Olivine-dominated A-type asteroids in the Main Belt: Distribution, Abundance and Relation to Families
Francesca E. DeMeo, David Polishook, Benoit Carry, Brian J. Burt, Henry H. Hsieh, Richard P. Binzel, Nicholas A. Moskovitz, Thomas H. Burbine
OOlivine-dominated A-type asteroids in the Main Belt: Distribution, Abundance andRelation to Families
Francesca E. DeMeo a , David Polishook b , Benoˆıt Carry c , Brian J. Burt d , Henry H. Hsieh e,f , Richard P. Binzel a , Nicholas A.Moskovitz d , Thomas H. Burbine g a Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 USA b Department of Earth and Planetary Sciences, Weizmann Institute of Science, Rehovot 0076100, Israel c Observatoire de la Cte d’Azur, Boulevard de l’Observatoire, 06304 Nice Cedex 4, France d Lowell Observatory, 1400 West Mars Hill Road, Flagsta ff , AZ 86001, USA e Planetary Science Institute, 1700 E. Ft. Lowell Road, Suite 106, Tucson, AZ 85719, USA f Institute of Astronomy and Astrophysics, Academia Sinica, P.O. Box 23-141, Taipei 10617, Taiwan g Department of Astronomy, Mount Holyoke College, South Hadley, MA 01075, USA
Abstract Di ff erentiated asteroids are rare in the main asteroid belt despite evidence for ∼
100 distinct di ff erentiated bodies in the meteoriterecord. We have sought to understand why so few main-belt asteroids di ff erentiated and where those di ff erentiated bodies orfragments reside. Using the Sloan Digital Sky Survey (SDSS) to search for a needle in a haystack we identify spectral A-typeasteroid candidates, olivine-dominated asteroids that may represent mantle material of di ff erentiated bodies. We have performed anear-infrared spectral survey with SpeX on the NASA IRTF and FIRE on the Magellan Telescope.We report results from having doubled the number of known A-type asteroids. We deduce a new estimate for the overallabundance and distribution of this class of olivine-dominated asteroids. We find A-type asteroids account for less than 0.16% ofall main-belt objects larger than 2 km and estimate there are a total of ∼
600 A-type asteroids above that size. They are foundrather evenly distributed throughout the main belt, are even detected at the distance of the Cybele region, and have no statisticallysignificant concentration in any asteroid family. We conclude the most likely implication is the few fragments of olivine-dominatedmaterial in the main belt did not form locally, but instead were implanted as collisional fragments of bodies that formed elsewhere.
Keywords:
ASTEROIDS, SPECTROSCOPY
1. Introduction
The Missing Mantle Problem, also known as the GreatDunite Shortage, is a decades-old question in planetary sci-ence (Chapman 1986; Bell et al. 1989) that seeks to under-stand the perceived shortage of olivine-dominated mantle ma-terial in the main asteroid belt, identified spectrally as A-types(Bus and Binzel 2002; DeMeo et al. 2009). In the classical the-ory of asteroid di ff erentiation, a body would form an iron-richcore, an olivine-dominated mantle, and a pyroxene-rich basalticcrust. Over time, the clear lack of observed mantle material hashad various interpretations. Earlier on, the “battered to bits”scenario suggested through collisionary processes these bodieshad been ground down below the detection thresholds of obser-vational surveys (Burbine et al. 1996). More modern theoriesposit that the lack of mantle material suggests there was no sig-nificant population of di ff erentiated bodies in the main belt, andthat di ff erentiated planetesimals instead formed much closer tothe Sun, in the terrestrial planet region. For a review of themissing mantle problem and the evolution of proposed solu-tions, see DeMeo et al. (2015). For a review of di ff erentiationsee Scheinberg et al. (2015) and Wilson et al. (2015). For a re-view of the dynamical history, impact scenarios, and meteoritesof di ff erentiated bodies see Scott et al. (2015). Searches for basaltic (crustal) di ff erentiated materialthroughout the main belt have proven successful (e.g.,Moskovitz et al. 2008; Solontoi et al. 2012; Leith et al. 2017).Basaltic asteroids are easily identified spectrally in both thevisible and near-infrared wavelengths by the deep and narrowone-micron and deep and broad two-micron absorption bands.The interior of a di ff erentiated asteroid should be metal-rich.Spectrally, this composition falls within the X-type - or M-type defined by the Tholen taxonomy (Tholen 1984) if albedodata are available and within an intermediate range - however,these spectral classes are compositionally degenerate. Due tothe much larger uncertainty in spectrally identifying metal-richasteroids, we do not explore a search for them in this work.An additional way to search for di ff erentiated bodies thathave been heavily or completely disrupted is to identify spec-tral A-type asteroids, characterized by a very wide and deep1-micron absorption indicative of large concentrations ( > ff erentiated asteroids(Benedix et al. 2014). An alternate theory for pallasites put Preprint submitted to Icarus January 10, 2019 a r X i v : . [ a s t r o - ph . E P ] J a n orth by Tarduno et al. (2012) is that they result from a majorimpact of a molten iron core from one body with the mantle ofa di ff erentiated second body. The red slopes of A-types are ex-pected to be due to space weathering as shown in experimentsas shown by Sasaki et al. (2001); Brunetto et al. (2006). Fora detailed compositional analysis of previously known olivine-dominated asteroids, see Sanchez et al. (2014). Not all A-types,however, are expected to be di ff erentiated material (Sunshineet al. 2007), a point explained further in the discussion section.Preliminary studies of the abundance and distribution of A-type asteroids were performed by Carvano et al. (2010) and De-Meo and Carry (2013, 2014) using the Sloan Digital Sky Survey(SDSS). However, while visible wavelengths are useful to iden-tify candidate objects, observing these potential targets in thenear-infrared is critical (see Fig. 1) to identify if their spectraare truly consistent with an olivine-rich mineralogy. Roughlyhalf of all objects classified as A-types based on visible-onlydata do not show the characteristic strong, broad 1 micron fea-ture in the near-ir (see Fig. 1) and are thus not consistent withmantle material (Burbine and Binzel 2002; DeMeo et al. 2009).Similarly for V-types, not all objects classified based on visible-only data are proven to be basaltic, although the success rate isroughly 90% (Moskovitz et al. 2008).In this work we have two goals: 1) to determine the dis-tribution and abundance of olivine-dominated mantle materialacross the main belt to shed light on their origin as locally-formed or subsequently-implanted and 2) to search for di ff eren-tiated fragments within asteroid families to constrain the levelof di ff erentiation in the interiors of larger parent asteroids.For Goal 1, we identify 155 A-type candidates and take mea-surements of 60 of them. New observations presented heremore than double the number of known A-type asteroids. Wepresent the spectra, determine the positive detection rate of A-type asteroids based on SDSS candidates, and calculate the totalexpected A-types according to their size distribution and mass.For Goal 2, we identify 69 candidates for di ff erentiated mate-rial within families and take measurements of 33 of them, 12 ofwhich do not overlap with the first set of observations.[Figure 1 about here.]
