Compositional properties of planet-crossing asteroids from astronomical surveys

Context. The study of planet-crossing asteroids is of both practical and fundamental importance. As they are closer than asteroids in the Main Belt, we have access to a smaller size range, and this population frequently impacts planetary surfaces and can pose a threat to life. Aims. We aim to characterize the compositions of a large corpus of planet-crossing asteroids and to study how these compositions are related to orbital and physical parameters. Methods. We gathered publicly available visible colors of near-Earth objects (NEOs) from the Sloan Digital Sky Survey (SDSS) and SkyMapper surveys. We also computed SDSS-compatible colors from reflectance spectra of the Gaia mission and a compilation of ground-based observations. We determined the taxonomy of each NEO from its colors and studied the distribution of the taxonomic classes and spectral slope against the orbital parameters and diameter. Results. We provide updated photometry for 470 NEOs from the SDSS, and taxonomic classification of 7,401 NEOs. We classify 42 NEOs that are mission-accessible, including six of the seven flyby candidates of the ESA Hera mission. We confirm the perihelion dependance of spectral slope among S-type NEOs, likely related to a rejuvenation mechanism linked with thermal fatigue. We also confirm the clustering of A-type NEOs around 1.5-2 AU, and predict the taxonomic distribution of small asteroids in the NEO source regions in the Main Belt.


Introduction
Asteroids are the remnants of the building blocks that accreted to form the terrestrial planets and the core of the giant planets in the early Solar System 4.6 Gy ago.Asteroids are also the origin of the meteorites that fell on the planets, including the Earth.These meteorites represent the only possibility to study in detail the composition of asteroids in the laboratory (e.g., Consolmagno et al., 2008;Cloutis et al., 2015), with the exception of the tiny samples of rock, provided by return-sample missions: JAXA Hayabusa (Yurimoto et al., 2011) and Hayabusa-2 (Tachibana et al., 2022), as well as the soon due NASA OSIRIS-REx (Lauretta et al., 2017).
In contrast to targeted sample collection, we cannot choose the origin of meteorites striking the Earth.Identifying their source regions is therefore crucial to determining the physical conditions and abundances in elements that reigned in the protoplanetary nebula around the young Sun (McSween et al., 2006).From the analysis of a bolide trajectory, it is possible to reconstruct a meteorite's heliocentric orbit (Gounelle et al., 2006), although such determinations have been limited to only a few meteorites (Granvik & Brown, 2018).Among the different dynamical classes of asteroids, the near-Earth and Mars-crosser asteroids (NEAs and MCs), whose orbits cross that of the telluric planets, form a transient population.Their typical lifetime is of only a few million years before they are ejected from the Solar System, fall into the Sun, or impact a planet (Gladman et al., 1997).We refer here to near-Earth objects (NEOs) in a liberal sense, encompassing both asteroid-like and comet-like objects whose orbits cross that of a terrestrial planet (hence including NEAs, MCs, and some Hungarias).
These populations are of both scientific and pragmatic interest.As they are closer to the Earth than the asteroid belt, we have access to smaller objects from groundbased telescopes.Their orbital proximity implies a much smaller impulsion to reach them with a spacecraft and make them favorable targets for space exploration (Abell et al., 2012).On the other hand, these objects could potentially pose a threat, and studying their properties is a key aspect in planning risk mitigation (Drube et al., 2015), of which the National Aeronautics and Space Administration (NASA) Demonstration for Autonomous Rendezvous Technology (DART) and European Space Agency (ESA) Hera missions are lively demonstrators (Rivkin et al., 2021;Michel et al., 2022).
We focus here on the compositional properties of a large corpus of NEOs as part of the NEOROCKS project (Dotto et al., 2021), whose goal is the characterization of the NEO population.The article is organized as follows:.In Section 2 we present the data we have collected and the way in which we are building a large catalog of NEOs with visible col-ors (including a refinement of the photometry of the NEOs present in the SDSS catalog, Appendix B).We then present in Section 3 the way in which we determine the taxonomic class of each NEO.We focus on the taxonomy of the potential targets for space missions in Section 4, and finally, we discuss the distribution of taxonomic classes, the effect of space weathering and planetary encounters, and NEO source regions in Section 5.

Data sources
In this section, we describe the data sets we collect, how they compare in terms of precision, and the way in which we merge them into a single catalog of colors.The entire process is summarized in Figure 1.

