11institutetext: Instituto de Astrofísica de Canarias (IAC), C/ Vía Láctea,
s/n, E-38205, La Laguna, Spain
11email<EMAIL_ADDRESS>22institutetext: Department of Astrophysics,
University of La Laguna, Tenerife, Spain 33institutetext: Institute of Space
and Astronautical Science (ISAS), Japan Aerospace Exploration Agency (JAXA),
Sagamihara, Kanagawa, Japan 44institutetext: Centro de Estudios de Física del
Cosmos de Aragón (CEFCA), Plaza San Juan, 1, E-44001 Teruel, Spain
55institutetext: Institut d’Astrophysique Spatiale, Université Paris-Saclay,
CNRS, F-91405 Orsay, France. 66institutetext: Université Côte d’Azur,
Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Bd de
l’Observatoire, CS 34229, 06304 Nice Cedex 4, France

# Asteroid reflectance spectra from $Gaia$ DR3: Near-UV in primitive
asteroids††thanks: Tables with the computed parameters of the 0.7 $\mu$m band
are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/

F. Tinaut-Ruano 1122 J. de León 1122 E. Tatsumi 33 D. Morate 44 M. Mahlke 55
P. Tanga 66 J. Licandro 1122

(Received 27/11/2023; accepted 27/02/2024)

###### Abstract

Context. In the context of charge-coupled devices (CCDs), the ultraviolet (UV)
region has mostly remained unexplored after the 1990s. Gaia DR3 offers the
community a unique opportunity to explore tens of thousands of asteroids in
the near-UV as a proxy of the UV absorption. This absorption has been proposed
in previous works as a diagnostic of hydration, organics, and space
weathering.

Aims. In this work, we aim to explore the potential of the NUV as a diagnostic
region for primitive asteroids using Gaia DR3.

Methods. We used a corrective factor over the blue part of $Gaia$ spectra to
erase the solar analog selection effect. We identified an artificial relation
between the band noise and slope and applied a signal-to-noise ratio (S/N)
threshold for $Gaia$ bands. Meeting the quality standards, we employed a
Markov chain Monte Carlo (MCMC) algorithm to compute the albedo threshold,
maximizing primitive asteroid inclusion. Utilizing one- and two-dimensional
(1D and 2D) projections, along with dimensionality-reduction methods (such as
PCA and UMAP), we identified primitive asteroid populations.

Results. We uncovered: (a) the first observational evidence linking UV
absorption to the 0.7 $\mu$m band, tied to hydrated iron-rich phyllosilicates;
and (b) a 2D space revealing a split in C-type asteroids based on spectral
features, including UV absorption. The computed average depth (3.5 $\pm$ 1.0
%) and center (0.70 $\pm$ 0.03 $\mu$m) of the 0.7 $\mu$m absorption band for
primitive asteroids observed with $Gaia$ is in agreement with the literature
values.

Conclusions. In this paper, we shed light on the importance of the UV
absorption feature to discriminate among different mineralogies (i.e., iron-
rich phyllosilicates vs. iron-poor) or to identify taxonomies that are
conflated in the visible (i.e., F-types vs. B-types). We have shown that this
is a promising region for diagnostic studies of the composition of primitive
asteroids.

###### Key Words.:

Gaia – asteroids – UV – spectra – Diameter – Albedo

##  1 Introduction

The study of primitive asteroids is essential to understanding the formation
and evolution of the Solar System. These asteroids are believed to be remnants
of the early stages of planetary formation, containing the most pristine
material of the Solar System. Thus, studying the composition of primitive
asteroids is the closest approach to the original composition of the
protoplanetary disk.

In the visible to the near-infrared (up to 2.5 $\mu$m), the spectra of
primitive asteroids are typically featureless, with the sole exception of a
shallow absorption band centered at 0.7 $\mu$m, associated with the presence
of Fe-rich phyllosilicates (Vilas, 1994). The most diagnostic wavelength
region for primitive asteroids is near 3-$\mu$m, where absorption bands, due
to hydroxyl OH and centered around 2.7-2.9 $\mu$m, (Hendrix & Vilas, 2019) or
even water ice, centered at $\sim$3.1-3.2 $\mu$m, are present (Rivkin et al.,
2015). Intriguingly, another characteristic of primitive asteroids is their
spectral behavior at wavelengths below $\sim$0.5$\mu$m, where a drop-off in
the reflectance could appear. It is caused by an absorption band in the
ultraviolet (UV) due to a ferric oxide intervalence charge transfer (IVCT) and
associated with Fe-bearing phyllosilicates (Vilas & Gaffey, 1989). However,
due to Earth’s atmosphere, it is impossible to observe both regions completely
from the ground and, thus, space-based observations are needed to properly
study them.

However, we have recently shown a tentative but promising connection between
the NUV absorption and the 0.7 $\mu$m and 3 $\mu$m absorptions associated with
Fe-rich phyllosilicates, indicating that the NUV region might be used as a
proxy for hydration in primitive asteroids using ground-based data from SDSS
and ECAS surveys, as well as NUV to visible spectra obtained with the 3.6-m
Telescopio Nazionale Galileo (TNG), located on the island of La Palma, Spain
(Tatsumi et al., 2022, 2023). Those previous works motivated the present
study, where we aim to further explore this connection by investigating the
spectral behavior of primitive asteroids observed from the $Gaia$ space
telescope in the NUV. The paper is organized as follows. In Section 2, we
describe the $Gaia$ dataset and the selection criteria for our samples.
Section 3 presents the methodology used to analyze the samples, including the
definition of several features that we measured over the reflectance spectra
(slopes and band parameters) and the unsupervised dimensionality-reduction
algorithms that we used. In Section 4 we present and discuss the obtained
results. Finally, in Section 5, we summarize our findings and describe their
implications for future works.

##  2 Dataset

We used the reflectance spectra of asteroids provided by $Gaia$ DR3 (Gaia
Collaboration et al., 2023). The reflectance spectra were obtained by dividing
each epoch spectrum by the mean of the solar analog stars selected and then
averaging over the set of epochs. The resulting spectrum consists of 16
reflectance values (hereafter, also referred to as ”bands”) covering a
wavelength range from 0.374 to 1.034 $\mu$m, with a resolution of 0.044
$\mu$m, and normalized to unity at $0.550\pm 0.025$ $\mu$m. From the original
number of objects provided by $Gaia$ DR3 (60,518), more than a third (26,577)
have data for all 16 bands. However, less than a sixth (9,926) have all the
bands observed with the best quality flag for every one of the bands.

As we are looking for as much information as available for primitive asteroids
among the 60,518 asteroids in $Gaia$, our first selection criterion is to use
the albedo to identify primitive ones. We obtained the albedo value, available
for 41,720 asteroids, from the SsODNet (Berthier et al., 2023) using the
Python tool $Rocks$111https://github.com/maxmahlke/rocks. Various authors have
used slightly different values for the albedo to distinguish among primitive
and non-primitive asteroids, with the typical value being around 10% (Tholen,
1984; Campins et al., 2010; Tatsumi et al., 2023). We searched for the best
albedo value to select the primitives among the $Gaia$ sample.

In Fig. 1, we show the number of asteroids that were classified in Tholen
(1984), with available $Gaia$ spectra, which have an albedo value lower than a
given albedo threshold (amax). All the taxonomies that we refer to hereafter
are based on Tholen (1984). By taking amax=0.5 we can separate mainly E-types.
With amax=0.12, we lose 93% of the S-, M-, A-, and V-types. Only when we go
down to amax=0.07, we lose 11% of the original sample of C, P, D, F, B, G, and
T asteroids, which are what we consider primitive in this work. Applying a
Markov chain Monte Carlo approach, in which we randomly selected 80% of the
total sample, over 1000 iterations, and computed the albedo which maximizes
the number of primitive asteroids over non-primitives (S, M, E, A, and V), we
obtain an albedo threshold of 0.105 $\pm$ 0.017. From here on, we only deal
with the 15,529 asteroids with known albedo smaller than 0.105 and for which
$Gaia$ measured a spectrum. Literature sources used to compile both albedo and
diameter for those asteroids are listed in Table A. X-types were not used for
the albedo calculation as they include E-, M-, and P-types having no albedo
information at the time Tholen classified them. P-types were defined in the
Tholen taxonomy as low albedo X-types. Thus, the remaining X-types present in
the sample after we applied the albedo cut-off, were re-classified as P-types.

Figure 1: Remaining objects classified in Tholen (1984) with Gaia spectra
after different albedo thresholds are applied (amax). The threshold amax=0.105
maximizes the number of primitives.

Once we have separated primitive asteroids from the total sample, we computed
several spectral slopes by least square fitting of the normalized reflectance
in different wavelength ranges (see Fig. 2): from 0.374 to 0.418 $\mu$m
($s1$); from 0.418 to 0.506 $\mu$m ($s2$); from 0.506 to 0.726 $\mu$m ($s3$);
and from 0.726 to 0.902 $\mu$m ($s4$). If a band is missing or the quality
flag is not the best in the particular wavelength range of a spectral slope,
we decided not to compute it. That leaves 3,778 primitive asteroids with $s1$,
14,582 with $s2$, 15,084 with $s3$, and, finally, 15,170 have $s4$ computed.

Figure 2: Median of $Gaia$ spectra for each primitive taxonomy, with the
wavelength regions used to compute each spectra slope marked as black vertical
lines.

