CONSTRAINING THE PHYSICAL PROPERTIES OF NEAR-EARTH OBJECT 2009 BD

The physical properties of near-Earth objects (NEOs) provide important hints on their origin, as well as their past physical and orbital evolution. The most accessible physical properties are the diameter, d, and the geometric albedo, p_V, which have been measured for more than 1000 NEOs with diameters down to slightly less than 100 m in two large-scale programs, the Warm Spitzer NEO survey "ExploreNEOs" (Trilling et al. 2010), and the "NEOWISE" project (Mainzer et al. 2011), using the Wide-field Infrared Survey Explorer (Wright et al. 2010). Recently, Mainzer et al. (2014) measured the sizes and albedos of the smallest optically discovered NEOs (d > 10 m) from NEOWISE data. Little is known about the physical properties of even smaller NEOs, which constitute the bulk of the NEO population. Knowledge of the physical properties of such small NEOs, some of which pose an impact threat to the Earth, is of importance for understanding their evolution and estimating the potential of destruction in case of an impact, as well as for designing the most promising mitigation mission.

Further information on asteroid physical properties are available only for select objects with relatively large sizes, which make up only a fraction of the whole asteroid population. Such properties include, but are not limited to, the bulk density, ρ, thermal inertia, Γ, and the obliquity, γ, all of which affect non-gravitational forces that act upon the body and alter its orbit compared to a Keplerian one. Two important effects are the Yarkovsky effect (see, e.g., Bottke et al. 2006) and the solar radiation pressure (Vokrouhlický & Milani 2000).

The bulk density, ρ, provides the simplest way of gaining insight into asteroid interiors. Solid rock, or monolithic, bodies have high bulk densities (ρ  ∼  3 g cm⁻³), whereas those of rubble-pile bodies, aggregates of smaller particles that are consolidated by their self-gravity or other adhesive forces (Chapman 1978), can be significantly lower as a result of "macroporosity." Macroporosity refers to cavities and void spaces that occur between the irregularly shaped individual constituents (see Richardson et al. 2002; Britt et al. 2002, for a discussion). Britt et al. (2002) found that most asteroids show a significant degree of macroporosity, in support of the hypothesis that most asteroids must have been disrupted in the course of high-velocity impacts over the age of the solar system (Chapman 1978). Small asteroids are generally thought of as being individual pieces of compact debris that were generated in disruptive collisions (Pravec et al. 2002); hence, their macroporosity is expected to be low and their bulk density high compared to that of rubble-pile asteroids.

Thermal inertia, Γ, describes the ability of the surface material to store thermal energy: high-thermal-inertia material heats up slowly and re-emits the thermal energy only gradually, whereas low-thermal-inertia material can be approximated as being in instantaneous thermal equilibrium with the incoming insolation (see, e.g., Spencer et al. 1989). Examples for materials of low and high thermal inertia are regolith (30–50 SI units, 1 SI unit equals 1 J m⁻² s^−0.5 K⁻¹; Spencer et al. 1989; Putzig et al. 2005) and bare rock (>2500 SI units; Jakosky 1986), respectively. Measurements of the thermal inertia of medium-to-large sized NEOs (d > 100 m) revealed values of 100–1000 SI units (Delbo' et al. 2007).

Both the thermal inertia and the bulk density of asteroids can be derived by modeling the effect of non-gravitational perturbations on the object's orbit (see, e.g., Chesley et al. 2014). Assuming a homogeneous bulk density of the constituent particles, usually derived from laboratory measurements of meteorite-equivalent material, allows for constraining the degree of macroporosity of the asteroid.

NEO 2009 BD was discovered on 2009 January 16, at a distance from the Earth of only 0.008 AU (Buzzi et al. 2009). Its orbit is very Earth-like with a period of 400 days (JPL Solution 41). The escape velocity of 2009 BD with respect to the Earth is among the lowest for known objects (v_∞ ∼ 1 km s⁻¹), making it a worthwhile candidate mission target.

