The NEO Surveyor Near-Earth Asteroid Known Object Model

The near-Earth object (NEO) population is made up of asteroids and comets that are on orbits that take them close to Earth. NEOs are defined as objects with orbits that bring them closer than 1.3 au (perihelion distance q ≤ 1.3 au) from the Sun. They consist of both active and nonactive bodies, where the near-Earth comets make up about 5%–15% of the NEO population (Wetherill 1987, 1988; Bottke et al. 2002; Bauer et al. 2017; Granvik et al. 2018). In this paper, we will focus on the near-Earth asteroid (NEA) population exclusively.

The NEAs can be split into four main subpopulations. The largest of these subpopulations is the Apollos, named after one of its members, (1862) Apollo. They are defined as objects with semimajor axis a > 1. au and perihelion distance q ≤ 1.017 au, consisting mainly of objects whose orbits cross the orbit of the Earth. The Amors, named after their archetype object (1221) Amor, are defined as objects with perihelion distance 1.017 au < q ≤ 1.3 au. The Amors are the second-largest group, consisting of objects whose orbits are entirely outside the Earth's orbit. The Atens are defined as objects with semimajor axis a < 1 au and aphelion distance Q > 0.983 au. They consist of objects with orbits that are mainly inside the orbit of the Earth but cross the orbit of the Earth. The smallest of the four subpopulations is the Atiras, named after the first known object of its kind, (163693) Atira. These objects have orbits with aphelion Q ≤ 0.983 au, putting their entire orbit inside the Earth's orbit. Figure 1 shows the four subpopulations in the semimajor axis and eccentricity space.

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The Minor Planet Center (MPC) ⁵ maintains the official catalog of observations and orbital elements for asteroids, comets, and natural satellites in our solar system. At the beginning of 2023 June, the MPC Catalog contained orbits and observations of more than 32,100 NEAs, of which about a quarter are potentially hazardous asteroids (PHAs), which have a minimum orbital intersection distance (MOID) of ≤0.05 au. Usually the definition of PHAs includes a selection criterion of H_V ≤ 22 mag, with this being traditionally used as a proxy for a diameter of ≥140 m. However, in this work, we consider any object with MOID ≤ 0.05 au to be a PHA, as a dark object with a diameter of 140 m can have an absolute magnitude as faint as H_V ∼ 24 mag.

The Apollos make up ∼51.2% of this cataloged data set; ∼40.8% of the cataloged NEAs are Amors, and ∼7.8% are Atens. Less than 0.2% of the known NEAs are Atiras. Figure 2 shows that the cumulative fractions are relatively stable up to about absolute magnitude H_V ∼ 20 mag, but for higher absolute magnitudes, the fraction of NEAs that are Atens starts rising slightly. The relative fraction of Amors and Apollos remains stable until H_V ∼ 24 mag; at higher absolute magnitude values, the fraction of Apollos starts rising significantly. These fractions are influenced by observational biases, especially at smaller sizes (higher absolute magnitudes), due to the observational geometry. A closer look at these observational biases will be discussed in Section 4.

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In studies of NEAs, two diameter regimes have become important: the objects thought to be larger than 1 km and the population between 140 m and 1 km. The largest objects, with effective diameters larger than 1 km, impact infrequently. But these objects possess the power to cause global extinction events (Alvarez et al. 1980). It is estimated that these objects pose about 90% of the risk from asteroid impacts, and the "Spaceguard" (Milani et al. 1990; Morrison 1992) goal of discovering 90% of asteroids in this size range was created to address this risk. This goal was found to have been completed around 2010 (Mainzer et al. 2011a; Granvik et al. 2018). Community studies (Stokes et al. 2003, 2017; National Academies of Sciences, Engineering, and Medicine 2019) have found that after the Spaceguard goal was achieved, the majority of the remaining risk lay with asteroids larger than 140 m, which are capable of creating significant local or regional damage upon impact. The George E. Brown, Jr. Near-Earth Object Survey Act was passed by the United States Congress in 2005, directing that NASA by 2020 detect and track more than 90% of all NEOs larger than 140 m in effective diameter. ⁶ New discoveries have been dominated by the Catalina Sky Survey (CSS; MPC observatory codes 703 and G96) and Pan-STARRS (PS; MPC observatory codes F51 and F52) over the last decade, together accounting for 80%–92% of discoveries every year covering that time period. In Section 2.1, we will take a closer look at the discovery statistics over the last decade and their implications for understanding the current completeness level of the known NEA population.