Collecting data sets
We gathered the colors of NEOs from four recently published sources: the Sloan Digital Sky Survey (SDSS, Sergeyev & Carry, 2021), the SkyMapper Southern Survey (SMSS, Sergeyev et al., 2022), the Gaia DR3 visible spectra (Gaia, Galluccio et al., 2022), and a compilation of ground-based spectra (Classy, Mahlke et al., 2022).For the last two sources, we converted the reflectance to colors in order to obtain the largest possible homogeneous data set (Appendix A).
Each SDSS observation sequence contains quasisimultaneous measurements in five filters (u, g, r, i, z), providing colors of all combinations.There is a constant time difference between two exposures in consecutive filters, equal to 57 s.The largest time difference between two exposures occurs for the g and r filters, and is approximately 230 s.The initial SDSS catalog contains 11,142 individual multi-filter observations of 5,425 unique NEOs.For each NEO, we computed the weighted mean of each color from multiple measurements.Owing to potential biases on the SDSS photometry for fast-moving NEOs (Solano et al., 2014;Carry et al., 2016), we remeasured 470 NEO colors on SDSS frames (see Appendix B).
The SkyMapper includes several observing strategies.A shallow six-filter sequence with exposure times between 5 s and 40 s, a deep ten-image sequence of uvgruvizuv with 100 s exposures, and pairs of deep exposures in (g,r) and (i,z).This observing strategy, in conjunction with the enhanced sensitivity in g and r, implies a predominance of g − r colors in the results, but almost always leads to the measurement of at least one photometric color obtained within 2 min (see Sergeyev et al., 2022, for more details).The initial SkyMapper catalog contains 12,001 individual observations of 3,149 unique NEOs.We computed the asteroid color indexes by limiting the observation time between two filters to 20 minutes and weighted the mean color of multiple asteroid measurements whenever possible.Through this method, we retrieved 9,212 colors of 2,081 individual NEOs.The SkyMapper filters are slightly different from those of SDSS.We thus converted the SkyMapper colors into SDSS colors using color-transformation coefficients that were computed from a wide range of stellar classes (Sergeyev et al., 2022).
Gaia DR3 (Collaboration et al., 2016;Vallenari et al., 2022) contains 60,518 low-resolution reflectance spectra of asteroids (Galluccio et al., 2022).Among these, 838 are NEOs, of which 199 have not been recorded in other catalogs.These optical spectra range from 374 to 1034 nm, meaning that they almost fully overlap with SDSS g to z filters (see Figure A.1).We thus converted the Gaia reflectance spectra to SDSS colors to homogenize the data set.We detail the procedure in Appendix A.
The Gaia DR3 represents the largest catalog of asteroid reflectance spectra.However, the spectra of NEOs have regularly been acquired with ground-based facilities for decades, often over a larger wavelength range and with a higher spectral resolution (e.g., NEOSHIELD2, MITH-NEOS, and MANOS surveys, see Perna et al., 2018;Binzel et al., 2019;Devogèle et al., 2019).Therefore, we used the preprocessed and resampled ground-based spectra from Mahlke et al. (2022), which comprises 4,548 spectra of 3,157 unique asteroids.We extracted 1,072 spectra of 846 unique NEOs and converted them to SDSS colors with the same procedure as for the Gaia data (Appendix A).

Comparing data sets
Before merging the four catalogs of colors, we checked for systematic differences in colors and uncertainties among the four data sets.To do this, we did not restrict the comparison to NEOs, but used all of the available asteroid colors from the entire four data sets: 400,894 for SDSS, 139,220 for SMSS, 60,518 for Gaia, and 3,157 for ground-based (Classy).
We cross-matched the asteroid colors from the other sources to the SDSS, which contains the largest number of asteroids and is used as a reference here.We found 67,921, 28,948, and 1,951 asteroids in common for the SMSS, Gaia, and Classy catalogs, respectively.We then computed the color difference between the SDSS and the other catalogs.The distribution of these differences were normal for all pairs of filters and catalogs, with mean values close to zero (Figure 2).The spread (standard deviation) of these differences reflects a combination of several effects: the measurement uncertainties of each catalog (either magnitudes or spectra), the potential effect of asteroid rotation (due to the non-simultaneous acquisition of asteroid images in different filters; see, e.g., Carry, 2018) and observations at different phase angles (Sanchez et al., 2012;Galluccio et al., 2022;Cellino et al., 2020).
The detailed results of this comparison are presented in Table 1.There are small systematic offsets between catalogs on average, much smaller than their standard deviation but larger than the standard error (σ/ √ n, where n is the number of observations).For instance, SMSS matches SDSS with an average g-r color difference of 0.033 mags and a standard deviation of 0.106 magnitude.This was determined using 44,005 shared g-r color measurements that had an error of less than 0.1 magnitude.Although the systematic offset is three times smaller than the standard deviation, the standard error is approximately 0.0005.Therefore, these systematic biases were corrected by adding the precomputed offsets for each color before merging the data sets.
As visible in Figure 2, the width of the color difference distributions is largest between SDSS and SMSS, because both catalogs have the largest color uncertainties.Once the color difference between the catalogs is corrected, the standard deviation can be independently computed as We present a detailed comparison of the color differences and uncertainties in Appendix C. Based on this analysis, we note that some uncertainties are either over-or underestimated (e.g., Gaia and SMSS, respectively), and we applied multiplicatively correcting factors to select the best color value between identical asteroid color measurements in the catalogs (see Table C.1).   1.The mean and standard deviation of the color difference between SDSS and the other samples.The number of asteroids in each of the samples is also reported.We limit the SDSS sample to asteroids with uncertainties below 0.1 mag.
Fig. 4. Distribution of absolute magnitude of MCs (blue) and NEAs (orange).The diameter scale is a guideline, computed with an average albedo of 0.24.

Merging data sets
We merged the four data sets based on asteroid designation (we used the rocks * interface to the name resolver of SsODNet † , see Berthier et al. 2022).Each catalog contains NEOs that have not been measured in the others.
The most prolific source is the SDSS, which contains 4,398 unique NEOs, followed by SkyMapper, with 964 unique NEOs.The Classy and Gaia catalogs contain 507 and 199 unique NEOs, respectively.For NEOs present in more than one catalog, the color with the smallest uncertainty is selected.This results in a catalog of 7,401 NEOs (i.e., NEAs and MCs) with at least one color measurement, which we call NEOROCKS.We collected the ancilllary parameters of each asteroid in our sample with SsODNet, including orbital elements and albedo, for instance.The description of the catalog is presented in Appendix E.
We present in Figure 3 the orbital distribution of the NEOROCKS sample and detail in Table 2 the dynamical classes, including 2277 NEOs (Aten, Amor, Apollo, and Atira) and 5124 MCs.We also included the Hungarians that, owing to their eccentricity, have a perihelion within the orbit of Mars in the MC sample.
The absolute magnitudes in the NEOROCKS catalog extracted from the virtual observatory Solar System open database network (SsODNet) (Berthier et al., 2023) show a bimodal distribution (Figure 4), resulting from the typical larger distance of MCs compared with NEAs.The average absolute magnitude of the NEAs is 19.2 ± 2.0, while it is 17.8±1.3for MCs.Assuming an albedo of 0.24 for all NEOs results in an average diameter of 0.40 +0.61  −0.24 km for NEAs and 0.76 +1.34  −0.35 km for MCs, covering a complessive range from ≈ 10km down to 50m.We chose this albedo as it is the mean albedo of S-type asteroids (Mahlke et al., 2022), the most represented taxonomic class among NEOs (Section 5 and, e.g., Binzel et al. (2019)).

