11institutetext: Florida Space Institute, University of Central Florida,
Florida, USA
11email<EMAIL_ADDRESS>22institutetext: Instituto de Astrofísica de
Canarias, C/Vía Láctea s/n, 38205 La Laguna, Spain 33institutetext:
Universidad de La Laguna (ULL), E-38205, La Laguna, Spain 44institutetext:
Fundación Galileo Galilei - INAF, Rambla José Ana Fernández Pérez, 7, 38712
Breña Baja, Santa Cruz de Tenerife, Spain 55institutetext: Departamento de
Astrofísica, Observatório Nacional, Rio de Janeiro, 20921-400, Brazil
66institutetext: Department of Physics, University of Central Florida,
Florida, USA 77institutetext: Faculty of Natural Sciences, Norwegian
University of Science and Technology (NTNU), 7491, Trondheim, Norway

# A comparative analysis of the outer-belt primitive families

M. N. De Prá 11 N. Pinilla-Alonso 11 J. Carvano 55 J. Licandro 2233 D. Morate
55 V. Lorenzi 4422 J. de León 2233 H. Campins 66 T. Mothé-Diniz 77

(April 08, 2020 )

###### Abstract

Context. Asteroid families are witnesses to the intense collisional evolution
that occurred on the asteroid belt. The study of the physical properties of
family members can provide important information about the state of
differentiation of the parent body and provide insights into how these objects
were formed. Several of these asteroid families identified across the main
belt are dominated by low-albedo, primitive asteroids. These objects are
important for the study of Solar System formation because they were subject to
weaker thermophysical processing and provide information about the early
conditions of our planetary system.

Aims. We aim to study the diversity of physical properties among the Themis,
Hygiea, Ursula, Veritas, and Lixiaohua families.

Methods. We present new spectroscopic data, combined with a comprehensive
analysis using a variety of data available in the literature, such as albedo
and rotational properties.

Results. Our results show that Themis and Hygiea families, the largest
families in the region, present similar levels of hydration. Ursula and
Lixiaohua families are redder in comparison to the others and present no sign
of hydrated members based on the analysis of visible spectra. Conversely,
Veritas presents the highest fraction of hydrated members.

Conclusions. This work demonstrates a diverse scenario in terms of the
physical properties of primitive outer-belt families, which could be
associated with dynamical mixing of asteroid populations and the level of
differentiation of the parental body.

###### Key Words.:

asteroids family – outer-belt – spectroscopy – Themis – Hygiea – Veritas –
Lixiaohua – Ursula

##  1 Introduction

Asteroid families are remnants from the main-belt collisional history, and are
identified by clusters in the proper orbital parameters (Hirayama, 1918;
Zappala & Cellino, 1992; Nesvorný et al., 2015). Members of an asteroid family
consist of fragments of a parent body that were disrupted after experiencing
an energetic collision in the past. The study of physical properties among
family members, such as composition, degree of aqueous alteration, and
spectral diversity, can provide important information about the state of
differentiation of the parent body (Cellino et al., 2002). Knowledge of the
internal structure of asteroids is particularly difficult to obtain, yet is
critical to understand how, when, and where these objects were formed and to
shed light on the formation and evolutionary history of the Solar System.

Several asteroid families identified across the main belt are dominated by
low-albedo, primitive asteroids (Nesvorný et al., 2015; Nesvorny, 2015). These
objects are of particular importance to the study of the formation of the
Solar System because they were subject to low thermophysical processing or
none at all, and can provide information about the early conditions of our
planetary system. Furthermore, investigations of the surface composition of
these objects show that they can contain hydrated minerals, water ice, and
organic materials (Vilas, 1994; Fornasier et al., 2014; Campins et al., 2010;
Rivkin & Emery, 2010; Licandro et al., 2011; Takir & Emery, 2012; Rivkin et
al., 2015, 2019). These discoveries corroborate the hypothesis that primitive
asteroids are a potential source of Earth’s water and organic material
(Morbidelli et al., 2000).

Advances in the characterization of primitive asteroids show that they present
almost featureless visible and near-infrared (NIR) spectra, with a variety of
surface colors from blue to red (for a review see DeMeo et al. 2015). A common
feature observed in several of these objects across the asteroid belt is the
0.7 $\mu$m absorption band, characteristic of hydrated minerals (Vilas, 1994;
Carvano et al., 2003; Fornasier et al., 2014). The number of objects
presenting this feature peaks at the central belt and decreases at the Cybele
region, delimiting the hydration zone (Rivkin, 2012; Fornasier et al., 2014;
De Prá et al., 2018). As part of the PRIMitive asteroid spectroscopic survey
(PRIMASS), we studied the visible spectroscopy of eight primitive asteroids
families in the inner belt and identified a mix of anhydrous and hydrated
families in that region, where the percentage of hydrated members in a family
can reach nearly 80% (de León et al., 2016; Morate et al., 2016, 2018, 2019).

Primitive asteroid families are observed across the whole main belt, and they
become the dominant population in the outer belt where most of their mass is
contained (DeMeo & Carry, 2014). Nesvorný et al. (2015) identified nine large
($N>300$ members) primitive families in this region (Fig. 1): Themis, Hygiea,
Ursula, Veritas, Lixiaohua, Alauda, Theobalda, Euphrosine, and Meliboea.

Figure 1: Orbital properties of large outer-belt asteroid families. The studied families are shown in colors, while those that are not studied in this work are represented by dark gray dots. The light gray dots represent the background. Asteroid | a | e | i | Age | Members | Spectra | SDSS | MOVIS | WISE | ALCDEF
---|---|---|---|---|---|---|---|---|---|---
Family | (au) |  |  (∘) | (Gyr) |  (N∘) |  (N∘) |  (N∘) |  (N∘) |  (N∘) |  (N∘)
Themis | 3.135 | 0.153 | 10.149 | $2.5\pm 1.0$ | 4782 | 59 | 774 | 284 | 2312 | 443
Hygiea | 3.142 | 0.136 | 1.084 | $2.0\pm 1.0$ | 4854 | 25 | 783 | 182 | 2234 | 149
Veritas | 3.174 | 0.066 | 5.103 | $0.0083\pm 0.0005$ | 1294 | 17 | 234 | 34 | 715 | 41
Ursula | 3.129 | 0.092 | 9.164 | $<3.5$ | 1466 | 7 | 266 | 71 | 957 | 70
Lixiaohua | 3.153 | 0.197 | 3.215 | $0.15\pm 0.05$ | 756 | 35 | 110 | 24 | 514 | 28
Table 1: Outer belt families identified by Nesvorný et al. (2015) and studied
in this work. See text for details.

The first detection of water ice in the asteroid belt was made on (24) Themis,
the largest member of its homonymous family (Campins et al., 2010; Rivkin &
Emery, 2010). Recent works proposed that water ice is also present in large
outer-belt asteroids (Takir & Emery, 2012; Rivkin et al., 2019). Additionally,
the first observed main-belt comet (MBC), an active asteroid with proposed
sublimation-driven activity, is also a member of the Themis family. (Hsieh et
al., 2004; Hsieh & Jewitt, 2006). Hsieh et al. (2018) proposed that there are
seven MBCs which are linked to four families in outer belt: Themis, Lixiahoua,
Alauda, and Theobalda.

The Themis family is one of the most highly studied families in the
literature, in which both water ice and hydrated minerals have been observed
among family members. Castillo-Rogez & Schmidt (2010) and Marsset et al.
(2016) interpreted these results as the product of a partial differentiation
of the Themis parent body. The spectroscopic properties of the Lixiaohua
family were studied in De Prá et al. (2020), and although it is also a MBC-
bearing family, it was found to present distinct properties from the Themis
group, which can be interpreted as a difference in composition and/or
differentiation level.

The aforementioned studies of outer-belt objects suggest that the hydrated to
icy transition is likely to occur at the outer belt. In this work, we
performed a comparative study of the physical properties among the outer-belt
families by means of new spectroscopic data combined with data gathered from
public catalogs. In Section 2 we describe the spectroscopic observations and
data-reduction techniques. The analysis of these data is presented in Section
3, and we include the data available from public catalogs to extend the
analysis to study the albedo, parent body size, and rotational properties of
these families. The results for each family are presented in Section 4. In
Section 5, we compare results across the families and discuss the implications
of these findings.

