Lucy Observations of the DART Impact Event

All of the Lucy observations discussed here were taken with L'LORRI (Weaver et al. 2023), which is the highest-resolution and most sensitive optical imager on the Lucy spacecraft. L'LORRI has two image formats: the 1 × 1 format has 1024 × 1024 optically active pixels, while the 4 × 4 format combines four rows and four columns of data during the CCD readout, resulting in images with 256 × 256 pixels. All of the L'LORRI images obtained during the DART impact investigation were taken in the 4 × 4 format, with each individual pixel subtending 40595 on a side, which projects to a spatial scale of 371 km at Didymos. L'LORRI's full field of view (FOV) is 173516 × 173492, independent of CCD format.

The L'LORRI images were processed by the Lucy calibration pipeline, which included exposure time correction (when necessary), bias subtraction (a two-step process), frame transfer correction, and flat-fielding, as described further in Weaver et al. (2023). The calibrated images have low-signal level (≤5 DN) scattered light artifacts, probably associated with the presence of the bright Earth only 28° from the instrument boresight. We first removed an average background level from each each image (using row and column averages in two separate passes), and then we subtracted a background image that removed essentially all the scattered light artifacts. This background image was created using three different median images: one was the straight median of 280 pre-impact 9.9 s images, one was a median of 124 pre-impact 9.9 s images that had Didymos in the same location, and one was a median of 156 pre-impact 9.9 s images that had Didymos in a different location. The straight median of 280 images had faint residuals of Didymos in two locations (the same locations as in the other two median images), but those areas were replaced by the appropriate areas of the other two median images, producing a final background image that essentially had no trace of Didymos itself. All of the analysis discussed here employed these background-subtracted L'LORRI images. Figure 2 shows a composite image of Didymos, produced by combining 280 of the background-subtracted pre-impact images. Each of the images included in the composite had an exposure time of 9.9 s, which means that the total on-target exposure time was 2772 s (46.2 minutes).

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From a robust mean of the pre-impact 9.9 s L'LORRI images, we derive a Didymos system signal level (integrated over the point-spread function) of 36.89 ± 1.65 DN s⁻¹, where the error refers to the standard deviation (σ) of all the individual measurements (265 points total, after deleting outliers), not the error in the mean. Note that this error includes light-curve variation intrinsic to Didymos, which has an amplitude of ±4%. We used the observed spectral energy distribution (SED) of Didymos and the L'LORRI exposure time calculator to determine a "color correction" (0.054) that allowed us to convert the measured L'LORRI count rate to a V-mag in the standard Johnson–Cousins magnitude system (Weaver et al. 2023). The mean pre-impact V-mag of Didymos measured by L'LORRI (15.099 ± 0.049) is within the range of values predicted (14.96 ≤ V ≤ 15.11) using the absolute V-mag (H_v = 18.160 ± 0.042) and phase law (G = 0.20 ± 0.02) cited by Pravec et al. (2012). All the L'LORRI V-mags given in this paper quote 1σ measurement uncertainties, as determined by the S/Ns of the relevant observations. We note, however, that there is an additional absolute calibration uncertainty that depends on the SED of the target (Weaver et al. 2023), which we estimate to be ∼3% for a Didymos-like SED.

