Asteroid Family Associations of Active Asteroids

We find that active asteroid P/2015 X6 (PANSTARRS) is linked to the Aeolia family, which is believed to have formed in a cratering event ∼100 Myr ago (Spoto et al. 2015), although Bolin et al. (2018) suggest that it could potentially be much younger (≲20 Myr). P/2015 X6 becomes linked with the Aeolia family at ${\delta }_{c}=36\,{\rm{m}}$ s⁻¹ (Figure 1), which is actually outside the optimum cutoff distance (${\delta }_{c}=20\,{\rm{m}}$ s⁻¹) determined for the family by Nesvorný (2015). As can be seen in Figure 1, though, P/2015 X6 still lies well within the "plateau" region of the family growth plot (see Section 2) for the Aeolia family, so we still regard it as a likely family member.

The family lies just inside the 13J:5A and 3J−1S−1A MMRs (Figure 2). P/2015 X6 lies close to those two resonances, indicating that it may be unstable over long timescales. This potential instability is reflected by its small t_ly value (Table 1). Given that P/2015 X6 is also relatively distant in proper element space from the core of the family (and in fact is actually outside the ${\delta }_{c}$ cutoff established by Nesvorny 2015), its membership in the Aeolia family may be considered somewhat uncertain.

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The largest member of the family, (396) Aeolia, has been spectroscopically classified as a Xe-type asteroid (Neese 2010) and has been reported to have a geometric albedo of p_V = 0.126 ± 0.019 and effective radius of r_e = 19.6 ± 0.2 km (Mainzer et al. 2016). All other family members that have been taxonomically classified have been classified as C-type asteroids. The average reported albedo of Aeolia family members is $\overline{{p}_{V}}=0.107\pm 0.022$ (see Table 2), although albedos of individual family members have been reported to range widely from ${p}_{V}\sim 0.05$ to ${p}_{V}\sim 0.15$, suggesting that the family could have a mix of primitive and nonprimitive members (or alternatively, that individual reported albedo values have large uncertainties).

One important caveat that applies here, as well as to discussions of the physical properties of other families that follow below, is that albedos reported by Mainzer et al. (2016; and many others) are generally calculated using absolute V-band magnitudes (H_V) computed using photometric data compiled by the Minor Planet Center from a wide range of observers and surveys. However, Pravec et al. (2012) found that while cataloged absolute magnitudes for larger asteroids (${H}_{V}\lesssim 10$) were generally consistent with results from an independent, targeted observing campaign to verify H_V values for several hundred main-belt and near-Earth asteroids, cataloged H_V values for smaller asteroids (${H}_{V}\gg 10$) exhibited systematically negative offsets up to ${\rm{\Delta }}{H}_{V}\sim -0.5$ relative to independently measured values. In many cases, the eventual resulting offsets between cataloged albedo values and recalculated albedo values using revised H_V values were within the originally reported uncertainties of the cataloged albedo values, but nonetheless, we note that albedo values discussed here, particularly for the smaller asteroids that dominate the families we discuss in this paper, should be regarded with some caution.

A dust modeling analysis of the activity of P/2015 X6 indicates that the object underwent sustained dust loss over a period of at least two months, suggesting that the observed activity was sublimation driven (Moreno et al. 2016a), making the object a likely MBC.

We find that active asteroid 324P/La Sagra (formerly designated P/2010 R2) is linked to the Alauda family, which has been determined to be 640 ± 50 Myr old (Carruba et al. 2016a). 324P becomes linked with the Alauda family at ${\delta }_{c}=108\,{\rm{m}}$ s⁻¹ (Figure 3), just within the optimum cutoff distance (${\delta }_{c}=120\,{\rm{m}}$ s⁻¹) determined for the family by Nesvorný (2015).

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The family is found between the 9J:4A and 2J:1A MMRs and is crossed by the 13J:6A MMR as well as other two- and three-body MMRs (Figure 4). It is bounded above in proper inclination space by the Euphrosyne family and below by the Luthera family, and is also adjacent to the Danae and Erminia families in proper semimajor axis space, separated by the 9J:4A MMR. Some exchange of objects may be possible between the Alauda family and surrounding families via the ${\nu }_{6}$ secular resonance (which connects it to the Danae region), and various three-body MMRs (which connect it to the Euphrosyne and Luthera families; Machuca & Carruba 2012). Several subfamilies and clumps within this region have been identified (Machuca & Carruba 2012), but 324P is not linked to any of them at ${\delta }_{c}$ values smaller than the ${\delta }_{c}$ value at which it is linked to the main Alauda family.

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The largest member of the family, (702) Alauda, has been spectroscopically classified as a B-type asteroid (Neese 2010), possesses a small satellite, and has been reported to have p_V = 0.061 ± 0.011, r_e = 95.5 ± 1.0 km, and a bulk density of ρ = 1570 ± 500 kg m⁻³ (Bus & Binzel 2004; Rojo & Margot 2011; Mainzer et al. 2016). Other family members have been taxonomically classified as B-, C-, and X-type asteroids and have been reported to have a low average albedo of $\overline{{p}_{V}}=0.066\,\pm 0.015$ (see Table 2), indicating that they are likely to have primitive compositions. No significant two- or three-body MMRs intersect the candidate Gorchakov family region (Figure 6), although Haghighipour (2009) nonetheless found 238P to be unstable after approximately 20 Myr, likely due to its relatively large eccentricity and proximity to the 2J:1A MMR.