Taxonomy
Taxonomy is a convenient way to summarize observations into a simpler set of labels that describe categories of objects that share the same properties.Asteroid taxonomy is based on the spectral signatures of the light reflected by the surface (e.g., Belskaya et al., 2015;Reddy et al., 2015).Widely used asteroid taxonomy schemes include those of Tholen (1984), using visible colors and albedo, and DeMeo   et al. ( 2009), using visible and near-infrared spectrum (itself an extension of Bus & Binzel, 2002, based on the visible spectrum).These have recently been unified into a taxonomy using both visible and near-infrared spectra and albedos (Mahlke et al., 2022).

Classification of multi-color NEOs
We used the same approach as earlier works on photometry, deriving consistent classification with spectroscopy (e.g., DeMeo & Carry, 2013;Popescu et al., 2018;Sergeyev & Carry, 2021).We converted reference spectra into colors (Appendix A) and used them to define the taxonomic class in the photometry space.To determine the taxonomic class of each asteroid, we employed the probabilistic approach of Sergeyev et al. (2022), which involves computing the intersection between the volume occupied by the color (with uncertainty) of an object and the regions of each taxonomic class.We updated the regions to match the recent taxonomy by Mahlke et al. (2022) instead of using the templates from Bus-DeMeo (DeMeo et al., 2009) and computed the probability for each asteroid belonging to each of the ten broad taxonomy complexes: A, B, C, D, K, L, Q, S, V, and X.
The final taxonomy for each asteroid was selected based on the most probable taxonomic complex.We also provided the second-highest probability taxonomic complex.Asteroids with a likelihood of less than 10% fitting into any taxonomy complex were labeled as U (unclassified).(Appendix E).
We present in Figure 5 the color-color distribution of 2341 NEOs for which taxonomy is predicted with a probability higher than 20%.This constraint was selected to avoid the visual overloading of the figure.The distribution follows the reported color distribution of asteroids in the SDSS filter system (Nesvorný et al., 2005;Parker et al., 2008;Carry et al., 2016).We also present a comparison of pseudo-reflectance spectra based on the photometry of our sample with the template spectra of the taxonomic class from Mahlke et al. (2022) in Figure 6.The correspondence of the SDSS median spectra with the template spectra confirms the chosen taxonomy boundaries.The method provides a reliable way to determine the taxonomic classification of NEOs using photometry data.With the increasing number of NEOs discovered every year, it is becoming increasingly important to be able to classify these objects accurately and efficiently.Spectroscopy is the most accurate method for determining asteroid taxonomy, but it is time-consuming and requires a significant amount of telescope time.On the other hand, photometry data can be obtained much more efficiently, making it a more practical choice for large-scale surveys.

Classification based on a single color
Many observations in the present data set have a significantly better signal-to-noise ratio in the g and r filters.Furthermore, some of the asteroids from the SMSS sample only have g-r color.Thus we also classified asteroids from this single color.We utilized the g-r color of one million asteroid observations from Sergeyev & Carry (2021) to build a reference distribution.We fitted this distribution with two normal distributions, corresponding to two wide complexes (carbonaceous, C 1 , and silicates, S 1 ).We used these two distributions to compute the probability that a NEO belongs to each wide complex, based on its g-r color.Whenever the difference between the probabilities was smaller than 20 percent, we marked these asteroids as unclassified.We present the g-r color distribution of NEOs in Figure 7.It is of course a cruder classification than the classification based on three colors.However, it allows for discrimination between "red" (S, A, V, L, and D) and "blue" objects (C and B) in a manner similar to Erasmus et al. (2020).A significant number of the unclassified asteroids belong to the X complex, while the remainder are of the D-and K-asteroid types.(Figure 8).Although a taxonomy based on a single color may appear limited, we present in Figure 8 the confusion matrix between the one-and three-color classes.The C 1 and S 1 classes accurately separate asteroids belonging to the C complex from those displaying an absorption band of around 1 micron (which are redder: K types, L types, and S complex).
As a final step, we merged the taxonomy obtained with three colors (g-r, g-i, and i-z) and that with a single color only (g-r).The former is preferred over the latter (Appendix E).If neither approach could classify an asteroid, we set the classification method to "none."

Distribution of taxonomy and albedos
The prevalence of S types is striking (Figure 9).It is notable that the distribution presented here is influenced by the selection function of the observations, which introduces a bias, mainly due to the fact that the surveys used here are magnitude limited, which will impact different taxonomic classes of different albedos (DeMeo & Carry, 2013;Marsset et al., 2022).The albedo is an important characteristic related to the composition of asteroids (Tholen, 1989;Mahlke et al., 2022).For instance, asteroids in the B, C, and D classes have low albedos (below 10%) while maficsilicate-rich asteroids (e.g., A, Q, and S types) have albedos around 0.24.The main advantage of taking the albedo into account is the possibility to split the degenerate X complex into high albedo E-type asteroids (albedo above 0.30), moderate albedo M (metallic) asteroids, and the "dark" P asteroids (below 0.10).
We used SsODNet (Berthier et al., 2022) to retrieve the albedo of the NEOs in our data set for a consistency check.In Figure 10 we compare the i-z and g-r colors of 898 NEOs that have estimated albedo values.There is an overall agreement between the range of albedos for the different taxonomic complexes, although outliers are visible.These outliers are a consequence of either misclassifications or biased albedos (Masiero et al., 2021), or both.Mismatches occur mainly in classes with highly different albedos but similar colors, such as D-and L-type asteroids (here, some D types have albedos around 0.2, more consistent with L types).
The albedo distribution of X types reveals that approximately 45% of them are actually P types.The fraction of M types is approximately 45% and the remaining 10% are high-albedo E-type asteroids (Usui et al., 2013).However, P-type asteroids are very similar to C-type asteroids in both color and albedo, and can therefore be misclassified.

