# Asteroid Family Physical Properties

Joseph R. Masiero NASA Jet Propulsion Laboratory/Caltech Francesca DeMeo
Harvard/Smithsonian Center for Astrophysics Toshihiro Kasuga Planetary
Exploration Research Center, Chiba Institute of Technology Alex H. Parker
Southwest Research Institute

###### Abstract

  * An asteroid family is typically formed when a larger parent body undergoes a catastrophic collisional disruption, and as such family members are expected to show physical properties that closely trace the composition and mineralogical evolution of the parent. Recently a number of new datasets have been released that probe the physical properties of a large number of asteroids, many of which are members of identified families. We review these data sets and the composite properties of asteroid families derived from this plethora of new data. We also discuss the limitations of the current data, and the open questions in the field.

##  1 INTRODUCTION

Asteroid families provide waypoints along the path of dynamical evolution of
the solar system, as well as laboratories for studying the massive impacts
that were common during terrestrial planet formation. Catastrophic disruptions
shattered these asteroids, leaving swarms of bodies behind that evolved
dynamically under gravitational perturbations and the Yarkovsky effect to
their present-day locations, both in the Main Belt and beyond. The forces of
the family-forming impact and the gravitational reaccumulation of the
collisional products also left imprints on the shapes, sizes, spins, and
densities of the resultant family members (see chapter by Michel et al., in
this volume). By studying the physical properties of the collisional remnants,
we can probe the composition of the parent asteroids, important source regions
of transient populations like the near-Earth objects, and the physical
processes that asteroids are subjected to on million- and billion-year
timescales.

In the thirteen years since the publication of Asteroids III, research
programs and sky surveys have produced physical observations for nearly two
orders of magnitude more asteroids than were previously available. The
majority of these characterized asteroids are members of the Main Belt, and
approximately one third of all known Main Belt asteroids (MBAs) with sizes
larger than a few kilometers can be associated with asteroid families. As
such, these data sets represent a windfall of family physical property
information, enabling new studies of asteroid family formation and evolution.
These data also provide a feedback mechanism for dynamical analyses of
families, particularly age-dating techniques that rely on simulating the non-
gravitational forces that depend on an asteroid’s albedo, diameter, and
density.

In Asteroids III, Zappalà et al. (2002) and Cellino et al. (2002) reviewed the
physical and spectral properties (respectively) of asteroid families known at
that time. Zappalà et al. (2002) primarily dealt with asteroid size
distributions inferred from a combination of observed absolute H magnitudes
and albedo assumptions based on the subset of the family members with well-
measured values. Surveys in the subsequent years have expanded the number of
measured diameters and albedos by nearly two orders of magnitude, allowing for
more accurate analysis of these families. Cellino et al. (2002) discussed the
spectroscopic properties of the major asteroid families known at that time.
The principal leap forward since Asteroids III in the realm of spectroscopy
has been the expansion of spectroscopic characterization to near-infrared
(NIR) wavelengths. The development of more sensitive instrumentation covering
the $1~{}\mu$m and $2~{}\mu$m silicate absorption features and new observing
campaigns to acquire NIR spectra for a large number of objects have
revolutionized studies of asteroid composition and space weathering.

By greatly expanding the number of family members with measured physical
properties, new investigations of asteroid families can be undertaken.
Measurements of colors and albedo allow us to identify outliers in our
population lists and search for variations in surface properties of family
members that might indicate heterogeneity of the parent body or weathering
processes. Diameter measurements let us build a size frequency distribution
and estimate the original parent body size, both of which are critical to
probing the physics of giant impacts. Spectra provide detailed mineralogical
constraints of family members, allowing for more sensitive tests of space
weathering and parent heterogeneity, albeit for a smaller sample size, while
also probing the formation environment and allowing for comparisons to
meteorite samples.

In this chapter, we highlight the datasets that have been obtained since
Asteroids III which have greatly expanded our ability to understand asteroid
families. We discuss their implications for specific families, and tabulate
average photometric, albedo, and spectroscopic properties for 109 families
identified in the chapter by Nesvorný et al. in this volume. We also discuss
the key questions that have been answered since Asteroids III, the ones that
remain open, and the new puzzles that have appeared over the last decade.

##  2 NEW DATA SETS

The field of asteroid research has benefited in the last 13 years from a huge
influx of data. Many of these large sets of asteroid characterization data
(including photometric and thermophysical data) have been ancillary results of
surveys primarily designed to investigate astrophysical sources beyond the
solar system. Simultaneously, observing programs designed to acquire more
time-intensive data products such as asteroid spectra, photometric light
curves, or polarimetric phase curves have also blossomed. We review below the
main datasets that have advanced family characterization in recent years.

2.1 Optical colors from SDSS

The Sloan Digital Sky Survey (SDSS, York et al. 2000) produced one of the
first extremely large, homogeneous data sets that contained information about
asteroid surface properties at optical wavelengths. These data are archived in
the SDSS Moving Object Catalog
(http://www.astro.washington.edu/users/ivezic/sdssmoc/sdssmoc.html) which
currently contains $471,569$ entries of moving objects from survey scans
conducted up to March 2007. The catalog entries can be associated with
$104,449$ unique known moving objects, however $\sim 250,000$ entries do not
have corresponding associations in the orbital element catalogs implying the
potential for a significant benefit from future data mining efforts.

While the SDSS 5-color photometric system ($u,g,r,i,z$, with central
wavelengths of $0.3543~{}\mu$m, $0.4770~{}\mu$m, $0.6231~{}\mu$m,
$0.7625~{}\mu$m, $0.9134~{}\mu$m, respectively) was not designed with asteroid
taxonomy in mind (unlike previous surveys such as the Eight Color Asteroid
Survey, Zellner et al. 1985a), the sheer size of the dataset coupled with its
extremely well-characterized performance has made SDSS an immensely valuable
asset for defining asteroid families and exploring their properties. The near-
simultaneous optical color information obtained during the course of the SDSS
survey can be used to infer the spectroscopic properties of tens of thousands
of asteroids at optical wavelengths.

The Sloan Digital Sky Survey, primarily designed to measure the redshifts of a
very large sample of galaxies, serendipitously observed many asteroids over
the course of its several survey iterations. Under standard survey operations
with $53.9$ second exposures, its five-color camera was sensitive to
stationary sources as faint as $r\sim 22.2$, with similar performance in $u$
and $g$ and somewhat brighter limits in $i$ and $z$ ($21.3$ and $20.5$,
respectively). To enable the accurate determination of photometric redshifts,
high-precision internal and absolute calibrations were essential. The care and
effort expended on these calibrations carried over into the dataset of moving
object photometry, resulting in the largest well-calibrated dataset of multi-
band asteroid photometry to date.

As of the latest data release, the Moving Object Catalog 4 (MOC4, Parker et
al. 2008) contains asteroid observations from $519$ survey observing runs. The
automatic flagging and analysis of moving objects required that they be
brighter than magnitude $r=21.5$. The brightest object in the sample is
$r’\sim 12.91$, giving the survey a dynamic range of over 8.5 magnitudes. The
large sample size and dynamic range of this survey make it a powerful tool for
studying luminosity functions of dynamically- or photometrically-selected sub-
populations of the moving objects, of which asteroid families are a natural
example.

Because of the much smaller sample size of asteroids with $u$-band
observations having photometric errors $<0.1~{}$mag ($44,737$, compared with
$442,743$ with a similar precision in $r$-band), most large-scale asteroid
studies using the SDSS photometry have considered only the four longer-
wavelength bands. These are often further collapsed into two principle
components, the $a^{\star}$ color
($a^{\star}=0.89\left(g-r\right)+0.45\left(r-i\right)-0.57$) and the ($i-z$)
color (see Ivezić et al. 2001).

Using the SDSS data set, Ivezić et al. (2002) showed that asteroid families
are easily identified from their optical colors. They found four primary color
classes of families, which describe one of four characteristic compositions:
Vesta, Koronis, Eos, and Themis. Jedicke et al. (2004) and Nesvorný et al.
(2005) expanded upon this to investigate space weathering and find that older
asteroid families have steeper spectral slopes from 0.55 to 1 micron than
younger asteroid families.

Szabó & Kiss (2008) used SDSS photometry to constrain the shape distributions
of eight large asteroid families. By assuming the observed magnitude
differences between different epochs of observation were uncorrelated, they
showed that both older families and families closer to the Sun tend to have
more spherical shape distributions. This effect is what would be expected for
a system where small-scale cratering collisions redistributed material into
gravitational lows, resulting in a more spherical shape.

Parker et al. (2008) used the family color relationships found by Ivezić et
al. (2002) as a springboard to refine the definition of asteroid families
beyond solely dynamical relationships. The ability to spectrophotometrically-
refine the sample of objects linked to each family meant family membership
could be extended further into the background, and allowed the identification
of diffuse family “halos” of compositionally-distinct objects (Parker et al.
2008, Broz̆ & Morbidelli 2013, Carruba et al. 2013). Overlapping but
compositionally-distinct families such as Flora and Baptistina are easily
separated with the addition of color information.

Using the wealth of SDSS data, Carvano et al. (2010) modeled established
taxonomic classes to define the SDSS color parameters of each class. They then
used these constraints to perform photometric taxonomic classifications of
SDSS-observed asteroids, including many large asteroid families. This
technique was later extended by DeMeo & Carry (2013) to better distinguish the
boundaries between taxonomic classes. This taxonomic strategy can be applied
to future photometric surveys to rapidly classify asteroids as a tool for
improving family associations. While the resulting taxonomic grouping is of
lower certainty than spectroscopic classification, spectrophotometric taxonomy
offers a fast way to quantify the spectral behavior of large numbers of
asteroids and provide high-quality candidates for spectroscopic followup.

2.2 Visible and IR Spectroscopic Surveys

Spectroscopic measurements provide unparalleled sensitivity to the
mineralogical features on the surfaces of asteroids. As members of families
come from the same progenitor object, surveys of many family members allow us
to probe the composition of that parent body and search for mineralogical
changes indicative of geological processes during the parent’s formation and
early evolution. For families shown to have homogeneous spectral properties,
these surveys can also be used to identify outlier objects that are
compositionally distinct from the family, especially large objects that can
present serious complications to the analysis of family evolution.

A major focus in the study of families has been the characterization of the
effects of space weathering on the surfaces of atmosphereless bodies. Recent
work using dynamical simulations to determine the ages of asteroid families
(see the chapter by Nesvorný et al. in this volume for a discussion of these
works) has opened a new avenue into investigating the potential effects of
space weathering on asteroid surfaces. Assuming that the family-forming impact
completely refreshed the surfaces of family members, we can look for families
with similar compositions but different ages to search for spectral changes
that would be the hallmark of space weathering. A number of researchers have
conducted spectroscopic surveys of families to this end, although the results
of these studies have been somewhat conflicting (e.g. Nesvorný et al. 2005,
Willman et al. 2008, Vernazza et al. 2009, Thomas et al. 2011, Thomas et al.
2012).

