The Debiased Compositional Distribution of MITHNEOS: Global Match between the Near-Earth and Main-belt Asteroid Populations, and Excess of D-type Near-Earth Objects

We present 491 new NIR spectra of 420 NEOs mainly between 100 m and 3 km in diameter (Figure 1). These observations were collected for the most part between 2015 January and 2021 February through the MITHNEOS program, with the exception of 10 spectra acquired earlier (between 2003 and 2013), but inadvertently never published before. Combined with our previously published spectra (Binzel et al. 2019), this leads to a data set of NIR spectral measurements for a total of 976 NEOs (many with multiple measurements available) that we analyze in this work.

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Spectroscopic observations were conducted with the 3 m IRTF located on Maunakea, Hawaii. We used the SpeX NIR spectrograph (Rayner et al. 2003) combined with a 08 × 15'' slit in the low-resolution prism mode to measure the spectra over the 0.7–2.5 μm wavelength range. Series of spectral images with 120 s exposure time were recorded in an AB beam pattern to allow efficient removal of the sky background by subtracting pairs of AB images. Asteroid observations were alternated with measurements of calibration stars known to be very close spectral analogs to the Sun: Hyades 64 and Landolt's (1983) stars 93-101, 98-978, 102-1081, 105-56, 107-684, 107-998, 110-361, 112-1333, 113-276, and 115-271. We typically observe three different stars each night to be able to identify possible outlier measurements and to mitigate spectral variability across the observations by computing a mean stellar spectrum from the three measurements. An in-depth analysis of these calibration stars is provided in Marsset et al. (2020).

Data reduction and spectral extraction followed the procedure outlined in Binzel et al. (2019). We summarize it briefly here. Reduction of the spectral images was performed with the Image Reduction and Analysis Facility and Interactive Data Language, using the Autospex software tool to automatically write sets of command files (Rivkin et al. 2005). Reduction steps for the science targets and their corresponding calibration stars included trimming the images, creating a bad pixel map, flat-fielding the images, sky subtracting between AB image pairs, tracing the spectra in both the wavelength and spatial dimensions, co-adding the spectral images, extracting the spectra, performing wavelength calibration, and correcting for air-mass differences between the asteroids and the corresponding solar analogs. Finally, the resulting asteroid spectra were divided by the mean stellar spectra to remove the solar gradient.

All reduced spectra collected through MITHNEOS and information about their observing conditions are made rapidly available to the community by being posted online at http://smass.mit.edu/minus.html. Thumbnail figures of the new spectral data set are presented in Appendix A (the complete figure set is available only in the online journal). The corresponding list of spectra, including results of our spectral analysis, information about the NEOs's physical and orbital properties, observing conditions, and ER probabilities (Section 3.3), is provided in Table 7 in Appendix D.

Taxonomic classification of our new data set was performed as follows. For any spectra for which a thermal tail is detected, a correction to remove the thermal component was applied before classification as described in Section 2.3. Spectra were then run through the Bus−DeMeo principal component analysis (PCA) online classification tool (DeMeo et al. 2009) developed by Stephen M. Slivan and publicly available at http://smass.mit.edu/busdemeoclass.html. We refer the readers to Tholen (1984), Tholen & Barucci (1989), and Bus (1999) for explanations of the PCA method applied to asteroid spectroscopy.

Spectra that have both visible and NIR data available are typically assigned a unique class through this method. Spectra with only NIR data, which includes the majority of our data, are typically assigned multiple possible classes through the tool, and the data either are degenerate (cannot be assigned a unique class because insufficient wavelength coverage exists) or require visual inspection to identify features that indicate the class. Spectra in the S complex (S, Sq, Sr, Sv, and Q types) that are not assigned a unique class with the online tool were then classified according to their 1 μm band spectral properties using the DeMeo et al. (2014) decision tree (see their Figure 3).

The classes of the C and X complexes (B, C, Cb, Cg, Cgh, Ch, X, Xc, Xe, Xk, and Xn types) are generally distinguished with features at visible wavelength ranges, so spectra with only NIR data are assigned "C,X" in most cases. Three exceptions are Xn and Xk types that display a 0.9 μm feature and C types that have a clear broad feature centered near ∼1.3. Additional slope criteria were also used to help distinguish classes. "C,X" spectra with negative spectral slopes were assigned a B type, and those with an NIR slope greater than or equal to 0.20 and 0.38 μm⁻¹ were assigned an X type and D type, respectively.

A final visual inspection was performed for all spectra to ensure that classifications were sensible. As part of the visual inspection process, we append the notation ":" to the spectral class to indicate uncertainty when a spectrum does not clearly, unambiguously fall within that class. Objects with uncertain taxonomic assignment due to a low signal-to-noise ratio (S/N) are marked with the "::" notation. Some spectra were assigned the value "U" and are considered Unusual and Unclassified, as they do not acceptably fall within any defined class. These objects include 143992, 302830, 453707, and 2012 TM₁₃₉. Spectra marked with "::" or classified as "U" were not used in our analysis. Final classifications are provided in Table 7 in Appendix D.