2009 BD is considered the primary candidate mission target for NASA's Asteroid Robotic Retrieval Mission (ARRM; NASA Asteroid Initiative Web Site 2013). The mission concept involves capturing an asteroid and dragging it onto a new trajectory that traps it in the Earth–Moon system, where it will be further investigated by astronauts. As a result of 2009 BD's Earth-like orbit, its next encounter with the Earth–Moon system will be in late 2022, when the proposed capture through ARRM would take place. The current mission design requires the target asteroid to have a diameter of 7–10 m and a total mass of ∼500 metric tons (NASA Solar System Exploration Mission Web Site 2013). The orbital parameters and absolute magnitude, H, which is the apparent magnitude of an object at a distance of 1 AU to the Sun and the observer, of 2009 BD are well-known, providing accurate orbital predictions (Micheli et al. 2012a). However, there is no albedo-independent determination of its diameter, which is a crucial variable in the ARRM mission planning.

We report here on observations of 2009 BD using the Infrared Array Camera (IRAC) on the Spitzer Space Telescope, which provides the only practical means to constrain the physical properties of 2009 BD in the next decade. The main goals of our observations were two-fold: measure the size and therefore determine the suitability of 2009 BD as an ARRM mission target, and constrain other physical properties like bulk density and thermal inertia of an asteroid at a size range that is so far unprecedented.

We observed 2009 BD with IRAC (Fazio et al. 2004) on-board the Spitzer Space Telescope (Werner et al. 2004) in Program ID 90256 using Director's Discretionary Time. A total of 25 hr of observation time was split into three astronomical observation requests (AORs): 49092096 (observation mid-time: 2013 October 13, 16:23 UTC; 8 hr elapsed time), 49091840 (October 14, 00:20 UTC; 8 hr), and 49091584 (October 14, 20:54 UTC; 9 hr). The observation window was selected based on Spitzer observability. Based on flux density predictions derived with the near-Earth asteroid thermal model (Harris 1998), a detection in IRAC channel 1 (3.6 μm) seemed to be unlikely. Hence, all available observing time was used on channel 2 (4.5 μm) observations, where the predicted flux density was greater than the predicted 5σ IRAC channel 2 sensitivity during the observation window.

In our observations, individual AORs used the "moving single" object mode to track in the moving frame of 2009 BD. A medium cycling dither pattern was used with a 100 s frame time. In order to provide the most accurate pointing during our observations, the JPL Horizons online Solar System data and ephemeris computation routine, which provides the Spitzer pointing information, was updated to include non-gravitational effects in the prediction of the orbit. We modeled non-gravitational perturbations as

$$\begin{equation} \mathbf {a}_{{\rm NG}} = (A_1 \hat{\mathbf {r}} + A_2 \hat{\mathbf {t}}) \left(\frac{1 \ \mathrm{{\rm AU}}}{r}\right)^2\, \end{equation} \tag{ 1 }$$

where $\hat{\mathbf {r}}$ and $\hat{\mathbf {t}}$ are the radial and transverse directions, respectively, and r is the heliocentric distance. A₂/r² models the transverse component of the Yarkovsky effect (Bottke et al. 2006), whereas A₁/r² models the solar radiation pressure (Vokrouhlický & Milani 2000) and the radial component of the Yarkovsky effect. This is similar to the comet-like model for non-gravitational perturbations (Marsden et al. 1973). The orbital fit (JPL Solution 41) to the observations yields A₁ = (57.03 ± 7.79) × 10⁻¹² AU/d² and A₂ = (− 113.02 ± 7.89) × 10⁻¹⁴ AU/d² (see also the entry for 2009 BD in the JPL Small-Body Database Browser 2013, as of 2013 October 24). The correlation coefficient between A₁ and A₂ is 0.81. The orbital fit is based on 180 optical observations over the interval from 2009 January 16.3 to 2011 June 21.0. The positional uncertainty of 2009 BD as seen by Spitzer at the time of the observations was ±50 in right ascension and ±04 in declination at a 3σ confidence level. For comparison, IRAC offers a square field of view with a width of 52 and a pixel scale of 12/pixel (Warm Spitzer Observer's Manual 2012). Hence, the accuracy of the orbit determination for 2009 BD is sufficient to determine its position to within a few IRAC pixels (see Section 5.1 for a more detailed discussion).

