# Near-infrared spectroscopic indices for unresolved stellar populations. II.
Index measurements

D. Gasparri,1 L. Morelli,1 V. D. Ivanov,2,3 P. François,4 A. Pizzella,5,6 L.
Coccato,2 E. M. Corsini,5,6 E. Dalla Bontà,5,6 L. Costantin,7,8 and M.
Cesetti9
1Instituto de Astronomía y Ciencias Planetarias, Universidad de Atacama,
Copayapu 485, Copiapoó, Chile
2European Southern Observatory, Karl-Schwarzschild-Strasse 2, D-85748 Garching
bei München, Germany
3European Southern Observatory, Avenida Alonso de Córdova 3107, Vitacura,
Santiago, Chile
4GEPI, Observatoire de Paris, PSL Research University, CNRS, Université Paris
Diderot, Sorbonne Paris Cité, 61 Avenue de l’Observatoire, F-75014 Paris,
France
5Dipartimento di Fisica e Astronomia “G. Galilei”, Università di Padova,
vicolo dell’Osservatorio 3, I-35122 Padova, Italy
6INAF-Osservatorio Astronomico di Padova, vicolo dell’Osservatorio 5, I-35122
Padova, Italy
7Centro de Astrobiología (CSIC-INTA), Ctra de Ajalvir km 4, Torrejón de Ardoz,
E-28850 Madrid, Spain
8INAF-Osservatorio Astronomico di Brera, via Brera 28, I-20121 Milano, Italy
9Independent Scholar, viale degli Aironi 4, I-30021, Caorle (VE), Italy
E-mail<EMAIL_ADDRESS>
(Accepted 2021 August 17. Received 2021 July 22; in original form 2021 April
10.)

###### Abstract

We measured the equivalent width of a large set of near-infrared (NIR,
0.8–2.4$\ \mu$m) line-strength indices in the XShooter medium-resolution
spectra of the central regions of 14 galaxies. We found that two aluminum
indices Al at 1.31 $\mu$m and Al1 at 1.67 $\mu$m and the two CO indices CO1 at
1.56 $\mu$m and CO4 at 1.64 $\mu$m are tightly correlated with the velocity
dispersion. Moreover, the NIR Al and CO1 indices show strong correlations with
the optical Mg2 and Mgb indices, which are usually adopted as $alpha$/Fe-
enhancement diagnostics. The molecular FeH1 index at 1.58 $\mu$m tightly
correlates with the optical $\langle$Fe$\rangle$ and [MgFe]’ indices, which
are used as total metallicity diagnostics. The NIR Pa$\beta$ index at 1.28
$\mu$m has a behaviour similar to the optical H$\beta$ index, which is a
diagnostic of mean age. We defined two new composite indices,
$\langle$Al$\rangle$ and [AlFeH], as possible candidates to be used as NIR
diagnostics of total metallicity and $\alpha$/Fe enhancement. The NIR
$\langle$Al$\rangle$ index has a strong correlation with the optical Mg2 and
Mgb indices, while the [AlFeH] index is tightly correlated with the optical
$\langle$Fe$\rangle$ and [${\rm MgFe}$]′ indices. The distribution of the data
points in the NIR Pa$\beta$-$\langle$Al$\rangle$ and Pa$\beta$-[AlFeH]
diagrams mimic that in the optical [${\rm MgFe}$]′-H$\beta$ and the
Mgb-$\langle$Fe$\rangle$ diagrams, which are widely used to constraint the
properties of the unresolved stellar populations. We concluded that some NIR
line-strength indices could be useful in studying stellar populations as well
as in fine-tuning stellar population models.

###### keywords:

infrared: galaxies – galaxies: abundances – galaxies: stellar content –
galaxies: formation – surveys

††pubyear: 2021††pagerange: Near-infrared spectroscopic indices for unresolved
stellar populations. II. Index measurements–References

##  1 Introduction

Since the 1970s when the modern era of galaxy spectroscopy began with the
introduction of image intensifiers (e.g., Image Dissector Scanner at Lick
Observatory (Robinson & Wampler, 1972), many advances were done in the
knowledge of unresolved stellar populations by investigating optical spectra
of galaxies. Nowadays, the line-strength index analysis (e.g., Worthey et al.,
1994; Morelli et al., 2008; Vazdekis et al., 2010; Costantin et al., 2019) and
full spectral fitting (e.g. Sarzi et al., 2006b; Koleva et al., 2009; Morelli
et al., 2015) are standard tools to recover the star-formation history of
galaxies.

Although some pioneeristic works on the strongest near-infrared (NIR, 0.8–2.4
$\mu$m) spectral absorption features date back to the 1990s (Silva et al.,
1994; Origlia et al., 1997), only recently the increasing size and efficiency
of NIR detectors have allowed a comprehensive spectroscopic study of the
$IYJHK$ bands making the NIR domain complementary to the optical range in
studying the stellar populations of galaxies. The need of observing the
optical range at high redshifts triggered the building of the new generation
of NIR-optimised spectrograph (e.g, Mobasher et al., 2010; Cuby et al., 2010;
Cirasuolo et al., 2011), which also offer the chance of having high-quality
data to investigate in detail the NIR spectral energy distribution of nearby
galaxies.

This gives some advantages. For example, the luminosity fraction of stars of
early spectral types diminishes as the wavelength increases (Bica, 1988) and
we can actually isolate the asymptotic giant branch (AGB) and red giant branch
(RGB) components. Indeed, the contribution of stars outside the AGB-RGB
branches is negligible in the $K$ band for all the galaxies independently of
their Hubble type (Kotilainen et al., 2012). Nevertheless, the AGB and RGB
phases are still poorly understood and very difficult to model in the NIR
(Röck et al., 2017; Riffel et al., 2019). On the other hand, the reduced
effect of reddening with respect to the optical range is a crucial advantage
of NIR and it allows to peer into on highly obscured galaxies, otherwise
impossible to be investigated (Engelbracht et al., 1998; Ivanov et al., 2000).
In this context, analysing NIR spectra could help to better understand the
connection between the presence of dust and young stellar populations, as
found for example by Peletier et al. (2007) in the central regions of early-
type spirals. The major observational drawback for NIR spectroscopy is the
strong contamination produced by telluric absorption and atmospheric emission
lines which overlap to interesting spectral features of galaxies even at low
redshift (François et al., 2019).

Different sets of NIR line-strength indices were developed since the early
1980s (Jones et al., 1984; Bica & Alloin, 1987; Cenarro et al., 2003) mainly
focusing on the calcium triplet (CaT) and hydrogen Paschen lines (see Cenarro
et al., 2001, for an extensive review).

Mannucci et al. (2001) investigated some NIR features, at low resolution
($300<R<600$) and facing severe line blending, in a sample of 28 nearby
galaxies covering all the Hubble sequence. Silva et al. (2008) studied some
$K$ band line-strength indices, including the strong CO molecular feature at
2.30 $\mu$m and Ca and Na indices, in a sample of 11 early-type galaxies in
the Fornax cluster. Cesetti et al. (2009) performed low-resolution ($R=1000$)
spectroscopy of 14 early-type galaxies in the wavelength range 1.5–2.4 $\mu$m,
covering the strong Mg feature at 1.50 $\mu$m. Kotilainen et al. (2012)
focused onto the strongest Mg, Si, and CO features detected in the central
regions of a sample of 29 quiescent spiral galaxies, which they measured at a
resolution of $R\sim 600$ in the $H$ and $K$ bands. Röck (2015) defined and
investigated some new line-strength indices in the $JHK$ bands, including
those of the aluminium 1.30 $\mu$m line and other Mg lines. Riffel et al.
(2019) measured several line-strength indices from $I$ to $K$ band in 16
luminous infrared spiral galaxies observed at a resolution of $R=1000$ and in
19 early-type galaxies from literature.

With the increasing number and quality of NIR spectra, large stellar libraries
have been assembled, which either limited to the $JHK$ bands (Ivanov et al.,
2004) or cover the entire NIR range, like the NASA Infrared Telescope Facility
(IRTF) spectral library (Rayner et al., 2009; Villaume et al., 2017) and the
more recent XShooter spectral library (XSL Arentsen et al., 2019). These are
the base for defining and calibrating new NIR line-strength indices and for
building more complete and reliable single stellar population (SSP) models.
The end products of the SSP models are spectra of single burst of star
formations at fixed age, metallicity, and abundance of $\alpha$-elements (Röck
et al., 2015; Röck et al., 2016; Vazdekis et al., 2016). If the assumption of
a SSP or of dominating SSP is not valid (e.g., for E+A galaxies or for
particular galaxy components) the SSP models can be combined with different
luminosity of mass weights to mimic the spectra of multi-component stellar
populations (e.g., Cappellari & Emsellem, 2004) and to also account for an
additional gaseous component (e.g., Sarzi et al., 2006a). This can be done
using either the typical line-strength indices (Mehlert et al., 2003; Sánchez-
Blázquez et al., 2006), or combining the analysis of a set of line-strength
indices (e.g., Zibetti et al., 2017; Costantin et al., 2019), or through a
full spectral fitting analysis (e.g. Morelli et al., 2013; Costantin et al.,
2021).