Shortly after the publication of Asteroids III, large scale visible wavelength
(0.45-0.9 microns) spectral surveys were published that were major driver of
asteroid compositional studies. Bus & Binzel (2002) and Lazzaro et al. (2004)
published 1341 and 820 asteroid spectra, respectively, providing a wealth of
data for asteroid studies. Also around this time near-infrared spectrometers
became widely available, such as SpeX on the NASA IRTF (Rayner et al. 2003).
The near-infrared provides wavelength coverage that allows better
characterization of silicate features (Burbine & Binzel 2002, Gaffey et al.
1993). While no single large observing campaign has been initiated for main
belt asteroids in the near-infrared, many small programs have been carried out
that targeted specific asteroid families (Sunshine et al. 2004; Mothe-Diniz et
al. 2005; Vernazza et al. 2006; Mothe-Diniz et al. 2008a; Mothe-Diniz &
Nesvorný 2008b; Mothe-Diniz & Nesvorný 2008c; Willman et al. 2008; Harris et
al. 2009; Reddy et al. 2009; de Sanctis et al. 2011; Reddy et al. 2011; Ziffer
et al. 2011; de Leon et al. 2012). A compilation of spectral taxonomic
classifications of asteroids is given in the Planetary Data System by Neese
(2010) and is periodically updated. We highlight here some of the specific
families that were the subject of spectral investigations.

Vernazza et al. (2006) obtained spectra of Karin family members, finding them
to be very similar to OC meteorites. Willman et al. (2008, 2010) extended this
survey in an attempt to constrain space weathering rates for asteroid
surfaces, finding that spectral slopes are altered on the billion year
timescale. Harris et al. (2009) surveyed the Karin family using thermal
infrared spectroscopy, and found albedos lower than expected for fresh
asteroid surfaces, implying space weathering alters albedos on the million
year timescale, in conflict with the Willman et al. results.

Nathues (2010) used visible and NIR spectroscopy of 97 Eunomia family members
to study the potential differentiation history of the family parent. They show
that the majority of family members have S-type taxonomy and the parent body
was likely not fully differentiated, but may have undergone partial
differentiation. Fieber-Beyer et al. (2011) obtained NIR spectroscopy of 12
Maria family members. From these data they associate this family with
mesosiderite-type meteorites, a type iron-rich meteorite thought to originate
from a differentiated parent body.

Ziffer et al. (2011) obtained NIR spectra of 13 asteroids in the Themis and
Veritas families and find distinct differences in the spectral behavior of the
two families. They associate both families with CM2 chondrites, but find no
evidence for space weathering of C-type objects.

Reddy et al. (2009,2011) performed a spectroscopic survey of the Baptistina
family aimed at constraining the composition of the family members. They found
a range of compositions represented, but smaller objects as well as (298)
Baptistina itself show clear association with LL-type ordinary chondrites.
Ordinary chondrite meteorites show two distinct compositional phases, one at
albedos similar to S-complex asteroids and one that is darker with muted
silicate absorption bands. This darker material has been associated with
former surface regolith which had gases implanted by the solar wind and was
later re-lithified and impact-shocked, resulting in a significantly different
reflectivity with only a nominal difference in composition (Britt & Pieters,
1991). Studies of the recent Chelyabinsk meteorite (Kohout et al. 2014, Reddy
et al. 2014) further confirm that shock-darkening may play a critical role in
the evolution of asteroid family spectra (cf. Cellino et al., 2002).

Licandro et al. (2012) used the Spitzer space telescope to measure mid-
infrared spectra for eight members of the Themis family, and determined their
albedos and diameters. They were also able to constrain the surface thermal
inertia and set limits on the surface composition, showing that family members
must have a very low surface density.

Jasmim et al. (2013) performed a spectroscopic survey of objects classified as
Qp in the SDSS spectrophotometric system in the Vesta family, but were not
able to find any significant differences between these objects and canonical
V-type asteroid spectra. This highlights the potential ambiguities in
spectrophotometric taxonomic classifications, and the need for further
spectroscopic followup of interesting asteroids to confirm their spectral
behavior.

Recently, Vernazza et al. (2014) mineralogically analyzed spectra of six
S-complex asteroid families and 83 background S-type objects and compared
these results to compositions of various ordinary chondrite meteorites. They
found a bimodality in their olivine/pyroxene mineral diagnostic for S-type
asteroids which traces the compositional gradients measured for metamorphosed
meteorites with a range of iron contents. This bimodality also extended to
families, with Koronis, Agnia, Merxia, and Gefion more closely matching high-
iron ordinary chondrites and Eunomia and Flora matching either low-iron
chondrites from the interiors of bodies or ordinary chondrites from the near-
surface regions showing little metamorphism. Mineralogical assessment of near-
infrared spectra thus offers a new method of probing the compositions and
metamorphic histories of these S-complex families.

2.3 Infrared Space Surveys

Recent improvements in mid-infrared detector technology have spurred renewed
interest in their use for astronomical observations. Ground-based thermal
infrared detectors can obtain data for a small subset of the brightest
targets, however the thermal background prohibits large-scale surveys of
smaller asteroids. The space environment, however, is ideal for thermal
infrared surveys of the sky, and two recent satellites have obtained all-sky
survey data at mid-infrared wavelengths of a large number of asteroids. A more
complete discussion of these surveys is presented in the chapter by Mainzer et
al. in this volume, and so here we only highlight a few relevant aspects.

The AKARI space telescope was launched on 21 Feb 2006 and surveyed the sky at
two thermal infrared wavelengths from 6 May 2006 until the telescope-cooling
liquid helium was exhausted on 28 August 2007, covering over $96\%$ of the sky
(Murakami et al. 2007, Ishihara et al. 2010). The “Asteroid Catalog Using
AKARI” (AcuA, Usui et al. 2011,
http://darts.jaxa.jp/ir/akari/catalogue/AcuA.html) database summarizes the
asteroid survey data. Using the Standard Thermal Model (Lebofsky et al. 1986,
Lebofsky & Spencer 1989), diameters and visible albedos were derived for
$5120$ asteroids.

AKARI also performed spectroscopic observations of 70 asteroids during the
warm mission phase after the cryogen was exhausted, many of which are the
largest members of asteroid families. These observations provide unique
spectroscopic data covering the wavelength range from $2-5~{}\mu$m (Usui et
al., 2011; Usui et al., 2015, in preparation). Kasuga et al. (2012) present
physical properties of Cybele family members determined from this dataset, and
discuss the taxonomic composition of this family by combining spectrally
derived taxonomy with infrared photometry.

The Near-Earth Object Wide-field Infrared Survey Explorer (NEOWISE) mission
launched on 14 December 2009 and surveyed the entire sky at four infrared
wavelengths over the course of its cryogenic mission. The survey continued
during its post-cryogenic and reactivated missions at the two shortest
wavelengths. The NEOWISE data catalogs and images are publicly archived at the
NASA/IPAC Infrared Science Archive
(http://irsa.ipac.caltech.edu/Missions/wise.html) and contain thermal infrared
measurements of over 150,000 asteroids (Mainzer et al., 2011, 2014). Many of
these were identified as members of asteroid families, allowing for the
determination of diameter and albedo distributions for an unprecedented number
of families.

Masiero et al. (2011) presented albedos and diameters for over 120,000 Main
Belt asteroids, including over 32,000 members of 46 families from Nesvorný
(2012). They showed that the albedo distribution within a family is usually
very narrow, but some families have significant contamination from background
objects or show a mixing of multiple families that overlap in proper-element
space. Masiero et al. (2013) split the Main Belt into distinct orbital and
albedo components and showed that overlapping families such as Polana and
Hertha (aka Nysa) can be distinguished easily.

Masiero et al. (2013) used the NEOWISE diameters to measure the size-frequency
distribution (SFD) for 76 asteroid families that they identify in their data.
The SFD can be computed as $N\propto D^{\alpha}$ where $N$ is the number of
objects with diameter greater that $D$ and $\alpha$ is the SFD slope. They
found that larger families tended to show cumulative SFD slopes that converge
toward the value of $\alpha=-2.5$ as expected for a collisionally equilibrated
population (Dohnanyi 1969), while smaller families have a wider dispersion.
The family associated with (31) Euphrosyne has an anomalously steep SFD slope,
which Carruba et al. (2014) explain as the result of a dynamical draining of
the largest family fragments by the $\nu_{6}$ resonance, which runs through
the center of this family in semimajor axis-inclination space.

Ali-Lagoa et al. (2013) used the NEOWISE albedo measurements to show that the
Pallas family has visible and infrared albedos that are distinct from the
majority of B-type asteroids. Masiero et al. (2014) presented the $3.4~{}\mu$m
albedo distributions of 13 asteroid families. They found that the asteroid
families form three distinct groupings of albedos at this wavelength.
Additionally, the Eos family has unique near-infrared reflectance properties,
which likely traces a mineralogy not seen elsewhere in the Main Belt.

2.4 Asteroid Light Curves and Phase Curves

Over the last decade, a number of groups have carried out surveys of asteroid
light curves, many focusing on the properties of specific families. Light
curve analysis from a single epoch can provide rotation periods and
constraints on amplitude, while multi-epoch observations can allow for
rotational pole determination, shape model fitting, searches for binarity, and
detection of non-principal axis rotation. The binary fraction is an important
test of formation mechanisms, while pole determination for a significant
number of family members allows for constraints on YORP evolution of family
spin states.

One of the key results from these lightcurve studies has been the confirmation
of the YORP effect on spin poles of objects with similar ages (Vokrouhlický et
al. 2003). The YORP mechanism results from asymmetries in the thermal re-
emission of absorbed light, creating a torque on the asteroid. This can alter
the rotation rate of these objects, but also is predicted to rapidly reorient
the spin poles of most small objects to be perpendicular to the body’s orbital
plane. This will result in spin poles clustered near $0^{\circ}$ and
$180^{\circ}$ from the orbital pole, and a spin rate distribution differing
from the Maxwellian distribution that is expected for a collisionally
equilibrated system. Slivan et al. (2003, 2008, 2009) measured light curves
for 30 members of the Koronis family, showing a strongly anisotropic
distribution of spin poles and a non-Maxwellian rotation rate distribution,
both consistent with YORP-induced rotation changes.

Surveys of other families have come to similar conclusions: Warner et al.
(2009) surveyed the Hungaria family asteroids and determined rotation
properties for over 100 of these objects. They find a significant excess of
slow-rotators, which they attribute to YORP-induced spin down, as well as a
binarity fraction of $15\%$, similar to the NEA population. Kryszczyńska et
al. (2012) surveyed 55 objects in the Flora family to determine their rotation
periods and poles. They found that the Flora family rotation rates are non-
Maxwellian, as is expected from long-term YORP evolution. Kim et al. (2014)
determined rotation properties for 57 Maria family members, finding an excess
of prograde rotation states consistent with the predictions of YORP and
Yarkovsky evolution resulting in retrograde rotators moving into the 3:1
Jupiter resonance and being removed from the family.