The L'LORRI investigation of the DART impact event was divided into eight separate observational phases, starting 12 hr before the impact and ending 24 hr afterward (Table 1). L'LORRI could not resolve the binary, but instead recorded the total brightness of the system, which increased after the DART impact owing to reflected sunlight from the ejecta. The first two phases were designed to obtain baseline photometry of the Didymos system covering both the Didymos–Dimorphos mutual orbit period (11.92 hr) and the rotational period of Didymos (2.26 hr). In both phases, we took sets of five 9.9 s exposures, with a new image taken every 10 s for each set. In phase 1, each set was repeated every 900 s, while each set was repeated every 420 s for phase 2. Phase 3 covered the impact event itself at 1 s cadence, starting 3 minutes before impact and ending 4 minutes afterward. Lucy had a clear view of the predicted DART impact site, theoretically enabling L'LORRI to detect an optical flash in the unlikely event that it was brighter than Didymos itself (see later discussion). L'LORRI observations during phases 4–8 were designed to monitor the temporal and spatial evolution of ejecta associated with the impact event. In each of those phases, pairs of images with different exposure times were taken, and the pairs were repeated at the cadences listed in Table 1. The shorter exposure times (0.1 s) were taken to ensure that there would be no CCD saturation even if the DART ejecta cloud was unexpectedly bright, but none of the 9.9 s images were saturated, so the shorter exposures were excluded from our analysis of phases 4–8. A total of 1549 L'LORRI images were taken during the Lucy-DART campaign, but our analysis is restricted to 1137 images (i.e., excluding the 412 images with 0.1 s exposure times). Finally, we note that the Lucy-DART observing plan had to be finalized several months in advance of its execution on the spacecraft (this is the nominal timeline for the Lucy mission planning process), and the L'LORRI images could not be downlinked to the ground until ∼3 weeks after the DART impact.

Figure 3 displays L'LORRI photometry of the Didymos system spanning all eight phases of the Lucy-DART program. For all the plotted points, the measured signal (DN s⁻¹) is derived from aperture photometry using a 3-pixel-radius (1113 km radius projected distance at Didymos) circular aperture centered on Didymos after subtraction of a background signal derived from the mode of the pixels contained in an annular region with an inner radius of 10 pixels and an outer radius of 15 pixels from the centroided Didymos location. The pre-impact photometry shows only small signal variations (∼8% peak-to-trough amplitude) consistent with the ground-based pre-impact light curve (see Thomas et al. 2023). A periodogram analysis of the pre-impact L'LORRI 9.9 s exposures shows a well-defined rotational period of 2.266 ± 0.004 hr (1σ), which is consistent with the known rotational period of Didymos (2.2600 ± 0.0001 hr; Pravec et al. 2006) at the 2σ level. The L'LORRI pre-impact light-curve data are also consistent with the known Didymos–Dimorphos orbital period (11.92 hr), but the relatively short sampling period (12 hr pre-impact) is not long enough to definitively determine the orbital period.

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The impact time at the DART spacecraft was 2022 September 26 23:14:24.183 ± 0.0015 s UTC (Daly et al. 2023), which, after accounting for the light-travel time, translates to an impact time of 2022 September 26 23:15:26.944 UTC as viewed from the Lucy spacecraft. The impact of the DART spacecraft into Dimorphos resulted in a sharp rise in the signal from the Didymos system, which was produced by light from the subsequently released ejecta. As confirmed by observations from multiple other facilities (see Fitzsimmons et al. 2023), the ejecta could be divided into two different groups: the "fast ejecta," which were moving away from Didymos with sky-projected speeds up to a few kilometers per second, and much slower moving ejecta (≲1 m s⁻¹) that stayed within a single L'LORRI pixel for the entire duration of the Lucy-DART program. The pre-impact mean signal level was 36.89 ± 1.65 DN s⁻¹, the mean signal level of the slow ejecta was 116.11 ± 2.11 DN s⁻¹, and the peak signal level of the fast plus slow ejecta (derived from a single 4.9 s image taken 305 s after impact) was 175 ± 2 DN s⁻¹. Thus, we find that the slow ejecta was responsible for 57.4% ± 2.2% of the total post-impact brightness increase measured by L'LORRI, while the fast ejecta was responsible for 42.6% ± 2.3% of the post-impact brightness increase. The V-mag values associated with the pre-impact and post-impact signals are provided in Figure 3. The spatial morphology of the ejecta is displayed in Figure 4.