##  2 Observations and data reduction

We collected low-resolution spectra for 29 asteroid members of the Themis,
Hygiea, and Veritas families (Table 1, Figs. 1, 2, 3 ). The data were obtained
using the Goodman High-Throughput Spectrograph (GTHS) at the 4.1m SOAR
telescope on Cerro-Pachón, Chile. We used a setup with grating of 300 lines/mm
and the slits of 1.03” in 2011, and 1.68” in 2012 with no second-order
blocking filter, which provided an effective spectral interval of 0.4-0.87
$\mu$m. Observations were made on a total of six nights across the semesters
of 2011A and 2012B. We also obtained two sequences of calibration quartz lamps
immediately before and after target acquisition in order to reduce systematic
errors. At least one solar analog was observed at different air masses during
each night.

We used quartz lamps for the flat-field correction of the images, while the
HgAr lamps were used for the wavelength calibration. The reduction was made
using standard techniques: images were bias- and flat-field corrected and the
spectra were extracted, background subtracted, and wavelength calibrated in
sequence. This procedure was repeated for the three sub-exposures, and then
averaged to produce a final spectrum for each target.

Figure 2: Weighted average visible slope (left) and NIR slope (right) vs.
albedo for five outer-belt asteroid families.

To obtain asteroid reflectance spectra, we divided the object spectrum by the
spectra of solar analogs. We analyzed the spectra of the solar analog stars to
detect small differences in color introduced during the observations, caused
for example by inconsistent centering of the star in the slit. These
differences could propagate into the reflectance spectrum of the target
through the reduction process. The first step was to apply an atmospheric
extinction correction. This effect is dependent on the airmass and the
wavelength, with shorter wavelengths and higher air masses experiencing
greater extinction. To minimize the extinction effect from the difference in
airmass between the stars and the target, we applied a correction to the
spectra of the object and the stars. In the absence of extinction coefficients
for Cerro Pachón, we used the mean extinction coefficients for La Silla,
because this observatory is located relatively close and at similar altitude
to Cerro Pachón. A study of the variation of extinction coefficients from
different sites suggested it is mostly influenced by the altitude of the site.
For each night, we divided all of the spectra of the solar analogs by one used
as reference, typically the one at lower airmass. Ideally, the result of this
division should be a slopeless flat spectrum, with a normalized flux value of
around 1. The star observations that appeared to present outliers (i.e., an
uncommon shape relative to the others and/or spectral inclination variation
above 5$\sigma$) were discarded and the asteroid reflectance spectra were
obtained using the remaining stars. Finally, all reflectance spectra were
normalized to 1 at 0.55$\mu$m.

The data reduction was made by combining scientific Python libraries (Van Der
Walt et al., 2011; Jones et al., 2001; Astropy Collaboration et al., 2013;
Price-Whelan et al., 2018; Hunter, 2007) with IRAF111IRAF is distributed by
the National Optical Astronomy Observatories, which are operated by the
Association of Universities for Research in Astronomy, Inc., under cooperative
agreement with the National Science Foundation. tasks, called through the
PyRAF222PyRAF is a product of the Space Telescope Science Institute, which is
operated by AURA for NASA. library.

##  3 Analysis

In addition to the 29 spectra observed, we collected all available spectra in
the literature of members of Themis, Hygiea, Veritas, Ursula, and Lixiaohua
families (Xu et al., 1996; Bus & Binzel, 2004; Vilas et al., 2006; Lazzaro et
al., 2007; De Prá et al., 2020). In particular, the spectroscopic analysis of
the Lixiaohua was recently presented in De Prá et al. (2020), in which we used
the same methodology described in this section. Therefore, the individual
analyses of each spectrum of the Lixiaohua family are not presented in this
paper. In addition to the spectroscopic characterization, we include the
albedo, diameters, visible and NIR colors, and rotational periods of each
family. Table 1 includes the orbital parameters of the largest member of each
family, the family age from Brož et al. (2013), the number of members with
observed spectra (both observed in this work and taken from the literature),
members with SDSS colors (Carvano et al., 2010; Hasselmann et al., 2011), NIR
MOVIS colors Popescu et al. (2016), WISE albedos and diameters Mainzer et al.
(2016), and rotational properties with U¿2 (Warner et al., 2009).

###  3.1 Spectroscopic analysis

The entire analysis of the spectroscopic data was performed using the CANA
package (De Pra et al., 2018)333CANA code is available though
https://cana.readthedocs.io. In order to analize the spectra, we performed a
taxonomical classification, and we also computed (whenever the wavelength
coverage allowed it) four different parameters. These parameters are: visible
slope (visible - red-mode), NIR slope (NIR), hydration feature (visible - red-
mode), and turn-off point (visible - blue-mode).

The visible slope was measured using the angular coefficient in a linear fit
to the spectrum in the wavelength range of 0.5-0.9 $\mu m$, normalized to 0.55
$\mu m$. The spectral slopes are expressed in units of $\%/1000$Å. The
associated error is the sum of the systematic error introduced by the solar
analogs division, and the error of the fit estimated by a Monte-Carlo method
with 1000 iterations, where the spectra reflectance was resampled considering
the spectrum S/N. Although the results presented are the quadratic sum of the
described error sources, the systematic error is the strongly dominating term.

We looked for the presence of hydrated minerals through the identification and
characterization of an absorption band centered at around 0.7 $\mu m$. For
this task we used the wavelength range of 0.55-0.88 $\mu m$. The spectral
continuum was estimated by a linear fit within the 0.55-0.57 and 0.84-0.88
$\mu m$ intervals. Thereafter, we removed the continuum from the spectrum and
fit a fourth-order spline in the 0.55-0.88 $\mu m$ range. We identified the
hydration band if the minimum reflectance of the fit was close to 0.7 $\mu m$,
at a depth greater than $1\%$ and of $3\sigma$ of the spectrum S/N.

A common feature in primitive asteroids is a turn-off in the slope at
approximately 0.5 $\mu m$. We characterized the presence of this feature using
the data available in the 0.4-0.7 $\mu m$ range, applying the same methodology
as described in De Prá et al. (2018).

Figure 3: SFD for the five outer-belt asteroid family. The orange line
represents the power-law fit that was used to include the contribution of
small-sized members into the calculation of the family’s parent body size.

Taxonomic classification of the asteroids was carried out by minimization of
the chi-squared between the spectrum of a given object and the templates from
the DeMeo et al. (2009) taxonomic system. This procedure was performed using
the combined spectra with data from all wavelength ranges available. If the
spectrum was sampled only at visible wavelengths, we adjusted the class to fit
the Bus & Binzel (2002) scheme. The results for the spectroscopic analysis are
shown in Table LABEL:tab:results.

###  3.2 Public photometric catalogs

In addition to the spectroscopic data, we collected data of the families
available from public databases. Visible colors were extracted from the SDSS
(Carvano et al., 2010; Hasselmann et al., 2011), NIR color from the MOVIS
catalog (Popescu et al., 2016), and geometric albedos from the NEOWISE survey
(Mainzer et al., 2016).

We calculated the visible and NIR spectral slopes from the data available in
these databases such that they are comparable with the ones derived from the
spectroscopic data. We estimated the angular coefficient from a linear fit
using the reflectances on g, r, and i SDSS filters, normalized at 0.55 $\mu m$
for the visible slope; and using the Y, H, and K VISTA filters, normalized in
1.2 $\mu m$ for the NIR slope. The criteria for the choices of filters was
based on selecting the highest number of objects that were observed in at
least three filters and covering almost the same wavelength range as the
spectroscopic data ($0.5-0.9\leavevmode\nobreak\ \mu m$ and
$1.0-2.3\leavevmode\nobreak\ \mu m$). To estimate the uncertainties, we
created 1000 clones of each observation by drawing random values for the
reflectance in each filter using normal distributions with means equal to the
listed reflectance value and variances equal to the listed uncertainties. The
resultant spectral slope distribution was then fitted with a Gaussian curve,
the mean and variance of which were then adopted as the nominal value for the
spectral slope and its uncertainty, respectively, expressed in units of
$\%/1000$Å. Finally, the mean visible and NIR slopes of each family were then
estimated by a weighted average, using the slope uncertainties as the weights.
A weighted average, with the uncertainties provided by the NEOWISE catalog,
was used to estimate the mean albedo for each family. The results of this
analysis are shown in Fig. 2 and Table 2.