Photometric and morphological analysis of the activity of 324P/La Sagra in 2010 suggested that it was likely to be sublimation driven (Hsieh et al. 2012c), a conclusion that was strengthened by the detection of recurrent activity in 2015 (Hsieh & Sheppard 2015), making the object a likely MBC. The object's nucleus has been measured to have r_e = 0.55 ± 0.05 km (assuming an R-band albedo of p_R = 0.05; Hsieh 2014b).

We find that active asteroid 238P/Read (formerly designated P/2005 U1) is linked to a candidate asteroid family that we designate here as the Gorchakov family. 238P becomes linked with the candidate Gorchakov family at ${\delta }_{c}\,=\,45\,{\rm{m}}$ s⁻¹ (Figure 5). The largest member of the family, (5014) Gorchakov, has been reported to have p_V = 0.057 ± 0.008 and r_e = 9.7 ± 0.1 km (Mainzer et al. 2016), where its low albedo suggests that it may have a primitive composition. Other family members have been classified as C-type asteroids and have been reported to have a low average reported albedo of $\overline{{p}_{V}}=0.053\pm 0.012$ (Table 2), indicating that they are likely to have primitive compositions. No significant two- or three-body MMRs intersect the candidate Gorchakov family region (Figure 6), although Haghighipour (2009) nonetheless found 238P to be unstable after approximately 20 Myr, likely due to its relatively large eccentricity and proximity to the 2J:1A MMR.

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The activity of 238P is strongly believed to be sublimation driven based on numerical dust modeling of its activity in 2005 (Hsieh et al. 2009b) and observations of recurrent activity on two additional occasions in 2010 and 2016 (Hsieh et al. 2011b, 2016), making the object a likely MBC. The object's nucleus has been estimated to have r_e ∼ 0.4 km (assuming p_R = 0.05; Hsieh et al. 2009b). While we find that 238P is currently associated with the candidate Gorchakov family, Haghighipour (2009) has suggested that it may have been a former member of the Themis family that has since migrated in eccentricity away from the family. This hypothesis is supported by 238P's small t_ly value (Table 1), indicating that it is dynamically unstable, although the existence of a plausible dynamical pathway from the Themis family to 238P's current location has not yet been definitively demonstrated.

Active asteroids 313P/Gibbs (formerly designated P/2014 S4) and 358P/PANSTARRS (formerly designated P/2012 T1) have been previously linked to the Lixiaohua family (Hsieh et al. 2013, 2015b), which has been determined to be 155 ± 36 Myr old (Novaković et al. 2010a). The Lixiaohua family has a size–frequency distribution consistent with being the result of a catastrophic disruption event (Novaković et al. 2010b; Benavidez et al. 2012). 313P becomes linked with the Lixiaohua family at ${\delta }_{c}=21\,{\rm{m}}$ s⁻¹, and 358P becomes linked with the family at ${\delta }_{c}=13\,{\rm{m}}$ s⁻¹ (Figure 7), both well within the optimum cutoff distance (${\delta }_{c}=45\,{\rm{m}}$ s⁻¹) determined for the family by Nesvorný (2015).

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The family resides in a dynamically complex region of orbital element space in the asteroid belt (Figure 8) and is affected by several weak two- and three-body MMRs (see Figure 8) and potential close encounters with large asteroids, particularly Ceres, resulting in chaotic diffusion in all three proper elements (a_p, e_p, and i_p; Novaković et al. 2010b). Both 313P and 358P have small t_ly values (Table 1), indicating that they are relatively unstable over long timescales. About 20% of Lixiaohua family members also have similar or smaller t_ly values, however, so the small t_ly values of 313P and 358P do not necessarily indicate that they are likely to be recently implanted interlopers, but may instead simply reflect the complex dynamical environment of the family resulting in general instability for a large number of its members.

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The largest member of the family, (3556) Lixiaohua, has been spectroscopically classified as a C- or X-type asteroid (see Nesvorný et al. 2005) and has been reported to have p_V = 0.035 ± 0.004 and r_e = 10.04 ± 0.02 km (Mainzer et al. 2016). Other family members have been classified as C-, D-, and X-type asteroids and have been reported to have $\overline{{p}_{V}}=0.044\pm 0.009$, indicating that they are likely to have primitive compositions.

The activity of 313P is strongly believed to be sublimation driven based on both numerical dust modeling and observations showing that it has been active on at least two occasions in 2003 and 2014 (Hsieh et al. 2015b; Jewitt et al. 2015a, 2015d; Hui & Jewitt 2015), making the object a likely MBC. Photometric monitoring of 358P while it was active in 2012 suggests that its activity is likely to be due to sublimation, making the object a likely MBC as well.

We find that active asteroid component P/2013 R3-B (PANSTARRS) is linked to the recently identified Mandragora family, which has been determined to be 290 ± 20 kyr old (Pravec et al. 2017). P/2013 R3-B becomes linked with the Mandragora family at ${\delta }_{c}=59\,{\rm{m}}$ s⁻¹ (Figure 9), within the optimum cutoff distance (${\delta }_{c}=65\,{\rm{m}}$ s⁻¹) determined for the family by Pravec et al. (2017). P/2013 R3-A is not formally linked to the family at the present time.

