11institutetext: Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS,
Laboratoire Lagrange, Bd de l’Observatoire, CS 34229, 06304 Nice Cedex 4,
France
11email<EMAIL_ADDRESS>22institutetext: V. N. Karazin Kharkiv
National University, 4 Svobody Sq., Kharkiv 61022, Ukraine 33institutetext:
INAF - Osservatorio Astrofisico di Torino, via Osservatorio 20, 10025, Pino
Torinese (TO), Italy 44institutetext: Harvard-Smithsonian Center for
Astrophysics, 60 Garden St., MS 15, Cambridge, MA, 02138, USA

#  Gaia DR3 asteroid reflectance spectra: L-type families, memberships, and
ages

Applications of Gaia spectra

R. Balossi 11 P. Tanga 11 A. Sergeyev 11 2 2 A. Cellino 33 F. Spoto 55

###### Abstract

Context. The Gaia Data Release 3 (DR3) contains reflectance spectra at visible
wavelengths for 60,518 asteroids over the range between 374-1034 nm,
representing a large sample that is well suited to studies of asteroid
families.

Aims. We want to assess the potential of Gaia spectra in identifying asteroid
family members. Here, we focus on two L-type families, namely Tirela/Klumpkea
and Watsonia. These families are known for their connection to Barbarian
asteroids, which are potentially abundant in calcium-aluminum rich inclusions
(CAIs).

Methods. Our method is based (1) on a color taxonomy specifically built on
Gaia data and (2) the similarity of spectra of candidate members with the
template spectrum of a specific family.

Results. We identified objects in the halo of Tirela/Klumpkea, along with
possible interlopers. We also found an independent group of eight asteroids
erroneously linked to the family by the hierarchical clustering method (HCM).
Consequently, the knowledge of the size distribution of the family has been
significantly improved, with a more consistent shape at the larger end. The
Watsonia family is a more intricate case, mainly due to its smaller size and
the less marked difference between the spectral types of the background and of
the family members. However, the spectral selection helps identify objects
that were not seen by HCM, including a cluster separated from the family core
by a resonance.

Conclusions. For both families, the V-shape is better defined, leading to a
revised age estimation based on the memberships established mainly from
spectral properties. Our work demonstrates the advantage of combining the
classical HCM approach to spectral properties obtained by Gaia for the study
of asteroid families. Future data releases are expected to further expand the
capabilities in this domain.

###### Key Words.:

small bodies – asteroid families – Gaia mission

##  1 Introduction

The publication of asteroid reflectance spectra in Gaia DR3 (Gaia
Collaboration et al., 2023) has been followed up by studies that exploit the
large sample of more than 60,000 objects. The applications concern individual
objects part of larger groups (Hasegawa et al. 2022, Carruba et al. 2024,
Minker & Carry 2023), primitive asteroids, and families (Ferrone et al. 2023,
Delbo et al. 2023, Tatsumi et al. 2023), and near-Earth Asteroids (Sergeyev et
al., 2023), as well as comparisons with andesitic meteorites (Galinier et al.,
2023). While the exploitation of Gaia asteroid spectra at a high signal-to-
noise ratio (S/N) appears to be generally rather straightforward, the DR3
sample poses some difficulties for fainter targets, especially concerning the
behavior at the longest visible wavelengths. This is a known limitation
already discussed in Gaia Collaboration et al. (2023), specific to this first
large data release, which should be overcome in future publications. A less
problematic, systematic bias in the extreme blue-violet region has been
identified before (Tinaut-Ruano et al., 2023).

The main goal of this article is to assess the potential impact of the
increased number of spectra available over family membership, thanks to Gaia
DR3. This aspect involves classification attempts based on spectra alone and
validation via comparisons to memberships derived by hierarchical clustering
methods (HCM) alone, based on proper elements (Zappala et al. 1990, Milani et
al. 2016). Also, albedo is exploited in the following when appropriate. We
base our approach on quantitatively computing the similarity of spectra and,
separately, by a classifier that groups asteroids into spectral classes. Our
classifier, based on machine learning, has been optimized specifically on Gaia
spectra and provides the two most probable taxonomies for each asteroid.

Two L-type families are selected for this study, namely Tirela/Klumpkea and
Watsonia. They present spectral similarities and both harbor so-called
Barbarians, asteroids characterized by a peculiar polarimetry (Cellino et al.
2006, Gil-Hutton et al. 2008, Gil-Hutton et al. 2014, Cellino et al. 2014,
Bendjoya et al. 2022). Their scattering properties and reflectance spectra
have been associated with the possible large abundance of calcium-aluminum
rich inclusions (CAIs) in a CV–like matrix, with a low degree of thermal or
aqueous alteration (Sunshine et al., 2008; Devogèle et al., 2018). Barbarians
could represent an interesting ancient population preserving the trace of
highly inhomogeneous accretion (with a preferential segregation of some highly
refractory material) in the early protoplanetary disk. A recent finding that
the variety of CV chondrites available could at least partially match the
observed variety of Barbarians (and in general, L-type) asteroids (Mahlke et
al., 2023) adds further uncertainty and interest to the interpretations about
the nature of this category of objects. In addition, the two selected families
differ in several aspects, in particular, the position in the belt (middle
belt for Watsonia, outer belt for Tirela); the albedo; the size distribution;
and the number of known members. Thus, they offer a very different context to
test our approach. Eventually, our spectra-based membership was used to re-
compute the age of the family, based on the same approach as Spoto et al.
(2015).

We stress here that by adopting the spectral similarity as the main driver for
our family member selection, we are enforcing the commonly accepted paradigm
of compositional homogeneity within the family. The consequence, to some
extent, is that we may suppress the possible evidence of any heterogeneity.
However, some of the approaches we use here can also be adapted when looking
for spectral diversity inside families, especially with future Gaia releases
where the S/N of reflectance spectra is expected to increase for all the
published asteroids.

In the process, we compare our family memberships to those obtained by the
HCM. Some cautions are due for this comparison, as several HCM implementations
exist in practice and they are not all equivalent. In general, they differ by
the approach used to define the cutoff distance in the proper element space
(corresponding to a difference in velocity), used as a limit for linking
family members. Beyond a certain distance, the ”chaining” effect occurs (i.e.,
an overlap of neighboring families) and the family tends to merge into a
background of small asteroids. Since, in the following, we mainly consider the
HCM implementation by Milani et al. (2014, 2016), we recall here that their
procedure consists of choosing different quasi-random levels (defining
velocity limits) for several intervals of heliocentric distance, thereby
taking into account local differences in the asteroid population. Also, they
divide the search for family membership into several steps of increasing
distance, from family core to halo. It is thus clear that the details of the
membership are dependent on parameters that are specific to each family
identification effort. However, we do not expect these differences to
substantially affect our approach, as the Gaia survey is limited in depth, in
principle at absolute magnitude G$\sim$20.5, but in practice, also by the
quality of the spectra. We show that our sample is incomplete below 5–8 km in
diameter in the Main Belt. For the larger asteroids on which we base this
work, the membership is not very sensitive to differences in the HCM
implementations.

