Pre-impact Albedo Map and Photometric Properties of the (65803) Didymos Asteroid Binary System from DART and Ground-based Data

This study provides a pre-impact map of the albedo of the Double Asteroid Redirection Test (DART) target Dimorphos corrected for all the effects of viewing geometry, as well as an estimate of photometric roughness for the hemisphere imaged by DART. Other photometric properties are derived for the (65803) Didymos binary system based on DART and ground-based measurements obtained at JPL’s Table Mountain Observatory. The roughness, geometric albedo, phase curve and phase integral, and single particle phase function are typical of the S-family of asteroids. The major remaining uncertainty lies in the behavior of the phase curve below 7°. These results provide a baseline for comparison with Hera measurements, leading to an understanding of the quantitative effects of the kinetic impactor mitigation strategy.


Introduction
Alongside NASA's campaign to search for and track near-Earth objects (NEOs) is the development of mitigation strategies for deflecting or disrupting an NEO on a collision trajectory to Earth.The Double Asteroid Redirection Test (DART) mission was NASA's first demonstration of the kinetic impactor technique, with a goal of quantifying the orbital change in the companion of the asteroid (65803) Didymos, Dimorphos (Cheng et al. 2018;Chabot et al. 2023;Cheng et al. 2023;Daly et al. 2023;Li et al. 2023).Launched from Vandenberg Space Force Base on 2021 November 24, the DART spacecraft impacted Dimorphos on 2022 September 26 and decreased its orbital period by an unexpectedly large 33 minutes (Thomas et al. 2023).An image taken of the binary system from Palomar Observatory 3.5 days after impact is shown in Figure 1: a large dust tail is still prominent.
Although DART was primarily a technology demonstration, valuable scientific data were returned during its short mission.Perhaps most striking are a few images of Dimorphos obtained just seconds before impact, enabling a modestly robust analysis of the physical state of its surface.This pre-impact characterization is important to quantify the effects of the collision and optimize mitigation efforts, as well as to understand the nature of its surface.The European Space Agency's Hera spacecraft plans on performing a detailed investigation of the post-impact Dimorphos beginning in 2026, so it is important to establish a baseline characterization of the asteroid.
Data returned from the spacecraft were limited owing to the mission's modest cost, focused goal, and emphasis on technology rather than science.For example, the solar phase angle excursion is limited to ∼59°, and only one hemisphere was imaged at high spatial resolution (∼20 cm pixel −1 ).We thus included as part of our investigation a program to obtain a solar phase curve at Table Mountain Observatory (TMO); as an NEO, Dimorphos travels through a large range of solar phase angles.Of course, our observations include the binary system, so our telescopic photometric measurements apply to both bodies, except for roughness, which could be derived from the image of Dimorphos obtained prior to impact.
The prime goal of this investigation is to provide a preimpact photometric baseline of Dimorphos by quantifying the albedo of the asteroid, its surface roughness, and several fundamental photometric parameters, including the single particle phase function, which is related to the size of surface particles, and the single scattering albedo.Characteristics of the pre-impact surface such as friability, cohesiveness, and compaction, among others, can be traced directly to the postimpact observations to be gathered by Hera, enabling better mitigation strategies.One key missing characteristic is the surface compaction state, which can be modeled with observations very close to opposition (<6°).The smallest possible solar phase angle from the TMO campaign was 6°.7.The system goes through solar phase angles <1°prior to the Hera encounter in 2026, but of course these measurements will be dominated by Didymos and a small amount (∼4%) from the post-impact Dimorphos.Didymos could also show alterations by the impact as well, as particles from the long-lived ejecta caused by the impact may have accreted onto its surface.
The second goal of this investigation is to understand the placement of Didymos-Dimorphos in the family of asteroids, especially the S-family.For example, its albedo can be related to the effects of space weathering, as this process lowers the surface albedo of S-type asteroids (Pieters et al. 2000;Hapke 2001).The S-family of asteroids spans a large range of albedos (Tedesco et al. 1989), and that range can be related not only to composition but also to the amount of space weathering and thus surface age (Binzel et al. 1996).Regolith scattering properties can be related to the interactions between Dimorphos and Didymos, such as tidal effects and transfer of regolith particles from one body to the other.Finally, comparison of photometric parameters such as roughness, compaction state, and the size of regolith particles with those of other asteroids and planetary bodies enables a comparison of evolutionary processes among asteroids, other small bodies, and planetary surfaces in general.