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The projected speeds of the fast-moving ejecta were measured by looking carefully at the L'LORRI photometry and finding where the ejecta entered, or exited, either the target aperture or the background annular region, and when the Didymos system brightness settled down to a relatively constant value after all the fast ejecta had left the synthetic apertures and no new ejecta were being produced. The timings of these inflections in the photometry are noted in Figures 3 and 5, the latter being a zoomed-in version of the former. The fastest ejecta started to leave the target aperture ∼305 ± 5 s after impact, which corresponds to a projected outflow speed of ∼3.6 ± 0.1 km s⁻¹. The target signal starts to dip below the eventual asymptotic value ∼1094 s after impact, which is when ejecta moving with a speed of ∼1.7 km s⁻¹ starts entering the background annulus. All of the fast ejecta seem to have exited the outer radius of the background region by ∼6 hr after the impact, which implies that the slowest of the fast ejecta had projected speeds of ∼0.26 km s⁻¹. We also measured the location of the peak brightness (which presumably defines the location of peak mass outflow for the fast ejecta; see Figure 4) and derived a projected speed of ∼1.4 ± 0.2 km s⁻¹. All the above fast ejecta outflow speeds are consistent with those derived from measurements at other facilities (Fitzsimmons et al. 2023; Graykowski et al. 2023).

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L'LORRI's unobscured view of the DART spacecraft impact into Dimorphos motivated us to design an observing plan that enabled searching for a thermally generated optical impact flash associated with the impact event. In laboratory impact experiments, the self-luminous impact flash typically lasts less than a millisecond (Ernst & Schultz 2003), but lunar meteoroid impact flashes can last up to 600 ms (Ortiz et al. 2002). Analysis of the temporal evolution of the flash detected when the Deep Impact spacecraft impacted into comet 9P/Tempel (when a 370 kg projectile was directed at 10.3 km s⁻¹ into the comet nucleus; A'Hearn et al. 2005) showed that there were three different phases: (1) a relatively faint "first light," (2) a very bright "central flash" that saturated the images, and (3) self-luminous light from a downrange-moving "vapor plume" (Ernst & Schultz 2007). The morphology of the latter vapor plume resembles the outflowing partial shell of optical emission associated with the fast ejecta detected from multiple facilities (including Lucy) after the DART impact event, but the Deep Impact vapor plume was only visible within the first second after that impact, whereas the shell of fast ejecta from the DART impact event could be tracked for multiple minutes. We were interested in determining whether L'LORRI could detect any "central flash" from the DART impact, in addition to the outflowing ejecta.

Although L'LORRI can take exposure times as short as 1 ms, the maximum cadence of L'LORRI images is 1 Hz. And for exposure times smaller than 1 s, there is effectively a "dead time" of 100 ms in each 1 s interval (in addition to a frame scrub and frame transfer, each lasting ∼12 ms, ∼76 ms is set aside for various detector processing steps), producing a "window" of up to 900 ms when imaging can take place. Given the uncertainties in the exact impact time (more than 1 s when the Lucy-DART observing program was being designed) and the uncertainty in the timing of L'LORRI exposures (the requirement is 1 s for planning, but ground calibration suggests that the post-observation time-tagging should be accurate at the 1 ms level), we decided to use L'LORRI exposure times of 900 ms to improve the chances that the impact time would land somewhere within L'LORRI's exposure window. Indeed, the DART impact time was 99 ms after the start of one of the L'LORRI images and 801 ms before the end of that image, which means that that image successfully captured the impact event.

Figure 6 shows the photometry for the ejecta only (i.e., the pre-impact Didymos signal has been subtracted) starting 50 s before impact and extending to 100 s after impact. There is a rapid rise in signal during the first 2 s, a leveling-off of the signal for ∼5 s, another rapid rise in signal starting at ∼7 s, followed by a steady rise for the next ∼40 s and a very minor increase in signal after that. However, there is no obvious "flash" because the image that captured the impact event has a signal level that is 2–3 times smaller than the signal in the following image. Presumably there was an impact flash, but its duration must have been so short that its integrated brightness was extremely diluted over the 900 ms exposure time and was dwarfed by the signal from scattered sunlight produced by any ejected material, whose signal was present (and increasing) over the entire 900 ms exposure.