This is relatively new field of extragalactic research and it still lacks a
reliable system of line-strength indices to be used as a diagnostic tools like
the Lick/IDS ones (Faber et al., 1985; Worthey et al., 1994; Worthey &
Ottaviani, 1997; Thomas et al., 2003). With the aim of filling this void, in
Cesetti et al. (2013) and Morelli et al. (2020) we developed a set of
spectroscopic diagnostics for stellar physical parameters based on NIR
spectral features in the wavelength range 0.8–5 $\mu$m.

In (François et al., 2019, Paper I hereafter), we presented a sample of high
signal-to-noise ratio (SNR) galaxy spectra obtained at medium resolution
($R\sim 4000-5000$) with the XShooter spectrograph (Guinouard et al., 2006)
mounted at the Very Large Telescope (VLT) of the European Southern Observatory
(ESO). These spectra simultaneously map the optical and NIR ranges of galaxy
spectral energy distribution, making easier the direct comparison of spectral
properties of unresolved stellar populations in these regimes. The purpose of
this paper is to analyse these XShooter spectra focusing onto the NIR bands to
investigate the wide set of line-strength indices defined by Cesetti et al.
(2013) and Morelli et al. (2020).

We structured the paper as follows. We introduce our dataset in Section 2. We
describe the measurements of the NIR line-strength indices in Section 3. We
investigate our final set of 40 NIR line-strength indices in Section 4 and
show the correlation among the NIR line-strength indices and with central
velocity dispersion of the galaxies. We focus on the age and metallicity
indicators in Section 5 and show the correlations with with the optical
Lick/IDS line-strength indices. Finally, we discuss the results in Section 6
and present our conclusions in Section 7.

##  2 Spectroscopic data

Medium-resolution spectroscopy was performed performed with the UVB ($R\sim
4000$), VIS ($R\sim 5400$) and NIR ($R\sim 4300$) arms of the ESO XShooter
spectrograph for a sample of 14 nearby galaxies (Prop. Id. 086.B-0900, PI:
Cesetti, M.). The morphological type of the sample galaxies ranges from E to
Sc, central stellar velocity dispersion is between 36 and 335 $\rm
km\;s^{-1}$, and distance is comprised between 13 and 62 Mpc.

The spectra were obtained along the major axis of the galaxies and were co-
added along the spatial direction to map a central region of $1.5\times 1.5$
arcsec2, which corresponds to an area ranging from $65\times 65$ pc2 to
$430\times 430$ pc2 depending on distance, with a typical SNR$\,\sim\,100$
Å-1. In Paper I, we measured the Mg, Fe, and H$\beta$ line-strength indices of
the Lick/IDS system (Faber et al., 1985; Worthey et al., 1994),
$\langle$Fe$\rangle$ mean index (Gorgas et al., 1990), [${\rm MgFe}$]′
combined index (Thomas et al., 2003), and their uncertainties following
Morelli et al. (2004, 2012, 2016). We derived the stellar population
properties of the sample galaxies using the SSP models by Johansson et al.
(2010) and found that ages range from 0.8 to 15 Gyr and metallicities ([Z/H])
from $-0.39$ to $+0.55$ dex.

Considering the SNR, spatial and spectral resolution, wavelength range of the
spectra as well as the Hubble type, age, and metallicity of the sample
galaxies, our data have an unprecedented quality with respect to previous
works and they represent an excellent resource for studying stellar
populations in the NIR bands.

##  3 Definition and measurement of NIR line-strength indices

###  3.1 Line-strength index measurement

In the past 15 years, different authors defined and tested an increasing set
of NIR line-strength indices as possible diagnostic tools (e.g. Silva et al.,
2008; Cesetti et al., 2009; Röck et al., 2015; Riffel et al., 2019, and
references therein). Here, we adopted the definitions given by Cesetti et al.
(2013) for the line-strength indices in $I$ and $K$ bands and by Morelli et
al. (2020) for the $Y$, $I$, and $H$ bands, which rely onto the concept of
sensitivity maps to identify the spectral features which are more sensitive to
age and metallicity. Considering the spectral range of our data, we identified
and measured 75 NIR line-strength indices. This is one of the largest and most
complete set of NIR line-strength indices investigated so far.

For each sample galaxy, we measured the equivalent width (EW) of all the above
NIR line-strength indices as done by Cesetti et al. (2013) and Morelli et al.
(2020) for the IRTF stellar library. In this paper, we adopted the same
spatial aperture used for the measuring the optical line-strength indices in
Paper I. We measured the SNR of each NIR line-strength index in the two
adjacent continuum bands. Ten out of 14 galaxies have a SNR$\,>\,100$ Å-1 for
all the line-strength indices, whereas the line-strength indices of NGC 3423,
NGC 4415 and NGC 7424 have SNR$\,<\,$30 SNR Å-1. In the case of NGC 1600, the
contamination due to the residuals of the sky subtraction prevented us to
measure all the NIR line-strength indices. The errors on indices were derived
from photon statistics and CCD read-out noise, and calibrated by means of
Monte Carlo simulations. For each line-strength index in each spectrum, we
generated 1000 simulations.

We corrected the EWs to zero velocity dispersion following the method of Silva
et al. (2008) and Cesetti et al. (2009). We broadened the spectra of the giant
stars with a spectral type ranging from K0 to M3 in the IRTF library up to 400
$\rm km\;s^{-1}$ with bins of 50 $\rm km\;s^{-1}$. For each NIR line-strength
index, we calculated the correction coefficients with a spline interpolation
of the average broadened EW. In addition, as a sanity check we considered
different samples of stars including the supergiants stars and/or extending to
late G-type stars, and considering stellar spectra from the XSL library. The
correction coefficients are consistent within the uncertainties and match
those calculated by Cesetti et al. (2013) and Morelli et al. (2020) for giant
K-type stars. The uncertainties on the correction coefficients were estimated
following a similar approach of the coefficient determination. We calculated
the rms of the EWs of the stellar spectra with respect to the mean values for
any velocity-dispersion broadening value of any NIR line-strength index. We
made a spline interpolation of the rms values as a function of broadening and
considered this function as representative of the uncertainties associated to
the correction coefficients relative to the considered line-strength index.
The uncertainties in the index EW increase according to the applied
multiplicative factor as pointed out by Trager et al. (2000). For the total EW
uncertainties, we also considered the uncertainties associated to the
correction coefficients, which we added in quadrature to the intrinsic errors.

As the result of the velocity dispersion correction, we identified three
groups of NIR line-strength indices:

  * •

The Ca2, Nadk, and CO12 indices are almost insensitive to the velocity
dispersion broadening with a maximum variation with respect to the zero
velocity-dispersion value smaller than $20\%$ at $\sigma=400$ $\rm km\;s^{-1}$
(Cesetti et al., 2013). The rms of the correction coefficients is
significantly small ($<10\%$).

  * •

The Mg, Al, Si, and molecular line-strength indices, with the exception of few
TO line-strength indices, are very sensitive to the velocity dispersion
broadening with a maximum variation with respect to the zero velocity-
dispersion value larger than $50\%$ at $\sigma=400$ $\rm km\;s^{-1}$ (Morelli
et al., 2020) although the rms of the correction coefficients is small
($<20\%$).

  * •

Many Fe and H line-strength indices are very weak and extremely sensitive to
the velocity dispersion broadening and the rms of the correction coefficients
is very large ($>50\%$).

We decided to investigate only NIR line-strength indices with a SNR$\,>\,20$
Å-1 following Morelli et al. (2020) and to exclude from further investigation
the following indices:

  * •

Pa2, Pa3, Pa4, FeClTi, CSi, Pa$\epsilon$, TiOA, TiOB, Fe, VO, Siy, Pa$\gamma$,
C, K2B, K1, Fe2, Br13, FeH2, Br11, FeI, since they have correction
coefficients for the velocity dispersion broadening with an rms$\,>\,50\%$;

  * •

FeCr, FeI, Br$\delta$, Ca1k, Fe23, Sik, Ca2k, Ca3k, Ca4k, Pa5, Pa6, Na, and
Br$\gamma$, which could be contaminated by telluric absorption and atmospheric
emission;

  * •

Br16 and CO5, because they are clearly contaminated by other spectral
features.

The index denomination follows the definitions by Cesetti et al. (2013) and
Morelli et al. (2020), which are based on the main element that produces the
spectral feature. When more than one line-strength index is identified with
the same name, we added a suffix that refers to the NIR band where it is
observed. We did not detect NIR emission lines in any of the spectra of the
sample galaxies.