Observations
This investigation relies on two prime data sets: images acquired by the Didymos Reconnaissance and Asteroid Camera for Optical navigation (DRACO) prior to impact that were obtained at a solar phase angle of 59°, and a solar phase curve of the Didymos-Dimorphos system obtained at TMO between 2022 October 21 and 2023 February 10 UTC.The DRACO data are well suited to constructing an albedo map (ideally a map of normal reflectance, which has all the effects of viewing geometry eliminated) and deriving photometric roughness, while the phase curve from TMO is ideal for determining the geometric albedo, the phase integral, the single scattering albedo, and the single particle phase function.Unfortunately, no observations at opposition to model the compaction state of the surface were obtained, or even possible, during the 2022-2023 apparition.The asteroid will go through an opposition with a phase angle <1°in 2024 and 2026 before the Hera encounter.We also obtained data with the 200-inch Hale telescope at Palomar Observatory on 2022 September 30, but because of the extensive, still extant dust tail of the asteroid (Figure 1), these observations were not suited to accomplishing photometric measurements.
We planned our observing run to capture the maximum excursion in solar phase angle, with 5°increments in data, except at small phase angles (less than ∼18°), where we planned measurements every degree.Gaps exist where the Moon approached within an angular distance of ∼30°.This range is shown in Figure 2 with both planned and successful observations (the slight offsets between the two data sets are due to ephemeris updates).We obtained 22 nights from 2022 October 21 to 2023 February 10 UTC with TMO's 1.0 m Boller and Chivens telescope and the 2 K Spectral Instruments CCD camera.Our field of view was 6 2 × 6 2, and we obtained a total of 1128 images using a Sloan ¢ r filter with an effective wavelength of 0.62 μm.We covered ∼150 minutes of data each night outside of the mutual events.Our exposure time was 60 s in 2022 October and extended all the way to 240 s in 2023 February as the asteroid brightness dimmed from 15.7 to 18.7 mag.Both maximum and minimum solar phase angles were obtained at 76°in October and 6°.7 in January, along with dense coverage in between.Most of our nights were clear, with an average seeing around 2 5 (range 1 5-4 8), but to cover the full phase curve, we occasionally observed during light cirrus or periods of poor seeing.Data were averaged over one rotation period of 135 minutes.Figure 3 is a typical observation from TMO, and Table 1 summarizes the observations.
Our dual data sets accentuate the importance of using a combination of spacecraft and ground-based observations to extend the capabilities of both collections of data.Spacecraft measurements generally provide spatial resolution, while ground-based observations cover a wider temporal excursion -particularly for flyby missions, or less than flyby missions, such as DART-and a larger range in solar phase angles.For photometric modeling, a large excursion in solar phase angle is required to perform robust and unique fits to physical parameters.The single particle phase function and surface roughness are tightly correlated and thus difficult to uniquely determine.The most effective way to disentangle these two parameters is to determine the roughness from resolved spacecraft images and then separately determine particle phase function from a well-determined solar phase curve (Helfenstein et al. 1988;Buratti 1991;Buratti et al. 2004).

