitions.

##  4 Results and discussion

###  4.1 FeH sextet line lists (visible)

The results of three CC calculations for FeH are shown in Fig. 3. The
uppermost trace shows the CC function using the g ${}^{6}\Phi$ \- a
${}^{6}\Delta$ mask alone (117 reference lines in range 20058-20459 cm-1, or
488.65-498.41 nm), and the lowest one uses 116 $\Delta\Omega=\Delta\Lambda$
lines in range 18621-18952 cm-1 (527.50-536.88 nm) in the e ${}^{6}\Pi$ \- a
${}^{6}\Delta$ system. The RVs determined from Gaussian profile fits to the e
- a and g - a correlation peaks differ by 75 m/s. The central trace shows the
sharper and cleaner result obtained when combining these two.

Figure 3: CC functions between the Stokes-I spectrum of the weakly magnetic
star GJ 1002 and (g-a), (e-a), and (g-a + e-a) masks. The curves are shifted
vertically for convenience. The S/Ns on correlation peaks are 7.8 from (g-a),
7.5 from (e-a), and 10.6 from the combined mask.

The g-a and e-a line lists give consistent RV determinations for GJ 1002,
(RV=-40.01$\pm$ 0.03 km s-1), in good agreement with the literature value
indicated in Table 1. Combining the two masks results in a S/N improvement of
the order of $\sqrt{2}$ in the central trace of Fig. 3, as expected from
approximately doubling the number of lines in the mask. We retained the
combined (g-a plus e-a) mask, and applied it next to spectra from increasingly
magnetically active stars. The results are shown in Fig. 4, with CC functions
for four of the stars listed in Table 1. All four show sharp correlation
peaks, confirming that these sextet transitions do contribute to the M-star
spectra. The S/Ns between 7 and 10 in the correlation peaks suggest that this
contribution is significant. The RVs reported in Table 2 are very close to
those obtained from the literature, from Lafarga et al. (2020). The 30%
increase in full-width at half maximum from lowest to topmost trace in Fig. 4
probably reflects a combination of increasing stellar rotation and magnetic
activity.

Figure 4: CC curves (normalised to unity) for Stokes-I spectra of the four
sample M stars using the combined (g-a plus e-a) mask, with 213 lines. Fits to
Gaussian profiles gave: GJ 412 B : RV= 69.1(2), fwhm = 8.8(4) km s-1; GJ 406 :
RV= 19.45(3), fwhm = 6.9(4) km s-1; GJ 49 RV= -6.4(1), fwhm = 6.7(3) km s-1;
and GJ 1002 : RV= -40.01(3), fwhm = 5.9(3) km s-1. The 1$\sigma$ uncertainty
is quoted in parentheses in units of last digit.

To ensure that these correlation peaks are not chance matches, we ran the same
CC calculations with line lists for FeD reported recently by Harvey et al.
(2023). As expected, none of the stellar spectra produced a correlation peak
with FeD data.

#### Laboratory results.

The question then becomes how to generate reliable effective Landé factors for
each of the transitions listed in the g ${}^{6}\Phi$ -a ${}^{6}\Delta$ and e
${}^{6}\Pi$ \- a ${}^{6}\Delta$ datasets. Our laboratory work establishes that
the electronic states involved do not follow pure Hund’s coupling cases (a) or
(b) according to the state symmetry, so some work is required to guide models,
before the least squares deconvolution calculations habitually employed to
determine longitudinal magnetic field from stellar Stokes-V spectra (Donati et
al., 1997) can be applied. Models for unperturbed electronic states (Semenov
et al., 2016; Western, 2017) can give a useful starting point, but need
refining. To initiate this study, some laser excitation spectra were recorded
(at UNB) in static magnetic fields up to 0.6 tesla. Figure 5(a) illustrates a
simple Zeeman pattern, with a splitting of 0.61 cm-1 (=0.17 $\AA$) between the
two $\sigma$ profiles of a P line with unresolved $\Lambda$-doubling. The
individual MJ components are unresolved at Doppler resolution ($\approx$
0.01$\AA$) with our discharge source. The Zeeman pattern shown in Fig. 5(b)
for the Q2(3.5) line is more complex, with well-resolved $\Lambda$-doubling in
zero-field conditions. At 0.56 tesla, the partially resolved MJ structure of
the Q2(3.5) line extends over 0.7 Å. Contributions from the two
$\Lambda$-components overlap. The e ${}^{6}\Pi$\- a${}^{6}\Delta$ system
clearly has potential for magnetic field diagnostics, and we are pursuing this
study in the laboratory.

