Search for dust near Bennu

A sequence of images centered on Bennu was obtained using the OCAMS PolyCam and MapCam imagers. The image sequence was median co-added on the motion of Bennu to produce a map of the dust near Bennu. Dust would have exhibited itself as diffuse features either around Bennu, trailing Bennu in the anti-solar direction, or trailing Bennu along its orbit.

PolyCam dust plume search images were collected on 11 September 2018 when Bennu was at a range of 1.05 million km and phase angle of 43 degrees. The MapCam images were collected on the following date when Bennu was at a range of 1.00 million km and phase angle of 44 degrees. On these dates, PolyCam covered a region of Bennu’s orbit extending 7300 km leading and trailing Bennu. MapCam covered a region along Bennu’s orbit that extends 35,000 km leading and trailing Bennu.

The 11 and 12 September dates were chosen because Bennu’s apparent position in J2000 celestial coordinates placed it in a part of the Milky Way that is relatively less dense in stars. From the beginning of the Approach phase to the time of the spacecraft’s second asteroid approach maneuver (15 October), Bennu traversed a very dense part of the Milky Way as seen from the spacecraft. Although none of the dates were optimal, 11 and 12 September were the best available while also maximizing the region of space around Bennu that was searched for dust.

Modeling of possible dust trails for Bennu

The model of ref. 6 was implemented to model potential dust trails from Bennu. We use an adapted version of the code originally developed by Jean-Baptiste Vincent37. The Vincent version of the model uses numerical integration to track the position and velocity of a dust particle that is ejected from the surface of the parent body. This is opposed to the analytical equations first proposed in ref. 6. Most of the adaptations we made involve changing the location of observing from Earth to the spacecraft’s position. This allowed us to generate trail locations as a function of right ascension and declination.

For simplicity, we assumed constant particle sizes as a function of beta as opposed to implementing a particle size distribution found in other versions of this model A particle size for a particular syndyne can be calculated from Eq. 3 in ref. 6. To estimate times in which the earliest particles ejected, trails from our model were plotted over the median co-added images of Bennu from the hazards search. The combined plot was visually inspected to determine at what time each trail would leave the field-of-view of the co-added image. The range of particle sizes used to estimate ejection time are for beta values of 0.01 and 0.1. This corresponds to grain sizes of 66.1 and 3.3 microns respectively.

Determining the bound on the mass loss rate

To provide a bound on the mass loss rate of a detectable coma, we adapt a method38 used for members of the Centaur population. The goal of this method is to estimate the total mass of a possible coma from light measured using photometry of an annulus between two circular apertures. We also estimate the approximate time that dust would remain in the given annulus. Dividing these two quantities provides us with a mass loss rate.

A median co-add of images from the Dust Search campaign was created, and then two photometry measurements of Bennu at radii of 20 and 30 arcseconds were measured. The IRAF phot package was used to determine instrumental magnitude of these apertures. We also corrected for sections of the point spread function leaking into the coma annulus as suggested in ref. 38. These magnitudes were transformed into a R-band magnitude system where the apparent magnitude of the Sun is known (for Eq. 3).

Equations 1, 3, and A4 in ref. 38 were used to calculate the bound mass in the annulus between the two photometric apertures. Phase angle, Bennu-Sun distance, and Bennu-OSIRIS-REx distances were calculated from Bennu’s ephemeris using JPL HORIZONS. The phase darkening correction was interpolated from the phase darkening curve developed in refs. 12,39. To convert from cross-section to mass (equation A4), we assume that the R-band albedo is equal to the V-band albedo and set it to a value of 0.045. We assume the same particle sizes, a + = 1 cm and a - = 0.1 micron38,40.

The residence time is calculated from Eq. 4 in ref. 38. We adopt an outflow velocity of 25 m s−1, which is the estimated value of the ejection velocity for 67P/Churyumov-Gerasimenko at perihelion41. This value is chosen since the perihelion of 67P is close to the Bennu-Sun distance during the hazards search (1.3 vs. 1.2 au). It also agrees with measurements taken of the ejection velocity from the Rosetta mission42.

Search for natural satellites around Bennu

Dedicated searches for natural satellites in orbit around Bennu were conducted on 10 separate dates. A summary of the observing circumstances and detection limits of each date is given in Supplementary Table 1. Observations were collected over the course of 5 h (between 4:00 and 9:00 UTC) on each date.

Each date of the search consisted of 3 × 3 mosaic fields with approximately 10% overlap between each field. Each field was imaged between 15 and 30 times over a span of time allowing an object with Bennu rates of motion to move between 5 and 30 pixels relative to the background stars. This dwell time on each field ranged from 4.2 to 25.7 min depending on Bennu’s varying rates of relative motion. Each field was visited between 2 and 4 times on each date. As a result, each field was imaged 60 times per date. Exposure times ranged from 5 s to 0.15 s. Shorter exposure times were used during the later search dates to avoid saturation and pixel blooming near the asteroid. The shorter exposure times were set to still allow the detection of satellites as small as 10 cm.