The article is organized as follows. In Sect. 2, we briefly describe the
color-based taxonomy used to classify Gaia spectra. In Sect. 3, we present our
analysis on the Tirela/Klumpkea family, focused on its membership compared to
HCM and a determination of its age. In Sect. 4, a similar analysis for the
Watsonia family is illustrated. Finally, in Sect. 5, our results and future
prospects are presented.

##  2 Classifying Gaia spectra

Figure 1: Density plot of all the reflectance spectra of L- type asteroids
observed by Gaia. Darker areas correspond to the overlap of a larger number of
spectra.

Widely recognized asteroid taxonomy schemes, such as those proposed by Tholen
(1984) and by DeMeo et al. (2009), along with the more recent framework
proposed by Mahlke et al. (2022), systematically classify asteroids based on
their reflectance spectra and albedo measurements. The concept of asteroid
taxonomy is based on analyzing the reflective properties of asteroids to
determine their surface composition. This classification system leverages the
spectral signatures reflected by asteroid surfaces, which indicate their
compositional characteristics. These methods have been instrumental in linking
observable traits to the surface composition of asteroids, thereby providing
insights into their mineralogical makeup.

Figure 2: Albedo distribution of the objects located within the
Tirela/Klumpkea region. Left panel: NEOWISE albedo distribution for the
objects of the complete sample (in blue), of the Gaia sample (in yellow), of
the family members listed in AstDyS (in red) and of the family members listed
in AFP (in green). The vertical black dotted line at $\rho_{V}=0.12$ separates
low albedo from high albedo objects. Right panel: Distribution in the $(a,e)$
plane of the objects located within the Tirela/Klumpkea region. Blue points
have $\rho_{V}<0.12$, red points have $\rho_{V}>0.12,$ and grey points do not
have albedo measurements. Figure 3: Template spectrum of the Tirela/Klumpkea
family (in green). The reflectances have been computed by averaging the Gaia
spectra of (1040) Klumpkea (in blue) and (1400) Tirela (in orange). The error
bars represent the squared sum of their respective uncertainty. In light blue
the region within which the spectra of the family members identified by our
analysis lie within an interval of one standard deviation.  Figure 4:
$\chi^{2}$ distribution of the objects observed by Gaia within the
Tirela/Klumpkea region. Left panel: Distribution in the $(\chi^{2},\rho_{V})$
plane. Red points have $\rho_{V}$ ¿ 0.12 and $\chi^{2}>2$, blue points have
$\rho_{V}$ ¿ 0.12 and $\chi^{2}<2$, green points have $\rho_{V}$ ¡ 0.12 and
$\chi^{2}<2$ and finally grey points have $\rho_{V}$ ¡ 0.12 and $\chi^{2}>2$.
Right panel: Distribution in the $(a,1/H)$ plane of the points reported in the
left panel.  Figure 5: $\chi^{2}$ distribution for objects in the
Tirela/Klumpkea region with $\rho_{V}>0.12$. The red vertical line indicates
the limit in $\chi^{2}$ to separate family members from the background.

The reflectance spectrum from Gaia was segmented into 16 distinct wavelength
bands, covering a range from 0.374 to 1.034 micrometers, each with a bandwidth
of 0.044 micrometers. For every reflectance measurement, the dataset includes
quality flags that detail the quality of the data and identify any encountered
issues, in addition to providing information on flux uncertainties.
To classify Solar System objects (SSOs), it is necessary to compare their
reflectance spectra with established taxonomy templates. One method for
classifying spectra is to use machine learning (ML) algorithms (Mahlke et al.,
2022). Machine learning algorithms can learn from data and make predictions
based on learned patterns. To train the model, labeled datasets are required,
which are then used to classify new data. However, the task is complicated by
systematic variations, particularly in the blue and red parts of the spectra
(Tinaut-Ruano et al., 2023), as well as the presence of noise, and missing
data values. These factors may lead to inaccurate classification of asteroids.
To address this issue, a generally adopted method is based on identifying and
adjusting for systematic differences in Gaia spectra. This is done by
comparing them with etalon spectra obtained, for example, from ground-based
observations of the same asteroids. This method involves creating a
compensation model, which may be affected by outliers and missing values. The
model requires interpolations and extrapolations of Gaia reflectance data,
which introduces additional limitations. Therefore, we employed an alternative
strategy that does not rely on etalon spectra.

The method we used to prepare the training dataset was to utilize the Gaia
spectra in their original form, which had been previously classified by
ground-based spectral observations. These spectra were then used to train a
random forest classifier (Breiman, 2001). The random forest classifier is an
ensemble learning method that constructs multiple decision trees during
training and outputs the class which is the mode of the classes of the
individual trees. This classic ML classifier is well-suited for classifying
Gaia spectra due to its robustness to overfitting and missed values, and its
ability to handle large multilabel datasets with higher dimensionality.

The foundation of our asteroid taxonomy is built upon matching Gaia asteroids
with the most comprehensive spectral database available to date, as compiled
by Mahlke et al. (2022). The spectral classification system used in their work
was adopted, but consolidated into eight primary classes for analysis: A, C,
D, K, L, S, V, and X types. This merging strategy streamlines classification
following the Gaia spectra limits while preserving the essential distinctions
between major asteroid types. This training dataset included more than 1,000
asteroids with known spectral types, 35 of which belong to the L- class. The
reflectance distribution template for L-type asteroids obtained from the Gaia
dataset using this method is shown in Fig. 1.The sudden change in the slope
below 0.45 microns visible in the plot is a consequence of a flaw related to
Gaia spectra, which mostly affects faint objects.
The random forest classifier was trained on this dataset and the resulting
model was used to classify the Gaia spectra. The identification of L-type
asteroids in the visible domain presents some challenges, as their reflectance
spectra in the visible can be sometimes similar to S-, K-, and D- types.
Despite this difficulty, the accuracy of the classification of L-type
asteroids with our approach reaches 87%, which is a good result given the
complexity of the task. The classifier outputted the two most probable classes
for each asteroid, along with the associated probabilities. The classification
results were then used to identify the most probable spectral type for each
asteroid, which was then used to determine the asteroid’s membership in the
L-type family.
More details on the classification method can be found in Sergeyev & Carry (in
preparation).

