MAIN-BELT ASTEROIDS WITH WISE/NEOWISE: NEAR-INFRARED ALBEDOS

Figure 1 shows p_W1 and p_W2 for all main-belt asteroids with sufficient data to constrain these parameters, compared to the fitted diameter. The W1 band is more sensitive than the W2 band (single-frame 5σ sensitivity of ∼0.22 mJy versus ∼0.31 mJy respectively; Cutri et al. 2012), and W1 detections are less frequently contaminated by thermal emission, which means we are able to measure p_W1 for more asteroids than those with p_W2 measurements (2835 versus 679). Both data sets show a strong bias against small, low-albedo asteroids, which is expected for data that require measurement of a reflected light component. A further bias against dark objects in p_W2 due to rising thermal emission overtaking the small reflected light component is also present. From the data available, we see no evidence for a nonuniform distribution of p_W2, in contrast to p_W1, which shows three significant albedo clumps at p_W1 ∼ 0.06, p_W1 ∼ 0.16, and p_W1 ∼ 0.4.

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Visible albedos for over 136,000 main-belt asteroids were presented in Masiero et al. (2011, 2012a). These measurements were based on the conversion of apparent visible magnitudes from a wide range of predominantly ground-based surveys to absolute H_V magnitudes when the orbit was determined by the MPC. Absolute magnitude is then converted to a predicted apparent magnitude during the epoch of the WISE/NEOWISE observations, often after assuming a photometric G parameter (see Bowell et al. 1989) and assuming that rotational variations are averaged over during the set of thermal infrared observations. These conversions and assumptions will instill additional uncertainty in the p_V determinations beyond what would be expected from uncertainties in the flux measurements and from thermal modeling. As a result, the fractional error on p_V is typically 50%–100% larger than the fractional error on diameter from thermal model fits.

We compare the NIR albedos presented here to these visible albedos in Figures 2 and 3. For the majority of objects, p_W1 traces p_V and can thus be used as an analog when p_V is not available. The uncertainties of the p_W1 measurements in our data are smaller than the errors on p_V, and thus act as a better constraint of the surface properties. The relationship between p_W2 and both p_V and p_W1 is less distinct and varies over a large range of values for objects spanning high and low p_V and p_W1 albedos.

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Comparing the p_V distribution to Figure 10 from Masiero et al. (2011), we see that our sample contains significantly fewer low-albedo objects than would be expected from a random sample of all main-belt asteroids. The lack of low-albedo objects is due primarily to the observational selection effect imprinted on our data set by the requirement that the objects be detected in W1 and/or W2 in reflected light. This bias will increase as albedo decreases, preferentially selecting objects with higher albedos. A survey with deeper sensitivity in these wavelengths would allow us to probe smaller sizes at all albedos, but would still be subject to the same observational biases.

Following Grav et al. (2012), we can use our albedo measurements as a proxy for spectral slope from visible wavelengths through the NIR. Objects that fall above the one-to-one relationship in the top portion of Figure 3 will have a red spectral slope across the wavelengths plotted, while objects below this relation will have a blue spectral slope. As p_W2 is the most poorly probed of the three parameters, there will be inherent detection biases against blue spectral slopes from objects that "drop out" and fall below our W2 detection threshold. For this reason, objects with the bluest slopes, particularly low-albedo objects, will be under-represented in our fits of p_W2.

To better compare the spectral slope information, in Figure 4, we show the difference in albedo between p_V, p_W1, and p_W2 normalized to the measured p_W1 value. Objects with positive values have a red spectral slope, while objects with negative values have a blue slope. High-albedo objects (p_W1 > 0.1) tend to show red slopes from visible to W1 wavelengths, and then blue slopes between W1 and W2. This behavior is similar to what is observed for Eucrite meteorites at these wavelengths (Reddy et al. 2012b), and what would be expected from extrapolating a typical S-type asteroid spectrum (DeMeo et al. 2009). High-albedo objects without a measured p_W2 albedo show similar visible–W1 slopes to those with a measured p_W2.