This new classified data set was then combined with previously classified spectra from MITHNEOS (Binzel et al. 2019). In the case where an asteroid was observed multiple times and had distinct taxonomic types assigned to its spectra, the most frequently assigned taxonomic type was selected for that asteroid (for instance, if an asteroid was observed three times and two of its spectra were classified as Sq, whereas the third one was classified as Sw, then the final classification was Sq). If an asteroid had an equal number of two different taxonomic types assigned to its spectra, then the spectrum with the highest S/N was used for final classification.

At Earth's distance from the Sun, an atmosphere-less body with a strongly absorbing surface (low albedo) can reach an equilibrium temperature of ∼300 K, i.e., high enough to emit detectable amounts of thermal flux at NIR wavelengths (e.g., Lebofsky & Spencer 1989; Abell 2003; Rivkin et al. 2005; Reddy et al. 2009, 2012; Binzel et al. 2019). We report here the detection of 17 new objects with an excess NIR thermal flux in our data set. In order to remove thermal excess prior to taxonomic assignment, we applied the near-Earth asteroid thermal model (NEATM) developed by Harris (1998) using a model by Volquardsen et al. (2007) and implemented by Moskovitz et al. (2017) as described in Binzel et al. (2019). We adopt the same fixed parameter values of those works: emissivity of 0.9, slope parameter G = 0.15, and thermal infrared beaming parameter η according to the equation in Masiero et al. (2011) based on phase angle at the time of observation. Appendix B provides the η value used in the model and resulting albedo.

Our aim is to derive the bias-corrected compositional distribution of the overall NEO population, as well as of populations coming from individual ERs in the asteroid belt and beyond. A main bias affecting surveys of small bodies in the solar system is the one that favors the discovery and characterization of bright objects. When observed at visible and NIR wavelengths, for similar sizes, high-albedo asteroids reflect more light from the Sun and therefore can be more easily discovered and characterized than the low-albedo ones. This leads to an observational preference for classes of high-albedo bodies such as the A, Q, S, E, M, and V types compared to classes of dark objects such as the C, P, and D types.

In order to quantify this effect, let us consider a population of NEOs with albedos between p_v and p_v + dp_v , sizes between D and D + dD, and heliocentric distances between r and r + dr. At a given location on the sky, the number of objects is given by

$$\begin{eqnarray}&&n(r,D,{p}_{v})=K\,f(D)g(r)h({p}_{v}){{dp}}_{v}\,{dr}\,{dD},\end{eqnarray} \tag{ 1 }$$

where f(D) is the size distribution of the NEO population, g(r) its radial distribution, h(p_v ) its albedo distribution, and K a normalization constant to obtain the desired number density unit (e.g., number of objects per square degree).

Ignoring phase effects, the apparent magnitude of an object relates to its diameter D and albedo p_v in the following way:

$$\begin{eqnarray}&&m=C-5\,{\mathrm{log}}_{10}(D)-2.5\,{\mathrm{log}}_{10}({p}_{v})+5\,\mathrm{log}(r{\rm{\Delta }}),\end{eqnarray} \tag{ 2 }$$

where Δ is the geocentric range of the object and C is a constant that defines the absolute magnitude system.

Writing the size D in terms of absolute magnitude m and its derivative with respect to m using Equation (2), and assuming that the size distribution of the population can be approximated by a power law of the form f(D) = AD^−α , where A is a normalization constant and α is the power-law slope, Equation (1) can be rewritten in terms of p_v and m as

$$\begin{eqnarray}&&\begin{array}{l}n(r,D,{p}_{v})=\displaystyle \frac{-\mathrm{ln}(10){KA}}{5}\,h({p}_{v}){p}_{v}^{\tfrac{\alpha -1}{2}}\\ \times \ g(r){r}^{1-\alpha }{{\rm{\Delta }}}^{1-\alpha }{10}^{\tfrac{(1-\alpha )(C-m)}{5}}{{dp}}_{v}\,{dm}\,{dr}.\end{array}\end{eqnarray} \tag{ 3 }$$

For a homogeneous population of NEOs named "x" all sharing the same albedo (meaning that h_x (p_v ) = δ(p_v,x − p_v ), where δ is the Dirac delta function) and with distances between r₀ ≤ r ≤ r₁, the number of objects with magnitudes between m₀ and m₁ is

$$\begin{eqnarray}&&\begin{array}{l}{N}_{x}=\displaystyle \frac{-\mathrm{ln}(10){K}_{x}A}{5}\,{p}_{v,x}^{\tfrac{\alpha -1}{2}}\,{\int }_{{r}_{0}}^{{r}_{1}}{\int }_{{m}_{0}}^{{m}_{1}}\\ \times \ g(r){r}^{1-\alpha }{{\rm{\Delta }}}^{1-\alpha }{10}^{\tfrac{(1-\alpha )(C-m)}{5}}{dm}\,{dr}.\end{array}\end{eqnarray} \tag{ 4 }$$

