Radar and Optical Characterization of Near-Earth Asteroid 2019 OK

From CW echo-power spectra we can measure various radar properties, such as the radar cross section in each polarization (σ_OC , σ_SC ), the circular polarization ratio (μ_C ), the bandwidth (B), and the radar albedo (${\hat{\sigma }}_{{OC}}$), which are related to the physical properties of the target. We obtained 11 transmit–receive cycles (scans) during close to 4 minutes (Table 1). The data reported here were acquired, calibrated, and integrated using standard radar techniques for CW experiments (e.g., Ostro 1993; Black 2002; Magri et al. 2007). All quantitative analysis were performed on unsmoothed spectra. The background noise level is fit and removed to make the mean level zero, and the signal scaled to standard deviations above the background noise. Figure 2 shows a montage of each individual scan and the weighted sum of all 11 scans at 2 Hz effective resolution, Gaussian smoothed to reduce the effects of self-noise. The solid line corresponds to the signal power that is received in the OC sense to that transmitted and the dotted line to the signal power received in the SC sense as that transmitted. The cross sections (σ_OC , σ_SC ) are derived from the integrated echo power in the stated polarization. The OC polarization is dominated by specular scattering with some contribution from diffuse scattering (e.g., Black 2002), while the SC is more representative of the diffuse scattering that takes place due to reflections from rubble, craters, ridges, and other structures on the wavelength scale of the transmitted signal (e.g., Virkki & Muinonen 2016). The average radar cross sections for 2019 OK were σ_OC = 620 m² and σ_SC = 205 m², where each value has a 2% relative uncertainty due to statistical noise and 35% relative uncertainty due to systematic uncertainties in the calibration. This estimated 35% systematic uncertainty is larger than the standard 25% at Arecibo because the pointing was poorer than normal due to cable elongation in hot weather.

The ratio of the radar cross sections (σ_SC /σ_OC ) is the circular polarization ratio (μ_C ). It serves as an initial estimate of surface roughness (Ostro 1993; Black 2002; Virkki & Muinonen 2016) and has been linked to composition by correlation to some taxonomic types (Benner et al. 2008; Aponte-Hernández et al. 2020). We measured a circular polarization ratio of 0.33 ± 0.03 for the weighted sum of all scans. This indicates that 2019 OK is unlikely to be a V-type (μ_C ≈ 0.603 ± 0.088) or an E-type (μ_C ≈ 0.892 ± 0.079) asteroid, and is more likely to be an S-type (μ_C ≈ 0.26 ± 0.05) or a C-type (μ_C ≈ 0.285 ± 0.12) body; the latter one is favored (Benner et al. 2008; Thomas et al. 2011).

The measured Doppler bandwidth (B) depends upon the object's rotation period, diameter, and the subradar latitude. We used Equation (2) (Ostro et al. 2002), in which the rotation period (P_rot ) is expressed in terms of the diameter (D), wavelength (λ), and subradar latitude (δ). We assume an equatorial view (δ = 0, $\cos (\delta )=1$), to obtain a range of possible rotation rates at the measured bandwidth:

$$\begin{eqnarray}&&B=\displaystyle \frac{4\pi D\cos (\delta )}{\lambda {P}_{{rot}}}.\end{eqnarray} \tag{ 2 }$$

To determine the bandwidth, we analyzed the data in each individual unsmoothed CW scan, and then summed over all scans to obtain an echo's edge-to-edge bandwidth of 38 ± 2 Hz. This bandwidth is significantly larger than what is typically seen in small NEAs (D < 200 m) of ∼1–10 Hz, which is an indicator of a rapid rotation rate. Bandwidths observed in individual scans reached a minimum of 31 Hz and a maximum of 43 Hz, but there is no clearly repeated pattern, in part due to short observation time and intervals of observations being on the same order as the rotation period. We performed a weighted average of the edge-to-edge bandwidth measurement of each scan's echo, yielding a bandwidth of 39 ± 2 Hz. Each scan measures the instantaneous bandwidth, and variation over time is expected for a rotating nonspherical object. For the above bandwidths and a diameter of no less than 70 m and no more than 130 m (see Section 3.2), we find the rotation period (P_rot ) can range from approximately 0.05 hr to 0.09 hr (3 to 5 minutes), respectively, not excluding a faster rotation period for nonequatorial subradar latitudes ($\cos (\delta )\lt 1$).