Table 1: The final set 40 NIR line-strength indices investigated in this paper. The references are 1 = Morelli et al. (2020); 2 = Cenarro et al. (2001); 3 = Cesetti et al. (2013); 4 = Ivanov et al. (2004); 5 = Silva et al. (2008); 6 = Cesetti et al. (2009); 7 = Riffel et al. (2019); 8 = Origlia et al. (1993); 9 = Conroy & van Dokkum (2012); Villaume et al. (2017); 10 = McLean et al. (2003); Cushing et al. (2005), 11 = Röck et al. (2015). Index | Dominated by | Line limits | Blue continuum | Red continuum | Main | Additional
---|---|---|---|---|---|---
name |  | ($\mu$m) | ($\mu$m) | ($\mu$m) | Reference | Reference
Pa1 | H i (n=3) |  0.8461–0.8474 |  0.8474–0.8484 |  0.8563–0.8577 | 2 |
Ca1 | Ca ii |  0.8484–0.8513 |  0.8474–0.8484 |  0.8563–0.8577 | 2 |
Ca2 | Ca ii |  0.8522–0.8562 |  0.8474–0.8484 |  0.8563–0.8577 | 2 |
Ca3 | Ca ii |  0.8642–0.8682 |  0.8619–0.8642 |  0.8700–0.8725 | 2 |
Mgi | Mg i |  0.8802–0.8811 |  0.8776–0.8792 |  0.8815–0.8850 | 3 |
Ti | Ti i |  0.9780–0.9795 |  0.9750–0.9760 |  0.9800–0.9810 | 1 |
FeH | FeH |  0.9900–0.9950 |  0.9840–0.9850 |  0.9985–0.9995 | 1 | 9,10
Pa$\delta$ | HI |  1.0040–1.0067 |  1.0020–1.0030 |  1.0067–1.0077 | 1 |
FeTi | Fe i, Ti i |  1.0390–1.0408 |  1.0198–1.0210 |  1.0438–1.0446 | 1 |
CN | CN |  1.0868–1.0882 |  1.0640–1.0650 |  1.0892–1.0902 | 1 |
Sr | Sr ii |  1.0913–1.0923 |  1.0892–1.0902 |  1.0978–1.0988 | 1 |
K1A | K i |  1.1670–1.1714 |  1.1560–1.1585 |  1.1716–1.1746 | 1 | 9,10
K1B | K i |  1.1765–1.1800 |  1.1716–1.1746 |  1.1805–1.1815 | 1 | 9,10
Mgj | Mg i |  1.1820–1.1840 |  1.1805–1.1815 |  1.1855–1.1875 | 1 | 7
Sij | Si i |  1.1977–1.2004 |  1.1910–1.1935 |  1.2050–1.2070 | 1 |
SiMg | Si i, Mg i |  1.2070–1.2095 |  1.2050–1.2070 |  1.2050–1.2070 | 1 |
K2A | K i |  1.2415–1.2455 |  1.2350–1.2380 |  1.2460–1.2490 | 1 | 7,10
Pa$\beta$ | H i |  1.2795–1.2840 |  1.2755–1.2780 |  1.2855–1.2873 | 1 |
Al | Al i |  1.3115–1.3168 |  1.3050–1.3075 |  1.3230–1.3250 | 1 | 9,11
Mg1h | Mg i |  1.4850–1.4910 |  1.4830–1.4850 |  1.4910–1.5000 | 1 | 7
Mg2h | Mg i |  1.5000–1.5080 |  1.4910–1.5000 |  1.5100–1.5120 | 1 | 7,4
CO1 |  12CO(2,0) |  1.5570–1.5635 |  1.5480–1.5500 |  1.5930–1.5940 | 1 | 7
Br15 | H i |  1.5670–1.5720 |  1.5480–1.5500 |  1.5930–1.5940 | 1 |
Mg3h | Mg i |  1.5730–1.5800 |  1.5480–1.5500 |  1.5930–1.5940 | 1 | 7
FeH1 | FeH |  1.5820–1.5860 |  1.5480–1.5500 |  1.5930–1.5940 | 1 | 4,7,8
Sih | Si i |  1.5870–1.5910 |  1.5480–1.5500 |  1.5930–1.5940 | 1 | 4,7,8
CO2 |  12CO(2,0) |  1.5950–1.6000 |  1.5930–1.5940 |  1.6160–1.6180 | 1 | 7
CO3 |  12CO(2,0) |  1.6180–1.6220 |  1.6160–1.6180 |  1.6340–1.6370 | 1 | 8
CO4 |  12CO(2,0) |  1.6390–1.6470 |  1.6340–1.6370 |  1.6585–1.6605 | 1 |
Fe3 | Fe i |  1.6510–1.6580 |  1.6340–1.6370 |  1.6585–1.6605 | 1 |
Al1 | Al i |  1.6705–1.6775 |  1.6585–1.6605 |  1.6775–1.6790 | 1 |
COMg |  12CO(2,0), Mg i |  1.7050–1.7130 |  1.6920–1.6960 |  1.7140–1.7160 | 1 | 4
Br10 | H i |  1.7350–1.7390 |  1.7250–1.7280 |  1.7440–1.7480 | 1 |
Mg1k | Mg i |  2.1040–2.1110 |  2.1000–2.1040 |  2.1110–2.1150 | 4 |
Nadk | Na i |  2.2000–2.2140 |  2.1934–2.1996 |  2.2150–2.2190 | 6 |
FeA | Fe i |  2.2250–2.2299 |  2.2133–2.2176 |  2.2437–2.2497 | 5 |
FeB | Fe i |  2.2368–2.2414 |  2.2133–2.2176 |  2.2437–2.2497 | 5 |
Cad | Ca i |  2.2594–2.2700 |  2.2516–2.2590 |  2.2716–2.2888 | 6 |
Mg2k | Mg i |  2.2795–2.2845 |  2.2700–2.2720 |  2.2850–2.2874 | 5 |
CO12 |  12CO(2,0) |  2.2910–2.3070 |  2.2516–2.2590 |  2.2716–2.2888 | 3 |

###  3.2 Final set of indices

The final set of NIR line-strength indices contains 40 entries listed in Table
1.

We performed a visual inspection of the spectra of the sample galaxies and our
conclusions are in line with previous works (e.g. Silva et al., 2008; Conroy &
van Dokkum, 2012; Röck et al., 2017; Alton et al., 2018) and can be summarised
as it follows:

  * •

As expected (Alton et al., 2018), the strongest line-strength indices from
molecular features are those related to the CO bands, in particular the CO12
index at 2.30 $\mu$m. The COMg index at 1.71 $\mu$m is the strongest non-CO
molecular feature. Other molecular indices, like Ti, FeTi, CN, and FeH1 are
weaker but still detectable. The FeH Wing-Ford index, a known gravity
diagnostic (Schiavon et al., 1997; Conroy & van Dokkum, 2012), is very weak
for almost all the sample galaxies confirming the findings by Alton et al.
(2017).

  * •

The strongest line-strength indices from atomic lines are those related to Ca,
Mg, and Al, in particular the Ca1, Ca2, and Ca2 indices at $\sim 0.85$ $\mu$m,
Mg2h index at 1.50 $\mu$m, and Al1 index at 1.67 $\mu$m. The Nadk index at
2.20 $\mu$m and Sij index at 1.59 $\mu$m are remarkable features. The Fe line-
strength indices are generally weak. The line-strength indices from atomic
lines in the $K$ band are weak, but reside in a spectral region free of
contamination.

  * •

Pa1, Pa$\delta$, and Pa$\beta$ are the strongest indices among those related
to hydrogen. The Pa1 virtually disappears for NGC 1600 and NGC 3115 due to
velocity dispersion broadening, with a correction coefficient greater than
$80\%$. Therefore, the Pa1 EW for these two galaxies has to be considered with
caution. The Br15 index is the strongest feature of the Brackett series, but
it is always weaker than the Paschen indices. The Br10 index is very weak in
all the sample galaxies.

The EW and corresponding uncertainty of the NIR line-strength indices measured
with high accuracy for the sample galaxies are listed in Tables 2
(SNR$\,>\,100$ Å-1 ) and 3 (SNR$\,<\,100$ Å-1 ).

Table 2:  The equivalent widths in Å of the NIR line-strength indices of the
sample galaxies with high SNR ($\,>\,100$ Å-1 ).