The data were reduced using a method tailored to faint NEOs, based on the ExploreNEOs program (Trilling et al. 2010). In this method, a mosaic of the field is constructed from the data set itself and then subtracted from the individual Basic Calibrated Data (BCD) frames. During these observations, the target had an apparent motion of ∼04 during each 100 s frame, so background stars were trailed only very slightly in individual BCDs. We were therefore able to generate a high signal-to-noise mosaic of the field to subtract from the BCDs. After subtraction of the background mosaic, regions near the peaks of background sources (which had small residuals) and bright cosmic ray artifacts were also masked in the individual BCDs, in order to minimize the background noise. The processed BCDs were then mosaicked in the reference frame of the moving object for each AOR, and the results from the three AORs combined to produce a final mosaic that included the full set of 800 100 s frames.

We did not detect 2009 BD in this final co-added map (Figure 1, right), from which we derive a 3σ upper limit to the flux density of 2009 BD of 0.78 μJy.

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The lack of a clear detection of 2009 BD in our observations precludes a direct determination of its physical properties. In order to be able to indirectly constrain the physical properties of 2009 BD, we take a probabilistic approach that combines a thermophysical model with a model of the non-gravitational effects on the asteroid's orbit. Based on the upper-limit flux density provided by our Spitzer observation and available astrometric measurements, the combination of both models allows us to constrain the physical properties of 2009 BD. The combination of the two models provides proper accounting for the mutual dependencies of the individual physical properties that impact both models, which would not be possible using a more simple thermal model.

We model the non-gravitational effects on the orbit of 2009 BD, namely the solar radiation pressure and the Yarkovsky effect, as a function of d, Γ, ρ, γ, and other parameters in a numerical approach. For the solar radiation pressure we assume (Vokrouhlický & Milani 2000)

$$\begin{equation} {\mathbf {a}}_{\mathrm{SRP}} = \left(1 + \frac{4}{9}\ A \right) \cdot \Psi \cdot \frac{G_S}{c} \cdot \frac{\hat{\mathbf {r}}}{r^2}, \end{equation} \tag{ 2 }$$

where A is the Bond albedo, Ψ is the area-to-mass ratio of the object (see, e.g., Micheli et al. 2012a), G_S = 1370 W m⁻² is the solar constant, and c is the speed of light. For the Yarkovsky effect, we use the model approach described by Vokrouhlický et al. (2000), which fully captures both the diurnal and the seasonal components of the Yarkovsky effect. The model asteroid is assumed to be spherical and the heat transfer is solved analytically using the linearized heat transfer equation (Vokrouhlický 1998; Vokrouhlický & Farinella 1999). By fitting all available astrometric data of 2009 BD, the model derives ρ and Γ as a function of γ and d, as well as the goodness-of-fit parameter χ².

The thermophysical model approximates the surface temperature distribution of 2009 BD and is used in this work to determine the thermal-infrared emission from its surface as a function of its physical properties. The model accounts for the spin axis orientation (represented by γ), rotational period, thermal inertia, and surface roughness. We assume a spherical shape of 2009 BD; the diameter derived with the model is hence the diameter of a sphere with the same volume as the real shape of 2009 BD. Surface roughness causes infrared beaming, an effect that focuses thermal emission radiated toward the observer, and is modeled as emission from spherical craters (see Mueller 2007, for more details). The model, which is mostly identical to the one discussed by Mueller (2007), solves the heat transfer equation numerically for a large number of plane surface facets that form a sphere. The monochromatic flux density derived by the model is turned into an IRAC channel 2 in-band flux density, i.e., it is color corrected, using the appropriate channel 2 response function and assuming a blackbody spectrum of the instantaneous thermal equilibrium temperature for 2009 BD (Trilling et al. 2010). Furthermore, the contribution from reflected solar light is added to the calculated flux density using the method described by Mueller et al. (2011, and references therein), assuming an infrared/optical reflectance ratio of 1.4.