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Low-albedo objects (p_W1 < 0.1) behave quite differently from their high-albedo counterparts. While slightly red from the visible to W1, these objects show a wide range of visible–W2 and W1–W2 slopes, from neutral in color to very red. An important caveat to this is shown by the objects without p_W2 fits, which have slopes ranging from moderately red to significantly blue. Blue-sloped objects would be much fainter in W2 than W1 and thus would drop out from detection or be dominated by thermal emission in W2. It is probable that there is a population of these objects with blueW1–W2 slopes that are not represented in our plots. Extrapolating from the NIR spectra of low-albedo objects from DeMeo et al. (2009), we associate our objects that have red visible–W1 slopes with C-type and D-type objects. We can similarly associate the objects having blue-slopes with B-type asteroids; however, we note that only ∼1% of objects studied by DeMeo et al. (2009) were identified as B-type asteroids, while ∼10% of the asteroids in our study have low albedo and blue spectral slope. From Neese (2010), we find that the majority of our blue-sloped objects that have Bus–DeMeo taxonomic classifications are identified as B or Ch class objects, the latter of which represents a fraction of the spectroscopic sample comparable to the fraction of our sample in this group. Our blue slope may be indicative of the presence of mineralogical absorption features in the spectra of low-albedo objects at the wavelengths covered by W1.

Asteroids with D-type taxonomic classifications become increasingly common as distance from the Sun grows, from the main belt through the Jupiter Trojan population (DeMeo & Carry 2013). These objects, especially the Jupiter Trojans, were likely implanted from a more distant reservoir during the early chaotic evolution of the solar system (Morbidelli et al. 2005) and thus represent primitive material distinct from objects that formed in the warmer region of the main belt. NIR albedo can be used to probe the distribution of these objects and differentiate between classes of primitive bodies. Grav et al. (2012) compare p_W1 and p_W2 to distinguish asteroids with D-type taxonomic classification from those with C- and P-type, and are able to determine the overall population fraction of D-type objects in the Jupiter Trojan and Hilda populations. They find that the majority of Jupiter Trojans are D-type at all sizes, while the Hilda population transitions from a minority of D-types at diameters D > 40 km to a majority at smaller sizes.

Following Grav et al. (2012), we show in Figure 5 an expanded view of the objects with lowest infrared albedos. We highlight the region of albedo space that is occupied by D-type asteroids in the Trojan and Hilda populations. The diameter and albedo fits from Grav et al. (2012) rely on the same model and assumptions as we use here, and thus comparisons between the two populations should only depend on the random error associated with the fits. Only 2% of all objects for which we measure p_W1 and p_W2 fall in this region; with the exception of (114) Kassandra and (267) Tirza (which are spectrally classified as T- and D-type objects, respectively), all other candidate D-type objects are in the outer main belt and have diameters between 10 km <D < 40 km, consistent with the diameter regime where D-types dominate the Hilda asteroids. One object, (1755) Lorbach, is identified as an S-type in Neese (2010), but this classification relies on only two optical colors. For the outer main belt, we do not see a significant population of D-type objects like what is observed in the Hildas and Trojans (DeMeo & Carry 2013), but this is expected from the lower efficiency of dynamical implantation compared with the Hilda and Trojan populations Levison et al. (2009).

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We find no objects in the inner main belt with albedos consistent with D-type objects. This is in contrast to the results of DeMeo et al. (2014) who find a small population of these bodies; however, this difference can be understood through the selection effects in our survey. Although our sample probes a large number of objects with semimajor axis, a < 2.5 AU, only a handful have low albedo. Inner-main-belt low-albedo asteroids are more likely to have significant thermal emission in W2, thus we are not able to determine p_W2 for these objects and they will not appear in our analysis.

Figure 5 shows a group of objects with low visible and W1 albedos (p_V, p_W1 < 0.1) but high W2 albedo (p_W2 > 0.1), which also appear as the objects with the reddestW1–W2 slopes in Figure 4. This class of object does not have an analog in the Jupiter Trojan or Hilda populations (Grav et al. 2012) where we find parallels to other low-albedo MBA populations. Objects from this group that have spectroscopic or photometric taxonomic classifications in PDS are typically designated as C-type or a related subclass (Neese 2010). There are occasional objects with other classifications such as X-, F-, and S-, or dual classifications. Though, in these cases, often the designation is based on only two color indices and thus is of low reliability. It is possible that this group could represent a different class of objects that is not found in the more distant solar system populations, or instead could be a failure of the thermal model to converge for certain objects with low albedos.