Index | NGC 584 | NGC 636 | NGC 897 | NGC 1357 | NGC 1425 | NGC 1700 | NC2613 | NGC 3115 | NGC 3377 | NGC 3379
---|---|---|---|---|---|---|---|---|---|---
Pa1 | 0.50 $\pm$ 0.12 | 0.56 $\pm$ 0.10 | 0.52 $\pm$ 0.13 | 0.45 $\pm$ 0.07 | 0.35 $\pm$ 0.05 | 0.19 $\pm$ 0.06 | 0.52 $\pm$ 0.09 | 1.04 $\pm$ 0.25 | 0.44 $\pm$ 0.07 | 0.50 $\pm$ 0.12
Ca1 | 1.40 $\pm$ 0.12 | 1.49 $\pm$ 0.09 | 1.49 $\pm$ 0.14 | 1.44 $\pm$ 0.07 | 1.46 $\pm$ 0.05 | 1.37 $\pm$ 0.13 | 1.38 $\pm$ 0.08 | 1.23 $\pm$ 0.14 | 1.46 $\pm$ 0.07 | 1.41 $\pm$ 0.13
Ca2 | 3.42 $\pm$ 0.08 | 3.61 $\pm$ 0.06 | 3.60 $\pm$ 0.08 | 3.57 $\pm$ 0.05 | 3.67 $\pm$ 0.04 | – | 3.43 $\pm$ 0.06 | 3.44 $\pm$ 0.08 | 3.59 $\pm$ 0.05 | 3.31 $\pm$ 0.07
Ca3 | 2.46 $\pm$ 0.05 | 3.15 $\pm$ 0.04 | 2.89 $\pm$ 0.06 | 3.12 $\pm$ 0.04 | 3.14 $\pm$ 0.03 | – | 3.15 $\pm$ 0.05 | 2.97 $\pm$ 0.07 | 3.05 $\pm$ 0.04 | 2.87 $\pm$ 0.05
Mgi | 0.36 $\pm$ 0.06 | 0.72 $\pm$ 0.06 | 0.53 $\pm$ 0.07 | 0.73 $\pm$ 0.05 | 0.64 $\pm$ 0.04 | 1.37 $\pm$ 0.13 | 0.72 $\pm$ 0.06 | 0.54 $\pm$ 0.05 | 0.55 $\pm$ 0.04 | 0.88 $\pm$ 0.07
Ti | 0.61 $\pm$ 0.04 | 0.53 $\pm$ 0.04 | 0.59 $\pm$ 0.04 | 0.58 $\pm$ 0.03 | 0.62 $\pm$ 0.05 | -0.07 $\pm$ 0.03 | 0.75 $\pm$ 0.04 | -0.33 $\pm$ 0.20 | 0.26 $\pm$ 0.05 | 0.88 $\pm$ 0.13
FeH | 1.56 $\pm$ 0.34 | 0.94 $\pm$ 0.21 | 2.02 $\pm$ 0.45 | 1.04 $\pm$ 0.20 | 0.81 $\pm$ 0.14 | 3.15 $\pm$ 0.75 | 1.01 $\pm$ 0.21 | 0.55 $\pm$ 0.22 | 0.59 $\pm$ 0.12 | -0.08 $\pm$ 0.07
Pa$\delta$ | 0.75 $\pm$ 0.11 | 0.63 $\pm$ 0.10 | 0.83 $\pm$ 0.13 | 0.52 $\pm$ 0.07 | 0.82 $\pm$ 0.07 | 0.90 $\pm$ 0.12 | 0.52 $\pm$ 0.12 | 0.84 $\pm$ 0.13 | 0.77 $\pm$ 0.09 | 0.66 $\pm$ 0.12
FeTi | 0.41 $\pm$ 0.04 | 0.40 $\pm$ 0.04 | 0.28 $\pm$ 0.03 | 0.24 $\pm$ 0.03 | 0.22 $\pm$ 0.04 | 0.34 $\pm$ 0.03 | 0.10 $\pm$ 0.02 | 0.37 $\pm$ 0.03 | 0.34 $\pm$ 0.03 | 0.34 $\pm$ 0.03
CN | 0.62 $\pm$ 0.05 | 0.62 $\pm$ 0.04 | 0.54 $\pm$ 0.05 | 0.43 $\pm$ 0.03 | 0.41 $\pm$ 0.03 | 0.62 $\pm$ 0.05 | 0.50 $\pm$ 0.03 | 0.56 $\pm$ 0.06 | 0.52 $\pm$ 0.03 | 0.59 $\pm$ 0.04
Sr | -0.14 $\pm$ 0.04 | -0.13 $\pm$ 0.03 | -0.10 $\pm$ 0.04 | -0.23 $\pm$ 0.04 | -0.13 $\pm$ 0.02 | -0.11 $\pm$ 0.03 | -0.03 $\pm$ 0.02 | -0.14 $\pm$ 0.04 | -0.15 $\pm$ 0.03 | -0.14 $\pm$ 0.04
K1A | 0.67 $\pm$ 0.06 | 0.48 $\pm$ 0.05 | 0.34 $\pm$ 0.04 | 0.40 $\pm$ 0.04 | 0.79 $\pm$ 0.04 | 0.49 $\pm$ 0.05 | 0.75 $\pm$ 0.04 | 0.46 $\pm$ 0.09 | 0.26 $\pm$ 0.05 | 0.60 $\pm$ 0.09
k1B | 0.66 $\pm$ 0.05 | -0.28 $\pm$ 0.04 | 0.90 $\pm$ 0.06 | 0.28 $\pm$ 0.04 | 0.20 $\pm$ 0.05 | 1.07 $\pm$ 0.06 | 0.83 $\pm$ 0.05 | 1.01 $\pm$ 0.09 | 1.23 $\pm$ 0.06 | 0.69 $\pm$ 0.05
Mgj | 1.17 $\pm$ 0.07 | 0.28 $\pm$ 0.05 | 1.26 $\pm$ 0.07 | 0.87 $\pm$ 0.07 | 1.72 $\pm$ 0.21 | 1.16 $\pm$ 0.06 | 0.93 $\pm$ 0.08 | 1.12 $\pm$ 0.12 | 1.27 $\pm$ 0.07 | 1.03 $\pm$ 0.08
Sij | 0.89 $\pm$ 0.06 | 1.06 $\pm$ 0.06 | 1.09 $\pm$ 0.07 | 0.98 $\pm$ 0.06 | 0.87 $\pm$ 0.04 | 0.89 $\pm$ 0.05 | 0.84 $\pm$ 0.05 | 0.63 $\pm$ 0.06 | 1.02 $\pm$ 0.05 | 0.84 $\pm$ 0.05
SiMg | 0.59 $\pm$ 0.04 | 0.57 $\pm$ 0.04 | 0.51 $\pm$ 0.05 | 0.61 $\pm$ 0.05 | 0.57 $\pm$ 0.03 | 0.45 $\pm$ 0.03 | 0.69 $\pm$ 0.05 | 0.28 $\pm$ 0.05 | 0.46 $\pm$ 0.04 | 0.42 $\pm$ 0.06
K2A | 1.06 $\pm$ 0.04 | 0.99 $\pm$ 0.04 | 1.44 $\pm$ 0.06 | 1.02 $\pm$ 0.03 | 0.57 $\pm$ 0.02 | 0.69 $\pm$ 0.03 | 0.81 $\pm$ 0.03 | 1.07 $\pm$ 0.04 | 0.91 $\pm$ 0.02 | 0.97 $\pm$ 0.03
Pa$\beta$ | 1.94 $\pm$ 0.08 | 1.99 $\pm$ 0.08 | 1.52 $\pm$ 0.08 | 1.63 $\pm$ 0.07 | 1.69 $\pm$ 0.05 | 1.80 $\pm$ 0.08 | 1.98 $\pm$ 0.08 | 1.72 $\pm$ 0.08 | 1.67 $\pm$ 0.06 | 1.56 $\pm$ 0.07
Al | 1.99 $\pm$ 0.08 | 1.54 $\pm$ 0.06 | 1.83 $\pm$ 0.08 | 1.72 $\pm$ 0.06 | 1.04 $\pm$ 0.02 | 2.05 $\pm$ 0.11 | 1.58 $\pm$ 0.05 | 2.04 $\pm$ 0.09 | 1.53 $\pm$ 0.07 | 2.04 $\pm$ 0.09
Mg1h | 1.48 $\pm$ 0.38 | 1.75 $\pm$ 0.38 | 1.57 $\pm$ 0.43 | 1.73 $\pm$ 0.32 | 1.58 $\pm$ 0.22 | 1.93 $\pm$ 0.53 | 1.28 $\pm$ 0.25 | 1.91 $\pm$ 0.61 | 1.78 $\pm$ 0.37 | 1.72 $\pm$ 0.47
Mg2h | 4.26 $\pm$ 0.20 | 4.44 $\pm$ 0.16 | 4.34 $\pm$ 0.24 | 4.47 $\pm$ 0.15 | 3.89 $\pm$ 0.10 | 4.39 $\pm$ 0.23 | 4.31 $\pm$ 0.14 | 4.44 $\pm$ 0.32 | 4.45 $\pm$ 0.17 | 3.70 $\pm$ 0.23
CO1 | 5.02 $\pm$ 0.21 | 4.99 $\pm$ 0.19 | 5.23 $\pm$ 0.23 | 4.38 $\pm$ 0.18 | 4.10 $\pm$ 0.16 | 4.61 $\pm$ 0.20 | 4.32 $\pm$ 0.20 | 5.21 $\pm$ 0.23 | 4.87 $\pm$ 0.19 | 5.14 $\pm$ 0.22
Br15 | 1.46 $\pm$ 0.28 | 1.96 $\pm$ 0.31 | 1.85 $\pm$ 0.39 | 1.75 $\pm$ 0.26 | 1.38 $\pm$ 0.18 | 1.69 $\pm$ 0.34 | 1.44 $\pm$ 0.25 | 1.24 $\pm$ 0.29 | 0.93 $\pm$ 0.17 | 1.95 $\pm$ 0.39
Mg3h | 7.20 $\pm$ 0.31 | 6.61 $\pm$ 0.27 | 6.20 $\pm$ 0.29 | 6.68 $\pm$ 0.27 | 6.11 $\pm$ 0.23 | 6.34 $\pm$ 0.28 | 5.76 $\pm$ 0.26 | 6.64 $\pm$ 0.31 | 5.75 $\pm$ 0.24 | 6.40 $\pm$ 0.29
FeH1 | 2.64 $\pm$ 0.24 | 2.41 $\pm$ 0.20 | 2.52 $\pm$ 0.26 | 2.47 $\pm$ 0.20 | 2.54 $\pm$ 0.18 | 2.12 $\pm$ 0.21 | 1.94 $\pm$ 0.19 | 2.56 $\pm$ 0.27 | 2.06 $\pm$ 0.18 | 2.56 $\pm$ 0.25
Sih | 4.59 $\pm$ 0.16 | 4.15 $\pm$ 0.15 | 4.48 $\pm$ 0.17 | 4.15 $\pm$ 0.15 | 4.48 $\pm$ 0.15 | 4.20 $\pm$ 0.15 | 4.42 $\pm$ 0.17 | 4.39 $\pm$ 0.15 | 3.96 $\pm$ 0.14 | 4.29 $\pm$ 0.16
CO2 | 3.55 $\pm$ 0.27 | 3.67 $\pm$ 0.24 | 3.34 $\pm$ 0.24 | 3.76 $\pm$ 0.19 | 3.47 $\pm$ 0.16 | 3.56 $\pm$ 0.25 | 3.29 $\pm$ 0.20 | 3.41 $\pm$ 0.29 | 2.71 $\pm$ 0.17 | 3.09 $\pm$ 0.21
CO3 | 4.85 $\pm$ 0.19 | 4.52 $\pm$ 0.18 | 4.69 $\pm$ 0.18 | 4.94 $\pm$ 0.20 | 4.50 $\pm$ 0.16 | 4.11 $\pm$ 0.18 | 4.27 $\pm$ 0.18 | 3.98 $\pm$ 0.17 | 4.55 $\pm$ 0.17 | 3.74 $\pm$ 0.15
CO4 | 3.80 $\pm$ 0.08 | 4.27 $\pm$ 0.08 | 4.22 $\pm$ 0.09 | 3.77 $\pm$ 0.09 | 3.94 $\pm$ 0.08 | 4.14 $\pm$ 0.08 | 3.30 $\pm$ 0.07 | 4.31 $\pm$ 0.10 | 4.47 $\pm$ 0.08 | 4.02 $\pm$ 0.08
Fe3 | -0.20 $\pm$ 0.07 | 0.62 $\pm$ 0.12 | 0.99 $\pm$ 0.23 | 1.17 $\pm$ 0.20 | 0.19 $\pm$ 0.06 | 0.81 $\pm$ 0.19 | 0.35 $\pm$ 0.08 | 0.48 $\pm$ 0.16 | 1.13 $\pm$ 0.18 | 0.21 $\pm$ 0.08
Al1 | 4.05 $\pm$ 0.38 | 3.88 $\pm$ 0.24 | 4.42 $\pm$ 0.39 | 3.64 $\pm$ 0.17 | 3.39 $\pm$ 0.23 | 3.43 $\pm$ 0.31 | 3.44 $\pm$ 0.21 | 4.45 $\pm$ 0.50 | 4.08 $\pm$ 0.21 | 4.11 $\pm$ 0.41
COMg | 5.25 $\pm$ 0.12 | 5.16 $\pm$ 0.11 | 4.71 $\pm$ 0.11 | 5.22 $\pm$ 0.12 | 5.18 $\pm$ 0.10 | 4.59 $\pm$ 0.11 | 5.01 $\pm$ 0.11 | 4.99 $\pm$ 0.12 | 5.02 $\pm$ 0.11 | 4.95 $\pm$ 0.11
Br10 | 1.24 $\pm$ 0.09 | 1.16 $\pm$ 0.07 | 1.74 $\pm$ 0.11 | 1.25 $\pm$ 0.07 | 1.19 $\pm$ 0.06 | 1.45 $\pm$ 0.09 | 1.08 $\pm$ 0.07 | 1.32 $\pm$ 0.09 | 1.18 $\pm$ 0.08 | 1.13 $\pm$ 0.09
MgIk | 2.02 $\pm$ 0.07 | 1.64 $\pm$ 0.06 | 1.81 $\pm$ 0.07 | 1.77 $\pm$ 0.07 | 1.08 $\pm$ 0.05 | 1.56 $\pm$ 0.05 | 1.97 $\pm$ 0.06 | 1.31 $\pm$ 0.05 | 1.37 $\pm$ 0.05 | 1.20 $\pm$ 0.04
Nadk | 5.22 $\pm$ 0.24 | 5.56 $\pm$ 0.22 | 4.34 $\pm$ 0.23 | 5.28 $\pm$ 0.17 | 3.73 $\pm$ 0.17 | 5.22 $\pm$ 0.25 | 3.89 $\pm$ 0.15 | 5.71 $\pm$ 0.33 | 5.02 $\pm$ 0.19 | 4.12 $\pm$ 0.20
FeA | 1.00 $\pm$ 0.06 | 1.49 $\pm$ 0.10 | 1.05 $\pm$ 0.08 | 1.09 $\pm$ 0.08 | 1.27 $\pm$ 0.08 | 2.04 $\pm$ 0.11 | 1.00 $\pm$ 0.07 | 1.18 $\pm$ 0.08 | 1.47 $\pm$ 0.07 | 1.10 $\pm$ 0.08
FeB | 1.13 $\pm$ 0.08 | 1.11 $\pm$ 0.10 | -0.04 $\pm$ 0.03 | 0.59 $\pm$ 0.07 | 0.60 $\pm$ 0.08 | 1.24 $\pm$ 0.09 | 0.61 $\pm$ 0.06 | 0.30 $\pm$ 0.03 | 0.36 $\pm$ 0.04 | 0.26 $\pm$ 0.04
Cad | 2.26 $\pm$ 0.11 | 1.81 $\pm$ 0.17 | 2.62 $\pm$ 0.16 | -0.46 $\pm$ 0.20 | 3.60 $\pm$ 0.19 | 2.94 $\pm$ 0.11 | 1.48 $\pm$ 0.13 | 3.57 $\pm$ 0.14 | 3.28 $\pm$ 0.11 | 2.93 $\pm$ 0.12
Mg2k | 1.15 $\pm$ 0.09 | 1.07 $\pm$ 0.11 | 0.62 $\pm$ 0.07 | 0.96 $\pm$ 0.05 | 0.52 $\pm$ 0.08 | 0.30 $\pm$ 0.05 | 1.52 $\pm$ 0.17 | 0.66 $\pm$ 0.06 | 0.80 $\pm$ 0.05 | 0.67 $\pm$ 0.05
CO12 | 23.48 $\pm$ 0.21 | 21.47 $\pm$ 0.27 | 18.42 $\pm$ 0.25 | 24.85 $\pm$ 0.33 | 20.40 $\pm$ 0.22 | 20.95 $\pm$ 0.18 | 23.22 $\pm$ 0.23 | 23.40 $\pm$ 0.26 | 23.26 $\pm$ 0.15 | 22.30 $\pm$ 0.20