One of the fundamental problems in the field of planetary defense is that the goals outlined by Spaceguard and the George E. Brown, Jr. Act are defined in diameter, since impact energy depends on diameter to the third power (∼D³); therefore, accurate knowledge of diameter is important for constraining impact energy. The current major surveys obtain observations at visible wavelengths, allowing for the derivation of orbital parameters and absolute magnitude, but these bandpasses do not allow for direct derivation of the effective spherical diameter. The absolute magnitude at visible wavelengths, H_V , is defined as the theoretical visible magnitude an object would have if it was 1 au from the Sun and Earth at zero phase angle. If the reflectivity of the object is known, i.e., the visible geometric albedo, the size of the object can be determined by $D=(1329/\sqrt{{p}_{V}})\ast {10}^{-0.2H}$ (Tedesco et al. 1992), where D is the diameter in kilometers, p_V is the geometric albedo at visible wavelengths, and H_V is the absolute magnitude. Traditionally, an albedo of p_V = 0.14 has been assumed, which yields H_V = 22 mag for an object with a diameter of 140 m and H_V = 17.75 mag for an object with a 1 km diameter. However, infrared missions like IRAS (Tedesco et al. 1992, 2002), NEOWISE (Mainzer et al. 2011a, 2011b; Wright et al. 2016), and Akari (Usui et al. 2011) showed that the geometric albedo for asteroids varies from about 2% to 60%, with the dark component of the population having a Maxwellian distribution peaking at ∼3% and the rest in a Maxwellian distribution peaking at ∼17% (Wright et al. 2016). About 40% of the NEOs of a given size have p_V < 0.1 (Mainzer et al. 2011c). This introduces complexity in understanding the completeness for effective diameter-limited samples when a majority of observations are obtained at visible wavelengths. Wright et al. (2016) examined what equivalent H_V magnitude would be required in order to reach 90% completeness for NEAs larger than 140 m considering the double Maxwellian distribution of the NEA albedo distribution derived by the NEOWISE mission. They found that in order to reach 90% survey completeness for this size range, a 90% completeness of objects with H_V ≤ 23 mag is needed. We thus use H_V ≤ 23 mag as the appropriate proxy for objects larger than 140 m in this paper, rather than the traditional H_V = 22 mag.

In this paper, we examine the known population of NEAs and how this population will be observed by the NEO Surveyor (NEOS) mission (Mainzer et al. 2023) and compliment its expected performance. NEOS is part of the next-generation surveys for asteroids that could impact the Earth. Previously known as NEOCam (Mainzer et al. 2015), NEOS is a space mission designed to detect, track, and characterize NEAs using thermal emission observations. It recently passed NASA's preliminary design review phase and is scheduled to launch in 2027 September. It is designed to catalog more than two-thirds of the PHAs larger than 140 m in diameter by the end of its nominal 5 yr mission. NEOS uses a reference model of synthetic asteroids and comets to gauge its performance and progress against this goal. See Mainzer et al. (2023) for additional information on the NEOS reference model. However, since the catalog of NEAs and PHAs is not empty at the time of the start of the NEOS mission, it is important to determine a set of proxy objects in the synthetic reference model that represents the currently known objects. This allows for understanding of what types of objects among the current MPC catalog are unlikely to be detected by NEOS and thus would count toward the cataloging goal and which objects that are currently known are likely to also be detected by NEOS, providing both optical and thermal observations that allow for determination of both diameter and geometric albedo. While future ground-based surveys, such as the Vera Rubin Observatory (Vereš & Chesley 2017; Jones et al. 2018), will also contribute to the total number of cataloged NEOs, the actual performance of these future surveys is still in the planning phases, which could potentially have large impacts on their performance in terms of NEO discovery. A study of the performance of the Vera Rubin Observatory (then the Large Synoptic Sky Telescope) and its synergy and overlap with NEOS (then the NEOCam mission) can be found in Grav et al. (2016). Thus, this paper provides a worst-case scenario, where no additional future NEAs are assumed to have been discovered prior to the NEOS launch.

We note that this paper uses data from the MPC catalog extracted on 2023 September 5. The orbits and absolute magnitudes of objects cataloged by the MPC are in a constant state of flux, as additional observations are continuously being submitted by observers from around the world. In this paper, we compare our results to those of Harris & Chodas (2021), but we note here that recent recalculations in the absolute magnitudes for NEOs cataloged has yielded a revision in the number of large NEOs (A. W. Harris, 2023, personal communications). ⁷ The revision resulted in a change of ∼100 fewer NEOs with H_V < 17.75 mag compared to the data used in Harris & Chodas (2021), meaning that the NEOs were, on average, revised to 0.13 mag fainter. This is in line with Pravec et al. (2012), comparing the absolute magnitudes from the MPC catalog with a list of asteroids with high-precision photometric observations, which found that the absolute magnitudes in the MPC catalog were, on average, 0.3 mag too bright.

We examine the current status of the NEA and PHA populations cataloged by the MPC (Section 2). In Section 3, we discuss the NEOS mission, along with the NEOS Survey Simulator (NSS) and the NEOS reference model, two tools used to predict the performance of the NEOS mission in detecting, tracking, and characterizing small bodies in our solar system during its 5 yr nominal mission. The NEOS Known Object Model (KOM) is described in Section 4; this model is applied to the NEOS reference model to determine which of the synthetic objects would be expected to be present in the currently known population. Section 5 examines what portion of the known population is detected by the NEOS survey and which objects remain undetected at the end of the 5 yr nominal mission. Finally, Section 6 discusses the findings of this paper.

