# Polarimetry of Didymos-Dimorphos: Unexpected Long-Term Effects of the DART
Impact

Zuri Gray Armagh Observatory & Planetarium, College Hill, Armagh, BT61 9DG, UK
Mullard Space Science Laboratory, Department of Space and Climate Physics,
University College London, Holmbury St. Mary, Dorking, Surrey RH5 6NT, UK
Nordic Optical Telescope, Rambla José Ana Fernández Pérez 7, ES-38711 Breña
Baja, Spain  Stefano Bagnulo Armagh Observatory & Planetarium, College Hill,
Armagh, BT61 9DG, UK  Mullard Space Science Laboratory, Department of Space
and Climate Physics, University College London, Holmbury St. Mary, Dorking,
Surrey RH5 6NT, UK  Mikael Granvik Department of Physics, PO Box 64, FI-00014
University of Helsinki, Finland  Asteroid Engineering Laboratory, Luleå
University of Technology, Box 848, SE-98128 Kiruna, Sweden  Alberto Cellino
INAF, Osservatorio Astrofisico di Torino, I-10025 Pino Torinese, Italy
Geraint H. Jones Mullard Space Science Laboratory, Department of Space and
Climate Physics, University College London, Holmbury St. Mary, Dorking, Surrey
RH5 6NT, UK  The Centre for Planetary Sciences at UCL/Birkbeck, Gower Street,
London WC1E 6BT, UK  Ludmilla Kolokolova Department of Astronomy, University
of Maryland, College Park, MD 20742-2421, USA  Fernando Moreno Instituto de
Astrofísica de Andalucía, CSIC, Glorieta de la Astronomia s/n, E-18008
Granada, Spain  Karri Muinonen Department of Physics, PO Box 64, FI-00014
University of Helsinki, Finland  Olga Muñoz Instituto de Astrofísica de
Andalucía, CSIC, Glorieta de la Astronomia s/n, E-18008 Granada, Spain
Cyrielle Opitom Institute for Astronomy, University of Edinburgh, Royal
Observatory, Edinburgh, EH9 3HJ, UK  Antti Penttilä Department of Physics, PO
Box 64, FI-00014 University of Helsinki, Finland  Colin Snodgrass Institute
for Astronomy, University of Edinburgh, Royal Observatory, Edinburgh, EH9 3HJ,
UK

(Received 29 August 2023; Accepted 21 November 2023)

###### Abstract

We have monitored the Didymos-Dimorphos binary system in imaging polarimetric
mode before and after the impact from the Double Asteroid Redirection Test
(DART) mission. A previous spectropolarimetric study showed that the impact
caused a dramatic drop in polarisation. Our longer-term monitoring shows that
the polarisation of the post-impact system remains lower than the pre-impact
system even months after the impact, suggesting that some fresh ejecta
material remains in the system at the time of our observations, either in
orbit or settled on the surface. The slope of the post-impact polarimetric
curve is shallower than that of the pre-impact system, implying an increase in
albedo of the system. This suggests that the ejected material is composed of
smaller and possibly brighter particles than those present on the pre-impact
surface of the asteroid. Our polarimetric maps show that the dust cloud
ejected immediately after the impact polarises light in a spatially uniform
manner (and at a lower level than pre-impact). Later maps exhibit a gradient
in polarisation between the photocentre (which probes the asteroid surface)
and the surrounding cloud and tail. The polarisation occasionally shows some
small-scale variations, the source of which is not yet clear. The polarimetric
phase curve of Didymos-Dimorphos resembles that of the S-type asteroid class.

Polarimetry – minor planets, asteroids: individual (Didymos,Dimorphos)

††thanks: Email<EMAIL_ADDRESS>
##  1 Introduction

The Double Asteroid Redirection Test (DART) mission aimed to study and
demonstrate the effectiveness of the kinetic impact technique for deflecting
potentially hazardous asteroids and, in doing so, estimate the momentum
transfer efficiency ($\beta$) of the impact (Daly et al., 2023). At 23:14 UT
on September 26th 2022, the DART spacecraft successfully collided with its
target, Dimorphos – the moonlet of near-Earth asteroid, Didymos. Following the
impact, observations revealed a greater-than-expected change in Dimorphos’
orbital period (Thomas et al., 2023), as well as the formation of a dust cloud
and tail due to material ejection (Li et al., 2023; Opitom et al., 2023). The
DART mission provided a rare opportunity to study the characteristics and
behaviour of an ejecta cloud, which is essential for enhancing our
understanding of the global properties of asteroids and the dynamics of their
collisions, thus, improving our ability to assess and mitigate potential
future asteroid threats.