In both the orbital and the thermophysical model we adopt the absolute magnitude H = 28.43 ± 0.12 (Micheli et al. 2012a), the photometric slope parameter G = 0.18 ± 0.13 (derived as the average from all G measurements of asteroids, see JPL Small-Body Database Search Engine 2013), and the rotation period P = 2^{(2  ±  0.5)} hr (which is consistent with observations by Tholen et al. 2013, P ⩾ 3 hr) throughout this work.

The mutual dependencies among physical properties used by the orbital and the thermophysical model require an iterative solution of the problem. In a first approximation, we constrain the possible ranges of γ and d. As the negative value of A₂ suggests a retrograde rotation (see Farnocchia et al. 2013), we sample the obliquity γ from 90° to 180°. We investigate the possible range of d using the thermophysical model, based on an 3σ upper-limit flux density measurement (0.78 μJy). Figure 2 shows the predicted flux density at 4.5 μm as a function of the diameter and the thermal inertia for the faintest possible model asteroid, providing the largest possible diameter range for 2009 BD with a smooth surface, γ = 180°, and the shortest rotation period consistent with observations (P ⩾ 3 hr; Tholen et al. 2013). From this plot, we constrain the possible diameter range of 2009 BD to <8 m, as a result of our upper-limit flux density determination. Note that we do not force a lower-limit diameter constraint, so we do not a priori exclude high geometric albedos.

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Sampling d < 8 m and 90° < γ < 180° with the orbital model provides further constraints on 2009 BD's properties. Intriguingly, we find for each pair (d, γ) two local minima in the orbital fit χ², representing two physically possible solutions. The "low-Γ" solution displays a low thermal inertia of the order of 10 SI units with a high bulk density ρ, whereas the "high-Γ" solution stands out with a thermal inertia of more than 1000 SI units and a low bulk density. Figure 2 shows both solutions in thermal inertia as a function of the diameter. Based on the orbital fit solutions, we can also further constrain the obliquity (low-Γ: $\gamma =170{^{\circ }}_{-20}^{+10}$, high-Γ: $\gamma = 180{^{\circ }}_{-5}^{+0}$, uncertainties are 1σ) and we can confidently rule out that 2009 BD is smaller than 2.6 m. For diameters smaller than that, the orbital model is unable to converge on a physically meaningful solution (see Section 5.2 for a detailed discussion).

We utilize our intermediate results to derive diameter distributions for both solutions using the thermophysical model, based on the thermal inertia constraints and the Spitzer upper-limit flux density measurement. We generate a sample of synthetic objects with pairs (d, Γ) that comply with normal distributions around the thermal inertia solutions shown in Figure 2. We sample the other model input parameters (H, G) according to normal distributions or log-normal distributions (P) within the ranges given in Section 3. We use $\gamma =170{^{\circ }}_{-20}^{+10}$ and $\gamma = 180{^{\circ }}_{-5}^{+0}$ for the low-Γ and the high-Γ solution, respectively, and for the surface roughness we randomly pick one of four different roughness models (no, low, default, and high roughness; see Mueller 2007). We model each synthetic sample object and derive its IRAC in-band flux density combined with contributions from reflected solar light, which we then compare with the 3σ upper-limit flux density as derived from our observations. In case the sample object flux density is lower than the upper limit, we regard this individual synthetic object a possible configuration for 2009 BD and add its diameter to the distribution. The final solution-specific diameter distributions are shown in Figure 3 and the derived nominal values and uncertainties are listed in Table 1. Nominal values represent the median values of the respective distributions; uncertainties are standard deviations, σ, of a normal distribution fitted to those values higher than the median of the distribution. Figure 3 shows that this approach reasonably describes the range of values lower than the median, which deviates from the shape of a normal distribution. We derive albedo values for the high- and low-Γ solutions similarly, using separate values of σ for albedos higher and lower than the median, allowing for asymmetric uncertainties.