Phase Curve
Our data reduction and on-chip photometry followed the procedures outlined in Mommert (2017).To generate biascorrected and flattened science images, we used the "imred" package. 6Within the reductions we used the Gaia DR3 star catalog (Gaia Collaboration et al. 2023) for both astrometric plate solutions and photometry.Field stars used for calibrations were limited to those with solar colors, which typically allowed for about a dozen calibration stars.Photometry for field stars used an aperture based on the curve of growth, while we manually selected the photometric aperture for Didymos, usually in the range 8″-24″.
After obtaining calibrated Didymos photometry for individual frames, we deselected those measurements known to take place during mutual events and obtained a nightly mean over one 135-minute rotation period.We assigned qualitative data weights for each individual night based on weather and seeing values.
Figure 4 shows the reduced phase curve of the system.The curve is remarkably linear, with a phase coefficient of 0.033 ± 0.001 mag deg −1 .The extrapolation of the curve to 0°yields a reduced opposition magnitude in the R filter of 18.17 ± 0.04, or 18.36 ± 0.04 in the V filter, assuming a V − R of 0.19 (Moskovitz et al. 2024).The image shows that the phase curve of the system is typical of an S-type asteroid between 6°and ∼40°and then drops off more steeply at larger solar phase angles, but not as steeply as a typical C-type asteroid (Helfenstein & Veverka 1989;Li et al. 2015).The graph also illustrates another point: a simple extrapolation to 0°i s almost certainly not valid for this asteroid, and additional observations at opposition in 2024 and 2026 are required for a complete solar phase curve.These results are in good agreement with those of Hasselmann et al. (2024).
The geometric albedo is a fundamental photometric parameter.It is a measure of the integral brightness of a celestial body at a solar phase angle of 0°, compared to a perfectly diffusing disk of the same size (Horak 1950).We computed the geometric albedo (p) in both the R and V filters with the following formula (Horak 1950): where m target is the mean opposition magnitude of the asteroid system, m Sun is the magnitude of the Sun at the same wavelength, R is the semimajor axis of Earth (1 au), ρ is the radius of the combined cross section of both objects (379 m, assuming dimensions of 819 × 801 × 607 m for Didymos and 179 × 169 × 115 m for Dimorphos), ¢ r is the semimajor axis of the system (1.644 au), and Δ is the distance between the system and Earth at opposition (0.644 au).We obtain a visible geometric albedo of 0.16 ± 0.02, which is identical to that obtained earlier (Daly et al. 2023) and slightly lower than the average of ∼0.20 for S-type asteroids (e.g., Tedesco et al. 1989).The geometric albedo in the Sloan r filter is 0.19 ± 0.02.
However, these values are probably incorrect, as they do not include the effects of any opposition surge.If an opposition surge of 0.41 mag between 6°and 0°from a conglomerate S-type phase curve is assumed (Helfenstein & Veverka 1989), the visible geometric albedo is 0.23 ± 0.02, which is slightly high for an S-type asteroid.This uncertainty underscores the importance of obtaining opposition measurements.
The other limitation on this work is that our measurements of the phase curve are of the aggregate system: the value for the geometric albedo assumes that the two objects are the same.Barnouin et al. (2024) state that Dimorphos is "slightly brighter" than Didymos, a finding that is consistent with its younger age and less darkening due to space weathering.In addition, the post-impact measurements of both bodies may be affected by contamination from the dust tail created by the impact.
The phase integral, q, which expresses the directional scattering properties of a planetary body, is given by where Φ(λ) is the disk-integrated normalized phase curve normalized to unity at 0°(we assumed the linear y-intercept depicted on the y-axis in Figure 4 as our normalization point).
Using a four-point Gaussian quadrature formula (Chandrasekhar 1960) and making the reasonable assumption that the values at 110°and 149°(the two phase angles in the quadrature that we did not observe) are 0.05 and 0.01, respectively, based on values of objects of similar albedo at these phase angles (e.g., Buratti et al. 2017, Figure 1), we obtain a value of 0.48 ± 0.04.The Bond albedo, defined as A B = p•q, is 0.09 ± 0.01.Because our phase curve was obtained in the R  filter, this value applies to that wavelength.The bolometric Bond albedo is this quantity integrated over all wavelengths of reflected light.It is a measure of the energy balance on a planetary surface (total energy out/total energy in) and represents a fundamental parameter for understanding energy balance on a celestial body.Unfortunately, we lack measurements for the solar phase curve of the system in additional wavelengths.