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The 9J:4A MMR falls near the cluster, very nearly coinciding with the proper semimajor axes of P/2013 R3-A and P/2013 R3-B (Figure 10). This means that those objects are likely to be dynamically unstable on long timescales, a conclusion supported by the objects' small t_ly values (Table 1), and may not in fact share a common origin with other Mandragora family members. If the parent body of P/2013 R3-A and P/2013 R3-B was originally a member of the candidate Mandragora family, though, destabilization by the 9J:4A MMR or nongravitational outgassing forces could explain why P/2013 R3-A has diffused away from the family in proper eccentricity. A third possibility is that P/2013 R3-A could simply not be linked to the Mandragora family due to poor proper element determination resulting from large uncertainties in the osculating orbital elements of both fragments. A more detailed backward integration analysis like that performed by Pravec et al. (2017) for other members of the family would help to clarify the membership status of both fragments and should be performed in the future.

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The largest member of the Mandragora family, (22280) Mandragora, has been reported to have p_V = 0.046 ± 0.006 and r_e = 4.9 ± 0.1 km (Mainzer et al. 2016; Pravec et al. 2017). No family members have been taxonomically classified, but those with measured albedos have been reported to have $\overline{{p}_{V}}=0.056\pm 0.019$, indicating that they are likely to have primitive compositions. This conclusion is also supported by the C-type-like V − R colors measured for the two largest members of the family reported by Pravec et al. (2017).

When P/2013 R3 was discovered, the object had already split into multiple fragments, which then disintegrated further over the following several months. Analysis of follow-up observations suggested that the comet likely broke apart due to stresses from rapid rotation (Jewitt et al. 2014a, 2017). Jewitt et al. (2014a) concluded that gas pressure alone was insufficient to cause the catastrophic disruption of the comet, although individual fragments were observed to exhibit secondary dust emission behavior indicative of being driven by sublimation, perhaps of newly exposed interior ices, making the object a likely MBC.

Active asteroids 133P (also designated (7968) Elst-Pizarro) and 176P (also designated (118401) LINEAR) have been previously linked to the Themis family (e.g., Boehnhardt et al. 1998; Hsieh 2009). While MBC 288P was previously found to be associated with the Themis family, we find that it becomes linked with the family at ${\delta }_{c}=77\,{\rm{m}}$ s⁻¹, outside the nominally established ${\delta }_{c}$ for the family. 133P becomes linked with the family at ${\delta }_{c}=33\,{\rm{m}}$ s⁻¹, and 176P becomes linked with the family at ${\delta }_{c}=34\,{\rm{m}}$ s⁻¹ (Figure 11), both well within the optimum cutoff distance (${\delta }_{c}=60\,{\rm{m}}$ s⁻¹) determined for the family by Nesvorný (2015). Nesvorný et al. (2003) estimated the age of the Themis family to be 2.5 ± 1.0 Gyr, but due to large uncertainties caused by its old age and dynamical environment, other estimates for the age of the Themis family range from as little as 500 Myr to nearly the age of the solar system (∼4.5 Gyr; Spoto et al. 2015; Carruba et al. 2016a).

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Meanwhile, 133P has been previously determined to also be linked to the Beagle family, which is a subfamily of the Themis family and has been estimated to be <10 Myr old (Nesvorný et al. 2008). 133P becomes linked with the Beagle family at ${\delta }_{c}=19\,{\rm{m}}$ s⁻¹ (Figure 12), within the optimum cutoff distance (${\delta }_{c}=25\,{\rm{m}}$ s⁻¹) determined for the family by Nesvorný (2015).

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The Themis family was one of the original asteroid families identified by Hirayama (1918). Because the Themis family is adjacent to the 2J:1A MMR (see Figure 13), it is believed that a significant number of family members may have been captured and scattered by the resonance since the family's formation (Morbidelli et al. 1995).

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The largest member of the family, (24) Themis, has been spectroscopically classified as a B- or C-type asteroid (Neese 2010) and has been reported to have p_V = 0.069 ± 0.010, r_e = 97.8 ± 2.2 km, and an estimated density of ρ = 1810 ± 670 kg m⁻³ (Carry 2012; Mainzer et al. 2016). Notably, a near-infrared absorption feature attributed to water ice frost was detected in spectra of both Themis (Campins et al. 2010; Rivkin & Emery 2010) and another large member of the family, (90) Antiope (Hargrove et al. 2015). No evidence of outgassing in the form of spectroscopic detections of outgassing has yet been found, though (Jewitt & Guilbert-Lepoutre 2012; McKay et al. 2017). The Themis family in general is dominated by C-complex asteroids, many of which exhibit spectra indicative of aqueously altered mineralogy and are similar to carbonaceous chondrite meteorites (Florczak et al. 1999; Ziffer et al. 2011).

The Beagle family is entirely contained within the Themis family (see Figure 13), suggesting that it formed from the fragmentation of a parent body that was itself a Themis family member. Despite the now commonly used name of the family, Nesvorný et al. (2008) noted that it is possible that (656) Beagle may not actually be a real member of the family that bears its name, as its slight eccentricity offset from the other family members (Figure 14) would require the invocation of an unusual ejection velocity field to explain it.

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No formal taxonomic classification has been reported for the largest member of the family, (656) Beagle, but it has a spectrum consistent with C-complex asteroids (Kaluna et al. 2016; Fornasier et al. 2016) and has been reported to have p_V = 0.045 ± 0.005 and r_e = 31.3 ± 0.3 km (Mainzer et al. 2016). Other family members have been taxonomically classified as B- and C-type asteroids and have been reported to have $\overline{{p}_{V}}=0.080\pm 0.014$ (see Table 2), indicating that they are likely to have primitive compositions.