##  3 Application to the Klumpkea/Tirela collisional family

###  3.1 Membership

Tirela is an asteroid family first identified by Nesvorný et al. (2005) and
successively reidentified in the space of proper elements by different
authors, such as Masiero et al. (2013) and Milani et al. (2014), who used
different implementations of the HCM algorithm. The latter ones in particular
found a different membership to the family and renamed it the Klumpkea family.
The Tirela/Klumpkea family is located at the edge of the outer Main Belt, at
semi-major axis $a=3.12$ AU, and it possesses high eccentricity and
inclination, $e=0.20$ and $i=16.8^{\circ}$. The family is characterized by a
high geometric albedo (0.2 - 0.3), whereas the background asteroids in the
same region generally have low albedos and belong to the C- complex. The
spectra of Tirela/Klumpkea members are reported in Mothé-Diniz & Nesvorný
(2008) and in Devogèle et al. (2018), who report the family to consist of L-
types. Milani et al. (2016), using the V-shape method described in Spoto et
al. (2015) determined an age of about 660 Myr.

To identify the Tirela/Klumpkea family using Gaia spectra alone, we first
considered all asteroids contained within a region in the 3D space of proper
elements centered on the cluster of identified Tirela/Klumpkea members with
3.00 AU $<a<$ 3.23 AU, $0.15<e<0.25$ and $0.27<\sin(i)<0.33$. In addition to
the family members, this wide region contains numerous background asteroids
and other families (or at least part of them). The proper elements $a$, $e$,
and $\sin(i)$ and the absolute magnitudes, $H$, were retrieved from the
Asteroid Family Portal (AFP, Novaković et al. 2022), while the albedos,
$\rho_{V}$, were extracted from the WISE/NEOWISE survey (Masiero et al.,
2011). For objects observed more than once by WISE, the weighted average of
their measurements was taken.
Overall, 8175 objects were found to be located within the selected region,
1574 of which were listed as part of the family in the Asteroids-Dynamic Site
(AstDyS, Milani et al. 2014). Among the total sample, 704 objects presented a
spectrum in the Gaia DR3, while only 41 objects had a spectrum published from
other sources. A total of 1887 objects instead already had colors determined
from photometric observations.

Among the total sample, 1928 objects possessed a NEOWISE albedo. Similarly,
out of the 704 objects in the Gaia sample, 548 had a NEOWISE albedo. The
distribution of the albedos is reported in the left panel of Fig. 2, where the
complete sample is shown in blue, the set having Gaia spectra in yellow and
the family members included in AstDyS in red. A bimodal distribution, expected
in the selected volume of proper elements, stands out, with a separation
around $\rho_{V}=0.12$. Given the position in the outer belt, the narrow peak
at low albedos corresponds to dark background asteroids. The broad peak at
higher albedos consists of Tirela/Klumpkea family members plus a few asteroids
belonging to the S- complex; given the rough spectral similarity with the L-
types, it could also be family members missed by the HCM classifiers. AstDyS’s
membership contains few low albedo objects, which are likely interlopers.

The left panel of Fig. 2 also reports in green the distribution of the family
members included in the AFP classification system. This scheme, also based on
an HCM algorithm, includes a large number of low albedo objects, which very
likely are interlopers. We therefore discarded the AFP classification system
and retained AstDyS as the only literature source of comparison with our work.
Throughout the paper we will use the abbreviations Mi16 when specifically
referring to the paper Milani et al. (2016) and HCM when referring to the
classification scheme first developed in Milani et al. (2014) and implemented
in AstDyS. Moreover, to update the membership with more recent proper elements
(extracted from AFP, version of October 2022) and to check the detailed
hierarchy of the clustering process, we also re-ran the HCM independently.

The correlation between high albedos and family membership is confirmed by the
distribution in the proper elements space, as shown for the $(a,e)$ plane in
the right panel of Fig. 2, where the points have been subdivided according to
the albedo. Objects with $\rho_{V}>0.12$ concentrate in the family core
centered between 3.09 AU and 3.15 AU. Some scattered high albedo objects are
also present, in a range of semi-major axes similar to the family core, and in
the resonances. Objects with $\rho_{V}<0.12$ instead are scattered without a
preferred distribution, except for a small cluster at 3.05 AU which is the
Aegle family. This analysis proves that the family members of Tirela/Klumpkea
can be separated from the background using the albedo, which in turn
correlates with the spectral type.

This evidence motivated us to develop a procedure to identify the family
members using Gaia spectra alone, without the support of albedos. This allowed
us, in principle, to find family members whose albedo has not yet been
measured. The procedure is based on two selection filters, which an object
must pass in order to be considered a family member. The first filter
quantifies the spectral similarity between an object and the largest members
of the family, whose spectra are combined to create a family template
spectrum. The second filter is instead based on the color taxonomy described
in Sect. 2. Only objects whose spectral types are the same as the largest
fragments of the Tirela/Klumpkea family are considered to be part of it.

Figure 6: Spectral types of the objects observed by Gaia in the
Tirela/Klumpkea region. In blue, we show objects with $\chi^{2}>2$; in red
objects, with $\chi^{2}<2$.  Figure 7: V-shape of the Tirela/Klumpkea family
members retrieved from this work. Left panel: Distribution in the $(a,1/D)$
plane of the family members identified from Gaia spectra (in blue). Red
crosses are resonant objects, while objects circled in black on the outer side
are excluded from the family for their distance from the V-shape. The only
excluded object on the left is rejected by the V-shape fit procedure. The two
black lines are the fitted V-shape for $N=13$ (see Fig. 11). The numbers mark
the positions of (1040) Klumpkea and (1400) Tirela. Right panel: Distribution
in the $(a,1/D)$ plane of Tirela/Klumpkea members retrieved from Gaia
observations. Blue points are objects in common between this work and the HCM,
while red stars are objects that are not linked by the HCM.