At the beginning of 2023 June, the MPC catalog contained more than 32,100 NEAs. Of these, just over 3000 NEAs have been numbered, indicating that their orbits are well known and do not require additional observations to maintain accurate positional predictions over the next century. An additional ∼2000 NEAs have observations spanning more than 10 yr, with 10% of these spanning more than 20 yr, all of which should become numbered in the near future. Only a third of the known NEAs have multi-opposition orbits, with observations at two or more opposition epochs. A majority of the NEAs are only observed during their discovery apparitions, with almost half having been observed for less than 7 days, leaving them basically lost and in need of rediscovery to further refine their orbital parameters.

As mentioned above, the NEA population is divided into four subpopulations. However, the MPC catalog has a heavy observational bias toward certain of these subpopulations, especially the Atens and Apollos, as these objects tend to come much closer to the Earth and can thus be observed at much smaller sizes. Therefore, it is important to look at absolute magnitude–limited samples of the NEAs when considering fractions. When looking at the population of 853 objects with H_V < 17.75 mag, the fraction of objects in the subpopulations are 0.9%, 3.9%, 50.1%, and 45.1% for the Atiras, Atens, Apollos, and Amors, respectively. For the more than 13,000 NEAs with H_V < 23 mag, the proxy we are using for 140 m, the fractions have changed slightly to 0.2%, 5.1%, 49.2%, and 45.5% for the Atiras, Atens, Apollos, and Amors, respectively.

Figure 2 shows the fractions for the four subpopulations when including all objects with a certain absolute magnitude range. The fractions stay relatively consistent to about H_V ∼ 24 mag, where the observational effects favoring discovery of Apollos and Atens become apparent. There is an increase in the number of Atens from 3.9% at H_V ≤ 17.75 mag to 5.1% at H_V ≤ 23 mag, which comes at the expense of the Atira and Apollo subpopulations. This increase in numbers could be due to the effect of observational biases being more strongly apparent at smaller absolute magnitudes than those of the Apollos and Amors. Alternatively, the change could represent a real increase in Atens compared to other populations due to a difference in the source populations replenishing this subpopulation (Bottke et al. 2002). The relative fractions of objects discussed in this section are used when generating the NEOS reference model, which generates a synthetic population of NEAs by using physical parameter models derived using the NEOWISE mission for each subpopulation (Mainzer et al. 2012, 2023).

2.1. The Discovery Rate of NEOs

The number of discoveries of NEAs per year has sharply increased over the last few decades, from 27 discoveries in 1992, to 485 discoveries in 2002, to 991 discoveries a decade ago, to 3189 discoveries in 2022 (see Table 1 and Figures 3 and 4). These steady increases are due to the increases in effort and funding and improvement in technology, as touched upon in Section 1. While the total number of discoveries has sharply increased over the last decade, there has been a significant shift toward discovery of smaller objects. In 2012, objects with H_V < 23 mag made up almost 50% of all discoveries, but in 2022, that number declined to about 23% of discoveries for that year. This trend mirrors the trend seen in the largest objects (H_V ≤ 17.75 mag), which constituted more than half of the discoveries in the mid-1980s. By the late 1990s, they only made up a quarter of the discoveries, even though the number of discovered objects had gone up dramatically (from ∼tens of discoveries to more than 200 objects). Since then, the number of discoveries per year of objects with H_V ≤ 17.75 mag stayed at more than 45 objects for 8 yr before declining steadily year by year to the handful of objects discovered per year currently. This is due to the fact that the objects in this size regime are nearing observational completeness, with the remaining objects being increasingly difficult to discover due to their orbital geometry.

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Table 1. The Yearly Discovery Statistics over the Last Decade

Year	Total	H ≤ 17.75		17.75 < H ≤ 23		23 ≤ H
2011	897	19	2.1%	477	53.2%	401	44.7%
2012	991	15	1.5%	480	48.4%	496	50.1%
2013	1029	11	1.1%	500	48.6%	518	50.3%
2014	1480	8	0.5%	651	44.0%	821	55.5%
2015	1551	7	0.5%	688	44.4%	856	55.2%
2016	1874	7	0.4%	731	39.0%	1136	60.6%
2017	2039	7	0.3%	743	36.4%	1289	63.2%
2018	1825	5	0.3%	614	33.6%	1206	66.1%
2019	2438	6	0.3%	750	30.8%	1682	69.0%
2020	2958	3	0.1%	829	28.0%	2126	71.9%
2021	3093	5	0.2%	730	23.6%	2358	76.2%
2022	3189	4	0.1%	725	22.7%	2460	77.1%

Note. Note that the H magnitude of all NEAs evolves as more observations are reported; thus, the reported numbers above might vary by a few objects when using a different MPC catalog instance than used here.