In the process of analyzing the quality of the data, we computed the parameter
$\rm{S/N_{\rm ref}}(\lambda)=R(\lambda)/R_{\rm error}(\lambda)$, where
$R(\lambda)$ is the normalized reflectance value at one particular band, and
$R_{\rm error}(\lambda)$ is its associated error calculated by (Gaia
Collaboration et al., 2023). When searching for potential systematics, we
discovered a trend in $s1$ and $s2$ versus $\rm{S/N_{ref}}$, shown in the
upper panels of Fig. 3. We observe a decrease in those slopes with decreasing
values of $\rm{S/N_{ref}}$, which seems to be an artifact and unrelated to any
other physical parameter (albedo, diameter, orbital parameters, or taxonomy).
On the contrary, the values of $s3$ and $s4$ do not present any tendency (see
lower panels of Fig. 3), and their variation, ranging from -1 to 2 $\mu$m-1,
is consistent to the ones observed in other spectroscopic surveys, as in Bus &
Binzel (2002). As we are not able to explain nor correct the trends observed
for $s1$ and $s2$, we decided to use the $\rm{S/N_{ref}}$ value as a
threshold: the selected value is such that we minimize the number of asteroids
showing the trend and we maximize the number of asteroids with reliable values
of the spectral slopes. Therefore, we calculated $s1$ only for those asteroids
with $\rm{S/N_{ref}}(0.374)>70$, resulting in a total of 522 asteroids. In the
same way, $s2$ is calculated for the 1,331 asteroids, which have a signal-to-
noise ratio of S/Nref(0.418) $>$ 50.

Figure 3: Density plots of the computed slopes versus $\rm{S/N_{ref}}$ at
different bands. Vertical black lines indicate the minimum S/N${}_{\rm
ref}(\lambda)$ to be selected.

Apart from this observed trend, the last three bands after 0.902 $\mu$m are
often affected by large random errors Gaia Collaboration et al. (2023). As we
will not compute anything beyond 0.902 $\mu$m, we did not use those bands.
Furthermore, $Gaia$ spectra came from two different photometers (red and blue)
and the band at 0.632 $\mu$m is problematic for bright objects (see Ceres and
Vesta spectra at Fig. 13 and 14 of Gaia Collaboration et al. (2023)) as it is
the joining region between them (Gaia Collaboration et al., 2023). Despite
this problem, we decided to use this particular band in our computations as it
is close to the center of the 0.7 $\mu$m absorption band, a key feature in our
study. We tested all our computations with and without this band. When we used
it, as it has more variance because of its systematics, the loading in the
principal component base is overestimated for this band (see Fig 7) but the
principal component space is still similar. Nevertheless, without the band at
0.632 $\mu$m, many more fake detections of the 0.7 $\mu$m band are present in
our algorithms.

##  3 Methodology

Before starting any computation, we corrected the four bluest bands of $Gaia$
spectra. The selection of solar analogs by the $Gaia$ team included a large
number of the most commonly used stars by the planetary science community
(Gaia Collaboration et al., 2023). Such stars can be used to get asteroid
reflectance spectra at wavelengths beyond 0.5 $\mu$m without any problems.
However, as we have shown in Tatsumi et al. (2022), they do not have a Sun-
like spectral behavior at the wavelengths below 0.5 $\mu$m, introducing an
artificial reddening in that region. As we are interested in the near-UV part
of the $Gaia$ spectra, we computed a multiplicative correction factor in
Tinaut-Ruano et al. (2023), which we applied to all asteroid spectra used in
this work.

To study the properties of primitive asteroids we used all the available
information that we can extract from the $Gaia$ spectra, as well as other
physical parameters available. We use the spectral slopes defined in the
previous section and shown in Fig. 2, as well as combinations having physical
meaning. For example, the value ($s1-s2$) indicates how much the slope changes
around 0.418 $\mu$m, as it does ($s2-s3$) for 0.506 $\mu$m. Both of them are
indeed describing the amount of drop-off in NUV reflectance, namely, the
beginning of the UV absorption. As another example, the value ($s4-s3$) is
related to the curvature of the spectra around $\sim$0.7 $\mu$m, namely, the
presence of the 0.7 $\mu$m absorption band.

We searched for other available information on the asteroids. Albedo values,
previous taxonomical classification, and diameters were obtained using the
Python tool $Rocks$ from Berthier et al. (2023). To check if an asteroid
belonged to a particular collisional family, we used the lists from Nesvorný
et al. (2015). To look for trends, clusters, and/or correlations we used
different techniques. We applied principal component analysis (PCA) and
uniform manifold approximation and projection (UMAP) to the asteroid
reflectance spectra, but also to a set of spectral parameters: $s$, defined as
the spectral slope over the NUV-visible wavelength range (0.418 to 0.902
$\mu$m), $s2$, ($s2$-$s3$), and ($s4$-$s3$). The choice of these particular
parameters will be explained in Section 4.

The PCA is a dimension reduction technique that aims to transform a dataset
into a new coordinate system by finding orthogonal linear combinations of the
original features, called principal components, that retain as much
information as possible while reducing the dimensions. The variance of the
data along each axis is maximized, with the first principal component
capturing the most variance, the second one capturing the second most, and so
on. Previous authors have used PCA to define and visualize the distribution of
taxonomic classes and find the combination of reflectances that describes the
spectral features (Tholen, 1984; Bus & Binzel, 2002). We carried out two
different PCAs: the first one tried to replicate the one done by Bus & Binzel
(2002) but used only primitive asteroids. Thus, we flattened the spectra by
dividing it by the slope computed as a least squared fit of the reflectances
between 0.418 $\mu$m to 0.902 $\mu$m and used those slope-removed reflectances
without standard deviation nor mean scaling for the PCA (following
Bus&Binzel’s notation, we refer to these components as PC’). The second one
does not use reflectances, but four parameters that describe the spectral
shapes of the different asteroid taxonomies. These parameters are: visible
slope $s$, as computed in Bus & Binzel (2002), blue slope $s2$, change in
slope at 0.5 $\mu$m ($s2$-$s3$), and change in slope at 0.7 $\mu$m ($s4$-$s3$)
(see Fig 2). As these parameters have different value ranges, we have to scale
the dataset before doing the PCA. The standard scaling of each set of
variables changes their distribution closer to a normal distribution by
subtracting each mean and dividing by each standard deviation. Both PCAs are
applied over 1,331 asteroids as we are discarding the bluest filter for this
study.

The uniform manifold approximation and projection (UMAP) is another
dimensionality-reduction algorithm, using non-linear feature coefficients. It
tries to learn the manifold structure of the data and find low-dimensional
representations (usually 2D) that preserve the topological structures of the
original data. That means that points that are closer in the 2D
representations are also closer in the $n$-dimensional space, with n=4 in this
case ($s$, $s2$, $s2$-$s3$, and $s4$-$s3$). The combination of those 4
variables, to arrive at the 2D space, does not have to be linear. Further
information on UMAP can be found in Sainburg et al. (2021). To implement it we
used the library umap222https://umap-learn.readthedocs.io/en/latest/ for
Python with the parameters: n_neighbors=100, min_dist=0, and random_state=0.

To compute the band depth for the 0.7 $\mu$m absorption band, we fit a model
based on a flat spectrum normalized at 0.55 $\mu$m and having a Gaussian
absorption in the wavelength range from 0.55 to 0.91 $\mu$m. Usually, these
parameters were computed by subtracting a continuum and then fitting a
Gaussian or a polynomial to the absorption band. However, due to the low
resolution of the $Gaia$, in this classical approach, the continuum is fitted
using only two or three points in the shoulders of the band, and this
introduces errors and unrealistic band depth measurements for a large fraction
of the asteroid sample. Our model uses instead all the available $Gaia$ bands
in the wavelength range and thus, reduces the errors and provides more
reliable measurements. The chosen model can be described as:

$r(\lambda)=(m\times\lambda+1-m\times
0.55)\left(1-de^{\frac{-(\lambda-\lambda_{c})^{2}}{2w^{2}}}\right),$ (1)

where $r(\lambda)$ is the normalized reflectance, $m$ is the slope of the
continuum fitted across the entire wavelength range (in $\mu$m-1), $d$ is the
band depth (in values from 0 to 1), $\lambda_{c}$ is the center of the
0.7-$\mu$m band (in $\mu$m), and $w$ is the width of the band computed as the
standard deviation of the Gaussian. The free parameters on this model are $m$,
$d$, $\lambda_{c}$, and $w$. To avoid overfitting of Gaussians between Gaia
spectral bands we decided to establish a lower limit of 0.035 $\mu$m in $w$, a
value that is 50% larger than half of the wavelength resolution (i.e., 0.022
$\mu$m). The upper limit is based on a visual inspection of tens of $Gaia$
spectra, where we see that the wider absorption bands (that are not simply
concavity of the spectra) have a $w$ value of 0.085 $\mu$m.

##  4 Results and discussion

In this section, we present the distribution of the computed spectral slopes,
as well as their combinations, for the final sample of 15,529 primitive
asteroids in $Gaia$ DR3 with an albedo in the literature (references at 2).
Density plots relating different parameters can also help to obtain relations
between variables or to identify differences between groups of asteroids.
Objects already classified are also helpful in identifying features in density
plots and associating them with taxonomies. We present also the results of
applying both PCA and UMAP algorithms, and any correlation with taxonomy,
diameter, albedo, and membership to collisional families. Taxonomic
classifications were obtained from Tholen (1984) as it is the work with the
most similar wavelength coverage and spectral resolution to $Gaia$. Asteroids
having uncertain or multiple taxonomic classifications are not considered
here.

###  4.1 General behaviors of primitive asteroids

We present the distribution of computed slopes for our sample of asteroids in
Fig. 4. The upper panel shows the slope distributions for all the primitive
asteroids in our sample (in gray), and the lower panel shows the same but for
those asteroids classified by Tholen as C, P, D, F, B, T, and G. Vertical
lines indicate the median values of each taxonomic class computed using the
$Gaia$ data and shown in Table 1, together with the number of asteroids for
each taxonomy in between parentheses. The number of bins for the histograms is
computed as the integer part of the square root of the number of asteroids
available for each slope.

Figure 4: Slope distributions (from $s1$ at left to $s4$ at right) for all the
asteroids in our sample (upper panel) and for those classified by Tholen
(1984) (lower panel). Vertical lines indicate the computed median for each
taxonomical class. The title of each column indicates the total number of
asteroids with such slope computed. B- and T-types have five or fewer members
with computed $s1$, thus, we decided not to show them in the corresponding
plots. Table 1: Median values of slopes for each taxonomy.