Table 3: The equivalent widths in Å of the NIR line-strength indices of the sample galaxies with low SNR ($\,<\,100$ Å-1 ). Index name | NGC 1600 | NGC 3423 | NGC 4415 | NGC 7424
---|---|---|---|---
Pa1 | -0.82 $\pm$ 0.28 | 0.56 $\pm$ 0.13 | 0.31 $\pm$ 0.05 | 0.25 $\pm$ 0.08
Ca1 | 0.98 $\pm$ 0.14 | 1.95 $\pm$ 0.16 | 1.28 $\pm$ 0.06 | 1.35 $\pm$ 0.10
Ca2 | 3.23 $\pm$ 0.09 | 3.97 $\pm$ 0.19 | 3.37 $\pm$ 0.07 | 3.51 $\pm$ 0.11
Ca3 | 3.07 $\pm$ 0.10 | 3.12 $\pm$ 0.08 | 3.13 $\pm$ 0.09 | 3.84 $\pm$ 0.14
Mgi | 0.57 $\pm$ 0.08 | 0.28 $\pm$ 0.04 | 0.71 $\pm$ 0.05 | 0.48 $\pm$ 0.05
Ti | 0.43 $\pm$ 0.07 | 1.02 $\pm$ 0.14 | 0.41 $\pm$ 0.15 | 0.35 $\pm$ 0.08
FeH | – | – | – | –
Pa$\delta$ | – | – | – | –
FeTi | 0.18 $\pm$ 0.05 | – | – | –
CN | – | 1.16 $\pm$ 0.10 | 0.16 $\pm$ 0.10 | –
Sr | – | 0.05 $\pm$ 0.10 | -0.18 $\pm$ 0.06 | 0.14 $\pm$ 0.11
K1A | – | 1.16 $\pm$ 0.20 | 1.11 $\pm$ 0.14 | 1.02 $\pm$ 0.33
k1B | – | 0.30 $\pm$ 0.20 | 0.61 $\pm$ 0.12 | 1.73 $\pm$ 0.34
Mgj | 1.46 $\pm$ 0.15 | 1.04 $\pm$ 0.11 | – | –
Sij | 1.15 $\pm$ 0.12 | 0.24 $\pm$ 0.15 | 0.53 $\pm$ 0.14 | 0.95 $\pm$ 0.23
SiMg | – | – | – | –
K2A | – | – | – | –
Pa$\beta$ | 1.45 $\pm$ 0.10 | 1.97 $\pm$ 0.29 | – | 3.03 $\pm$ 0.50
Al | 1.99 $\pm$ 0.12 | 1.72 $\pm$ 0.16 | 0.86 $\pm$ 0.14 | -0.10 $\pm$ 0.49
Mg1h | 1.04 $\pm$ 0.35 | 2.05 $\pm$ 0.48 | 2.85 $\pm$ 0.24 | –
Mg2h | 4.19 $\pm$ 0.36 | – | – | –
CO1 | – | – | – | –
Br15 | 1.87 $\pm$ 0.62 | 1.53 $\pm$ 0.51 | 2.38 $\pm$ 0.29 | –
Mg3h | 5.86 $\pm$ 0.38 | – | – | –
FeH1 | 2.25 $\pm$ 0.38 | 1.52 $\pm$ 0.46 | 2.15 $\pm$ 0.25 | 0.77 $\pm$ 0.78
Sih | 3.32 $\pm$ 0.20 | 3.68 $\pm$ 0.45 | 4.17 $\pm$ 0.25 | 3.88 $\pm$ 0.76
CO2 | 3.44 $\pm$ 0.40 | 3.08 $\pm$ 0.23 | – | –
CO3 | 4.57 $\pm$ 0.23 | – | 4.22 $\pm$ 0.23 | 5.19 $\pm$ 0.43
CO4 | 4.01 $\pm$ 0.13 | 1.93 $\pm$ 0.20 | 2.96 $\pm$ 0.25 | 2.76 $\pm$ 0.39
Fe3 | – | – | 1.71 $\pm$ 0.29 | 0.02 $\pm$ 0.35
Al1 | 4.56 $\pm$ 0.60 | 2.28 $\pm$ 0.18 | 3.98 $\pm$ 0.15 | 1.96 $\pm$ 0.26
COMg | – | 3.85 $\pm$ 0.19 | – | –
Br10 | 2.29 $\pm$ 0.16 | 1.29 $\pm$ 0.20 | 0.87 $\pm$ 0.20 | –
MgIk | – | – | – | –
Nadk | – | – | – | –
FeA | – | – | – | –
FeB | – | – | – | –
Cad | – | – | – | –
Mg2k | – | – | – | –
CO12 | – | – | – | –