Figure 4: Rotation frequency vs. diameter for each family. The orange line
delimits the estimated critical period. For Veritas and Lixiaohua, the small
number of determined periods prevents the determination of this value.

###  3.3 Parent body sizes

We estimated the parent body diameter (PB) for each family based on the work
of Brož & Vokrouhlický (2008). To build the size–frequency distribution (SFD),
we obtained diameters of the family members from the WISE survey (Mainzer et
al., 2016). Objects with a geometric albedo $p_{v}>0.12$ were removed in order
to consider only objects that could have a primitive surface and minimize the
presence of interlopers. For the objects that did not have a determined
diameter, we estimated it using the following equation:

$D=\frac{1329\times 10^{-0.2H}}{\sqrt{p_{fam}}},$ (1)

where H is the absolute magnitude of the object and $p_{fam}$ is the mean
geometric albedo of the respective family. Figure 3 shows the SFD for each
family, where it is possible to observe that there is an inflection point in
the diameter distribution towards the smaller objects. We consider, as an
approximation, that this inflection is related to an observational bias and
use these points as the cutoff in diameter ($D_{c}$) to define the sample
completeness. The volume of the PB ($V_{PB}$) can be estimated using:

$V_{PB}=V_{c}+\int_{0}^{D_{c}}(\alpha\log_{10}(D)+\beta)\leavevmode\nobreak\
dD,$ (2)

where $V_{c}$ is the the sum of volumes of the objects with $D>D_{c}$. The
second term is the integral of a power-law fitted considering $D>D_{c}$, where
$\alpha$ and $\beta$ are the coefficients of the fit. The integral limits are
set from $0$ to $D_{c}$ in order to add the contribution of the small-sized
members. Finally, the diameter of PB ($D_{PB}$) is estimated assuming a
spheroidal shape:

$D_{PB}=\sqrt[3]{\frac{6}{\pi}V_{PB}}.$ (3)

Figure 3 shows that, with the exception of Hygiea, the SFDs for all famailies
are well approximated by a power law in the regime of $D>D_{c}$. In the case
of Hygiea, we also defined an upper limit in diameter to constrain the region
where the power law was fitted.

Although we use the power-law fitting to minimize the errors on the parental
body size derived from the observational bias on smaller members, there are
several sources of error in this estimate. For example, the individual errors
in the diameter of the family members available in the WISE catalog are not
considered here. Additionally, family members can be removed from the region,
for example through Yarkovsky-driven evolution or chaotic diffusion by
crossing resonances with giant planets. The process followed to identify
families considers a cutoff in velocity, which typically leaves a halo of
potential family members with similar surface properties, but with slightly
distinct orbital parameters that are not considered as belonging to the
families (Nesvorný et al., 2015). Finally, even though we defined a range in
geometric albedo to minimize the presence of interlopers, there should still
be objects that are not true members of the family but that occupy the same
region and may have been added in the SFD. The procedure of selecting only the
family members with albedo $p_{v}>0.12$ revealed that 1 to 12% of the family
members can be outliers.

###  3.4 Density

The analysis of asteroid rotational properties performed by Pravec & Harris
(2000) showed that objects larger than 0.15 km do not rotate faster than 11
revolutions per day. This spin barrier is interpreted by means of a rubble-
pile structure model, in which rotation with periods exceeding the critical
value would cause asteroid breakup (Pravec & Harris, 2007). The smaller
objects with faster rotation are thought to be monolithic collisional
fragments with stronger cohesion forces.

In a cohesionless rubble pile, the critical value for the spin barrier is
dependent on bulk density (Eq. 4). The bulk density of a body depends on both
the grain density of the material and the total porosity in the body. The
grain density is related to the composition, while the porosity is linked
mostly to the collisional history of the body. Asteroid families with distinct
formation histories, composition, and differentiation level should present
differences in densities, which would be reflected by distinct spin barriers.

We performed an estimate of the density of the family members based on their
rotational properties. This analysis considers two a priori hypotheses: 1) all
objects with diameter within the 4-20km range in a family that are close to
the spin barrier have the same density, and 2) the original spin distribution
reached the spin barrier, or the family has existed for a sufficiently long
time for YORP effects to increase the spin up to the spin barrier. Considering
this scenario and assuming that the structure of objects with diameters in the
4-20 km range can be approximated by a cohesionless rubble pile (Pravec &
Harris, 2000), we can use the following equation to infer these properties:

$\rho\approx\frac{(1+\Delta m)}{(P_{crit}/3.3)^{2}},$ (4)

where $\rho$ is the bulk density, $P_{crit}$ is the critical value for the
rotation period (in hours), and $\Delta m$ is the amplitude of the rotational
light curve. For this analysis, we use a spherical shape approximation, where
$\Delta m=0$.

To determine the critical value for each family, we searched for cataloged
rotational periods of family members in the Asteroid Light curve DataBase
(LCDB), Updated 2019 August 14 (Warner et al., 2009), with the U parameter of
the light curve equal to or higher than two. The U parameter is defined based
on the quality and coverage of light curve used to estimate the rotational
period, a value of 2 is the recommended value for statistical analysis and
indicates that the light curve was not completely observed and that the period
uncertainty can reach up to 30%. The number of objects per family that
satisfies this criteria is shown in Table 1. Figure 4 shows the frequency
versus diameter plot for each family with the respective critical period
value.

We note that the number of cataloged rotational periods per family can be too
small for the determination of a spin-barrier. This is seen especially in the
case of the Lixiaohua and Veritas families. Additionally, these families
possess the two youngest estimated ages in our sample (Table 1), and their
spin distribution could be less affected by the YORP effect and collisional
evolution, so much so that they do not yet present a spin barrier. We note
that the estimated densities are the result of a tentative approach that will
become more robust as we increase the number of determined rotation periods.

##  4 Results

Asteroid | Vis. Slope | Vis. Slope | IR Slope | Turn-off | Hydrated | 3-micron | MBC | Albedo | PB | PB | LM/PB | Density
---|---|---|---|---|---|---|---|---|---|---|---|---
Family | spec. | SDSS | MOVIS | members | members | feature | members |  | TW | Durda07 | TW |
| (%/1000Å) | (%/1000Å) | (%/1000Å) | Nf (Ns) | Nf (Ns) | (shape) | (number) |  | (km) | (km) |  |
Themis | $-0.2\pm 1.6$ | $0.5\pm 1.6$ | $1.7\pm 1.5$ | 11 (21) | 8 (59) | rounded | 3 | $0.066\pm 0.033$ | 286 | 451 | 0.68 | 1.2
Hygiea | $0.3\pm 3.7$ | $0.4\pm 2.1$ | $1.6\pm 1.8$ | 10 (13) | 3 (25) | ceres/rounded | 0 | $0.068\pm 0.042$ | 492 | 442 | 0.88 | 1.5
Veritas | $1.0\pm 1.3$ | $1.6\pm 1.5$ | $1.3\pm 3.1$ | 14 (15) | 13 (17) | - | 0 | $0.068\pm 0.062$ | 135 | 177 | 0.88 | -
Ursula | $2.8\pm 1.5$ | $3.7\pm 3.3$ | $2.3\pm 2.0$ | 4 (4) | 0 (7) | rounded | 0 | $0.058\pm 0.063$ | 226 | 280 | 0.83 | 0.8
Lixiaohua | $3.0\pm 3.2$ | $2.8\pm 1.7$ | $1.1\pm 1.5$ | 5 (30) | 0 (35) | - | 2 | $0.043\pm 0.081$ | 69 | 220 | 0.51 | -
Table 2: Average physical properties of outer-belt families. We present values
for parent-body diameters (PB) obtained in this work (TW) and by Durda et al.
(2007) (Durda07) for comparison. The ratio between the diameter of the
families’ largest member and that of the parent body (LM/PB) are shown only
for diameters obtained in this work. Nf represents the number of objects that
present the feature, while Ns is the number of spectra for which the
wavelength was appropriate to perform the feature analysis.