Another key product from radar observations is the derivation of the radar albedo (${\hat{\sigma }}_{{OC}}$), which is a measure of surface reflectivity where an albedo of one denotes a perfect reflector (assuming a spherical target; Ostro 1993; Magri et al. 2001; Black 2002). To first order, the radar albedo can be calculated as ${\hat{\sigma }}_{{OC}}={\sigma }_{{OC}}/{{\rm{A}}}_{{Proj}}$, where the projected area (A_Proj ) is based on the presumed diameter and assuming a spheroidal shape. We obtain ${\hat{\sigma }}_{{OC}}$ to be in the range of 0.16 (D = 70 m) to 0.047 (D = 130 m). Using the model developed by Hickson et al. (2018, 2020), we estimated the near-surface mass density of 2019 OK. In their work, they presented an expansion of Magri et al. (2001) to calculate near-surface bulk densities (ρ_bulk ) for NEAs using radar albedos and compositional information from meteorite analogs.

From the relationship between ${\hat{\sigma }}_{{OC}}$ and the Fresnel reflection coefficient (R) ($R={\hat{\sigma }}_{{OC}}/g$), where g is the backscatter gain (assumed to be 1.2), the near-surface permittivity can be estimated by the relationship between the circular polarization ratio (making certain assumptions when estimating, R) and near-surface density. We find an approximate permittivity of 4.65 (D = 70 m) and 2.22 (D = 130 m). It is important to note that these surfaces are not homogeneous and subsurface scattering from voids, grain composition variation, and diffuse scattering play a role (Hickson et al. 2018) in our estimated values for . The used model does not necessarily account for individual cases, which could also play a role.

We then take the same assumptions regarding backscatter gain (g) and diffuse circular polarization as in Equations (5) and (7) of Hickson et al. (2020) to calculate the near-surface bulk density of 2019 OK. We include our own values for σ_OC and μ_C (Table 2) and assume 2019 OK is C- or S-type, where the grain density of the meteorite analog is roughly 2.8 to 3.5 g cm⁻³ (Consolmagno et al. 2008). We obtained ρ_bulk = 1.2 g cm³ for D = 70 m with a porosity of 0.6, and ρ_bulk = 0.8 g cm⁻³ for a 130 m object with a porosity of 0.8. By inspection, of these calculation one can see that some level of cohesion is necessary to hold the asteroid together against the disintegration due to centrifugal forces. We explore this further in Section 4.

Table 2. Radar-derived Physical Parameters for 2019 OK

Parameter	Value
Absolute Magnitude (H, mag)	23.3 ± 0.3
Diameter (D, m)	70 to 130
Rotation Period (Prot , hr)	0.05 to 0.09
Geometric Albedo (pV)	0.05 to 0.17
Radar albedo (${\hat{\sigma }}_{{OC}})$	0.05 to 0.16
Triaxial ratios-Elongation (a: b)	1.16:1
Circular polarization ratio (μC )	0.33 ± 0.03
Bandwidth (B, Hz)	39 ± 2
OC cross section (σOC , m2)	620% ± 35%
SC cross section (σSC , m2)	205% ± 35%
Minimum cohesion (k, Pa)	350

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When the target's S/N is high enough, we can resolve the echo in delay (range) and Doppler frequency by transmitting a coded waveform with a characteristic modulation interval known as the baud (e.g., Taylor et al. 2019). For this observation, phase modulation bandwidths used were 0.25 MHz for a 4 μs baud and 2 MHz for a 0.5 μs baud. The 17 scans shown in Figure 3 correspond to the 0.5 μs phase modulation, with a range resolution of 75 m per pixel in delay. From Figure 3, we see that all signals were contained within one or two range bins for 0.5 μs images, rendering it essentially unresolved at a 75 m resolution. The images from 18:10 to 18:13 span two pixels, and those from 18:13 to 18:15 are in a single row (75 m in range). The last image at 18:16 appears to be in two rows again, with the pixel in the second row at 4.7σ.