The family template spectrum is shown in Fig. 3, whose reflectance has been
computed from a weighted average of the spectra of (1400) Tirela and (1040)
Klumpkea, the two largest fragments of the family, shown in orange and in
blue, respectively. Popescu et al. (2012) propose five possible statistical
criteria for curve matching based on the $\chi^{2}$ method and the correlation
coefficient. We tested all these methods obtaining very similar results and we
chose to use a modified version of the classical $\chi^{2}$, which was the one
with the best performance. We stress here that an optimal combination of
multiple criteria might perform even better, however it would probably affect
the results only very marginally. Such an optimization is beyond the scope of
this article and may be implemented for future studies. In addition, this is
just a first step to filter out interlopers from the family. The important
selection to identify family members is in fact conducted using the color
taxonomy. The modified version of the classical $\chi^{2}$ that we defined is
based on the procedure adopted in Avdellidou et al. (2022). For each object
$\chi^{2}$ is computed as:

$\chi^{2}=\sum_{\lambda}\frac{[G(\lambda)-\beta
T(\lambda)]^{2}}{\sigma_{G}(\lambda)^{2}+\sigma_{T}(\lambda)^{2}}\ \ \
\textrm{with}\ \ \
\beta=\frac{\sum_{\lambda}T(\lambda)G(\lambda)}{\sum_{\lambda}T(\lambda)^{2}},$
(1)

where $G(\lambda)$ is the Gaia reflectance, $\sigma_{G}$ its uncertainty,
$T(\lambda)$ is the family template reflectance, and $\sigma_{T}(\lambda)$ its
uncertainty; also, $\beta$ is a factor taking into consideration that the
spectra could be arbitrarily normalized. However, this is not the case here
since both Gaia spectra and the template are normalized at 550 nm and
therefore $\beta=1$.

Family members in principle should present spectra similar to the template and
therefore should have small $\chi^{2}$ values. On the other side, background
objects should differ from the template, resulting in large $\chi^{2}$ values.
The left panel of Fig. 4 reports the distribution in the $(\chi^{2},\rho_{V})$
plane of the objects observed by Gaia with a NEOWISE albedo. The right panel
reports the same points in the $(a,1/H)$ plane where the V-shape of the family
should stand out. The $(\chi^{2},\rho_{V})$ plot clearly shows two main
clusters, again separated in two albedo categories, plus some scattered data
points.
We further divide the distribution into four subgroups, by exploiting both the
albedo bi-modality (split at $\rho_{V}=0.12$) and a threshold on $\chi^{2}$.
This threshold, $\chi^{2}=2$, has been chosen from the distribution of
$\chi^{2}$ for objects with albedo $\rho_{V}>0.12$, reported in Fig. 5 and
clearly showing a large number of asteroids at low $\chi^{2}$, plus a queue of
outliers. Of course, the exact value needed to discriminate spectra similarity
is arbitrary and can be ambiguous for objects that are very close to it.
These criteria result in the following partitioning:

  * •

Grey points in Fig. 4 (left panel): low albedo and large $\chi^{2}$. They are
the background asteroids belonging to the C- complex uniformly distributed in
space.

  * •

Red points: high albedos and large $\chi^{2}$. They are S- complex asteroids
with spectra deviating from the family template.

  * •

Blue points: high albedos and low $\chi^{2}$. They belong to the S- complex
and they present spectra similar to the family template. In the right panel,
they are clearly compatible with a V-shape for the family.

  * •

Green points: low albedos and low $\chi^{2}$. This may appear contradictory,
suggesting that dark background asteroids exhibit spectra similar to the
family template. However, in reality, they are faint objects with spectra
affected by large error bars, thus resulting in a low value of $\chi^{2}$.

Figure 8: Distribution in the $(a,e)$ and $(a,\sin(i))$ planes for objects
located in the Tirela/Klumpkea region. The left column reports the
distribution of the family members retrieved from this work. Blue points are
in common with the HCM, red objects are not. The right column reports the
distribution of all asteroids located within the Tirela/Klumpkea region from
which the HCM family members have been removed.  Figure 9: Size distribution
for the family members retrieved from this work (blue line), for the family
members in common in this work and the HCM (orange dashed line), for all the
objects identified by the HCM (green dash-dotted line) and for the objects
identified by the HCM without the interlopers of Table 1 (red dotted line).
Figure 10: Distribution in the $(a,1/D)$ plane of the HCM interlopers (orange
crosses) and the Tirela members identified in this work (blue points).

From this distribution, it is clear that a selection based only on spectral
similarity would include both low- and high-albedo objects (the last two
categories above). To address this aspect, we conducted an additional
selection based on the taxonomy derived from the spectra, outlined in Sect. 2.
The resulting distribution of spectral types is shown by Fig. 6, divided into
two categories by the $\chi^{2}>2$ threshold. A good correlation between the
$\chi^{2}$ value and the spectral types is observed, with S- complex objects
exhibiting spectra similar to the family template ($\chi^{2}<2$) and C-
complex objects with spectra diverging from the template ($\chi^{2}>2$). There
are a few C- and X- types with $\chi^{2}<2$: these are the green points in
Fig. 4, faint objects with noisy spectra. In fact, they present an average
absolute magnitude of $H=14.0$, slightly less than the average of the total
sample, $H=13.5$. In addition, the average S/N of their spectra is 19.6,
notably smaller than the average of the other points, $S/N=46.8$, and close to
the limit of $S/N=13$ defined by Gaia Collaboration et al. (2023) for the
publication of spectra in Gaia DR3. The distribution also shows that L- type
asteroids degenerate with S- types and partially with D- types, probably due
to the large dispersion of the spectra reflectances in the near-infrared (Gaia
Collaboration et al., 2023).
To understand the degree of degeneracy between the L- and S- types and the
other classes we analyzed the second most probable class retrieved from the
classifier for the objects with $\chi^{2}<2$ and initially classified as A-,
C-, D-, K-, V-, and X- types. We obtained that about 2/3 of D- types, 2/3 of
K- types, half of X- types, and all A- types received as second classification
the L- or the S- classes. The C- and V- types instead turned out to present
spectra with a shape very different from the family template.

Figure 11: Illustration of the fitting procedure of the V-shape of the
Tirela/Klumpkea family for $N$ ranging between 8 and 16, where $N$ is the
number of objects contained within a bin. The blue points are the family
members, the black circles are the points used for the fit, the black lines
are the fitted V-shapes and the red dashed lines are the bin subdivisions. The
title of each panel reports the values of the inner slope, the outer slope,
and their ratio.

We therefore decided to consider as family members the S- and L- types with
$\chi^{2}<2$ and among the A-, D-, K-, and X- types with $\chi^{2}<2$ those
which received L- or S- as the second most probable class. This allows to
include in the family L- types that are misclassified by the taxonomy or that
present flawed Gaia spectra, accepting the minor risk of including in the
family faint interlopers which may present a small $\chi^{2}$ only because of
highly noisy spectra. All C- and V- types have instead been discarded from the
family.