###  4.1 Themis

We increased the number of members with observed spectra to reach a total of
59 family members by adding family data available in the literature (Florczak
et al., 1999; Mothé-Diniz et al., 2005; Ziffer et al., 2011; Licandro et al.,
2012; de León et al., 2012; Kaluna et al., 2016; Fornasier et al., 2016;
Landsman et al., 2016; Marsset et al., 2016). The mean visible slope was
estimated at $-0.17\pm 1.58\%/1000$Å, and 13% of the sample showed the 0.7$\mu
m$ feature. The majority of the objects were classified as belonging to
C-class, with a significant fraction of B-types, hence the negative mean
slope. This value is consistent, considering the errors, with the $0.45\pm
1.64\%/1000$Å estimated using SDSS data for 563 objects. There were 21 out of
the 59 spectra with appropriate wavelength coverage for the Turn-off analysis,
11 of which showed this feature. The critical wavelength for the Turn-off
change can vary significantly from 0.49-0.67 $\mu m$. The MOVIS data provided
a mean NIR slope of $1.65\pm 1.47\%/1000$Å, slightly higher than the $0.12\pm
0.07\%/1000$Å obtained using spectroscopic data by Ziffer et al. (2011). The
latter work used the wavelength range of 1.6-2.3 $\mu$m to measure the slope,
which is distinct from the 1.0-2.15 $\mu$m provided by the MOVIS data, which
was used in this work. Additionally, these latter authors found that many
Themis family members can show a concave positive curvature in the spectra.
Both factors could be influencing the slope determination from the photometric
data.

The Themis parent body size was estimated to be approximately 286 km, in
agreement with the value obtained by Brož et al. (2013), which was calculated
in a similar manner. However, this value is considerably smaller than those
obtained using different techniques by Durda et al. (2007) and Tanga et al.
(1999), of 451 km and 369 km respectively. Nonetheless, the estimated values
of PB provide a range of $\left.LM\middle/PB\right.$ (largest member diameter
divided by the parent body size) from $0.51-0.68$, which is compatible with a
catastrophic event being the origin for the family.

The analysis of the rotational properties of 443 Themis family members
presented the most well-defined spin barrier among the studied families. The
critical period at $\sim 3$h provides an estimate of the bulk density of $1.2$
g/cm3. The bulk density of (24) Themis was estimated at $1.81\pm 0.67$ g/cm3
by Carry (2012), while Descamps et al. (2007) studied the binary asteroid (90)
Antiope, a member of the Themis family, and found a density of $1.25\pm 0.05$
g/cm3. Both values are in agreement with the estimate in this work, accounting
for the error bars. Another binary member of the family, (379) Huenna, was
studied by Marchis et al. (2008), who found a bulk density of $0.9\pm 0.1$
g/cm3, slightly under the value estimated by the spin-barrier method. However,
the diameter used to estimate (379) Huenna bulk density was higher than the
one provided by Mainzer et al. (2016), and a smaller diameter would return a
higher value for the density. Additionally, it is of note that larger objects
($D>30$ km) can follow a different regime in terms of cohesive forces and
density, as proposed by Pravec & Harris (2000).

###  4.2 Hygiea

The Hygiea family showed very similar properties to the Themis family at the
studied wavelengths, with a mean slope of $0.30\pm 3.68\%/1000$Å
(spectroscopic) and $0.40\pm 2.09\%/1000$Å (photometric) in visible
wavelengths, and $1.07\pm 1.53\leavevmode\nobreak\ \%/1000$Å in the NIR.
However, there is a higher diversity in spectral slope than in Themis. Most of
the targets were also classified as C-class, with a significant B-type
contribution. Approximately $15\%$ of the family members present the 0.7 $\mu
m$ hydration band, and 12 out of 17 objects show the turn-off feature.

Asteroid (10) Hygiea is the largest object in the outer-belt region, and the
fourth largest in the main belt. The diameter cataloged by Mainzer et al.
(2016) for (10) Hygiea is of $\sim 533$ km, considerably higher than the
previous estimate from Tedesco (1994) of $\sim 407$ km. A recent work of
Vernazza et al. (2019) using a direct imaging technique estimated an
equivalent diameter of $\sim 434$ km. We adopted this latter value for the
object and to construct the family SFD. The parental body size was estimated
at 486 km, with $LM/PB\sim 0.89$. Durda et al. (2007) estimated the family PB
to be 440 km, in good agreement considering that these latter authors used a
different technique and a smaller diameter for (10) Hygiea. Figure 3 reveals
an excess of large asteroids which is characteristic of a shattering event,
where most of the family mass is distributed among the largest members. These
values are influenced by the presence of other large asteroids besides (10)
Hygiea, such as (52) Europa and (159) Aemilia, with respective diameters of
$\sim 303$ km and $\sim 125$ km. Both of these objects were identified as
Hygiea family members by Nesvorný et al. (2015), but not in Vernazza et al.
(2019) and Carruba (2013). The exclusion of these objects from the family
would produce a smaller parent body, where the second-largest body would be
(1599) Giomus with a diameter of 52 km. The presence of (52) and (159) can
significantly change the interpretation of the collisional event that formed
the family and of the nature of the family parent body.

A rotation period has been derived for 149 members of the Hygiea family. The
spin barrier is defined at $\sim 2.7$h, which provides a density estimate of
$1.5$ g/cm3. In Vernazza et al. (2019), the authors estimated a bulk density
of $1.944$ g/cm3 for (10) Hygiea, which is in reasonable agreement with the
$2.19\pm 0.42$ g/cm3 calculated by Carry (2012). These values are considerably
higher than our estimates. However, (10) Hygiea is considerably larger than
the regime where we use the cohesionless approximation (4-20 km). Also,
considering that this object could be a differentiated body, and could have
different layers of material and levels of compaction, a higher value of this
object density is plausible and not contradictory to the possibility that
smaller objects could have lower densities. Carry (2012) also estimated a
density of $1.52\pm 0.39$ g/cm3 for (52) Europa, which is in agreement with
the value obtained in this work.

Figure 5: Whisker plot of the visible slope distribution in each family. The
boxes represent the average and standard deviation of the slope distribution,
while the solid black line inside of the box represents the median. The black
dots represent single slope measurements of family members, with the error
bars showing the maximum and minimum values.

###  4.3 Veritas

The Veritas family showed the highest spectral homogeneity among its members,
with a mean visible slope of $1.00\pm 1.30\%/1000$Å (spectroscopic) and
$1.61\pm 1.50\%/1000$Å (photometric) and a high content of hydrated members
reaching 77% of the sample. Of the 16 objects analyzed in this family, 14 show
the Turn-off feature. The majority of the objects’ spectra were classified in
the C-complex, especially as Ch-type, which reflects the high level of
hydrated members in the family. This result is in agreement with that of
Mothé-Diniz et al. (2005). The mean NIR slope was estimated at $1.31\pm
3.12\%/1000$Å, higher than the $-0.04\pm 0.03\%/1000$Å obtained using
spectroscopic data obtained by Ziffer et al. (2011). These latter authors
noted that, in contrast to the Themis family, the NIR spectra for the Veritas
family show a concave negative curvature. As in the Themis family case, the
wavelength range used to determine the slope and the curvature in the spectra
could be influencing the different values obtained in this work.

The Veritas parental body size was estimated at 136 km, which is slightly
smaller than the 177 km obtained by Durda et al. (2007). Both values are in
agreement with those of Brož et al. (2013), who estimated the Veritas PB at
100-177 km. The small number of cataloged rotational periods for Veritas
members prevents us from obtaining an estimate of the family spin barrier and
density limit.

###  4.4 Ursula

The Ursula family present a spectroscopic mean slope of $2.77\pm
1.46\%/1000$Å, compatible with the $3.71\pm 3.25\%/1000$Å estimated using SDSS
data. Based on NIR colors, Ursula showed the reddest mean slope among the
studied families. None of the objects exhibited the 0.7 $\mu m$ feature,
indicating that the family might have a low hydrated mineral content. Although
the spectra for (375) Ursula obtained by Bus & Binzel (2004) and Vilas et al.
(2006) presented similar spectral slopes, there is a significant difference in
the shape of the spectra, and the data from the latter work might suggest a
hydration feature.