Slope | Taxonomy
---|---
[1/$\mu$m] | C (#) | G (#) | P (#) | T (#) | D (#) | B (#) | F (#)
$s1$ | 1.18 (130) | 1.50 (9) | 0.76 (45) | – (5) | 0.48 (11) | – (4) | 0.55 (13)
$s2$ | 0.68 (138) | 1.04 (10) | 0.59 (64) | 0.88 (6) | 0.68 (22) | 0.52 (6) | 0.07 (24)
$s3$ | 0.01 (145) |  $-0.05$ (9) | 0.32 (67) | 0.74 (6) | 0.87 (32) |  $-0.13$ (6) |  $-0.04$ (28)
$s4$ | 0.29 (145) | 0.32 (10) | 0.35 (67) | 0.69 (6) | 1.03 (33) | 0.06 (6) | 0.04 (28)
($s1-s2$) | 0.50 (130) | 0.47 (9) | 0.12 (45) | – (5) |  $-0.22$ (11) | – (4) | 0.39 (13)
($s2-s3$) | 0.67 (138) | 1.01 (9) | 0.25 (64) | 0.18 (6) |  $-0.15$ (22) | 0.61 (6) | 0.14 (24)
($s4-s3$) | 0.23 (145) | 0.37 (9) | 0.07 (67) |  $-0.20$ (6) | 0.11 (32) | 0.15 (6) | 0.10 (28)

#: In between parentheses are the number of asteroids used to compute the
median.
–: The median is not computed for those slopes where 5 or fewer asteroids were
available.

The spectral slope space is useful for separating some of the taxonomies and
inspecting their general behavior. D-types (in pink) have slightly red spectra
in the NUV (low $s1$), getting redder as moving towards longer wavelengths,
with a very red slope (very high values of $s3$ and $s4$) that makes them
quite easy to differentiate from the rest of the classes. F-types (in red) are
flat in the whole spectral range, but the $s1$ shows a slight red slope (i.e.,
the positive slope at the wavelengths below 0.418 $\mu$m). This could be
interpreted as the F-types having the beginning of the UV absorption around
0.418 $\mu$m. They also show the flattest spectral slopes in $s2$, where they
separate from the other taxonomies. For $s3$ and $s4$, P, T, and D types, have
the largest slope values (in this order) of all the primitive taxonomies. On
the other hand, G-types have the largest $s2$, namely, the UV absorption
starts below 0.506 $\mu$m. The largest values of $s1$ are for G-types as they
have the deepest UV absorptions. C-types have a similar behavior to G-types
but with less pronounced UV absorption. P-types have a slightly decreasing
slope with increasing wavelength. B-types have a similar behavior to F-types,
but the transition from red slope to flat is observed at 0.506 $\mu$m,
indicating that the beginning of the UV absorption is at longer wavelengths
than that of F-types.

Figure 5: Distribution of slopes for the primitive asteroids in our sample
(upper panel) and those classified by Tholen (1984) (bottom). Vertical lines
indicate the computed median for each taxonomical class. The title of each
column indicates the total number of asteroids with such difference computed.
B- and T-types have less than five members with computed $s1$, thus, we
decided not to show them in the ($s1$-$s2$) plot. The rightest column does
have not a shared x-axis as the general ($s3$-$s4$) distribution is much wider
than the classified ones.

Combining some of the computed slopes allows us to better separate between
those taxonomies that have a change in slope in a certain wavelength (see Fig.
5). For example, all the G-types and some C-types have an absorption band at
0.7 $\mu$m, which translates into their high values of $s4$-$s3$ (right column
of Fig. 5). The negative median value of ($s2-s3$) for the D-types indicates a
spectral flattening below 0.5 $\mu$m, in agreement with Emery & Brown (2003);
Wong et al. (2019), which is a unique and reveals the opposite behavior with
respect to the rest of primitive taxonomies. F-types show a larger value for
($s1-s2$) than for the other combinations, as is expected from their larger
values of $s1$ and the close value to 0 for the rest of the slopes. That shows
that their UV absorption begins at 0.4 $\mu$m. Finally, ($s2-s3$) shows a bi-
modality in the general distribution (top center panel of Fig. 5). Large
values of ($s2-s3$) seem to be related to a change in spectral slope around
0.5 $\mu$m for the B-types, and the presence of a 0.7 $\mu$m absorption band
together with strong UV absorption for the G-types and some C-types.

In Figure 6, we plot ($s2-s3$) vs. ($s4-s3$) in the upper panel and ($s1-s2$)
vs. ($s2-s3$) in the lower panel using density plots (gray hatches) of all
available asteroids with those differences computed. Asteroids classified by
Tholen (1984) are marked with colored dots representing different taxonomies,
the crosses indicate the median value of each taxonomy using the same color
code, and the size of the error bar is the interquartile range. In the upper
panel, we can see the correlation between ($s2-s3$), which is related to the
absorption in the UV, and ($s4-s3$), which can be considered as a proxy of the
0.7-$\mu$m band. We note that for the case of D and F types, which do not
present usually the 0.7-$\mu$m feature, they have small but positive values of
($s4-s3$). Those values (and a visual inspection) suggest a straight to
slightly concave-up-shaped spectrum on both taxonomies. The existence of
concave-up and concave-down D-types has been previously noticed by different
authors (Barucci et al., 1987; Fitzsimmons et al., 1994; Carvano et al.,
2003). Meanwhile, the F types are generally negative in $s3$ and flat in $s4$,
generating this slightly concave-up shape.

We searched for potential correlations between ($s2-s3$) and ($s4-s3$) using a
simple Pearson correlation coefficient (PCC). We found a PCC value of 0.7 for
the asteroids with P, C, and G taxonomies. Apart from that, F and D taxonomies
have the smallest values of ($s2-s3$), even with negative values (i.e.,
smaller UV absorption up to 0.4 $\mu$m). That tells us again that their
spectra are getting bluer towards short wavelengths, at least until 0.4
$\mu$m. On the other hand, G-types have the strongest UV absorption (larger
$s2-s3$ values) and the deeper 0.7-$\mu$m band (larger $s4-s3$ values). That
is expected as G types were described by Tholen as primitive asteroids with
large UV absorption and they usually present the 0.7 $\mu$m Tholen (1984); Bus
& Binzel (2002). P-types distribute around the central part of the density
plot, between C-G and F-D taxonomies. They present a red to flat spectra with
increasing wavelength. One part of the bi-modal C-type distribution overlaps
with the non-hydrated P-types, while the other part overlaps with the hydrated
G-types. This separation is decreased without the NUV part of the spectra as
shown in Mahlke et al. (2022) for other equivalent taxonomies. C-types present
the hydration band and a stronger UV absorption more often than P types, but
with shallower bands than G types, as defined by Tholen (1984).

Inspecting now the general density distribution we see a maximum in density
populated by P-, F-, and, some C-types. Following the correlation, the most
populated area to the upper right is mainly populated by C- and G-types. This
high population seems to be related to the bi-modality in the ($s2-s3$) seen
in Fig. 5. From the central maxima to the left, we found a slight overdensity
presumably related to D- and F-types.

Figure 6: Density plot of ($s2-s3$) vs. ($s4-s3$) for the 1,241 asteroids with
these computed slopes in $Gaia$ DR3 (upper panel). Colors represent asteroids
classified by Tholen (1984). The crosses mark the median of each taxonomy and
the size of the error bars is the interquartil range. The lower panel shows
the same density plot, but for ($s2-s3$) vs. ($s1-s2$). In this case, a total
of 498 asteroids had those slopes computed in $Gaia$ DR3. We only include here
the taxonomies with more than five members with computed $s1$ (i.e. C, P, G,
D, and F).

In the lower panel of Fig. 6, we explore the UV absorption more in detail. The
unity line (black line) where objects that have the same change in slope at
0.5 $\mu$m as at 0.4 $\mu$m would fall, namely, a constant absorption,
including linear spectral shape located around (0, 0). C-, P- and D-types are
on the unity line, with C- types having a huge dispersion in the space but
with positive values in both slope differences with slightly smaller ($s1-s2$;
seen as a concave-down shape between 0.374 and 0.726 $\mu$m); P-types also
have positive values in both slope differences but smaller than C-types;
D-types have negative values for both slope differences, which translates into
a concave-up shape in the same wavelength range, i.e., a flattening towards
bluer wavelengths. The only taxonomy with a median value above the unity line
is the F-type, showing that the change in slope is higher at 0.4 $\mu$m than
it is at 0.5 $\mu$m. Below the unity line, we found G-types with larger values
of ($s2-s3$) than ($s1-s2$), which implies a stronger increase in slope for
decreasing wavelength around 0.5 $\mu$m than around 0.4 $\mu$m. Taking a look
at the general distribution, we can see two local maxima, one below the unity
line close to (0.75, 0.5), and another above the line, close to the F-type
median. This bimodality suggests the existence of two different groups: one
with larger values of ($s2-s3$) and slight dispersion on ($s1-s2$), indicating
that the beginning of the UV absorption is at 0.5 $\mu$m and the decrease in
reflectance continues towards 0.4 $\mu$m (G-types and some C-types); the other
with lower values of ($s2-s3$) and with a higher dispersion on ($s1-s2$),
ranging from small or negative values (i.e. P- and D-types, respectively) to
large values of ($s1-s2$), which indicate a UV absorption starting at 0.4
$\mu$m (F-types). Gaffey & McCord (1978) have suggested that the location of
the UV absorption edge is diagnostic of composition for meteorites with albedo
matching C-type asteroids, an absorption beginning at 0.5 $\mu$m reveal the
presence of iron-rich clay mineral, while an absorption edge at 0.4 $\mu$m
could be due to either an iron-poor clay mineral or iron-rich olivine and
pyroxene.