The objects selected in this way are clustered between 3.08 AU and 3.18 AU,
which have been adopted as boundaries in semi-major axis for the family. This
region is cut by numerous high-order mean motion resonances with Jupiter, the
most important of which are 13/6J, 15/7J, and 21/10J (Radović et al., 2017).
We thus defined three regions at 3.104 AU $<a<$ 3.108 AU, 3.127 AU $<a<$ 3.130
AU, and 3.17 AU $<a<$ 3.18 AU within which an asteroid is considered to be in
resonance. Resonant objects may in principle belong to the family, but their
eccentricities have been pumped up (or down) and their evolution in semi-major
axis, due to the Yarkovsky drift, has been halted (Nesvorný et al., 2002). For
the analysis that follows, objects in resonances are neglected, regardless of
their spectral types.

To identify a V-shape for the family in the $(a,1/D)$ plane, we computed the
diameters $D$ of the selected objects from their albedo $\rho_{V}$. The albedo
is either extracted from NEOWISE, when available, or assigned from the average
albedo of the family, $\rho_{V}=0.23\pm 0.08$. This value is also compatible
with $\rho_{V}=0.204\pm 0.100$ reported in Mi16. The resulting distribution in
the $(a,1/D)$ plane of the family members is reported in the left panel of
Fig. 7. A rather well-separated cluster of large asteroids on the outer side,
circled in black, respect the two criteria on spectra similarity and therefore
are selected as family members by our procedure. However, they are well
separated by a gap from the V-shape of the family, and moreover are almost as
big as (1400) Tirela and (1040) Klumpkea, which would imply a very improbable
size distribution. These objects were also not linked to the family by the
HCM. We therefore exclude these objects from the family. The V-shape of the
family is quite well defined in the outer side until small diameters, while in
the inner side it is cut by the 11:5 mean motion resonance with Jupiter.
Interestingly, the two largest fragments of the family are slightly shifted in
semi-major axis compared to the vertex of the V-shape.
The blue points in the left panel of Fig. 7 are the final family members
retrieved from Gaia observations, which are used in a later step to analyze to
place constraints on the age of the family. They are reported in the right
panel of Fig. 7, where they are compared to the family identified by the HCM.
It is clear that at diameters $D<7$ km, our method identifies objects that the
HCM does not link to the family, but that are well compatible with the
V-shape. We detected 173 objects within the family for $D<7$ km, 54 of which,
the 31%, were not identified by the HCM. For $D<3$ km, we instead identified
24 objects, 14 of which were not linked by the HCM.
A total of 201 family members were retrieved from the Gaia spectra and the
color taxonomy. The complete family membership for the Tirela/Klumpkea family
is reported in the Zenodo repository
111https://doi.org/10.5281/zenodo.12704069.

The spatial distribution of these objects in the $(a,e)$ and $(a,\sin(i))$
planes is reported in the left column of Fig. 8, where the colors and symbols
follow the right panel of Fig. 7. The objects in common between our work and
the HCM form the family’s core, while the objects we retrieved are more
dispersed and harder to identify for the HCM. The right column of Fig. 8
includes all asteroids in the proper element volume around the family.
Although objects classified as family members by the HCM have been subtracted,
a diffuse halo extending the family volume is visible. The distribution of our
additional family members appears qualitatively compatible with this diffuse
halo.

Table 1: Interlopers included in the HCM family.

Number | Spectral Type | NEOWISE Albedo
---|---|---
(3667) | D | 0.06
(7411) | C | 0.04
(18399) | X | 0.04
(24878) | C | 0.06
(29391) | C | 0.05
(42521) | C | 0.05
(44519) | C | 0.04
(65676) | X | 0.06
(160278) | C | 0.04

  * •

Interlopers larger than 10 km included in the family by the HCM. The columns
report the number of the asteroid, the spectral type retrieved from the color
taxonomy and the NEOWISE albedo.

We also compared the new cumulative size distribution for the membership that
we establish to the one by the HCM, reported in Fig. 9. As expected, the
additional members identified at small diameters by our selection produce a
modest slope increase at $D<$ 7 km due to the halo objects.
The HCM distribution instead includes more objects and extends to smaller
diameters, since the HCM is less limited in absolute magnitude than Gaia
observations. However, the most interesting aspect is that the HCM includes in
the family at least eight objects as large as (1400) Tirela and (1040)
Klumpkea, which were instead discarded by our selection. As listed in Table 1,
they belong to the C- complex and present a low albedo. They are thus very
likely to be interlopers that can be identified as such only from their
spectral properties. This conclusion is supported by their position relative
to the V-shape of the family (Fig. 10), which is generally external to the
family boundaries and far from the vertex of the distribution. The resulting
size distribution without these interlopers is much closer to what is observed
in other families, with only one or two dominating remnants.

Among these eight interlopers, six were already identified by Radović et al.
(2017) using an automated procedure to exclude interlopers from asteroid
families. However, Radović et al. (2017) also report (1400) Tirela to be an
interloper, which we included in the family instead. This is coherent with the
spectra of few Tirela/Klumpkea members reported in Devogèle et al. (2018),
which underline the spectral similarity between (1400) Tirela and the other
family members.
We also stress here that other interlopers could remain in the HCM data set,
but it is more difficult to identify them for D$<$7–10 km, due to the lower
quality of the spectra and the absence of albedo measurements.
The family membership retrieved by our run of the HCM is very similar to the
one of AstDyS and, therefore, the overall results do not change between the
two versions.

###  3.2 Age determination

In order to fit the V-shape and constrain the age of the Tirela/Klumpkea
family, we developed a procedure based on the work by Milani et al. (2014) and
Spoto et al. (2015) to determine the slopes of the sides of the V-shape. The
first step requires us to select the intervals of semi-major axis and size
defining the V-shape. The boundaries in the semi-major axis are taken between
3.08 AU and 3.18 AU, the same as in Mi16, while the upper limit in $1/D$ is
taken where the sides depart from the V-shape and become vertical. Given the
limited number of members within the family, the choice of the $1/D$
significantly limits the reliability of the boundary slope, especially for the
inner side, which is clearly less extended and defined. This leads us to adopt
$1/D=0.22\ $km-1 for the inner side and $1/D=0.35\ $km-1 for the outer side.
The y-axis is then divided into $n$ bins, $i=\left(1,2,...,n\right)$, such
that each bin contains the same number of objects $N$. Spoto et al. (2015)
implemented an automatic procedure which, given the number of asteroids inside
the family, provides the best value of $N$ for the subdivision in bins. In
this work, we explored a range of $N$ instead, repeating the binning for $N$
between 8 and 16.