We estimated the parent body diameter at 226 km, which is slightly larger than
the 203 km estimated by Brož et al. (2013) and smaller than the 280 km
measured by Durda et al. (2007). The rotational distribution suggests a spin
barrier with a critical rotational period of $\sim 3.6$h, which provides an
estimate for the density for the Ursula family of $\sim 0.8$ g/cm3 .

###  4.5 Lixiaohua

The results for the spectroscopic analysis of the Lixiaohua family are
described in De Prá et al. (2020), where we found a mean slope of $3.03\pm
3.22\%/1000$Å (spectroscopic) and $2.79\pm 1.72\%/1000$Å (spectrophotometric)
in visible wavelengths, and of $1.07\pm 1.53\%/1000$Å in the NIR. The
Lixiaohua is the darkest of the studied families, with mean albedo of
$0.043\pm 0.081$ (Fig. 2).

In this work, we extended the analysis by calculating the parent body size,
estimated at $PB\sim 69$ km and the ratio $\left.LM\middle/PB\right.\sim
0.51$, which are consistent with a catastrophic disruption event. This PB
value is significantly smaller than the one estimated by Durda et al. (2007),
of $\sim 220$ km, who also provide $\left.LM\middle/PB\right.\sim 0.16$. The
latter value suggests that the majority of the parent-body mass was scattered
or lies in the smaller undiscovered family members. There are only 28
Lixiaohua members with determined rotational periods. The analysis of Fig. 4
suggests that the family spin barrier might be considerably low. However, more
data are needed to obtain any conclusive density estimate.

##  5 Discussion

The analysis of the outer-belt families Themis, Hygiea, Veritas, Ursula, and
Lixiaohua reveals a diversity of physical properties. In Table 2, we present
the results for the spectroscopic properties, parent-body sizes, densities,
and include information that contributes to this discussion: the 3 $\mu$m band
information extracted from the literature (Campins et al., 2010; Takir &
Emery, 2012; Rivkin et al., 2019) and the presence of main-belt comets (Hsieh
et al., 2018). In particular, the presence of hydrated and ice-bearing objects
in a single family can be considered an indication of partial differentiation
of the parental body, as proposed for the Themis family. Castillo-Rogez &
Schmidt (2010) and Marsset et al. (2016) suggested that these two materials
could be representatives of different layers in the internal structure of the
family’s parent body. Hydrated minerals, which are typically formed by the
interaction of liquid water with silicates such as olivine, would have formed
in the inner layers that experienced higher temperature and pressure
conditions, while the water ice could remain nearly unaltered in the external
layers. In contrast, an undifferentiated body should present members with only
hydrated minerals or water ice, but not both.

Figure 5 shows the median and mean slope of each family with associated
variance and minimum and maximum values, while Figure 2 shows the albedo
visible and NIR slopes obtained from public catalogs. Themis, Hygiea, and
Veritas families show neutral visible slopes compatible with C-type asteroids,
with a higher variability in the Hygiea family. In contrast, Ursula and
Lixiaohua show slightly reddish slopes, related to P-type objects.

We identified different hydrated fractions among the families. The two large
C-type families Themis and Hygiea show a similar percentage of hydrated
members at $13-15\%$, while the smaller Veritas family shows a higher fraction
of hydrated members, reaching $87\%$. The Veritas family also shows the
highest fraction of members showing the turn-off feature. This feature in
C-type objects is attributed to ferric oxide intervalence charge transfer
transition Feierberg et al. (1985); Vilas (1995). Hendrix & Vilas (2019)
proposed the absence of the feature could be related to a higher degree of
space weathering. This result could explain why Themis is the oldest family in
our sample and shows a lower fraction of turn-off members, in contrast to
Veritas, which is the youngest and might show younger surfaces. However, it is
worth noting that Themis and Hygiea are considerably closer in age than each
is to Veritas.

Ursula and Lixiaohua show no unambiguous indication of hydrated members. One
difference between the spectra of these families is seen in the fraction of
members that exhibit the Turn-off feature. However, the analysis of the Ursula
family is based on only four objects and more data are needed to make a proper
comparison of this feature between these families.

The sample of families covers a wide range of parental body sizes, from 69 to
492 km. The approach used by Durda et al. (2007) compared the SFD of the
families with ones simulated using a combination of smooth-particle
hydrodynamics (SPH) and N-body codes. Their results provide estimates
typically larger than those calculated in this work, with the exception of the
Hygiea family. The major differences are found in the case of Themis and
Lixiaohua families. In both cases, the higher parental body size suggests that
most of the mass is located in the small-sized members, or was detached from
the family through dynamical evolution, or lost in the dust produced by the
collision. While that could be the case for Themis, it is unlikely that the
largest fraction of the mass from the Lixiaohua progenitor was lost, and a
smaller parent body size than the one proposed by Durda et al. (2007) is more
likely.

Carry (2012) estimated an average bulk density of $1.33\pm 0.58$ g/cm3 for
C-type objects, in agreement with the values we estimated for the Themis and
Hygiea families. Carbognani (2017) used a similar methodology to the one
described in this work and found a lower limit for the density of C-types of
$0.90\pm 0.05$ g/cm3. A possible interpretation for this scenario is that
there could exist C-type asteroids with lower densities than the members of
Themis and Hygiea, which could be explained by variations in grain density
(composition) and porosity. For the Ursula family, the low value for density
is compatible with the P-/D-types and cometary nuclei (Carry, 2012), which is
in agreement with the family spectroscopic properties.

The largest members of Hygiea, Themis, and Ursula have been observed in the
3.0 $\mu$m region. The Themis family members (24) Themis and (90) Antiope both
show a ”rounded” feature associated with the presence of water-ice on their
surfaces (Campins et al., 2010; Rivkin & Emery, 2010; Takir & Emery, 2012).
Usui et al. (2019) presented the spectrum of (24) Themis obtained by the Akari
space telescope, where they identified two features: one at 2.7 $\mu$m
associated with hydrated minerals, and another at around 3.071 $\mu$m related
to water ice. Another indication of water ice as a constituent of the family
composition is the presence of three MBCs, in which the cometary activity is
suggested to be sublimation-driven (Hsieh et al., 2018). As proposed by
Castillo-Rogez & Schmidt (2010) and Marsset et al. (2016), a possible
explanation for the spectral diversity of Themis, which includes hydrated
members, MBCs, and surface ice on two family members, is that the Themis
parent body could be partially differentiated.

The spectrum of (375) Ursula was observed by Rivkin et al. (2003). At that
time the absorption feature was considered to be similar to the one in (1)
Ceres. However, as noted by Rivkin et al. (2019), the band would now be
classified as similar to the one in (24) Themis, also suggesting the presence
of water ice in the family. In contrast with Themis, the Ursula family shows
little to no sign of hydrated members. The spectroscopic properties and the
low density of the Ursula family suggest that the parent body was formed in a
similar region to the P-/D-type asteroids and possible cometary nuclei, beyond
the snow line.

In the case of the Hygiea family, the analysis by Takir & Emery (2012) of (10)
Hygiea showed an absorption feature classified as similar to the one in (1)
Ceres (Takir & Emery, 2012). However, Rivkin et al. (2019) recently acquired
seven additional spectra for the object, three of which were described as
“rounded’ or “Themis-like”, three as “Ceres-like”, and one as hydrated
(“Sharp” or “Pallas-like”). The Ceres-like absorption feature is interpreted
as being due to the presence of ammoniated minerals, while the Sharp or
Pallas-like feature is related to the presence of hydrated minerals. Usui et
al. (2019) identified two significant features at 2.72 and 3.08 $\mu m$ in the
spectrum of (10) Hygiea and a small 3.1 $\mu m$ feature as well as a weaker
feature at 2.7 $\mu m$ in the spectrum of (52) Europa. These features are
related with hydrated minerals and water ice, respectively. Rivkin et al.
(2019) also acquired four spectra of (52) Europa, the second-largest member of
the Hygiea family, and all of these presented rounded or Themis-like features,
attributed to water-ice. However, Takir & Emery (2012) suggested that (52)
Europa shows a distinct band shape classified as Europa-like, which could lead
to a distinct compositional interpretation. The variability in IR spectra for
(10) Hygiea could be attributed to a heterogeneous surface. However, Mothé-
Diniz et al. (2001) and Vernazza et al. (2019), using different techniques,
did not find evidence of strong surface inhomogeneity for this object. As
suggested by Rivkin et al. (2019), additional data are needed to fully
characterize the surface of (10) Hygiea.