Therefore, the number ratio R_obs of observed objects from two distinct subpopulations ("x" and "y") with similar size distributions and radial distributions but distinct albedos and overall number densities would be

$$\begin{eqnarray}&&{R}_{\mathrm{obs}}(\lt m)=\frac{{N}_{\mathrm{obs},x}}{{N}_{\mathrm{obs},y}}(\lt m)=\frac{{K}_{x}}{{K}_{y}}(\lt m)\times {\left(\frac{{p}_{v,x}}{{p}_{v,y}}\right)}^{2.5\beta },\end{eqnarray} \tag{ 5 }$$

where we substituted $\beta =\tfrac{\alpha -1}{5}$, and where $\tfrac{{K}_{x}}{{K}_{y}}(\lt m)={R}_{\mathrm{true}}(\lt m)$ represents the true intrinsic magnitude-limited ratio of objects from the two subpopulations of NEOs.

The albedo bias affecting the detected population of objects can therefore be accounted for by using an estimate of the average albedo of the taxonomic classes and knowledge about the power-law slope β of the absolute H magnitude–frequency distribution (HFD) of the population. This method was previously used, e.g., by Stuart & Binzel (2004) for the NEO population and by Marsset et al. (2019) and Schwamb et al. (2019) in the case of trans-Neptunian objects.

Two main improvements are made here compared to the work of Stuart & Binzel (2004). First, we take advantage of the increased number of spectroscopic (this work) and albedo (e.g., Mainzer et al. 2011) measurements to better constrain the average albedo of each taxonomic class of NEOs. Second, we make use of the numerical model of Granvik et al. (2018) to probabilistically link each object in our data set to specific ERs in the asteroid belt, thereby allowing a compositional investigation of individual ERs.

We stress that Equation (5) was derived under a number of simplifying assumptions and ignoring physical effects, such as differential phase darkening (e.g., Luu & Jewitt 1989; Sanchez et al. 2012; Perna et al. 2018; Mahlke et al. 2021), that could further bias our sample. Additional biases inherent to targeted small body surveys are discussed by Devogèle et al. (2019, see their Section 5). Despite ignoring these effects, we show in Section 4.2 that our debiasing technique allows us to account for most of the composition difference between NEOs and their predicted ERs in the asteroid belt, confirming that albedo variation is the dominant surface property affecting NEO discovery and characterization surveys.

The first set of observables needed to debias the compositional distribution of NEOs by use of Equation (5) is the set of albedos of the different classes of objects in our data set. Albedo measurements for these objects were retrieved from the following catalogs and papers: Delbo et al. (2003), IRAS (Ryan & Woodward 2010), ExploreNEOs (Trilling et al. 2010), AKARI (Usui et al. 2011), NEOWISE (Mainzer et al. 2011; Nugent et al. 2016; Masiero et al. 2017, 2018), and NEOSurvey (Trilling et al. 2016). For each object, an average value was calculated whenever multiple measurements were available, weighting by the inverse of the squared uncertainty on the measurements.

Our classified spectra (Section 2.2) were then grouped into a broad range of taxonomic classes, A, B, C, D, Q, S, K, L, V, and X types, and a median albedo was calculated for each class. The X complex was further subdivided into E, M, and P types (Tholen 1984) based on albedo values, whenever available. Specifically, an object was classified as P type if p_v ≤ 7.5%, M type if 7.5% < p_v ≤ 30%, and E type if p_v > 30%. X-complex objects without any albedo measurement available were attributed a P type or an M type randomly, weighting the probabilities of the spectral type assignment by the P-to-M ratio measured in the asteroid belt (DeMeo & Carry 2013). Median albedos of the taxonomic classes are reported in Table 1. Asymmetric uncertainties were calculated by 1σ clipping the distribution of albedo values in each class and then measuring the one-sided rms of the remaining distribution in both directions. Due to the low number of albedo measurements, no reliable uncertainties could be measured for the A and K classes.