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Table 1. Physical Properties of 2009 BD

Parameter	Low-Γ Solution	High-Γ Solution
Diameter d (m)	2.9 ± 0.3	4 ± 1
Albedo pV	$0.85_{-0.10}^{+0.20}$	$0.45_{-0.15}^{+0.35}$
Obliquity γ (°)	$170_{-15}^{+10}$	$180_{-5}^{+0}$
AMR Ψ (× 10−4 m2 kg−1)	$1.8_{-0.2}^{+0.3}$	$2.2_{-0.2}^{+0.4}$
Bulk density ρ (g cm−3)	$2.9_{-0.5}^{+0.5}$	$1.7_{-0.4}^{+0.7}$
Macroporosity (%)	$10_{-10}^{+20}$	$45_{-30}^{+15}$
Total mass (metric tons)	$36_{-8}^{+10}$	$55_{-25}^{+30}$
Thermal inertia Γ (SI units)	$30_{-10}^{+20}$	2000 ± 1000

Note. Uncertainties depict the 1σ confidence interval.

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Based on the solution-specific diameter ranges, we finally constrain the other physical properties of 2009 BD using the orbital model. Figure 4 shows how obliquity is constrained by the orbital fit χ². By mapping the distribution in obliquity to the distributions in thermal inertia (Figure 5) and bulk density (Figure 6) we obtain our final estimates for the bulk density, thermal inertia, and total mass for both solutions, as listed in Table 1. The reported 1σ error bars account for the uncertainties of the input physical parameters used to model the Yarkovsky accelerations (e.g., diameter and absolute magnitude) and the uncertainty resulting from the astrometry. The individual physical properties derived from both the low-Γ and the high-Γ solution are discussed in Section 5.2.

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5.1. Observations and Spitzer Pointing

5.2. Physical Properties

By combining the orbital and the thermophysical model we are able to constrain a variety of physical properties of 2009 BD by taking advantage of the mutual dependencies of the individual properties. The range of each physical property is confined based on purely physical considerations. The only properties that are not derived as part of the modeling process are H, G, and P (see Section 3), which are based on observations of 2009 BD or general properties of the asteroid population. We discuss those physical properties that are constrained in the modeling process.

We derive a volume-equivalent diameter of 2.9 ± 0.3 m and a geometric albedo of $p_V = 0.85_{-0.10}^{+0.20}$ for the low-Γ solution and d = 4 ± 1 m and $0.45_{-0.15}^{+0.35}$ for the high-Γ solution. Both albedo solutions exhibit relatively high albedos compared to albedo measurements of other NEOs (Trilling et al. 2010; Mainzer et al. 2011). The diameter results agree within uncertainties, allowing for a more generalized formulation: 2009 BD's diameter is 2.6 < d < 7 m at a 3σ confidence level. Note that despite the fact that we did not detect 2009 BD, we are able to constrain the diameter in both cases with uncertainties that are rather low compared to the typical 20% diameter uncertainty derived from ExploreNEOs data (Harris et al. 2011). We are able to confine the diameter to such a narrow range due to constraints given by the physics of the orbital model and the upper-limit flux density derived from our observations. As a matter of fact, a diameter lower than 2.6 m implies a high Bond albedo, which in turn reduces the size of the Yarkovsky effect and prevents our model from matching the magnitude of the observed acceleration. The advantage of this definition of the lower limit is that we do not a priori rule out the possibility that 2009 BD has an extremely high albedo, which is the case for the low-Γ solution. Although relatively rare, similarly high albedos have been found by both the ExploreNEOs (Trilling et al. 2010) and the NEOWISE projects (Mainzer et al. 2011). Based on spectral work by Thomas et al. (2011), both albedo results are compatible with a E/S/V/Q-type taxonomic classification for 2009 BD.