In order to test if these objects are a result of a failure of the fitting routine, we take all objects in our fitted population with p_W1 < 0.1 and compare the set with p_W2 ⩾ 0.1 to the set with p_W2 < 0.1 (referred to as "low–high" and "low–low," respectively). The low–high and low–low test sets are approximately the same size (44 versus 48 objects) and have similar distributions of semimajor axes, eccentricities, inclinations, p_V, and p_W1. The primary difference between these two groups is that the low–high objects have significantly smaller heliocentric distances at the time of observation than the low–low objects, resulting in higher subsolar temperatures. The diameters of the low–high objects are also characteristically smaller than those of the low–low group; however, we cannot distinguish whether this is an actual difference between the groups or if it is a change in sensitivity as a result of the low–high objects being closer to the Sun and telescope at the time of observation, and thus warmer and brighter.

The asteroid (656) Beagle is a particularly interesting case for testing the differences between these two sets of objects. NEOWISE observed this asteroid at two different epochs, both while fully cryogenic, with good sensitivity at all four bands. One epoch of observations results in an NEATM best fit that falls into the low–low group, while the other epoch falls into the low–high group. The low–high epoch data were taken when Beagle was 0.21 AU closer to the Sun (2.82 AU versus 3.03 AU for the low–low case), following the trend seen for the overall population. The best fit for NEATM in the low–high epoch has a beaming parameter of η = 1.46 and a diameter of D = 62 km while the low–low epoch has best-fit values of η = 1.03 and D = 48 km, which is the reverse of the diameter trend mentioned above. This large disagreement in diameter is not unexpected given the difference in the best-fit beaming parameter, which is inversely proportional to the fourth power of the subsolar temperature used in the NEATM model, and thus will change the model's emitted flux.

The observations used for our fits were visually inspected, as well as compared to the WISE all-sky atlas of stationary sources, and show no significant contamination by background stars or galaxies. We note that (656) Beagle has a large amplitude lightcurve (A >1 mag) and a period of 7.035 hr (Menke 2005). Although large amplitudes can increase uncertainty in the fits, our data consist of 12 data points over 1 day and 15 data points over 1.25 days, thus both epochs cover multiple rotations. As such, light curve variations should be averaged over by our fits and should only contribute a small amount to the total uncertainty in the fit.

As a test of our model, we perform an NEATM fit using only bands W1, W2, and W3 as constraints, assuming that the W4 measurements are anomalously high, and a fixed beaming parameter of η = 1.0. When using a fixed beaming parameter, we cannot adequately constrain p_W2, thus we assume it is equal to p_W1. For these restricted fits, both epochs converge to diameters that agree to within 10%, but they cannot reproduce the measured magnitudes as well as the full-fit case. Because we are using one fewer constraint but two fewer variables, this is not surprising. The fits for (656) Beagle given by Masiero et al. (2011) are nearly identical to these restricted fits, but also cannot fully reproduce the measured magnitudes, particularly for the low–high epoch. Restricting our model further and only fitting W1 and W3, we find that both epochs converge to nearly identical diameters, and visible and infrared albedos.

We can understand these results by looking at where the best-fit model deviates from the data. For the low–high epoch, the full NEATM fit cannot simultaneously reproduce the W2, W3, and W4 fluxes simultaneously, with the W2 and W4 measurements showing excesses not observed in W3. Our full model finds a best-fit solution allowing W3 and W4 to determine the diameter and beaming, which under-produces flux in W2, but corrects that by increasing p_W2. If we ignore the W4 measurements, the W2 and W3 fluxes still cannot be reproduced in the low–high epoch solely with thermal emission and reflected light without resorting to extreme changes in p_W2.

One possible explanation for the disagreement between epochs is that we are observing significant differences between the thermal emission in the morning and afternoon hemispheres of the asteroid. If (656) Beagle has a relatively high thermal inertia, then there may be a significant lag to the thermal re-emission of incident light that is not accounted for in the NEATM model. Our two epochs of observation are at phase angles of α ∼ 20°, but on opposite sides of the body. (656) Beagle is on a low-inclination orbit, thus if we assume the rotation pole is oriented perpendicular to the orbital and ecliptic planes and that the rotation is prograde, then the data from the low–high epoch would correspond to the afternoon hemisphere and the data from the low–low epoch would correspond to the morning hemisphere. Future work will implement a full thermophysical model of this object to test if the W2 and W4 excesses can be explained by a morning/afternoon dichotomy. For all other objects in the low–high group, which were only observed at a single epoch, we cannot currently differentiate between poor fits to the beaming parameter and actual excesses in the W2 and/or W4 bands.