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We calculated the image drift (a slow but steady variation in the target's observed delay, due to slight errors in the ephemeris; see Section 3.3) by comparing the ephemeris used for the observation with the ephemeris from weeks later which incorporated all of the available astrometry, both from the radar observations and available optical observations. If some of the change in the signal position was due to range drift, it would be in the downward direction. Drift cannot explain the last image compared to previous ones. There must be a dimension of the asteroid that is at least 70 m to consistently span two pixels in about half the images. These radar estimates do not necessarily exclude smaller dimensions in some orientations, such as those discussed in Section 2 (D < 70 m). The object could have a larger diameter and be somewhat elongated, giving a similar variation in the 0.5 μs images. In all, the object could be big enough to fill multiple pixels, or be small but split between two pixels; hence, we adopt 70–130 m as the most likely size range for 2019 OK.

In an attempt to extract as much information as possible from the data, we extracted the bandwidths from the delay (range)–Doppler scans (Figure 4). The bandwidth variation did not present any obvious periodicity. The average bandwidth for the 21 scans (63 s of data) of the 4 μs set was 40 Hz (3.8 Hz resolution). For the 0.5 μs data, the average was of 39 Hz (3.8 Hz resolution) in a set of 17 scans (51 s of data). The limited observation duration and unresolved size for 2019 OK did not allow us to obtain shape information. However, the small change in bandwidth and changes in range extent suggest a nonspherical body.

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Immediately after the CW observations, we used the JPL On-Site Orbit Determination software (OSOD; Ostro 1996) to update the observing ephemeris in real time and improve the 3σ uncertainties on pointing, Doppler, and range. The center of the echo in the CW data was displaced by +31 Hz relative to the optical-only prediction (a ∼0.5σ correction relative to the 190 Hz 3σ uncertainty of Ephemeris 1), which translates to a correction in the line-of-sight velocity of 1.95 m s⁻¹ for the Doppler-only correction to Ephemeris 1. Refitting the orbit using the Doppler correction produced Ephemeris 2, which predicted the RTT to 2019 OK to be reduced by 721.8 μs or, equivalently, that 2019 OK was 108 km closer to Earth. As discussed in Section 3, an important capability of radar techniques is the ability to measure the Doppler frequency shift and range with high precision. For the ranging and imaging, the submitted delay astrometry corresponds to line-of-sight distance corrections of −21.81 μs (−3.27 km) for 4 μs data and −22.59 μs (−3.39 km) for 0.5 μs data (Figure 3), showing a range drift of almost the same amount, while changing observation setup (5 minutes). These radar measurements reduced the uncertainties in 2019 OK's position at the time of our observations (18:00 UTC on 2019 July 25) by a factor of 4 in plane-of-sky position, a factor of 20 in Doppler frequency, and a factor of 1500 in range.

The orbit condition code or uncertainty parameter is given in relation to the in-orbit longitude runoff in seconds of arc per decade, and it quantifies the uncertainty of an orbital solution considering the uncertainties in the perihelion passage time and in the orbital period. It is an integer ranging from 0 (runoff <1.0 arcsec per decade) to 9 (runoff > 146,502 arcsec per decade) ¹³ ; it is derived from the Q criterion in Marsden et al. (1978). Based on 31 optical measurements, 2019 OK's U parameter was 6. After adding one Doppler and two delay measurements to the orbit solution computation (Arecibo solution #3), the Earth-encounter predictability window was increased, from the discovery apparition (2019) only, to over 100 years, revealing the closest currently predicted Earth encounter to be in 174 years, at a distance of 0.027 46 au on 2196 February 24. The uncertainty parameter was reduced to U = 4.

The first certain detection of a fast-rotating asteroid (FRA), one that is rotating significantly faster than 2.1 hr, was 1998 KY₂₆ with a rotation period of P_rot = 0.18 hr (10.8 minutes), H = 25.6, and a diameter of 30 m (Ostro et al. 1998; Warner et al. 2009). From the Light Curve Database (LCDB) 2020 May release (Warner et al. 2009), we find 165 asteroids with rotation periods equal to or shorter than the slowest rotation period of 2019 OK, P_rot < = 0.14 hr, assuming a D = 200 m (see Section 2). Figure 5 shows where 2019 OK is located with respect to the small fast rotators and the general asteroid population.