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Currently, the number of yearly discoveries with H_V ≤ 23 mag has stabilized at an average of 731 objects per year. Harris & Chodas (2021) found that there are between 31,341 objects with H_V < 22.75 mag and 47,577 objects with H_V < 23.25 mag, so we assume from this that there are ∼39,500 objects with H_V < 23 mag. There are about 13,400 objects with H_V ≤ 23 mag in the current MPC catalog, which means that to reach 90% completeness for H_V ≤ 23 mag, as prescribed by Wright et al. (2016) in order to ensure 90% completeness for NEAs larger than 140 m, the current surveys would need to discover an additional 22,000 objects with H_V ≤ 23 mag. At the current discovery rate, this would take more than 30 yr. As discussed for the objects with H_V ≤ 17.75 mag, it is expected that the number of discoveries per year will decline as the completeness of the objects with H_V ≤ 23 mag increases. This would significantly extend the time it would take for the current surveys to reach 90% survey completeness for NEAs with diameters larger than 140 m.

The NEOS is a NASA mission designed to find, catalog, and characterize NEAs. It is a single-instrument 50 cm space telescope operating in two infrared-wavelength channels, centered on 4.6 and 8 μm. At these wavelengths, thermal emission from NEAs dominates the observed flux due to their surface temperatures of 200–300 K. Situated at the Sun–Earth L1 Lagrange point, the mission will perform a nominal 5 yr survey, observing the field of regard of 45°–120° solar ecliptic longitude angle in the range of ±40° ecliptic latitude on either side of the Sun. Each of these sides takes about 6–7 days to complete, allowing NEOS to provide self-follow-up of its discoveries, as most of the moving objects will not have left the field of regard by the time the area is reobserved about 2 weeks later. NEOS is designed to catalog more than two-thirds of the PHAs larger than 140 m in diameter (Mainzer et al. 2023) by the end of its nominal 5 yr mission, with current models showing that it will reach more than 80% completeness for PHAs larger than 140 m. For a more in-depth description of NEOS and its mission, see Mainzer et al. (2023).

The NEOS project team has built a simulation tool, the NSS (Mainzer et al. 2015, 2023; Grav et al. 2016; Masiero et al. 2023), to understand the performance of the mission in making progress toward its design and the George E. Brown, Jr. goal. An integral part of evaluating the success of the NEOS mission is the use of the NEOS reference model, which contains a synthetic NEA population that the project uses as a "yardstick" against which progress is measured. The NEA population of the reference model contains ∼25,000 objects with diameters larger than 140 m. A kernel density estimator (Scott 1992; Virtanen et al. 2020) method using the NEA known population with H_V < 20 mag serves as the input for the orbital elements, and the NEOWISE data set (Mainzer et al. 2011b, 2012) is used as the basis for the model objects' physical properties (see Mainzer et al. 2023 for a more in-depth discussion of the NSS and the NEOS reference model). While the reference model is built using a size–frequency and albedo distribution based on the NEOWISE results, Figure 5 shows that the model is consistent with the absolute magnitude distribution found in the MPC catalog as of the end of 2023 March. All of the results described in this work are based on running at least 10 instances of the NEA reference model through our modeling in a Monte Carlo approach.

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In order to understand the progress of the NEOS mission toward the George E. Brown, Jr. goal, it is necessary to understand which of the synthetic objects in the reference model represent the objects that have already been found and cataloged by the MPC. The NSS uses a simple model to mimic the performance of the historical surveys over the last few decades. The model starts in 1970 and runs forward, tracking which objects in the reference model would be detected and when. For our analysis purposes, we assume that all discovery ends at the date of analysis, in this case the end of 2022, in order to understand a worst-case scenario. We can also extend the model to predict which discoveries would be made up to the 2027 NEOS launch date for a best-estimate analysis as well.

The NSS model for determining what portion of the NEAs in the NEOS reference model are to be considered discovered at the start of the NEOS mission, hereafter called the KOM, uses four parameters that change with time. The four parameters controlling the KOM are the limiting magnitude, the size of the field of regard in ecliptic longitude and latitude, and the chance of discovery if the object is found to be inside the field of regard and brighter than the limiting magnitude. The model uses time steps of 30 days and computes the ecliptic position of each object in an instance of the reference model for each time step. The brightness of each object, V, is calculated using $V={H}_{V}+5\mathrm{log}({\rm{\Delta }}\ast r)-2.5\mathrm{log}(F(G,\alpha ))$, where Δ is the observer-to-object distance, r is the heliocentric distance of the object, α is the phase angle of the object, and F() and G are the phase function and phase coefficient defined in Bowell et al. (1989). The field of regard is centered on the opposition point as seen from the Earth and on the ecliptic plane and has a half-width and half-height as shown in Table 2 (third and fourth columns, respectively). If the object is found to be in the field of regard and brighter than the limiting magnitude (see second column of Table 2) for the time step considered, the object has a chance of being considered discovered equal to that given in the fifth column in Table 2.