Figure 5: Zeeman patterns in the e-a system of FeH, showing (a) the P1(4.5)
line ($\uplambda_{\textnormal{vac}}$=533.76 nm) at zero field and at 0.53 T,
with unresolved $\Delta$MJ = +1 and -1 components equidistant from the zero-
field line centre, and (b) the Q2(3.5) line
($\uplambda_{\textnormal{vac}}$=532.54 nm), recorded at 0.56 T, with better-
resolved structure. Note the extended wavenumber scale. Simulations (calc) use
effective gJ Landé factors optimised from the experimental profiles.

Analysis yields effective Landé factors intermediate between Hund’s case (a)
and Hund’s case (b) limiting values. For P1(4.5), g${}^{\prime}_{J}$ =1.393
and g${}^{\prime\prime}_{J}$ = 1.344 ; for Q2(3.5), we find
g${}^{\prime}_{Je}$ =0.906, g${}^{\prime}_{Jf}$=0.887 and
g${}^{\prime\prime}_{Je,f}$ = 1.312. The statistical uncertainties were 0.001.

###  4.2 FeH quartet line lists (infrared)

The F ${{}^{4}\Delta}$ \- X ${}^{4}\Delta$ system of FeH around 1 $\upmu$m has
been extensively studied, and is well established as a diagnostic for
conditions in cool stellar objects (Wallace et al., 1998; Dulick & Valenti,
2000; Shulyak et al., 2010; Reiners & Basri, 2007). We focus here on the E
${{}^{4}\Pi}$ \- A ${}^{4}\Pi$ system in the H band, and the E ${{}^{4}\Pi}$
\- X ${}^{4}\Delta$ system in the J band, as they are ideally suited to
detection with SPIRou, and for analysis of stellar spectra. An extensive high-
temperature line list for the E ${{}^{4}\Pi}$ \- A ${}^{4}\Pi$ system around
1.6 $\upmu$m and for the E ${{}^{4}\Pi}$ \- X ${}^{4}\Delta$ near 1.3
$\upmu$m, (see Fig. 1), was published by Balfour et al. (2004), following
their analysis of a thermal emission spectrum of FeH produced in a King
furnace (T 2400 $\deg$ C), recorded at the NSO at Kitt Peak (NSO archive
catalogue 1983/01/19#2). Wallace & Hinkle (2001) searched for these
transitions in stellar spectra recorded in the 1990s, but reported ‘A cross
correlation of E-A line positions from the King furnace spectrum with an
archival high-resolution 4 m FTS spectrum of the M2 dwarf GJ 411 shows a clean
peak at the stellar velocity even though the S/N ratio is not high enough to
allow detection of individual lines’. The situation is much improved now, with
the sensitivity and resolution offered by SPIRou. The SPIRou spectrum from GJ
411 shows very clear matches with the NSO spectrum in the E-A region (see Fig.
6), and a very similar plot is obtained for AD Leo (GJ 388). This
rehabilitates FeH in the 1.3–1.6 micron region for stellar diagnostics. Souto
et al. (2020) also mentioned this, and added a caveat to the effect that the
reliability of FeH as a temperature indicator is limited by the present
precision of $g$ factors.