###  4.2 Dimensional reduction: PCA and UMAP

After inspecting the general behavior of the different spectral slopes and
their combinations, we carried out a PCA over the 12 available reflectance
bands between 0.418 and 0.902 $\mu$m similar to what was done by Bus & Binzel
(2002). Although the initial datasets are different, as Bus & Binzel (2002)
are including also non-primitive asteroids, their PC3’ shape in the principal
component base is similar to the shape of our PC2’ (ours is shown in the upper
panel of Fig. 7, whereas theirs is in Fig. 4 of Bus & Binzel (2002)). We used
only dark objects, where the UV absorption and the 0.7 $\mu$m are shaping most
of the spectra (mainly G- and C-types), and this is represented by our PC2’.
In the same way, they found that ”the transformation involving PC3’ is
especially useful” in isolating asteroids with spectra of ”either a strong UV
absorption and shortward of 0.55 $\mu$m or a 0.7-$\mu$m phyllosilicate
feature.” Our results show that the slope ($s$) and the PC2’ are enough to
spread the different primitive taxonomies. As PC2’ represents the UV and the
0.7 $\mu$m absorptions, in the lower panel of Fig. 7, the G-types and some
C-types are those with the largest PC2’ values, and the taxonomies having
linear spectra in the visible and the smaller absorption up to 0.4 $\mu$m have
the lowest PC2’ scores.

Figure 7: Results from the PCA applied over the reflectance spectra. The upper
panel shows the two first components of our PCA. These loading values
(elements of the eigenvectors, plotted as a function of wavelength) are used
to weight the individual $Gaia$ bands when calculating principal component
scores. In the lower panel, we show the principal component space of visible
slope $s$ versus PC2’ score. The grey hatch represents the density
distribution of the 1,290 $Gaia$ asteroids that have good quality data between
0.418 to 0.902 $\mu$m. Those classified by Tholen are overplotted with color
markers. Crosses correspond to the median for each taxonomy and the size of
the error bars is the interquartile range.

We decided to apply a PCA over selected features, that describe the different
types of primitive spectra. Those features are visible slope ($s$) as defined
before; $s2$, that allows to easily differentiate F-types from the rest of
taxonomies (see Fig. 4); $s2-s3$, which is a proxy of the beginning of the UV
absorption and presents an interesting bi-modality (see Fig. 4); and $s4-s3$,
that is a proxy of the 0.7 $\mu$m absorption band. The results of the PCA are
shown in Fig. 8. In the lower panel, we can see a very similar distribution to
the one shown in the lower panel of Fig. 7. This is expected, as PC2 is
weighting the slope more than any other feature (see the upper panel of Fig.
8) and PC1 is taking care of the NUV and the 0.7 $\mu$m absorptions. However,
if we look carefully we can see how the PC2 preserves the bi-modality observed
for $s2-s3$ in Fig. 5, separating C-types in two regions, one shared with
P-types and the other with G-types.

Figure 8: Results from the PCA applied over the spectral parameters: $s$,
$s2$, $s2$-$s3$, and $s3$-$s4$. The upper panel shows the first three
components of the PCA. These loading values (elements of the eigenvectors) are
used to weight each parameter when calculating principal component scores. In
the lower panel, we show the principal component space of PC2 versus PC1. The
grey hatch represents the density distribution of the 1290 $Gaia$ asteroids
that have good quality data between 0.418 and 0.902 $\mu$m. Those classified
by Tholen are overplotted with color markers. Crosses correspond to the median
for each taxonomy and the size of the error bars is the interquartile range.

Trying to go further in this analysis, we explored another dimensionality-
reduction algorithm, the UMAP. The resulting 2D representation for all the
available $Gaia$ spectra (in grey) is shown in the upper left panel of Fig. 9,
together with those asteroids classified by Tholen. The other panels in the
same figure show the values of the computed depth of the 0.7 $\mu$m absorption
band (in %), the logarithm of the asteroid diameter in kilometers, and the
asteroid albedo values, displayed with a color scale shown to the right of
each panel. It is important to remark that the axes do have not a simple
physical meaning due to the nonlinearity of the method. However, we can infer
the spectral properties of a region in the UMAP space based on the selected
parameters by looking at 13. Using UMAP, the bimodality observed for the
C-types becomes clearer than in any other previous representation. It is
important to remark that asteroids that are closer in this 2D space are going
to be closer in the original 4D space defined by $s$, $s2$, ($s2-s3$), and
($s4-s3$). We have to note that the shape of the distribution is quite similar
to the one obtained with the PCA following a flip in the vertical axis. In
this UMAP 2D representation, we can separate most of the taxonomical classes.
In particular, C-types seem to be distributed in two clusters: 1) C-types that
have an absorption band at 0.7 $\mu$m, associated with iron-rich
phyllosilicates and that share the space with G-types in the upper left panel
of Fig. 9; 2) and C-types that do not have the band and share the space with
P- and B-types. This result is also observed in the upper right panel of Fig.
9, where we do not see a smooth transition from low to high values of the band
depth, but two clear clusters instead (i.e., either the band is present or is
not): the 78% of the C-G cluster members have a 0.7 $\mu$m band detected by
our model fitting, while the 66% of the members C-P-B region have no band
detections. Furthermore, the median band depth in the hydrated C-G members is
3.9%, deeper than the median depth for the hydrated ones in the C-P-B region
(2.15%). We suggest that the C-G cluster is generated because we are including
the NUV down to 0.418 $\mu$m; the absorption in the UV is correlated with the
absorption in 0.7 $\mu$m (see Fig. 6), and we are selecting for the UMAP the
features that better describe the behavior of primitive spectra. All that adds
extra information that helps separate the hydrated C-types from the rest.

We also have a few detections of the 0.7-$\mu$m absorption band in the regions
populated with F-, B-, and D-types. This is not the first time this feature
has been detected in taxonomical types different from C-types. Morate et al.
(2016) found that 14.3%, 28.6%, and 36.4% of the X-, B-, and T-types,
respectively, in the Erigone collisional family showed this feature. Similar
values are also observed for primitive taxonomies in the Sulamitis collisional
family (Morate et al., 2018). Furthermore, hydration in other types than C was
also found in Mahlke et al. (2022), using infrared wavelengths.

We have tried this algorithm also over the whole spectral dataset, but the
clustering was not as clear, likely due to the increase in variability in
certain bands due to their poorly understood systematics errors that are
softened by the slope computation.

Figure 9: 2D representation of feature space composed by $s$, $s2$, ($s2-s3$),
and ($s4-s3$), after applying UMAP. The upper left panel shows all available
$Gaia$ spectra in grey, and those classified by Tholen are overplotted in
colors following the taxonomy code. Crosses correspond to the median for each
taxonomy and the size of the error bars is the interquartile range in all the
panels. In the upper-right and lower panels, we have added the following
information: the computed depth of the 0.7 $\mu$m band (in %), the logarithm
of the asteroid diameter in kilometers, and the albedo, with an associated
color scale shown in the right of each panel. The axes do not have a physical
interpretability due to the nonlinearity of the method. From Figure 13, we can
infer the physical properties of the UMAP space based on the parameters used
to compute the space.

###  4.3 Albedo and diameter

Looking at the lower right panel of Fig. 9, where the color depends on the
albedo, we found that the brightest objects among the primitives are in the
region populated with T-types. The asteroids in this region have a median
value of albedo of 0.087 versus 0.048 as the median of the rest of the sample.
The darkest are among the P- and C-types (with and without the 0.7 $\mu$m
band), in good agreement with Mainzer et al. (2011b). Similarly, and regarding
the size at the lower left plot, we found that the F-type region is populated
with the smallest asteroids among the primitives, with the median size of the
asteroids in this region being 22 km, which is below the percentile 25 of the
rest of the sample (26 km). This result was also found by Tatsumi et al.
(2022). Finally, if we look carefully at the cluster of asteroids with 0.7
$\mu$m absorption band in the upper right panel of Fig. 9, it seems that those
with deeper absorptions (in yellow) have smaller diameters (dark blue in the
lower-left panel of Fig. 9).

We explore further this apparent trend in the density plot of the diameter
versus the depth of the 0.7 $\mu$m absorption band in Fig. 10. Although a
visual inspection suggests the presence of such a trend, it is important to
note that smaller asteroids have lower S/Nref (as defined in Section 2) since
the $Gaia$ bands (or points) have larger errors for these asteroids. This
translates into a larger fraction of unrealistic values for the depth, both
negative values and large ones. We know from other studies that the maximum
depths observed for the 0.7 $\mu$m band in primitive asteroids are around 7-8%
(Fornasier et al., 2014; Morate et al., 2016, 2018, 2019), so measurements
above these values are most likely due to the noise. In the case of the band
center, we also see a larger dispersion of values for the smaller sizes in the
right panel of Fig. 10. Nevertheless, and as previously pointed out by
Fornasier et al. (2014), the visible spectra of hydrated asteroids show other
absorption bands, centered at 0.6 and 0.8-0.9 $\mu$m, and associated to charge
transfer transitions in iron oxides (Hunt & Ashley, 1979; Feierberg et al.,
1985; Vilas, 1994), which can contribute to the observed dispersion in the
values for the band center. From the results shown above we can only conclude
that the average band depths (3.5 $\pm$ 1.0 %) and band centers (0.70 $\pm$
0.03 $\mu$m) obtained for the primitive asteroids observed with $Gaia$ are in
good agreement with the values found in the literature.

Figure 10: Density plot of the diameter of hydrated asteroids versus their 0.7
$\mu$m band depth (left panel) and the center of their band (right panel).

After analyzing the UMAP 2D-distributions we searched for any further
relationship between the physical parameters and the slopes. When plotting the
visible slope, $s,$ against the asteroid diameter (or asteroid absolute
magnitude $H$), we observed what seemed to be an increase in the slope
dispersion with decreasing size (increasing $H$), generating what appeared to
be two inverted-triangle-shaped distributions (Fig. 11a): one centered at the
median $s$ of C-types and the other close to the median slope of D-types. The
one for C-types is similar to the distribution obtained by Morate et al.
(2019) using a smaller sample of primitive asteroids, all of them being
members of collisional families of the inner main belt. We note that to
properly compare their results with this study, we re-computed the visible
spectral slope using the same wavelength range as in the study cited above,
namely, from 0.55 to 0.90 $\mu$m. To explain this behavior, they hypothesize
that larger asteroids have more heterogeneous surfaces with different grain
sizes, crater ages, and compositional units, thus implying different spectral
slopes among their surfaces. Their unresolved spectra will result in
neutralized spectra with a mean slope of all the material. Meanwhile, smaller
asteroids have a more homogeneous surface as they are sampling a smaller
fraction of the parent body, thus exhibiting a wider variety of spectral
slopes. Furthermore, space weathering is seen to redden some carbonaceous
materials, like CV/CO carbonaceous chondrites, while blueing others, as is the
case for some types of CI/CM chondrites (Lantz et al., 2018), contributing to
the above-mentioned variety.