The values given in Table 2 are derived through a combination of methods. The first step is data analysis of the MPC catalog (downloaded on 2023 June 30) to determine which observatories dominate the various time periods over the last century (see Figure 6). By the end of the 1970s, only 80 NEAs were known, having been discovered by 22 different observatories, of which Palomar was the only site with more than a dozen discoveries (van Houten et al. 1970, 1984). The next decade, from 1980 to 1989, saw a doubling of the number of known NEAs to 185, with 10 additional telescope recording discoveries. Palomar, MPC site 675, dominated with 67 discoveries in this decade, with no other site achieving double-digit NEA discoveries. Over the next 6 yr, Palomar continued its work with ∼10 new discoveries per year, but this time period saw the rise of the Spacewatch survey at Kitt Peak, MPC site 691, which discovered 134 new NEAs over this time period (Gehrels & Jedicke 1996). Spacewatch was quickly superseded by the dawn of the Lincoln Near-Earth Asteroid Research (LINEAR; Stokes et al. 2000; Stuart 2001) program, MPC site 704, in 1997. LINEAR was the first observatory to reach more than 100 discoveries in the following year. LINEAR continued dominating the discovery of NEAs for 7 yr, discovering an average of 234 NEAs per year, until being superseded as the leading NEA discovery site by the CSS, MPC sites 703 and G96, in 2005 (Larson 2007; Zavodny et al. 2008; Granvik et al. 2018). CSS held the position as the leading yearly NEA discoverer for almost a decade, discovering an average of 477 new NEAs each year over this period. The next major change in the search for NEAs came in 2011, with the introduction of the first of the PS telescopes (Denneau et al. 2013; Chambers et al. 2016), MPC site F51. By 2013, the field, led by the CSS and PS, had increased the number of discoveries to more than a thousand NEAs per year, of which more than 90% were discovered by those two dominating surveys. By the following year, the PS had matched the CSS in NEA discoveries per year at 616 new NEAs for PS and 618 new NEAs for CSS that year. In 2016, the CSS improved the equipment at their MPC site G96, more than doubling the discoveries per year at that site. This was followed just 2 yr later in 2018 by the introduction of the second telescope, MPC site F52, by PS, which gave this project a modest boost of ∼40% new discoveries per year.

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For each of these time periods, we use the discovery observations in the MPC catalog from the known population of asteroids in the inner solar system (excluding any objects discovered past the orbit of Jupiter) to determine a starting point for each of the four parameters (see Figure 7 for an example of the magnitude parameter). Once the starting point has been determined, the KOM is run for a grid of values around these starting values, comparing the number of objects in the MPC catalog with the number of objects identified by the KOM as known for each time period and the absolute magnitudes of less than 17.75 mag, and less than each magnitude from 19 to, and including, 23 (the set [< = 17.75, < = 19, < = 20, < = 21, < = 22, < = 23]). The grid steps start at 0.5 mag for the limiting magnitude, with five degree steps for each field of regard parameter and 5% for the chance of discovery parameter. If none of the grid points yield an average of less than 10% difference for each magnitude limit at the end of the each time period, the grid points are halved, and the KOM is run for each of the new grid points. The resulting model parameter value represents the average value for that time period. We caution that the KOM is a simple first-order model that uses average values over the stated time periods. Additional parameters, such as rate of motion cuts or different latitude limits for each hemisphere, are not considered, as initial tests show that this added granularity does not significantly improve the model results.

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Figure 8 shows the discoveries of NEAs with H_V limits ranging from 17.75 (the traditional proxy of the 1 km objects) to 23 (the proxy of 140 m objects) mag from 1980 to 2022 from both the MPC catalog and the KOM. The most prominent feature is the sharp increase in discoveries of NEAs in 1999, coinciding with the emergence of the LINEAR survey run by Lincoln Labs in New Mexico (Stokes et al. 2000). Another slight increase happens in the mid-2000s with the introduction of the CSS (Larson 2007), operated by the University of Arizona, and then again in the early 2010s by the introduction of the PS project, operated by the University of Hawaii (Denneau et al. 2013; Chambers et al. 2016).

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Applying this model to an instance of the reference model, one can then compare the objects that are considered discovered in the reference model to the known population from the MPC catalog. Figure 8 shows the number of discoveries of NEAs for different limits of absolute magnitude, H_V , from 17.75 to 23 mag, which approximately spans the range from 1 km to 140 m. The number of discoveries reported to the MPC is given by the solid lines, while 10 instances of the NEA reference model (using a minimum diameter of 40 m) are plotted as dashed lines. Note that a model going down to 40 m is needed to evaluate the discovery rate down to the 140 m proxy of H_V ∼ 23 mag, since an object with an effective diameter of 40 m and albedo of 0.5 would have an absolute magnitude of H_V ∼ 23.4 mag. The KOM follows the major trends of the known population at all absolute magnitude cuts modeled. The final number of KOM objects with H_V ≤ 17.75 mag identified as found at the end of 2022 was an average of 4.7% more than the number of objects with H_V < 17.75 mag in the MPC catalog of known objects. A total of 10 random realizations of the NEA reference model were created and processed through the KOM to assess the uncertainty (see Table 3). For the next three absolute magnitude limits of H_V ≤ 19, 20, and 21 mag, the KOM underestimates the number of discovered objects by 12.1%, 13.1%, and 8.3%, respectively. For the H_V < 22 mag set, the KOM is in excellent agreement with the corresponding set from the MPC catalog, only overestimating the number of known objects by 1.7%. The difference grows again for H_V ≤ 23 mag, where the KOM overestimates the number of known objects by 12.0%, on average, over the 10 randomly generated realizations of the NEA reference model.