Figure 6:  Spectrum of GJ 411 recorded on SPIRou (corrected for RV) with
reference spectra of OH (Hitran database; Gordon et al. 2022) and FeH E-A
bands in blue taken from the NSO spectrum. OH features dominate, but many
matches with FeH are obvious. The I/Ic scale refers to GJ 411, corrected for
baseline continuum. The scales for FeH and OH are arbitrary.

Figure 7 illustrates the outcome of CC calculations to determine RVs for the
stars GJ 411, GJ 388 and GJ 873 from spectra recorded with SPIRou (including
barycentric Earth RV corrections) using the E-X and E-A line lists. The
threefold difference in the S/N in the correlation functions derived from
these two infrared bands partly reflects the transition dipole moments for the
two electronic systems: the E-X bands were actually weaker in the NSO spectrum
than E-A, despite a higher population density in the electronic ground state.
Magnetically inactive GJ 411 gives the sharpest correlation function. For
magnetically active GJ 388, the E-A system at 1.6 $\upmu$m gives RV=12.24(1)
km s-1 and the E-X mask 12.22(1) km s-1 with a slightly broader correlation
peak. The values are compatible with literature values. Both masks perform
less well for GJ 873, although the RV determination of -0.08(1) km s-1 remains
compatible with the values of $0.28\pm 0.13$ and $0.36\pm
0.13\leavevmode\nobreak\ {\rm km\;s^{-1}}$ derived in Morin et al. (2008).
Degraded performance could equally be the consequence of more than one species
contributing to the stellar spectrum. Both the E-X and E-A masks are currently
less than optimal because we used a zero-field mask for lack of Landé factors
when both GJ 388 and GJ 873 are known to be magnetically active (see Table 1).

Figure 7: CC curves for the Stokes-I spectrum of stars GJ 411, GJ 388, and GJ
873 with line positions and intensities extracted from the NSO spectrum of FeH
(Kitt Peak archive). 2094 lines are listed in the E-X system 6320–7400 cm-1
(1.35–1.58 $\upmu$m), and 1613 in the E-A system 5200-6322 cm-1
(1.58–1.92$\upmu$m). Laboratory data were weighted by relative intensities in
both calculations.

Approximate Landé factors for the E-A system, estimated from
spectropolarimetric studies of sunspots (Asensio Ramos et al., 2004), suggest
that neither electronic state follows the limiting Hund’s case coupling
schemes, but no high-resolution laboratory data measurements are yet
available. Our attempts to remedy this were unsuccessful, probably because the
chemistry producing FeH from iron pentacarbonyl and hydrogen atoms yields
mostly ground state products. In fact, we failed to detect E-A transitions
even in zero field conditions in laser excitation, using a low-power diode
laser and InGaAs detector. Zeeman studies were therefore out of the question.
Future work will probably aim to use pump-dump laser experiments via stronger
transitions to obtain this information.

###  4.3 CrH A-X system at 862 nm

CrH has been adopted as a diagnostic tool in the context of L-type brown dwarf
stars (Kuzmychov & Berdyugina, 2013; Kuzmychov et al., 2017) and even
exoplanetary atmospheres (Braam et al. (2021)), but less for the atmospheres
of M-type stars (Pavlenko (2014)). It would be reasonable to expect CrH
signatures to appear alongside, or even overlapping with, FeH features,
between 750 nm and 1 $\upmu$m. We included Paschen-Back effects in CrH to
improve spectral masks and then used them with the CC technique to test for
the presence of CrH in some red dwarf stars. The calculated mask changes
enormously with magnetic field, as illustrated in Fig. 8 where the upper trace
shows a simulation with $\Delta$MJ = $\pm$1) transitions only, corresponding
to $\perp$ linear polarisation in the laboratory with respect to magnetic
field orientation.

Figure 8:  Calculated R lines near the CrH A-X (0-0) band origin. The black
line is at zero field. The red line is a simulation at 0.7 tesla, ($\Delta$MJ
= $\pm$1) transitions only, with the vertical scale multiplied by 5.