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We have used the L'LORRI data to constrain the properties of the central flash. As a criterion for flash detection, we require the signal from the L'LORRI image overlapping the DART impact to be at least as bright as the signal in the following L'LORRI image. The overlap image has a signal of 15.4 ± 8.2 DN s⁻¹, while the next image has 37.4 ± 8.2 DN s⁻¹. Thus, we assume that a signal of 40 DN s⁻¹ in the overlap image is sufficient to claim detection of the flash. We assume an SED of a 4000 K blackbody for the self-luminous ejecta; Schultz et al. (2007) suggested 3900–4200 K as the range for the Deep Impact central flash. We assume that the duration of the flash is 100 ms, which gives the following relations:

$$\begin{eqnarray}&&(\mathrm{CF})\,\times \,(100\,\mathrm{ms})\,=\,(40\,\mathrm{DN}\,{{\rm{s}}}^{-1})\,\times \,(900\ \mathrm{ms})\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&\to \,\mathrm{CF}=360\,\mathrm{DN}\,{{\rm{s}}}^{-1},\end{eqnarray} \tag{ 2 }$$

where "CF" refers to the average central flash signal rate for a 100 ms time interval somewhere within the L'LORRI exposure containing the DART impact time. With the above assumptions, we find that a flash having V = 12.85, or brighter, and a duration of 100 ms would have been detected by L'LORRI. Thus, a flash lasting 100 ms would have needed to be ∼8 times brighter than the pre-impact Didymos system to have been detectable by L'LORRI.

Given that the kinetic energy of the DART impact was only about half that of the Deep Impact event (∼11 GJ vs. ∼19 GJ), we would expect the DART flash to have a lower brightness, a shorter duration, and a cooler temperature compared to Deep Impact. Thus, our inability to detect the DART flash with L'LORRI is not surprising; shorter exposure times, faster image cadences, and possibly a more sensitive camera are required to characterize optical flashes for these types of impacts.

Figure 7 compares the L'LORRI photometry to that obtained from the Asteroid Terrestrial-impact Last Alert System (ATLAS; Tonry et al. 2018) facility in South Africa. In both cases, the photometry refers to the signal collected in apertures projecting to the same physical size at Didymos (∼1100 km radius aperture). The ATLAS photometry discussed here was taken through the "cyan" filter, usually referred to as the "c band," which covers a wavelength range of 420–650 nm (at the 50% of peak sensitivity values). We have subtracted a constant value from the raw ATLAS magnitudes so that its pre-impact value is identical to L'LORRI's measured V-mag, and we note that this should not affect the magnitude difference measured post-impact. Although the exposure times and cadence of the L'LORRI and ATLAS measurements were very different (0.9 s exposures for L'LORRI vs. 30 s exposures for ATLAS; samples taken every 1 s for L'LORRI vs. 41 s for ATLAS), both show similar rise times post-impact and plateau at approximately the same times. But the amplitude of the signal increase is significantly larger for the ATLAS points: the ATLAS plateau is 2.46 mag brighter (i.e., a brightness increase by a factor of 9.64) than the pre-impact value, while the L'LORRI plateau is only 1.69 mag brighter (i.e., a brightness increase by a factor of 4.74).

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Given that the L'LORRI data were taken at a significantly smaller phase angle compared to that of Earth-based facilities (319 vs. 532), we first explored whether phase effects alone might explain the Lucy versus ATLAS discrepancy. The results discussed above are consistent with the following brightness relations:

$$\begin{eqnarray}&&{{\rm{B}}}_{{\rm{L}}}{}^{{\rm{E}}}+{{\rm{B}}}_{{\rm{L}}}{}^{{\rm{D}}}\,=\,{{\rm{B}}}_{{\rm{L}}}{}^{{\rm{T}}}\,;\,\,{{\rm{B}}}_{{\rm{G}}}{}^{{\rm{E}}}+{{\rm{B}}}_{{\rm{G}}}{}^{{\rm{D}}}\,=\,{{\rm{B}}}_{{\rm{G}}}{}^{{\rm{T}}}\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&{{\rm{B}}}_{{\rm{L}}}{}^{{\rm{T}}}/{{\rm{B}}}_{{\rm{L}}}{}^{{\rm{D}}}\,=\,4.74\,;\,\,\ {{\rm{B}}}_{{\rm{G}}}{}^{{\rm{T}}}/{{\rm{B}}}_{{\rm{G}}}{}^{{\rm{D}}}\,=\,9.64\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}&&\to \ {{\rm{B}}}_{{\rm{L}}}{}^{{\rm{D}}}\,=\,(0.21){{\rm{B}}}_{{\rm{L}}}{}^{{\rm{T}}}\,;\,\,\ \to \ {{\rm{B}}}_{{\rm{G}}}{}^{{\rm{D}}}\,=\,(0.10){{\rm{B}}}_{{\rm{G}}}{}^{{\rm{T}}}\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}&&\to \ {{\rm{B}}}_{{\rm{L}}}{}^{{\rm{E}}}\,=\,(0.79){{\rm{B}}}_{{\rm{L}}}{}^{{\rm{T}}}\,;\,\,\ \to \ {{\rm{B}}}_{{\rm{G}}}{}^{{\rm{E}}}\,=\,(0.90){{\rm{B}}}_{{\rm{G}}}{}^{{\rm{T}}},\end{eqnarray} \tag{ 6 }$$