Carruba (2013) and Rivkin et al. (2014) suggested that (10) Hygiea could be an
interloper of the family. However, the object is consistent with the family
members at the wavelength regions analyzed in this work. Additional
investigations at different wavelengths are necessary to confirm or reject
this hypothesis. The large diameter of the family’s parent body and the
similarity of surface properties between (10) Hygiea and the differentiated
body (1) Ceres (Rivkin et al., 2019) suggest that the parent body and/or (10)
Hygiea have also undergone differentiation.

On the other hand, Veritas and Lixiaohua do not seem to be differentiated. As
discussed in De Prá et al. (2020), the Lixiaohua family shows evidence of
water ice through the presence of two MBCs among its members and no trace of
aqueous alteration. In contrast, the Veritas family shows a large fraction of
hydrated members, which indicates compositional homogeneity. Michel et al.
(2011) proposed that the asteroid (490) Veritas, the largest member of the
homonymous family, could be an interloper in the family. However, the
spectroscopic properties of the asteroid are consistent with a highly
homogeneous family.

The sizes of the parent bodies of both the Lixiaohua and Veritas families are
below 150 km, which is considerably smaller than the parent bodies of Themis
and Hygiea. Combined with their spectroscopic properties, this suggests that
these families did not originate from the break-up of differentiated bodies.
The differences in spectral properties between these two families suggest that
they were formed at different places and/or times in the early Solar System,
where the Veritas parent body might have formed sooner and was more exposed to
radiogenic heating.

##  6 Conclusions

We present new spectroscopic data for the outer-belt families Themis, Hygiea,
and Veritas, and include data available in the literature for the Ursula and
Lixiaohua families. Our analyses reveal the diversity of surface properties
among the families, where the Themis, Hygiea, and Veritas families present
neutral mean slopes in the visible and NIR wavelengths. In contrast, Ursula
and Lixiaohua families present reddish mean slopes. The analysis of the albedo
reveals that the Lixiaohua is also the darkest among these families. The
number of hydrated members varies significantly: 77% of Veritas members show
the 0.7 $\mu$m feature, while Lixiaohua and Ursula show no evidence of
hydration.

In addition to the spectroscopic analysis we also estimated the parental body
size of each family and the density based on their rotational properties. The
parental body sizes of Themis and Hygiea are the largest among the families,
and in combination with the analysis of the distribution of physical
properties among their members, suggests that these families could have
undergone a partial differentiation process. In contrast, Lixiaohua and
Veritas present smaller parent body sizes, and are unlikely to have gone
through such processing. The Ursula parent body is of intermediate size, and
more data are required to understand the origin of the family. We estimated
the density limits for the members of the Themis, Hygiea, and Ursula families,
where the first two present densities compatible with C-type asteroids, and
the latter with P-type, in agreement with their spectroscopic properties.

The results of the analysis performed in this work suggest a diverse scenario
for the formation of the parent bodies of the families studied. The
differences between Themis, Hygiea, and Veritas could be related to the
initial masses of their progenitors, while Ursula and Lixiaohua could have
formed in separate and distinct regions of the protoplanetary disk, and were
scattered to their current orbits. However, additional investigations of the
compositions and physical properties of their members and further analyses of
the remaining primitive outer-belt families are required to test these
hypotheses. The continuation of the PRIMASS and future data releases of
asteroid spectra from Gaia will greatly contribute to enhancing the analysis
of these populations.

###### Acknowledgements.

M. De Prá acknowledges funding from the Prominent Postdoctoral Program of the
University of Central Florida. N. Pinilla-Alonso acknowledges support from the
17-PDART17-2-0097 project funded by the PDART-ROSES 2017 program. J. Licandro
acknowledge support from the AYA2015-67772-R (MINECO, Spain). J. de León
acknowledges support from MINECO under the 2015 Severo Ochoa Program
SEV-2015-0548 and the AYA-2017-89090-P. This work is based in part on
observations obtained at the Southern Astrophysical Research Telescope (SOAR),
which is a joint project of the Ministério da Ciência, Tecnologia, Inovação e
Comunicações (MCTIC) do Brasil, the U.S. National Optical Astronomy
Observatory (NOAO), the University of North Carolina at Chapel Hill (UNC), and
Michigan State University (MSU).

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##  Appendix A Additional figures and tables

Table 1: Asteroids observational conditions - visible Asteroid | Asteroid | Family | Date | Time Start | Slit | Airmass | $V$ | $\alpha$ |  TEXP | Solar
---|---|---|---|---|---|---|---|---|---|---
Number | Name | Name |  | (UT) |  ($"$) |  | $(mag)$ |  (∘) | (s) | Analogs
268 | Adorea | Themis | 2012-03-27 | 07:55 | 1.68 | 1.08 | 12.48 | 12.60 | 60.0 | 1,2,3,4
561 | Ingwelde | Themis | 2011-02-08 | 01:44 | 1.03 | 1.765 | 16.29 | 19.01 | 360.0 | 1
1581 | Abanderada | Themis | 2011-02-01 | 06:56 | 1.03 | 1.263 | 15.53 | 15.52 | 480.0 | 1
1674 | Groeneveld | Themis | 2011-02-08 | 02:07 | 1.03 | 1.97 | 16.00 | 18.51 | 360.0 | 1
1782 | Schneller | Themis | 2012-03-27 | 06:01 | 1.68 | 1.113 | 15.89 | 4.37 | 420.0 | 1,2,3,4
2534 | Houzeau | Themis | 2011-02-01 | 04:29 | 1.03 | 1.557 | 16.12 | 2.64 | 320.0 | 1
2563 | Boyarchuk | Themis | 2011-02-08 | 05:23 | 1.03 | 1.347 | 16.18 | 14.74 | 480.0 | 1
2918 | Salazar | Themis | 2012-03-29 | 04:32 | 1.68 | 1.14 | 16.55 | 1.29 | 480.0 | 1,3,5
5429 | 1988 BZ1 | Themis | 2011-01-31 | 06:14 | 1.03 | 1.497 | 16.55 | 2.48 | 540.0 | 1
5594 | Jimmiller | Veritas | 2011-01-31 | 01:58 | 1.03 | 1.66 | 16.66 | 5.97 | 400.0 | 1
6343 | 1993 VK | Veritas | 2012-03-27 | 00:48 | 1.68 | 1.48 | 17.83 | 12.06 | 600.0 | 1,2,3,4
6374 | Beslan | Veritas | 2011-02-01 | 02:44 | 1.03 | 1.36 | 17.06 | 8.33 | 600.0 | 1
7231 | Porco | Veritas | 2012-03-29 | 07:07 | 1.68 | 1.2 | 17.86 | 17.97 | 600.0 | 1,3,5
9860 | Archaeopteryx | Veritas | 2012-03-29 | 06:02 | 1.68 | 1.29 | 18.03 | 2.63 | 600.0 | 1,3,5
13537 | 1991 SG | Veritas | 2012-03-29 | 08:21 | 1.68 | 1.253 | 18.07 | 8.90 | 720.0 | 1,3,5
14264 | 2000 AH142 | Veritas | 2012-03-28 | 04:01 | 1.68 | 1.18 | 17.90 | 1.81 | 600.0 | 1,4,5
24638 | 1981 UC23 | Veritas | 2012-03-28 | 05:19 | 1.68 | 1.11 | 17.71 | 1.46 | 600.0 | 1,4,5
45378 | 2000 AD118 | Veritas | 2012-03-27 | 02:12 | 1.68 | 1.15 | 17.32 | 4.81 | 600.0 | 1,2,3,4
1209 | Pumma | Hygiea | 2012-03-27 | 08:13 | 1.68 | 1.14 | 15.29 | 11.73 | 360.0 | 1,2,3,4
3626 | Ohsaki | Hygiea | 2012-03-27 | 03:48 | 1.68 | 1.313 | 17.39 | 10.46 | 600.0 | 1,2,3,4
5116 | Korsor | Hygiea | 2011-02-08 | 07:16 | 1.03 | 1.16 | 17.47 | 14.76 | 540.0 | 1
5794 | Irmina | Hygiea | 2011-02-01 | 01:47 | 1.03 | 1.473 | 17.57 | 12.08 | 600.0 | 1
6415 | 1993 VR3 | Hygiea | 2012-03-27 | 04:46 | 1.68 | 1.123 | 17.05 | 2.01 | 600.0 | 1,2,3,4
15134 | 2000 ED92 | Hygiea | 2011-02-08 | 03:01 | 1.03 | 1.402 | 17.34 | 3.35 | 495.0 | 1
23916 | 1998 SD131 | Hygiea | 2012-03-27 | 03:03 | 1.68 | 1.203 | 17.43 | 0.52 | 600.0 | 1,2,3,4
24358 | 2000 AV117 | Hygiea | 2012-03-28 | 02:35 | 1.68 | 1.323 | 17.30 | 4.53 | 600.0 | 1,4,5
24956 | 1997 SN10 | Hygiea | 2012-03-29 | 03:16 | 1.68 | 1.192 | 17.86 | 2.16 | 600.0 | 1,3,5
25829 | 2000 DU108 | Hygiea | 2012-03-27 | 08:44 | 1.68 | 1.29 | 17.72 | 9.08 | 600.0 | 1,2,3,4
26719 | 2001 HQ5 | Hygiea | 2012-03-29 | 02:16 | 1.68 | 1.29 | 17.68 | 2.62 | 600.0 | 1,3,5
Solar Analogs: (1) L102-1081, (2) L107-684, (3) L107-998, (4) HD44594, (5) HD144584 |  |
Figure 1: Visible spectroscopy of asteroids from the Themis family. Spectra of
the same objects that were observed by different works are shown in red. The
blue lines represent the turn-off point. Figure 2: Visible spectroscopy of
asteroids from the Hygiea family. Spectra of the same objects that were
observed by different works are shown in red. The blue lines represent the
turn-off point. Figure 3: Visible spectroscopy of asteroids from the Veritas
family. The blue lines represent the turn-off point.