Table 1. Median Albedo of Taxonomic Classes for NEOs and MBAs

	NEOs (MITHNEOS)		MBAs (DeMeo & Carry 2013)
Taxon	pv	Nobj a	pv	Nobj a
A	⋯	2	0.26 ± 0.05	33
B	${0.09}_{-0.04}^{+0.05}$	16	${0.06}_{-0.01}^{+0.02}$	866
C	${0.04}_{-0.01}^{+0.04}$	13	${0.06}_{-0.02}^{+0.03}$	5018
D	${0.04}_{-0.02}^{+0.03}$	9	${0.08}_{-0.02}^{+0.03}$	428
Q	${0.25}_{-0.04}^{+0.07}$	70	${0.23}_{-0.05}^{+0.06}$	46
S	${0.24}_{-0.05}^{+0.04}$	256	0.25 ± 0.05	6697
K	⋯	4	0.16±0.05	902
L	0.12 ± 0.04	17	${0.17}_{-0.05}^{+0.04}$	692
V	${0.34}_{-0.07}^{+0.08}$	16	0.35 ± 0.06	718
E	${0.55}_{-0.12}^{+0.07}$	23	${0.51}_{-0.18}^{+0.11}$	43
M	0.15 ± 0.03	29	0.14 ± 0.03	770
P	0.03 ± 0.01	26	0.05 ± 0.01	752

Note.

^a Number of objects used to compute the median albedo value of the taxonomic class.

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Because the number of NEOs with measured albedos was low for some taxonomic classes in our data set, we further used the WISE catalog of MBAs (Masiero et al. 2011) to derive albedo values for the subsample of taxonomically classified MBAs from the photometric Sloan Digital Sky Survey (SDSS; DeMeo & Carry 2013). This data set provides one to two orders of magnitude more classified objects than our NEO data set, with the exception of the class of spectrally "fresh" Q-type asteroids more commonly found among NEOs (e.g., Binzel et al. 2010). Again, the derived median albedo of each class and its associated uncertainties are reported in Table 1. The values are globally consistent with the ones measured for the NEO sample. We note, however, that aside from the B types, carbonaceous bodies (C, P, and D types) have lower albedos in the NEO population than in the asteroid belt. This could be due to a change in the optical properties of these bodies as they get closer to the Sun, to NEO observations being performed at higher phase angles on average (Perna et al. 2018), or simply to a sample size effect. While we acknowledge that asteroid surfaces can be spectrally altered as they evolve in the NEO space, our analysis uses the taxonomic albedo values derived from the main-belt data set, which we consider more reliable because they are based on a much larger number of measurements.

The second set of parameters needed to debias our sample are the power-law indices β of the NEO H magnitude distribution, which are both ER dependent and magnitude dependent. We retrieved these parameters for the seven ERs explored by Granvik et al. (2018), namely (by order of increasing distance to the Sun):

• 1.  
  the Hungarias ¹² (Hun)—a group of high-inclination (i ∼ 20°) asteroids isolated at the innermost edge of the main belt (a < 2.0 au) by the 4:1 MMR of Jupiter;
• 2.  
  the ν₆ complex, which delimits the inner edge of the main belt;
• 3.  
  the Phocaeas (Pho)—another group of high-inclination (i ∼ 25°) bodies isolated inside of the 3:1 MMR (a < 2.5 au);
• 4.  
  the 3:1, 5:2, and 2:1 complexes of MMRs near 2.5, 2.8, and 3.3 au, respectively;
• 5.  
  the JFCs.

Note that in the Granvik model, the ν₆, 3:1, 5:2, and 2:1 complexes each regroup several resonances. For instance, the ν₆ complex includes the ν₆ secular resonance, as well as the 4:1 and 7:2 MMRs with Jupiter.

β parameters were retrieved by fitting the HFDs of each ER by a single power-law function over two absolute magnitude ranges, H < 19 and 19 ≤ H < 23, and measuring the slope of the fitting functions. These magnitude ranges were chosen because of (1) the range of magnitudes of the MITHNEOS objects (∼90% fall within 15 < H < 23) and (2) the slope break of the NEO H magnitude distribution near H = 19 (Granvik et al. 2018).

Each NEO in our data set was then linked to a probability distribution function of ERs (and therefore of H magnitude distributions) by use of the model of Granvik et al. (2018). Specifically, given the orbital elements (a, e, i) and H magnitude of the object as input, we computed its probability distribution function, comprising seven discrete values for each of the seven regions. ER probabilities are provided for each new object in our data set as part of Table 7 in Appendix D. The fractional abundances of a given taxonomic group of NEOs in the seven ERs were then obtained by simply dividing its summed ER probabilities by the summed probabilities of the complete set of NEOs.

One object in our data set, (3552) Don Quixote, has a semimajor axis of a = 4.26 au falling slightly beyond the range of distances in the model of Granvik et al. (2018), which has an outer boundary at 4.2 au. ER probabilities for this object were derived by changing its semimajor axis from 4.26 to 4.19 au, assuming that the probabilities do not vary significantly between neighboring cells of the model.

Our sample also includes three active comets. Two of these objects, 162P/Siding Spring (2004 TU12) and 169P/NEAT (2002 EX12), have orbital properties fully consistent with those of JFCs, while the third one, P/2006 HR30 (Siding Spring), belongs to the family of Halley-type comets. Due to its uniqueness in our data set, P/2006 HR30 was not considered in the rest of our analysis.