Hanus̆ et al. (2011, 2013) used shape models derived from light curve
inversion to study the spin pole positions of ten asteroid families. They
found a clear distinction in spin pole direction, where objects at semimajor
axes smaller than the largest remnant have retrograde rotations while objects
at larger semimajor axes have prograde rotations, as is expected from a system
evolving under the Yarkovsky effect.

Using the large amount of photometric data available from the Minor Planet
Center and the AstOrb database kept by Lowell Observatory, Oszkiewicz et al.
(2011, 2012) rederived the photometric phase functions of all known asteroids,
applying the improved $H,G_{1},G_{2}$ and $H,G_{12}$ phase equations. They
find that asteroid families show statistically similar phase slope parameters
and that the major taxonomic complexes can be statistically differentiated.
However, these distributions overlap, significantly limiting the use of phase
curve parameters for direct family or taxonomy identification. Bowell et al.
(2014) searched the Lowell data for statistical anisotropies in the ecliptic
longitude distribution of rotation poles for asteroid family members. They
show that the four largest groups considered (the Flora, Vesta, and Koronis
families, and the Nysa-Polana complex) have anisotropic spin longitude
distributions showing an excess in the $30-110^{\circ}$ longitude range and a
dearth in the $120-160^{\circ}$ longitude range, consistent with the
distribution seen for the Main Belt as a whole. The authors suggest this may
be due to pole reorientation by the YORP effect, but that extensive modeling
is required as well as consideration of potential selection biases.

2.5 Polarimetric Surveys of Families

Measurement of the polarization of light scattered off the surface of an
atmosphereless body as a function of phase angle can be used as an independent
constraint on the object’s albedo (Cellino et al., 1999). Although the
magnitude range accessible to polarimetric observations is comparable to that
of NIR spectroscopy, multiple nights are required for each object to constrain
the phase behavior and there are fewer available imaging polarimeters that are
well-calibrated than NIR spectrometers. As such, there are fewer asteroids
with measured polarimetric properties, however polarimetric studies provide
unique data on asteroid surface properties that can be important for
disentangling ambiguities in other characterization surveys.

Cellino et al. (2010) polarimetrically surveyed the Karin and Koronis families
as an independent test of the effect of space weathering on asteroid albedo.
They find no significant differences between the albedos of Karin and Koronis,
implying that space weathering must act on timescales shorter than the $\sim
6~{}$million year age of the Karin family.

Cellino et al. (2014) conducted a survey of the linear polarization phase
curves of Watsonia asteroid family members, searching for analogs to the
unusual polarization of (234) Barbara. Barbara and the related “Barbarian”
objects have unusual polarimetric properties indicative of unique surface
mineralogy and are taxonomically identified as Ld-type objects from spectra.
They found that seven of the nine objects surveyed show indications of a
surface rich in spinel, one of the oldest minerals in the solar system
(Burbine et al., 1992). This implies that the Watsonia parent object has
undergone little-to-no mineralogical processing since the formation of the
first solids in the protosolar disk (Sunshine et al., 2008), and may have been
one of the oldest unprocessed bodies in the Solar system.

##  3 COLOR, SPECTRA, ALBEDO, AND SIZE DISTRIBUTIONS OF FAMILIES

With the wealth of asteroid physical observations now available, we can
determine the average characteristic properties for families. As the
literature contains many different collections of family lists, here we focus
on the consolidated list presented in the chapter by Nesvorný et al. in this
volume. This improves our sensitivity to subtle physical differences between
families, especially the biggest families where the large sample size can
greatly reduce the scatter in measured properties among individual members. We
can also use these data to reject outlier objects from family lists,
particularly when the family of interest is of distinct composition from other
nearby families or the majority of background objects. Here we discuss some of
the recent applications of the new physical property data that has become
available.

3.1 Homogeneity of Families and Use of Physical Properties to Distinguish
Outliers

Family-forming collisions are expected to liberate material from a large
fraction of the parent body’s volume. Many of the resulting family members are
likely to be accumulations of smaller ejecta, potentially from a range of
lithologies within the parent (see the chapter by Michel et al. in this
volume). For a heterogeneous parent body, we would expect to see a range of
colors, spectra, and albedos among the resultant family members, while a
homogeneous parent would instead produce a family with very narrow
distributions of these properties. While it is possible that the family formed
from an impact on a homogeneous parent by an impactor of a different
composition could show heterogeneity, statistically the mass of any probable
impactor impactor will be only a small fraction of the mass of either the
parent or the ejecta, and so would be unlikely to be a significant contaminant
to globally averaged properties obtained from remote sensing. Sub-families
resulting from second-generation impacts could also show subtle property
differences compared to the original family due to the reset of any space
weathering processes, however this would be most obvious only for very young
families (e.g. Karin).

Early surveys of asteroid family spectra and colors indicated that with the
exception of a handful of outliers (e.g. the Nysa-Polana complex) families had
narrow distributions of physical properties, indicative of homogeneous parent
bodies (see Cellino et al., 2002 and references therein). This enabled the
extrapolation of measured physical properties for a handful of family members
to the entire family. As many of the largest remnants of family formation had
been studied for decades, this became a boon to family research.

However, with the availability of physical property data for large numbers of
family members, we can now use this data to remove interloper objects from
family lists when they have a different color, albedo, or spectrum from the
bulk of the family. Refining family lists in this way is particularly
important for improving the accuracy of age-dating techniques. In the past few
years, a number of research groups have been actively using these data to this
end, in an effort to better understand the formation and evolution of families
and the parent bodies they came from (e.g. Novaković et al. 2011; Broz̆ et al.
2013; Masiero et al. 2013; Carruba 2013; Walsh et al. 2013; Carruba et al.
2013; Hanus̆ et al. 2013; Milani et al. 2014).

3.2 Combined Properties of Individual Families

Using the various data sets presented above, we provide in Table 1 the average
SDSS colors, average optical and NIR albedos, majority taxonomic type, and SFD
slopes (as well as the diameter range that the SFD was fit to) for the
families given in the chapter by Nesvorný et al. in this volume. We also
present a visualization of the average albedo, SDSS colors and spectra for
families with sufficient data in Figure 1. While mean values are often useful
for extrapolating properties of family members that were not observed, or for
comparing families to each other or other ground-truth data, there are
important caveats that cannot be ignored. Sample size considerations and the
uncertainty on individual measurements are the most critical of these caveats:
average values based on a small number of objects or even a single object
should be considered potentially spurious, and treated as such. We include
those values here for completeness.

Visible albedo mean values were derived by fitting a Gaussian to the
distribution of all measured $\log{p_{V}}$ values, following the technique
Masiero et al. (2011) applied to the NEOWISE data, and the quoted error gives
the width of the observed distribution. The uncertainty on the mean value,
when comparing mean albedos of various families, will be the measured Gaussian
width over the square root of the sample size; thus for large families the
mean albedos can be known quite accurately, even if individuals have large
uncertainties. Family NIR albedo values are a median of the $3.4~{}\mu$m
albedos given in Masiero et al. (2014).

2.2 Masiero_fig1.eps

Figure 1: Average solar-corrected SDSS colors (points) and sample optical/NIR
spectra (from SMASS) for all asteroid families listed in Table 1 with
sufficient data. Plots are scaled such that the interpolated reflectance at
$0.55~{}\mu$m equals the average visible geometric albedo ($p_{V}$) for the
family from all infrared surveys. The “N” in the bottom right of each plot
indicates the number of SDSS observations used, and taxonomic class is given
when available. Note the reflectance scale in each plot is different.

Size frequency distributions (SFDs) were computed for all families with more
than $100$ measured diameters from all infrared surveys and were found by
fitting a power law to the cumulative size distribution, using only those bins
with more than $5$ objects (to reduce the influence of the large remnants) and
less than half the total sample (to minimize the effects of incomplete
diameter sampling at small sizes). Tabulated SDSS colors were calculated by
performing an error-weighted mean of all observations having SNR$>10$ in the
$g$,$r$,$i$, and $z$ bands used to calculate $a^{\star}$ and $i-z$. Family
taxonomy is given only for cases where a majority of family members with
taxonomic classes had the same class. If no subclass (e.g. Ch, Sq, Ld) had a
majority, but a majority of members were in the same complex, that complex is
listed (e.g. C, S, L). For each of these parameters we include the number of
objects used to compute the listed value.

Although we implicitly assume that the variation in observed properties is a
result of statistical uncertainties and that all family members should have
the same physical properties, this is not necessarily true. Outlier objects
may be statistical flukes, or background contamination, but they just as
easily may be interesting pieces of the parent body warranting further study,
a determination that cannot be made or captured here. Additionally, a single
mean value ignores any size-dependent effects in the data, either real or
imposed by detection or sample-selection biases.

Only a proper debiasing of each survey accounting for observing geometry,
detector sensitivity, and detection efficiency can determine the true value
for each parameter. This is particularly important for cases of mismatched
sensitivities, such as the SDSS $r$ vs $z$ magnitudes needed for colors or the
NEOWISE W3 flux vs ground-based $H_{V}$ magnitude needed for albedo
determination; only objects seen in both datasets will have a measured value
which strongly biases the outcome as a function of apparent brightness. Thus
Table 1 is meant as a overarching guide, but caution is mandated for any
interpretation of values or trends.

A number of low albedo families can only be identified when the low albedo
population of the Main Belt is considered independently. This is due to the
bias toward discovery of high-albedo objects by ground-based visible-light
surveys. As the population of high albedo asteroids is probed to smaller sizes
(and thus larger numbers) these families will overwhelm traditional HCM
techniques, particularly the calculation of the quasi-random level needed to
assess the reality of a given family, making low albedo families harder to
identify. Masiero et al. (2013) circumvented this by considering each albedo
component separately, and by restricting their sample to objects detected in
the thermal infrared, which is albedo-independent (see the chapter by Mainzer
et al. in this volume for further discussion). As the sample of known
asteroids continues to increase, development of new techniques for the
identification of asteroid families from the background population (e.g.
Milani et al. 2014) will increase in importance.

Below we discuss individual families that merit specific mention based on
recent research. We include the PDS ID number from Nesvorný et al. (2012) both
below and in Table 1 for easier association with other work and with the
family dynamical properties given in the chapter by Nesvorný et al. in this
volume.

3.2.1 Hungaria

The Hungaria asteroid family (PDS ID 003) occupies a region of space interior
to the rest of the Main Belt and with an orbital inclination above the
$\nu_{6}$ secular resonance. This region is an island of stability between the
major resonances that dominate this area of the solar system, and likely
samples a unique region of the protoplanetary disk (Bottke et al. 2012).
Warner et al. (2009) analyzed light curves of $129$ Hungaria asteroids,
finding a significant excess of very slow rotating bodies. They also showed
that the binary fraction of this population is $\sim 15\%$, comparable to the
fraction seen in the NEO population.