2. Observations
A major breakthrough towards e ffi cient spectroscopicsearching comes from the Sloan Digital Sky Survey (SDSS).SDSS has been in operation for over a decade with the pri-mary objective of imaging extragalactic objects (York et al.2000), but also catalogs the photometric measurements (u, g,r, i, z with central wavelengths 0.3551, 0.4686, 0.6166, 0.7480,and 0.8932 µ m.) of moving objects that pass through its field(Ivezi´c et al. 2001). Over one hundred thousand asteroids havebeen observed, many with multiple measurements. These mea-surements can be converted into spectral reflectance and can bewell-characterized by two single dimensions: i-z, which indi-cates the potential depth of a 1-micron absorption band, and slope (see work by Parker et al. 2008; Carvano et al. 2010; De-Meo and Carry 2013). While this low resolution and limitedwavelength range certainly cannot fully characterize a body’smineralogy, it provides enough information to filter for more in-teresting targets. Among the hundreds of thousands of (spectro-scopically) observable asteroids, finding unique or interestingobjects was previously like looking for a needle in a haystack.Searching with SDSS colors has been proven successful forbasaltic asteroids (e.g., Masi et al. 2008; Moskovitz et al. 2008;Du ff ard 2009) and for identifying hydration in asteroids (Rivkin2012). SDSS is a powerful tool that allows us to focus our ef-forts rather than conducting blind surveys.Candidate A-types were chosen among objects observed inthe Sloan Digital Sky Survey (SDSS) Moving Object Catalog(MOC). We use the fourth release (MOC4), including observa-tions prior to March 2007. A subset of these data is selectedbased on quality as described in DeMeo and Carry (2013).From this subset we create a list of objects with at least one ob-servation with gri-slope greater than 2.15 and less then 4.0 anda z-i value greater than -0.4 and less than -0.115 with class notequal to V (gri-slope and z-i are as defined in DeMeo and Carry(2013), see Fig 2 for a visual of the parameter space). The areadefined here is broader than for A-types in DeMeo and Carry(2013) to increase the number of potential candidates and toexplore the parameter space that is not classified. We visuallyinspected all of the observations from this list and remove ob-jects for which the data do not look accurate (for example onepoint is spuriously high, creating the false impression of a highgri-slope). We also remove objects for which there are manyobservations, and most of which are not A-type-like. Our fi-nal list includes 155 SDSS main-belt candidate A-types, 65 ofwhich have been observed multiple times. The full list is pro-vided in Supplementary Table 1 and plots of the SDSS colorsfor these candidates are provided in Supplementary Figure 1.The observational circumstances for the 60 asteroids measuredspectroscopically in this work are provided in Table 1.For the purposes of this statistical study we use the A-typeboundary limit described above. However, we took additionalobservations of A-type candidates outside of those bounds totest the boundary robustness. We measured 18 A-type candi-date spectra outside the formal boundaries and confirmed oneas an A-type Section 3.2. See Supplementary Table 2 and Sup-plementary Figures 2 and 3.[Figure 2 about here.] Using the same SDSS data and classifications as in the pre-vious section, we searched for A-type candidates and V-typecandidates within asteroid families. We used the membershipsfrom Nesvorn´y (2010) to identify strict family membership,although we did include observations of candidates that wereslightly outside of these boundaries, marked in the notes col-umn of Supplementary Table 3. We identified 69 candidates fordi ff erentiation in or near asteroid families based on either beingan olivine-rich (A-type) candidate or a basaltic candidate iden-tified by an indication of a deeper than typical 1-micron absorp-2ion band (classified as V, R, Q, or U). The U class stands for‘unusual‘ or ‘unclassifiable‘ and fell outside the boundaries ofour formal classification system but are still good candidates forthis work. We observed 33 candidates, 12 of which are uniqueto the family search, the others overlap with the full A-type dis-tribution search described in the previous section. Most targetswere in the Flora and Eunomia families. See Table 2 for obser-vational circumstances. Observations were taken on the 3-meter NASA Infrared Tele-scope Facility at the Mauna Kea Observatory. We use the in-strument SpeX (Rayner et al. 2003), a near-infrared spectro-graph in low resolution mode over 0.8 to 2.5 µ m.Objects are observed near the meridian (usually < ff erent positions (typically denoted A and B) ona 0.8 x 15 arcsecond slit aligned north-south. Exposure timesare typically 120 seconds, and we measure 8 to 12 A-B pairs foreach object. Solar analog stars are observed at similar airmassthroughout the night. We use the same set of solar analogs asthe SMASS program (Binzel et al. 2004, 2006) that have beenin use for over a decade. Uncertainties in spectral slope on theIRTF using these consistent set of stars at low airmass is esti-mated to be around 5% of the measured slope value. Observa-tions were taken in good weather conditions and observationsof other objects throughout the night provide confidence thatthere were no major systematic slope issues.Reduction and extraction is performed using the Image Re-duction and Analysis Facility (IRAF) provided by the NationalOptical Astronomy Observatories (NOAO) (Tody 1993). Cor-rection in regions with strong telluric absorption is performedin IDL using an atmospheric transmission (ATRAN) model byLord (1992). The final spectrum for each object is created bydividing the telluric-corrected asteroid spectrum by the averageof the telluric-corrected solar star spectra throughout that night.More detailed information on the observing and reduction pro-cedures can be found in Rivkin et al. (2004) and DeMeo andBinzel (2008). Observations were taken on the 6.5-meter Magellan Tele-scope at Las Campanas Observatory. We use the instrumentFolded-port InfraRed Echellette (FIRE; Simcoe et al. 2013) inhigh-throughput, low-resolution prism mode with a slit widthof 0.8 arcsecond oriented toward the parallactic angle. Expo-sures of 180 seconds were used for asteroids to avoid saturationdue to thermal emission from the instrument and telescope atthe long wavelength end (past 2.2 µ m).The readout mode sample-up-the-ramp was used for asteroidobservations requiring exposure times in multiples of 10.7 sec-onds. For stars readout mode Fowler 2 was used. Standard starschosen were a combination of well-established solar analogsused for the past decade in our IRTF program and newly mea-sured G2V stars that are dimmer and better suited for a larger,southern hemisphere telescope. Standard stars typically neededto be defocused to avoid saturation. Neon Argon lamp spectra were taken for wavelength calibration. Quartz lamp dome flatswere taken for flat field corrections. Observations and reductionprocedures are similarly described in DeMeo et al. (2014)For FIRE data reduction, we used an IDL pipeline designedfor the instrument based on the Spextool pipeline (Cushing et al.2004). Typically, sky correction is performed by AB pair sub-traction of images. In this case, because this slit is long (50”)we did not use an AB dither pattern and instead use nearby skyalong this list from the same exposure. The FIRE reductionpipeline is built for this sky subtraction method.[Table 1 about here.][Table 2 about here.]
3. Results
From three decades of asteroid spectral observations only ∼
15 A-type asteroids have been discovered, that have beenconfirmed to be olivine-dominated from near-infrared spectro-scopic measurements (e.g. Cruikshank and Hartmann 1984;Tholen 1984; Bus and Binzel 2002; de Le´on et al. 2004; DeMeoet al. 2009; Sanchez et al. 2014; Borisov et al. 2017; Polishooket al. 2017). In our survey we have detected 21 A-type asteroids(20 in the statistical work presented here, plus asteroid (11616)observed outside of the strict candidate boundaries) more thandoubling the number of known A-types. Spectra of the con-firmed A-types are plotted in Fig. 3. The survey spectra that arenot A-types are plotted in Supplementary Figure 4. We note thatone asteroid (1709) is extremely red with a deep 1-micron bandthat is typically characteristic of an A-type, however, the bandcenter is shifted shortward of 1.0 micron. We overplot it withan average A-type spectrum to highlight the spectral di ff erence.We prefer to keep our sample of A-types restrictive, thus weexclude (1709) from an A-type classification. In Fig. 4 we plotthe survey results in orbital space. The orbits of the confirmedand rejected candidates as well as the unobserved candidatesare shown. [Figure 3 about here.]We use the results of this survey to calculate the expectednumber of A-types throughout regions of the main belt. Over-all, we confirm 20 A-types out of 60 candidates, a 33% suc-cess rate. In fact, the success rate is the same for objects ob-served once and more than once by SDSS (14 /
42 for singly-observed and 6 /
18 for multiply observed objects), whereas forsimilar work for D-types (DeMeo et al. 2014) the success ratefor multiply-observed objects was higher (1 / / ≤ a < ≤ H < ± / ± + − A-types with H magnitude <
17 ( ∼ ∼
600 throughout therest of the paper.We calculate the frequency of A-types broken down by re-gion (Inner, Middle, Outer etc), semi-major axis bin, and size(H magnitude). The results are provided in Table 4. We findthat half of the ∼
600 A-types in the main belt with H < ≤ H <
17. A-types are roughlyevenly distributed throughout the 3 main regions of the mainbelt (inner, middle, and outer). There is no statistically signif-icant di ff erence between the 3 regions: the fraction of A-typesis 0 . + . − . % of the inner belt, to 0 . + . − . % of the middle belt,to 0 . + . − . % of the outer belt. The Hungaria and Cybele re-gions do not have many candidates, thus those results are moreuncertain.In Table 1 we list the albedo for any asteroid when avail-able in the literature. The average for A-types in our sampleis 0.28 ± .
09 and for comparison the average for S-types in oursample is 0.34 ± .
11. The average size of the bodies in thesetwo sets is around 5km, and both sets include 16 objects. Thealbedos of A-types are statistically indistinguishable from S-types in our dataset. [Figure 4 about here.][Table 3 about here.][Table 4 about here.]