The differences between the sample of synthetic objects identified by the KOM as known at the end of 2022 and those existing in the MPC catalog as seen in Table 3 are not surprising. Not only is the KOM a simplistic model, but the reference model makes a number of assumptions at smaller sizes due to the lack of information at sizes below 140 m. Specialty surveys, such as those conducted at low ecliptic solar elongation and NEOWISE (Mainzer et al. 2011b, 2012), account for about ∼10% of the discovered objects. These surveys generally have shallower limiting magnitudes or cover less area than the dominant opposition surveys. Since the KOM does not model these surveys, it is expected that it falls short in identifying objects in the NEA population, especially for H_V ∼ 18.5–20.5 mag, which is the absolute magnitude range over which most of the specialty surveys have found objects that are not observable by the opposition surveys. For example, NEOWISE had discovered 393 NEAs by the end of 2022. Of these, 170 have H_V ≤ 20 mag, which alone accounts for almost a quarter of the average difference of 730 objects when the KOM applied to 10 instances of the reference models is compared to the MPC catalog. For the H_V ≤ 21 mag range, NEOWISE has discovered 274 NEAs, which accounts for ∼30% of the difference between the KOM and the MPC catalog. On the flip side, at H_V ≤ 22 mag, the 328 NEA discoveries by NEOWISE would represent an increase of ∼3% in the difference between the model and catalog. To put these numbers in better perspective, we can examine the sample of H_V ≤ 23 mag, the new proxy for 140 m NEAs. At this size range, Mainzer et al. (2011b, 2012) estimated that the uncertainty in our models is ±3000 for NEAs larger than 100 m. According to Harris & Chodas (2021), the completeness level at H_V ≤ 23 mag is ∼30%, which means that our model assumptions introduce an error of ±1000 NEAs, which is significantly higher than the influence of surveys like NEOWISE not being included in the KOM.

The difference between the KOM and the known catalog of NEAs described above may also be partially driven by the assumptions used to generate the NEA reference model. The overabundance of objects found in the KOM for NEA with H_V is consistent with our reference model having an overabundance of objects with H_V ∼ 23 mag. Mainzer et al. (2011b, 2012) estimated that there are 20,500 ± 3000 NEAs larger than 100 m. The NASA NEO Science Definition Report (SDT; Stokes et al. 2017) increased this to ∼25,000 NEOs larger than 140 m while acknowledging that this new estimate was larger than the previous result. This was attributed to using a single size–frequency distribution slope in the range 70 m < D < 1.5 km, but they believed that the differences reflect the uncertainties that exist in the current size–frequency estimates. Thus, by selecting a reference model with 25,000 NEAs larger than 140 m in line with the SDT (Mainzer et al. 2023), the difference between the KOM and the MPC catalog of 1602 objects represents only ∼35% of this uncertainty, which is on the same order as the completeness for H ≤ 23 mag derived by Harris & Chodas (2021). Heinze et al. (2021) also found that NEOs smaller than H_V ∼ 22.5 mag are more common than expected using extrapolation of the size–frequency distribution at larger sizes. In conclusion, it is clear that our understanding of the size–frequency distributions smaller than H_V ∼ 22.5 mag is not well understood, which is exactly the range where a survey like NEOS will be most efficient. It is thus not unreasonable to conclude that the differences between the model presented in this paper and the MPC catalog at H ≤ 23 mag are primarily driven by an overabundance of these objects in our reference model.

Some other reasons for the differences between the number of objects detected by the KOM and the number of objects cataloged by MPC have been considered. As seen in Figure 2, the fractions based on the known population remain relatively stable over the absolute magnitude range covered in this analysis, and the relative fraction of objects as a function of diameter is kept constant during the construction of the NEA reference model. However, the distribution among the subpopulations shown in Figure 2 is based on the raw observed data and may contain observational biases that are not well understood and therefore not incorporated into the KOM. Other similar assumptions, such as the albedo distribution being the same across all diameter bins for each subpopulation, may also not hold, but these assumptions remain the best knowledge we currently have about the NEA population. Furthermore, the reference model makes a number of assumptions at smaller sizes due to the lack of information at sizes below 140 m. It is possible that a break in the size–frequency distribution exists somewhere around ∼100 m, although the location and magnitude of this break remain uncertain (Harris & D'Abramo 2015; Granvik et al. 2018; Harris & Chodas 2021). Such a break would change the relative number of NEAs in the different absolute magnitude limit samples, with objects of 100 m having absolute magnitudes of H_V ∼ 21–25 mag. It is in part due to the uncertainty of the validity of these assumptions that the future generation of surveys, such as NEOS, are of such importance. These future surveys are key in testing our current assumptions and knowledge about the NEA population and will provide new and improved NEA reference models that will help us better understand the danger the NEA population poses.