The albedos for Hungaria family members derived from the NEOWISE data by
Masiero et al. (2011) have values significantly larger than $p_{V}>0.5$,
however this is an artifact of bad absolute magnitude fits for these objects
in orbital element databases, which when corrected bring the best-fit albedo
values to the range of $0.4<p_{V}<0.5$ (B. Warner, private communication).
Spectroscopic and SDSS color studies of the Hungaria family show the
classification to be X-type, which when combined with the very high albedos
translates to an E-type classification (Carvano et al. 2001; Assandri & Gil-
Hutton, 2008; Warner et al. 2009) Polarimetric observations by Gil-Hutton et
al. (2007) of the overall Hungaria region indicate inconsistencies in the
polarimetric behavior of asteroids in and around the Hungaria family.

3.2.2 Flora

The Flora family (PDS ID 401) is a large S-type family residing in the inner
Main Belt. The largest remnant, (8) Flora, has an orbit just exterior to the
$\nu_{6}$ resonance, and only the half of the family at larger semimajor axes
is seen today. The $\nu_{6}$ resonance is particularly good at implanting
asteroids into the NEO population (Bottke et al. 2000), meaning that Flora
family members are likely well-represented in the NEO population and meteorite
collections. Recent spectroscopic observations of Flora family members have
been combined with analyses of meteorite samples to link the LL chondrite
meteorites to the Flora family (Vernazza et al. 2008; de Leon et al. 2010;
Dunn et al. 2013). This provides an important ground-truth analog for
interpreting physical properties of S-type objects in the Main Belt and near-
Earth populations. We note that in contrast to previous analyses, Milani et
al. (2014) did not identify a family associated with Flora, instead finding
that candidate member asteroids merged with the Vesta and Massalia families,
or potentially are part of their newly identified Levin family. However, the
Vesta family has a distinct $i-z$ color that is not shown by Flora family
members (see Table 1), making these populations easily distinguished by their
photometric properties. While the Flora and Massalia populations overall have
properties that are consistent within uncertainties, the difference between
the mean albedos of these two populations suggests they in fact are different
populations.

3.2.3 Baptistina

Over the past decade, the Baptistina family (PDS ID 403) has been the focus of
a number of investigations, leading to controversy over the physical
characteristics of these asteroids. Initial investigations assumed the family
had characteristics similar to C-type asteroids (e.g. low albedo) based on
spectra of the largest member (298) Baptistina (Bottke et al., 2007). This was
used in numerical simulations to show that Baptistina was a probable source of
the K/T impactor. Further spectral investigations of a 16 large family members
found compositions more analogous to LL chondrites, ruling out a C-type
association (Reddy et al., 2011). However, a major difficulty in studying this
family is the significant overlap in orbital element-space with the much
larger Flora family (or with the Levin family, according to Milani et al.
(2014)), making it difficult to ensure that the spectral studies were probing
Baptistina and not Flora. Using albedos to separate these families finds a
mean albedo of $p_{V}=0.16$, which is not consistent with either C-type or LL
chondrite compositions (Masiero et al. 2013). Recent analysis of the
Chelyabinsk meteorite samples showed that shock darkening of chondritic
material could produce an albedo consistent with the Baptistina family without
altering the composition (Reddy et al. 2014) offering a potential solution to
the seemingly contradictory information about this family, but future work
will be necessary to confirm this hypothesis.

3.2.4 “Nysa-Polana”

In the years leading up to Asteroids III it had become increasingly clear that
Nysa-Polana, interpreted as a single entity, was likely to be a short-lived
phenomenon. Cellino et al. (2001) presented a spectroscopic study of 22
asteroids associated with the group, and found that the group was best
understood as two compositionally distinct families partly overlapping in
orbital element space, one associated with the F class in the Tholen taxonomy
and one with the S class, while (44) Nysa was compositionally distinct and
potentially not associated with either family.

Masiero et al. (2011) showed that the albedo distribution of the $\sim 3000$
asteroids identified as part of the Nysa-Polana complex were strongly bimodal,
unlike the majority of families. Although overlapping in semimajor axis-
inclination space, the high- and low-albedo components occupy distinct regions
of semimajor axis-eccentricity space, supporting the theory that they are two
distinct populations coincidentally overlapping as opposed to a single parent
body that was composed of two distinct mineralogies.

Using albedo as a discriminant, Masiero et al. (2013) were able to uniquely
identify two separate families, a low-albedo one associated with (142) Polana,
and a high-albedo one with (135) Hertha (PDS ID 405), while (44) Nysa no
longer linked to either family. In Table 1 we continue to refer to the high-
albedo family as “Nysa” despite the evidence to the contrary, for consistency
with other literature. Walsh et al. (2013) expanded on this, and used the
family albedos to reject objects with S-type physical properties and focus on
the low-albedo component of the Nysa-Polana group. Using dynamical
constraints, they were able to further sub-divide the low-albedo component of
this group into two distinct families, which they identify as the Eulalia
family and the “new Polana” family. They estimate ages for each of these
families of $0.9-1.5~{}$billion years and $>2~{}$billion years, respectively.
Conversely, Milani et al. (2014) identify the whole complex as associated with
Hertha and split this region into two components by combining dynamics and
physical properties, which they identify as the Polana and Burdett families
(low and high albedo, respectively).

3.2.5 Vesta

The Vesta asteroid family (PDS ID 401) has historically been one of the most
well-studied families, due to its clear association with one of the largest
known asteroids, the high albedos and locations in the inner Main Belt making
members favorable for ground-based observations, and association with the HED
meteorites leading to the interpretation of (4) Vesta as a differentiated
parent body (McCord et al., 1970; Zappala et al., 1990; Binzel & Xu 1993;
Consolmagno & Drake, 1977; Moskovitz et al., 2010; Mayne et al., 2011). With
the recent visit of the Dawn spacecraft to (4) Vesta (see the chapter by
Russell et al. in this volume) ground-truth data can be compared to remote-
sensing observations of family members. Additionally, constraints on the ages
of the major impact basins of $1.0\pm 0.2~{}$billion years for Rheasilvia and
$2.1\pm 0.2~{}$billion years for Veneneia (Schenk et al. 2012) set strong
constraints on the possible age of Vesta family members. Milani et al. (2014)
find that the Vesta family splits into two subgroups in their analysis, which
they attribute to these two events.

The Vesta family has a unique mineralogical composition in the Main Belt,
making it easily distinguishable in color-, albedo-, or spectral-space. In
particular, members stand out from all other asteroids in terms of their high
albedo, low $i-z$ color, and deep $1~{}\mu$m and $2~{}\mu$m absorption bands.
This has prompted searches for objects with similar properties at more distant
locations in the Main Belt (e.g. Moskovitz et al. 2008; Duffard & Roig, 2009;
Moskovitz et al., 2010; Solontoi et al. 2012). These bodies could only have
evolved from the Vesta family via a low-probability series of secular
resonances (Carruba et al. 2005, Roig et al. 2008a), and may be indicative of
other parent bodies that were differentiated. To date only a few candidate
objects from these searches have been confirmed to be V-type, indicating that
the collisional remnants of the other differentiated objects that must have
formed in the early solar system has likely been dynamically erased.

3.2.6 Eunomia

The Eunomia family (PDS ID 502) is an old, S-type family located in the middle
Main Belt. Spectral evidence presented by Lazzaro et al. (1999) indicates that
the Eunomia family may have originated from a partially differentiated parent
body. Natheus et al. (2005) and Nathues (2010) investigated the physical
properties of the Eunomia largest remnant and 97 smaller family members as a
probe of the composition and differentiation history of the original parent
body. They found that the largest remnant shows two hemispheres with slightly
different compositions that support an interpretation of the impact causing
significant crust-loss and some mantle-loss on a partially-differentiated
core. Milani et al. (2014) found two subfamilies within Eunomia, which they
attribute to separate cratering events.

3.2.7 Eos

The Eos family (PDS ID 606) represents the primary reservoir of K-type
asteroids in the Main Belt, and can easily be identified by their $3.4~{}\mu$m
albedo (Masiero et al. 2014). This spectral class has been proposed as the
asteroidal analog of the CO and CV carbonaceous chondrite meteorites (Bell et
al. 1988; Doressoundiram et al. 1998; Clark et al. 2009). This would imply
that the Eos family is one of the best sampled collisional families in our
meteorite collection, and would mean that many of these samples do not probe
the C-complex asteroids as had frequently been assumed.

Mothé-Diniz & Carvano (2005) compared spectra of (221) Eos with meteorite
samples and inferred that the Eos parent body likely underwent partial
differentiation. Mothé-Diniz et al. (2008a) extended this work to 30 Eos
family members and found mineral compositions consistent with forsteritic
olivine consistent with a history of differentiation or a composition similar
to CK-type meteorites. However, Masiero et al. (2014) instead interpret the
surface properties as consistent with shock-darkening of silicates (cf. Britt
& Pieters 1994, Reddy et al. 2014). Future work will enable us to resolve the
ambiguity in the composition of these objects. The Eos family represents one
of the key fronts of advancing our understanding of family formation that has
been opened by our wealth of new data.

3.2.8 Themis

The Themis family (PDS ID 602) is one of the largest low-albedo families in
the Main Belt. The majority of Themis family members are classified as
C-complex bodies (Mothe-Diniz et al. 2005; Ziffer et al. 2011). Spectral
surveys have found variations in the spectral slope among Themis members,
ranging from neutral to moderately red (Ziffer et al. 2011; de Leon et al.
2012). As the first asteroid discovered to show cometary activity (133P Elst-
Pizzaro) is dynamically associated with Themis, Hsieh & Jewitt (2006) searched
150 other Themis family members for signs of cometary activity, discovering
one additional object: (118401) 1999 RE70. The periodic nature of this
activity points to volatile sublimation as the probable cause, as opposed to
collisions or YORP spin up (see the chapter by Jewitt et al. in this volume)
meaning that the Themis family members, and (24) Themis itself, likely harbor
subsurface ice. Further, Rivkin & Emery (2010) and Campins et al. (2010)
reported evidence of water ice features on the surface of (24) Themis. If this
icy material was primordial to the Themis parent and not implanted by a later
impact, this would set constraints on where the Themis parent formed relative
to the “snow line” in the protosolar nebula. These objects are also likely to
be a new reservoir of water, and may have contributed to the volatile content
of the early Earth.

3.2.9 Sylvia

The Sylvia family (PDS ID 603) in the Cybele region, resides at the outer edge
of the Main Belt ($3.27<a\leq 3.70~{}$AU, Zellner et al., 1985b), beyond the
2:1 Jupiter mean motion resonance. These asteroids, along with the objects in
the Hilda and Jupiter Trojan populations, likely have limited contamination by
materials from the inner solar system, and represent a pristine view of the
materials present near Jupiter at the end of planetary migration. The Nice
model proposed that these asteroids are trans-Neptunian objects (TNOs) that
were scattered inward during the chaotic phase of planetary evolution (Levison
et al., 2009), however the Cybeles show different spectral characteristics
from the Hildas and Trojans, and thus may represent the material native to
this region of the solar system.