Comparison with previous surveys
We compared the distribution of taxonomic classes of the present NEOROCKS sample with the three previous main spectral surveys of NEOs: MITHNEOS (Binzel et al., 2019), NEOSHIELD (Perna et al., 2018), and MANOS (Devogèle et al., 2019) (see Figure 11).The NEOROCKS sample overlaps almost completely with the NEOSHIELD-2 and MANOS catalogs because the Classy data include all available ground-based spectral observations.The overlap with MITHNEOS is limited to approximately half of this catalog, for which a majority of spectra only cover the near-infrared range.While differences are visible (and partly expected owing to the size dependence of taxonomic distribution; e.g., Devogèle et al., 2019), we note an overall agreement with the different data sets.
The confusion matrix presented in Figure 12 indicates that there is a high level of agreement in the taxonomic classification of S-, V-, and X-type asteroids.However, some confusion is observed among the less common classes in the NEOs population, particularly K versus L and (A, L, Q) versus S. Additionally, a significant number of C-type asteroids were classified as part of the wide X asteroid complexes, which also include P-type asteroids that share similar photometry and albedo properties with C-type asteroids.This highlights both the strengths and limitations of using broadband colors as the basis for taxonomic classification.

Targets accessible to space missions
As opposed to other domains in astrophysics, the Solar System can almost be considered as a close neighborhood.Distances are small enough that we have sent space probes (some of which returned), providing ground-truths for Earth-based studies and leading to great discoveries, such as satellites of asteroids (Chapman et al., 1995;Belton et al., 1995), the asteroid-meteorite link (Fujiwara et al., 2006;Yurimoto et al., 2011), and cryo-volcanism (on Ceres, Küppers et al., 2014;Ruesch et al., 2016), for instance.Since the 1990s, opportunities to encounter an asteroid during an interplanetary mission have been considered, and dynamical studies have been conducted to find candidates for potential flyby missions (e.g., Di Martino et al., 1990;Agostini et al., 2022).These candidates are often at the origin of characterization efforts to select the actual target of the flyby and prepare the spacecraft operations during the short encounter (e.g., Doressoundiram et al., 1999;Carry et al., 2010).As a result, there have been almost as many encounters (seven) during opportunity flybys ‡ as targeted encounters with asteroids § (ten).
We searched in the present NEOROCKS data set for any candidate of upcoming space missions (e.g., NASA JANUS, JAXA Hayabusa-2 extension, Scheeres et al., 2020;Yano et al., 2022) and found many objects (  A critical parameter in selecting a space mission target is the amount of energy required to reach it.This quantity is often expressed as the total change of velocity, ∆v.We collected ∆v computed and provided by L. Benner ¶ and for NEOs in our NEOROCKS catalog with a ∆v < 6.5 km, the typical ∆v required for a mission to Mars.We present in Table 4 the taxonomy of these 42 mission-accessible NEOs.‡ (21) Lutetia (Rosetta), ( 243) Ida (Galileo), ( 253) Mathilde (NEAR Shoemaker), ( 951) Gaspra (Galileo), ( 2867) Šteins (Rosetta), ( 9969) Braille (Deep Space 1), ( 5525) Annefrank (Stardust).

Discussion
We used the derived colors and taxonomic classes to address several topics.In Section 5.1Space weatheringsubsection.5.1, we discuss the space weathering for the NEOs in the S complex.We then present the distribution of A types in Section 5.2Distribution of A typessubsection.5.2.We finally discuss the taxonomic distribution of small asteroids in the source regions of NEOs in Section 5.4Source regionssubsection.5.4.