We discovered an A-type (11616) 1996 BQ2 with a semi-major axis of 3.4 AU and inclination of 15 degrees, a locationthat places it within the Cybele region (3.3 ≤ a < ≤ a < We observed 33 A- and V-type candidates within or near as-teroid families. Twelve candidates are unique to this study andare not part of the general A-type distribution survey. The con-firmed A- and V-type spectra are plotted in Fig. 5. The full setof spectra are plotted in Supplementary Figure 5. A summaryof the results for each family is presented in Table 5. Note wedid not search for V-types in any families in the inner belt. Thepresence of the Vesta family and the large number of V-typesassociated with that family would make it di ffi cult to unam-biguously link a V-type in the inner belt with any other family.We find one V-type in the Eunomia family, asteroid (66905)(see Fig 5). We find one A-type asteroid, (17818), in the Gefionfamily, and one, (92516), near the Vesta family (although itis formally outside the family boundaries defined by Nesvorn´y(2010)). We find three A-types dynamically linked to the Florafamily, (16520), (139045), and (34969). Asteroid (16520) isalso dynamically within the Baptistina family. In Fig 6 we showa “butterfly” plot of the Flora family with semi-major axis andH magnitude showing how the family spreads in distance withsmaller size due to the Yarkovsky e ff ect (Burns et al. 1979; Bot-tke et al. 2006). Two of the three A-types are relatively small,making it more challenging to rule out that they could be in-terloper, background bodies. Family membership is more sub-stantively addressed in Section 3.4.We perform a statistical analysis of the di ff erentiated frag-ments confirmed within families to determine if the frequencywithin any family is significantly di ff erent than for the generalmain-belt A-type population determined from Sec 3.1. Resultsare provided in Table 5. Binomial statistics are calculated withn (number of trials), v (number of successes), and p (probabil-ity of success) where n is the family total number of objects, vis the estimated number of A- or V-types in the family roundedto a whole number, and p is 0.0016, calculated as the confirma-tion rate of A-types in the general main-belt population as 52 / < v).Even though the fraction of A-types in the Flora and Gefionfamily is higher than the general main-belt A-type population(0.41% and 0.57% respectively compared to 0.16%), we findthere is an 88.2% and 84.6% chance that there should be fewerA-types in the Flora and Gefion families respectively than wefind for the general A-type population. Neither of these resultsraise to the level of statistical significance, thus we find no com-pelling evidence for di ff erentiation within families.[Figure 5 about here.]4Table 5 about here.][Figure 6 about here.] A challenge in identifying di ff erentiation within families isthe ever-present potential for interlopers caused by the limita-tions of dynamical methods for distinguishing between familymembers and background objects, especially for large and oldfamilies (which are typically highly dispersed in orbital ele-ment space) in densely populated regions of the asteroid belt(Migliorini et al. 1995). The Flora family is a good exampleof such a challenging case, as it is located in a crowded re-gion of the inner asteroid belt near several other families, in-cluding the Baptistina, Vesta, Massalia, and Nysa-Polana fam-ilies (Dykhuis et al. 2014), is considered unusually dispersedin eccentricity and inclination relative to other asteroid families(Nesvorn´y et al. 2002), and is a ff ected by a number of nearby orcrossing dynamical resonances (Vokrouhlick´y et al. 2017). Assuch, membership lists for the Flora family constructed usingthe widely-employed Hierarchical Clustering Method (HCM)for family identification (Zappala et al. 1990, 1994) are sus-pected to have a significant fraction (perhaps as high as 50%)of interlopers from neighboring families and the backgroundpopulation (e.g., Migliorini et al. 1995; Dykhuis et al. 2014;Oszkiewicz et al. 2015).Consideration of compositional information, such as colorsor albedos, is often included in family classification e ff orts tohelp remove interlopers from lists of family members (e.g., No-vakovi´c et al. 2011; Masiero et al. 2013), under the assump-tion that family members should be relatively compositionallyhomogeneous having originated from the same parent body,assuming that the parent body itself was compositionally ho-mogeneous (e.g., Ivezi´c et al. 2002; Cellino et al. 2002). Byremoving compositional outliers, however, this approach thennecessarily limits our ability to search for taxonomic variabilityamong objects considered to be “true” members of a particularfamily.To assess the likelihood independent of compositional con-siderations that the A- and V-type objects that we find within ornear asteroid families could be interlopers, we perform a simpleanalysis based on dynamical methods and considerations alone.Focusing on the Flora family, where we find three A-type aster-oids among the family members we observed, we perform dy-namical integrations of all 12 Flora family members we studiedand an additional twenty of the lowest numbered asteroids inthe family to characterize their dynamical behavior over time.We generate four dynamical clones per object, which combinedwith each original object, gives a total of five test particles perobject, where the dynamical clones are Gaussian-distributed inorbital element space (characterized by σ values of 1 × − AUfor semimajor axes, 1 × − for eccentricities, and 1 × − ◦ forinclinations) and centered on each object’s osculating orbital el-ements as of 2017 January 1. The sigma values for the clonesare very conservative. For example asteroid (139045) has 1sigma errors on a, e, i of 1 × − , 4 × − , and 6 × − , respec-tively, orders of magnitude smaller than assumed here. We then perform forward integrations for 100 Myr using the Bulirsch-St¨oer integrator in the Mercury numerical integration softwarepackage (Chambers 1999). We include the gravitational e ff ectsof all eight major planets and treat all test particles as massless.Non-gravitational forces are not considered in this analysis.We find that all test particles associated with observed Florafamily members remained stable against ejection from the so-lar system (defined as occurring when the semimajor axis, a ,of an object exceeds 100 AU) over the entire integration pe-riod. One dynamical clone of one of the A-type asteroids foundin the family (16520) underwent an excursion in semimajoraxis of ∆ a ∼ .
025 AU over the course of the integration,but all other test particles associated with A-type asteroids re-mained extremely stable, undergoing maximum excursions of ∆ a < .
005 AU. The vast majority of the other test particlesassociated with observed Flora family members exhibited sim-ilar stable behavior, although three dynamical clones of non-A-type asteroids underwent relatively large excursions in semi-major axis ( ∆ a > .