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Two regimes govern the spin limits for general solids: the strength regime (D < 300 m) and the gravity regime (D > 10 km) (Pravec & Harris 2000). The limits to the macroscale composition of the case of fast-rotating bodies have been shown by several authors (e.g., Pravec & Harris 2000; Holsapple 2007; Polishook et al. 2016, 2017 and references therein) to be governed by the internal strength of the body. Monoliths (with a rugged surface) or rubble piles with enough cohesion rendering them capable of holding their structure via Van der Waals forces (i.e., Scheeres et al. 2010) are examples of objects requiring some internal strength to keep them from flying apart. Following the aforementioned works (Pravec & Harris 2000; Holsapple 2007; Polishook et al. 2016, 2017), we calculated the Drucker–Prager (D-P) yield criterion. The D-P criterion is presented here as in Polishook et al. (2016), as a dependency on two constants, the cohesion k and a slope constant Φ, which, in turn, depends only on the angle of friction ϕ (${\rm{\Phi }}=\tfrac{2\sin \phi }{\sqrt{3}(3-\sin \phi }$), which we set at ϕ = 35°. With this angle, we can constrain the body's minimum cohesion. The cohesion increases only slightly with increasing friction angle. More details are provided in Holsapple (2007) and Polishook et al. (2017). To obtain k from Equation (8) in Polishook et al. (2016), we first solved their Equations (2) to (4), which define the shear stresses average in vector form. For this work, the density is denoted by ρ given in g cm⁻³, P_rot is the object's rotation period converted to angular frequency, G_c is the gravitational constant (6.673 × 10⁻¹¹ m³ kg⁻¹ s⁻²), and A_xyz are dimensionless quantities that depend only on the asteroid triaxial ratios as in Polishook et al. (2016). Here we used A_x = A_y = A_z = 2/3 values as Holsapple (2007), where a, b, and c denote the axis radius. In the next section, we use the methods above to calculate the cohesion for 2019 OK. We used the published work for cohesion for 2001 OE84 (Polishook et al. 2017) and 2005 GD65 (Polishook et al. 2016) as validation of our methods and results.

We begin by estimating the axial ratio of 2019 OK by approximating the lightcurve amplitude. We chose the ATLAS (T05) data set listed on NEODyS-2 ¹⁴ for this estimate because it provided a uniform sample (eight observations) over a long enough interval to cover multiple rotations (0.63 hr), at a low phase angle (≈10°). The apparent change in magnitude was ${\rm{\Delta }}H={H}_{\mathrm{Max}}-{H}_{\mathrm{Min}}=0.33$ mag. The corresponding flux ratio (e.g., Gaffey 1989) is 1.36. The flux is proportional to the apparent area of the body at the time of observation (Equation (3)). Then, the maximum change in magnitude as the object rotates (the lightcurve amplitude) is an estimate of the change in that area. We take the square root of the area ratio to obtain the axial ratio, a/b = 1.16. This is dependent on the viewing geometry, but is at least a lower bound:

$$\begin{eqnarray}&&{\rm{\Delta }}H=-2.5{\mathrm{log}}_{10}\left(\displaystyle \frac{{{Flux}}_{2}}{{{Flux}}_{1}}\right).\end{eqnarray} \tag{ 3 }$$

To estimate limits of cohesion (k) for 2019 OK, we studied two shapes: a sphere and an ellipsoid. We considered densities of 1 to 3 g cm⁻³ for the ranges of rotation rates and diameters mentioned earlier (Sections 2 and 3). For an ellipsoid, the axial ratios define constants depending only on the shape to derive k for a given object (Polishook et al. 2016). Using Equation (3) (for the case of the ellipsoid), we assumed a prolate shape with axial ratios of 1.16:1:1. The apparent diameter boundary range of D = [70: 130 m], in average, needs a minimum cohesion to avoid catastrophic disruption is between 350 Pa and 400 Pa for the case of the sphere at a density of 1 g cm⁻³ as well as for the ellipsoid at same density at the smallest diameter (70 m). For larger sizes or higher densities, the necessary cohesion increases up to 1 kPa for the largest diameter (130 m) at highest density (3 g cm⁻³). In comparison, Earth mineral aggregates are 1–100 kPa for fractured rocks and up to a few MPa for crystalline rocks (i.e., Turcotte & Schubert 1982). However, this strength is much less than even the weakest rocks seen on Earth, and is much weaker than any meteorite that has survived travel through the Earth's atmosphere.