Based on the simultaneous detection of some objects with phyllosilicate absorption features and the presence of the apparently ice-bearing 133P in the family, Kaluna et al. (2016) concluded that the Beagle parent body was most likely composed of a heterogeneous mixture of ice and aqueously altered material. Meanwhile, spectroscopic observations of samples of both Beagle and Themis family asteroids showed that Beagle family asteroids are spectrally bluer, have higher albedos, and exhibit smaller spectral slope variability than background Themis family asteroids, suggesting that the Beagle parent body could have been a particularly blue and bright interior fragment of the original Themis parent body (Fornasier et al. 2016).

133P has been observed to be active during four perihelion passages (in 1996, 2002, 2007, and 2013) with intervening periods of inactivity, where dust modeling results indicate that dust emission took place over periods of months during its 1996, 2002, and 2013 active epochs (Boehnhardt et al. 1998; Hsieh et al. 2004; Jewitt et al. 2014b). As such, 133P's activity is strongly believed to be the result of sublimation of volatile ices, although it is possible that the object's rapid rotation (${P}_{\mathrm{rot}}=3.471\pm 0.001\,\mathrm{hr}$) may also play a role in helping to eject dust particles (Hsieh et al. 2004). 133P's nucleus has been taxonomically classified as a B- or F-type asteroid (Bagnulo et al. 2010; Licandro et al. 2011) and has been reported to have p_R = 0.05 ± 0.02 and r_e = 1.9 ± 0.3 km (Hsieh et al. 2009a). While the presence of water ice has not yet been definitively spectroscopically confirmed on 133P, Rousselot et al. (2011) reported that its spectrum could be consistent with a mixture of water ice, black carbon, tholins, and silicates, but they acknowledged that such a compositional interpretation was not unique.

176P's nucleus has been taxonomically classified as a B-type asteroid (Licandro et al. 2011) and has been reported to have p_R = 0.06 ± 0.02 and r_e = 2.0 ± 0.2 km (Hsieh et al. 2009a). Numerical dust modeling of its activity in 2005 indicated that it was likely to be due to a prolonged dust emission event, pointing to sublimation as the mostly likely driver of the activity (Hsieh et al. 2011a), making the object a likely MBC. However, numerous observations during the object's next perihelion passage in 2011 revealed no evidence of recurrent activity, which could either suggest that the object did not actually exhibit sublimation-driven activity when observed in 2005, or that the object's activity had simply become attenuated to an undetectable level during the following orbit passage (Hsieh et al. 2014).

We find that active asteroid P/2016 J1-A/B (PANSTARRS) is linked to the Theobalda family. P/2016 J1-A becomes linked with the Theobalda family at ${\delta }_{c}$ = 23 m s⁻¹, and P/2016 J1-B becomes linked with the family at ${\delta }_{c}$ = 30 m s⁻¹ (Figure 15), both well within the optimum cutoff distance (${\delta }_{c}=85\,{\rm{m}}$ s⁻¹) determined for the family by Novaković (2010). Novaković (2010) further determined via two independent methods (chaotic chronology and backward integration) that the family was likely produced 6.9 ± 2.3 Myr ago by a cratering impact on a d = 78 ± 9 km parent body. A detailed dynamical analysis of this family was performed by Novaković (2010), who found that it is crossed by several three-body MMRs (Figure 16), making the region significantly chaotic.

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The largest member of the family, (778) Theobalda, has been spectroscopically classified as an F-type asteroid (Neese 2010) and has been reported to have p_V = 0.079 ± 0.010 and r_e = 27.7 ± 0.4 km (Mainzer et al. 2016). Other family members have been taxonomically classified as C-, F-, and X-type asteroids and have been reported to have $\overline{{p}_{V}}$ = 0.062 ± 0.016 (see Table 2), indicating that they are likely to have primitive compositions.

P/2016 J1 was characterized by Hui et al. (2017) and Moreno et al. (2017), who found mass loss rates of $\lesssim \,1\,\mathrm{kg}$ s⁻¹ for both components of the object (P/2016 J1-A and P/2016 J1-B). Both sets of authors also found that both components were continuously active over a period of three to nine months, strongly suggesting that the activity was sublimation driven, making the object a likely MBC. Hui et al. (2017) also estimated that the two largest fragments, J1-A and J1-B, have radii of 140 m < r_e < 900 m and 40 m < r_e < 400 m, respectively, and broadband colors similar to C- or G-type asteroids.

Active asteroid 288P/(300163) 2006 VW₁₃₉ has been previously linked to a 7.5 ± 0.3 Myr old asteroid family designated as the 288P family (Novaković et al. 2012b). A plot showing the growth of the family as a function of δ_c is shown in Figure 17. The 11-member 288P family was analyzed in detail by Novaković et al. (2012b), who found that it was likely formed in a disruptive event characterized as being intermediate between a catastrophic disruption and a cratering event. It is located in close proximity to the Themis family, with which it merges at ${\delta }_{c}\sim 75\,{\rm{m}}$ s⁻¹, separated by a number of weak two- and three-body MMRs. These MMRs may contribute to a number of dynamically unstable interlopers, which were excluded from the family by Novaković et al. (2012b) based on a backward integration method (BIM) analysis (see Nesvorný et al. 2002). The 288P family is roughly bound by the 9J:4A MMR at 3.0307 au on one side and is crossed by the 20J:9A MMR at 3.0559 au (Figure 18).