05 AU) over the course of the integra-tions. Meanwhile, all test particles with the exact osculatingelements of the 20 low-numbered Flora family members thatwe did not observe also remained stable over the duration ofour integrations, although nine of the dynamical clones of theseobjects were ejected during our integrations. We construct con-tour plots showing the relative density of intermediate positions(in time steps of 10,000 years) in orbital element space overthe duration of our integrations occupied by all test particles(i.e., original objects and dynamical clones) associated with thethree A-type asteroids found in the Flora family, as well as (8)Flora itself for reference. We find the dynamical evolution of allthree A-type asteroids to be qualitatively similar to that of Floraas well as most of the other Flora family members for which wealso performed dynamical integrations.[Figure 7 about here.]Long-term dynamical stability does not necessarily guaran-tee that an object is a true member of an asteroid family, asthere is no a priori condition that requires members of asteroidfamilies to be dynamically stable. However, if we had foundshort dynamical lifetimes for the A-type asteroids we find in theFlora family, it would have suggested that these objects werelikely to have been recently delivered to their current locations,therefore increasing the likelihood that they could be interlop-ers, especially if other members of the family are significantlymore dynamically stable. That said, given the numerous dy-namical resonances that cross the region, even true members ofthe Flora family may currently have short dynamical lifetimesdue to the Yarkovsky e ff ect nudging them towards more unsta-ble regions over time. Indeed, nearly 50% of Flora family mem-bers identified by Nesvorny (2015), including one of the A-typeasteroids we found in the family (16520), have Lyapunov timesof t ly <
100 kyr (typically the threshold under which an objectis considered dynamically unstable), according to a syntheticproper element catalog retrieved from the AstDyS website on http://hamilton.dm.unipi.it/astdys/ t ly values that are anomalous for the fam-ilies with which they are associated (Figure 8). As such, whilethese results should not be regarded as definitively establishingthat these objects are true members of their respective fami-lies, we nonetheless conclude for now that we find no anoma-lous dynamical behavior with respect to other family membersthat might suggest that these objects are likely to be interlop-ers. As such, we conclude for now that we find no anomalousdynamical behavior with respect to other family members thatmight suggest that these objects are likely to be interlopers. Wenote though that Yarkovsky drift could cause family membersto eventually evolve onto orbits similar to those of a nearbyA-type background object, or vice versa, thus making the fam-ily members and the A-type object e ff ectively indistinguishablefrom each other using dynamical criteria, even though the A-type object is an interloper. Therefore, as before, while theseresults are suggestive, they should not be interpreted as defini-tively establishing that these objects are true members of theirrespective families. [Figure 8 about here.]More sophisticated methods have been employed in attemptsto distinguish true members of a family from interlopers, suchas the modeling of the dynamical evolution (including theYarkovsky e ff ect) of suspected interlopers from their assumedorigin points (e.g., Carruba et al. 2005), or the use of a fam-ily’s “core” in orbital elements (where the fraction of interlop-ers is assumed to be relatively low) to establish the range ofreflectance properties of the family before expanding consider-ation to the rest of the family (e.g., Dykhuis et al. 2014). If andwhen individual interlopers can be reliably identified, an au-tomated method has also been developed to remove additionalassociated interlopers that were linked to the family through theuse of HCM via “chaining” through the initially identified in-terloper (Radovi´c et al. 2017). Such detailed analyses of eachof the families we studied here is beyond the scope of this work,particularly given the low incidence of A-type asteroids foundin the families we studied, and thus the minimal evidence ofdi ff erentiation in those families. Nonetheless, in the event thatstronger evidence of di ff erentiation in these or other families isfound in the future, these methods may be worth considering toensure that any compositional diversity found within a familyis truly due to di ff erentiation of the parent body and not subse-quent contamination by interlopers. Correcting for observational incompleteness is beyond thescope of this work. However, here we explain the completenessfactors to consider. These questions include 1) How complete isthe SDSS at a given H magnitude? 2) How complete is the MPCat the same magnitude? 3) How does one account for the factthat a 2 km body has a di ff erent average H magnitude depend-ing on its taxonomic class? In DeMeo and Carry (2013) andDeMeo and Carry (2014) an upper H magnitude limit of 15.5was chosen because the SDSS survey was sensitive to even thedarkest asteroid class at that magnitude.In this work we are pushing down to 2 km (H ∼ ∼ ff erently incomplete for eachclass.For example, the SDSS is biased towards observing the high-albedo A-types over the darker classes. Therefore, we are over-estimating the fraction of A-types relative to other classes inSDSS, excluding the inner main belt which is sensitive down toH = ff ect when we apply the fractions from SDSS to the MPCnumbers to determine the total number of A-types at each dis-tance and size range. For example, in 2013 we estimated that inthe H =
4. Discussion
Overall, we find A-types well distributed throughout themain belt in distance and inclinations suggesting there is nosingle main-belt common origin. In Fig. 9 we show the num-ber of A-types as a function of size and of semi-major axis.Even though A-types are more numerous at smaller sizes, theyremain generally the same fraction of the population - as thepopulation increases at smaller sizes so does the number of A-types. We also look at how the A-type sample is distributedacross the main belt compared to the S- and C-types. A sim-ilar distribution could indicate a similar delivery mechanism.For S and C we use the number of bodies in each bin from theSDSS dataset classified by DeMeo and Carry (2013), and cal-culate the fraction by dividing by the total number of S and Cfor each sample (bounded by H magnitude, main-belt region, orsemi-major axis) such that the percentage of each type sums to100% over the whole region. For the main-belt regions, the dis-tribution of A-types is generally consistent with that of S-types,although the A-type distribution is flatter since S-types peak inthe middle belt. The A-type distribution is not consistent withthe C-types that make up only a small fraction of the inner beltand increase dramatically, peaking in the outer belt.[Figure 9 about here.]6ost of the mass of A-types ( > kg.See Ga ff ey et al. (2015) for an in-depth spectral analysis ofEleonora. We show the mass of A-types in each size range inFig. 10. The total mass of A-types we find here is comparableto that calculated in DeMeo and Carry (2013) that uses densi-ties from Carry (2012), and di ff erences can be attributed to theassumptions for density and diameter for the mass calculationand to a better understanding of the false positive rate. For thesize range we sample in this survey (12 ≤ H <
17 or diame-ters of approximately 2 ≤ D <
12 km), the total A-type mass inthe main belt (according to asteroids discovered through Jan-uary 2018) is 3 x 10 kg, two orders of magnitude less thanEleonora itself. In our sample alone, the mass distribution foreach H magnitude bin is 35, 28, 20, 12 and 5% respectively forH =
12, 13, 14, 15, 16.The focus of this paper is on implications for di ff erentiationamong small bodies, however, not all olivine-dominated bodiesare di ff erentiated (Burbine 2014). A nebular (primitive) originis expected for bodies with ferroan olivine compositions (fay-alite Fe SiO ), and a magnesian olivine (forsterite Mg SiO )composition indicates di ff erentiation. Using a Modified Gaus-sian Model (MGM) Sunshine et al. (2007) studies 9 large A-type asteroids measuring the 1- µ m band parameters. She finds7 of 9 in her study are di ff erentiated and 2 of 9 (289 Nenettaand 246 Asporina) are of nebular origin. This indicates thatonly 80% of A-types are di ff erentiated, and any estimate of ac-tual di ff erentiated material should be corrected by this factor.Future work will perform similar models of the spectra fromthis survey to better constrain the fraction that are di ff erentiatedversus nebular. The overall results we find here should remainqualitatively the same and general conclusions still valid evenif a fraction are found to be primitive.[Figure 10 about here.] In a visible-wavelength survey (Perna et al. 2018) of near-Earth objects Popescu et al. (2018) detected 8 A-type objectsout of a sample of 147. DeMeo et al. (2009) find in their spectralsample that 50% of visible-wavelength A-types remain A-typewith near-infrared data (see Table 3 from that work). Even fac-toring in a lower success rate the number of A-types in the workby Popescu represents ∼ >
20. Even though the MITHNEOS samplespans a broader H range (primarily between 16 ≤ H < >
20 is 162, com-parable to that of Popescu et al. (2018). MITHNEOS observedone of the A-type NEOs in Popescu et al.’s sample (444584) which was classified as an Sq-type based on diagnostic near-infrared data.Six asteroids in MITHNEOS were classified as A- or Sa-type. Four of those classifications - for asteroids (6053),(275677), (366774), and 1993 TQ2 - were based on visible-wavelength data, two with spectra and two with colors ((Binzelet al. 2004; Ye 2011; DeMeo and Carry 2013; Kuroda et al.2014)). Two asteroids, (5131) and 2014 WQ201, with near-infrared spectra are classified as Sa in Binzel and DeMeo (tted).The quality of the data for 2014 WQ201 was poor and had itbeen a part of this survey it would not have been classified asconfidently olivine-dominated. Our preferred calculation, in-cluding (5131) and excluding 2014WQ201 based on data qual-ity results in an olivine-dominated percentage of the NEO popu-lation of 0.14% (1 / >
20 to be consistent with (Popescuet al. 2018) is 1 /