where "B" refers to the brightness, subscript "L" refers to Lucy, subscript "G" refers to Ground (i.e., ATLAS), superscript "E" refers to the ejecta, superscript "D" refers to Didymos (the solid body), and superscript "T" refers to the total.

If we now define "ϕ_SB" as the solid-body phase factor ratio at 32° (Lucy) versus 53° (ground) and "ϕ_E" as the ejecta phase factor ratio at 32° versus 53°, we can write

$$\begin{eqnarray}&&{{\rm{B}}}_{{\rm{L}}}{}^{{\rm{D}}}/{{\rm{B}}}_{{\rm{G}}}{}^{{\rm{D}}}\,=\,{\phi }_{\mathrm{SB}}\,;\,\,\ {{\rm{B}}}_{{\rm{L}}}{}^{{\rm{E}}}/{{\rm{B}}}_{{\rm{G}}}{}^{{\rm{E}}}\,=\,{\phi }_{{\rm{E}}}\end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray}&&\to \ ({{\rm{B}}}_{{\rm{L}}}{}^{{\rm{D}}}/{{\rm{B}}}_{{\rm{L}}}{}^{{\rm{E}}})({{\rm{B}}}_{{\rm{G}}}{}^{{\rm{E}}}/{{\rm{B}}}_{{\rm{G}}}{}^{{\rm{D}}})\,=\,{\phi }_{\mathrm{SB}}/{\phi }_{{\rm{E}}}.\end{eqnarray} \tag{ 8 }$$

And substituting the values from Equations (5) and (6) above, we can write

$$\begin{eqnarray}&&{\phi }_{\mathrm{SB}}/{\phi }_{{\rm{E}}}\,=\,(0.21/0.79)(0.90/0.10)\,=\,2.39.\end{eqnarray} \tag{ 9 }$$

Thus, the solid-body phase factor ratio must be ∼2.39 times larger than the ejecta phase factor ratio to reconcile the post- to pre-impact Lucy versus ATLAS brightness ratios. But we already know ϕ_SB: using G = 0.2 (Pravec et al. 2012) gives ϕ_SB = 1.68, and we immediately see that ϕ_E must be less than 1 (ϕ_E = 1.68/2.39 = 0.70). That is, explaining the Lucy versus ATLAS pre- to post-impact brightness discrepancy purely as a phase-angle effect requires the ejecta phase function to be increasing between 32° and 53°.

A scattering function that rises with increasing phase angle generally implies the presence of small, forward-scattering dust particles (Lolachi et al. 2023). It is likely that the impact of the DART spacecraft into Dimorphos produced a population of small particles that were explosively ejected from the system at relatively high speeds. We note that if the initial brightness increase was only ∼2.0 mag, then a phase law similar to that measured for typical cometary dust particles (Schleicher & Bair 2011) could fully explain the smaller post- to pre-impact brightness ratio measured by L'LORRI.