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The two members of the family with measured albedos have been reported to have ${p}_{V}$ = 0.077 ± 0.037 and ${p}_{V}$ = 0.103 ± 0.077, giving $\overline{{p}_{V}}$ = 0.090 ± 0.021 (see Table 2), indicating that they may have relatively primitive compositions. The activity of 288P seen in 2011 is believed to be sublimation driven based on numerical dust modeling (Hsieh et al. 2012b; Agarwal et al. 2016), making the object a likely MBC, where this conclusion was further strengthened by the recent confirmation in 2016 that the object is recurrently active (Agarwal et al. 2016). The nucleus of 288P has been classified as a C-type asteroid, has an effective absolute magnitude of H_V = 17.0 ± 0.1 (equivalent to r_e ∼ 1.3 km, assuming p_V = 0.04), and has recently been confirmed to be a binary system with approximately equally sized components (Licandro et al. 2013; Agarwal et al. 2016, 2017).

We find that active asteroid P/2016 G1 (PANSTARRS) is linked to the Adeona family, which is estimated to have formed in a cratering event ∼700 Myr ago (Benavidez et al. 2012; Carruba & Nesvorný 2016; Milani et al. 2017). P/2016 G1 becomes linked with the family at ${\delta }_{c}=44\,{\rm{m}}$ s⁻¹ (Figure 19), within the optimum cutoff distance (${\delta }_{c}=50\,{\rm{m}}$ s⁻¹) determined for the family by Nesvorný (2015).

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The Adeona family's orbital evolution was investigated in detail by Carruba et al. (2003), who found that perturbations from large asteroids like Ceres could affect the inferred ejection velocities of family members, but should have minimal effect on the spread of the family's semimajor axis distribution. The sharp cutoff of the family at the 8J:3A MMR at 2.706 au (Figure 20) is attributed to family members drifting into the resonance under the influence of the Yarkovsky effect and becoming scattered in eccentricity, thus becoming unrecognizable as family members. The family is also crossed by several other two-body, three-body, and secular resonances (Carruba et al. 2003).

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The Adeona family is notable in that the members of the family that have been spectroscopically classified have C- and Ch-type classifications, while the nearby background population is dominated by S-type asteroids. The largest member of the family, (145) Adeona, has been spectroscopically classified as a C- or Ch-type asteroid (Neese 2010) and has been reported to have p_V = 0.061 ± 0.010, r_e = 63.9 ± 0.2 km, and ρ = 1180 ± 340 kg m⁻³ (Carry 2012; Mainzer et al. 2016). Adeona has been spectroscopically characterized by Busarev et al. (2015), who also found spectroscopic features indicative of hydrated silicates and hydrated oxides. An unexplained sharp increase in reflectivity between 0.4 μm and 0.7 μm was also noted and interpreted as possibly being indicative of a cloud of sublimed or frozen ice particles, but this interpretation has yet to be confirmed. Other family members have been reported to have $\overline{{p}_{V}}$ = 0.060 ± 0.011 (see Table 2), indicating that they are likely to have primitive compositions. The family's C-type members also exhibit evidence of aqueous alteration and have been judged to be consistent with the breakup of a CM chondrite-like body (Mothé-Diniz et al. 2005).

Moreno et al. (2016b) found that P/2016 G1's active behavior is best interpreted as the result of a short-duration event about one year prior to perihelion, consistent with an impact that then led to the observed disintegration of the object, making the object a likely disrupted asteroid. Those authors also found an upper limit of r_e ∼ 50 m for any postdisruption fragments.

We find that disrupted asteroid 354P/LINEAR (formerly designated P/2010 A2) is linked to the Baptistina family (despite being initially suspected of being a member of the Flora family; e.g., Snodgrass et al. 2010). Masiero et al. (2012b) determined the family's age to be between 140 and 320 Myr old, depending on the physical properties assumed for its family members, while Carruba & Nesvorný (2016) estimated the family's age to be 110 ± 10 Myr old. 354P becomes linked with the family at ${\delta }_{c}=43\,{\rm{m}}$ s⁻¹ (Figure 21), within the optimum cutoff distance (${\delta }_{c}=48\,{\rm{m}}$ s⁻¹) determined for the family by Nesvorný (2015).

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The Baptistina family is located in a crowded region of the inner main belt near several other families, including the Flora, Vesta, Massalia, and Nysa-Polana families (Dykhuis et al. 2014). Notably, the Chicxulub impactor responsible for the Cretaceous/Tertiary (K/T) mass extinction on Earth was linked to the Baptistina family by Bottke et al. (2007), although more recent studies revising the age and composition of the family have cast doubt on this claim (e.g., Reddy et al. 2009, 2011; Carvano & Lazzaro 2010; Masiero et al. 2012b). The family is roughly bound by the 11J:3A MMR on one side and the 10J:3A MMR on the other side (Figure 22).

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The largest member of the family, (298) Baptistina, has been spectroscopically classified as an X- or Xc-type asteroid (Lazzaro et al. 2004) and has been reported to have p_V = 0.131 ± 0.017 and r_e = 10.6 ± 0.2 km (Mainzer et al. 2016). Other family members that have been physically characterized have been taxonomically classified as S- and X-type asteroids and have been reported to have $\overline{{p}_{V}}=0.179\pm 0.056$ (see Table 2), indicating that they are not likely to have primitive compositions.