162 or 0.6%.Among the Mars Crossers in the MITHNEOS data set (1951)Lick is a well-studied A-type (de Le´on et al. 2004). Onemore near-infrared spectrum was classified as A-type, asteroid(367251), however, the quality of this spectral data was verypoor. Two additional Mars Crossers were classified as A- orSa-type base on visible-wavelength data originally published inBinzel et al. (2004).A-types have also been discovered in the Mars Trojan popu-lation. Asteroid (5261) Eureka has been known to have a uniquespectrum (Rivkin et al. 2007), and even though it has the char-acteristic red spectrum and wide, deep 1- µ m absorption bandof an A-type it is distinct from all other A-types because the 3minima of the 1 µ m band are deeper making the whole featuremore bowl-shaped than V-shaped. Borisov et al. (2017) andPolishook et al. (2017) performed near-infrared spectroscopicmeasurements of a few other Mars Trojans in the same cloudand found that a number of them had spectra similar to that ofEureka, suggesting they are a mini-family and are fragmentsof a parent body that may have been disrupted in that location.Polishook et al. (2017) put forth the theory that these fragmentscould have originated from Mars itself, following a large impact(such as the one that formed the Borealis basin) that excavatedolivine-rich material from the Martian mantle. Their dynamicalmodel also showed that A-types found in the Hungaria familymight also have resulted from that same impact. Given that the meteorite record suggests there existed ∼ ff erentiated parent bodies, it has been surprising no evidencefor significant di ff erentiation of asteroids and within asteroidfamilies has been seen. The photometric colors and albedos ofthe ∼
100 known asteroid families (Nesvorn´y et al. 2015; Mi-lani et al. 2014) tend to be very homogeneous (Parker et al.2008; Masiero et al. 2011). Through spectroscopic investiga-tion, however, a number of families have been identified asremnants of di ff erentiated parent bodies: Vesta (McCord et al.1970; Consolmagno and Drake 1977; Binzel and Xu 1993),7erxia, Agnia (Sunshine et al. 2004; Vernazza et al. 2014),Maria (Fieber-Beyer et al. 2011) and Hungaria (Ga ff ey et al.1992; Kelley and Ga ff ey 2002). Two families have been identi-fied as candidates for at least partial di ff erentiation: Eos and Eu-nomia. The Eos family was found to have mineral compositionsconsistent with forsteritic olivine (Moth´e-Diniz and Carvano2005; Moth´e-Diniz et al. 2008). Other studies, however, haveshown Eos more closely resembles CO and CV carbonaceouschondrite meteorites (Bell 1988; Doressoundiram et al. 1998;Clark et al. 2009). The Eunomia family has been linked to par-tial di ff erentiation by Nathues et al. (2005); Nathues (2010).For a review of the physical properties of asteroid families seeMasiero et al. (2015)In this work, we find very little evidence for full di ff erentia-tion in families in the classical sense of forming a basaltic crust,olivine-rich mantle, and iron core. There were very few olivine-rich candidates available to survey to begin with, and most ofthose candidates were found to be false positives. The Merxiaand Agnia families, for example, that are suggested to be can-didates for di ff erentiation, had 64 and 91 members with SDSScolors, respectively, with 0 and 6 di ff erentiated candidates ineach. None of those 6 candidates were observable in our sur-vey. The Flora family is the only one with multiple “mantle”fragments, but their presence within the Flora family is not sta-tistically distinct from the background A-type population. There are four broad explanations for why we do not see anabundance olivine-dominated (or basalt-rich) bodies within themain belt: These bodies 1. were ground down to sizes belowour observational threshold in the “battered to bits” theory (Bur-bine et al. 1996), 2. are masked as another spectral type due tosurface processes such as space weathering. 3. formed early inthe terrestrial planet region and fragments were later implantedinto the Main Belt, or 4. our understanding of asteroid di ff eren-tiation is incomplete and a thick olivine-rich mantle may not becommonly formed.We have established that there is no significant unknownmantle material in the main asteroid belt down to diameters of ∼ ff ect the sur-faces of asteroids, and thus change their interpreted composi-tion from spectral measurements. Space weathering is one ofthe more common processes a ff ecting the surfaces of airlessbodies. Bombardment by high-energy particles and microm-eteorites causes chemical changes to the surface material thatproduces a variety of changes in the measured properties suchas changes in albedo as well as spectral band depth and spec-tral slope (for a review, see Clark et al. 2002; Chapman 2004;Brunetto et al. 2015). The continuum of the spectrum of olivineis neutral, whereas the A-type asteroids we measure have someof the reddest slopes in the inner solar system. This redden-ing e ff ect has been reproduced in irradiation laboratory exper-iments that mimic the space environment (Sasaki et al. 2001;Brunetto et al. 2006). While the prominent one-micron absorp-tion band becomes less pronounced after irradiation, it remainsclearly identifiable. Shock darkening from collision is anotherprocess that a ff ects the surfaces of asteroids (Britt and Pieters1989; Reddy et al. 2014; Kohout et al. 2014). While shock-ing has been seen to darken the surfaces of ordinary chondritemeteorites to the point where the absorption band is severelydepressed, it is not clear that this is a common process is in theasteroid belt or that it would act globally across multi-kilometerbodies. The fact that significant spectral diversity exists in themain belt and that collisions for multi-kilometer bodies are rel-atively rare suggests that while this is a notable process, it doesnot a ff ect the majority of asteroids. Given these arguments, it isunlikely that a large population of olivine-dominated materialis spectrally hidden within another class of objects.The third explanation for the dearth of A-types is that dif-ferentiated planetesimals did not form in the Main Belt. In-stead, they formed early in the terrestrial planet region at apoint where the abundance of Al was high. Thermal mod-eling of some iron meteorite parent bodies that were heated by Al finds that these objects could have accreted less than 0.4million years after the formation of CAIs (Calcium AluminumInclusions) (Kruijer et al. 2017), the earliest condensates in theSolar nebula. In this tumultuous early period in Solar Systemhistory, collisions were much more frequent. Mantles could bestripped from their cores in events such as low-velocity hit-and-run collisions (Asphaug and Reufer 2014; Scott et al. 2015).Any fragments that survive these collisions would then needto be implanted into the Main Belt to remain on stable orbitsto be observed today. Three dynamical scenarios have beenproposed to achieve implantation: 1. gravitational scatteringamong planetary embryos (Bottke et al. 2006), 2. the GrandTack planetary migration period (Walsh et al. 2011, 2012), and3. the Nice Model planetary migration period (Morbidelli et al.2005, 2015; Scott et al. 2015). See the discussion by Scott et al.(2015) in
Asteroids IV as dynamical implantation is their pre-8erred scenario. Each of these methods may produce a di ff erentimplantation signature, and our constraint of a uniform distri-bution may help distinguish among dynamical models.Finally, it is also possible that iron meteorite parent bodieseither did not form extensive olivine mantles or di ff erentiationis hidden by a primitive crust that is still preserved. Elkins-Tanton et al. (2011) modeled that partial di ff erentiation of chon-dritic material could create a di ff erentiated interior with an un-heated crust. Asteroid (21) Lutetia is a candidate for this sce-nario because it has surface spectral properties consistent with achondritic composition, but it has a high bulk density measuredby the Rosetta mission. Work by Weiss et al. (2012) attributethis to internal di ff erentiation, although Vernazza et al. (2011)suggest Lutetia’s spectral and physical properties are consistentwith the primitive meteorite class enstatite chondrites. Giventhe spectral homogeneity of asteroid families that essentially al-low us to probe the interior of larger parent bodies, it is not clearthat this type of partial di ff erentiation is common in the asteroidbelt. Dawn observations of (4) Vesta have found no evidence foran olivine-dominated mantle. Large impact craters on Vesta’sSouth Pole, which could have excavated down to depths of 60-100 km (Clenet et al. 2014), did not expose significant amountsof olivine (Ammannito et al. 2013). Clenet et al. (2014) findsthat the crust-mantle boundary is deeper than 80 km. The rangeof Mg compositions of olivine in howardites (Lunning et al.2015), which are believed to be fragments of Vesta, are consis-tent with forming through partial melting (e.g., Wilson and Keil2012) and not with full-scale melting in a whole-mantle magmaocean.A recent model of di ff erentiation of Vesta-sized bodies ar-gues that olivine-dominated mantles would not form (Elkins-Tanton et al. 2014). These models finds that the first crys-tallizing mineral would be olivine, which would settle to thecore-mantle boundary. Samples of these core-mantle bound-aries would be pallasites. However, due to the high viscosityof the molten mantle, only the earliest-forming crystals withsizes of several cm would settle. The remaining mantle mate-rial would then solidify in bulk and not result in the significantaccumulation of olivine crystals (Scheinberg et al. 2015). The large survey data publicly available today such as SDSS(York et al. 2000; Ivezi´c et al. 2001), WISE (Mainzer et al.2011; Masiero et al. 2011), and VISTA (McMahon et al. 2013;Popescu et al. 2016) with tens to hundreds of thousands ob-servations have greatly advanced our ability to characterize themain-belt population as a whole and to focus in on finer de-tails of the compositional structure of the main belt. We expectupcoming surveys will provide equally if not even greater in-sight through larger numbers of observations and better qual-ity data. These include Gaia (Gaia Collaboration et al. 2016),Euclid (Carry 2018), and LSST (LSST Science Collaborationet al. 2009). For questions related to olivine-dominated mate-rial and di ff erentiation, we will look to these surveys to identifymore candidates at broader locations and smaller sizes than pre-viously available. By providing orders of magnitude improvement on the ac-curacy of orbits, and visible spectra for 300,000 asteroids(Mignard et al. 2007) Gaia will allow minute identification offamily members, helping identifying interloper and opening thedoor to extensive searches of in-homogeneity in parent bodiesof families.The LSST is expected to discover millions of main-belt as-teroids, and hundreds of thousands of NEAs. With multi-band photometry in a set of filter similar to that of the SDSS,broad compositional classification will be possible, pushing ourknowledge to smaller sizes, and allowing a clear link to be es-tablished between the NEA and their source regions in the MB.The apparent contradiction of small samples of NEA as men-tioned here should vanish in the LSST era.However, both surveys will operate in the visible only. Asshown here, the ambiguity in spectral classification will af-fect both, and near-infrared data will be crucial to identify raremineralogies such as the olivine-rich A-types discussed in thepresent study. The ESA mission Euclid, to be launched in 2020,is expected to observe about 150,000 small bodies (mainly MB)over its six-year mission, in the visible and three infrared broad-band filters, enabling additional compositional investigations(Carry 2018).