For each ER, the compositional distribution was derived separately for H < 19 and H > 19, and each magnitude range was debiased independently by use of Equation (5), albedo values from Table 1, and β slope values from Table 2. The debiased fractional abundances from the two magnitude ranges were then summed, weighted by the number of observed objects in each range, and renormalized to obtain the final bias-corrected compositional distribution of the ER. The resulting debiased population is presented and compared to the observed population in Section 4.1.

In an attempt to validate NEO migration models, the main question we aim to address is the following: does the compositional distribution of NEOs match their predicted dynamical source populations in the asteroid belt? The answer will also help us investigate composition change with size in the asteroid belt.

In order to obtain representative samples of the source populations feeding each ER in the main belt, we used the spectrally classified SDSS data set of DeMeo & Carry (2013). The first step consisted of reexamining the size completeness limit of this data set as a function of heliocentric distance and spectral class. To do so, it is a common practice to fit the size–frequency distribution (SFD) of the data set by a single power law and then by measuring the size at which the SFD deviates from the power law. The issue with this method stems from the fact that distinct composition classes with distinct albedos necessarily have distinct size completeness limits. The completeness limit of a compositionally mixed population will necessarily lead to an underestimation of the number of dark bodies in the population and an overestimation of the number of bright objects.

This effect is illustrated in Figure 2, where we compared the SFD of the taxonomically classified data set of DeMeo & Carry (2013) to the SFDs of its dark (B-, C-, P-, and D-type asteroids) and bright (A, S, Q, K, L, V, E, and M types) subcomponents. It is clear from this figure that the dark subpopulation deviates from the fitted single power-law function at a slightly larger diameter than the overall population, and an even larger diameter compared to the bright subpopulation. For instance, in the inner belt, the dark classes deviate at a diameter of 4 km, whereas the overall population deviates near a diameter of 2 km. While this difference might seem small, it triggers important implications for the resulting composition of the size-limited sample owing to the steep SFD of the asteroid belt. This steep distribution implies that most objects in a size-limited sample are close to the lower-size boundary and therefore to the potentially incorrect completeness limit.

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To mitigate this bias, we adopted a conservative approach consisting of deriving the size completeness limit from the dark subpopulation alone (DeMeo & Carry 2013 had a similar approach that consisted of deriving absolute magnitude cuts for each taxonomic class individually). By doing so, we derive size completeness limits of 4 km for the inner belt (defined as inward of the 3:1J MR, i.e., semimajor axis a < 2.5 au), 4.5 km for the middle belt (between the 3:1J and 5:2J MMR, i.e., 2.5 <a < 2.8 au), and 7.0 km for the outer belt (beyond the 5:2J, i.e., a > 2.8 au; Figure 2). These values constitute the lower-size boundary of our MBA comparison sample. The upper boundary was chosen to be 3 km larger, in order to obtain a large number of objects in our comparison sample while still being in a range of sizes that is not too different from our NEO data set.

Next, we built a representative sample of each source population feeding the ERs. This was achieved by measuring the ranges of initial semimajor axis and inclination values of the test particles ending up in the ERs in the dynamical simulation of Granvik et al. (2018, see their Figure 3, second panel) and selecting MBAs falling within these ranges of values. Selection criteria for each source population are summarized in Table 3. Unfortunately, the resulting low number of Hungaria MBAs (22 objects) does not allow any statistically significant comparative analysis between Hungaria NEOs and these objects. Increasing the upper size boundary of the Hungaria comparison sample only adds a few objects to the sample.

Next, we evaluated the statistical robustness of the resulting taxonomic ratios in our comparison data sets. To do so, the lower and upper size limits of the data sets were varied independently over a 1 km range, with incremental steps of 0.1 km, in order to measure the variation of the taxonomic ratios as a function of varying size boundaries. For instance, in the case of the inner-belt ERs (the ν₆, 3:1J, and Phocaea), the lower size limit was varied from 4 to 5 km while keeping the upper limit fixed to 7 km, and then the upper limit was varied from 7 to 6 km while keeping the lower limit fixed to 4 km. This resulted in a total of 22 data sets for each ER from which the taxonomic ratio uncertainty linked to size boundary selection, defined as the 1σ variation of the taxonomic ratios, was measured. Final error bars on the taxonomic ratios of the comparison data sets are the quadratic sum of the Poisson uncertainties (i.e., $\sqrt{N}$, where N is the number of objects in the data set) and the size boundary uncertainties.

The MITHNEOS data set and the SDSS-derived MBA comparison sample are composed of spectroscopic and photometric data collected over two distinct wavelengths ranges: the NIR range (0.7–2.5 μm) for MITHNEOS, and the visible range (0.3–1.0 μm) for SDSS. Several taxonomic classes of asteroids can only be distinguished in one of these two wavelength ranges. This is the case, in particular, for the C and X complexes that are often indistinguishable in the NIR (see Section 2.2). Similarly, Q- and S-type asteroids can hardly be distinguished at low spectral resolution in visible wavelengths.