We included in Fig. 11a the 2$\sigma$ region obtained by Morate et al. (2019),
using their Eq. (5), and represented them as two red dashed lines, as well as
those asteroids classified using Tholen taxonomy. The two lines define a
region and if the observed tendency is real, it is expected that ”the spread
in spectral slopes is contained within the limits of this region”, as
explained in Morate et al. (2019). For the whole sample of primitive asteroids
among $Gaia$, we see that 99.1% of the asteroids lie on the right side of the
left straight line, but a large number of objects are also located to the
right of the right straight line. Looking at the different taxonomies, this
distribution seems to be related to taxonomies such as P-, T-, and in
particular, D-types. It seems that D-types (light pink) follow a similar
inverted triangular shape to that of the C-types (green) and that there are
very few big objects in between the two inverted triangles. To properly
interpret this distribution of the visible slope, we first separated the main
belt asteroids from the dynamical populations beyond the main belt, namely,
the Cybeles (with semi-major axis $3.3<a<3.7$ au), the Hildas ($3.7<a<4.2$
au), and what we call here the Trojans, which include all asteroids having
$a>4.2$ au. The four populations are plotted with different colors in Fig.
11b. It is clear from this plot that the population beyond the main belt is
responsible for the second inverted triangle, associated with D-types.

Once we have separated main-belt asteroids from the populations beyond, we
have to consider the main belt’s actual size-frequency distribution (SFD). It
is a well-known fact that there are several ”bumps” in the main belt’s SFD
(see, e.g., Fig. 1 in Bottke et al., 2005) different parts of the distribution
having different gradients. In particular, a significant change in the
gradient of the SFD occurs at $H$ = 12 ($D\sim$ 20 km for $p_{V}$ =0.07),
which is the value where we start to see many more objects in the belt; the
cloud of objects starts to disappear for $H>$ 14-15, where we start to have an
actual observational bias (problems to detect small asteroids). In the region
between 20 and 100 km (i.e., 8 $<H<$ 12), the gradient of the SFD is
significantly smaller (almost flat) and we have a density of asteroids that
increases slowly with $H$. Indeed, if we compute the distribution of the
visible spectral slope for 8 $<H<$ 12 and 12 $<H<$ 16 (shown in Fig. 11c), we
can see that the two distributions overlap. The median value of the
distribution for larger asteroids is $0.21^{+0.29}_{-0.18}$ $\mu$m, meanwhile
for the distribution for the smaller asteroids is $0.25^{+0.32}_{-0.22}$
$\mu$m. We, therefore, conclude that the trend between size and visible slope
observed by Morate et al. (2019) for the inner belt primitive families is not
observed for the entire main belt population; instead, the dispersion of
spectral slope values observed for the smaller asteroids is simply due to the
actual SFD of the main belt. A further analysis of the primitive families will
be done with the DR4.

We performed the same exercise for the dynamical populations beyond the main
belt, with their corresponding histograms (also shown in Fig. 11d, e, and f).
For the Hildas and Cybeles, we observed a bimodal distribution for 8 $<H<$ 12,
with the objects concentrating at spectral slopes between 0.2 and 0.6 $\mu$m-1
(P-types, on average) and spectral slopes $>$ 0.6 $\mu$m-1 (T-types and
D-types). This behavior has been previously observed by other authors (Shepard
et al., 2008; Gil-Hutton & Licandro, 2010; De Prá et al., 2018). For 12 $<H<$
16, they are equally distributed among D- and P- taxonomies. To explain the
larger fraction of P-types at $H<$12 observed for the Hildas, these authors
invoked a combination of space weathering and resurfacing, and a wavy size
distribution produced by the Hildas being in a stable 3:2 resonance with
Jupiter, surrounded by unstable regions. This process, however, does not work
for the Cybeles, since these objects are not orbiting in a mean motion
resonance.

In the case of the Trojans, we obtained the well-known bimodal spectral slope
distribution for asteroids with 8 $<H<$ 12, which was not observed for
asteroids with 12 $<H<$ 16 (Fig. 11f). This behavior was also detected by Wong
& Brown (2015) for the L4 swarm, using data from SDSS and an 8.2m Subaru
telescope. In addition, the two slope distributions are slightly different,
with the bigger asteroids (8 $<H<$ 12) having slightly redder slopes than the
smaller ones (12 $<H<$ 16). This was also observed by Roig et al. (2008) for
the background Trojan asteroids (i.e., not members of a family), also having
high orbital inclinations ($\sin{i}>$ 0.2) and by Wong & Brown (2015) for the
L4 swarm. In both cases, the authors invoked collisional evolution, either by
fragmentation or by collisional resurfacing (red objects converted to less-red
objects upon collision) to explain their findings. They concluded that
collision may have not played a major role in shaping the magnitude
distribution of the bigger Trojans since captured by Jupiter.

Figure 11: (a) Replication of Figure 7 from Morate et al. (2019), but using
primitive asteroids among the $Gaia$ DR3 dataset. Colors indicate objects
classified with Tholen taxonomy. Red lines are the 2$\sigma$ dispersion of the
sample as in Morate et al. (2019), corresponding to their Equation 5. (b) Same
as (a) but with main belt asteroids (in grey) separated from Cybeles (in
green), Hildas (in blue), and Trojans (in red). See the main text for the
semi-major axis values used to separate these populations. (c), (d), (e), and
(f) show the visible spectral slope distribution for the four dynamical
populations observed for absolute magnitudes $8<H<12$ (in blue) and $12<H<16$
(in beige).

###  4.4 Families

Collisional families are believed to be the direct outcome of a disruptive
and/or cratering event and thus, their members are expected to be composed of
similar material and to be exposed at a similar time to space. In Fig. 12, we
present with colored crosses the median values of $s2-m$ (with $m$ as the
slope obtained from our fitting model described in Eq. 1) and the depth of the
0.7$\mu$m absorption band for the members of a total of six collisional
families, all from the $Gaia$ sample. The size of the crosses corresponds to
the dispersion of the values. We show here only those families having five or
more members with computed $s2$ slope and with a 0.7$\mu$m band depth bigger
than zero: (Adeona: 12, Chloris: 5, Mitidika: 5, Themis: 35, Meliboea: 11, and
Alauda: 15). The slope difference $s2-m$ is indicative of the strength of the
UV absorption. We observe, within the dispersion of the points, a correlation
between that strength and the depth of the 0.7 $\mu$m absorption band, with
the families having a stronger UV absorption presenting a deeper band. This
result reinforces the findings described in Section 4.1. Again, a further
analysis of the primitive families will be carried out with DR4.

Figure 12: Scatter plot of the median values of $s2-m$ ($s2$ described in Fig.
2 and $m$ in Eq. 1) and the 0.7 $\mu$m band depth for the primitive families
that have 5 or more asteroids with computed $s2$ and band depth bigger than
zero (Adeona: 12, Chloris: 5, Mitidika: 5, Themis: 35, Meliboea: 11, and
Alauda 15). The size of the crosses is the dispersion of the values of the
families.

##  5 Conclusions

In this work, we have aimed to make a detailed study of the spectral features
of primitive asteroids using the $Gaia$ DR3, paying special attention to the
UV absorption feature, which can be inferred below 0.4 – 0.5 $\mu$m. We
analyzed 15,529 asteroids over the spectral range from 0.374 to 0.902 $\mu$m.
Our main results can be summarized as follows:

  * •

For C, P, and G-type asteroids, the 0.7-$\mu$m absorption band is correlated
with the UV absorption when including the bluest part of the spectra. These
two absorption features are signatures of iron-rich phyllosilicates and
indicative of high degrees of hydration in the minerals.

  * •

Using combinations of slopes as descriptors of the reflectance spectra in both
PCA and UMAP (dimensionality-reduction algorithms), we observed a bimodality
distribution of the C-types. One cluster displayed the 0.7 $\mu$m band and the
UV absorption, as with the G-types, and the other one did not display the band
at all.

  * •

F-types, which could not be identified without the use of the NUV wavelengths,
display the beginning of the UV absorption around 0.4 $\mu$m. We also found
hints that they are consistently smaller than other taxonomies. To confirm
these results, we would need further exploration in the laboratory as well as
more observations containing the UV-blue part of the spectra.

  * •

We obtained average values for band depth (3.5 $\pm$ 1.0 %) and central
wavelength (0.70 $\pm$ 0.03 $\mu$m) for the hydrated objects in $Gaia$ DR3.
This is in good agreement with previous works. We noticed that for smaller
asteroids the reflectance spectra are noisier and the obtained values of depth
and central wavelength have a larger dispersion.

  * •

We reproduced the $H$ vs. visible slope presented in Morate et al. (2019) for
the primitive families of the inner asteroid belt. They claimed larger
dispersion of slope values for smaller asteroids is not observed when using
the entire population of primitive main belt asteroids among $Gaia$ DR3. For
the populations beyond the main belt, namely, Cybeles, Hildas, and Trojans, we
found similar slope distributions as those found the literature, with both
Cybeles and Hildas presenting bimodal distributions for $H<12$.

All these results shed light on the importance of having spectral data at the
shortest wavelengths to better characterize the primitive taxonomies, showing
that this is a promising region for diagnosing the composition of the
primitive asteroids.