An alternate possibility is that these fits are indicative of problems with the flux measurement of partially saturated sources in the WISE data. Cutri et al. (2012) discuss the process by which fluxes are measured for saturated sources through PSF-fitting photometry. Flux measurements are available for sources many magnitudes above the brightness where the central pixel saturates through fitting of the PSF wings; however, for very bright sources in bands W2 and W3, there appears to be a slight over estimation of the fluxes. None of the objects we fit here had W2 magnitudes in this saturated regime; however, the majority of objects with p_W1 < 0.1 had W3 magnitudes in this problematic region.

We correct for saturation estimation issues in our thermal model; however, there is potential that the error for asteroidal sources cannot be adequately described by this correction, which was calibrated for stars. The difference in the spectral energy distributions through the W3 bandpass of hot, blue stars and cooler, red asteroids could potentially result in differences deep in the wings of the PSF for each type of source that is not fully encompassed by the color correction. These subtle changes can have a significant impact on saturated sources where only the wings are available for profile fitting; however, there are an insufficient number of well-calibrated, W3-bright sources with the appropriate spectral energy distribution to correct for this effect. Although this error may only have a small effect on other physical parameters within our modeled systematic uncertainties, due to W2's position on the Wien's side of main-belt asteroid thermal emission for some of our objects, a small change in W3 can result in a large change in W2 flux, and thus our interpretation of the W2 albedo. As such, caution is strongly encouraged when interpreting fits for objects with very bright W3 magnitudes (W3 <4 mag).

The distributions of visible albedos for members of each asteroid family have much narrower spread than the albedo distribution of the main belt as a whole (Masiero et al. 2011), which is expected from a population resulting from the collisional breakup of a single parent body. As the (4) Vesta family shows a narrow albedo distribution but originated from a differentiated body, we do not expect the albedo distributions of other cratering-event families that may have been partially or fully melted to differ significantly from nondifferentiated families. It is possible that families formed from the complete disruption of a differentiated parent body may show a broader albedo distribution, though we do not see any evidence for a case like this in our data. Visible albedo can also be used to improve family membership lists by rejecting outlier objects that are dynamically similar to the family (Masiero et al. 2013; Walsh et al. 2013). Using the refined family lists from Masiero et al. (2013), we investigate the distribution of p_W1 for families as a more accurate tracer of the surface properties of these asteroids.

Figure 6 shows the distribution of p_W1 albedos for the 8 families where more than 20 members had a p_W1 albedo measurement. Asteroid families break into three clear groupings, following the three peaks in the albedo distribution shown in Figure 3. Our data set depends on reflected light measurements, so high-albedo families are over-represented in the distribution compared with the population of all known families, which is dominated by low-albedo families. The only low NIR-albedo family with more than 20 measured objects was (24) Themis; however, other families such as (10) Hygiea, (145) Adeona, (276) Adelheid, (511) Davida, (554) Peraga (equivalent to other lists' Polana family), and (1306) Scythia also show low NIR albedos, but these families contain only a small number of objects with measured p_W1. The families (4) Vesta, (8) Flora, (15) Eunomia, (208) Lacrimosa, (472) Roma, and (2595) Gudiachvili all have high p_W1 and show only a small spread in mean albedo, while (135) Hertha (equivalent to other lists' Nysa family) and (254) Augusta join them at a lower significance level.