Initial analysis of 354P in 2010 indicated that the apparent cometary activity was likely to be due to a physical disruption of the asteroid by either an impact or rotational spin-up (Jewitt et al. 2010; Snodgrass et al. 2010), making this object a likely disrupted asteroid. A detailed analysis of the 2010 HST images led Agarwal et al. (2013) to conclude that the disruption of 354P was most likely due to rotational destabilization, although measurements showing the largest remaining fragment has a spin rate (P_rot = 11.36 ± 0.02 hr) well below the critical spin rate for rotational disruption and revised dust modeling results appear to indicate that, in fact, an impact disruption was the most likely cause of the object's observed activity in 2010 (Kim et al. 2017a, 2017b). 354P was the first active asteroid determined to exhibit activity that was not due to sublimation, making it the first recognized disrupted asteroid.

We find that active asteroid 311P/PANSTARRS (formerly designated P/2013 P5) is linked to a candidate asteroid family that we designate here as the Behrens family. 311P becomes linked with the family at ${\delta }_{c}=46\,{\rm{m}}$ s⁻¹ (Figure 23). While we have not performed a detailed assessment of the likelihood that the Behrens family is real in this work, one line of evidence that the Behrens family may be real comes from the long rotational period of the asteroid (1651) Behrens, estimated to be ${P}_{\mathrm{rot}}\sim 34\,\mathrm{hr}$. One possible explanation for such a long period is angular momentum "splash" due to a disruptive collision (Cellino et al. 1990; Takeda & Ohtsuki 2009). If real, the Behrens cluster is likely to be relatively young, based on the small size of its largest body. Unfortunately, this hypothesis will be difficult to confirm using the backward integration method (e.g., Novaković et al. 2012a, 2012b) because the orbits of most of the family members are unstable over long timescales.

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The Behrens family is intersected by the 11J:3A MMR with Jupiter. This MMR also passes close to 311P itself (Figure 24), suggesting that 311P may be unstable over long timescales, consistent with its relatively small t_ly value (Table 1). As such, its membership in the Behrens family may be considered somewhat uncertain.

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The largest member of this candidate family, (1651) Behrens, has been reported to have p_V = 0.318 ± 0.052 and r_e = 4.5 ± 0.1 km (Mainzer et al. 2016), the former of which suggests that it likely does not have a primitive composition, although no formal taxonomic classification is currently available for the object. Other family members that have been physically characterized have been taxonomically classified as Q-, S-, and V-type asteroids and have been reported to have $\overline{{p}_{V}}=0.248\pm 0.026$ (see Table 2), indicating that they are not likely to have primitive compositions.

At the time of its discovery, 311P exhibited at least six dust tails believed to have been produced by multiple impulsive mass shedding events caused by rapid rotation of the nucleus near its critical limit (Jewitt et al. 2013, 2015b), making the object a probable disrupted asteroid. Attempts to confirm that the nucleus of 311P has a rapid rotation rate have thus far been unsuccessful, however, with some observations even suggesting that it could be rotating unusually slowly (e.g., Hainaut et al. 2014). The nucleus has been estimated to have r_e = 0.20 ± 0.02 km (Jewitt et al. 2015b) and has been found to have broadband colors consistent with being a S-type asteroid (Hainaut et al. 2014).

Active asteroid 331P/Gibbs (formerly designated P/2012 F5) has been previously determined to be associated with a family that was designated the Gibbs cluster and estimated to be just 1.5 ± 0.1 Myr old (Novaković et al. 2014). A plot showing the growth of the family as a function of δ_c is shown in Figure 25. No significant two- or three-body MMRs intersect the Gibbs cluster region (Figure 26), making both 331P and the overall cluster relatively dynamically stable. The parent body of the cluster has been estimated to be ∼10 km in diameter, where Novaković et al. (2014) concluded that the estimated mass ratio between the largest fragment and the parent body indicate that the disruption that created the cluster was likely intermediate between a catastrophic disruption and a cratering event, assuming that the cluster was formed by an impact event. A more recent analysis, however, including observations to determine the rotational periods and sizes of cluster members, suggests that the cluster may instead have been formed by rotational fission (Pravec et al. 2017).

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The physical properties of this cluster were studied by Novaković et al. (2014), who noted that two members for which SDSS observations were available appear to be Q-type objects and also conducted a small-scale search for other active cluster members (none were found). 331P's nucleus has been estimated to have r_e = 0.88 ± 0.01 km (Drahus et al. 2015) but has not yet been taxonomically classified. Dust modeling has suggested that the long, thin dust trail observed for 331P was most likely produced by an impulsive emission event, such as an impact (Moreno et al. 2012; Stevenson et al. 2012), or possibly by mass ejection due to rotational destabilization of the nucleus given that its rotation period was found to be ${P}_{\mathrm{rot}}=3.24\pm 0.01\,\mathrm{hr}$ (Drahus et al. 2015), making the object a likely disrupted asteroid.

We confirm the finding of Sheppard & Trujillo (2015) that active asteroid (62412) 2000 SY₁₇₈ is linked to the Hygiea family. (62412) becomes linked with the Hygiea family at ${\delta }_{c}=37\,{\rm{m}}$ s⁻¹ (Figure 27), well within the optimum cutoff distance (${\delta }_{c}=60\,{\rm{m}}$ s⁻¹) determined for the family by Nesvorný (2015). The Hygiea family has a size–frequency distribution consistent with being the result of a catastrophic disruption of a monolithic parent body (Durda et al. 2007; Benavidez et al. 2012) and has been determined to be 3.2 ± 0.4 Gyr old (Carruba et al. 2014).