On 23 to 28 October 2018, only PolyCam was used. Observations between 30 October and 11 November 2018 used a combination of MapCam and PolyCam. Each post–30 October search consisted of a 3 × 3 MapCam mosaic and a single PolyCam field centered on Bennu. The 30 and 31 October PolyCam fields were not used for satellite searching as Bennu was located near the edge or outside the small PolyCam field-of-view due to the greater navigational uncertainty after the third asteroid approach maneuver.

Three different methods were utilized to search for satellites within the OCAMS images. The first involved manually blinking the 15 or 30 images taken per field per visit for moving objects. The second combined, or stack and shifted, all of the images taken during a visit on the motion of Bennu. The combined images minimized the signal of background stars while enhancing the brightness of objects moving at the rate of Bennu. The third search method used the moving object detection software of the Catalina Sky Survey (CSS) to automatically detect satellites19. The CSS software was used on 5 images at a time. Due to the large number (15–30) images taken per visit, up to 6 different combinations of the images were run through the CSS software enabling multiple opportunities for detection. The software approach was not used on 23–25 October due to the slow apparent motion of Bennu and any satellites relative to the background stars. It was also not applicable on 30–31 October and 10–11 November due to the short exposure times used and the low number of detectable background stars.

The sensitivity and efficiency of the satellite search was improved by conducting a search for Earth Trojan Asteroids (ETAs) during the outbound cruise phase in February 201743,44 By exercising the entire moving object detection process, lessons learned during the ETAs search resulted in changes to detection software, number and cadence of observations, exposure times, and the use of both PolyCam and MapCam.

OCAMS disk-integrated photometry calibration

The combination of the OCAMS narrow point spread function (PSF) with its detector’s strongly non-uniform pixel response makes photometric calibration using standard stars more challenging than expected. A dedicated calibration campaign has yielded valuable insights but disappointing results. A second campaign incorporating lessons learned from our first attempt is planned. In the interim, we use defocused images of open star cluster NGC 3532 to derive an absolute radiometric calibration for the PolyCam. We then use near simultaneous MapCam and PolyCam observations of Bennu to transfer this calibration to the MapCam.

During outbound cruise, PolyCam acquired a through-focus sequence of images of NGC 3532. In one of these images, stars are defocused enough to cover approximately 100 pixels, thereby minimizing the effects of aliasing. We exclude stars near the edge of the detector or in pixel regions which do not behave like the bulk of the detector. Stars for which any raw counts are out of the linear range for PolyCam (<12,500 DN) are also rejected. Despite the significant defocus, stars are still well resolved and can be automatically detected, identified and measured. Stars close to each other are also excluded. Visual inspection of each of the remaining stars is used to exclude a further 95 stars with PSF indicative of one or more unresolved companions, leaving 187 stars in our sample. In addition to being an open cluster, NGC 3532 is also a diffuse nebula, so we estimate and remove the local background of the nebula at each star.

Given the panchromatic filter’s 650 nm center wavelength, the integrated star flux is then compared to the R magnitude reported by the American Association of Variable Star Observers (AAVSO) NGC 3532 Standard Field catalog. The fit between the logarithm of measured DN/s and the AAVSO Catalog m R magnitudes is very good (R = 0.998). When corrected to the OSIRIS-REx reference temperature that fit is:

$$m_{\mathrm{R}} = - 2.5Log10(DN/s(PolyCam \hskip3pt T_{ref})) + 18.2180$$ (1)

By design all OCAMS panchromatic filters have identical bandpasses. This allows us to use Bennu as a proxy to extend PolyCam’s absolute calibration to the MapCam. To do this, we use a pair of PolyCam and MapCam images taken on 25 November 2018. Between the two images Bennu rotated one full rotation plus 1 min and 47 s (2.5 degrees). As a result, Bennu presents essentially the same face to the cameras in both images. We estimate how much this difference could affect our calibration, by comparing the integrated flux in PolyCam images taken 7 min before and 7 min after the one used to compare with MapCam. The integrated flux difference between those images is approximately 0.5%.

PolyCam and MapCam imaged Bennu at slightly different phase angles (Δα = 0.4 degrees). In the time between the two images the spacecraft also closed in on Bennu by approximately 1.5 km. Correcting for these effects we estimate that the integrated flux observed by MapCam should be 1.4% greater than PolyCam’s.