We compare the derived bulk density solutions for 2009 BD with measured bulk densities of asteroids with diameters of 10 km or smaller. Density data are taken from the list compiled by Baer et al. (2012) and the literature (see Table 2). All measurements are plotted in Figure 7. Macroporosity is derived as unity minus the ratio of the asteroid's bulk density and the bulk density of meteorite-equivalent material. Meteorite-equivalent bulk densities are taken from Britt et al. (2002, Table 2). Due to ambiguities in the identification of the asteroidal origin of meteoritic material, we use average bulk densities derived from meteoritic material as proxies for asteroidal bulk densities of individual taxonomic types. Hence, we assume S and Q-type asteroids to have an average bulk density of 3.3 ± 0.1 g cm⁻³, as derived from H/L/LL ordinary chondrites, and C-type and B-type asteroids to have an average bulk density of 2.6 ± 0.5 g cm⁻³, as derived from different types of carbonaceous chondrites. For V-type asteroids we assume an average bulk density of $2.9_{-0.4}^{+0.5}$ g cm⁻³ as derived from howardite-eucrite-diogenite (HED) meteorites (Macke et al. 2011). Consolmagno et al. (2008) give a mean bulk density of enstatite chondrites, which likely originate from E-type asteroids, of 3.5 ± 0.2 g cm⁻³.

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Table 2. Physical Properties of Small Asteroids

Object	Diameter	Albedo	Tax.	Bulk Density	MPor.	Γ	References
	(km)		Type	(g cm−3)	(%)	(SI)
(1580) Betulia	4.57 ± 0.46	0.08 ± 0.02	C	⋅⋅⋅	⋅⋅⋅	180 ± 50	1
(1862) Apollo	1.55 ± 0.07	0.20 ± 0.02	Q	2.85 ± 0.68	$15_{-15}^{+25}$	$140_{-100}^{+140}$	2, 3
(3749) Balam	(7.2 ± 0.4)a	(0.15)a	(S)b	(2.61 ± 0.45)a	$20_{-15}^{+15}$	⋅⋅⋅	4
(3908) Nyx	1.0 ± 0.2	0.15 ± 0.08	V	0.9 ± 0.2c	$70_{-15}^{+10}$	⋅⋅⋅	5, 6, 7
(25143) Itokawa	0.320 ± 0.001	0.30 ± 0.10	S	1.90 ± 0.13	$40_{-10}^{+10}$	700 ± 100	1, 8, 9
(33342) 1998 WT24	0.35 ± 0.04	0.6 ± 0.2	E	⋅⋅⋅	⋅⋅⋅	200 ± 100	1, 10
(54509) YORP	0.09 ± 0.01	0.20 ± 0.02	S/V	⋅⋅⋅	⋅⋅⋅	700 ± 500	1
(66391) 1999 KW4	1.33 ± 0.07	(0.25)d	S	2.00 ± 0.26	$40_{-10}^{+10}$	⋅⋅⋅	5, 11
(101955) Bennu	0.50 ± 0.02	0.05 ± 0.01	B	1.2 ± 0.1	$55_{-15}^{+10}$	650 ± 100	12, 13
(162173) 1999 JU3	0.87 ± 0.03	0.07 ± 0.01	C	⋅⋅⋅	⋅⋅⋅	400 ± 200	3, 14
(175706) 1996 FG3	1.71 ± 0.07	0.044 ± 0.004	C	⋅⋅⋅	⋅⋅⋅	120 ± 50	15, 16
(185851) 2000 DP107	0.81 ± 0.18	(0.14)d	(S)d	1.65 ± 0.84	$50_{-30}^{+25}$	⋅⋅⋅	17
(308635) 2005 YU55	0.31 ± 0.01	0.07 ± 0.01	C	⋅⋅⋅	⋅⋅⋅	580 ± 230	18, 19
(341843) 2008 EV5	0.37 ± 0.01	0.13 ± 0.05	C	⋅⋅⋅	⋅⋅⋅	450 ± 60	19, 20
2000 UG11	0.23 ± 0.03	(0.23)d	(S)d	1.47 ± 0.7	$55_{-25}^{+20}$	⋅⋅⋅	21
2002 CE26	3.50 ± 0.40	0.07	(C)e	0.9 ± 0.5	$65_{-30}^{+20}$	⋅⋅⋅	22
2002 NY40	0.28 ± 0.03	0.34 ± 0.06	Q	⋅⋅⋅	⋅⋅⋅	550 ± 450	23, 24
2003 YT1	1.06 ± 0.06	(0.52)d	V	2.01 ± 0.70	$30_{-30}^{+30}$	⋅⋅⋅	25, 26