Space weathering
The surface of atmosphereless bodies in the Solar System is aging from micro-meteorite impacts and ions of the solar wind, commonly referred to as space weathering (Chapman, 2004).Space weathering changes the properties of the top-most surface layer (nanometer thick, Noguchi et al., 2011), as function of exposure (age and heliocentric distance) and composition.Thanks to laboratory experiments (e.g., Sasaki et al., 2001;Strazzulla et al., 2005;Brunetto et al., 2006), the effect of space weathering on mixtures of olivines and pyroxenes (such as A, S, and V types) is well understood (Brunetto et al., 2015): it reddens and darkens surfaces.Its effects on the reflectance of more primitive material linked with carbonaceous chondrites (such as B-and C-types) is less straightforward, with both blueing and reddening as possible outputs (Lantz et al., 2017;Lantz et al., 2018) 4. Mission-accessible NEOs (∆v < 6.5 km) with a taxonomy probability above 0.5.
In the case of S types, the effect is expected to be very fast, changing ordinary chondrite-like material (the Q types) into S types in less than a million years (Vernazza et al., 2009).The presence of Q types among asteroids implies that their surfaces are young.Considering the short timescale for space weathering (longer than the timescale to be injected from the Main Belt, Gladman et al., 1997), some rejuvenating mechanisms must be present (Marchi et al., 2012).
Q-type asteroids were originally found among NEOs only, so planetary encounters were proposed as a rejuvenation mechanism (Nesvorný et al., 2005;Nesvorný et al., 2010;Binzel et al., 2010).However, this early observation was due to an observing bias: the fraction of Q increases  toward smaller diameters, which are harder to observe at larger distances (Thomas et al., 2012;Carry et al., 2016).As space weathering is a continuous process (ultimately resulting in asteroids being classified into two groups: S and Q), the observed trend of shallower slopes among S/Q asteroids with smaller diameters explains this bias, and can be explained by a resurfacing due to landslides or failure linked with Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) spin-up (Graves et al., 2018).
Recently, Graves et al. ( 2019) tested another mechanism for rejuvenation among NEOs: a cracking mechanism due to thermal fatigue (Viles et al., 2010;Delbo et al., 2014).Based on almost 300 NEOs (from Lazzarin et al., 2004;Lazzarin et al., 2005;Binzel et al., 2004), this model explains the overall behavior of spectral slope against perihelion, which was apparently misinterpreted as being linked to planetary encounters.
In the present section, we use the large NEOROCKS catalog to address the question of space weathering.Our sample contains 1,175 S-type and 196 Q-type asteroids whose taxonomy is based on three colors with a probability higher than 0.2.We chose to use both the taxonomic types (i.e., the Q/S ratio) and the spectral slope as indicators of space weathering.The former highlights the fraction of very fresh surfaces in the sample, while the latter is more nuanced, with the weathering creating a continuous trend from blue to red surfaces.
We first studied the size dependence of space weathering of S-type asteroids.We present in Figure 14 their spectral slope (computed over the g and i filters, expressed in %/µm consistently with reflectance spectroscopy) against their diameter.A similar plot for the Q/S ratio is provided in  (Harris & Lagerros, 2002) and assuming an albedo of S-type asteroids p V = 0.24.The slope of S-type asteroids is constant for asteroids smaller than approximately 1-5 km, and increases for larger asteroids.This is consistent with the previous report by Binzel et al. (2004).Such behavior was indeed already reported (e.g., Thomas et al., 2012;DeMeo et al., 2023) and explained by resurfacing through YORP spin-up and failure (Graves et al., 2018).The decrease in the Q/S ratio for the smallest NEOs may be attributed to the increasing number of monoliths, for which resurfacing may be difficult.
In Figure 15, we present the relationship between the spectral slope of S-type asteroids and their perihelion.Our analysis shows a probable trend of increasing spectral slope with a more distant perihelion, which is consistent with the findings of previous studies Graves et al. (2019).The spectral slope remains constant until approximately 1.3-1.4AU, beyond which it again increases.As noted by Graves et al. (2019), this last behavior is likely an observing bias: the farther away the asteroids, the less we observe small diameters, and the fraction of fresh surfaces is not constant with diameters (Carry et al., 2016;Graves et al., 2018).A spectral slope value variation is 0.86±0.07(%/µm)/AUfrom 0.2 to 0.8 AU and is 0.64 ± 0.07(%/µm)/AU beyond 1.4 AU.Our analysis shows that within the orbit of Venus, the spectral slope is higher than previously estimated by Graves et al. (2019), who reported a value of 0.52 ± 0.21%/µm/AU.This behavior is also visible in the fraction of Q and S types (Figure 16).There is a strong correlation between the Q/S ratio and the perihelion distance, with the fraction of Q types increasing across a wide range of distances from 0.2 to 1.6 AU.A similar trend was observed by (Devogèle et al., 2019), who compared the perihelion distribution of 138 Stype NEOs to that of 178 NEOs, including 91 Sq and 87 Q subtypes for perihelions ranging from 0.7 to 1.0.Outside this range, however, their data showed a flat behavior.The recent study by (DeMeo et al., 2023) presents an almost linear trend of increasing Q-type asteroid fraction with decreasing perihelion in an interval from 0.5 to 1.3 AU, very similar to our result presented here.
We then tested the level of space weathering against planetary encounters, using the minimum orbit insertion distance ‖ (MOID) as an indicator of the proximity to the planets (following, e.g., Binzel et al., 2010).The Q/S ratio is shown as a function of MOID for the Earth, Venus, and Mars in Figure 17.While there is a trend of increasing fractions of Q-type asteroids toward smaller MOIDs, it happens at distances too far to be due to the planetary encounter and apparently is the result of the correlation with   the perihelion distance.(Carry et al., 2016;Graves et al., 2019).For the Earth, it even drops for MOIDs below the lunar distance, counterintuitively (a similar situation occurs for Mars).We note that here we use the current MOID of each NEO, while Binzel et al. (2010) argued in favor of probing the dynamical history of individual objects (which is beyond the scope of the present analysis).
We finally tested the ratio of Q to S types with the orbital inclination.The ratio is overall flat, with a shallow peak around 15 • and an increase above 30 • .The slightly decreasing fraction of Q asteroids in the inclination range of 15-35 • corresponds to the inclination range of the Hungarias and Phocaeas.The maximum Q/S ratio at 5 • reported by (DeMeo et al., 2023) on 477 S types is three times larger than that of our sample.This disparity may be attributed to differences in the asteroid samples and variations in the techniques employed to distinguish between Qand S-type asteroids.
The present sample contains 1,371 S-and Q-type NEOs, a factor of 2-3 larger than the previous studies.We confirm the trend of decreasing spectral slope (increasing fraction of Q-types) toward smaller diameters.We did not detect a clear signature against orbital inclination.There is a clear increase in the fraction of Q types with smaller perihelion (also visible in the decrease in spectral slope), pointing to a strong effect of thermal fatigue in refreshing asteroid surfaces.