Kasuga et al. (2012) studied the size- and albedo-distributions of the Sylvia
asteroid family to better understand the history of these bodies. They found
that the largest Cybeles ($D>80~{}$km) are predominantly C- or P-types, and
the best-fit power law to the size distribution is consistent with a
catastrophic collision. However the estimated mass and size of the parent body
lead to collisional timescales larger than the age of the solar system,
assuming an equilibrium collisional cascade. These are comparable to the
timescales for the Hildas, although they find that the Trojan population is
consistent with collisional origin. Numerical simulations of the collisional
formation and dynamical evolution of the Cybeles will allow for a more
detailed study of the history of this population.

3.3 Relationship between albedo and color

Almost every major taxonomic class of asteroid is represented in the list of
asteroid families. Using the physical property data described above, we can
investigate relationships between the averaged physical properties for each
family. By nature of the large sample sizes, the SDSS colors and optical
albedos are the best-determined parameters for the majority of families.
Figure 2 shows the composite $a^{\star}$ and $i-z$ colors derived for each
family from SDSS compared to the composite optical albedo as determined via
thermal radiometry. There is a clear linear correlation between the SDSS
$a^{\star}$ color and the log of the albedo, although with significant
scatter. The $i-z$ color is approximately flat for low and moderate albedos,
but decreases noticeably for high albedo families. It is important to again
note that these data are subject to observational selection and completeness
biases, and so these relations should be interpreted with caution.

2 Masiero_fig2.eps

Figure 2: Average SDSS $a^{\star}$ and $i-z$ colors compared with optical
albedos for asteroid families, as given in Table 1

##  4 DISCUSSION

4.1 Correlation of Observed Properties with the Primordial Composition of the
Main Belt

When considering the distributions of colors and albedos, asteroid families
fall in one of only a small number of groupings. The Hungaria, Vesta, and Eos
families have unique properties that distinguish them from all other families.
Similarly, the Watsonia family shows unique polarimetric properties. While the
properties of these families can be used to efficiently identify family
members and mineral analogs, it is more difficult to relate the mineralogy and
history of these families to that of the currently observed Main Belt as a
whole (although they may be good analogs for now-extinct populations, cf.
Bottke et al. 2012).

Conversely, almost all other families fall into either the S-complex or the
C-complex, both of which can be further subdivided by spectral taxonomic
properties. Given the number of different parent bodies with these
compositions, it has been inferred that these two complexes are probes of the
pristine material from the protoplanetary disk in this region of the solar
system. However, studies of the evolution of the giant planets in the early
solar system call into question the specific locations these bodies originated
from (e.g. Gomes et al. 2005). One possible scenario, known as the “Grand
Tack” (Walsh et al. 2012), postulates that the protoplanetary core of Jupiter
migrated through the planetesimal disk, evacuating the Main Belt region of its
primordial material and repopulating it with material from both inward and
outward in the disk (see the chapter by Morbidelli et al. in this volume). In
this case, the two different compositional complexes would represent these
implanted objects. Further study of the physical properties of asteroid
families and the other small body populations of the solar system will allow
us to test this theory.

4.2 Properties of Observed Families Contrasted with the Background Population

Using computed $a^{\star}$ colors from the SDSS MOC 4, Parker et al. (2008)
divided asteroid families into blue and red groups, tracing the C and S
taxonomic complexes, respectively. For both groups, they found that family
membership as a fraction of total population increased with decreasing
brightness from $\sim 20\%$ at $H_{V}=9$ to $\sim 50\%$ at $H_{V}=11$. For
objects with absolute magnitudes of $H>11$ the fractions of blue and red
asteroids in families diverge, with blue objects in families making up a
smaller fraction of the total population while red objects stay at the levels
seen at brighter magnitudes, however it is unclear what contribution the
survey biases have to these observed differences. If this difference in
behavior is indeed a physical effect, it may indicate a difference in internal
structure or collisional processing rates between the two populations.

When exploring the taxonomic distribution of asteroids as a function of
distance from the Sun, families have been problematic because the large number
of homogeneous objects concentrated in small regions of orbital-element space
can skew the results. Studies of the overall distributions of physical
properties therefore typically use only the largest member of the family,
removing the smaller members (e.g. Mothe-Diniz et al. 2003). Alternatively,
the distribution could be explored by volume or mass, in which case all family
members may be included because their individual volumes or masses contribute
to the whole (e.g. DeMeo & Carry 2013).

A comprehensive study of the taxonomic contribution of families to the
population of small asteroids has not yet been undertaken, however
disentangling families from the background is critical to correctly
interpreting an overall picture of the compositional make up of the asteroid
belt and how the asteroid belt and the bodies within it formed. Distinguishing
between families and the background becomes increasingly difficult at smaller
sizes where orbital parameters have evolved further due to gravitational and
non-gravitational forces. Even the background itself is likely composed of
many small families forming from small parent bodies (Morbidelli et al. 2003).

4.3 Families as Feeders for the NEO Population

The Yarkovsky and YORP non-gravitational effects play a critical role in
repopulating the near-Earth objects with small bodies from the Main Belt
(Bottke et al. 2000). Primordial asteroids with diameters of $\sim 100~{}$m
should be efficiently mobilized from their formation locations into a
gravitational resonance over the age of the solar system, limiting the
contribution of these objects to the currently observed NEO population.
However, family formation events act as an important source of objects in this
size regime, injecting many thousands of small asteroids into the Main Belt
with each impact (Durda et al. 2007). The complete census of family physical
properties, combined with better estimates for family ages that can now be
made, enable us to trace the history of specific near-Earth asteroids from
their formation in the Main Belt to their present day orbits. For the same
reasons, recently fallen meteorites are also good candidates for comparisons
to asteroid families, however the differences between the surface properties
we can observe on asteroids and the atmosphere-selected materials surviving to
the ground complicate this picture.

4.4 Families Beyond The Main Belt

Although the vast majority of known asteroid families are in the Main Belt,
massive collisions resulting in family formation events are not unique to this
region of the solar system. While the near-Earth asteroid population is
dynamically young (Gladman et al. 2000) and thus these objects have a low
probability of undergoing collisional breakup, the more distant reservoirs
that date back to the beginning of the solar system are expected to undergo
the same collisional processing as the Main Belt, albeit with lower impact
velocities. Searches for young families in both the NEO and Mars Trojan
populations have yielded only a single candidate family cluster associated
with (5261) Eureka (Schunová et al. 2012; Christou 2013). Dynamical families
have been identified in the Hilda, Jupiter Trojan, and TNO populations. The
first two populations are trapped in long-term stable resonant orbits with
Jupiter, providing a population that has suffered far less dispersion than the
majority of Main Belt families. Similarly, the TNO population is cross-cut by
a range of Neptune resonances, some of which are similarly long-term stable.
The Yarkovsky and YORP effects are greatly diminished for all three
populations compared to the Main Belt (especially the TNOs) due to the larger
distances to the Sun, further reducing the dispersion of collisional
fragments.

Grav et al. (2012) present visible and infrared albedos for the Hilda and
Schubart asteroid families found in the 3:2 Jupiter mean motion resonance.
Using these albedos, they show the Hilda family is associated with D-type
taxonomy, while the Schubart family is associated with C or P-type taxonomy.
The Hilda population in general is dominated by C and P-type objects at the
largest sizes, but transitions to primarily D-class at the smallest sizes
measured, which may be indicative of the effect of the Hilda family on the
overall population (Grav et al. 2012; DeMeo & Carry, 2014). However we note
that recent family analysis by Milani et al. (2014) showed that the Hilda
family was not statistically significant using their methodology, in contrast
to previous work.

The Jupiter Trojans are comprised of the L4 and L5 Lagrange point swarms which
lead and trail Jupiter (respectively) on its orbit. Multiple families have
been identified in each of the swarms (Milani 1993, Beaugé & Roig, 2001),
however there is some debate as to the significance of these families (cf.
Broz̆ & Rozehnal, 2011). Fornasier et al. (2007) combined measured spectra
from multiple sources (Fornasier et al. 2004, Dotto et al. 2006) to
characterize Trojan family members. In the L5 cloud, members of the Aneas,
Anchises, Misenus, Phereclos, Sarpedon, and Panthoos families were found to
have spectra with moderate-to-high spectral slopes, with most members being
classified as D-type. The background population had a wider range of slopes
and taxonomies from P- to D-type (Fornasier et al., 2004).

In the L4 cloud members of the Eurybates, 1986 WD and 1986 TS6 families were
studied. The 1986 WD and 1986 TS6 family members had featureless spectra and
high slopes resulting in a classification for most as D-types, while the few
with lower slopes were placed in the C- and P-classes. Eurybates members,
however, have markedly different spectra with low to moderate slopes splitting
the classifications evenly between the C- or P-classes (Fornasier et al. 2007,
DeLuise et al. 2010). Roig et al. (2008b) used the SDSS data to investigate
asteroid families in the Jupiter Trojan population, and found that the
families in the Trojan populations account for the differences in the
compositional distributions between the L4 and L5 clouds. In particular, the
families in the L4 cloud show an abundance of C- and P-type objects not
reflected in the L5 families or the background populations in either cloud.

The TNO population covers a much larger volume of space than any of the
populations of objects closer to the Sun, but is also estimated to contain
over 1000 times the mass of the Main Belt. Collisions resulting in
catastrophic disruptions are believed to have occurred at least twice in the
TNO population. Pluto’s five (or potentially more; Weaver et al. 2006)
satellites speak to a massive collision, which will be a key area of
investigation of the New Horizons flyby of the Pluto system.

The dwarf planet Haumea is highly elongated with a very short rotational
period ($\sim 4$ hours), is orbited by two small satellites, has a relatively
high density, and has a spectrum that is consistent with nearly pure water
ice. These properties are thought to be the result of a mantle-shattering
collisional event, though the details of this event remain contentious. A
group of TNOs with colors substantially bluer than the typical neutral-to-
ultra-red surfaces of the Kuiper Belt, all sharing high inclinations similar
to Haumea, has been identified as a collisional family produced by this event
(Brown et al. 2007). Because of the orbital velocity regimes in trans-
Neptunian space, collisional families are in general unlikely to be identified
there through dynamics alone (as they are in the asteroid belt). It was only
through the unique composition of the family members (akin to the extremely
distinct photometric properties of the Vesta family members) that the Haumea
family could be readily identified. This implies that more collisional
families may be hiding in the TNO population, but cannot be spotted by orbits
alone.

Although massive collisions dominated the solar system environment during the
epoch of planet building, they also played an important role in shaping all of
the major populations of small bodies during the subsequent $\sim 4$ billion
years. Collisional evolution, although stochastic in nature, was a major
determinant in the structure of the solar system we see today (see the chapter
by Bottke et al. in this volume).

##  5 OPEN PROBLEMS AND FUTURE PROSPECTS

The effect of space weathering on asteroidal surfaces still remains an
important topic for future exploration (see the chapter by Brunetto et al. in
this volume for further discussion). The range of studies carried out so far
have found a wide dispersion of results, both in terms of the timescale of
weathering and the specific effects on various taxonomic classes. Studies to
date have relied on the assumption that all asteroids with similar taxonomic
types have identical mineralogical compositions, or have been based on a
single pair of families known to be compositionally identical but with
different ages (i.e. Karin and Koronis). As deeper surveys and dynamical
analysis techniques begin to increase the number of identified cases of
family-within-a-family, physical studies of these interesting populations will
allow better measurements of the specific effects and timing of space
weathering processes.