We performed CC function calculations, taking masks first from the usual zero-
field atlas from Burrows et al. (2002) and then from a series of predictions
generated with parameters from our PGOPHER fits, taking the ¡B¿ values cited
in Table 2. The PGOPHER predictions between 11502 and 11610 cm-1, or 862 – 869
nm, were restricted to upper state levels v=0,
N${}^{\prime}\leavevmode\nobreak\ \leq$ 15, and calculated for $\Delta$MJ =
$\pm$1 transitions at chosen magnetic field strength. The outcome is shown in
Fig. 9, with the correlation function with the zero-field atlas shown above
the result for non-zero ¡B¿ in each case. The reference atlas performed very
well for GJ 1002, which is known to be a weakly active star with low magnetic
flux. The peak at RV -39.71(2) km s-1 matches determinations from atomic data.
The zero-field atlas actually gives a flatter baseline and narrower
correlation peak than the PGOPHER mask at 0.08 T, from which the RV value is
-39.31(2) km s-1.

The correlation functions taken from field-free masks are particularly
unconvincing for GJ 873, T = 3341 K, ¡B¿ = 0.453 tesla, and GJ 412B, T = 3000
K, ¡B¿ = 0.73 tesla although the telescope spectra are of comparable quality.
The baselines of the correlation functions calculated for the reported ¡B¿
values (red lines) are somewhat smoother in Fig. 9. However, it is also clear
that the sharpness of the correlation function decreases with magnetic field
strength. Several factors contribute. One is that the spectrum becomes quasi-
continuous under the combined effect of Zeeman/Paschen-Back splittings. A
second is that large ‘$v$ sin$i$’ contributions from (rapid) stellar rotation
broaden individual line profiles, and a third is that an average field
strength in the direction of observation is assumed, ignoring any stellar
magnetic field complexity. This will also blur the spectrum.

Figure 9:  CCs (normalised to unity) between spectra of increasingly
magnetically active stars and CrH masks. A zero-field mask was used to compute
the results shown in black. The strongly magnetically active stars give less
noisy correlation plots when the Paschen-Back effect is included (shown in
red). The correlation peak positions are sensitive to ¡B¿. This is clearest
for GJ 412B.

Having found that the CC functions with CrH data yielded plausible RV values,
though performing less well for the stars with low RVs, we tried to use a
similar approach to see if we could also determine average magnetic field
strengths from CC peaks, using the S/N in the correlation peak as criterion
for optimisation. We took GJ 412B as a test case. Masks were calculated for
¡B¿ = 0 to 0.8 tesla, in steps of 0.1 T. The S/N was highest (7) for the mask
calculated at 0.6 T, giving a RV of 69.12(1) km s-1. At 0.7 T, the RV
determined from the CC function was 69.78(2) km s-1. This implies that the A-X
system of CrH is not necessarily the best diagnostic for magnetic field
because of the density of lines, unless reliable RV information is available
from other observations. Given a strong constraint on RV, the CC functions
allow us to retrieve average magnetic field strengths to $\pm$ 0.1 T for GJ
412B and GJ 873 spectra. Laboratory work on CrH is still in progress, and we
will discuss the use of CrH for M-dwarf magnetometry in a subsequent paper.

Figure 10 compares the spectra from ESPaDOnS close to the origin band of the
A-X system of CrH with simulations from PGOPHER. The simulations took
convolutions of line lists with profiles taking into account stellar rotation,
limb-darkening, micro- and macro- turbulence, instrumental resolution and
Doppler widths. The stellar parameters come from the literature (see Table 2).
CrH features are not difficult to recognise in this R-head region for the
cooler stars in our selection. There are some matches for the warmest star in
our selection, GJ 49 with T = 3805 K. Even though the visual match for GJ 388
is less convincing, the corresponding correlation function in Fig. 9 suggests
CrH is present. FeH persists at higher temperatures: the FeH Wing-Ford bands
near 1 $\upmu$m are more prominent in these spectra.