Notes. This table lists measured physical properties of asteroids with diameters of 10 km or smaller. Data in brackets are based on assumptions (see below). In the case of multi-component systems, diameters and bulk densities refer to the average numbers of the combined system (diameters are those of a volume-equivalent sphere). The macroporosity ("MPor.") is derived through division of the asteroid's bulk density by the bulk density of the respective meteorite-equivalent material (see text for details). Comparison data for 2009 BD can be found in Table 1. ^aBased on an assumed albedo. ^bBased on its flora family membership (Marchis et al. 2008). ^cDensity estimate assumes a thermal inertia according to Delbo' et al. (2007). ^dAlbedo derived from the equivalent diameter and the H magnitude (JPL Small-Body Database Browser 2013). ^eTaxonomic type assigned based on albedo determinations by Thomas et al. (2011). References. (1) Mueller 2007; (2) Rozitis et al. 2013; (3) Bus & Binzel 2002; (4) Marchis et al. 2008; (5) Binzel et al. 2004; (6) Benner et al. 2002; (7) Farnocchia et al. 2014; (8) Fujiwara et al. 2006; (9) Abe et al. 2006; (10) Kiselev et al. 2002; (11) Ostro et al. 2006; (12) Müller et al. 2012; (13) Chesley et al. 2014; (14) Müller et al. 2011; (15) Wolters et al. 2011; (16) Thomas et al. 2011; (17) Margot et al. 2002a; (18) Müller et al. 2013; (19) Somers et al. 2010; (20) Alí-Lagoa et al. 2013; (21) Margot et al. 2002b; (22) Shepard et al. 2006; (23) Roberts et al. 2007; (24) Müller et al. 2004; (25) Brooks 2006; (26) Sanchez et al. 2013.

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Figure 7 (center panel) shows that most objects with diameters 100 m <d < 10 km have macroporosities higher than 30%, consistent with a rubble-pile nature (Britt et al. 2002). There is no clear trend in either bulk density or macroporosity with the diameter of the object. Using the derived bulk density of 2009 BD ($2.9_{-0.5}^{+0.5}$ g cm⁻³ for the low-Γ solution, $1.7_{-0.4}^{+0.7}$ g cm⁻³ for the high-Γ solution), and a mean bulk density of (3.2 ± 0.3) g cm⁻³ derived as the average of the S/Q/V/E-type asteroid material bulk densities listed above, we derive a degree of macroporosity of $10_{-10}^{+20}$% or $45_{-30}^{+15}$%. Hence, our low-Γ solution is most consistent with a monolithic nature of 2009 BD, whereas the high-Γ solution suggests a rubble-pile nature (Britt et al. 2002).