Distribution of A types
A types are a rare type of asteroids in the Main Belt.Their spectra exhibit a broad and deep absorption band around 1 µm, indicating an olivine-rich composition (e.g., Rivkin et al., 2007).They have been thought to originate from the mantle of differentiated planetesimals (Cruikshank & Hartmann, 1984), leading to the "missing mantle issue" (Burbine et al., 1996).The origin of A types is still debated (Sanchez et al., 2014;DeMeo et al., 2019), although, the study of Mars Trojans indicates that certain A-type asteroids could be fragments that were ejected from Mars (Polishook et al., 2017;Christou et al., 2021).
The fraction of A-type asteroids by number in the entire Main Belt is estimated at about 0.16% and are believed to be homogeneously distributed (DeMeo et al., 2019).We report here a fraction of 2.5 ± 0.2% A types among NEOs (focusing on classifications with a probability higher than 0.5).This much higher fraction of A types has already been reported by both the MANOS and NEOSHIELD-2 surveys (Fig. 11Comparison of the distribution of taxonomic classes of the NEOROCKS sample computed from (g-r, gi, i-z) color indexes with the MITHNEOS, NEOSHIELD, and MANOS spectral surveysfigure.11, from 1.7 to 5.5%, Popescu et al., 2018;Devogèle et al., 2019).While a classification based on visible wavelengths only may overestimate the fraction of A (misclassified from red S types owing to space weathering or observations at high phase angles, Sanchez et al., 2012), the fraction of A types among NEOs appears to be an order of magnitude higher than in the Main Belt.Finally, Devogèle et al. ( 2019) reported a concentration of A types with a semi major axis close to that of Mars (1.5 AU).
We present in Figure 18 the fraction of A-and S-type NEOs as a function of semi major axis.While S types are evenly distributed, A types are concentrated between the orbit of Mars and the 4:1 resonance with Jupiter, similar to the report by Devogèle et al. (2019).Most A-type NEOs seem to be related to the Hungarias.In this region, the fraction of A-type asteroids increase by up to 4%.So, while the majority of the Hungarias are C and E types (DeMeo & Carry, 2014;Lucas et al., 2019), approximately 3% of asteroids in this region are A types.

The dependence of asteroid colors on phase angle
The color of an asteroid is determined by the light it reflects, which is influenced by the composition of its surface material.However, the observed color of an asteroid can also change with the phase angle, which is the angle between the observer (usually Earth), the asteroid, and the Sun (Belskaya & Shevchenko, 2000;Waszczak et al., 2015).This change in color with phase angle is likely due to the way light scatters off the asteroid's surface.At higher phase angles, the light we see is more likely to have been scattered multiple times within the asteroid's surface before being reflected back to us.This multiple scattering can cause a redder object to appear bluer and vice versa, al-though this effect is only noticeable for phase angles of less than 7.5 degrees (Alvarez-Candal et al., 2022b).Considering the change in asteroid color with phase angle can be important for accurate taxonomy classification using color analysis techniques (Colazo et al., 2022).
However, the exact mechanisms behind this color change with phase angle are still not fully understood and are an active area of research.The shape of the asteroid, its rotational state, and the macroscopic roughness of its surface can also influence the observed color and its change with phase angle (Carvano & Davalos, 2015).
To investigate the impact of the phase effect on asteroid colors, we compared both the SDSS and SMSS data sets with the absolute magnitude colors from the study by (Alvarez-Candal et al., 2022a).The histograms of the g-i difference between the two data sets are shown in Figure 19.
We also selected asteroids that were observed at phase angles of greater than 20 degrees and had a phase difference of more than 5 degrees between observations.Subsequently, we determined the slope of the asteroid's g-i color as a function of phase angle.We found that color slope changes randomly and is comparable to the uncertainties in color.
To investigate the trends among "red" and "blue" asteroids, we subdivided the asteroid data set into two groups based on their g-i colors.A red group is indicative of silicate asteroids, and a blue group is representative of carbonaceous asteroids.With this analysis, we did not catch any trends toward reddening or bluing within these subsets.The random behavior of asteroid color slope indicates that more significant factors, such as the shape of the asteroid and uncertainties in photometry, may have a greater influence on the observed color and consequently on asteroid taxonomy.
Given that the phase effect could significantly alter the colors of asteroids only at large phase angles, and considering that our sample does not include NEOs observed at phase angles exceeding 40 degrees, we conclude that we cannot precisely predict and then correct the phase effect.Therefore, we did not take the phase effect into account in the color analysis of the NEOs data set.

Source regions
Investigating the orbital and size characteristics, as well as the origin of NEOs, is a crucial area of research in planetary sciences (Binzel et al., 2015;Abell et al., 2015).The dynamical pathway from the source regions to the planetcrossing space is a crucial foundation for studying both in- Phocaea: 34 20.Taxonomic distribution of NEAs as per the seven-region model, previously calculated by (Granvik et al., 2018) dividual NEAs and broader population-level questions.Understanding these distributions gives a holistic understanding of the dynamics, origins, and potential risks associated with NEAs.
To deduce the probable origins of NEAs, we relied on what is known of their orbital properties in conjunction with previously simulated probabilities of seven-region * * escape regions by Granvik et al. (2018).We assigned each asteroid to its most probable origin area by employing a three-dimensional grid of orbital elements and a value of absolute magnitude as the fourth parameter.The grid includes semi major axis, a, eccentricity, e, and inclination, i, which was predicated on the calculations previously detailed in the research of Granvik et al. (2018).The orbital elements of these celestial bodies were obtained from the Minor Planet Center (MPC) database.
The most abundant source of NEOs is the ν 6 , which limits the inner border of the Main Belt.We predict it to be dominated by mafic-silicate-rich asteroids (S, Q, V, see Figure 20).The distribution of taxonomic classes is almost similar for the other source regions in the inner belt: the 3:1 MMR limiting the inner and middle belt, and the Phocaea and Hungaria regions.The fraction of mafic-silicaterich asteroids decreases for source regions located further from the Sun (5:2 and 2:1 MMR, JFC).These are dominated by opaque-rich asteroids (B, C, D, see Figure 20).Despite the observation biases (mainly related to albedo) and the relative low number of NEOs predicted to originate from the outer regions, our results are in close agreement with Marsset et al. (2022), in line with the current understanding of taxonomic distribution (DeMeo & Carry, 2014), but in a smaller size range.* * ν6 secular resonance, 2:1, 3:1, 5:2, mean-motion resonances (MMR) with Jupiter, high inclination Phocaeas and Hungarias, and Jupiter family comets (JFC)