Albedo Map
The DRACO images returned prior to the impact provides a data set to derive a map of normal reflectance and photometric roughness of one hemisphere of Dimorphos.Standard procedures have been developed over the years to create maps of normal reflectance, which has all the effects of viewing geometry removed (e.g., Buratti et al. 1990Buratti et al. , 2017;;Buratti & Mosher 1991, 1995;Hofgartner et al. 2023).Publicly available software such as Integrated Software for Imagers and Spectrometers (ISIS)7 and Video Image Communication And Retrieval (VICAR)8 have embedded subroutines that correct for these effects.
We made use of VICAR and the shape model (ver.003) and backplanes provided by the DART team (and deposited into the PDS small bodies node) to correct the geometry of the image.Figure 5 shows the backplanes for the incident and emission angles (the solar phase angle is 59°), along with images of the reflected specific intensity (I/F) with and without a geographical grid.An image of normal reflectance corrected for viewing geometry was constructed using the following equation (Squyres & Veverka 1981;Buratti & Veverka 1983;Buratti 1984): where I/F is the specific intensity, μ o is the cosine of the incidence angle (i), μ is the cosine of the emission angle (e), and f (α) is the surface solar phase function, which includes changes in intensity due to the physical character of the surface (roughness, the single scattering albedo, the single particle phase function, the compaction state of the optically active portion of the regolith, and coherent backscatter).Our going-in assumption was that A = 1 (a Lommell-Seeliger or lunar photometric function), which applies to low-albedo surfaces, but we found that a small "Lambert" component of about 5% provides the best fit.This small amount of multiple scattering  supports the possibility of the system having the higher albedo predicted by an S-type opposition surge, although the laboratory measurements of Veverka et al. (1978) suggest that multiple scattering effects can be neglected for normal reflectances less than 0.3.(More complicated models such as those of Hapke 1981Hapke , 1984Hapke , 1986Hapke , 1990 are not suited for this part of the investigation because the number of parameters to be fit, combined with the paucity of data, underconstrains the determination of those parameters.)After corrections are made for the incidence and emission angles, the effects of the physical phase function ( f (α)) were removed.For a purely Lommel-Seeliger object, the mean normal reflectance of the target is equal to the geometric albedo.With a 5% Lambert contribution to Equation (3), this approximation is still quite good.Following Equation (6) of Buratti & Veverka (1983), the geometric albedo of an object with A = 0.95 would be 0.17, which is very close to our value of 0.16 derived from the solar phase curve and size of the targets.Given the much greater uncertainties in the opposition surge, we normalized the average value of the albedo map to be 0.16, as shown in Figure 6.One of the more unique features of this map are the striations depicted on the surface.These structures are not artifacts, nor are they caused by an error in the shape model or geometric backplanes.As discussed in  Section 4, other asteroids, including Didymos, and some of the small ring moons of Saturn share similar features: the common explanation may be that they are caused by the placement of smaller, brighter surface particles.

Roughness
Albedo and roughness are the only photometric parameters that can be reliably determined for Dimorphos from DRACO observations because of solar phase angle constraints and the limitations of a rapid encounter.Macroscopic roughness encompasses facets ranging in size from aggregates of particles to boulders, trenches, and craters.These features alter the specific intensity of a planetary surface in two ways: the local incidence and emission angles are changed by alteration of the surface profile from that of a smooth sphere, and they remove radiation from the scene by casting shadows.In addition, surfaces are removed from the line of sight of the observer.Two formalisms have been developed to quantitatively model this effect: Hapke's mean slope model (Hapke 1984), and the crater roughness model, which defines rough facets by a craterlike shape defined by a depth-to-radius ratio (q) and fractional coverage (Buratti & Veverka 1985).Both models use idealized shapes: one way of visualizing the difference is to think of craters as concave features on the surface while the mean slope angles are convex features.We make use of the crater roughness model, which has been applied to 19P/Borrelly (Buratti et al. 2004), different terrains on Titan (Buratti et al. 2006), Phoebe (Buratti et al. 2008), and high-and lowalbedo terrains on Iapetus (Lee et al. 2010).The disk-resolved form of the model is particularly useful because it relates surface roughness to limb darkening, which occurs as the emission angle changes, rather than to solar phase angle.A major problem with using a disk-integrated solar phase curve to derive roughness is that roughness is convolved with other effects (such as the single particle phase function), and thus it cannot be derived uniquely (Helfenstein et al. 1988).Diskresolved measurements obtained by spacecraft are far more diagnostic of surface roughness than integral data sets.Furthermore, determining roughness from disk-resolved spacecraft data and fixing roughness parameters in further modeling fits leads to a more robust determination of other photometric parameters.Because we are in the geometric optics limit, the roughness model is wavelength independent for dark surfaces with a minimum of multiple scattering (which would partly illuminate primary shadows).Given that Dimorphos nearly follows a lunar (Lommel-Seeliger) photometric function, multiple scattering is minimal.
The roughness parameter can be determined uniquely from a spacecraft image (or sets of images) by the functional form of the model at any solar phase angle.Furthermore, we can "peer" below the resolution limit of the camera.Our model-as all current models-is scale invariant, with features as large as mountains and craters and as small as boulders or clumps of particles having the same effects.Helfenstein & Shepard (1999) show that small features-just clumps of a few particles -dominate, at least for the Moon, which is the only object for which we have ground truth.Thus, our model indicates the roughness of Dimorphos below the spatial resolution limit of the image we analyzed.
A scan of I/F extracted from the radiometric image in Figure 5 is shown in Figure 7(a), along with an approximate hand-adjusted best fit and a roughness fit based on a Python routine that employs Bayesian statistics (Mishra et al. 2021) in Figures 7(b)-(d).First, this image and resulting scan are ideal for fitting photometric roughness, as there is a wide range in emission angle that includes the characteristic inflection point at ∼75°(for a solar phase angle of 59°), which uniquely defines the functional form of the roughness model for each depth-toradius value.Second, the hand-adjusted (Figure 7(b)) fit is better than the formal fit (Figure 7(c)), and the formal fit appears to mesh with only part of the curve.This result suggests that the roughness varies over the surface of the asteroid.Figure 7(d) is a fit that shows quantitatively that different sections of Dimorphos possess very different roughness characteristics.The physical reason for this result awaits further investigation, perhaps by the Hera mission.One possible interpretation is that rough facets in the section with the striations-which is less rough according to the model-are infilled with fine dust, which in turn makes then brighter.Or perhaps there are more boulders in the rough area.An independent analysis centering on boulder counts and geologic analysis finds that the surface roughness varies significantly: generally lower elevations are smoother (Barnouin et al. 2024).Our scan traverses mainly smooth terrain (due to the need to capture a full range of emission angles), but even within this terrain there are substantial differences.Because our analysis peers below the resolution limit of the image, the two methods are thus not directly comparable, but both show substantial variations in roughness over Dimorphos.