Inside each bin, the points characterized by the smallest (inner side) and
largest (outer side) semi-major axes are selected. Apart from small $N$, the
two largest bodies (Tirela and Klumpkea) are never selected for the
computation of the slopes. Automatically including them in the fitting process
could be an option, however, this would give excessive weight to the few
largest objects, introducing a clear bias due to their displacement with
respect to the vertex. This shift could be related to the violent
fragmentation event with a non-negligible ejection velocity of the largest
fragments (Spoto et al., 2015).

Figure 12: Ages of the Tirela/Klumpkea family determined in this work, in
blue, compared to the ages reported in Mi16, in orange. The black dashed
vertical lines report the uncertainty on the age reported in Mi16.  Figure 13:
Template spectrum of the Watsonia family (in red). The reflectances have been
computed by averaging the Gaia spectra of (729) Watsonia (in blue), (1372)
Haremari (in orange), and (5492) Thoma (in green). In light blue, the region
within which the spectra of the family members identified by our analysis lie
within an interval of one standard deviation. The black dashed line reports
the spectrum of (980) Anacostia.  Figure 14: $\chi^{2}$ distribution of the
objects observed by Gaia within the Watsonia region. Left panel: Distribution
in the $(\chi^{2},\rho_{V})$ plane. Red points have $\rho_{V}$ ¿ 0.12 and
$\chi^{2}>2$, blue points have $\rho_{V}$ ¿ 0.12 and $\chi^{2}<2$, green
points have $\rho_{V}$ ¡ 0.12 and $\chi^{2}<2$ and finally grey points have
$\rho_{V}$ ¡ 0.12 and $\chi^{2}>2$. Right panel: Distribution in the $(a,1/H)$
plane of the points reported in the left panel.

The two sets of points are then fitted through a linear regression algorithm,
which finds the best straight lines approximating the two sides of the
V-shape. For each side, we compute the residuals of the linear regression and
their standard deviation, $\sigma_{r}$. Only one outlier is found at the level
of $2\,\sigma_{r}$, the threshold chosen for rejection, the point circled in
black on the inner side in the left panel of Fig. 7. This point (which is not
included in the family by the HCM either) is therefore discarded and the
linear regression is repeated on the new set of data points. The resulting
V-shapes are indicated in black in Fig. 11, which summarises the whole
procedure and reports the slope of the inner side, $S_{in}$, the slope of the
outer side, $S_{out}$, and their ratio, $R$.
The slope of the outer side remains almost constant with varying $N$, with
only small fluctuations that can be explained by the different points used for
the fit in each case. The inner side is instead less self-consistent since the
fit is conducted over a much smaller range in $D$. The inner slope is always
larger than the outer one by a factor of around 2, except at large $N$, when
relatively few points are used for the fit and the ratio exceeds 3. This could
indicate that the inner and the outer sides correspond to different ages,
which would suggest that the Tirela/Klumpkea family is the result of more than
one collisional event. However, this hypothesis can hardly be confirmed in the
future, as the inner side has probably been substantially eroded by the 11:5
and 13:6 mean motion resonances with Jupiter (centered at 3.075 and 3.105 AU,
respectively).

To convert the slopes into ages, it is necessary to determine a Yarkovsky
calibration, represented by the value of the drift $da/dt$ for a family member
with a unit diameter and spin axis obliquity equal to 0° for the inner side
and to 180° for the outer side (Spoto et al., 2015). Milani et al. (2014) and
Spoto et al. (2015) constrain the Yarkovsky calibration using (101955) Bennu
as a benchmark asteroid. However, (101955) Bennu is a B- type whose spectral
properties are very different from the two families considered in this work.
We therefore selected as reference asteroid (99942) Apophis, which instead is
an S- type and thus closer to Tirela/Klumpkea and Watsonia. Fenucci et al.
(2024) report a Yarkovsky drift of $-13.26$ AU/Myr for (99942) Apophis
measured with $S/N\approx 123$. The scaling formula thus becomes:

$\frac{da}{dt}=\left(\frac{da}{dt}\right)_{A}\ \frac{\sqrt{a}_{A}\
(1-e_{A}^{2})}{\sqrt{a}\ (1-e^{2})}\ \frac{D_{A}}{D}\
\frac{\widetilde{\rho_{A}}}{\widetilde{\rho}}\
\frac{\cos(\phi)}{\cos(\phi_{A})}\ \frac{1-\rho_{V}}{1-\rho_{V,A}},$ (2)

where $a$, $e$, $\widetilde{\rho}$ and $\rho_{V}$ are respectively the semi-
major axis, the eccentricity, the density and the albedo representative for
the family. Then, $\cos(\phi)$ is the spin axis obliquity and it is equal to
$\pm 1$ depending if the inner or the outer side is considered. $D=1$ km is
not the diameter of a real asteroid, but the reference value corresponding to
the inverse slope. Also, $a_{A}$ and $e_{A}$ are the semi-major axis and the
eccentricity of (99942) Apophis (Moskovitz et al., 2022), $D_{A}$ is its
diameter (Brozović et al., 2018), $\rho_{V,A}$, and $\cos(\phi_{A})$ are its
albedo and its spin axis obliquity (Berthier et al., 2023a).
The densities $\widetilde{\rho}$ and $\widetilde{\rho_{A}}$ are both unknown.
For (99942) Apophis, we assume the reference density for S- types reported in
Carry (2012), $2.70\pm 0.69$ g/cm3. For the family, we could have assumed the
reference density for L- types reported in the same work. However, this value
is quite inaccurate due to the limited number of large L- types with precise
measurements of mass and diameter. In addition, Sunshine et al. (2008) and
Mahlke et al. (2023) suggested that Barbarians are linked to CO and CV
meteorites, which are, in turn, related to C- types. We thus assumed for the
family the reference density for the C- class reported in Carry (2012),
$1.41\pm 0.69$ g/cm3. As in Spoto et al. (2015), we assume the Yarkovsky
calibration to be affected by a relative uncertainty of 0.3. We thus obtain a
result of $da/dt=(5.86\ \pm\ 1.76)\ 10^{-4}$ AU/Myr for the family.
Figure 12 reports the ages for the inner side ($200\ \pm 97$ Myr) and the
outer side ($467\ \pm 184$ Myr) compared to the values reported in Mi16. The
age found by our work for the outer side is larger than the one for the inner
side, but they are compatible within the error bars. The difference is
probably due to a poor accuracy of the fit in the inner side, due to the
limited extension of this region. In Fig. 12, we only give the case for $N=13$
(see Fig. 11), which is the one affected by the smallest uncertainties. For
every other value of $N,$ the ages for the two sides are always compatible
among them, except for $N=14$, which is very likely the result of an
inaccurate fit of the inner side.
The ages for the outer side are all compatible with Mi16, while the ages for
the inner side are systematically below it. This may suggest that the
Tirela/Klumpkea family is younger than previously thought. However, the ages
are affected by the choice of the reference asteroid and the values of the
densities used in Eq. (2), therefore this result cannot be considered as
definitive. Finally, our age estimation is compatible with Brož et al. (2013),
who exploited N-body numerical simulations and ultimately found the
Tirela/Klumpkea family to be younger than 1 Gyr.