Table 2: Results for the spectroscopic parametrization. (1) Reference labels are: 1- This work, 2- SMASS (Xu et al. 1996), 3-SMASSII (Bus & Binzel 2004), 4-S3OS2 (Lazzaro et al. 2007), 5 - Vilas et al. (2006), 6 - Mothé-Diniz et al. (2001). The symbols ’-’ indicate the spectra that do not show the feature and ’*’ where the wavelength coverage was not appropriate to evaluate the presence of the feature. Asteroid | Family | Taxonomic | Visible | Visible | Turn-off | Turn-off | 0.7 $\mu m$ | 0.7 $\mu m$ | 0.7 $\mu m$ | 0.7 $\mu m$ | ref1
---|---|---|---|---|---|---|---|---|---|---|---
Number |  | class | slope | slope error | point | point error | band depth | band depth | band center | band center |
|  |  | ($\%/1000$Å) | ($\%/1000$Å) | ($\AA$) | ($\AA$) | (%) | error (%) | ($\AA$) | error ($\AA$) |
10 | Hygiea | B | -2.191 | 1.000 | 6087 | 18 | - | - | - | - | 2
| Hygiea | C | 0.133 | 1.000 | 6010 | 39 | - | - | - | - | 3
| Hygiea | C | -0.072 | 0.031 | - | - | - | - | - | - | 6
52 | Hygiea | Cg | 2.227 | 1.001 | 6039 | 50 | - | - | - | - | 3
100 | Hygiea | S | 7.272 | 1.001 | * | * | - | - | - | - | 3
| Hygiea | A | 11.771 | 0.165 | - | - | - | - | - | - | 6
108 | Hygiea | Sv | 8.011 | 1.002 | * | * | - | - | - | - | 3
159 | Hygiea | Ch | -0.098 | 1.000 | 5345 | 15 | 2.294 | 0.102 | 6964 | 44 | 3
538 | Hygiea | B | -0.558 | 0.046 | - | - | - | - | - | - | 6
867 | Hygiea | B | -3.486 | 0.114 | - | - | - | - | - | - | 6
1107 | Hygiea | Xk | 2.782 | 1.000 | - | - | - | - | - | - | 3
1109 | Hygiea | D | 7.143 | 1.000 | * | * | - | - | - | - | 4
| Hygiea | D | 7.197 | 0.106 | - | - | - | - | - | - | 6
1209 | Hygiea | X | 2.813 | 0.020 | - | - | - | - | - | - | 1
| Hygiea | T | 6.663 | 1.001 | * | * | - | - | - | - | 4
| Hygiea | T | 6.367 | 0.208 | - | - | - | - | - | - | 6
1599 | Hygiea | S | 0.618 | 0.199 | - | - | - | - | - | - | 6
2436 | Hygiea | B | -3.540 | 0.231 | - | - | - | - | - | - | 6
3626 | Hygiea | B | -1.470 | 0.027 | 5212 | 30 | - | - | - | - | 1
4667 | Hygiea | B | -4.554 | 0.108 | - | - | - | - | - | - | 6
4955 | Hygiea | B | -3.420 | 1.000 | * | * | - | - | - | - | 4
5116 | Hygiea | C | 2.934 | 0.022 | 5297 | 12 | - | - | - | - | 1
5155 | Hygiea | C | -0.666 | 0.079 | - | - | - | - | - | - | 6
5794 | Hygiea | B | -6.217 | 0.065 | - | - | - | - | - | - | 1
6415 | Hygiea | B | -1.050 | 0.021 | 5125 | 21 | - | - | - | - | 1
15134 | Hygiea | B | -1.686 | 0.047 | - | - | - | - | - | - | 1
23916 | Hygiea | C | 0.297 | 0.023 | 5143 | 7 | 3.148 | 0.095 | 7119 | 21 | 1
24358 | Hygiea | Cb | 1.118 | 0.024 | 5013 | 22 | 2.361 | 0.095 | 7058 | 34 | 1
24956 | Hygiea | B | -1.476 | 0.027 | 4967 | 20 | - | - | - | - | 1
25829 | Hygiea | C | 0.304 | 0.032 | 5175 | 21 | - | - | - | - | 1
26719 | Hygiea | Xc | 4.151 | 0.031 | - | - | - | - | - | - | 1
24 | Themis | B | -0.852 | 0.021 | - | - | - | - | - | - | 3
| Themis | B | -0.808 | 0.022 | * | * | - | - | - | - | 4
62 | Themis | B | -1.790 | 0.037 | 5432 | 37 | 1.062 | 0.088 | 6741 | 50 | 3
| Themis | B | -2.074 | 0.014 | * | * | - | - | 6741 | 50 | 4
90 | Themis | Ch | -0.452 | 0.015 | * | * | 1.31 | 0.055 | 7087 | 28 | 4
| Themis | C | 0.409 | 0.024 | 6735 | 70 | - | - | 7087 | 28 | 3
171 | Themis | C | 0.269 | 0.017 | * | * | - | - | - | - | 4
| Themis | C | 0.666 | 0.022 | 5986 | 38 | - | - | - | - | 3
223 | Themis | Cb | 2.015 | 0.017 | * | * | - | - | - | - | 4
268 | Themis | Cb | 1.519 | 0.017 | * | * | - | - | - | - | 4
| Themis | C | 1.567 | 0.022 | - | - | - | - | - | - | 1
316 | Themis | C | -0.195 | 0.025 | * | * | - | - | - | - | 4
379 | Themis | C | 0.142 | 0.020 | 5728 | 39 | - | - | - | - | 3
383 | Themis | B | -1.918 | 0.055 | 5319 | 36 | - | - | - | - | 3
461 | Themis | X | 3.837 | 0.025 | * | * | - | - | - | - | 4
468 | Themis | C | 2.785 | 0.050 | * | * | - | - | - | - | 4
515 | Themis | Cb | 0.758 | 0.065 | - | - | - | - | - | - | 3
526 | Themis | Cb | 0.336 | 0.020 | * | * | - | - | - | - | 4
561 | Themis | Ch | 0.304 | 0.020 | 5219 | 29 | - | - | - | - | 1
621 | Themis | B | -0.905 | 0.034 | * | * | - | - | - | - | 4
767 | Themis | B | -2.318 | 0.031 | - | - | - | - | - | - | 3
846 | Themis | Cb | 0.912 | 0.026 | * | * | - | - | - | - | 4
848 | Themis | Cb | 0.619 | 0.019 | * | * | - | - | - | - | 4
936 | Themis | B | -1.363 | 0.014 | * | * | - | - | - | - | 4
954 | Themis | Cb | 0.783 | 0.028 | * | * | - | - | - | - | 4
981 | Themis | C | -0.002 | 0.018 | * | * | - | - | - | - | 4