Some remarkable, and apparently unique, ground-based spectroscopic observations of the DART impact event showed prominent optical emissions from the alkali metals sodium (Na), lithium (Li), and potassium (K) (Shestakova et al. 2023). These observations were conducted at roughly five air masses, which made absolute calibrations problematic, but the spatially resolved spectra clearly showed material flowing outward from Didymos with a projected speed of ∼1.5–1.7 km s⁻¹ and with the signal dominated by atomic line emission, not continuum associated with dust scattering, for spectral extractions offset from the location of Didymos. These authors suggested that the observed atoms were being released from dust clouds that were ejected at high speed following the DART impact event. Others (Fitzsimmons et al. 2023) have suggested that these atomic emissions formed in a vapor cloud ejected during the DART impact event and that these alkali atoms compose the bulk of the fast-moving ejecta seen emanating from the Didymos system. Fitzsimmons et al. (2023) also proposed that the wavelengths of these atomic emissions relative to the camera bandwidths (BWs) might explain the presence or absence of the partial shell of fast ejecta in the camera images.

If the emission in the outflowing ejecta is dominated by the atomic lines, this can have a profound effect on the observed post- to pre-impact brightness ratio of the Didymos system, as demonstrated by the following simplified relations:

$$\begin{eqnarray}&&{{\rm{S}}}_{\mathrm{Post}}{}^{{\rm{T}}}\,=\,{{\rm{S}}}_{\mathrm{Didy}}+{{\rm{S}}}_{{\rm{E}}}{}^{{\rm{T}}}\end{eqnarray} \tag{ 10 }$$

$$\begin{eqnarray}&&{{\rm{S}}}_{\mathrm{Pre}}{}^{{\rm{T}}}\,=\,{{\rm{S}}}_{\mathrm{Didy}}\end{eqnarray} \tag{ 11 }$$

$$\begin{eqnarray}&&{{\rm{S}}}_{{\rm{E}}}{}^{{\rm{T}}}\,=\,{{\rm{S}}}_{{\rm{E}}}{}^{\mathrm{Line}}+{{\rm{S}}}_{{\rm{E}}}{}^{\mathrm{Cont}}\end{eqnarray} \tag{ 12 }$$

$$\begin{eqnarray}&&\to \,{{\rm{S}}}_{\mathrm{Post}}{}^{{\rm{T}}}/{{\rm{S}}}_{\mathrm{Pre}}{}^{{\rm{T}}}\,=\,1+{{\rm{S}}}_{{\rm{E}}}{}^{T}/{{\rm{S}}}_{\mathrm{Didy}}\,=\,1+({{\rm{S}}}_{{\rm{E}}}{}^{\mathrm{Line}}+{{\rm{S}}}_{{\rm{E}}}{}^{\mathrm{Cont}})/{{\rm{S}}}_{\mathrm{Didy}},\end{eqnarray} \tag{ 13 }$$

where S_Post ^T is the total post-impact signal from the Didymos system, S_Didy is the signal from the pre-impact Didymos system, S_E ^T is the total ejecta signal, ${{\rm{S}}}_{\mathrm{Pre}}{}^{{\rm{T}}}$ is the pre-impact signal from the Didymos system, S_E ^Line is the ejecta signal from atomic lines, and S_E ^Cont is the continuum ejecta signal from dust particles. The second term of Equation (13) is the enhancement in the system signal level produced by the ejecta.

Assuming that the system throughput (i.e., the system quantum efficiency, or QE) is approximately constant over the BW of the instrument, including the region containing sodium line emission (which dominates the atomic line emissions according to Shestakova et al. 2023), then we can write

$$\begin{eqnarray}&&{{\rm{S}}}_{\mathrm{Didy}}=({F}_{\mathrm{Didy}})(\mathrm{QE})(\mathrm{BW})\end{eqnarray} \tag{ 14 }$$

$$\begin{eqnarray}&&{{\rm{S}}}_{{\rm{E}}}{}^{\mathrm{Line}}\propto ({n}_{\mathrm{Na}})(\mathrm{QE})\end{eqnarray} \tag{ 15 }$$

$$\begin{eqnarray}&&{{\rm{S}}}_{{\rm{E}}}{}^{\mathrm{Cont}}\propto ({n}_{\mathrm{dust}})(\mathrm{QE})(\mathrm{BW})\end{eqnarray} \tag{ 16 }$$