While the KOM provides a reasonable estimate of the discovery rates of the MPC catalog over the last few decades for a range of absolute magnitude bins, it is also important to make sure that the model is identifying all types of objects regardless of orbital elements and physical properties. Figures 9 and 10 compare the orbital elements of the synthetic population the KOM identified as found compared to the orbital elements of the known objects in the MPC catalog for two absolute magnitude limits. Both figures show agreement between the distributions in semimajor axis, eccentricity, and inclination. One noticeable difference in the H ≤ 23 mag sample is a slight underestimation of found Amor objects in the KOM, which indicates that the Amor population may be slightly underestimated in the NEOS reference model.

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We can also look at the observational biases that exist in a pure opposition survey, which is what the KOM represents. The lack of any Atira asteroids detected in the KOM is one of the clearest biases, but there are also interesting biases among the other subpopulations. When studying the fraction of objects detected as a function of H_V (see Figure 11), it is seen that for the larger objects, H_V ∼ 16 mag, the Amor subpopulation is favored by almost 3% higher completeness over objects in the Apollo subpopulation. This difference increases to almost 10% higher completeness at H_V ∼ 21 mag. At H_V > 23 mag, the difference in the chance of detection drops to close to zero between these two populations. For the Aten population, the observational biases are significant at larger sizes, with only ∼40% of objects detected in the 18 mag < H_V < 22 mag range. At fainter magnitudes, H_V > 23 mag, opposition surveys are more likely to detect Atens, relative to both Apollos and Amors. These biases are a combination of the observational geometry and the on-sky location where the survey is operating, primarily centered on opposition.

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Assuming that the KOM is a reasonable estimate of the known objects currently cataloged by the MPC, we examine the completeness of the current catalog. The cumulative completeness as a result of the KOM for objects with diameters larger than a specific diameter limit is shown in Figure 12. For the larger objects with D ≥ 1 km, the KOM finds a completeness of 87%, which is slightly below the 90% completeness found by Mainzer et al. (2011a) and Granvik et al. (2018). This is mainly due to the lack of low solar angle surveys in the KOM, with NEOWISE alone having contributed 351 new discoveries not accounted for in the KOM. Of these, at least 55 are larger than 1 km (Nugent et al. 2015, 2016; Masiero et al. 2017, 2020, 2021). On average, our 10 random realizations of the NEA reference model have 997 ± 39 NEAs larger than 1 km, with the KOM yielding a completeness of, on average, 88% ± 1% for this size regime. Thus, the additional discoveries provided by NEOWISE represent a significant portion of the difference between the completeness derived by the KOM and that found by Mainzer et al. (2011a) and Granvik et al. (2018).

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For the objects larger than 140 m, the KOM returns a completeness of ∼38.3% ± 0.3% at the end of 2022 when applied to 10 instances of the reference model. This is consistent with the completeness derived by Harris & Chodas (2021), which found 44% completeness for H_V < 22.25 mag, 34% completeness for H_V < 22.75 mag, and 25% completeness for H_V < 23.25 mag. Harris & Chodas (2021) relied mainly on optical observations and thus derived completeness estimates, both cumulative and differential, as functions of absolute magnitude. Figure 13 shows their results compared to the completeness modeled by the KOM across different absolute magnitude limits. It shows that KOM underestimates the completeness down to H_V ∼ 21 mag, which is consistent with the low solar elongation surveys, such as NEOWISE, not being modeled by KOM. At H_V ≤ 23 mag, our proxy for an effective diameter of 140 m, the KOM, and the Harris & Chodas (2021) results are in reasonable agreement. Note that the flattening of the cumulative distribution at H_V > 24 mag is due to the limit in H_V imposed by limiting the reference model used to 40 m or larger.

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One of the questions faced by the NEOS mission is understanding which synthetic objects identified as known by the KOM would and would not be seen by the observatory over its nominal mission. Objects that are both observed in the optical by ground-based surveys (such as those modeled as detected by KOM) and detected in the thermal by NEOS during its nominal 5 yr survey are of particular interest, as both their diameters and albedos can be determined. When applying the NSS with a nominal 5 yr survey planning model to the reference model for NEAs described in Mainzer et al. (2023), we find that for NEAs larger than 140 m, ∼77% of the ∼9750 objects that the KOM identified as currently known will also be detected and tracked by NEOS during its nominal survey. Thus, almost one-third of the NEAs larger than 140 m will have both optical and thermal observations collected at the end of the NEOS 5 yr mission, providing diameter and albedo for an order of magnitude more NEAs with diameters larger than 140 m than are available today (Mainzer et al. 2019; Masiero et al. 2021). Of course, there will also be numerous smaller NEAs with both optical and thermal measurements that will also significantly contribute to the understanding of the NEA populations' physical properties.