5. Conclusion
The main findings and conclusions of this work are • We confirm 21 A-type asteroids distributed throughoutthe main belt including the discovery of A-type asteroid(11616) in the Cybele region. We find 0.16% of the mainbelt is A-type, a very small fraction. We also rea ffi rm thatthere is no significant undiscovered olivine-dominated ma-terial down to ∼ • The fraction of A-types in the main belt is strikingly sim-ilar to what is found in the NEO population in the surveyby (Binzel and DeMeo tted) which ranges from 0.1-0.6%depending on the data included. • We estimate the total number of A-types in the main beltdown to ∼ ∼ > ≤ H < • The distribution as a function of semi-major axis is rela-tively flat. This flat distribution does not support a locally-formed theory as they span a wide semi-major axis rangeacross the belt where the dominant type transitions dramat-ically from S to C to P. Instead, the results are more in linewith the theory that these fragments were later implanted. • While we find 6 A- and V-type bodies dynamically asso-ciated with families, we find no statistically significant ev-idence that there has been di ff erentiation in these families,at least in the canonical sense of forming a basaltic crust,olivine-rich mantle, and iron-rich core. This work supports9vidence that asteroids in the main belt are generally notdi ff erentiated and that di ff erentiated material did not formlocally within the main belt. Acknowledgments
Observations reported here were obtained at the NASA In-frared Telescope Facility, which is operated by the Universityof Hawaii under Cooperative Agreement NCC 5-538 with theNational Aeronautics and Space Administration, Science Mis-sion Directorate, Planetary Astronomy Program. This paper in-cludes data gathered with the 6.5 meter Magellan Telescopeslocated at Las Campanas Observatory, Chile. We acknowledgesupport from the Faculty of the European Space AstronomyCentre (ESAC) for FD’s visit. DP is grateful to the AXA re-search fund. This material is based upon work supported by theNational Aeronautics and Space Administration under GrantNo. NNX12AL26G issued through the Planetary AstronomyProgram and by Hubble Fellowship grant HST-HF-51319.01-A awarded by the Space Telescope Science Institute, which isoperated by the Association of Universities for Research in As-tronomy, Inc., for NASA, under contract NAS 5-26555. MITresearchers performing this work were supported by NASAgrant 09-NEOO009-0001, and by the National Science Foun-dation under Grants Nos. 0506716 and 0907766. HHH ac-knowledges support from NASA Solar System Workings pro-gram 80NSSC17K0723. THB would like to thank the Remote,In Situ, and Synchrotron Studies for Science and Exploration(RIS4E) Solar System Exploration Research Virtual Institute(SSERVI) for support. Any opinions, findings, and conclusionsor recommendations expressed in this article are those of theauthors and do not necessarily reflect the views of the NationalAeronautics and Space Administration. 10 eferences
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Roughly half of all visible-data-only A-types are proven to be olivine-rich with near-infrared data (DeMeo et al. 2009) while the statistics arecloser to 9 in 10 for basalt-rich V-types (Moskovitz et al. 2008). This figure is modified from the original version in DeMeo (2007). igure 2: This plot shows the taxonomic boundaries for SDSS data defined in DeMeo and Carry (2013). Our A-type candidates are marked as triangles. Yellowtriangles were either not observed or observed and were not A-type. Green squares are confirmed A-types. We include candidates outside the formal boundaries ofA-types, because of their high slopes and indication of a 1-micron absorption band. igure 3: Plot of confirmed A-types based on near-infrared spectral measurements from this work. SDSS colors are plotted as red dots with red error bars. Thespectra are plotted in black. The gray region, overplotted on one spectrum, bounds plus and minus one sigma from the mean of the A-type class defined by DeMeoet al. (2009). Asteroids (16520), (17818), (34569), (92516), and (139045) are dynamically associated with asteroid families and are discussed further in Sec. 3.3. igure 4: Orbital distribution of A-types in the main belt. The top panel includes all candidates and survey results, the bottom panel shows only true A-type (olivine-dominated) bodies to highlight their locations. A sample of MBAs are plotted in gray to illustrate the orbital structure of the belt. SDSS candidates are plottedas black open circles. Green solid circles indicate A-types that have been confirmed with near-infrared data. Red X marks objects with follow up observationsthat do not classify as A-types. Previously known A-types are plotted as open green circles. It is apparent that A-types exist at all regions of the belt even at highinclinations. We note there is even an A-type past 3.3 AU in the Cybele region where even S-complex asteroids are rare (Sec. 3.2). This object, (11616) 1996 BQ2,was discovered in this work as part of the candidates that were outside of the boundaries used for the statistical work here. igure 5: Left: Spectrum of an observed V-type with an orbit within the Eunomia family (Sec. 3.3). The spectra of confirmed A-types within families are plottedwithin Fig. 3. The spectra of all observed candidates, including false positives are provided in Supplementary Figure 5. Right: Asteroid (11616) is an A-typediscovered within the Cybele region of the asteroid belt (Sec. 3.2). This asteroid was part of the set of observations of potential A-types that were not within theformal A-type candidate boundaries. igure 6: Plot of the Flora family as semi-major axis versus H-magnitude (top), proper eccentricity (middle), and proper inclination (bot). Gray dots are Florafamily members defined in Nesvorn´y (2010), red letters are the classifications of bodies observed in this work. igure 7: Contour plots (black lines) showing the relative density of intermediate positions (in time steps of 10,000 years) in orbital element space occupied byall test particles (i.e., original objects and dynamical clones) associated with A-types (a) 16520, (b) 34969, (c) 139045, and (d) (8) Flora (the largest member andnamesake of the Flora family) during the 100 Myr integrations described in the text. The left panel of each set of plots shows wide views (in terms of semimajor axisrange) of each object’s dynamical evolution with respect to the entire Flora family (synthetic proper elements for all family members identified by Nesvorny (2015)plotted with small gray dots for reference) and the right panel shows more detailed views of the regions of orbital element space occupied by the test particles foreach object during the integrations. Darker shaded blue areas indicate higher densities of intermediate orbital element positions. igure 8: Histograms of Lyapunov times in kyr from the AstDyS website for asteroids identified as members of the Eos, Eunomia, Flora, Gefion, Nysa-Polana,and Vesta families, as labeled, by Nesvorny (2015). Lyapunov times for A-type asteroids found in the Flora, Gefion, and Vesta families and the V-type asteroidfound in the Eunomia family in this work are marked with vertical line segments and numerical labels. Other vertical line segments mark Lyapunov times for otherfamily-associated objects observed in this work. igure 9: Top: The fractional distribution of the number of A-, S-, and C-types in each bin for H magnitude, region of the belt, and semi-major axis bin. For themain-belt regions, the distribution of A-types is generally consistent with that of S-types, although the A-type distribution is flatter, and is not consistent with thedistribution of C-types. Bottom Left: The expected number of A-types in the main belt in each H magnitude bin. Bottom Right: The expected number of A-typesgreater than ∼ <
17) as a function of semi-major axis. igure 10: The mass and number of A-types in each H magnitude range. The single largest A-type (354) Eleonora accounts for over 80% of the mass of all A-typeasteroids. However, the interior of an asteroid may not be representative of the spectrally measured exterior, particularly for a body as large as Eleonora. WhileA-types are most numerous at smaller sizes, with about half of them in the smallest size bin (16 ≤ H < ist of Tables able 1: Observational Circumstances and Taxonomic Results for the Survey of A-type Candidates Asteroid Designation Telescope Date Phase V H Albedo Albedo a Obs. (SDSS) (This Survey)1709 Ukraina IRTF 2011 / /
07 17.9 17 12.8 0.123 ± .
006 1 2 A,U S2036 Sheragul IRTF 2011 / /
06 24.9 17.2 12.7 0.300 ± .
044 1 4 A,U,V,S S2234 Schmadel IRTF 2012 / /
23 20.6 17.2 12.2 0.284 ± .
016 2 1 A R3385 Bronnina IRTF 2012 / /
16 11.5 15.3 12.3 0.363 ± .
081 2 2 A,S S3573 Holmberg IRTF 2012 / /
14 3 15.8 12.9 0.343 ± .