$$\begin{eqnarray}&&\to \ {{\rm{S}}}_{{\rm{E}}}{}^{{\rm{T}}}\propto (\mathrm{QE})({n}_{\mathrm{dust}}\ast \mathrm{BW}+{n}_{\mathrm{Na}})\end{eqnarray} \tag{ 17 }$$

$$\begin{eqnarray}&&\to \ {{\rm{S}}}_{{\rm{E}}}{}^{{\rm{T}}}/{{\rm{S}}}_{\mathrm{Didy}}\propto ({n}_{\mathrm{dust}}\ast \mathrm{BW}+{n}_{\mathrm{Na}})/({F}_{\mathrm{Didy}}\ast \mathrm{BW}),\end{eqnarray} \tag{ 18 }$$

where F_Didy is the absolute flux from the pre-impact Didymos system, n_Na is the number of sodium atoms in the FOV, and n_dust is the number of dust particles in the FOV.

Thus, we see that the enhancement term in the ratio of post- to pre-impact brightness is inversely proportional to BW if atomic sodium emission dominates the ejecta signal. If continuum dust emission dominates the ejecta signal, then the ratio of post- to pre-impact brightness should be independent of the instrument BW, neglecting any potential phase-angle effects. Although we have made simplifying assumptions here, it seems clear that the ratio of post- to pre-impact brightness can be significantly reduced by "resolution dilution" of the sodium signal for wide-BW instruments, if sodium emission is a significant fraction of the ejecta optical signal.

BW for L'LORRI is ∼375 nm, and BW for ATLAS is ∼230 nm (both are wavelength ranges at ∼50% of their peak QE), which implies that the ejecta enhancement term should be ∼1.6 times larger for ATLAS, assuming that the ejecta emission is dominated by sodium emission and phase-angle effects are negligible. Given that the L'LORRI enhancement term is 3.74 (= 4.74 − 1), we would expect the ATLAS enhancement term to be 6.1 and the ratio of post- to pre-impact system brightness to be 7.1, again assuming that the ejecta emission is dominated by sodium emission and phase-angle effects are negligible. However, the measured ratio of post- to pre-impact system brightness for ATLAS is 9.64, which suggests that effects other than resolution dilution are also playing a role.

We have modeled how the signal measured by L'LORRI is affected by the presence of sodium atoms in the fast ejecta, assuming that the sodium emissions are optically thin. First, we calculated the resonant scattering efficiency, or g-factors, for the two sodium lines (D1 and D2) using atomic parameters from the NIST chemistry workbook ¹⁵ and a high-resolution solar spectrum compiled by the International Halley Watch.

As shown in Figure 8, the sodium g-factors are strongly dependent on the heliocentric radial velocity ($\dot{r}$) of the sodium atoms. Sodium g-factors for various velocities relevant for the DART impact event are provided in Table 2. Assuming that emissions from sodium atoms produce a substantial portion of the light observed from the fast ejecta (i.e., the ejecta released within the first few minutes after the DART impact), the partial-shell structure associated with the fast ejecta might naturally be a consequence of the vastly different g-factors for the sodium atoms released in different directions relative to the Sun, with stronger emissions seen in the sunward-facing hemisphere owing to the larger g-factors at larger values of $\dot{r}$. Note also that light scattering from free atoms is isotropic, which implies a flat phase function for the ejecta if sodium atoms dominate the optical emission from the fast ejecta (see Section 2.4).

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Table 2. Sodium G-factors

$\dot{r}$	gD2	gD1	gtotal
(km s−1)	(photons s−1)	(photons s−1)	(photons s−1)
−6.287	2.30	1.65	3.95
−4.487	1.30	0.87	2.17
0.000	0.54	0.31	0.85

Note. The scattering efficiencies, or g-factors ("g"), of the two optical sodium resonance lines strongly depend on the heliocentric radial velocity ($\dot{r}$) of the sodium atoms in the ejecta cloud (see Figure 8). Sodium atoms ejected from the Didymos system during the DART impact event will have a range of $\dot{r}$ values depending on the direction and speed of their ejection. See the text for further discussion.