Figure 10: Comparison between models of part of the A-X (0,0) band of CrH
865.56 – 862.57 nm, with spectra (in colour) from the Narval (GJ 49 and GJ
388) and ESPaDOnS (GJ 1002, GJ 406, and GJ 412B) instruments. Blue curves are
for stars whose temperatures are $>$ 3000 K. The upper scale indicates
$\uplambda_{\textnormal{vac}}$ in nm.

###  4.4 NiH: Visible systems

Some 50 years ago, a few features in sunspot spectra were attributed to NiH
(Lambert & Mallia, 1971; Wöhl, 1971), but this has remained controversial. As
far as we know, there have been no reports of NiH signatures in the optical
spectrum of M-type stars. Figure 11 shows that features from several
electronic systems of NiH cover the optical spectrum, without forming
distinctive band-heads seen for CrH and FeH. There is no obvious region where
NiH features are likely to dominate a stellar spectrum. However, working with
this mask taken directly from dispersed fluorescence spectra recorded in Lyon
(Vallon et al., 2009; Ross et al., 2012; Harker et al., 2013), we now have
some evidence from CC peaks displayed in Fig. 12 that NiH does contribute to
the Stokes-I spectra of M stars.

Figure 11:  Laboratory fluorescence spectrum of NiH recorded at 0.7 T. The
upper graphs show three individual lines in 4.5 cm-1 windows to illustrate the
difference in Zeeman response at a given rotational quantum number in three
electronic systems. Note that the Zeeman patterns differ even for the two
$\Lambda$-doublet components of the P(5.5) line, in the top-left plot.

Only three of the M-type stars in our selection gave correlation peaks with
the full NiH mask cited in Sect. 3.2 (2167 lines), which covers a spectral
window 9970–19000 cm-1 (570–740 nm), and assumes that all three lowest-lying
electronic states are thermally populated in the stellar source. Fuxrther
tests showed there was no need to include the full laboratory spectrum in CC
calculations. Only transitions between 13000 and 17500 cm-1 originating from
the v=0 and 1 levels of the electronic ground state
X${}_{1}\;^{2}\Delta_{5/2},$ and from v=0 of X${}_{2}\;^{2}\Delta_{3/2}$,
actually contributed to the correlation peak. The optimised line selection is
included in supplementary data files. Figure 12 shows the resulting CC curves
using the reduced reference mask. Neither GJ 388 (illustrated in Fig. 12) nor
GJ 49, the warmest stars considered here, showed any evidence of correlation
with the NiH line list, but this (modest) increase in temperature does not
explain our observation.

Figure 12: CC functions (normalised to unity) for Stokes-I spectra of four
sample M stars using the mask from the zero-field NiH laboratory work of
Vallon et al. (2009) and Havalyova et al. (2021). The S/N is poor, but the RVs
of the strongest peaks match values derived from atomic data. NiH is not
detected in GJ 388, one of the warmest stars in our sample.

Gaussian fits to the CC functions of Fig. 12 gave RVs very close to the values
given in the literature (see Table 2). Testing with a mask of NiD lines gave
no correlation at all, also suggesting that the small correlation peaks are
not due to chance coincidences in line positions. We conclude that NiH is
present in these mid M-dwarf atmospheres, although we cannot say which of the
electronic bands make significant contributions. It is unsatisfactory in that
we cannot identify individual lines of NiH, but these (often widely spaced)
features overlap with more closely spaced lines in strong bands of TiO across
the visible and near-infrared spectrum, and make only minor contributions to
overall opacity.