Conclusions
We combined a large sample of colors of planet-crossing asteroids, combining broadband photometry from the SDSS and SMSS surveys and reflectance spectroscopy from the ESA Gaia mission and ground-based observations.We determined the taxonomy of 7,401 NEOs, with diameters from approximately 10 km to 50 m.The sample is dominated by S-type asteroids (approximately 45%), as occurs for other NEOs surveys.However, it is notable that the proportion of S types is overestimated due to observational bias.We also report a much higher (up to 4%) fraction of A types among NEOs as compared to the Main Belt.These A types are concentrated on a semi major axis between 1.5 and 2 AU.We confirm a strong dependence of the spectral slope of S types with perihelion, based on a sample of over one thousand objects.The distribution of slope is consistent with the recently proposed rejuvenation model through thermal fatigue.to ensure meaningful colors for taxonomy: typical color differences between classes are on the order of 0.1 mag (DeMeo & Carry, 2013), and the z filter is crucial for probing the presence of an absorption band around 1 µm (Carry et al., 2016), which has been one of the major discriminants in all taxonomies for the past half a century (Chapman et al., 1975).
First, we estimated the zero-point value of each SDSS frame.We identified non-saturated bright stars and measured their instrumental magnitude with aperture photometry.We then derived the slope and zero-point of individual frames by comparing these values with the photometry from the SDSS PhotoPrimary catalog (York et al., 2000), which contains only stationary sources.
Using the sep package, we identified all sources in cutout images centered on the predicted location of the asteroid.The SDSS images in different filters were obtained sequentially, with a delay of 17.7 s between each of the 54 s exposures.The position of the cut-out image of the asteroid hence changes in each filter, with the largest shift occuring between filters g and r.Therefore, we identified the NEOs in these two filters using SkyBoT (Berthier et al., 2006(Berthier et al., , 2016)), since it provides the best S/N and brackets the other observations.We then predicted the NEOs positions in other filters based on these determinations.We next checked the images visually to select only those NEOs not blended with stars.Whenever a NEO was observed on multiple epochs, we co-added the asteroid-centered cut-out images to increase the asteroid S/N prior to measuring its photometry.
We finally measured the magnitude of each NEO in each filter using an elliptical aperture to account for the PSF elongation due to the fast motion (

Appendix C: Estimation of color uncertainties
In order to select the optimal color value amongst multiple catalogs, we had to take into account color value uncertainty.Nevertheless, there may be situations where the reported photometric errors, calculated via diverse methodologies, do not align.For instance, such discrepancies can arise when uncertainties are quantified as either standard deviations or standard errors, particularly when these uncertainties do not follow a normal distribution.
The availability of color estimates for the same asteroids in the different catalogs allowed us to compare the difference in color distribution with photometric uncertainties.Color indexes, such as the g-r index, represent the difference in magnitude (brightness) between two different wavelength bands for a given object.Uncertainties in these indices can be calculated from the uncertainties in the photometric measurements for each band.
For example, in the g-r color index, the uncertainty can be calculated from the errors in the g and r magnitudes.For two different catalogs, we could represent these calculations as follows: gr1 err = g1 2 err + r1 2 err gr2 err = g2 2 err + r2 2 err .Here, g1 2 err and r1 2 err are the uncertainties of the g and r photometry from the first catalog, and g2 err and r2 err are the uncertainties from the second catalog.If we assume that the color of an asteroid does not change over time, we can calculate the difference in the color indices measured in two different catalogs.This can be done using the previously computed uncertainties: ∆(gr1 − gr2) = gr1 2 err + gr2 2 err , where ∆(gr1 − gr2) is the difference in the g-r color index between the two catalogs and gr1 err and gr2 err are the uncertainties of this color index in the first and second catalogs, respectively.
Estimating the uncertainty of stellar objects is a complex task.While internal errors could provide a reasonable uncertainty estimate, systematic errors may distort these results.It is important to keep in mind that published uncertainties may potentially contain distortions that have not been accounted for.If we consider that the published uncertainties might not be accurate, and the true uncer-  tainties are gr1 err * k1 and gr2 err * k2, where k1 and k2 are unknown factors, in this case, the difference in the color indices can be calculated as ∆(gr1 − gr2) = gr1 2 err * k1 2 + gr2 2 err * k2 2 .In instances where there are more than two catalogs at our disposal, we can calculate the color difference between each pair of catalogs.For example, if we have three catalogs, we can formulate the following: ∆(gr1 − gr2) = gr1 2 err * k1 2 + gr2 2 err * k2 2 ∆(gr1 − gr3) = gr1 2 err * k1 2 + gr3 2 err * k3 2 ∆(gr2 − gr3) = gr2 2 err * k2 2 + gr3 2 err * k3 2 .This formulation provides us with a system of three equations featuring three unknown variables (k1, k2, and k3).These equations can be resolved in order to estimate the authentic uncertainties inherent to each catalog.
In situations involving four catalogs (for instance, SDSS, SMSS, Gaia, and Classy, in our example), we can compute the color differences between every pair, resulting in a system of six equations with four unknowns.This system is generally resolved using a least squares method.The solutions derived from this system would produce the estimated authentic uncertainties associated with each catalog.We extracted the common asteroids from each of our four catalogs and obtained three samples for each of them.For example, for the SDSS catalog, we obtained SMSS, Gaia, and Classy cross-match samples that contain 54,283 27,158, and 1,807 of common asteroids, correspondingly.Cumulative distributions of color errors for four colors are presented in Figure C.1, where we can see the typical photometry error distribution of the SDSS and SkyMapper data that are limited by the magnitude.While the Gaia errors have a uniform distribution because the data have no dependence on the asteroid magnitude, the Classy data have no information about their errors, and therefore we generated random uniform errors in the range from 0 to 0.1 magnitudes.
The variation between the three distributions of the same catalog errors shows a different composition of the common samples.The correction coefficients of color uncertainties for each catalog, calculated using the least squares method, are presented in Table C.1.
We subsequently calculated the cumulative distribution of color differences between asteroids found in varying catalogs.In Figure C.2, we depict the declared cumulative error distribution of each catalog.It is observable that the distribution of the declared SMSS color uncertainties is overestimated compared with the computed distribution, especially within the SMSS ∩ SDSS sample.Conversely, the Gaia uncertainties seem to be underestimated, possibly owing to the manner in which we computed the uncertainties during the derivation of the color.