In order to allow a direct comparison of our NEO data set with the asteroid belt, we therefore merged objects belonging to the C and X complexes (more specifically, objects from the C complex and the low-albedo objects from the X complex, i.e., the P types) into a single class, hereafter simply named "C/P." Similarly, Q-type and S-complex asteroids were merged into a single class "S/Q."

The observed and debiased compositional distributions of the overall NEO population and individual ERs are shown in Figure 3. In agreement with previous works (e.g., Tholen 1984; Zellner et al. 1985; Tedesco & Gradie 1987; Veeder et al. 1989; Binzel et al. 2004; Carry et al. 2016; Perna et al. 2018; Binzel et al. 2019; Devogèle et al. 2019), the overall observed population is dominated by silicate-rich (S- and Q-type) bodies, accounting for ∼66% of objects in our data set. The two most proficient ERs, the ν₆ and 3:1J complexes, exhibit very similar distributions to one another (Pearson correlation coefficient of 99.8%). This is unsurprising considering that both ERs are dominantly fed by the inner-belt population of asteroids. As we move toward ERs located at larger heliocentric distances, the observed fraction of silicate-rich objects gradually decreases and the fraction of carbonaceous objects (B, C, P, and D types) increases, with the 2:1J and JFCs exhibiting the highest fractions (55%–62%) of carbonaceous objects. The relatively high fraction of silicate-rich objects among JFCs is here likely an artifact due to the low number of comets in our sample, as well as the correlated ER probabilities of the 3:1J, 5:2J, and JFCs.

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As expected, bias correction leads to greater fractional abundances of dark objects and smaller fractional abundances of bright objects in the NEO population. The abundance of silicate-rich objects decreases from 66% to 42% globally, while the abundance of carbonaceous objects increases from 23% to 48%. It is evident from Figure 3 that the effects of debiasing are both albedo dependent and ER dependent. The greater the difference in albedo between a specific taxonomic class of objects and the average population, the greater the change in fractional abundance. Similarly, the steeper the HFD of a given ER, the greater the change in dark-to-bright ratio when debiased. For instance, Hungaria NEOs are the least affected population owing to their flat HFD below H = 19 (β = 0.074), where most NEOs with high Hungaria ER probability are found in our data set.

Like the observed population, the debiased NEO population reflects a composition gradient in the main belt, with a decreasing fraction of silicate-rich bodies and an increasing fraction of carbonaceous bodies as a function of increasing heliocentric distance of the ER. In addition, NEOs from the various ERs exhibit a wide diversity of taxons supporting the idea of a well-mixed population of small (D < 2 km) asteroids in the main belt. This mixed distribution agrees well with the distribution of the smallest asteroids observed in the main belt (see Section 4.2) and contrasts with the more radially stratified distribution of large (D > 20 km) asteroids (DeMeo & Carry 2013). This difference between small and large asteroids is commonly attributed to the increased efficiency of the Yarkovsky drift, as well as dynamical pushes due to planetary encounters and resonant orbits toward smaller body sizes.

4.2.1. Global Compositional Match

Figure 4 compares the observed and debiased compositional distributions of NEOs derived in this work with their corresponding source populations in the asteroid belt, as defined in Table 3. For readability purposes, only the main (most populated) taxonomic classes of asteroids (B, C/P, D, S/Q, and V types) are shown. A second version of the figure showing every class is provided in Appendix C. Due to the low number of Hungaria MBAs in the relevant range of sizes (Section 3.4), this population of objects is not shown in the figure.

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The observed fractional abundances of each taxonomic complex were assigned Poisson error bars (${\sigma }_{N}=\sqrt{N}$). The error bars of the debiased fractional abundances were derived by propagating the Poisson uncertainty on the observed fractional abundances, the uncertainty on the albedo, and the uncertainty on β as computed by Granvik et al. (2018) for 17 <H < 22 (see their Table 4). Taxonomic abundances for the debiased NEOs and the comparison MBA source populations are provided in Table 4.

Table 4. Taxonomic Ratios of the Observed and Debiased NEO Populations, Compared to Their Source Regions in the Asteroid Belt