##  4 Results

In this section, adopting a completely phenomenological approach, we present
the properties of the NIR line-strength and their correlations with the
velocity dispersion of the galaxies.

###  4.1 NIR-NIR correlations

We started correlating each other the NIR line-strength indices to identify
the most promising diagnostic of the properties of unresolved stellar
populations. We adopted this approach with twofold aim of investigating the
possible linear correlations between the NIR line-strength indices related to
different elements and between the NIR line-strength indices based on the same
element. We performed a linear regression considering both X and Y
uncertainties through the data points and we calculated their Pearson
correlation coefficient $R$ with the CORR Pearson function of the PANDAS111W.
McKinney, pandas: a python data analysis library,
http://pandas.sourceforge.net Python package.

Fig. 1 displays the correlation map for the final set of 40 NIR line-strength
indices grouped by elements with increasing wavelength. For showing purposes,
we cut the colour scale to $|R|>0.5$. We refer to a moderate correlation if
$0.5<|R|<0.7$ and to a strong correlation when $|R|>0.70$. The reddest and
bluest squares mark to strongest correlations and anti-correlations,
respectively.

The plot diagonal hosts the correlations of the NIR line-strength indices with
themselves, which give a Pearson coefficient $R=1$ by definition. To avoid
spurious correlations due to large EW errors, we considered only the
correlations with $|R|>0.5$ for NIR line-strength indices with a SNR$\,>\,20$
Å-1, as done by Morelli et al. (2020). In some spectra, some line-strength
indices do not pass the SNR threshold because they are contaminated by
residuals of the subtraction telluric absorption and/or atmospheric emission,
while, in the same spectra, other line-strength indices always have
SNR$\,>\,20$ Å-1 (e.g. Pa$\beta$). Furthermore, we considered only the
correlations that still hold with $|R|>0.5$ when one random galaxy is removed
from the analysis to account for the small number statistics of our galaxy
sample.

We found that only 20 out of the possible 780 correlations between the NIR
line-strength indices and velocity dispersion are strong, while about 100
correlations can be classed as moderate (Fig. 1). The strongest correlations
between the NIR line-strength indices are shown in Fig. 2 and include the
Mg1h-Ca2 and FeH1-Mg3h correlations already discovered by Riffel et al.
(2019). In these cases, the slope and Pearson correlation coefficient obtained
for our sample galaxies are consistent with those found by Riffel et al.
(2019). The correlations between the Al1 and CO1 indices ($R=0.92$) and
between the Al1 and FeH1 indices ($R=0.83$) are strongest ones. The Pa$\beta$
index does not show any strong correlation with any of the line-strength index
based on hydrogen lines, which are in general very weak. On the other hand,
the Pa$\beta$ index tightly correlates with the Al and FeH1 indices (Fig. 2).

In Fig. 2 we also show the distribution of the morphological types of the
sample galaxies. We found that the EWs of metal line-strength indices (e.g.,
Al and FeH1) are larger for the early-type galaxies and smaller for the late-
type ones (see also Riffel et al. 2019). NGC 3423 and NGC 7424 have a distinct
behaviour with respect the other sample galaxies as they tend to lie in a
separate region of the parameter space. We suggest this is due to the fact
that they are the only two late-type, low velocity dispersion, young and
metal-poor galaxies of our sample (Paper I). Therefore, their stellar
populations are different from that of the early-type galaxies that constitute
most of our galaxy sample. For this reason, we considered these two galaxies
interesting to unveil the global trends observed in line-strength indices
moving from early to late-type galaxies. However, we are aware that this issue
needs further investigation by increasing the number of young late-type
galaxies.

###  4.2 NIR-$\sigma$ correlations

In the optical regime, the correlation between some optical line-strength
indices (e.g., Mg2, $\langle$Fe$\rangle$, and H$\beta$) and velocity
dispersion was first found for early-type galaxies (e.g., Burstein et al.,
1988; Bender et al., 1993; Bernardi et al., 1998; Mehlert et al., 2003) and
then it was demonstrated to hold also for late-type galaxies too (e.g.,
Moorthy & Holtzman, 2006; Sánchez-Blázquez et al., 2006; Morelli et al.,
2008). In the NIR domain, Cenarro et al. (2003) discovered a strong anti-
correlation between the CaT index and velocity dispersion in the central
regions of 35 early-type galaxies. Falcón-Barroso et al. (2003) found that
this anti-correlation also holds for spiral bulges. Finally, the correlation
between $K$-band line-strength indices (e.g., Na, Ca, and CO) and velocity
dispersion was pointed out by Silva et al. (2008); Mármol-Queraltó et al.
(2009); Röck et al. (2017).

We investigated the correlation between the NIR line-strength indices and
velocity dispersion of the sample galaxies and show their Pearson coefficient
in Fig. 1. We found that several NIR line-strength indices (Pa$\beta$, Br10,
Ca1, Ca2, Mg1h, SiMg, Al, Al1, CO1, CO4, FeH1, and CN) show moderate-to-strong
correlation with velocity dispersion. The strongest correlations between the
NIR line-strength indices and velocity dispersion are shown in Fig. 3.

We found that the Al and Al1 indices are tightly correlated with velocity
dispersion, while the Pa$\beta$ index shows a moderate anti-correlation with
it. This trend resembles what observed for the H$\beta$ index in the optical
regime (Ganda et al., 2007; Morelli et al., 2008). Among the CO indices, the
CO1 and CO4 indices display the stronger correlation with velocity dispersion.
In the first and second panel of Fig.3 correlations with the velocity
dispersion are shown for the optical Mg2 and the CaT. Their trends are
consistent with previous findings (Burstein et al., 1988; Cenarro et al.,
2003).

Figure 1: The correlation matrix for the final set of 40 NIR line-strength
indices and velocity dispersion for the sample galaxies. Different colours
correspond to different degrees of correlation according to Pearson
statistics. For sake of clarity, only the moderate and strong correlations and
anti-correlations (with Pearson coefficient $0.5<|R|<0.7$ and $|R|>0.7$,
respectively) are shown. The correlations of the NIR line-strength indices
with themselves and velocity dispersion with itself (giving $R=1$ by
definition) lie on the plot diagonal. Figure 2: The stronger correlations
between the NIR line-strength indices for the sample galaxies. Galaxies are
colour coded according to their Hubble type from the Lyon Extragalactic
Database (Makarov et al., 2014). The size of each circle is proportional to
the velocity dispersion of the galaxy. The best-fitting linear relations for
all the sample galaxies (red solid line) and excluding NGC 584, NGC 636, and
NGC 2613 (green dashed line) are shown with their Pearson coefficient. Figure
3: The stronger correlations between the NIR line-strength indices and
velocity dispersion for the sample galaxies. The symbols are the same as in
Fig. 2.

##  5 Age and metallicity indicators

In the previous sections, we found that some indices associated to metal
elements do correlate among themselves (e.g. Al, All, Pa$\beta$, CO1, FeH1).
The linear correlation between these indices, in addition to the fact that
their values are larger in more massive galaxies, as it happens for the metal
indices in the optical regime (Sánchez-Blázquez et al., 2006; Morelli et al.,
2008), is particularly interesting since it suggests a connection between them
and the metallicity of the galaxies.

In Section 4 we also found a trend between values of Pa$\beta$ and the
morphological type of the galaxies. Even if there are some notably exceptions,
the old spheroids of ellipticals and early-types show on average lower values
of Pa$\beta$ with respect to the bulges of spirals galaxies (Fig. 2 and Fig.
3). Since in general spheroids of ellipticals and early-type are older than
the bulges of late-type galaxies, this result is a hint that Pa$\beta$ could
be a good candidate to trace the age of the stellar populations.