Fig. 2 .
Fig.2.Distribution of color differences between the SMSS, Gaia, and Classy with respect to the SDSS data set, using asteroids commonly found in these data sets.The distribution was fitted with a Gaussian curve, represented by the black line.The central gray vertical line denotes the zero offset.

Fig. 3 .
Fig. 3. Distribution of the orbital elements of the NEOs, color-coded by dynamic class.

Fig. 7 .
Fig. 7. Distribution of g-r colors in SDSS asteroids and taxonomic categorization of NEOs.Top: Color distribution of one million asteroids obtained from the SDSS (Sergeyev & Carry, 2021) data set modeled by fitting a mixture of two Gaussians (represented by the black line).The two main taxonomic classes, silicate (depicted in orange) and carbonaceous (depicted in blue), were represented by the model.Bottom: Distribution of g-r colors and the taxonomy of NEOs analyzed using the two-component mixture model of the two primary classes in the SDSS data set (shown by lines).The carbonaceous and silicate taxonomy complexes are represented by blue and orange, respectively.Unclassified asteroids, where the probability of belonging to each complex is comparable, are represented in gray.

Fig. 10 .
Fig. 10.Colors and albedo of NEOs.Taxonomy is marked by colored letters (same color-code as in Fig. 5Color-color distribution NEOs with a taxonomy probability above 0.2, color-coded by taxonomic classesfigure.5).Vertical ranges between the panel indicate the one sigma range of albedo for each taxonomic class.(Mahlke et al., 2022).

Fig. 11 .
Fig. 11.Comparison of the distribution of taxonomic classes of the NEOROCKS sample computed from (g-r, g-i, i-z) color indexes with the MITHNEOS, NEOSHIELD, and MANOS spectral surveys.

Fig. 14 .
Fig. 14.Spectral slope of S types as a function of asteroid diameters (gray points), the weighted average in logarithmic size bins shown by red points.Weights were estimated by color uncertainty.

Fig. 15 .
Fig. 15.Spectral slope against perihelion for S types.Red dots and the shaded area are the running average and deviation, and blue lines are linear regressions on the running average.Although the entire sample presents a large spread, the running average shows two kinks.
Figure 16.The diameter of the asteroids (D) was estimated using their known absolute magnitude (H) via the equation D = 1329 • p −0.5 V • 10 −0.2H

Fig. 16 .
Fig. 16.Running mean of the ratio between the number of Q and S asteroids as a function of perihelion, inclination, and diameter.Shaded areas correspond to the uncertainties considering Poisson statistic for the Q/S ratio.

Fig. 17 .
Fig. 17.Running mean of the ratio between the number of Q and S asteroids as a function of their MOID with the Earth, Venus, and Mars.

Fig. 18 .
Fig. 18.Relative distribution of A-types along the semi-major axis.

Fig. 19 .
Fig. 19.Distribution of the difference between the SDSS g-i asteroid colors and absolute magnitude (H) colors from (Alvarez-Candal et al., 2022a) as a function of phase angle.

Fig
Fig. B.1.Examples of fast-moving NEOs in SDSS images.The color images are a combination of FITS images in g (green), r (red), and i (blue) filters.

Fig. B. 2 .
Fig. B.2. Photometry of 2006 UA on SDSS images, illustrating the elliptical aperture.The inner ellipse shows the region in which photons are counted.The two outer circles show the annulus used to estimate the sky background.
Figure B.2).We illustrate the improvement on the photometry in Figure B.3.These updated magnitudes are the ones used in the creation of the NEOROCKS data set.

Fig. B. 3 .
Fig. B.3.Colors of (277958) 2006 SP134 from individual SDSS catalog values (in blue) and from our elliptical photometry (orange).The color boxes represent the limits of taxonomic classes.

Fig. C. 1 .
Fig. C.1.Cumulative distributions of the difference of color for asteroids in SDSS and the rest of the catalogs (blue), as well as their color uncertainties obtained from photometry (orange).

Table 2 .
Distribution of NEOs among dynamic classes.

Table 3 .
Flyby candidates of the ESA Hera mission.At the top of the table are candidates from the shortlist targets, and at the bottom, the candidates from the longlist targets. .
color list: g-r, g-i, r-i, i-z Table E.1.Description of catalog that includes obtained colors, taxonomy, and orbital elements of NEOs. *