###### Acknowledgements.

FTR, JdL, and JL acknowledge support from the Agencia Estatal de Investigación
del Ministerio de Ciencia e Innovación (AEI-MCINN) under the grant ”Hydrated
Minerals and Organic Compounds in Primitive Asteroids” with reference
PID2020-120464GB-100.
FTR also acknowledges the support from the COST Action that fully found his
stay at OCA where he began to study the Gaia dataset. He also acknowledges the
OCA group of asteroids for their support and welcome during those days. He
also acknowledges the big effort by JdL and ET in this work.

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##  Appendix A References of visual albedos and diameters

Table 2: Data references used for albedos and diameters. Alí-Lagoa et al.
(2013, 2016, 2018, 2020); Alí-Lagoa & Delbo’ (2017); Bartczak et al. (2014);
Bauer et al. (2013); Berthier et al. (2014, 2023); Chavez et al. (2021); Clark
et al. (1999); Delbo (2004); Delbo’ & Tanga (2009); Duffard et al. (2014);
Ďurech et al. (2011); Fornasier et al. (2013); Grav et al. (2011, 2012a,
2012b); Hasegawa et al. (2013); Hanuš et al. (2013, 2015, 2017a, 2017b, 2018,
2020); Herald et al. (2019); Horner et al. (2012); Hung et al. (2022); Jiang &
Ji (2021); Li et al. (2016); Licandro et al. (2016); Magri et al. (2007b, a);
Mainzer et al. (2011a, 2012); Marchis et al. (2006, 2012); Marsset et al.
(2023); Masiero et al. (2011, 2012, 2014, 2017, 2020, 2021); Morgado et al.
(2021); Myhrvold et al. (2022); Nugent et al. (2015, 2016); Pravec et al.
(2012); Russell et al. (2016); Ryan et al. (2015); Ryan & Woodward (2010,
2011); Shepard et al. (2008); Sugita et al. (2019); Tedesco et al. (2002);
Thomas et al. (1999); Trilling et al. (2010); Usui et al. (2011); Vernazza et
al. (2020, 2021); Viikinkoski et al. (2017); Watanabe et al. (2019);Yang et
al. (2020)
---

##  Appendix B UMAP results

In Fig. 13, we show the resulting UMAP 2-D representation, but adding the
following information, from top to bottom, left to right: $s$, $s2$,
($s2$-$s3$), and ($s4$-$s3$). A color scale is shown to the right of each
panel, as in Fig. 9.

Figure 13: Same as Fig. 9 but using the four spectral features described in
the text: $s$, $s2$, $s2$-$s3$, and $s4$-$s3$. Crosses correspond to the
median for each taxonomy (following the same color code) and the size of the
error bars is the interquartile range.


# A Method to Load Tellurium in Liquid Scintillator for the Study of
Neutrinoless Double Beta Decay
(NIM A,Volume 1051, 2023, 168204 )

D.J. Auty  University of Alberta, Department of Physics, 4-181 CCIS, Edmonton,
AB T6G 2E1, Canada  D. Bartlett  Queen’s University, Department of Physics,
Engineering Physics & Astronomy, 64 Bader Lane, Kingston, ON K7L 3N6, Canada
S.D. Biller  University of Oxford, Department of Physics, Denys Wilkinson
Building, Keble Rd, Oxford OX1 3RH, UK<EMAIL_ADDRESS>D.
Chauhan  M. Chen  O. Chkvorets  Laurentian University, Department of Physics,
935 Ramsey Lake Road, Sudbury, ON P3E 2C6, Canada  S. Connolly  X. Dai  E.
Fletcher  K. Frankiewicz  Boston University, Department of Physics, 590
Commonwealth Avenue, Boston, MA 02215, USA  D. Gooding  C. Grant  S. Hall
SNOLAB, Creighton Mine No. 9, 1039 Regional Road 24, Sudbury, ON P3Y 1N2,
Canada  D. Horne  S. Hans  B. Hreljac  T. Kaptanoglu  University of
Pennsylvania, Department of Physics & Astronomy, 209 South 33rd Street,
Philadelphia, PA 19104-6396, USA  University of California, Berkeley,
Department of Physics, 366 Physics North MC 7300, Berkeley, CA 94720-7300, USA
B. Krar  C. Kraus  T. Kroupová  I. Lam  Y. Liu  S. Maguire  Brookhaven
National Laboratory, Chemistry Department, Building 555, P.O. Box 5000, Upton,
NY 11973-500, USA  C. Miller  S. Manecki  R. Rosero  L. Segui  M.K. Sharma  S.
Tacchino  B. Tam  L. Tian  J.G.C. Veinot  S.C. Walton  J.J. Weigand
Technische Universität Dresden, Faculty of Chemistry and Food Chemistry, 01069
Dresden, Germany  A. Wright  Institute of Particle Physics, Canada  M. Yeh  T.
Zhao

###### Abstract

A method has been developed to load tellurium into liquid scintillator so as
to permit searches for neutrinoless double beta decay with high sensitivity.
The approach involves the synthesis of an oil-soluble tellurium compound from
telluric acid and an organic diol. The process utilises distillable chemicals
that can be safely handled underground and affords low radioactive
backgrounds, low optical absorption and high light yields at loading levels of
at least several percent Te by weight.

###### keywords:

Scintillator, Tellurium, Neutrinoless Double Beta Decay

##  1 Introduction

The search for neutrinoless double beta decay ($0\nu\beta\beta$) is recognized
as one of the highest priority areas of modern particle physics research. The
observation of this lepton-number violating process would establish the
absolute mass scale of neutrinos, provide insight into Grand Unification and
lend weight to models of leptogenesis. [1].

One promising technique being employed by the SNO+ experiment [2] for such a
search involves loading a large volume of liquid scintillator based on linear
alkylbenzene (LAB) with a candidate $0\nu\beta\beta$ isotope. The use of large
self-shielding volumes of high purity liquids allows the potential for
realising very large quantities of relevant isotope with low levels of
background. Further, the ability to easily modify the liquid configuration and
separately assay different components offers a significant advantage for
probing any candidate signal and readily allows the implementation of further
improvements to purification and loading. A particularly interesting candidate
isotope in this regard is 130Te. Owing to the isotope’s large natural
abundance (34%), enrichment is unnecessary, making it considerably more
economical and practical to deploy large quantities.

A method for loading tellurium into organic liquid scintillator has been
developed based on the formation of oil-soluble compounds derived from
telluric acid (Te(OH)6, hereafter TeA) and organic diols in conjunction with
N,N-dimethyldodecylamine (DDA), which acts as a stabilisation/solubilisation
agent. While the method is amenable to a variety of diols, 1,2-butanediol (BD)
was selected due to its relatively low molecular weight (permitting a higher
fractional Te content), relatively low cost and ease of distillation. The
chemicals involved can thus all be purified to high levels, have high flash
points and are relatively safe to work with in underground environments. In
addition, both BD and DDA can be obtained via non-biogenic production
processes, which is important in order to maintain the low 14C levels needed
to allow low threshold operation of large liquid scintillation detectors. The
loading process results in low optical absorbance and good light output in
larger detectors for loading levels of at least several percent Te by weight.
This is particularly important for $0\nu\beta\beta$ experiments, where good
energy resolution is needed to reduce backgrounds from $2\nu\beta\beta$
events. Stability of the loading has been explicitly demonstrated to be at
least in excess of 5.5 years at room temperature. In addition, acrylic
compatibility of the loading technique was established via accelerated ageing
tests, in which stressed acrylic pieces were exposed to highly concentrated
($\sim$25%) Te-loaded LAB. No additional crazing or deterioration of the
mechanical integrity was observed within the sensitivity of the tests. Two
variants of the loading method are presented below, each resulting in slightly
different LAB-soluble mixtures of tellurium compounds with different
fluorescence quenching properties. Sources for the TeA[3], BD[4] and DDA[5]
used for these studies are provided in the references.

##  2 Loading Method

###  2.1 Overview

When BD is added to dilute aqueous solutions of TeA at room temperature,
condensation reactions lead to the attachment of up to two bidentate BD
ligands for each tellurium center, as indicated by nuclear magnetic resonance
(NMR) measurements in Figure 1. This dilute form with 2 attachments will
hereafter be referred to as DF2.

Figure 1: NMR spectra showing spontaneous formation of “precursor” TeA-diol
forms for dilute concentrations of TeA and BD in water at room temperature.
Representative forms are shown at the top. No peaks corresponding to 3
attached diols are seen (dashed box), implying a preference for 2 bidentate
attachments.

This condensation process is in equilibrium with hydrolysis reactions, as
indicated in Figure 2.

Figure 2: Equilibrium between condensation and hydrolysis reactions for BD and
TeA in water.

At higher concentrations of TeA, the environment is more acidic; the TeA has a
pH of $\sim$3.5 for a 10% aqueous solution and the BD ligand attachment
further increases the acidity. This tends to drive the equilibrium in the
direction of hydrolysis. The balance can be tipped back towards condensation
by adding N,N-dimethyldodecylamine (DDA) or heat to the system. Either
approach thus leads to the formation of precursor compounds that form the
basis for diol-loading of tellurium. Solubilisation in LAB can then be
accomplished by either 1) adding additional heat to form more complex
oligomers through further condensation reactions or 2) using an amine such as
DDA for neutralisation in water and to then associate a long carbon chain
through non-binding ionic interactions with the precursor compounds for
solubility in LAB. Details of these two approaches and properties of the
resulting Te- loaded scintillator (TeLS) mixtures will now be described. The
following nomenclature will be used: PC1 will refer to the precursor compounds
initially formed from the addition of heat; TeBD1 will refer to the oligomers
formed from further heating of PC1; PC2 will refer to the precursor compounds
initially formed via neutralisation; and TeBD2 will refer to the solubilised
pairing of PC2 and DDA.