Source	Taxon	% NEOs	% NEOs	% MBAs	Difference	Difference
Region		(Observed)	(Debiased)		(Observed)	(Debiased)
ν6	A	0.5 ± 0.3	0.3 ± 1.9	0.2 ± 0.1	0.3 ± 0.3	0.1 ± 1.9
	B	3.3 ± 0.8	${7.4}_{-3.2}^{+3.1}$	7.8 ± 0.7	4.5 ± 1.0	${0.4}_{-3.3}^{+3.1}$
	C/P	14.5 ± 1.1	${33.7}_{-11.5}^{+7.3}$	34.1 ± 1.4	19.7 ± 1.8	${0.4}_{-11.5}^{+7.4}$
	D	2.2 ± 0.6	${4.2}_{-2.5}^{+2.1}$	0.9 ± 0.1	1.3 ± 0.6	${3.3}_{-2.6}^{+2.1}$
	S/Q	67.2 ± 2.4	${44.4}_{-5.9}^{+5.7}$	40.5 ± 1.4	26.7 ± 2.8	${3.9}_{-6.1}^{+5.9}$
	K	1.0 ± 0.4	1.0 ± 0.8	1.9 ± 0.1	0.9 ± 0.4	0.9 ± 0.8
	L	3.8 ± 0.8	3.7 ± 1.6	2.7 ± 0.2	1.2 ± 0.8	1.0 ± 1.6
	V	3.5 ± 0.8	1.7 ± 2.5	8.4 ± 0.6	4.9 ± 1.0	6.8 ± 2.6
	E	1.2 ± 0.4	0.4 ± 3.6	0.2 ± 0.0	0.9 ± 0.4	0.2 ± 3.6
	M	2.9 ± 0.7	3.3 ± 1.2	3.2 ± 0.0	0.4 ± 0.7	0.0 ± 1.2
Pho	A	0.4 ± 1.2	0.4 ± 1.6	0.0 ± 0.0	0.4 ± 1.2	0.4 ± 1.6
	B	1.8 ± 2.5	3.4 ± 4.9	0.0 ± 0.0	1.8 ± 2.5	3.4 ± 4.9
	C/P	9.6 ± 4.1	18.2 ± 7.9	31.9 ± 2.8	22.4 ± 5.0	13.7 ± 8.4
	D	2.6 ± 3.0	2.8 ± 3.3	2.8 ± 1.1	0.2 ± 3.2	0.0 ± 3.5
	S/Q	77.0 ± 11.6	69.1 ± 10.5	59.7 ± 4.9	17.3 ± 12.6	9.4 ± 11.6
	K	1.5 ± 2.3	0.4 ± 0.8	1.4 ± 0.9	0.2 ± 2.5	1.0 ± 1.2
	L	1.0 ± 1.8	0.8 ± 1.5	0.0 ± 0.0	1.0 ± 1.8	0.8 ± 1.5
	V	5.0 ± 4.2	3.8 ± 3.5	1.4 ± 0.9	3.6 ± 4.3	2.4 ± 3.6
	E	0.4 ± 1.1	0.2 ± 2.1	0.0 ± 0.0	0.4 ± 1.1	0.2 ± 2.1
	M	0.6 ± 1.5	0.8 ± 1.9	2.8 ± 0.2	2.1 ± 1.5	2.0 ± 1.9
3:1J	A	0.5 ± 0.6	0.3 ± 3.4	0.2 ± 0.0	0.3 ± 0.6	0.1 ± 3.4
	B	3.9 ± 1.6	${8.3}_{-4.8}^{+4.7}$	5.4 ± 0.3	1.5 ± 1.7	${2.9}_{-4.8}^{+4.7}$
	C/P	15.3 ± 2.3	${34.3}_{-9.1}^{+7.3}$	34.6 ± 1.3	19.3 ± 2.6	${0.3}_{-9.2}^{+7.4}$
	D	4.7 ± 1.8	${8.5}_{-4.5}^{+4.2}$	1.5 ± 0.0	3.2 ± 1.8	${7.0}_{-4.5}^{+4.2}$
	S/Q	68.6 ± 4.8	43.3 ± 5.6	45.4 ± 0.9	23.1 ± 4.9	2.2 ± 5.6
	K	1.2 ± 0.9	1.1 ± 1.4	2.3 ± 0.1	1.1 ± 0.9	1.2 ± 1.4
	L	1.2 ± 0.9	1.1 ± 1.6	4.1 ± 0.2	2.8 ± 0.9	3.0 ± 1.6
	V	2.3 ± 1.2	1.1 ± 4.6	3.6 ± 0.4	1.3 ± 1.3	2.5 ± 4.7
	E	0.6 ± 0.7	0.2 ± 6.5	0.1 ± 0.0	0.5 ± 0.7	0.1 ± 6.5
	M	1.6 ± 1.1	1.8 ± 1.2	2.8 ± 0.0	1.2 ± 1.1	1.0 ± 1.2
5:2J	A	1.0 ± 1.1	0.5 ± 2.1	0.2 ± 0.1	0.8 ± 1.1	0.4 ± 2.1
	B	2.2 ± 1.7	4.0 ± 3.7	5.5 ± 0.6	3.2 ± 1.8	1.4 ± 3.7
	C/P	21.4 ± 3.6	${47.7}_{-9.2}^{+8.7}$	42.1 ± 1.5	20.7 ± 4.0	${5.5}_{-9.4}^{+8.9}$
	D	9.0 ± 3.3	${14.3}_{-5.8}^{+5.7}$	3.0 ± 0.4	6.0 ± 3.4	${11.3}_{-5.8}^{+5.7}$
	S/Q	60.7 ± 6.1	29.8 ± 3.7	29.6 ± 2.1	31.1 ± 6.5	0.2 ± 4.3
	K	1.3 ± 1.3	1.0 ± 1.1	8.8 ± 0.3	7.5 ± 1.3	7.8 ± 1.1
	L	1.5 ± 1.3	0.6 ± 1.3	4.3 ± 0.4	2.8 ± 1.4	3.7 ± 1.4
	V	1.3 ± 1.3	0.5 ± 2.9	0.2 ± 0.0	1.1 ± 1.3	0.3 ± 2.9
	E	0.2 ± 0.5	0.1 ± 4.8	0.1 ± 0.0	0.1 ± 0.5	0.0 ± 4.8
	M	1.4 ± 1.3	1.5 ± 1.4	6.2 ± 0.0	4.8 ± 1.3	4.7 ± 1.4
2:1J	A	0.3 ± 1.1	0.1 ± 0.6	0.0 ± 0.0	0.3 ± 1.1	0.1 ± 0.6
	B	12.7 ± 7.3	23.4 ± 13.4	9.8 ± 0.4	2.9 ± 7.3	13.6 ± 13.4
	C/P	38.9 ± 9.0	${59.9}_{-14.0}^{+13.9}$	64.9 ± 1.3	26.0 ± 9.1	5.0 ± 14.0
	D	3.6 ± 3.9	5.1 ± 5.5	5.6 ± 0.3	1.9 ± 3.9	0.5 ± 5.5
	S/Q	30.3 ± 7.9	7.2 ± 2.0	6.3 ± 0.6	24.1 ± 8.0	0.9 ± 2.1
	K	0.3 ± 1.1	0.1 ± 0.6	5.8 ± 0.6	5.5 ± 1.2	5.7 ± 0.9
	L	6.5 ± 5.2	1.2 ± 1.0	2.4 ± 0.2	4.1 ± 5.2	1.2 ± 1.1
	V	0.2 ± 1.0	0.0 ± 0.8	0.1 ± 0.0	0.2 ± 1.0	0.0 ± 0.8
	E	2.8 ± 3.4	0.3 ± 1.5	0.1 ± 0.0	2.7 ± 3.4	0.3 ± 1.5
	M	4.2 ± 4.2	2.6 ± 2.6	5.1 ± 0.0	0.9 ± 4.2	2.5 ± 2.6