We use the OCAMS radiometrically calibrated frad product to integrate Bennu’s flux and relate the two cameras. This product is a dark subtracted, flat fielded, radiometrically calibrated (frad = DN/s/277,035). After correcting for phase angle and distance changes, the calculated ratio between the two cameras is 24.902 and the derived calibration is given by:

$$m_{\mathrm{R}} = - 2.5Log10(MapCam\_frad\_PAN \times 24.90 \times 277,035) + 18.2180$$ (2)

Disk-integrated photometry modeling

The ground-based campaigns covered a range of phase angles from 15.0 to 95.6 degrees yielding an absolute magnitude (H v ) of 20.61 ± 0.20 and phase slope (B v ) of 0.040 ± 0.003 magnitude per degree of phase angle. We applied a known correlation between the slope of the linear phase function and the albedo of asteroids26,45 to estimate a global average geometric albedo of 0.030–0.04518 for Bennu. For the spacecraft phase function campaign, we acquired images daily between 2 October and 2 December 2018. These observations yielded photometric measurements covering a phase angle range from 0.7 to 86.5 degrees in the MapCam v filter (Supplementary Table 2).

The disk-integrated Lommel-Seeliger phase function model (with an exponential phase function and a polynomial in the exponent)27 is

$${\it{\Phi }}\left( \alpha \right) = p\left[ {1 + \sin \frac{\alpha }{2}\tan \frac{\alpha }{2}\ln \left( {\tan \frac{\alpha }{4}} \right)} \right]f(\alpha )$$ (3)

and

$$f\left( \alpha \right) = \exp (p_1\alpha + p_2\alpha ^2 + p_3\alpha ^3)$$ (4)

where α is phase angle in degrees; p is geometric albedo, and p 1 , p 2 , and p 3 are parameters that defines the shape of the phase function. Resulting parameters for the Lommel-Seeliger, as well as the IAU H,G, Muinonen H,G 1 ,G 2 and revised H,G 12 models are given in Supplementary Table 2.

We fitted the v-band phase function data of Bennu with both the original and the revised H, G 12 models29,30 We used the implementation of both H, G 12 models in the photometry module of the Python package for small-body planetary astronomy sbpy that is currently under development46. The non-linear fitting was performed with the Levenberg-Marquardt algorithm47 as implemented in the fitting module in astropy, which is a community-developed core Python package for astronomy48.

Rotation rate of Bennu

We obtained photometric measurements over two full asteroid rotations (around 8.6 h). We used the integrated flux from MapCam images by adding up the radiance from all of the pixels on Bennu to compute a lightcurve. We then compared these lightcurves with the predicted brightness using version 13 of the asteroid shape model35 (Fig. 4).

To compute the rotational acceleration, we followed the procedure from34, adding the data from these observations to the ground-based and Hubble Space Telescope observations from 1999, 2005, and 2012 as used in that work. We used the shape model from35 along with the rotation pole from49 and the observing geometry to compute synthetic lightcurve points using a Lommel-Seeliger photometric function for the observing times of the data. At each of the observation epochs, we adjusted the rotation phase of the model slightly to minimize chi-squared using the method of50 for the data taken at that epoch. We took the absolute phase uncertainty at each of those epochs to be the amount of rotation required to increase reduced chi-squared by 1. The phase uncertainties at each epoch (3.2,1.6, 8.0, and 1.8 degrees, respectively) are slightly larger than those reported in34, probably because the shape model used in that analysis was determined in part from those same lightcurve data, while this work uses a shape model from spacecraft imagery. There was no 2018 data point in the earlier analysis, as these data were not yet available.

Because the absolute rotation phase is known to within 10 degrees from34, there is no ambiguity in the absolute rotation phase, and we were able to fit a quadratic polynomial to the measured rotation phase as a function of observation time (Eq. 5).

$$P = W_0 + W_1T + W_2T^2$$ (5)

Since rotation rate is the time derivative of phase, W 1 is the rotation rate at T = 0 and 2W 2 is the rate of change of the rotation rate. In Fig. 3, we plot this curve using T = 0 at the time of the first ground-based observation on 20 September 1999.

Code availability

This paper was produced using a number of different software packages. In some cases, versions of publicly available software were used with no custom modifications. This includes the software used for photometric reductions and manually inspection of images for dust and satellites (IRAF, http://iraf.noao.edu/ and ds9, http://ds9.si.edu/site/Home.html).

We modified a version of the Comet Toolbox code (https://bitbucket.org/Once/comet_toolbox) to model potential dust trails from Bennu37. Dust mass and production rate spreadsheets are a straightforward implementation of the equations in38. Versions of the dust trail, dust mass and production rates software and spreadsheets are available upon request to editors and reviewers.

The moving object detection software used by the Catalina Sky Survey is proprietary19. Two other methods were used to inspect images for satellites and other moving objects that involved no custom software and replicated and exceeded the capabilities of the Catalina Sky Survey software. The visual inspection of blinked images method defined the lower size limit of detectable satellites (Supplementary Table 1). The visual methods used the following two publicly available software packages: (IRAF, http://iraf.noao.edu/ and ds9, http://ds9.si.edu/site/Home.html).