Advances in physical measurements of asteroid families have not uniformly
addressed the various parameters needed for a robust scientific investigation.
In particular, there has been only a nominal advancement in the measurement of
asteroid masses and densities, owing to the difficulty in determining these
parameters. Carry (2012) compiled known measurements of asteroid densities
into a comprehensive list, however only a handful of families have more than
one member represented, and for most the only measurement is of the largest
remnant body. A larger survey of densities including many family members over
a range of sizes would enable testing of family formation conditions via
reaccretion (cf. chapter by Michel et al. in this volume), as well as improve
family ages derived from numerical simulations of gravitational and Yarkovsky
orbital evolution (cf. chapter by Nesvorný et al. in this volume). This could
be accomplished by a more comprehensive search for binaries, or through
modeling of gravitational perturbations to asteroid orbits detectable in next-
generation astrometric catalogs.

One highly-anticipated survey will be carried out by the European Space
Agency’s Gaia mission (Hestroffer et al., 2010), which is expected to provide
spectral characterization of all objects down to an apparent magnitude of
$V=20$, including many asteroid family members (Campins et al. 2012; Delbo et
al. 2012; Cellino & Dell’Oro, 2012). This dramatic increase in the number of
characterized family members will enable a host of new investigations of the
composition and differentiation of family parent bodies. By spectrally probing
bodies as small as $\sim 2~{}$km, inhomogeneities in asteroid family
composition may begin to be revealed. Another key scientific product will be
refined astrometry for all asteroids which can be searched for gravitational
perturbations and used to determine the masses of the largest asteroids
(Mignard et al., 2007). This wealth of new data will feed into theoretical
models and numerical simulations, allowing us to improve the ages determined
from orbital evolution simulations (e.g. Masiero et al., 2012; Carruba et al.,
2014).

The collision events that form families are very rare, and the probability of
a massive collision in the next ten, hundred, or thousand years is vanishingly
small (see chapter by Bottke et al. in this volume). However, a new class of
active Main Belt objects has recently been identified that may none-the-less
provide a window into the collisional environment of the solar system (see the
chapter by Jewitt et al. in this volume for further discussion). While some of
these objects show repeated activity indicative of a cometary nature complete
with sub-surface volatiles, others are best explained by impact events. In
particular, the observed outburst events of P/2010 A2 (Jewitt et al. 2010) and
(596) Scheila (Jewitt et al. 2011) are consistent with impacts by very small
($D<50~{}$m) asteroids. As current and future sky surveys probe to smaller
diameters in the Main Belt, the frequency these events will be observed, or
even predicted in advance, will increase. Study of these small scale
disruptions offers an important constraint on impact physics in the low-
gravity environment of asteroids, and provides test cases for comparing to the
small-scale impact experiments that can be performed in Earth-based
laboratories.

Recently, Reddy et al. (2014) presented evidence that shock darkening may play
a role in altering the spectroscopic properties of chondritic materials in the
Baptistina and Flora families. If evidence for this effect is seen in other
families across a range of compositions, this technique may provide a method
for determining the conditions of family-forming impacts in the Main Belt, and
thus provide better constraints on the ages of families. This may also help
explain some of the differences observed in space weathering studies that find
albedo changes happen very quickly while spectral changes have long
timescales.

As new data sets have rapidly increased our ability to characterize asteroid
family members, and through this the parent body from which they originated,
one glaring question remains at the forefront of the field: where are the
families of differentiated parent bodies that were completely disrupted? Vesta
and its family members have given us a excellent example of the composition
and resultant albedo, color, and spectral properties of the crust of a
differentiated body (see the chapter by Russell et al. in this volume for
further discussion). However, searches for objects with similar properties in
different regions of the Main Belt have yielded no significant populations of
these basaltic crust and mantle fragments that should be leftover from these
collisions. On the other hand, data from iron meteorites has indicated that
differentiation of protoplanets, if not common, at a minimum happened multiple
times (see chapters by Elkins-Tanton et al. and Scott et al. in this volume
for further discussion). While it is possible that these collisions happened
at the earliest stages of the solar system’s formation and the evidence (in
the form of families) was erased during the epoch of giant planet migration
that is the foundation of the ’Nice’ model (see chapter by Morbidelli et al.
in this volume), a dynamical explanation of this problem would need to
preserve in the Main Belt the core material that still falls to Earth today.
Conversely, if these impacts happened after the last great shake up of the
solar system, a mineralogical explanation for how metallic cores could form
without leaving a basaltic ’residue’ in the Main Belt is required. The
limitations on what could not have happened that are being set by current
surveys are just as important as our discoveries of what did happen.

The next decade of large surveys, both ground- and space-based, promises to
expand our knowledge of asteroid physical properties by potentially another
order of magnitude beyond what is known today. In this data-rich environment,
family research will focus not just on individual families and their place in
the Main Belt, but on specific sub-groupings within families: on the knots,
clumps, and collisional cascade fragments that trace the disruption and
evolutionary dynamics that families have undergone. As the sizes of objects
probed reach smaller and smaller, we can expect to find more young families
like Karin and Iannini that can be directly backward-integrated to a specific
time of collision, improving our statistics of collisions in the last 10
million years. As catalogs increase in size, we can also expect to more
frequently have characterization data of objects both before and after they
undergo catastrophic disruption. This will enable us to test our impact
physics models on scales not achievable on Earth. Additionally, we will begin
to see a time when we routinely use remote sensing data of asteroids to not
just associate families but assess the mineralogy of family members as a probe
of the parent body. Asteroid family physical properties, numerical
simulations, and evolutionary theory will leapfrog off of each other, pushing
forward our understanding of the asteroids and of the whole solar system.

Acknowledgments. JRM was partially supported by a grant from the NASA
Planetary Geology and Geophysics Program. FED was supported by NASA through
the Hubble Fellowship grant HST-HF-51319.01-A, awarded by the Space Telescope
Science Institute, which is operated by the Association of Universities for
Research in Astronomy, Inc., for NASA, under contract NAS 5-26555. This
publication makes use of data products from the Wide-field Infrared Survey
Explorer, which is a joint project of the University of California, Los
Angeles, and the Jet Propulsion Laboratory/California Institute of Technology,
funded by the National Aeronautics and Space Administration. This publication
also makes use of data products from NEOWISE, which is a project of the Jet
Propulsion Laboratory/California Institute of Technology, funded by the
Planetary Science Division of the National Aeronautics and Space
Administration. Funding for the creation and distribution of the SDSS Archive
has been provided by the Alfred P. Sloan Foundation, the Participating
Institutions, the National Aeronautics and Space Administration, the National
Science Foundation, the U.S. Department of Energy, the Japanese
Monbukagakusho, and the Max Planck Society. The SDSS Web site is
http://www.sdss.org/. The SDSS is managed by the Astrophysical Research
Consortium (ARC) for the Participating Institutions. The Participating
Institutions are The University of Chicago, Fermilab, the Institute for
Advanced Study, the Japan Participation Group, The Johns Hopkins University,
the Korean Scientist Group, Los Alamos National Laboratory, the Max-Planck-
Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics
(MPA), New Mexico State University, University of Pittsburgh, University of
Portsmouth, Princeton University, the United States Naval Observatory, and the
University of Washington. This research is based on observations with AKARI, a
JAXA project with the participation of ESA. The authors wish to thank Bobby
Bus, Beth Ellen Clark, Heather Kaluna, and Pierre Vernazza for providing
proprietary spectra to include in Figure 1. We also thank the referees,
Alberto Cellino and Bobby Bus, and editor Patrick Michel for helpful comments
that improved this chapter.