##  4 The difficult case of Watsonia

Watsonia is an asteroid family first identified by Novaković et al. (2011),
who applied the classical HCM to high-inclination main belt asteroids.
Watsonia is located in the middle of the main belt, with 2.70 AU $<a<$ 2.83
AU, and it is characterized by low to moderate orbital eccentricities,
$0.10<e<0.15$, and high inclinations, $16.5^{\circ}<i<18.0^{\circ}$. Watsonia
lies in a region of the proper elements with a low density of asteroids, where
the difference in spectral type between the background and the family members
is less marked than in the Tirela/Klumpkea case, thus reducing the efficacy of
separating the family members from the background using Gaia data alone.
Watsonia is a very small family, with just a few tens of members reported in
the literature (e.g., the HCM identified only 80 members). Tsirvoulis et al.
(2014) tried to constrain the age of the family using the V-shape method, but
because of the low number of family members, these authors could not achieve a
precise estimation and they report an approximate age of $\sim$1 Gyr.

Figure 15: Spectral types of the objects observed by Gaia in the Watsonia
region. Blue are objects with $\chi^{2}>2$, red are objects with $\chi^{2}<2$.
Figure 16: Distribution in the $(a,1/D)$ plane of the Watsonia family members,
marked by the corresponding taxonomy class letters. In blue, we show objects
in common between our work and the HCM. In red, we show objects that are not
identified by the HCM. The grey circles indicate all the family members
identified by the HCM.  Figure 17: Comparison between the HCM membership (grey
circles) and our work (blue crosses) at different cutoff velocities in the
($a$, $H$) plane. The numbers mark the positions of (729) Watsonia and (980)
Anacostia.

To identify the Watsonia family, the same procedure implemented for
Tirela/Klumpkea was followed. First, all asteroids contained inside a region
centered on (729) Watsonia with 2.70 AU $<a<$ 2.83 AU, $0.105<e<0.150,$ and
$0.29<\sin(i)<0.31$ are considered. Again, the proper elements and the
absolute magnitudes are retrieved from the Asteroid Family Portal, and the
albedos from the NEOWISE survey. Only 227 asteroids are found within this
region, 56 of which present a spectrum in Gaia DR3, while only 6 of them had a
spectrum previously published from other sources. Among these, the three
brightest family members found by the HCM are selected to create a family
template spectrum (Fig. 13).

The same $\chi^{2}$ technique (Eq. 1) is then applied to quantify the
differences between the family template and the objects observed by Gaia. The
distributions in the $(\chi^{2},\rho_{V})$ and $(a,1/H)$ planes for the
objects within the Watsonia region are shown in Fig. 14. The points are
divided into four subgroups following the approach used for Tirela/Klumpkea.
The small number of objects however makes the result less sharply defined.

The spectral types resulting from the color taxonomy are reported in Fig. 15.
Despite the small statistics, there is a quite good agreement between spectral
types and $\chi^{2}$, with background objects with $\chi^{2}>2$ classified
into the C- class, while almost all D- and S- types are associated with
$\chi^{2}<2$.
Quite surprisingly only one object is classified as L- type, with even (729)
Watsonia itself included in the X- class. The only L- type, which in addition
has $\chi^{2}>2$, is (980) Anacostia, the lowest point around 2.74 AU in the
right panel of Fig. 14, whose puzzling proximity to the family has already
been discussed in the literature. Cellino et al. (2014) in particular mention
that (980) Anacostia and (729) Watsonia share similar semi-major axes and
inclinations and they present similarities in their physical properties, such
as being both Barbarians (Gil-Hutton et al. 2008, Gil-Hutton et al. 2014).
They speculated that the two objects might have a similar origin from an
ancient disruption of a large Barbarian parent body. This is also suggested by
the presence of other large Barbarians close to (729) Watsonia and (980)
Anacostia in the phase space of proper elements, such as (387) Acquitania and
(599) Luisa. The smallest fragments created in this event would have been
removed by the Yarkovsky drift, while the largest fragments had time to slowly
evolve in the proper elements, assuming their actual positions. In this
picture, Watsonia would be a second-generation family formed from the
disruption of one of the first-generation large fragments.
Our V-plot shows that (980) Anacostia seems to lie on the alignment of a
poorly defined right edge of the family. However, we find that in terms of the
reflectance spectra obtained by Gaia, (980) Anacostia slightly differs from
the Watsonia family, as reported in Fig. 13. As we will see further on, the
analysis of the HCM will not be conclusive for (980) Anacostia, although it
provides other interesting clues.

Analyzing the objects with $\chi^{2}<2$ and initially classified as C-, D- and
X- types, we find that about half of the C- and X- types and two-thirds of the
D- types receive S- or L- as second classification. For all of them, the
probabilities of the first and second classification are very similar and the
spectra closely resemble the family template spectrum. We thus decided to
consider as family members all S- types with $\chi^{2}<2$ and the C-, D- and
X- types with $\chi^{2}<2$, having S or L as the second most probable
classification. A total of 34 family members are retrieved from the Gaia
spectra and the color taxonomy. The complete family membership for the
Watsonia family is reported in the Zenodo repository
222https://doi.org/10.5281/zenodo.12704069.

The absolute magnitudes, $H,$ of the family members are converted into
diameters, $D,$ from the albedo, either extracted from NEOWISE or (when
unavailable) adopting the average albedo of the family, $\rho_{v}=0.16\pm
0.06$. The distribution of family members in the $(a,1/D)$ plane is reported
in Fig. 16, where every object is marked by the corresponding taxonomy class
letter. For the objects that did not receive S as the most probable class, but
that were still included in the family, their second most likely
classification is reported instead. The vertical dashed lines mark the
position of a resonance between 2.749 AU and 2.753 AU, within which Gaia did
not detect any object. The resonance lies very close to the position of (729)
Watsonia at 2.76 AU.
S- types are distributed all over the area, while the few L- types are mainly
found at $D>10$ km. The three asteroids used to create the template family
spectrum are indeed the three largest L- types.
Despite a limited statistic, the V-shape is recognizable especially in the
outer side. In addition, almost all objects at the right of the resonance are
included in the family by the HCM. This is not a coincidence, since most
family members identified by the HCM lie in this region, as shown by the grey
circles in Fig. 16. The most striking feature in Fig. 16 is the appearance in
the family of a set of objects at the left of the resonance (marked in red),
that are not identified by the HCM. In percentage, our analysis identifies
more objects in the inner side than the HCM, according to which the family
seems to be one-sided. This however could be the result of the limit cutoff
velocity chosen by AstDyS to define the family.