1003 | Themis | B | -1.980 | 0.040 | * | * | - | - | - | - | 4
1229 | Themis | B | -1.779 | 0.040 | * | * | - | - | - | - | 4
1302 | Themis | B | -4.068 | 0.020 | * | * | 2.497 | 0.067 | 6596 | 54 | 2
1340 | Themis | Ch | -0.974 | 0.018 | * | * | 1.448 | 0.055 | 7084 | 126 | 4
1487 | Themis | B | -1.431 | 0.021 | * | * | - | - | - | - | 4
1539 | Themis | B | -1.726 | 0.027 | 5356 | 32 | - | - | - | - | 3
| Themis | B | -0.612 | 0.016 | * | * | - | - | - | - | 4
1576 | Themis | B | -1.713 | 0.014 | * | * | - | - | - | - | 4
1615 | Themis | B | -1.198 | 0.014 | * | * | - | - | - | - | 4
1674 | Themis | C | 2.061 | 0.027 | - | - | - | - | - | - | 1
1691 | Themis | Cb | 0.396 | 0.022 | * | * | - | - | - | - | 4
1782 | Themis | B | -2.655 | 0.023 | 5013 | 16 | - | - | - | - | 1
2296 | Themis | Cb | 0.328 | 0.023 | * | * | - | - | - | - | 4
2489 | Themis | Cb | 0.608 | 0.017 | * | * | 1.343 | 0.053 | 6531 | 53 | 4
2519 | Themis | B | -1.495 | 0.028 | * | * | - | - | - | - | 4
2524 | Themis | Ch | -0.765 | 0.015 | * | * | - | - | - | - | 4
2525 | Themis | Ch | -0.760 | 0.017 | * | * | 1.432 | 0.059 | 6848 | 43 | 4
2534 | Themis | C | 1.340 | 0.033 | 5241 | 42 | - | - | - | - | 1
2563 | Themis | B | -3.897 | 0.020 | - | - | 2.994 | 0.075 | 6804 | 28 | 1
2659 | Themis | B | -1.276 | 0.026 | 5633 | 35 | - | - | - | - | 3
2708 | Themis | B | -2.543 | 0.088 | - | - | - | - | - | - | 3
2918 | Themis | B | -2.225 | 0.016 | 4977 | 12 | 1.444 | 0.055 | 6963 | 44 | 1
3128 | Themis | Cb | 0.280 | 0.023 | * | * | - | - | - | - | 4
3179 | Themis | Ch | 0.811 | 0.215 | - | - | - | - | - | - | 3
3274 | Themis | C | 0.478 | 0.032 | * | * | - | - | - | - | 4
3507 | Themis | B | -0.978 | 0.019 | * | * | - | - | - | - | 4
| Themis | Ch | 0.423 | 0.127 | - | - | - | - | - | - | 3
3615 | Themis | Cb | 0.810 | 0.024 | * | * | - | - | - | - | 4
3663 | Themis | C | 0.067 | 0.026 | * | * | - | - | - | - | 4
3832 | Themis | Cb | 0.547 | 0.028 | * | * | - | - | - | - | 4
4143 | Themis | Cb | 0.326 | 0.023 | * | * | - | - | - | - | 4
4759 | Themis | Ch | -0.293 | 0.027 | * | * | - | - | - | - | 4
4778 | Themis | X | 3.630 | 0.047 | * | * | - | - | - | - | 4
5045 | Themis | Cb | 0.100 | 0.034 | * | * | - | - | - | - | 4
5429 | Themis | B | -3.854 | 0.063 | - | - | - | - | - | - | 1
6297 | Themis | B | -0.147 | 0.031 | * | * | - | - | - | - | 4
8518 | Themis | Ch | -0.742 | 0.024 | * | * | - | - | - | - | 4
8906 | Themis | Ch | -0.928 | 0.059 | * | * | - | - | - | - | 4
490 | Veritas | Cgh | 1.745 | 0.024 | 5434 | 18 | 1.036 | 0.073 | 6902 | 38 | 3
1086 | Veritas | Ch | 0.081 | 0.022 | * | * | 4.424 | 0.073 | 7059 | 42 | 4
| Veritas | Ch | -0.248 | 0.051 | 5262 | 21 | 2.195 | 0.13 | 7059 | 42 | 3
2147 | Veritas | Ch | 1.213 | 0.106 | 5421 | 57 | 3.04 | 0.233 | 7276 | 57 | 3
2428 | Veritas | Ch | 0.039 | 0.099 | 5459 | 32 | 2.4 | 0.309 | 6959 | 77 | 3
2934 | Veritas | B | -1.175 | 0.128 | - | - | 3.634 | 0.448 | 6984 | 119 | 3
3090 | Veritas | Cg | 2.568 | 0.154 | 5738 | 50 | - | - | - | - | 3
3542 | Veritas | B | -0.462 | 0.152 | - | - | - | - | - | - | 3
5592 | Veritas | X | 2.792 | 0.040 | * | * | 3.32 | 0.095 | 7046 | 16 | 4
5594 | Veritas | Ch | 1.384 | 0.048 | 5558 | 20 | - | - | - | - | 1
6343 | Veritas | C | 2.355 | 0.035 | 5258 | 13 | - | - | - | - | 1
6374 | Veritas | Ch | 0.789 | 0.033 | 5201 | 18 | 2.99 | 0.117 | 7023 | 44 | 1
7231 | Veritas | C | 2.256 | 0.037 | 5222 | 17 | 3.351 | 0.134 | 7086 | 32 | 1
9860 | Veritas | B | -1.464 | 0.031 | 5030 | 12 | 3.32 | 0.122 | 7028 | 28 | 1
13537 | Veritas | Ch | 0.299 | 0.040 | 5284 | 19 | 1.74 | 0.1450 | 7159 | 49 | 1
14264 | Veritas | Ch | 1.582 | 0.026 | 5277 | 7 | 2.784 | 0.095 | 7056 | 23 | 1
24638 | Veritas | Ch | 0.144 | 0.025 | 5228 | 11 | 4.041 | 0.1 | 6992 | 21 | 1
45378 | Veritas | Cgh | 2.723 | 0.022 | 5241 | 9 | 1.567 | 0.078 | 7032 | 25 | 1
375 | Ursula | X | 3.432 | 0.022 | * | * | - | - | - | - | 5
| Ursula | Xk | 3.175 | 0.048 | 6164 | 48 | - | - | - | - | 3
601 | Ursula | C | 1.304 | 0.076 | 6267 | 16 | - | - | - | - | 3
| Ursula | C | 0.215 | 0.015 | * | * | - | - | - | - | 4
618 | Ursula | Cb | 1.558 | 0.012 | * | * | - | - | - | - | 4
973 | Ursula | X | 3.380 | 0.032 | * | * | - | - | - | - | 4
| Ursula | Xk | 4.208 | 0.067 | 5892 | 80 | - | - | - | - | 3
1306 | Ursula | T | 5.510 | 0.030 | * | * | - | - | - | - | 4
1520 | Ursula | Cg | 1.979 | 0.069 | 5848 | 130 | - | - | - | - | 3
5959 | Ursula | X | 2.368 | 0.035 | * | * | - | - | - | - | 4