Table 2: RVs determined from molecular data, and the parameters (taken from references quoted in Table 1) used for spectral simulations. Magnetic field effects were included for CrH simulations only. Data sources: aLafarga et al. (2020), bCristofari et al. (2022); Cristofari et al. (2023), cMorin et al. (2010), dFouqué, P. et al. (2023), eDonati et al. (2008), fKochukhov (2021), gReiners et al. (2022) Table B1. RV (km s-1) from | GJ 411 | GJ 1002 | GJ 49 | GJ 406 | GJ 388 | GJ 873 | GJ 412B
---|---|---|---|---|---|---|---
| Lalande 21185 |  |  | CN Leo | AD Leo | EV Lac | WX UMa
CrH A-X (0.86 $\upmu$m) |  | -39.31(2) | -4.96(1) | +19.25(1) | +12.58(1) | +1.18(1) | +70.81(2)
FeH E-A (1.6 $\upmu$m) | -84.89(1) |  |  |  | +12.24(1) | -0.08(1) |
FeH E-X (1.3 $\upmu$m) | -84.92(2) |  |  |  | +12.22(1) | -0.08(3) |
FeH (vis) |  | -40.01(3) | -6.4(1) | +19.45(3) |  |  | \+ 69.1(2)
NiH (vis) |  | -39.7(1) | (no CCF) | +19.8(1) | (no CCF) |  | +70.0(1)
Reference RV (km s )a | -85.01(2) | -40.12(2) | -6.30(2) | +19.28(2) | +12.29(2) | +0.35(3) | +69.16(2)
Parameters for simulations |  |  |  |
T (K) | 3601(51)a | 2980(33)b | 3805 | 2899(31)b | 3467(31)b | 3341(31)b | 3000
v sin $i$ (km s-1) | 1.5 [¡2]a | ¡0.1b,d | 1e | 2(1)b | 3(1)b | 3(1))b | 5c
Limb Darkening $\epsilon$ | 0.3 | 0.5 | 0.5 | 0.5 | 0.3 | 0.3 | 0.5
Micro-turbulence $\xi$ (km s-1) | 0.85 | 0.85 | 0.85 | 0.85 | 0.85 |  | 0.85
Macro-turbulence $\zeta$ (km s-1) | 1.35 | 1.35 | 1.35 | 1.35 | 2.3 | 2.3 | 1.35
Instrument resolving power | 70000 | 65000 | 65000 | 65000 | 70000 | 70000 | 65000
¡B¿ (tesla) | ¡0.02g | 0.08f | 0.08(2)f | 0.345(20)b | 0.303(6)b | 0.453(7)b | 0.73(3)f

The overview of RV determinations presented in Table 2 shows that RVs are for
the most part determined to within 0.5 km s-1 of the reference values taken
from Lafarga’s compilation. The 1 $\sigma$ statistical uncertainties quoted in
units-of-last-digit, obtained by fitting the clean part of the correlation
peak (away from baseline noise) to a Gaussian function, may be deceptively
small. It is not unusual for absolute RV values to be sensitive to choice of
mask and method. Carmona et al. (2023) discuss this in detail for AD Leo,
deriving RV = 12.695(5) km s-1 with SPIRou data and an infrared mask, and RV =
12.50(2) km s-1 when processing optical domain data with SOPHIE (Spectrographe
pour l’Observation des PHénomènes des Intérieurs stellaires et des
Exoplanètes); in both instances, dozens of measurements taken over many months
were averaged. Both values are considered reliable despite disagreement within
their quoted uncertainties, because the critical quantity is the relative
precision of measurement. Regular or random fluctuations in RV can be detected
and interpreted with respect to a mean value, and it is the variations around
the mean that are important for planet detection.

##  5 Conclusion

We investigated a small selection of early-to-mid M-type main sequence stars
of known small-scale fields, ¡B¿, up to 0.7 tesla, working with spectra
recorded with the ESPaDOnS and SPIRou instruments at the Canada France Hawaii
Telescope and Narval at the Bernard Lyot Telescope. We used existing optical
and near-infrared laboratory data for three molecular species, FeH, CrH, and
NiH, adding new laboratory measurements for CrH to establish reference line
lists. These lists (available for download from the CDS) were then used to
compute CC functions for our target stars in order to: confirm or refute the
detectability of these transition metal MHs in the high-resolution spectra of
cool dwarf stars; and assess their potential for precise velocimetry and
magnetometry. The line lists are intended to be used either as a binary mask
or with intensity patterns predicted from Boltzmann populations and
theoretical transition strengths, as implemented by Burrows et al. (2002).
They should be a useful supplement to established atomic reference lines,
particularly when band structures are at least partly resolved, because they
have the advantages of rarely being saturated and having less extensive
spectral wings.