028 3 2 A,S S6067 1990 QR11 IRTF 2012 / /
20 18.7 17.3 11.5 0.256 ± .
060 2 1 A S7057 1990 QL2 IRTF 2011 / /
01 20.3 16.9 13.6 0.41 ± .
15 4 1 A S7172 Multatuli IRTF 2012 / /
21 7.4 17.9 13.9 0.353 ± .
035 3 1 A S8838 1989 UW2 IRTF 2011 / /
01 14.1 16.6 11.4 0.239 ± .
023 2 9 9A A9404 1994 UQ11 IRTF 2012 / /
17 9.6 17.4 13.4 0.300 ± .
061 2 1 A S / L10715 Nagler IRTF 2013 / /
19 31 17.2 13.4 0.309 ± .
040 2 2 A,A A10977 Mathlener IRTF 2012 / /
20 1.2 17.1 14.9 0.327 ± .
092 2 1 A A11589 1994 WG Magellan 2011 / /
24 5.1 17.4 12.5 4 4A S11952 1994 AM3 IRTF 2012 / /
17 1.9 17 14.1 0.210 ± .
051 2 2 S,A S13577 Ukawa IRTF 2012 / /
22 6.9 17.4 14.8 1 A S13724 Schwehm IRTF 2012 / /
15 1.4 16.4 14.1 0.474 ± .
233 2 2 S,A S13816 Stulpner Magellan 2012 / /
28 13.3 18.1 14.2 3 2A,S S16520 1990 WO3 IRTF 2012 / /
23 2.7 17 14.2 0.325 ± .
178 2 4 3A,S A17375 1981 EJ4 Magellan 2013 / /
10 12.9 18.9 13.8 0.382 ± .
102 2 3 2S,A S17716 1997 WW43 IRTF 2013 / /
19 4.3 17.4 15.1 0.434 ± .
142 2 1 A S17818 1998 FE118 IRTF 2012 / /
20 18.4 17.4 12.9 0.217 ± .
040 2 1 A A17889 Liechty IRTF 2013 / /
17 8.1 17.5 14 0.481 ± .
190 2 1 A A18853 1999 RO92 IRTF 2013 / /
17 7.7 18.6 13.6 0.302 ± .
049 2 1 A A19312 1996 VR7 IRTF 2013 / /
01 10.7 18.6 14.8 1 A S19570 Jessedougl IRTF 2011 / /
01 10.8 17 13.2 1 A S19652 Saris IRTF 2012 / /
29 2.8 17.6 14 0.242 ± .
010 2 1 A A21646 Joshuaturn IRTF 2012 / /
22 6.7 18.4 14.4 0.289 ± .
128 2 1 A X21809 1999 TG19 IRTF 2012 / /
14 2.2 17.5 14 0.168 ± .
036 2 1 A A24673 1989 SB1 IRTF 2012 / /
22 10 17.3 13.9 0.355 ± .
048 3 1 A S27791 Masaru IRTF 2011 / /
01 15.8 17 14 0.565 ± .
095 2 1 A S29731 1999 BY2 IRTF 2011 / /
01 11.2 17.4 14.1 1 A S31393 1998 YG8 IRTF 2012 / /
23 2.8 17.3 14.8 0.467 ± .
116 2 1 A A33745 1999 NW61 IRTF 2011 / /
30 12.3 16.8 13.9 1 A S / Q34969 4108 T-2 Magellan 2013 / /
10 23.9 20.6 15.7 1 A A35102 1991 RT IRTF 2012 / /
16 9.9 16.9 14.6 2 S,A S35925 1999 JP104 IRTF 2011 / /
08 4 17.1 13.9 0.176 ± .
020 2 1 A A36256 1999 XT17 IRTF 2012 / /
20 10.8 17.3 12.5 0.186 ± .
033 3 1 A A39236 2000 YX56 Magellan 2013 / /
12 17.8 19.9 15.3 0.102 ± .
017 2 1 A C40573 1999 RE130 IRTF 2012 / /
23 12.9 17.9 13.5 0.319 ± .
033 2 1 A S44028 1998 BD1 IRTF 2013 / /
19 18.9 18.5 13.3 1 A S52228 Protos Magellan 2012 / /
11 20.7 19.1 13.6 0.271 ± .
176 2 1 A A59115 1998 XG3 IRTF 2013 / /
01 26.6 19.1 15.1 1 A S60631 2000 FC26 IRTF 2013 / /
01 7.5 18.7 14.5 0.218 ± .
074 2 1 A A75810 2000 AX244 IRTF 2012 / /
20 5 17.9 14.8 0.275 ± .
067 2 2 A A77653 2001 KH72 IRTF 2013 / /
18 6.2 18.2 13.9 1 A S81850 2000 KL60 IRTF 2013 / /
19 19.1 17.5 14.9 0.217 ± .
048 2 1 A S87812 2000 SL146 Magellan 2011 / /
24 21.7 18.9 14.4 2 A,X X91450 1999 RV24 IRTF 2012 / /
16 13.2 17.1 15.7 2 S,A S92516 2000 ND25 IRTF 2012 / /
20 4.7 17.6 14.8 2 S,A A95560 2002 EX98 IRTF 2014 / /
11 17.9 18.7 14.2 0.294 ± .
075 2 1 U A97335 1999 YF IRTF 2013 / /
17 8.4 17.7 16.5 1 A S98082 2000 RJ67 Magellan 2013 / /
09 14 19.9 15.5 1 A X105840 2000 SK155 IRTF 2011 / /
01 3.7 17.7 14.2 2 A A108209 2001 HS28 Magellan 2012 / /
11 18.5 19 16.1 1 A S111186 2001 WA8 IRTF 2013 / /
19 15.3 18.8 15.4 1 A C125739 2001 XH116 Magellan 2013 / /
11 17.3 20.3 15.7 1 U S139045 2001 EQ9 Magellan 2012 / /
12 15.9 18.4 15.9 1 A A175158 2005 EM66 IRTF 2013 / /
19 11.3 18.3 16.5 1 A S188330 2003 OU8 Magellan 2012 / /
31 5.3 19.3 13.8 0.284 ± .