###  2.2 Type I Loading: Solubilisation via Heating

In this approach, aqueous TeA (30-50% w/w) is combined in a 1:3 molar ratio
with BD. 125Te NMR and mass spectrometry measurements suggest that the initial
PC1 formations are largely Te monomers with two bidentate and one monodentate
BD attachments. The mixture is heated under vacuum to remove water at 70-80oC,
with care taken to avoid local temperatures above 90oC to inhibit side
reactions. The mixture is agitated and sparged with nitrogen gas to promote
water removal. As water is removed from the reaction system, additional
condensation reactions occur. This leads to the formation of a viscous and
complex mixture of short-chain oligomers in which the precursor compounds are
more fully substituted and linked together by BD. This is evident in the 125Te
NMR spectra as broadening of peaks, commonly seen in
polymerisation/oligomerisation, which re-form singlet peaks when the proton is
decoupled (Figure 3). Extensive oligomer formation is not observed if water is
not removed from the reaction, which is consistent with an equilibrium between
hydrolysis and condensation reactions. With continued heating and water
evaporation, the viscosity of the product increases. This observation is
suggestive of increasing molecular weight via oligomerisation and/or self-
interaction of the oligomers.

As the heating and water removal continues, the TeBD1 product becomes soluble
in LAB. The transition to solubility is rapid; the material changes from
largely insoluble in LAB to completely soluble in a very short period of time.
Typical water concentration is extremely low at the point of solubility
($<$0.1%). The sudden transition to solubility may be the result of structural
self-organisation of the oligomer chains. At the LAB solubility point, the
addition of a small amount of additional BD to the TeLS induces the formation
of two phases. Continued heating of the LAB soluble TeBD material results in
further evolution of the 125Te NMR (Figure 3), and increased “BD tolerance”.
Tolerance of BD addition can thus provide a useful diagnostic of reaction
progress. This is likely the result of structural evolution involving
continued dehydration within the oligomers.

Figure 3: 125Te NMR spectra of TeBD1 formed by oligomerisation as a function
of heating time.

Electrospray ionisation (ESI) Mass Spectrometry (MS) data for TeBD1 produced
with a 3:1 BD:TeA ratio is consistent with multiple species consisting of
short oligomer chains containing up to at least three Te centers (Figure 4).

Figure 4: Positive ion ESI mass spectra for TeBD1 synthesis via
oligomerisation at 80oC. The sample was heated for two hours beyond the LAB
solubility point. Possible structures for various peaks are shown in Figure 5.

Using the observed masses and elemental distributions, it is possible to
identify potential configurations of the various species in the MS spectra.
Illustrations of several such structures corresponding to the main peaks in
Figure 4 are shown in Figure 5.

Figure 5: Possible structures of dominant species identified in Figure 4.

The integrity of the TeBD1-LAB mixture is highly sensitive to the presence of
water. Indeed, over the long term, even tiny amounts of water ($\sim$hundreds
of ppm) can lead to the deterioration of TeBD1 oligomers as the result of
hydrolysis reactions that eventually lead to a loading instability, where
white crystalline Te-containing material appears either in the liquid itself
or attached to the glass of the sample container (see Section 3). In a
carefully controlled environment, TeBD1 in LAB can be stable for several years
or more. Nevertheless, it is advantageous to add a stabiliser to prevent
crystal formation and provide an environmentally robust loading protocol.

###  2.3 Solubilisation and Stabilisation with DDA

The stability of TeBD1 in scintillator can be dramatically improved by the
introduction of DDA. The principle solubilisation mechanism is believed to be
the formation of an association between OH groups in the Te compounds and
tertiary amino groups of DDA, effectively adding a long hydrocarbon tail to
the compounds, thereby promoting solubility in LAB and inhibiting further
oligomerisation. Tests indicate that DDA-protected TeLS is very stable and
robust against water exposure, as detailed in Section 4. The de-protonation of
the acidic oligomers by the amine has the added benefit of reducing the
fluorescence quenching in the scintillator. Based on observations of the light
yield, the optimal molar ratio of DDA to Te appears to be close to 0.5:1, with
a fairly broad maximum extending from $\sim$0.25-0.75 (Figure 6). Ratios in
this range were also found to work well for maintaining stability and
solubilising crystals in samples that had been exposed to water prior to DDA
addition.

Figure 6: Relative light level as a function of DDA molar concentration with
respect to Te for 1% loading in LAB with 2g/L PPO.

###  2.4 Type II Loading: Direct Solubilisation of PC2 Formations with DDA

Neutralisation and solubilisation of the precursor compounds in LAB can be
accomplished by first adding DDA to the initial reaction mixture with a molar
ratio of 0.5:1:2 for DDA:TeA:BD. In this case, formation of the precursor
compound (PC2) happens even in the absence of heat and that compound is then
directly solubilised into LAB via DDA through the ionic association described
above without the need for oligomerisation. This “cold synthesis” approach,
which need not take place in an aqueous environment, simply requires the
removal of water generated by the condensation reactions that take place
during compound formation in order to mix with LAB. This can be accomplished,
for example, via nitrogen sparging. Mass specrometry and NMR measurements
confirm that, when no heat is applied, the PC2 compounds that are solubilised
to form TeBD2 consist almost entirely of tellurium monomers with two bidentate
BD attachments (Figures 7-8). These are identical to DF2 formations in Figure
1, indicating a relatively weak association between almost all tellurium
species and DDA.

Figure 7: NMR spectrum of TeBD2 formed via direct DDA solubilisation with a
2:1 BD:Te ratio. Inset shows a zoomed view of main peak. Figure 8: ESI mass
spectrum of TeBD2 formed via direct DDA solubilisation with a 2:1 BD:Te ratio.
Inset shows a zoomed view of main peak.

It is of particular interest to note that the fluorescence quenching in this
approach is significantly reduced relative to oligomerisation, as discussed in
Section 4. This would allow for a notable increase in loading levels while
maintaining the same light output (and, hence, energy resolution).

###  2.5 Hybrid Loading

We briefly note in passing that mixed loading approaches are possible, where
heating is initially used to begin precursor formation and drive off the
majority of the water, at which point DDA is then employed to complete the
solubilisation. This is the approach being taken by SNO+, as it allows TeA to
be transported as a solution during the purification and synthesis, while also
permitting a more controlled and rapid solubilisation with DDA. The nature of
the forms produced and their fluorescence quenching characteristics (described
below) are, perhaps unsurprisingly, between those of Type I and Type II
approaches, with the specific mix dependent on the amount of heating used
before DDA is introduced.

##  3 Loading Stability

Over the course of TeLS development, many hundreds of samples have been
produced under various conditions and monitored for stability over several
years. The loading has been found to be robust with regard to environmental
conditions, aside from the addition of large amounts of acid or base or
exposure to water. As previously mentioned, TeBD1 that has not been stabilised
with DDA is highly water sensitive and even modest humidity exposure
($\sim$hundreds of ppm) can result in crystal formation on the timescale of
weeks to months, depending on the degree of exposure. X-ray crystallography
indicates these formations are composed of DF2 units. However, none of the
samples containing DDA have ever shown signs of such behaviour after more than
5.5 years of monitoring.

Separation effects have also been observed following humidity exposure,
particularly in samples without DDA, in which a heavier gel-like portion
containing Te settles to the bottom of the sample vial. This is believed to be
due to the association of water molecules with TeBD1 or TeBD2 rather than the
immediate hydrolysis of the compounds themselves. This phenomenon can be
sensitively tracked by monitoring the fluorescence yield of the mixture, which
increases as phase separation progresses owing to reduced fluorescence
quenching in the remaining portion of the scintillator. DDA dramatically
reduces the propensity for phase separation, but does not eliminate it
altogether in cases of extreme humidity exposure. However, even when
separation in samples involving DDA does occur, loading integrity can be
restored through the removal of water.

Studies of these separation effects were performed by standing open vials of
loaded scintillator with 2g/L of 2,5-Diphenyloxazole (PPO) in a sealed
container holding a $\sim$1 cm deep pool of water to create a high humidity
environment. Water beads in the samples were visible after a day, indicating
that they were saturated. The fluorescence yield was monitored by periodically
exposing samples to a 90Sr$/^{90}$Y source and measuring the light output with
a standard bialkalai photomultiplier tube. Figure 9 compares the endpoint of
the observed fluorescence spectra after 300s of counting relative to the
initial values as a function of time for 1% Te loading with TeBD1 following a
48hr humidity exposure for samples with and without DDA.

Figure 9: Relative fluorescence levels (inversely related to Te content) for
scintillator initially loaded with TeBD1 in a 1% Te concentration as a
function of time following a 48hr humidity exposure. Clear symbols represent
samples without added DDA and solid symbols represent samples with DDA added.
Data from duplicate samples of each type are shown to indicate the size of
sample variations.

The behaviours of TeBD1 + DDA and TeBD2 were studied for a much more extreme
exposure of 3 months. In both cases, the fluorescence yield after humidity
exposure approaches that of unloaded scintillator. XRF measurements confirm
that the majority of Te had been removed from the LAB phase at this stage. The
samples were then sparged with nitrogen gas for two hours to remove the water.
In both cases, XRF measurements indicated that full Te loading had been
recovered. Interestingly, the post-recovery TeBD1 + DDA fluorescence spectrum
exhibited a higher light yield compared to that before humidity exposure, but
matched well with the spectrum from TeBD2 (which has an intrinsically higher
light yield). This suggests that the larger TeBD1 formations may have been
broken down by hydrolysis into the smaller structures that were then
solubilised by DDA, effectively creating a TeBD2 loading.

##  4 Optical Properties

###  4.1 Light Yield

Figure 10 shows the relative light levels observed as a function of Te
loading. This is based on inferring the endpoint of a 90Sr/90Y source that is
placed beneath a standard borosilicate fluorescence vial containing the
scintillator sample and measuring the pulse height distribution observed using
a bialkalai PMT (Hamamatsu H11432-100). Measurement uncertainties are
dominated by systematics associated with sample preparations and variations in
the vial thickness, which alters the average energy of electrons that enter
the scintillator. The results of multiple samples in different vials are
therefore shown to indicate the spread in measurement values. The trends are
well described by the linear Stern-Volmer relationship, as shown in Figure 11.
For LAB with 2g/L PPO, it is seen that fluorescence quenching to half the
unloaded light level occurs at about 0.7% Te for TeBD1 and $\sim$1.8% Te for
TeBD2. These figures also indicate that, by tripling the PPO concentration to
6g/L, this can be further improved, with light levels halving at
concentrations of $\sim$3% Te, representing an effective reduction in
quenching by a factor of $\sim$3.5 relative to TeBD1 with 2g/L PPO.