Table 1: Physical properties of asteroid families

Number | Name | PDS ID | $<p_{V}>$ | $n_{p_{V}}$ | $<p_{NIR}>$ | $n_{p_{NIR}}$ | $<a^{\star}>$ | $<i-z>$ | $n_{SDSS}$ | SFD slope | SFD range (km) | Tax | $n_{tax}$
---|---|---|---|---|---|---|---|---|---|---|---|---|---
2 | Pallas | 801 | 0.134+/-0.026 | 49 | 0.114+/-0.047 | 10 | -0.14+/-0.03 | -0.01+/-0.08 | 13 | …+/-… | … | B | 8
3 | Juno | 501 | 0.262+/-0.054 | 125 | 0.488+/-0.000 | 8 | 0.08+/-0.05 | -0.03+/-0.07 | 87 | -2.427+/-0.108 | 2.7-7.3 | Sq | 1
4 | Vesta | 401 | 0.363+/-0.088 | 1900 | 0.465+/-0.156 | 54 | 0.12+/-0.05 | -0.26+/-0.10 | 2148 | -3.417+/-0.030 | 2.5-11.9 | V | 49
8 | Flora | 402 | 0.305+/-0.064 | 1330 | 0.440+/-0.082 | 142 | 0.13+/-0.06 | -0.04+/-0.07 | 922 | -2.692+/-0.030 | 2.8-12.2 | S | 74
10 | Hygiea | 601 | 0.070+/-0.018 | 1951 | 0.065+/-0.028 | 3 | -0.11+/-0.05 | 0.01+/-0.07 | 606 | -3.883+/-0.040 | 6.1-19.3 | C | 1
15 | Eunomia | 502 | 0.270+/-0.059 | 1448 | 0.374+/-0.088 | 148 | 0.13+/-0.05 | -0.03+/-0.06 | 798 | -3.091+/-0.033 | 4.4-17.6 | S | 30
20 | Massalia | 404 | 0.247+/-0.053 | 214 | …+/-… | 0 | 0.07+/-0.05 | -0.04+/-0.08 | 386 | -3.544+/-0.140 | 2.0-4.1 | S | 1
24 | Themis | 602 | 0.068+/-0.017 | 2218 | 0.074+/-0.030 | 86 | -0.11+/-0.04 | 0.01+/-0.06 | 640 | -2.313+/-0.017 | 7.3-55.6 | C | 7
25 | Phocaea | 701 | 0.290+/-0.066 | 715 | 0.355+/-0.203 | 119 | 0.10+/-0.11 | -0.04+/-0.08 | 252 | -2.663+/-0.039 | 3.5-14.6 | S | 39
27 | Euterpe | 410 | 0.270+/-0.062 | 45 | 0.493+/-0.000 | 1 | 0.11+/-0.05 | -0.04+/-0.08 | 42 | …+/-… | … | S | 1
31 | Euphrosyne | 901 | 0.059+/-0.013 | 742 | 0.082+/-0.173 | 5 | -0.08+/-0.05 | 0.04+/-0.06 | 169 | -4.687+/-0.082 | 7.3-18.4 | Cb | 1
44 | Nysa(Polana) | 405 | 0.289+/-0.074 | 1345 | 0.356+/-0.059 | 22 | 0.13+/-0.06 | -0.03+/-0.07 | 1544 | -3.083+/-0.030 | 2.5-13.0 | … | 0
46 | Hestia | 503 | 0.267+/-0.049 | 28 | 0.068+/-0.000 | 1 | 0.14+/-0.04 | -0.03+/-0.04 | 22 | …+/-… | … | Xc | 1
81 | Terpsichore | 622 | 0.050+/-0.010 | 57 | 0.053+/-0.000 | 1 | -0.08+/-0.03 | 0.08+/-0.10 | 15 | -4.371+/-0.508 | 5.0-7.3 | Cb | 1
84 | Klio | 413 | 0.059+/-0.014 | 107 | 0.089+/-0.031 | 3 | -0.06+/-0.04 | 0.05+/-0.08 | 23 | -2.478+/-0.129 | 3.3-8.0 | Ch | 1
87 | Sylvia | 603 | 0.051+/-0.012 | 121 | 0.082+/-0.000 | 1 | -0.07+/-0.05 | 0.09+/-0.11 | 20 | -3.339+/-0.232 | 7.0-12.4 | X | 1
89 | Julia | 540 | 0.225+/-0.036 | 2 | 0.339+/-0.000 | 2 | 0.05+/-0.02 | 0.12+/-0.07 | 3 | …+/-… | … | Ld | 1
96 | Aegle | 630 | 0.072+/-0.013 | 83 | 0.102+/-0.000 | 1 | 0.02+/-0.05 | 0.10+/-0.08 | 23 | -3.252+/-0.305 | 6.8-11.4 | T | 1
128 | Nemesis | 504 | 0.072+/-0.019 | 347 | 0.071+/-0.000 | 1 | -0.08+/-0.06 | 0.03+/-0.07 | 109 | -4.320+/-0.121 | 3.8-8.4 | C | 2
137 | Meliboea | 604 | 0.060+/-0.013 | 163 | 0.050+/-0.029 | 12 | -0.10+/-0.08 | 0.05+/-0.07 | 53 | -1.513+/-0.051 | 8.0-39.4 | Ch | 11
142 | Polana(Nysa) | n/a | 0.056+/-0.012 | 1130 | 0.061+/-0.006 | 3 | -0.12+/-0.10 | 0.00+/-0.08 | 375 | -3.177+/-0.041 | 3.6-12.4 | B | 3
144 | Vibilia | 529 | 0.065+/-0.011 | 180 | …+/-… | 0 | -0.10+/-0.04 | 0.04+/-0.07 | 35 | -3.137+/-0.135 | 4.5-9.7 | Ch | 1
145 | Adeona | 505 | 0.060+/-0.011 | 874 | 0.068+/-0.078 | 19 | -0.11+/-0.08 | 0.04+/-0.07 | 274 | -2.854+/-0.037 | 5.3-23.2 | Ch | 12
148 | Gallia | 802 | 0.251+/-0.059 | 24 | …+/-… | 0 | 0.10+/-0.03 | -0.06+/-0.06 | 15 | …+/-… | … | Sl | 1
158 | Koronis | 605 | 0.238+/-0.051 | 1089 | 0.325+/-0.059 | 67 | 0.09+/-0.07 | -0.02+/-0.08 | 810 | -2.451+/-0.026 | 5.1-32.0 | S | 34
163 | Erigone | 406 | 0.051+/-0.010 | 716 | 0.061+/-0.013 | 17 | -0.08+/-0.10 | 0.05+/-0.08 | 201 | -3.215+/-0.050 | 3.3-11.9 | Ch | 1
170 | Maria | 506 | 0.255+/-0.061 | 1361 | 0.370+/-0.068 | 69 | 0.12+/-0.05 | -0.02+/-0.07 | 809 | -2.637+/-0.025 | 3.5-24.8 | S | 23
173 | Ino | 522 | 0.244+/-0.069 | 90 | …+/-… | 0 | 0.09+/-0.05 | -0.06+/-0.07 | 93 | -3.141+/-0.268 | 2.7-4.6 | … | 0
221 | Eos | 606 | 0.163+/-0.035 | 3509 | 0.180+/-0.053 | 205 | 0.05+/-0.05 | 0.03+/-0.07 | 1692 | -2.222+/-0.013 | 5.6-47.3 | K | 30
283 | Emma | 607 | 0.047+/-0.011 | 260 | 0.118+/-0.113 | 2 | -0.07+/-0.06 | 0.04+/-0.08 | 75 | -3.442+/-0.113 | 6.7-15.3 | C | 1
293 | Brasilia | 608 | 0.174+/-0.048 | 110 | 0.224+/-0.017 | 4 | -0.04+/-0.04 | 0.05+/-0.07 | 78 | -3.462+/-0.243 | 3.7-6.4 | X | 2
298 | Baptistina | 403 | 0.179+/-0.056 | 581 | 0.390+/-0.198 | 25 | 0.01+/-0.09 | -0.02+/-0.09 | 321 | -3.254+/-0.063 | 2.5-7.2 | S | 9
302 | Clarissa | 407 | 0.048+/-0.010 | 44 | …+/-… | 0 | -0.14+/-0.04 | 0.00+/-0.06 | 10 | …+/-… | … | F | 1
313 | Chaldaea | 415 | 0.063+/-0.017 | 169 | 0.083+/-0.039 | 11 | -0.10+/-0.05 | 0.06+/-0.07 | 34 | -3.058+/-0.119 | 3.7-8.6 | C | 3
322 | Phaeo | 530 | 0.059+/-0.015 | 99 | 0.181+/-0.000 | 2 | 0.00+/-0.06 | 0.05+/-0.08 | 34 | -2.852+/-0.195 | 5.1-10.1 | D | 1
329 | Svea | 416 | 0.050+/-0.009 | 30 | 0.134+/-0.166 | 2 | -0.04+/-0.06 | 0.04+/-0.05 | 8 | …+/-… | … | C | 1
363 | Padua | 507 | 0.069+/-0.015 | 427 | 0.067+/-0.022 | 5 | -0.04+/-0.06 | 0.05+/-0.07 | 135 | -2.588+/-0.053 | 4.5-16.4 | X | 10
369 | Aeria | 539 | 0.180+/-0.011 | 22 | 0.266+/-0.000 | 6 | -0.05+/-0.04 | 0.03+/-0.09 | 18 | …+/-… | … | M | 1
375 | Ursula | 631 | 0.061+/-0.014 | 600 | 0.083+/-0.047 | 15 | -0.05+/-0.08 | 0.06+/-0.09 | 194 | -2.677+/-0.046 | 7.3-27.2 | … | 0
396 | Aeolia | 508 | 0.107+/-0.022 | 43 | 0.115+/-0.000 | 1 | -0.04+/-0.05 | 0.04+/-0.03 | 10 | …+/-… | … | Xe | 1
410 | Chloris | 509 | 0.084+/-0.031 | 171 | 0.081+/-0.095 | 10 | -0.05+/-0.08 | 0.06+/-0.05 | 59 | -2.814+/-0.103 | 5.2-14.0 | C | 8
434 | Hungaria | 003 | 0.456+/-0.217 | 527 | 0.727+/-1.692 | 9 | -0.01+/-0.08 | 0.04+/-0.10 | 636 | …+/-… | … | Xe | 14
480 | Hansa | 803 | 0.269+/-0.067 | 316 | 0.377+/-0.068 | 9 | 0.10+/-0.05 | -0.06+/-0.07 | 134 | -3.378+/-0.104 | 3.4-7.9 | S | 2
490 | Veritas | 609 | 0.066+/-0.016 | 697 | 0.068+/-0.011 | 3 | -0.07+/-0.04 | 0.05+/-0.08 | 207 | -2.744+/-0.043 | 5.8-22.6 | Ch | 8
495 | Eulalia(Polana) | n/a | 0.057+/-0.012 | 2008 | 0.066+/-0.029 | 15 | -0.12+/-0.05 | 0.01+/-0.07 | 531 | -2.687+/-0.021 | 3.0-18.4 | C | 13
569 | Misa | 510 | 0.052+/-0.013 | 287 | 0.064+/-0.027 | 3 | -0.07+/-0.07 | 0.03+/-0.08 | 79 | -2.508+/-0.067 | 4.0-13.3 | Ch | 1
589 | Croatia | 638 | 0.054+/-0.010 | 99 | 0.068+/-0.000 | 1 | -0.05+/-0.04 | 0.02+/-0.09 | 22 | -3.383+/-0.224 | 5.8-11.1 | X | 1
606 | Brangane | 511 | 0.112+/-0.028 | 44 | 0.137+/-0.000 | 2 | 0.07+/-0.04 | 0.09+/-0.06 | 20 | …+/-… | … | L | 1
618 | Elfriede | 632 | 0.052+/-0.012 | 36 | 0.063+/-0.000 | 1 | -0.09+/-0.05 | 0.06+/-0.05 | 8 | …+/-… | … | C | 1
623 | Chimaera | 414 | 0.054+/-0.012 | 63 | 0.049+/-0.000 | 3 | -0.05+/-0.03 | 0.09+/-0.10 | 20 | -2.586+/-0.235 | 3.8-7.2 | XC | 1
627 | Charis | 616 | 0.071+/-0.010 | 39 | 0.264+/-0.000 | 2 | 0.16+/-0.06 | 0.04+/-0.08 | 59 | …+/-… | … | X | 1
656 | Beagle | 620 | 0.080+/-0.014 | 30 | 0.070+/-0.006 | 5 | -0.12+/-0.03 | 0.01+/-0.06 | 16 | …+/-… | … | X | 1