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Globally, the debiased taxonomic abundances of NEOs closely match the taxonomic distribution of their predicted source populations in the asteroid belt. In Table 5, we provide the Pearson r coefficient and corresponding p-value for a correlation between the NEO and MBA populations. For each ER, we also provide the maximum difference between the measured taxonomic ratios of the NEO and MBA populations. In every case, the bias correction greatly improves the correlation between the NEOs and their source populations and significantly decreases the compositional gap between these populations.

Table 5. Results of Statistic Tests Used to Assess the Compositional Similarities of the Observed and Debiased Compositional Distributions of NEOs, Compared to Their Source Regions in the Asteroid Belt

Source Region	Observed NEOs versus MBAs				Debiased NEOs versus MBAs
	Coeff. of Correlation*	p-value a	Max. Diff. b	Taxon	Coeff. of Correlation*	p-value*	Max. Diff. b	Taxon
ν6	84.4%	2.2e-03	26.7 ± 2.8%	S/Q	98.4%	2.7e-07	6.8 ± 2.6%	V
Pho	91.8%	1.8e-04	22.4 ± 5.0%	C/P	96.4%	7.4e-06	13.7 ± 8.4%	C/P
3:1J	88.3%	7.0e-04	23.1 ± 4.9%	S/Q	98.3%	3.8e-07	${7.0}_{-4.5}^{+4.2}$%	D
5:2J	72.7%	1.7e-02	31.1 ± 6.5%	S/Q	94.7%	3.2e-05	${11.3}_{-5.8}^{+5.7}$%	D
2:1J	79.0%	6.5e-03	26.0 ± 9.0%	C/P	96.3%	8.0e-06	13.6 ± 13.4%	B

Notes.

^a Coefficient of correlation and p-value from Pearson r test. ^b Maximum difference in fractional abundance between the populations, with corresponding taxonomic class indicated in the following column.

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The global compositional match between NEOs and their predicted source populations in the asteroid belt provides a direct validation of the NEO migration model of Granvik et al. (2018) used in this work. This compositional match also argues against any drastic composition size trend in the asteroid belt, in the range of diameters studied here (i.e., from ∼10–4 km for the MBA data set down to typical NEO sizes, ∼3 km–100 m). Deviations from this compositional agreement are discussed in Section 4.2.2.

4.2.2. Local Compositional Differences