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The Hygiea family is roughly bound by the 9J:4A MMR at 3.0307 au on one side and the 2J:1A MMR at 3.2783 au on the other side (Figure 28). Carruba (2013) and Carruba et al. (2014) found that the region in which it is found likely contains a significant component of interlopers from the nearby Themis and Veritas families, which likely contribute low-albedo asteroids, and the Eos family, the likely origin of the few high-albedo asteroids found in the region. It also crosses two other smaller families (associated with (5340) Burton and (15755) 1992 ET₅) in proper element space. Besides the numerous two- and three-body resonances intersecting the region, Hygiea family members are also perturbed by numerous secular resonances, the Yarkovsky effect, and other massive asteroids, interestingly possibly including Hygiea itself (Carruba et al. 2014).

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The largest member of the family, (10) Hygiea, has been spectroscopically classified as a C-type asteroid (Mothé-Diniz et al. 2001; Neese 2010) and has been reported to have p_V = 0.072 ± 0.002, r_e = 203.6 ± 3.4 km, and ρ = 2190 ±420 kg m⁻³ (Mainzer et al. 2016; Carry 2012). The asteroid's spectrum includes an absorption feature centered at 3.05 ± 0.01 μm that has been classified as "Ceres-like" by Takir & Emery (2012). The corresponding feature on Ceres may be due to irradiated organic material and crystalline water ice, or perhaps iron-rich clays (Vernazza et al. 2005; Rivkin et al. 2006). Rotationally resolved spectroscopy of Hygiea has also revealed surface heterogeneity suspected of being due to heating by significant impact events (Busarev 2011). Other family members have been taxonomically classified as B-, C-, D-, S-, V-, and X-type asteroids (some of which may be interlopers; Mothé-Diniz et al. 2001; Carruba 2013; Carruba et al. 2014) and have been reported to have $\overline{{p}_{V}}$ = 0.070 ± 0.018 (see Table 2), indicating that most members are likely to have primitive compositions.

Dust emission observed from asteroid (62412) 2000 SY₁₇₈ in 2014 is considered likely to have been driven by rotational disruption, given the determination of a relatively rapid rotational period for the object of ${P}_{\mathrm{rot}}\,\sim \,3.33\,\mathrm{hr}$ (Sheppard & Trujillo 2015), making it a likely disrupted asteroid. The object's nucleus has been estimated to have an effective radius of r_e = 3.9 ± 0.3 km with a minimum axis ratio of $a/b\geqslant 1.51$, where measured colors and low albedo suggest that it is a C-type asteroid (Sheppard & Trujillo 2015).

From the perspective of finding new MBCs, because asteroid family members are thought to have similar compositions (e.g., Ivezić et al. 2002; Vernazza et al. 2006), it is logical to expect that asteroid families that contain a known, presumably ice-bearing MBC could contain other icy objects. It is this hypothesis that led Hsieh (2009) to search members of the Themis family (already known to contain 133P) for new MBCs, ultimately leading to the discovery of activity for asteroid (118401) LINEAR, now also designated as 176P. Meanwhile, dynamical studies have also shown that intrafamily collision rates may be elevated over local background rates, particularly for young families (e.g., Farinella & Davis 1992; Dell'Oro et al. 2002), suggesting that more potentially activity-triggering impacts on icy objects might occur in asteroid families, further increasing the chances of producing active MBCs.

In terms of characterizing both new and known MBCs, many MBC nuclei have been found to be quite small, with effective radii of ${r}_{e}\lesssim 1\,\mathrm{km}$ (see Table 1). Such objects are difficult to physically characterize because they are extremely faint (e.g., ${m}_{R}\sim 24\mbox{--}26\,\mathrm{mag}$; MacLennan & Hsieh 2012; Hsieh 2014b) when inactive far from the Sun, making reliable photometry, colors, or spectroscopy difficult to obtain at those times. Meanwhile, their surface properties also cannot be measured when they are closer to the Sun and therefore brighter, as this is where they become active and thus become obscured by coma dust. In these cases, identification of an associated asteroid family can allow for reasonable guesses of a MBC's taxonomic type and albedo by proxy using corresponding measurements of other asteroids in the same family.

The Themis family provides an illustrative example of this application of establishing links between MBCs and specific asteroid families because it contains two MBCs (133P and 176P) that have been individually characterized as B- or F-type asteroids and have been reported to have albedos of p_R = 0.05 ± 0.02 and p_R = 0.06 ± 0.02 (Hsieh et al. 2009a), where the family as a whole has been found to contain mostly C-complex asteroids (which include B- and F-type asteroids) and has been reported to have an average albedo of $\overline{{p}_{V}}=0.068\pm 0.017$ (Section 3.2.6; Table 2). This technique for inferring an MBC's taxonomic type is obviously subject to uncertainties due to possible differentiation of the family parent body, or if the MBC is an interloper or taxonomically dissimilar member of the background population or overlapping family. In the absence of other direct surface property measurements of MBC nuclei, fellow family members may nonetheless be able to provide useful information about the likely properties of those MBC nuclei from their dynamical associations alone.