Figure 10: Relative light yields as a function of percent Te loading for LAB
with 2g/L PPO and TeBD1 loading (crosses); TeBD2 loading (open circles); and
TeBD2 loading with boosted PPO (solid circles). Figure 11: Ratio of unquenched
to quenched fluorescence yields as a function of Te concentration for LAB with
2g/L PPO and TeBD1 loading (crosses); TeBD2 loading (open circles); and TeBD2
loading with boosted PPO (solid circles).

###  4.2 Transparency

The UV-vis extinction of TeBD compounds was measured using a variety of loaded
LAB samples containing 10% concentrations of Te. Some samples involved purely
heated solubilisation and some used a mixture of heated and DDA solubilisation
(no dependency on this was observed). In all cases, telluric acid was first
purified through thermal recrystallisation and solutions were then filtered to
remove insoluble impurities. The LAB, BD and DDA were also distilled.
Extinction curves were obtained using a 10 cm quartz cell in a PerkinElmer
Lambda-800 Spectrophotometer. These were then normalised in the region of 700
nm, far from the expected influence of TeBD absorption and where LAB
transparency is high, so that the contribution of LAB could be accurately
subtracted. Results were also cross-checked using a 5 cm cell. The resulting
LAB-subtracted curves are shown in Figure 12. These measurements are dominated
by systematic uncertainties, with the observed variations between samples due
to differences in sample preparation, including purification and filtering.
Extinction lengths at higher wavelengths are also at the limit of our
systematic uncertainties in subtracting the spectra. Nonetheless, excellent
transparency is indicated, even at these high loading levels, with extinction
lengths exceeding 10 m above $\sim$400 nm. The transparency at percent-level
loadings is therefore expected to be significantly better than this.

A large number of samples (mostly with 0.5% Te in LAB) have been monitored for
long periods of time to establish long term optical stability. In a subset of
cases, increased absorption was observed at lower wavelengths in the region
below $\sim$430 nm. In addition to the known UV sensitivity of DDA, a
dependence on the quality/age of the LAB and DDA was observed that related to
the amount of oxidation and/or free radicals present at the time of sample
preparation. If this activity is too high, this can lead to the observed
absorption increase. However, for samples produced from freshly purified stock
materials that were stored under dark conditions, no noticeable change in
absorption was observed over a timescale of more than 3 years at room
temperature. There is some indication that TeBD itself may act as an anti-
oxidant to maintain optical stability if starting from initially fresh stock
materials. The early introduction of antioxidants may also help further
mitigate these effects (currently under study).

Figure 12: Extinction length of TeBD for various 10% Te samples with
contributions from LAB subtracted. These measurements are dominated by
systematic uncertainties associated with sample preparation, including
purification and filtering. For extinction lengths above 10 m, the accuracy of
LAB subtraction also starts to become unreliable.

##  5 Pulse Shape Discrimination

The emission time profile of TeLS was measured using two fast 1” square
Hamamatsu PMTs, the R7600-U200 and the R5900. The R7600-U200 was used as the
trigger for the DAQ and provides the time zero for the system. It was
optically coupled to an UVT acrylic cube, which had a cylindrical volume
hollowed out and filled with nitrogen-bubbled Te-loaded scintillator. Either a
90Sr/90Y $\beta$ source or a 210Po $\alpha$ source was then deployed above the
scintillator. The R5900 (measurement PMT) was kept 30 cm from the source to
ensure a low coincidence rate, resulting in the R5900 detecting primarily
single photoelectrons. A Lecroy WaveRunner 606Zi 600 MHz oscilloscope was used
to digitize the signals for both PMTs. A comparison between the data for
$\beta$ and $\alpha$ particles is shown in Figure 13 for scintillator samples
of LAB+2g/L PPO loaded with 0.5% Te by weight. Nearly identical distributions
were obtained for either synthesis method. The difference in pulse shapes
between $\beta$ and $\alpha$ particles is comparable to that seen in other
liquid scintillation detectors, where good levels of PSD have been realised
[6].

Figure 13: A comparison of the emission time profiles of 0.5% Te-loaded
LAB+PPO under $\beta$ and $\alpha$ excitation.

The $\Delta$t spectrum can be fit using an empirical model consisting of the
sum of four exponentials:

$A_{1}\times\left[\frac{1}{\sqrt{2\pi\sigma^{2}}}e^{-\frac{(t-\mu)^{2}}{2\sigma^{2}}}\circledast\sum_{i=1}^{4}\frac{N_{i}}{\tau_{i}}e^{-t/\tau_{i}}\right]+A_{2}\times\left[\frac{1}{\sqrt{2\pi\sigma_{\rm
ap}^{2}}}e^{-\frac{(t-\mu_{\rm ap})^{2}}{2\sigma_{\rm ap}^{2}}}\right]+A_{3}$
(1)

The first component in Equation 1, with normalization $A_{1}$, consists of a
Gaussian detector response, with width $\sigma$ and mean $\mu$, convolved with
the scintillator emission timing, which is modeled as the sum of four
exponentials with time-constants $\tau_{i}$ and normalisations $N_{i}$, where
$\sum_{i}^{4}N_{i}=1$. The second component, with normalization $A_{2}$,
models a small after-pulsing peak, with $\Delta t\approx 160$, using a
Gaussian with width $\sigma_{ap}$ and mean $\mu_{ap}$. The values of
$\sigma_{ap}$ and $\mu_{ap}$ are constrained based on measurements with a
Cherenkov light source. The last component ($A_{3}$) models the flat dark-
rate, and the values of $\sum_{i}^{3}A_{i}=1$. Fit values for the
normalisations and time constants from Equation 1 for $\beta$ and $\alpha$
particle excitation are given in Table 1.

Particle | $N_{1}$ | $N_{2}$ | $N_{3}$ | $N_{4}$
---|---|---|---|---
$\beta$ | 0.72 $\pm$ 0.02 | 0.23 $\pm$ 0.02 | 0.02 $\pm$ 0.02 | 0.03 $\pm$ 0.02
$\alpha$ | 0.63 $\pm$ 0.02 | 0.23 $\pm$ 0.02 | 0.07 $\pm$ 0.02 | 0.07 $\pm$ 0.02
| $\tau_{1}$ | $\tau_{2}$ | $\tau_{3}$ | $\tau_{4}$
$\beta$ | 3.70 $\pm$ 0.26 | 10.0 $\pm$ 2.2 | 52.0 $\pm$ 12.0 | 500 $\pm$ 176
$\alpha$ | 3.69 $\pm$ 0.10 | 15.5 $\pm$ 1.3 | 79.3 $\pm$ 10.0 | 489 $\pm$ 164
Table 1: The fitted values for the normalisations and time constants from
Equation 1 for $\beta$ and $\alpha$ particle excitation of Te-loaded LAB+PPO.

##  6 Summary

A technique has been developed to efficiently load tellurium into organic
liquid scintillator to provide a highly sensitive means of searching for
neutrinoless double beta decay from 130Te (34% natural abundance). This is
accomplished by synthesising a group of compounds via condensation reactions
between telluric acid and 1,2-butanediol (BD), with N,N-dimethyldodecylamine
(DDA) acting as a stabilisation and solubilisation agent. Both BD and DDA can
be obtained via non-biogenic production processes, which is important in order
to maintain the low 14C levels needed to allow low threshold operation of
large liquid scintillation detectors. The chemicals involved can be easily
purified, have high flash points and can be handled underground in large
quantities with reasonable safety protocols. The loading method is also found
to be highly compatible with acrylic, which is important for detectors using
this as a buffer between scintillation and light detection regions. Two
variants of the approach have been presented: one in which solubilisation is
accomplished by oligomerisation via heating, with DDA added afterwards to
guarantee stability; and one in which DDA is added at the beginning to
directly solubilise precursor compounds. The latter approach yields improved
light output with fluorescence quenching reduced by a factor of $\sim$3
compared with the former. Both approaches result in a compound that is
completely miscible with LAB scintillator with excellent optical transparency
and loading stability verified to be at least in excess of 5.5 years at room
temperature. The methods detailed here allow for high light output for Te
loading at the level of at least several percent by weight in liquid
scintillator.

##  7 Acknowledgements

The authors wish to thank the SNO+ collaboration and SNOLAB for their support
and many useful discussions. This research was supported by: Canada: Natural
Sciences and Engineering Research Council, the Canadian Institute for Advanced
Research (CIFAR), Ontario Early Researcher Awards, Arthur B. McDonald Canadian
Astroparticle Physics Research Institute; Germany: the European Research
Council (ERC starting grant SynPhos-307616), the German Science foundation (WE
4621/6-1) and TU Dresden; UK: Science and Technology Facilities Council
(STFC); US: Department of Energy Office of Nuclear Physics, National Science
Foundation. Appropriate representations of the data relevant to the
conclusions have been provided within this paper. For the purposes of open
access, the authors have applied a Creative Commons Attribution licence to any
Author Accepted Manuscript version arising.

## References

  * [1] Kai Zuber, Neutrino Physics, 3rd edition, CRC Press, Boca Raton (2020)
  * [2] The SNO+ Collaboration, JINST, Volume 16 (2021)
  * [3] TeA Supplier: Vital Materials Co., LTD.; Manufactured by: First Rare Materials Co., LTD., Heyun Industrial Zone, Qingxin County, Qingyuan, Guangdong Province, China
  * [4] BD Supplier: Kowa American Co.; Manufactured by: Shinko Organic Chemical Industry, LTD.,18-26 Sumiyoshihama-Cho, Higashinada-Hu, Kobe-shi Hyyogo, 658-0042, Japan
  * [5] DDA Supplier: Albemarle Co.; Manufactured by: Albemarle Co., P.O. Box 729 Magnolia, Arkansas 71754-0729 USA
  * [6] H. O. Back et al., Nucl. Instrum. Meth. A, 584:98-113, (2008)