To better investigate the possible use the NIR line-strength indices as age
and metallicity indicators, we compared them with a set of optical indices
known to be the best diagnostics of unresolved stellar populations in
galaxies. We used the H$\beta$ index as age indicator, the
$\langle$Fe$\rangle$, Mg2, Mgb, and the [${\rm MgFe}$]′ (Thomas et al., 2003)
as metallicity tracers. We measured their values for all the sample galaxies
in Paper I.

###  5.1 Trends with age indicators

The H$\beta$ index is widely used as age indicator for unresolved stellar
populations (e.g., Worthey et al., 1994; Lee et al., 2000). We expect that
some the line-strength indices based on H we studied could represent the NIR
counterpart of the H$\beta$ index. Except for $Pa\beta$, we did not find any
strong trend with the H$\beta$ index of the Pa1, Pa$\delta$, Br15, and Br10
indices. However, these indices as we measured in our spectra are too weak
and/or contaminated by residuals of sky subtraction to allow a robust
comparisons with the H$\beta$ index.

Fig. 4 shows the correlation between the H$\beta$ and Pa$\beta$ indices. This
correlation is driven by the very young population resulting from the low SNR
spectrum of NGC 7424 ($R=0.91$), but it still holds ($R=0.58$) if we do not
consider this galaxy.

Figure 4: The correlation between the NIR Pa$\beta$ index and optical H$\beta$
index for the sample galaxies. The symbols are the same as in Fig. 2.

In Fig. 4 we noticed that three galaxies seems to be shifted with respect to
other sample galaxies having a $Pa\beta$ index $\sim 0.3$ dex larger compared
with galaxies of similar H$\beta$ index. They are the Sb galaxy NGC 584 and
the two elliptical galaxies NGC 636 and NGC 2613. They have an intermediate-
to-old age ($T=6-10$ Gyr) with super-solar metallicity ($[Z/{\rm
H}]=0.24-0.32$ dex) and $\alpha$/Fe enhancement ($[\alpha/{\rm Fe}]=0.20-0.25$
dex). To further investigate their behaviour, we fitted a linear relation by
excluding the three galaxies (Fig. 4). The Pearson coefficient improved from
$R=0.91$ to 0.97 and the correlation slope became slightly shallower, but it
did not change the increasing trend of the $Pa\beta$ index with the H$\beta$
index. We expect to strengthen this result and better constrain the slope of
the $Pa\beta$-H$\beta$ relation with more young galaxies in the high-end
region of the H$\beta$ index ($EW=3-5$ Å).

###  5.2 Trends with the metal indices

The optical Mg2 and Mgb indices are sensitive to $\alpha$ elements, while the
$\langle$Fe$\rangle$ index is sensitive to the abundance of the elements of
the iron group. They are used to infer the total metallicity and $\alpha$/Fe
enhancement together with the [${\rm MgFe}$]′ index.

We found that none of line-strength indices based on Fe of our NIR set shows a
strong correlation with the $\langle$Fe$\rangle$ index, with the partial
exception of two $K$-band FeA and FeB indices. However, considering the
weakness of these lines, we preferred to focus our attention to the stronger
FeH1 index.

In Fig. 5 we present the correlations between the Al, Al1, CO1, and FeH1
indices and the Mg2, Mgb, $\langle$Fe$\rangle$, and [${\rm MgFe}$]′ indices.
The strongest correlation between the NIR and optical line-strength indices
are the Al1-Mg2 ($R=0.87$), Al1-Mgb ($R=0.88$), CO1-Mgb ($R=0.88$), and
Al-$\langle$Fe$\rangle$ ($R=0.85$) correlations. The correlations between the
Al1 and CO1 indices and the [${\rm MgFe}$]′ index are poorer with respect to
those with the Mg2 index.

To improve the sensitivity of the NIR line-strength indices to the metallicity
of the galaxies, we defined two new line-strength indices by a linear
combination of those available in our set. First, we considered line-strength
indices due to same element and for which Fig. 1 shows at least a moderate
correlation with some of the optical indices. We did not find any notable
improvement with either the Mg or CO indices, whereas we noticed that
averaging the two Al indices into the combined $\langle$Al$\rangle$ index as

$\langle{\rm Al}\rangle=0.5(Al+Al1)$ (1)

improved the correlations with the Mg2, Mgb, $\langle$Fe$\rangle$, [${\rm
MgFe}$]′ indices. We further tightened these correlations by including the
FeH1 index to define the following combined [AlFeH] index as

$[AlFeH]=Al+0.5Al1+FeH1$ (2)

where we empirically determined the 0.5 coefficient for the Al1 index to
maximise the correlation with the [${\rm MgFe}$]′ index.

Fig. 6 shows the correlations between the two composite indices with velocity
dispersion and Mg2, Mgb, $\langle$Fe$\rangle$, and [${\rm MgFe}$]′ indices.
These two newly defined line-strength indices are the most effective NIR
indices to correlate with the optical metallicity indices. The
$\langle$Al$\rangle$ index traces very well the behaviour of the Mg indices
and maintains a strong correlation with the velocity dispersion, while the
[AlFeH] traces better the behaviour of the $\langle$Fe$\rangle$ and [${\rm
MgFe}$]′ indices.

Figure 5: The correlations between the NIR Al, Al1, CO1, and FeH1 indices and
optical Mg2, Mgb, $\langle$Fe$\rangle$, and [${\rm MgFe}$]′ indices for the
sample galaxies. The symbols are the same as in Fig. 2. Figure 6: The
correlations between the NIR $\langle$Al$\rangle$ and [AlFeH] NIR indices with
velocity dispersion and optical Mg2, Mgb, $\langle$Fe$\rangle$, and [${\rm
MgFe}$]′ indices for the sample galaxies. The symbols are the same as in Fig.
2. Figure 7: The distribution of the measured values of the optical H$\beta$
and [${\rm MgFe}$]′ indices (left panel), NIR Pa$\beta$ and
$\langle$Al$\rangle$ indices (central panel), and NIR Pa$\beta$ and [AlFeH]
indices (right panel) for the sample galaxies. The black and grey lines in the
left panel correspond to the predicted values of the H$\beta$ and [${\rm
MgFe}$]′ indices for a grid of mean ages and total metallicities according to
the models of (Johansson et al., 2010) for an $\alpha/Fe$ enhancement of
[$\alpha$/Fe] = 0.3 dex. Galaxies are colour coded according to their mean
age. Figure 8: The distribution of the measured values of the optical H$\beta$
and [${\rm MgFe}$]′ indices (left panel), NIR Pa$\beta$ and
$\langle$Al$\rangle$ indices (central panel), and NIR Pa$\beta$ and [AlFeH]
indices (right panel) for the sample galaxies. The black and grey lines in the
left panel correspond to the predicted values of the H$\beta$ and [${\rm
MgFe}$]′ indices for a grid of mean ages and total metallicities according to
the models of (Johansson et al., 2010) for an $\alpha/Fe$ enhancement of
[$\alpha$/Fe] = 0.3 dex. Galaxies are colour coded according to their total
metallicity. Figure 9: The distribution of the measured values of the optical
$\langle$Fe$\rangle$ and Mgb indices (left panel), NIR FeH1 and Al1 indices
(central panel), and NIR FeH1 and $\langle$Al$\rangle$ indices (right panel)
for the sample galaxies. The black and grey lines in the left panel correspond
to the predicted values of the $\langle$Fe$\rangle$ and Mgb indices for a grid
of total metallicities and $\alpha$/Fe enhancement according to the models of
(Johansson et al., 2010) for a mean age of 7 Gyr. Galaxies are colour coded
according to their $\alpha$/Fe enhancement.

##  6 Discussion

The Al and Al1 indices are among the strongest atomic features after the Mg
indices and they show a behaviour similar to the Mgb and Mg2 indices. The
origin of the only stable isotope of 27Al is still debated. According to
Nordlander & Lind (2017), it can be produced in neutron-rich environments or
via proton capture. In galaxies, the main sources may be the SNII explosion
and AGB stars, while SNIa explosion produce few or null aluminium. Pignatari
et al. (2016) draw very similar conclusions and pointed out the fact that the
production condition of 27Al is very similar to those of Mg. Considering also
the correlation with the velocity dispersion (Fig. 3), the Al indices could be
related to the formation and evolution of galaxies in the same way as the Mg2
and Mgb indices.

In the 0.8-2.5 $\mu$m range, there are only three iron features that might be
efficiently used as metallicity diagnostic. The two $K$-band FeA and FeB
indices have already been investigated (Silva et al., 2008), but they are weak
and located in a spectral region of low SNR in the spectra of our sample
galaxies. The FeH1 index is located in a spectral region relatively free from
telluric and atmospheric features and not contaminated by other lines. In our
sample galaxies, it is stronger than the FeH WingFord band. For stars the FeH1
index shows a dependence from surface gravity and metallicity (see Figs. D5
and D6 in Morelli et al. 2020). For galaxies the strong correlations of the
FeH1 index with the optical metal line-strength indices support the idea it
could be a good metallicity tracer.