Figure 17 reports the comparison between the family members identified in this
work and the membership obtained by our HCM at different cutoff velocities
$v_{cut}$ in the ($a$, $H$) plane. At the smallest cutoff velocity,
$v_{cut}=0.090$ km/s, the family membership retrieved by our HCM is very
similar to that of AstDyS, with most family members lying at the right of the
resonance. Increasing $v_{cut}$ the overall shape of the outer side remains
unchanged, while the HCM links more and more objects to the inner side at the
left of the resonance. At $v_{cut}=0.140$ km/s almost all family members
retrieved by our work are linked to the family by the HCM, while the slopes of
the inner and outer sides seem to be qualitatively compatible. Interestingly,
for this same limit, (980) Anacostia is also included in the family by the
HCM.

The scarcity of members in our limited data set prevents to have solid
statistics for the application of the full V-shape fitting method. To have an
approximate estimation of the age of Watsonia, we overplot the tentative
V-shape boundaries corresponding to specific ages (Fig. 18), calibrated from
Eq. (2) by considering the semi-major axis, eccentricity, and albedo of (729)
Watsonia and assuming the reference C- type density reported in Carry (2012),
following the link to the CV and CO meteorites suggested by Mahlke et al.
(2023) and Sunshine et al. (2008). The age of the Watsonia family seems to lie
somewhere in between the V-shapes corresponding to 0.5 Gyr and 1.0 Gyr, a
value in agreement with Tsirvoulis et al. (2014). However, due to the limited
number of family members and the large uncertainty on the Yarkovsky
calibration, this result is affected by large errors and thus can only be
considered as a rough estimate.

Figure 18: Family members in the $(a,1/D)$ plane fitted by V-shapes
corresponding to different ages. The green continuous line corresponds to 0.5
Gyr and the red dashed line to 1.0 Gyr.

##  5 Conclusions

Our classification of Gaia spectra, not using external etalon templates, is
successful in separating the main spectral types. Our analysis of specific
families shows that some expected ambiguities remain, especially when trying
to push the analysis toward family members of smaller sizes (i.e., with
fainter magnitudes and noisier spectra).
The two Barbarian families that we analyze here have slightly different
reflectance spectra, as shown by the distribution of taxonomy. This is
consistent with the differences already found in the past in polarimetric
parameters and when matching their members to meteorite spectra. Devogèle et
al. (2018) found that Watsonia, despite having anomalous polarimetry common to
other Barbarians, requires less extreme enrichment in CAIs to be modeled.
These two families also differ in their position in the belt and in the number
of members bright enough to be accessible to Gaia (Tirela/Klumpkea being the
richest).

The case of Tirela/Klumpkea is a significant benchmark for spectral
classification and family membership, in fact its members exhibit an albedo
markedly higher than the average background dominating the outer belt, where
it is situated. In this case, the comparison of albedo with Gaia spectra and
HCM membership allows us to identify interlopers among some large family
members.
Smaller members are also recovered by spectral similarity. Although in general
many of them do not have albedo measurements available, they qualitatively
scatter on the osculating elements plane on regions compatible with the
evolved family halo. A simulation of the dynamical evolution of the family,
outside the scope of this article, would be useful to further consolidate this
result.
Interestingly, the new members seem to better define the inner slope of the
V-shape of the family, resulting in a younger age (200 Myr) with respect to
Milani et al. (2016). The outer edge also appears younger but not by a
significant margin. Our determination of family membership eliminates the
large interlopers included by the HCM that polluted the V-shape and resulted
in a very peculiar size distribution.

The Watsonia family, as expected, is a more difficult case than
Tirela/Klumpkea, but it still represents an interesting application of our
approach. The limited number of objects around the family and the less marked
difference between the spectral types of the family members and the background
make the identification by Gaia data alone more difficult. However, Gaia
observed 56 objects inside the Watsonia region, thus representing a huge
improvement compared to the literature, where only six spectroscopic
observations for these objects have been reported .
Despite the fact that the V-shape boundaries remain poorly determined, we are
capable of identifying several new candidate family members that had not been
included in previous HCM-based classifications, drafting the structure of the
inner part of the V-shape. Interestingly, our new run of the HCM shows that at
the same cutoff velocity required to include the inner members, (980)
Anacostia appears in the membership. This evidence strengthens the physical
and dynamical links among different large Barbarians in the area, which
possibly stands as a sparse signature of an ancient breakup from which the
Watsonia parent body was originated, previously suggested by Cellino et al.
(2014) and others. A similar consideration could be applied to the large
asteroids that we find to be compatible to Tirela/Klumpkea in terms of
spectra, but that lie totally outside the core of the V-shape (left panel of
Fig. 7). Their presence and proximity may also indicate more ancient break-ups
of large L-type objects.

The reconstruction of a ”genealogy” leading to the currently observed families
would be a major milestone in understanding the origin and nature of L-type
families and Barbarians. We have shown how asteroid reflectance spectra by
Gaia can be used to work in this direction. Future releases from this same
mission will offer a larger sample of objects to study, with improved data
quality. Its exploitation, jointly with data coming from other surveys, can be
the key to future advances in our understanding of the origin and history of
the asteroid population.

###### Acknowledgements.

This work presents results from the European Space Agency (ESA) space mission
Gaia. Gaia data are being processed by the Gaia Data Processing and Analysis
Consortium (DPAC). Funding for the DPAC is provided by national institutions,
in particular, the institutions participating in the Gaia Multilateral
Agreement (MLA). The Gaia mission website is https://www.cosmos.esa.int/Gaia.
The Gaia archive website is https://archives.esac.esa.int/Gaia. RB Doctoral
contract is funded by Universitè de la Côte d’Azur. This project was financed
in part by the French Programme National de Planetologie, and by the BQR
program of Observatoire de la Côte d’Azur. We made use of the software
products: SsODNet VO service of IMCCE, Observatoire de Paris, and the
associated rocks library333https://github.com/maxmahlke/rocks (Berthier et
al., 2023b); Astropy, a community-developed core Python package for Astronomy
(Astropy Collaboration et al., 2013, 2018, 2022); Matplotlib (Hunter, 2007).

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