086 2 1 A S200832 2001 XC238 Magellan 2013 / /
09 10.2 18.5 15.8 1 A S a
1: Usui et al. (2011) http://darts.jaxa.jp/astro/akari/catalogue/AcuA.html
2: Masiero et al. (2011) http://cdsarc.u-strasbg.fr/viz-bin/Cat?J/ApJ/741/68
3: Masiero et al. (2012) http://cdsarc.u-strasbg.fr/viz-bin/Cat?J/ApJ/759/L8
4: Nugent et al. (2015) able 2: Observational Circumstances and Taxonomic Results for the Survey of Family Candidates Family Asteroid Designation Telescope Date Phase V H a Class Ref b Number or Name (UT) Angle (deg) Mag Mag Obs. (SDSS) (This Survey)Eos 1297 Quadea Magellan 2 / /
13 2.9 15.1 10.9 4 A,V,S,C C,X family-onlyFlora 2036 Sheragul IRTF 1 / /
11 24.9 17.2 12.7 4 A,U,V,S S AdistribFlora 7057 1990 QL2 IRTF 12 / /
11 20.3 16.9 13.6 1 A S AdistribNysa / Po 7172 Multatuli IRTF 7 / /
12 7.4 17.9 13.9 1 A S AdistribGefion 7302 1993 CQ IRTF 3 / /
12 4.2 16.5 12.3 1 V S family-onlyEunomia 13137 1994 UT1 IRTF 12 / /
12 10 16.4 13.2 1 V S family-onlyNysa / Po 13577 Ukawa IRTF 7 / /
12 6.9 17.4 14.8 1 A S AdistribEunomia 13816 Stulpner Magellan 3 / /
12 13.3 18.1 14.2 3 2U,S S AdistribFlora 16520 1990 WO3 IRTF 1 / /
12 2.7 17 14.2 4 3A,S A AdistribGefion 17818 1998 FE118 IRTF 3 / /
12 18.4 17.4 12.9 1 A A AdistribVesta 19570 Jessedouglas IRTF 12 / /
11 10.8 17 13.2 1 A S AdistribEunomia 20596 1999 RX188 IRTF 1 / /
14 23.8 19 14.4 2 U,V S family-onlyEunomia 21646 Joshuaturner IRTF 7 / /
12 6.7 18.4 14.4 1 A C,X AdistribFlora 24673 1989 SB1 IRTF 7 / /
12 10 17.3 13.9 1 A S AdistribFlora 27791 Masaru IRTF 12 / /
11 15.8 17 14 1 A S AdistribFlora 28218 1998 YA6 IRTF 12 / /
11 10.9 17.8 14.9 1 U S,K family-onlyEunomia 30366 2000 JC57 Magellan 2 / /
13 24.3 17.6 13 1 V S family-onlyEunomia 33745 1999 NW61 IRTF 4 / /
11 12.3 16.8 13.9 1 A S / Q AdistribFlora 34969 4108 T-2 Magellan 2 / /
13 23.9 20.6 15.7 1 A A AdistribNysa / Po 39236 2000 YX56 Magellan 2 / /
13 17.8 19.9 15.3 1 A C AdistribEunomia 44028 1998 BD1 IRTF 7 / /
13 18.9 18.5 13.3 1 A S AdistribFlora 45876 2000 WD27 IRTF 7 / /
12 24.1 18.4 14.5 1 U S family-onlyEunomia 46456 4140 P-L IRTF 7 / /
13 23.7 18.1 14.2 8 3S2AKL,X S family-onlyEunomia 55550 2001 XW70 Magellan 3 / /
12 25.6 19 14.8 1 V S family-onlyEunomia 66905 1999 VC160 Magellan 3 / /
12 24 19.7 14.9 1 V V family-onlyVesta 92516 2000 ND25 IRTF 3 / /
12 4.7 17.6 14.8 2 S,A A AdistribFlora 98082 2000 RJ67 Magellan 2 / /
13 14 19.9 15.5 1 A X AdistribFlora 108209 2001 HS28 Magellan 7 / /
12 18.5 19 16.1 1 A S AdistribEunomia 111140 2001 VV96 Magellan 3 / /
12 14.5 19.7 15.2 1 V S family-onlyFlora 125739 2001 XH116 Magellan 2 / /
13 17.3 20.3 15.7 1 U S AdistribFlora 139045 2001 EQ9 Magellan 7 / /
12 15.9 18.4 15.9 1 A A AdistribVesta 200832 2001 XC238 Magellan 2 / /
13 10.2 18.5 15.8 1 A S AdistribEunomia 222511 2001 TX47 Magellan 3 / /
12 17.6 20.7 15.8 2 R,V S family-only a We include a broad array of classes (A, R, V, Q, and U which represents ”unusual” or ”unclassifiable”) with deeper than average absorption bands that could bedi ff erentiated candidates. b In this family survey, some candidates overlap with the A-type distribution survey. We note here if they overlap or are only part of the family survey. able 3: Previously Known A-type Asteroids Number a Name Orbit b H a Ecc Incl Class Class Albedo Albedo Diam Est. Mass c Mag (AU) (deg) Source Source (km) (kg)113 Amalthea MB 8.7 2.37 0.087 5.0 Sa SMASS 0.2 53 1.57E + + + + + + + + + + + + + / Bus 0.2 11 1.32E + a We only include A-types confirmed with near-infarared data to be olivine-dominated. b MB = Main Belt, MC = Mars Crosser, MT = Mars Trojan, Hun = Hungaria c Mass is estimated as π r ρ . Where the radius is calculated from the H magnitude and the albedo from a survey where marked or 0.2 if unknown (0.2 is theaverage albedo of A-types in DeMeo and Carry (2013) based on survey data), and the density ρ is taken as 2 g / cm . This density is lower than that calculated forA-types in Carry (2012), but in the typical range for asteroids, thus keeping our mass estimates conservative. able 4: Calculation of total A-types in the Main Belt Boundary SDSS A-type a SDSS A-type b SDSS c SDSS A-type d MPC e MPC A-type f Poisson g Poisson Error h ErrorCandidates N Expected N objects Fraction N objects N Expected Lower Upper Lower UpperH mag i
12 9 3.0 1478 0.00203 4264 8.65 3.17 19.33 5.48 10.6713 25 8.3 4568 0.00182 15180 27.69 16.27 45 11.42 17.3114 47 15.7 9377 0.00167 48111 80.38 55.76 113.04 24.62 32.6615 48 16.0 10815 0.00148 124862 184.72 128.15 259.77 56.57 75.0416 23 7.7 5737 0.00134 221785 296.38 174.13 481.62 122.26 185.24Region j Hun 3 1.0 379 0.00264 2451 6.47 0.65 25.22 5.82 18.75Inn 70 23.3 10740 0.00217 83549 181.52 134.95 240.71 46.56 59.19Mid 51 17.0 12072 0.00141 148869 209.64 147.98 291.03 61.66 81.39Out 29 9.7 9118 0.00106 177897 188.6 116.93 290.45 71.67 101.84Cyb 1 0.3 139 0.00240 2433 5.83 0.58 22.75 5.25 16.92Semi-major k Axis (AU)2.2 21 7.0 3206 0.00218 21213 46.32 25.8 78.08 20.51 31.762.3 23 7.7 4445 0.00172 35702 61.58 36.18 100.06 25.4 38.492.4 20 6.7 2458 0.00271 22640 61.4 34.21 103.51 27.19 42.112.5 21 7.0 3945 0.00177 39275 69.69 38.83 117.48 30.86 47.792.6 17 5.7 4435 0.00128 54822 70.05 36.19 122.58 33.86 52.542.7 10 3.3 3387 0.00098 49376 48.59 17.82 108.53 30.78 59.932.8 4 1.3 1050 0.00127 18158 23.06 2.31 89.93 20.75 66.872.9 3 1.0 1617 0.00062 24380 15.08 1.51 58.8 13.57 43.723.0 13 4.3 2912 0.00149 56499 84.08 35.73 168.15 48.34 84.083.1 8 2.7 3110 0.00086 70667 60.59 22.22 135.33 38.38 74.733.2 4 1.3 734 0.00182 13589 24.68 2.47 96.27 22.22 71.593.3 1 0.3 68 0.00490 1014 4.97 0.5 19.39 4.47 14.41 a The number of SDSS A-type candidates in each defined bin. b The number of expected A-types in each bin based on the 33 % confirmation rate. c The total number of asteroids (regardless of class) in each bin in our SDSS sample defined from DeMeo and Carry (2013). d The fraction of each bin that is A-type calculated as N expected A-type / N objects. e The number of known asteroids in each bin according the to the Minor Planet Center MPCORB.dat dated January 7, 2018. f The number of total expected A-types in that bin calculated as MPC N objects / SDSS fraction A-type. g Lower bound on the number of A-types based on Poisson statistics. h Error calculated as MPC N A-type - Poisson Lower. i The first bin spans 12 ≤ H <
13 and similar for the other bins. Semi-major axis is bounded in these bins by 1.8 ≤ a < <
12 because most asteroids this bright saturated the SDSS detector during observations, meaning the SDSS sample was biased. Known large A-type asteroids arelisted in Table 3. j Regions are defined as Hungaria (1.8 ≤ a < > ≤ a < ≤ a < ≤ a < ≤ a < ≤ H magnitude <
17 for all regions. k H magnitude is bounded in these bins by 11 ≤ H magnitude < able 5: Summary for the Survey of Family Candidates Family Family a Num b Num c Confirmed d Est Num e A or V as f Binomial g Binomial h Total Cands Obs. A- or V-type in Fam % of Fam Cumulative (%) Exact (%)Eos 1010 3 1 0 0.00 0Eunomia 1124 18 12 1 1.50 0.1335 16.7 26.8Flora 1166 19 12 3 4.75 0.4074 88.2 2.9Gefion 437 5 2 1 2.50 0.5721 84.6 2.8NysaPolana 1080 7 3 0 0.00 0Vesta 1360 5 3 1 1.67 0.1225 11.5 26.9 a Number of objects in the family as identified by Nesvorn´y (2010) that have classifications in DeMeo and Carry (2013). b Number of A- or V-type candidates identified in the SDSS sample. c Number of A- or V-type candidates observed. d Eunomia had one confirmed V-type all other confirmations were A-type. e Calculated as Family Total * (N Confirmed / N Observed). f Calculated as Est Num in fam / Family Total. g Binomial statistics are calculated with n (number of trials), v (number of successes), and p (probability of success) where n is Family tot, v is Est Num in Famrounded to a whole number, and p is 0.0016, calculated as the confirmation rate of A-types in the general main-belt population as 52 / < v). h The exact binomial probability P is where P(X = v).v).