Photometric Modeling
With a phase curve created from both ground-based and preimpact DART data, and roughness already determined with the work described above, it is a straightforward exercise to fit global photometric parameters to the system.A full photometric model is summarized by the following expression for the reflectance r (Horak 1950;Chandrasekhar 1960;Goguen 1981;Hapke 1981Hapke , 1984Hapke , 1986Hapke , 1990Hapke , 1993Hapke , 2002Hapke , 2008)): where w is the single scattering albedo (the probability that a photon reflected from the surface will be scattered into 2π sr of space), B is the function representing the opposition surge (h and B 0 describe the shape and amplitude of the surge, respectively, which are related to the compaction state), P(α) is the single particle phase function, H(μ 0 , w) and H(μ, w) are Chandrasekhar's multiple scattering H-functions (Chandrasekhar 1960), and S(i, e, α) is the function describing macroscopic roughness.The single particle phase function is usually described by a oneor two-term Henyey-Greenstein phase function defined by g, where g = 1 is purely forward scattering, g = −1 is purely backscattering, and g = 0 is isotropic.For the case of objects with low geometric albedos (less than ∼0.3) such as the Didymos-Dimorphos system, multiple scattering is not significant, and the H-functions are close to unity, so the equation can be approximated by Equation (3).We thus see that f (α) contains much important information about the physical properties of the surface.Because we lack observations of the opposition surge of the system, parameters that depend on these observations will not be modeled.Instead, model parameters based on aggregate data for S-type asteroids (Helfenstein & Veverka 1989, partial data are shown in Figures 4 and 8) have been adopted (Table 2).Note that this sequence of fitting photometric parametersfitting roughness to disk-resolved data, then fitting the single scattering phase function and single scattering albedo with a well-defined phase curve-is far more robust than fitting parameters to a disk-resolved solar phase curve, as it is not possible to determine unique unconstrained parameters with disk-integrated data alone (Helfenstein et al. 1988).Many derived photometric parameters are more a function of the range of phase angles observed and modeled rather than an expression of anything physical on the surface.Photometric modeling has also come under scrutiny because the results may have little to do with physical reality (see Shepard & Helfenstein 2007; response by Hapke 2008).These issues can be ameliorated if one realizes that it is comparisons among the results of the models that are most useful (every model is a physical idealization).The models do yield fundamental information on how rough surfaces are and whether the surface is forward-or backscattering, for example.Forward-scattering  particles tend to be smaller, as photons are more likely to exit the particle in the forward direction before they are scattered again in the particle.
We closely followed the techniques of our previous work in fitting the model outlined by Equation (4) (e.g., Hillier et al. 1999Hillier et al. , 2021;;Buratti et al. 2022).We adopted the approximate, hand-adjusted best-fit roughness of q = 0.16 fit to the disk-resolved image, which is equivalent to a mean slope of 18°, an h of 0.020, and an S(0) of 0.97 to define the opposition surge.These values are the averages for S-types from Helfenstein & Veverka (1989) (S(0) is an earlier terminology for the amplitude of the opposition surge).We find a single scattering albedo of 0.126 ± 0.008 and a g of −0.36 ± 0.01.Note that these values are wavelength dependent and apply to the Sloan ¢ r filter, while the roughness is wavelength invariant (in principle at least). Figure 8 is a plot of the data shown with the model, and Table 2 provides a comparison of the results with other objects.These comparisons are important given the idealized nature of photometric models: it is the differences among kindred objects, and between different classes of objects, that offer clues to geophysical processes.For example, asteroids are more backscattering in general than icy moons and other higher-albedo bodies.One explanation for this trend is the presence of multiple scattering, which tends to scatter more isotropically, in bright surfaces.The table also illustrates the wildly different results that photometric modeling can produce (see, e.g., Rhea), a point that harks back to our warning that photometric fits are often just a function of the range in phase angles of the data set being fit.
Hapke's photometric model also yields results for the geometric albedo (p), the phase integral (q), and the Bond albedo (A B ).We find that these values (in the Sloan r filter) are 0.19, 0.38, and 0.073, respectively, which are in reasonable agreement with our results based on direct measurements from the solar phase curve, except for the substantially lower value of the phase integral.This discrepancy is due to the inclusion of the average S-type asteroid's opposition surge in the model, which "depresses" the phase curve and thus lowers the value of the area underneath it.The value from the TMO data with a linear extrapolation may have to be updated to a lower value if the system has a substantial opposition surge.However, the larger geometric albedo due to an opposition surge may "cancel out" this decrease.