We illustrate the dramatic change in the absorption spectrum expected to occur
when the magnetic response of CrH in its ${}^{6}\Sigma^{+}$ states is taken
into account, working with an effective Hamiltonian model to reproduce field-
free spin-rotation splittings in the excited state, for low rotational levels.
Even with this restricted database, we show that RVs and even magnetic field
strengths can be predicted from molecular data alone. Optimising the
wavelength range to be included in correlation calculations reduces
computation time and limits the influence of chance coincidences with other
species present. Above 869.4 nm, the CrH A-X 0-0 band overlaps with the 1-0
band of the F-X system of FeH, so it may be appropriate to truncate the CrH
mask to focus on diagnostics from chromium hydride alone. In doing this, we
find evidence for CrH in two of the warmer M stars in our selection, GJ 388
(AD Leo) and GJ 49. This was unexpected since, according to Allard et al.
(2013), CrH is expected to appear clearly only in cooler atmospheres, when
metal monoxides have condensed and contribute less to the gas phase spectrum.
Our work shows that the 860 nm band of CrH, already identified as a valuable
tool for L-type brown dwarf magnetometry (Kuzmychov et al. (2017)), can also
potentially help characterise the magnetic fields of mid-to-late M-dwarf
stars. Stokes-V measurements are likely to be particularly important in this
context because of the spectral density arising from spin-rotation couplings
in this optical system. Our simulations suggest that ¡B¿ values of the order
of 0.08 T could be determined readily from high-resolution Stokes-V spectra,
where Stokes-I features would remain unresolved and difficult to analyse from
line profiles.

Our study, using CC techniques in conjunction with well-chosen electronic
bands, has focused on showing that transition metal hydrides can be detected
in a small selection of cool stars. Therefore, adding these new transitions to
existing masks should help improve statistics for detection, perhaps even in
exoplanets! The possible signatures of CrH in a hot Jupiter, WASP-31b,
reported by Braam et al. (2021) were confirmed this year by Flagg et al.
(2023) and provide a huge incentive to pursue laboratory investigations.

##  6 Acknowledgements

This work was supported by the French Programme National de Physique Stellaire
of CNRS/INSU, (project LABSPIR / AO INSU AA 2022). We also acknowledge funding
from NSERC Canada, and we thank the SPIRou Legacy Survey consortium for
sharing data from the SPIRou instrument. JFD and AK acknowledge funding from
the European Research Council (ERC) under the H2020 research & innovation
programme via grant agreements #740651 NewWorlds (JFD ), and # 716155 SACCRED
(AK). SB, PF, AC, JF-D,JM, acknowledge funding from the French ANR under
contract number ANR18CE310019 (SPlaSH), and from the Investissements d’Avenir
programme (ANR-15-IDEX-02) via the ‘Origin of Life’ project of the Grenoble-
Alpes University.

This work is based on observations obtained at the Bernard Lyot (TBL) and
Canada France Hawaii (CFHT) telescopes. The TBL is operated by the Institut
National des Sciences de l’Univers of the Centre National de la Recherche
Scientifique of France (INSU/CNRS). The CFHT is operated by the CNRC (Canada),
INSU/CNRS (France) and the University of Hawaii. The authors wish to recognise
and acknowledge the very significant cultural role and reverence that the
summit of Maunakea has always had within the indigenous Hawaiian community. We
are most fortunate to have the opportunity to conduct observations from this
mountain. This work also benefited from the SIMBAD CDS database at URL
http://simbad.u-strasbg.fr/simbad, the NASA ADS system at URL
https://ui.adsabs.harvard.edu, the PolarBase database at URL
http://polarbase.irap.omp.eu/, and the ExoMol database at URL
https://www.exomol.com.

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