Another set of objects of interest is the objects that are already known that will not be detected by NEOS during its nominal mission. While neither diameter nor albedo can be determined for these objects, knowledge of their orbital parameters means that they will remain part of the catalog of known objects, contributing to the final PHA and NEA completeness reached at the end of the NEOS survey. The remaining objects, those that were identified as already known by the KOM but are not likely to be detected by the NEOS, contribute 8%–9% to the total completeness of the catalog at the end of the NEOS nominal mission. Figure 14 shows that the KOM-estimated survey completeness for NEAs larger than 140 m was ∼38% as of the end of 2022. Also shown is the completeness of a single random realization of the reference model for NEAs larger than 140 m, simulating the performance of the NEOS's nominal 5 yr survey. Without any prior knowledge from ground-based surveys, the cumulative completeness from NEOS's 5 yr nominal survey is ∼66% for this size regime. When combining the KOM and NEOS results, the final catalog of known objects would be ∼76% complete. For the PHAs, the completeness is predicted to be 82% (Mainzer et al. 2023) at the end of the NEOS 5 yr mission. As expected, NEOS and the KOM combine to find nearly all NEAs larger than 1 km.

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When looking at the albedo distributions, the observational biases toward the higher-albedo NEAs are clearly seen in the objects identified as cataloged by the KOM (see Figure 15). This feature was pointed out in Mainzer et al. (2011b, 2012). As with the NEOWISE results, NEOS is almost free of biases in albedo and detects objects of all albedos nearly equally well.

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Examining the orbital elements of the objects identified by the KOM and NEOS (see Figures 16–18) shows that ground-based surveys, according to the KOM, are slightly more efficient at detecting Amors (∼42% completeness at the end of 2022) compared to the Apollos (∼38% completeness) and Atens (∼35% completeness) for objects larger than 140 m. For the same size regime, NEOS is more efficient at detecting Atiras, Atens, and Apollos than Amors, with NEOS detecting ∼88% of Atiras, ∼95% of Atens, ∼71% of Apollos, and ∼57% of Amors during its 5 yr mission. The synergy between the currently known object catalog and the objects detected and tracked by NEOS becomes apparent when looking at the ∼9% of NEAs in the reference model larger than 140 m that are identified as cataloged and not seen by NEOS (see Figure 16). A majority, ∼59%, of this set of objects are Amors, followed by ∼40% Apollos and less than 1% Atens.

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When looking at the eccentricity distributions (see Figure 17), the combination of the currently cataloged objects and the objects discovered by NEOS account for almost all objects with eccentricity less than 0.4. The objects with higher eccentricity spend more time further away from the Earth's orbit and need to be closer to the perihelion point in their orbits to be detected and tracked. This can be remedied by extending the NEOS survey duration, giving these objects more time to approach their perihelia when passing through the NEOS field of regard. The inclination distributions (see Figure 18) show similar trends, with nearly all low-inclination objects being cataloged by a combination of the KOM and the NEOS. A vast majority of the objects that are not cataloged have inclinations of 15° or more.

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In this paper, we have shown that, using a simple model called the known object model (KOM), we can provide a reasonable estimate of which NEAs in the reference population model created for the NEO Surveyor (NEOS) mission are currently known. These objects represent the combined efforts of mainly ground-based surveys such as LINEAR (Stokes et al. 2000, 2002), the Catalina Sky Survey (Larsen et al. 2007), and the Pan-STARRS project (Wainscoat et al. 2010; Chambers et al. 2016). The simple model approximately recreates the NEA discovery rate recorded by the MPC catalog over a wide range of absolute magnitudes, H_V ∼ 17–23 mag.

When applying the KOM to a set of randomly generated realizations of the NEOS reference model, it is estimated that the catalog completeness of NEAs larger than 140 m at the end of 2022 stands at ∼38%, which is consistent with the results of Harris & Chodas (2021) when using H_V < 23 mag as a proxy for this population. It is further found that ∼77% of the objects larger than 140 m cataloged by the KOM are identified as also being detected by NEOS in a 5 yr nominal survey. The remaining set of objects larger than 140 m cataloged by the KOM and not detected by NEOS represents ∼9% of the total number of NEAs larger than 140 m in the NEOS reference model. These two sets of objects can be combined with the objects cataloged by NEOS to derive a modeled catalog completeness of ∼76% for NEAs larger than 140 m and ∼82% for PHAs larger than 140 m at the end of the NEOS 5 yr baseline mission (Mainzer et al. 2023).

This publication makes use of data products from the NEO Surveyor, which is a joint project of the University of Arizona and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration.

This publication also makes use of data products from NEOWISE, which is a project of the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration.

This publication also makes use of data products from the Wide-field Infrared Survey Explorer, which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration.

Software: NumPy (Harris et al. 2020), SciPy (Virtanen et al. 2020), Astropy (Astropy Collaboration et al. 2022), Jupyter (Kluyver et al. 2016).