Discussion and Summary
Investigating the effects of a kinetic impactor event is key to formulating a strategy to mitigate potential future impacts by NEOs.Specific changes to the physical character of the surface of an NEO can be defined by modeling the target before and after the impact.The main goal of this paper is to define the albedo of Dimorphos, corrected for the effects of viewing geometry, and its photometric properties just prior to the impact of the DART spacecraft.These results will provide a baseline for the investigation of the Hera spacecraft, which is due to arrive at Dimorphos in 2026.The secondary goal is to understand where this binary asteroid lies in the family of S-type asteroids.Each asteroid flyby or rendezvous mission seems to prove that each asteroid is different, and defining that diversity not only is scientifically important but also provides foundational information for mitigation strategies.
The image obtained by DRACO at 59°contained nearly half of Dimorphos's surface, and it is thus ideal for deriving both an albedo map and photometric roughness of the imaged terrain.Although the solar phase curve measured at TMO extended over a larger range than is typical for asteroids (those in the main belt are restricted to solar phase angles less than about 35°), we lack the critical measurements at opposition that are key to defining the geometric albedo.Extrapolating to 0°using the linear phase coefficient of 0.033 mag deg −1 (which holds until at least 6°.7) yields a visible geometric albedo of 0.16 ± 0.02, which is low for an S-type asteroid, but which is probably wrong, as almost all asteroids exhibit an opposition surge.There are exceptions, such as the C-type Jupiter Trojan 1173 Anchises (French 1987).Assuming a typical S-type opposition surge, the geometric albedo is 0.23 ± 0.02, which is more typical of S-types.The albedo map may need to be rescaled if a substantial opposition surge is observed in 2024-2026 when the solar phase angle is less than 1°.Perhaps the most intriguing feature of the map is the placement of albedo striations, which appear regardless of the photometric correction applied (Sunshine et al. 2023a(Sunshine et al. , 2023b)).It is not an artifact of the shape model either, as Figure 5 shows.Asteroid 25143 Itokawa shows similar but less extensive stripes with an adjacent pond of fine material, although the pond does not appear to be closely connected with the striations (Cheng et al. 2007;see Cartier 2019).The change in roughness on Dimorphos may be due to infilling of rough facets with dust from the impact that formed the striation.The asteroid's roughness is typical (Table 2), but the surface appears to be substantially smoother toward the ends of the radiating striations.The presence of fine-grained dust could also explain the higher albedo of the striations, as photons are less likely to be permanently absorbed into them.Other possibilities include flow features of surface dust, as on the inner small Saturnian moons (Buratti et al. 2019b), or tidal stress marks, such as those seen on Phobos. 9Although there are no other images of Dimorphos at additional geometries, an image of Didymos obtained by DRACO prior to the impact shows bright features on its surface and ponding of what appear to be fine particles. 10 The single particle phase function shows that the particles are slightly more backscattering than other S-family asteroids, while the single scattering albedo is lower than other S-asteroids investigated.This result suggests that the regolith particles are more opaque than those of the typical S-asteroid, perhaps because the small surface gravity of Dimorphos means that more small particles (which are more forward scattering) formed in impact events escape.The small particles that may explain the higher albedo striations could be localized to those regions.C-type asteroids tend to be more backscattering and of course lower albedo, so that could explain why the phase curve beyond ∼60°becomes somewhat "C-like" (see Figure 4).Hasselmann et al. (2023) also noted this deviation in the phase curve of the system.
One limitation of our results is that light represented in the DRACO image is barely included in the telescopic diskintegrated measurements: the DART-imaged hemisphere of Dimorphos is only about 4% of the integral brightness of the system.Crater counts by Barnouin et al. (2024) suggest that the age of Dimorphos is 1/30 that of Didymos.Because of the time-dependent accumulative effects of space weathering, gardening by meteoritic impacts, and other factors, there is no reason to expect that their surface properties would be comparable.This problem is compounded by the changes on both bodies due to the DART impact.Of course, our own current telescopic observations were obtained after the impact, and the degree of dust accumulation is unknown.Ground-based studies of the system between the two spacecraft visits will be obtained after significant accretion of dust and boulders on both bodies.Thus, the new ground-based data-including the key observations of the opposition surge-will not be strictly comparable to the pre-impact data.
Another tack is to search archived data from surveys to see whether there are prior pre-impact observations of the system near opposition.This task is beyond the scope and resources of our current project, but if it could be done as part of a future investigation, the results would help to quantify the effects of the impact, including the accumulation of dust on the surfaces of both bodies.Of course, this future data set would still possess the problem of being a composite of the entire Didymos-Dimorphos system.
On the more positive side, the albedo, roughness, and surface properties of at least one hemisphere of Dimorphos can be directly compared to Hera data.And this hemisphere is the area on which the impact occurred.Thus, the main goal of the DART mission-to understand key physical changes due to an impact to optimize mitigation strategies-will be realized.