The Pa$\beta$ line is the strongest hydrogen feature for all the galaxies in
our sample. We identified three galaxies, namely NGC 584, NGC 636, NGC 2613,
as possible outliers in the H$\beta$-Pa$\beta$ relation (Fig. 4) and we tested
their behaviour in the relations between the Pa$\beta$ index and Al, Al1, and
FeH1 indices (Fig. 2) as well as between the Pa$\beta$ index and velocity
dispersion (Fig. 3). Although in this case the three galaxies are difficult to
be identified as outliers due to their small shift with respect to the bulk of
the sample galaxies, we excluded them from the linear fit. The new best-
fitting relations are also shown in Figs. 2 and 3. The slope and Pearson
coefficient are nearly the same for the Al-Pa$\beta$ and $\sigma$-Pa$\beta$
relations, while the slope is steeper for the Al1-Pa$\beta$ and FeH1-Pa$\beta$
relations but the trend is the same as before. We conclude that with the
actual number of galaxies and their distribution in the parameter space we can
not firmly conclude on the outlier nature of these galaxies.

The Pa$\beta$ index does not suffer any significant contamination by other
elements. Morelli et al. (2020) probed that the index behaviour in the cool
IRTF stars is driven by temperature, with no trends with surface gravity and
metallicity. Cleri et al. (2020) showed that the Pa$\beta$ index could adopted
as a tracer of the star formation rate in galaxies, showing a similar (and
somewhat even better) behaviour with respect to the H$\alpha$ and H$\beta$
indicators. This supports our findings (Fig. 4) and it suggests that the
Pa$\beta$ index could be also considered as a good age tracer for unresolved
stellar populations in NIR.

We defined the $\langle$Al$\rangle$ and [AlFeH] indices to make available
stronger metallicity and $\alpha$/Fe enhancement indicators in the NIR. The
$\langle$Al$\rangle$ index tightly correlates with velocity dispersion and
optical Mg2 and Mgb indices (Fig. 6) in agreement with the theoretical
findings of Pignatari et al. (2016) and Nordlander & Lind (2017). The [AlFeH]
index is more sensitive to total metallicity, like the optical
$\langle$Fe$\rangle$ and [${\rm MgFe}$]′ indices.

Considering the above correlation, we performed the following speculative
analysis. In the left panels of Figs. 7 and 8, the values of H$\beta$ and
[${\rm MgFe}$]′ of the sample galaxies (Paper I) are compared to the model
predictions of Johansson et al. (2010) for a stellar population with
supersolar $\alpha$/Fe enhancement [$\alpha$/Fe] = 0.3 dex. In this parameter
space, the mean age and total metallicity of the galaxies are almost
insensitive to the variations of $\alpha$/Fe enhancement. The sample galaxies
are colour coded according to their mean age (Fig. 7) and total metallicity
(Fig. 8) which we derived in Paper I. For comparison, the values of
$\langle$Al$\rangle$ and [AlFeH] of the sample galaxies are shown as function
of Pa$\beta$ in the central and right panels of Figs. 7 and 8. The
distributions of data points in the $\langle$Al$\rangle$-Pa$\beta$ and
[AlFeH]-Pa$\beta$ diagrams nicely match that of the [${\rm MgFe}$]′-H$\beta$
diagram. Indeed, the younger and more metal-poor galaxies lie in the left
upper region, while the older and more metal-rich galaxies are in the right
lower region of all the three diagrams. Both the $\langle$Al$\rangle$ and
[AlFeH] indices are very effective in discerning total metallicity when
compared to the [${\rm MgFe}$]′ index. For intermediate ages galaxies, the
Pa$\beta$ index seems slightly less efficient than H$\beta$ in disentangling
mean ages.

In the left panel of Fig. 9, the values of Mgb and $\langle$Fe$\rangle$ of the
sample galaxies (Paper I) are compared to the model predictions of Johansson
et al. (2010) for a stellar populations with an intermediate age of 7 Gyr. In
this parameter space, the total metallicity and $\alpha$/Fe enhancement appear
to be almost insensitive to the variations of age. The sample galaxies in Fig.
9 are colour coded by their total $\alpha$/Fe enhancement, which we derived
using a linear interpolation between the model points with the iterative
procedure described in Morelli et al. (2008) and in Paper I. The values of
$\alpha$/Fe enhancement for the sample galaxies are reported in Table 4. For
comparison, the values of Al1 and $\langle$Al$\rangle$ of the sample galaxies
are shown as function of FeH1 in the central and right panel of Fig. 9,
respectively. The distribution of data points in the Al1-FeH1 and
$\langle$Al$\rangle$-FeH1 diagrams nicely match that of the
Mgb-$\langle$Fe$\rangle$ diagram. This is a promising result, although the
absence of galaxies with extremely high/low values of [$\alpha$/Fe] in our
sample makes difficult to evaluate the effectiveness of these NIR line-
strength indices in constraining the $\alpha$/Fe enhancement.

Following these results, we propose the NIR line-strength indices Pa$\beta$,
$\langle$Al$\rangle$, Al1, FeH1, and as possible counterparts of the optical
indices H$\beta$, [${\rm MgFe}$]′, Mgb, and $\langle$Fe$\rangle$ to
investigate the unresolved stellar populations in the NIR domain for spectra
with medium resolution ($R\sim 5000$) and high SNR ($>100$ Å-1).

##  7 Conclusions

We investigated a set 40 out of the 75 line-strength indices proposed by
Cesetti et al. (2013) and Morelli et al. (2020) in the $I$, $Y$, $J$, $H$, and
$K$ bands for a sample of 14 nearby galaxies observed with the ESO XShooter
spectrograph. The galaxies span all the Hubble morphological sequence with a
mean age range $0.8\leq{\rm age}\leq 15Gyr$ and a total metallicity range
$-0.39\leq[Z/{\rm H}\leq 0.55$ dex. Up to date, this is the largest set of
line-strength indices measured and tested in the NIR domain.

We found that some of the studied NIR line-strength indices are promising
candidate to constrain the properties of unresolved stellar populations in
galaxies. To further explore this idea, we compared them with the most-widely
used optical age and metallicity indicators.

The Al, Al1, CO1, and FeH1 indices were found to be strongly correlated with
the optical Mg2 and Mgb indices sensitive to $\alpha$/Fe enhancement and with
the $\langle$Fe$\rangle$ and [${\rm MgFe}$]′ sensitive to total metallicity.
The Pa$\beta$ index is tightly correlated with the H$\beta$ index sensitive to
mean age.

We defined two new combined indices $\langle$Al$\rangle$ and [AlFeH] to build
stronger metallicity and $\alpha$/Fe enhancement indicators in the NIR. The
$\langle$Al$\rangle$ index tightly correlates with velocity dispersion and
optical Mg2 and Mgb indices, while the [AlFeH] index is more correlated with
the $\langle$Fe$\rangle$ and [${\rm MgFe}$]′ indices.

For our sample galaxies, we found a similar distribution of the data points in
the optical [${\rm MgFe}$]′-H$\beta$ age-metallicity diagnostic diagram and in
our two NIR counterparts given by the $\langle$Al$\rangle$-Pa$\beta$ and
[AlFeH]-Pa$\beta$ diagrams. We also found a similar distribution of the data
points in the optical $\alpha$/Fe enhancement-metallicity diagnostic diagram
and in our two NIR counterparts given Al1-FeH1 and $\langle$Al$\rangle$-FeH1
diagrams. This means that a these new sets of NIR line-strength indices can be
taken as a promising starting point to derive the mean age, total metallicity,
and total $\alpha$/Fe enhancement in unresolved galaxies.

Our next step of our work will be extending the galaxy sample to the young
ages ($<5$ Gyr) and to a broader range of metallicities. This will allow us to
better address the differences in stellar populations of early-type galaxies
and spiral bulges. This analysis can also be useful as a benchmark to test the
new generation of NIR SSP models domain (e.g. Conroy & van Dokkum, 2012; Röck
et al., 2015; Vazdekis et al., 2016; Röck et al., 2017) which still require to
be fine-tuned with observational data (Riffel et al., 2019).

Table 4: The values of $\alpha$/Fe enhancement for the sample galaxies estimated with the models of Johansson et al. (2010). Galaxy | [$\alpha$/Fe] (dex)
---|---
NGC 584 | 0.20 $\pm$ 0.07
NGC 636 | 0.22 $\pm$ 0.04
NGC 897 | 0.28 $\pm$ 0.11
NGC 1357 | 0.28 $\pm$ 0.04
NGC 1425 | 0.13 $\pm$ 0.04
NGC 1600 | 0.30 $\pm$ 0.08
NGC 1700 | 0.30 $\pm$ 0.05
NGC 2613 | 0.25 $\pm$ 0.06
NGC 3115 | 0.26 $\pm$ 0.02
NGC 3377 | 0.33 $\pm$ 0.07
NGC 3379 | 0.28 $\pm$ 0.11
NGC 3423 | 0.08 $\pm$ 0.08
NGC 4415 | 0.31 $\pm$ 0.10
NGC 7424 | 0.15 $\pm$ 0.06

## Acknowledgements

EMC, EDB, and AP are supported by MIUR grant PRIN 2017 20173ML3WW$\\_$001 and
Padua University grants DOR1885254/18, DOR1935272/19, and DOR2013080/20. LC
acknowledges financial support from Comunidad de Madrid under Atracción de
Talento grant 2018-T2/TIC-11612 and from Spanish Ministerio de Ciencia,
Innovación y Universidades through grant PGC2018-093499-B-I00.

## Data Availability

The reduced sample galaxies spectra used in this paper have been presented and
analysed in (François et al., 2019). The reduced spectra are available upon
request to the authors.

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