Previous measurements of the thermal inertia of asteroids revealed values in the range ∼10–100 SI units for large main belt asteroids and higher values up to 1000 SI units for NEOs (see, e.g., Delbo' et al. 2007, and references therein). The lower thermal inertia of large bodies is generally ascribed to the presence of a thick layer of regolith, which has a low thermal inertia (see Section 1, as well as Spencer et al. 1989; Putzig et al. 2005). The right-hand panel of Figure 7 plots thermal inertia measurements of asteroids with ∼0.1 < d < 10 km. The plot reveals that 2009 BD's thermal inertia is extreme in this range, irrespective of which of our solutions better describes reality. The low-Γ solution is consistent with the presence of regolith, whereas the high-Γ solution is consistent with a bare rock nature of 2009 BD. A slight trend of increasing thermal inertia with decreasing diameter is visible in Figure 7, which was already discussed by Delbo' et al. (2007). Our high-Γ solution seems to be more consistent with this trend, presuming that this trend is valid for asteroids in the size regime of 2009 BD.

We summarize the properties of 2009 BD created by our two solutions in Figure 8. The low-Γ solution suggests that 2009 BD is a ∼3 m sized rocky body (ρ = 2.9 g cm⁻³) that is covered with a physically thin but optically thick layer of regolith-like material, causing it to exhibit a low thermal inertia (Γ = 30 SI units) and a high bulk density. This picture seems realistic in the sense that models show that even small asteroids can retain a layer of fine-grained dust on their surfaces (Scheeres et al. 2010; Sánchez & Scheeres 2014). The picture created by the high-Γ solutions shows 2009 BD as a 4 m sized rubble-pile asteroid (ρ = 1.7 g cm⁻³) that consists of individual bare rock slabs (Γ = 2000 SI units) and exhibits a macroporosity of 45%. This scenario seems to be more realistic due to the lower albedo that is required for this configuration. Despite the fact that some properties seem to favor one of the two results at a time, we are unable to rule out either of the configurations based on physical reasoning. In order to be able to commit to either solution, additional observations are necessary that are able to pinpoint one decisive physical property of 2009 BD, e.g., its thermal inertia or its bulk density. The thermal inertia can be further constrained using additional infrared observations or using in-situ measurements. The bulk density can be independently derived by measuring the gravitational attraction of the object on a nearby body or a rendezvous spacecraft.

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5.3. Discussion of the Modeling Technique

5.4. Implications

We derive two physically possible solutions for the physical properties of 2009 BD from our Spitzer observations, using thermophysical modeling and modeling of the non-gravitational forces acting upon this body. The first solution shows 2009 BD as a 2.9  ±  0.3 m sized massive rock body (ρ = 2.9  ±  0.5 g cm⁻³) with an extremely high albedo of $p_V=0.85_{-0.10}^{+0.20}$ that is covered with regolith-like material, causing it to exhibit a low thermal inertia ($\Gamma =30_{-10}^{+20}$ SI units). The second solution suggests 2009 BD to be a 4 ± 1 m sized rubble-pile asteroid ($\rho = 1.7_{-0.4}^{+0.7}$ g cm⁻³) with an albedo of $0.45_{-0.15}^{+0.35}$ that consists of individual bare rock slabs (Γ = 2000  ±  1000 SI units). We are unable to rule out either solution with the current knowledge.

The authors of this work thank Tom Soifer, Director of the Spitzer Space Telescope, for the time allocation to observe 2009 BD. We also would like to thank Paul Chodas for his support and many informative conversations. We thank an anonymous referee for useful suggestions that improved this manuscript. D. Farnocchia was supported for this research by an appointment to the NASA Postdoctoral Program at the Jet Propulsion Laboratory, California Institute of Technology, administered by Oak Ridge Associated Universities through a contract with NASA. The work of S. Chesley was conducted at the Jet Propulsion Laboratory, California Institute of Technology under a contract with the National Aeronautics and Space Administration. The work of D. Vokrouhlický was partially supported by the Grant Agency of the Czech Republic (grant P209-13-01308S). J. L. Hora and H. A. Smith acknowledge partial support from Jet Propulsion Laboratory RSA No. 1367413. This work is based on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA.

Facilities: Spitzer - Spitzer Space Telescope satellite