668 | Dora | 512 | 0.056+/-0.012 | 667 | 0.047+/-0.017 | 17 | -0.12+/-0.07 | 0.04+/-0.07 | 175 | -2.610+/-0.043 | 5.7-21.6 | Ch | 29
686 | Gersuind | 804 | 0.145+/-0.037 | 106 | 0.328+/-0.000 | 1 | 0.09+/-0.07 | 0.08+/-0.07 | 36 | -2.653+/-0.158 | 3.8-8.0 | … | 0
702 | Alauda | 902 | 0.066+/-0.015 | 687 | 0.071+/-0.013 | 26 | -0.10+/-0.06 | 0.03+/-0.07 | 197 | -2.707+/-0.042 | 9.2-36.7 | … | 0
709 | Fringilla | 623 | 0.050+/-0.014 | 51 | 0.212+/-0.788 | 2 | -0.03+/-0.06 | 0.09+/-0.08 | 24 | …+/-… | … | X | 1
729 | Watsonia | 537 | 0.134+/-0.019 | 51 | 0.181+/-0.000 | 2 | 0.08+/-0.04 | 0.07+/-0.02 | 12 | …+/-… | … | L | 2
752 | Sulamitis | 408 | 0.055+/-0.011 | 134 | 0.048+/-0.000 | 1 | -0.07+/-0.07 | 0.06+/-0.11 | 33 | -2.417+/-0.126 | 3.8-8.8 | Ch | 1
778 | Theobalda | 617 | 0.062+/-0.016 | 107 | 0.070+/-0.000 | 1 | -0.16+/-0.03 | 0.00+/-0.05 | 28 | -3.097+/-0.185 | 6.5-13.3 | … | 0
780 | Armenia | 905 | 0.056+/-0.013 | 28 | 0.060+/-0.000 | 2 | -0.05+/-0.01 | 0.03+/-0.04 | 4 | …+/-… | … | C | 1
808 | Merxia | 513 | 0.234+/-0.054 | 93 | 0.347+/-0.030 | 3 | 0.08+/-0.05 | -0.08+/-0.08 | 98 | -2.662+/-0.190 | 3.2-6.7 | S | 6
832 | Karin | 610 | 0.178+/-0.031 | 18 | 0.294+/-0.000 | 1 | 0.03+/-0.05 | -0.01+/-0.07 | 33 | …+/-… | … | S | 47
845 | Naema | 611 | 0.064+/-0.012 | 155 | 0.055+/-0.000 | 1 | -0.10+/-0.11 | 0.04+/-0.06 | 45 | -4.274+/-0.220 | 6.0-10.6 | C | 1
847 | Agnia | 514 | 0.238+/-0.060 | 110 | 0.389+/-0.015 | 3 | 0.04+/-0.05 | -0.07+/-0.08 | 179 | -3.055+/-0.165 | 3.8-8.0 | S | 8
909 | Ulla | 903 | 0.048+/-0.009 | 19 | …+/-… | 0 | -0.07+/-0.02 | 0.02+/-0.06 | 3 | …+/-… | … | X | 1
918 | Itha | 633 | 0.239+/-0.056 | 28 | 0.353+/-0.084 | 8 | 0.14+/-0.04 | -0.01+/-0.05 | 14 | …+/-… | … | Sl | 4
945 | Barcelona | 805 | 0.290+/-0.064 | 52 | 0.510+/-0.000 | 1 | 0.09+/-0.05 | -0.11+/-0.09 | 21 | …+/-… | … | Sq | 1
1128 | Astrid | 515 | 0.045+/-0.010 | 213 | 0.046+/-0.000 | 1 | -0.07+/-0.05 | 0.08+/-0.08 | 33 | -2.567+/-0.080 | 3.5-11.1 | C | 5
1189 | Terentia | 618 | 0.064+/-0.012 | 13 | 0.058+/-0.000 | 1 | -0.01+/-0.00 | 0.09+/-0.00 | 1 | …+/-… | … | Ch | 1
1222 | Tina | 806 | 0.128+/-0.042 | 26 | 0.137+/-0.000 | 1 | 0.01+/-0.00 | 0.03+/-0.05 | 3 | …+/-… | … | X | 1
1270 | Datura | 411 | 0.288+/-0.000 | 1 | …+/-… | 0 | 0.01+/-0.00 | -0.10+/-0.00 | 1 | …+/-… | … | S | 4
1272 | Gefion | 516 | 0.267+/-0.058 | 737 | 0.350+/-0.154 | 25 | 0.10+/-0.06 | -0.02+/-0.07 | 523 | -3.262+/-0.050 | 4.0-14.3 | S | 32
1303 | Luthera | 904 | 0.050+/-0.009 | 125 | 0.078+/-0.000 | 1 | 0.01+/-0.04 | 0.10+/-0.07 | 39 | -3.955+/-0.264 | 7.9-13.0 | … | 0
1332 | Marconia | 636 | 0.042+/-0.008 | 6 | 0.080+/-0.000 | 1 | …+/-… | …+/-… | 0 | …+/-… | … | L | 1
1400 | Tirela | 612 | 0.239+/-0.057 | 419 | 0.073+/-0.095 | 7 | 0.15+/-0.09 | 0.08+/-0.08 | 225 | -3.454+/-0.073 | 4.8-14.3 | Ld | 10
1484 | Postrema | 541 | 0.047+/-0.010 | 30 | 0.051+/-0.006 | 3 | -0.05+/-0.05 | 0.02+/-0.06 | 5 | …+/-… | … | B | 1
1658 | Innes | 518 | 0.259+/-0.057 | 195 | 0.318+/-0.149 | 8 | 0.09+/-0.06 | -0.04+/-0.07 | 163 | -3.385+/-0.128 | 3.1-7.0 | S | 2
1668 | Hanna | 533 | 0.052+/-0.011 | 102 | 0.048+/-0.000 | 1 | -0.09+/-0.03 | 0.08+/-0.05 | 20 | -3.502+/-0.240 | 3.9-7.2 | … | 0
1726 | Hoffmeister | 519 | 0.047+/-0.010 | 609 | 0.052+/-0.013 | 4 | -0.10+/-0.05 | 0.03+/-0.08 | 145 | -2.856+/-0.047 | 4.5-17.2 | C | 9
1892 | Lucienne | 409 | 0.228+/-0.029 | 19 | …+/-… | 0 | 0.09+/-0.03 | 0.00+/-0.09 | 10 | …+/-… | … | S | 1
2085 | Henan | 542 | 0.227+/-0.065 | 106 | 0.165+/-0.000 | 3 | 0.11+/-0.06 | -0.02+/-0.09 | 163 | -3.667+/-0.276 | 3.4-5.8 | L | 1
2262 | Mitidika | 531 | 0.066+/-0.014 | 279 | 0.060+/-0.013 | 10 | -0.11+/-0.06 | 0.01+/-0.08 | 71 | -2.832+/-0.091 | 4.6-11.4 | … | 0
2344 | Xizang | 536 | 0.134+/-0.044 | 18 | …+/-… | 0 | 0.04+/-0.05 | 0.08+/-0.07 | 12 | …+/-… | … | … | 0
2384 | Schulhof | 525 | 0.280+/-0.000 | 1 | 0.289+/-0.000 | 4 | 0.08+/-0.07 | -0.05+/-0.03 | 2 | …+/-… | … | … | 0
2732 | Witt | 535 | 0.261+/-0.053 | 124 | 0.347+/-0.018 | 3 | 0.15+/-0.07 | 0.01+/-0.08 | 190 | -3.114+/-0.173 | 3.8-7.7 | … | 0
2782 | Leonidas | 528 | 0.068+/-0.013 | 67 | …+/-… | 0 | -0.10+/-0.07 | 0.04+/-0.07 | 22 | -2.142+/-0.245 | 5.1-9.4 | … | 0
3152 | Jones | 538 | 0.054+/-0.004 | 14 | 0.061+/-0.000 | 1 | -0.02+/-0.00 | 0.04+/-0.01 | 2 | …+/-… | … | T | 1
3438 | Inarrados | 634 | 0.067+/-0.015 | 24 | 0.069+/-0.000 | 1 | -0.10+/-0.03 | 0.05+/-0.05 | 11 | …+/-… | … | … | 0
3556 | Lixiaohua | 613 | 0.044+/-0.009 | 367 | 0.053+/-0.011 | 3 | -0.06+/-0.05 | 0.04+/-0.09 | 95 | -3.499+/-0.098 | 6.8-15.7 | … | 0
3811 | Karma | 534 | 0.054+/-0.010 | 78 | …+/-… | 0 | -0.06+/-0.08 | 0.03+/-0.07 | 20 | -2.659+/-0.241 | 3.7-6.7 | … | 0
3815 | Konig | 517 | 0.049+/-0.011 | 135 | …+/-… | 0 | -0.08+/-0.02 | 0.06+/-0.06 | 25 | -3.032+/-0.150 | 4.1-9.2 | … | 0
4203 | Brucato | 807 | 0.064+/-0.017 | 233 | 0.041+/-0.009 | 2 | -0.11+/-0.05 | 0.05+/-0.07 | 45 | -3.604+/-0.109 | 5.3-13.3 | … | 0
4652 | Iannini | 520 | 0.309+/-0.033 | 18 | …+/-… | 0 | 0.01+/-0.04 | -0.08+/-0.06 | 21 | …+/-… | … | … | 0
5438 | Lorre | 527 | 0.054+/-0.002 | 2 | …+/-… | 0 | …+/-… | …+/-… | 0 | …+/-… | … | C | 1
5567 | Durisen | 624 | 0.043+/-0.010 | 16 | 0.050+/-0.000 | 1 | -0.02+/-0.03 | 0.11+/-0.05 | 4 | …+/-… | … | … | 0
5614 | Yakovlev | 625 | 0.046+/-0.008 | 25 | …+/-… | 0 | -0.08+/-0.00 | 0.07+/-0.01 | 2 | …+/-… | … | … | 0
7353 | Kazuia | 532 | 0.214+/-0.025 | 13 | …+/-… | 0 | 0.06+/-0.08 | -0.03+/-0.02 | 3 | …+/-… | … | L | 1
7468 | Anfimov | 635 | 0.166+/-0.061 | 10 | …+/-… | 0 | 0.23+/-0.03 | -0.14+/-0.09 | 13 | …+/-… | … | … | 0
7481 | SanMarcello | 626 | 0.194+/-0.054 | 27 | …+/-… | 0 | -0.05+/-0.04 | 0.04+/-0.06 | 18 | …+/-… | … | … | 0
9506 | Telramund | 614 | 0.237+/-0.063 | 46 | …+/-… | 0 | 0.09+/-0.05 | -0.02+/-0.09 | 33 | …+/-… | … | … | 0
10811 | Lau | 619 | 0.274+/-0.000 | 1 | …+/-… | 0 | 0.26+/-0.00 | -0.18+/-0.00 | 1 | …+/-… | … | … | 0
14627 | Emilkowalski | 523 | 0.149+/-0.046 | 4 | …+/-… | 0 | 0.06+/-0.00 | 0.11+/-0.00 | 1 | …+/-… | … | … | 0
15454 | 1998YB3 | 627 | 0.054+/-0.006 | 11 | …+/-… | 0 | -0.11+/-0.03 | 0.04+/-0.03 | 7 | …+/-… | … | … | 0
15477 | 1999CG1 | 628 | 0.095+/-0.030 | 68 | …+/-… | 0 | 0.04+/-0.04 | 0.05+/-0.06 | 25 | -4.768+/-0.602 | 4.3-6.0 | … | 0
16598 | 1992YC2 | 524 | …+/-… | 0 | …+/-… | 0 | 0.10+/-0.00 | -0.09+/-0.00 | 1 | …+/-… | … | Sq | 1
18405 | 1993FY12 | 615 | 0.173+/-0.049 | 15 | …+/-… | 0 | -0.04+/-0.03 | 0.07+/-0.08 | 12 | …+/-… | … | … | 0
36256 | 1999XT17 | 629 | 0.203+/-0.066 | 13 | …+/-… | 0 | 0.21+/-0.07 | -0.04+/-0.05 | 6 | …+/-… | … | … | 0
53546 | 2000BY6 | 526 | 0.139+/-0.000 | 1 | …+/-… | 0 | 0.04+/-0.03 | 0.06+/-0.04 | 9 | …+/-… | … | … | 0
106302 | 2000UJ87 | 637 | 0.045+/-0.004 | 12 | …+/-… | 0 | -0.10+/-0.04 | 0.05+/-0.04 | 3 | …+/-… | … | … | 0

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