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The (221) Eos family is the only one of the large families to have a moderate NIR albedo in between the high- and low-albedo populations, indicating that this family has surface properties that are rare among the large main-belt asteroids. The p_W1 values for this family confirm the observed moderate visible albedo as a separate grouping that could not be conclusively distinguished from the high p_V population by Masiero et al. (2013). The Eos family parent has a K-type spectral taxonomy in the Bus–DeMeo system (DeMeo et al. 2009). K-type objects are considered "end-members" of the classification scheme, and have a 1 μm absorption feature typically associated with silicates such as olivine, but are distinct in spectroscopic principal component space from the majority of S-class objects. Clark et al. (2009) and Hardersen et al. (2011) associate K-type objects with the parent body of carbonaceous chondrite meteorites, specifically CO chondrites, while Mothé-Diniz (2005) show evidence that (221) Eos may have been partially differentiated. Broz & Morbidelli (2013) calculate the time since the breakup of the (221) Eos family as 1.5–1.9 Gyr, making it one of the oldest main-belt families with a measured age. These observed properties, when taken together, paint the Eos family as having a unique evolutionary history that can be studied using remote observations in combination with hand samples from the meteorite record to trace the early history of the solar system.

We note that approximately half of the objects fit for the (298) Baptistina family had albedos similar to the Eos family, while the remainder appear to be drawn from the high-albedo group. This result is based on only a small number of measured Baptistina members, and thus is not conclusive; however, if confirmed, it would further impede attempts to assign a unique composition to this family (see Reddy et al. 2011) or determine its age and evolution (see Masiero et al. 2012b).

Figure 7 shows the proper orbital eccentricity and inclination of all objects with measured p_W1. The main belt is split into three regions by proper semi-major axis (a): the inner main belt (IMB; 1.8 AU <a < 2.5 AU), the middle main belt (MMB; 2.5 AU <a < 2.82 AU), and the outer main belt (OMB; 2.82 AU <a < 3.6 AU). We show separately the objects that were associated with an asteroid family by Masiero et al. (2013) and those that are members of the background population. The (221) Eos family stands out distinctly in the belt, though objects with similar p_W1 are present in the background population in all three regions.

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These plots show the clear trend of albedo decreasing with distance from the Sun; however, our observational bias against small, low albedo objects amplifies this effect. Broz et al. (2013), Carruba et al. (2013), and Masiero et al. (2013) observe halos of objects beyond the limits of typical family-identification techniques; however, we do not see evidence for these halos in the background population in our data set. Halos are typically associated with asteroids that have dispersed a large distance from the family center via Yarkovsky and gravitational forces, which will have smaller diameters than objects that were above our sensitivity limit for p_W1 determination. Our sample size, which is significantly smaller than what is typically used in surveys investigating family halos, may also contribute to their absence in our data.

In Table 2, we present the orbital and physical properties for all families identified in Masiero et al. (2013) that had at least one member with a fitted NIR albedo. We list the name of the family, the average proper orbital elements, the largest (D_max) and smallest diameter (D_min) represented in our sample, the W1 albedos with standard deviations, and the number of family members with data sufficient to fit. For reference, we also provide the mean, p_V, and standard deviation from Masiero et al. (2013). For cases where only a single body had a measured p_W1 (often but not always the parent body of the family), D_min is marked with a "..." entry and no standard deviation is given for the mean W1 albedo for families with less than 10 members. Asteroids that have been incorrectly associated with families may have very different mineralogies and thus spectral behavior in the NIR, which could make those objects more likely to fulfill the selection requirements for measured p_W1. Thus, particular caution is necessary when dealing with families suffering small number statistics, especially families with only a single p_W1-fit object. We note that the mean p_V albedos presented in Masiero et al. (2013) are based on larger numbers of objects and so will generally be more accurate than the mean p_W1 values given here.

It is also possible to use the W1 albedo to further refine family memberships, particularly for confused cases such as the Nysa–Polana complex. Masiero et al. (2013) divided this complex into a high-albedo component with largest body (135) Hertha and a low-albedo component with largest body (554) Peraga, which is nearly twice the diameter of (142) Polana. We use the NIR albedo to reject objects from the low-albedo family that had moderate visible albedos but W1 albedos characteristic of the high-albedo family. Asteroids (261), (1823), (2717), and (15112) can thus be rejected as members of the (554) Peraga group based on the W1 albedo. We note that because of a typo in Masiero et al. (2013) (135) Hertha was mistakenly listed as associated with (554) Peraga instead of with its own family, which we correct here. Walsh et al. (2013) present dynamical arguments to divide the (554) Peraga family into two sub-families; however, we are unable to see any distinction between these groups in either the visible or W1 albedo.