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We considered two extreme cases for the SED of the ejecta emission during the first few minutes after the DART impact: one SED assumes that all the fast ejecta emission is due to resonant scattering of sunlight by sodium atoms while the emission from the slow ejecta is due to continuum scattering of sunlight by dust particles, and one SED assumes that there is no sodium and all the emission (from both fast and slow ejecta) is due to continuum scattering of sunlight by dust particles. We also assume that the dust continuum emission has the same SED as Didymos itself (i.e., a typical S-type asteroid SED). In both cases, the total ejecta emission equals the values measured by L'LORRI. The results are displayed in Figure 9.

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The flux from sodium atoms is given by

$$\begin{eqnarray}&&{F}_{\mathrm{photon}}\,=\,L/(4\pi {{\rm{\Delta }}}^{2})\,=\,g* {n}_{\mathrm{Na}}/(4\pi {{\rm{\Delta }}}^{2})/{r}^{2},\end{eqnarray} \tag{ 19 }$$

where "F_photon" is the flux in photon units (photons cm⁻² s⁻¹ Å⁻¹), "L" is the luminosity of the sodium cloud (isotropic scattering), "Δ" is the distance from the Lucy spacecraft to the target (cm), "g" is the sodium g-factor at r = 1 au, "r" is the target's heliocentric distance (au), and "n_Na" is the total number of sodium atoms being observed.

Adopting a g-factor of 3.95, we calculate that the total flux from the sodium lines needed to account for all the fast ejecta emission is 1.9 × 10⁻¹¹ erg cm⁻² s⁻¹, which corresponds to a photon flux of 5.63 photons cm⁻² s⁻¹. Since the mass of a single sodium atom is 3.816 × 10⁻²³ g, the total mass of sodium in the cloud is ∼2.64 kg. The latter value is an upper limit in the sense that all of the fast ejecta optical emission is attributed to sodium, whereas some of that emission must be due to scattered sunlight from small dust particles. On the other hand, using a smaller sodium g-factor, which is appropriate for sodium atoms not moving directly toward the Sun, would result in more sodium atoms needed to produce the observed emission.

Assuming a composition for the ejecta that is similar to L or LL ordinary chondrites (which should be applicable to Didymos) and a relative sodium mass abundance of ∼0.7% (Jarosewich 1990, 2006), the total mass released in the fast ejecta could be as large as ∼2.64/0.007 = 380 kg, which is ∼66% of the DART spacecraft mass (579.4 kg; Cheng et al. 2023). However, sodium can be preferentially released during the heating of asteroidal material (Masiero et al. 2021), which means that the total mass in the fast ejecta might be smaller.

Using ground-based optical images, Graykowski et al. (2023) estimated the mass of dust in the fast ejecta: they derive 700 ± 120 kg if the average dust particle radius is ∼0.1 μm and 7000 ± 1200 kg if the average dust particle radius is ∼1 μm. The smaller value is comparable to the total fast ejecta mass derived above assuming chondritic abundance of sodium, but Graykowski et al. (2023) neglected emission from sodium and assumed that all the signal from the fast ejecta was due to scattered sunlight from small dust grains. We need to understand what fraction of the fast ejecta signal was due to sodium versus dust to determine more accurately the mass of the fast ejecta. We note that Graykowski et al. (2023) estimated a total mass of ∼10⁷ kg for the slow ejecta, assuming that all the slow ejecta signal was due to scattered sunlight from millimeter-sized dust. Using Atacama Large Millimeter/submillimeter Array observations taken several hours after the DART impact, Roth et al. (2023) calculated that the submillimeter continuum flux from the slow ejected could be produced by millimeter-sized grains having a total mass in the range ∼(0.9–5.2) × 10⁷ kg. Clearly, the slow-moving ejecta dominated the mass budget of the dust expelled from the DART impact event.

Jewitt et al. (2023) discovered multiple meter-sized boulders near Didymos during deep imaging with the Hubble Space Telescope on 2023 December 19, and they estimate a total mass of ∼5 × 10⁶ kg for those bodies. Thus, the mass ejected in large boulders during the DART impact event was comparable to the mass ejected in millimeter-sized particles.