Figure 1 .
Figure 1.Image obtained at Palomar Observatory on the 200-inch telescope on 2022 September 30 (3.5 days after the impact) in the Sloan r filter.

Figure 2 .
Figure 2. Planned and actual phase angle coverage at TMO during the 2022 October-2023 February campaign.The planned and actual phase angles and times do not exactly line up because of updates to the ephemeris.

Figure 3 .
Figure 3.A typical image of the Didymos-Dimorphos system obtained at TMO on October 21 11:05:37 UT, 25 days after impact.Didymos-Dimorphos is the object with the tail.

Figure 4 .
Figure 4.The reduced data for the TMO (blue squares).For comparison, aggregate curves for C-type and S-type asteroids are shown.The latter phase curves are from Helfenstein & Veverka (1989) and Li et al. (2015).The line is a linear least fit of 0.033 mag deg −1 .

Figure 5 .
Figure 5.The four panels represent (a) the radiometrically corrected image of the DART target, (b) the same image with a geographical grid of latitude and longitude, and (c, d) the backplanes of geometric information: the emission and incidence angles (panels (c) and (d), respectively) computed with the DART Project's shape model version 003 (Daly et al. 2023; Barnouin et al. 2024).The image was obtained 8.559 s before closest approach with a spatial resolution of 26 cm pixel −1 .

Figure 6 .
Figure 6.The normal reflectance of Dimorphos computed from the calibrated DRACO image with a corresponding color scale bar.The blue halo surrounding Didymos is a small residual signal in the background of the PDS image.

Figure 7 .
Figure 7. (a) The position of the scan we used for modeling macroscopic roughness based on the crater model ofBuratti & Veverka (1983).(b, c) Hand-adjusted fit that looks best and a formal fit to the depth-to-radius ratio, respectively.Panel (d) shows that much better fits can be obtained if the roughness changes with position.The upper 25%-30% of Dimorphos toward the limb is substantially rougher, as shown by the green model.The q-values of 0.25, 0.16, 0.19, and 0.79 correspond to Hapke mean slope angles(Hapke 1984) of about 18°, 12°, 14°, and 53°, respectively.

Figure 8 .
Figure 8.The composite data set from TMO and Helfenstein & Veverka (1989) for data at opposition (less than 6°.7) shown with the best-fit photometric model.

Table 1
Summary of Observations Obtained at TMO

Table 2
Photometric Modeling and Fundamental Photometric Parameters of Selected Objects in Comparison to Didymos/Dimorphos a No opposition surge.b Sloan r filter.c Assumed.