It is therefore interesting to note that, although only three MBC nuclei have been individually taxonomically classified (as B-, C-, or F-type asteroids) and two have been reported to have albedos (p_R ∼ 0.05), all MBCs with family associations belong to families containing primitive-type asteroids (see Section 4.1) that also have relatively low average reported albedos ($\overline{{p}_{V}}\lesssim 0.10$). Meanwhile, members of families associated with disrupted asteroids span a wider range of taxonomic types and reported albedos ($0.06\lt \overline{{p}_{V}}\lt 0.25$). These results are consistent with MBC activity being correlated to composition (i.e., whether an object contains primitive and therefore potentially icy material) and processes that produce activity in disrupted asteroids being less sensitive to composition (although may still have some dependence, e.g., to the extent that material density can affect an object's susceptibility to rotational disruption; Section 4.3).

The link between MBCs and very young asteroid families (e.g., 133P and the Beagle family; Section 3.2.6) is particularly interesting considering thermal models and impact rate calculations (e.g., Schörghofer 2008; Hsieh 2009; Prialnik & Rosenberg 2009) showing that ice may become depleted from the surface of a main-belt asteroid over gigayear timescales to the point at which small (meter-scale) impactors are unable to penetrate deeply enough to trigger sublimation-driven activity (see Hsieh et al. 2004; Capria et al. 2012; Haghighipour et al. 2016). However, if most MBC nuclei were produced in more recent fragmentation events (e.g., $\lesssim 10\,\mathrm{Myr}$), they may have much younger effective ages than their dynamical stability timescales would otherwise suggest, and they could possess more ice at shallower depths than expected.

In Figure 30, we illustrate a sequence of physical processes (some of which have been previously noted in the context of MBCs; e.g., Nesvorný et al. 2008; Hsieh 2009; Capria et al. 2012; Haghighipour et al. 2016) that could lead to active MBCs in young asteroid families. We begin with the premise that large icy asteroids can preserve ice over gigayear timescales in the main asteroid belt (see Schörghofer 2008; Prialnik & Rosenberg 2009), except that, by now, that ice has likely receded too deep below the surface to plausibly produce sublimation-driven activity (Figure 30(a)). However, if one of these objects is catastrophically disrupted (either by an impact event, as is commonly assumed, or a rotational fission event, as is suspected for some families by Pravec et al. 2017) (Figure 30(b)), after the sublimation and depletion of ice directly exposed by the initial disruption, the remaining subsurface ice on the resulting fragments (i.e., family members) might then be found at much shallower depths than before (Figure 30(c)). At these depths, that ice would then be more easily excavated by relatively small (and therefore relatively abundant) impactors. For asteroids formed in recent (≲10 Myr) fragmentation events where ice has not yet had time to recede again to significant depths, such small-scale disruptions should be able to trigger the sublimation-driven activity observed today on MBCs.

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Interestingly, with some exceptions, most MBC nuclei are small (kilometer scale or smaller; see Table 1). Smaller objects are collisionally disrupted on statistically shorter timescales than larger objects (Cheng 2004; Bottke et al. 2005), meaning that currently existing smaller objects are more likely to have been recently formed than larger objects. Thus, even those MBCs for which young families have not yet been associated may have also formed in recent disruptions of larger parent bodies. The current lack of identified young family associations for these MBCs could simply be due to other family members being too faint to have been discovered yet by current asteroid surveys. As surveys improve and find ever fainter asteroids, more young families will likely be discovered, and some of these will likely be associated with MBCs that currently lack identified young family associations.

We emphasize, however, that we do not expect young family associations to eventually be found for all MBCs. Some MBCs may have formed in recent disruptions from which they are the only remaining fragments of appreciable size, or where family members have rapidly dispersed and blended beyond recognition into the background asteroid population due to chaotic dynamical conditions. Some MBCs themselves may have been destabilized by chaotic dynamical conditions near their points of origins and are now interlopers at their present-day locations, far from their original families. Finally, for certain orbital obliquities and latitudes of subsurface ice reservoirs, thermal modeling indicates that shallow subsurface ice could remain preserved on an outer main belt asteroid over even gigayear timescales (Schörghofer 2008, 2016). Therefore, in these cases, a recent catastrophic disruption would not be required at all for ice to be accessible to excavation by small impactors.

As ongoing surveys continue to discover more asteroids, and particularly as future surveys discover smaller and fainter asteroids than are detectable now, continued searches for tightly clustered young families should be performed (e.g., Milani et al. 2014), perhaps using osculating or mean elements rather than proper elements to detect very young clusters (e.g., Nesvorny et al. 2006; Nesvorný & Vokrouhlický 2006; Pravec & Vokrouhlický 2009; Pravec et al. 2017; Rosaev & Plávalová 2017). Furthermore, as new young families are identified—especially ones associated with known MBCs, believed to contain primitive asteroids, or found in the outer main belt (i.e., a between the 5J:2A MMR at 2.8252 au and the 2J:1A MMR at 3.2783 au)—targeted observations or at least targeted close examination of survey data of members of these young families should be conducted to search for new MBCs.

This schematic model also suggests that thermal modeling work on volatile preservation in asteroids should take into account the fact that many icy asteroids found in the main belt today could actually have originated from the fragmentation of larger icy parent bodies some time in the relatively recent past. In these cases, the timescale over which volatile depletion from solar heating is expected to take place is not the age of the solar system, but rather the age of an object's associated asteroid family. As such, we suggest that thermal models computing ice retreat depths over gigayear timescales (e.g., Schörghofer 2008; Prialnik & Rosenberg 2009) may overestimate depths to ice at the present day, and that ice in primitive asteroids might be found at much shallower depths (and therefore be more accessible to activity-triggering impacts) than these models might indicate.