A worldwide observing campaign was initiated to observe this once in a
lifetime event using both ground-based and space telescopes, with polarimetric
observations being a crucial aspect. Polarimetry exploits the fact that
sunlight scattered by the surface of astronomical bodies becomes partially
polarised. For Solar System objects, the degree of linear polarisation is
measured as a function of phase angle $\alpha$, the angle between the Sun and
observer as seen from the target. It is found that all small Solar System
objects show a similar polarimetric phase angle dependence: the polarisation
is zero at zero phase angle, negative at small phase angles, zero at the so-
called inversion angle $\alpha_{0}$, and then positive at larger phase angles.
Thus, the polarimetric phase curve consists of the negative polarisation
branch (NPB) and the positive polarisation branch (PPB). The concept of
positive and negative polarisation refers to the reference direction that we
adopt to measure it: the flux perpendicular to the scattering plane (the Sun-
object-observer plane) minus the flux parallel to that plane, divided by the
sum of the two fluxes. The polarisation is said to be positive when it is
mostly oriented in the direction perpendicular to the scattering plane, and
vice versa for negative polarisation.

Despite general similarities, the overall shape of the polarimetric phase
curve will depend on the global properties unique to each object, including
the material composition, size distribution, shape and roughness (Shkuratov et
al., 2007; Escobar-Cerezo et al., 2017; Muñoz et al., 2021). Thus, certain
parameters describing this curve, including the minimum and maximum values of
polarisation, $P_{\rm{min}}$ and $P_{\rm{max}}$, and the phase angles at which
they occur, $\alpha_{\rm{min}}$ and $\alpha_{\rm{max}}$, as well as the
inversion angle and the slope of the curve at this angle h, will vary from
object to object. It is worth noting that $P_{\rm{max}}$ and
$\alpha_{\rm{max}}$ are rarely measured for asteroids. Due to the orbital path
and observing geometry of main-belt asteroids, the observable phase angle
range is typically $\sim 0-30^{\circ}$. Only some near-Earth objects (NEOs)
can be explored at larger phase angles when they pass sufficiently close to
Earth.

In this study, we report our extensive imaging polarimetric observations of
the Didymos-Dimorphos system. These observations allow us to determine the
polarimetric behaviour of the system in its original state (pre-impact) and
observe how it changes following the impact of the DART spacecraft (post-
impact). We also study and monitor the spatial and temporal evolution of the
ejecta dust cloud and tail in polarised light. An advantage of the use of
polarimetry compared to other techniques which rely heavily of intensity alone
is the fact that polarisation is measured as a ratio, i.e., a percentage. This
means it is not necessary to normalise the data in brightness in order to
compare data taken of the same object at different times. In this paper, we
present both qualitative and quantitative results. Further interpretation of
these results, as well as possible inter-data comparisons, will follow in
subsequent papers.

##  2 Observations

Imaging polarimetric observations of the Didymos-Dimorphos system were
obtained with FORS2 (FOcal Reducer/low dispersion Spectrograph 2) at the VLT
(Very Large Telescope) and ALFOSC (Alhambra Faint Object Spectrograph and
Camera) at the NOT (Nordic Optical telescope), with specific details provided
in Table 1. FORS2 is a multipurpose instrument capable of performing low-
resolution spectroscopic and imaging observations, as well as polarimetry when
equipped with the appropriate optics. Following the design first suggested by
Appenzeller (1967), the polarimetric setup of FORS2 consists of a rotatable
retarder waveplate followed by a Wollaston prism. The retarder waveplate
introduces a phase-shift between the orthogonal polarisation components of the
light (ordinary and extraordinary) while the Wollaston prism splits the light
into these two components. In imaging polarimetric mode, a Wollaston mask is
used to prevent the superposition of the beams split by the prism. The field
of view (FoV) is vignetted by the mask consisting of nine $6.8^{\prime}\times
22^{\prime\prime}$ strips. Approximately half of the observations were
performed with $1\\!\times\\!1$ binning and the other half with
$2\\!\times\\!2$ binning, with a pixel scale of $0.125"\rm{pixel}^{-1}$ and
$0.25"\rm{pixel}^{-1}$, respectively. This instrument setup allows the user to
measure the degree of polarisation using the so-called beam swapping
technique, which largely suppresses the effects of instrumental polarisation
(e.g. Bagnulo et al., 2009). For this, observations were taken with the
retarder-waveplate ($\lambda/2$ waveplate in this case) at eight different
position angles between $0^{\circ}-157.5^{\circ}$ increasing in steps of
$22.5^{\circ}$. In some cases, however, observations were taken with the
retarder-waveplate in position angles separated by increments of $45^{\circ}$
only, and with the instrument position angle set equal to the angle
perpendicular to the scattering plane (assuming that in the instrument
reference system, Stokes $U$ would be zero for symmetry reasons).

Linear polarimetry with ALFOSC is performed with a similar set up to that of
FORS2: a retarder waveplate is mounted in the FAPOL unit and a calcite plate
is mounted in the aperture wheel. The main difference, however, is the lack of
a Wollaston mask in ALFOSC, which prevents us from measuring the polarisation
of extended objects. The calcite plates produces a vignetted field of about
$2.7^{\prime}$ in diameter and the observed object is separated by about
$15"$. During each NOT observing night, two to four sets of observations were
performed in each filter with $2\\!\times\\!2$ binning, with the ($\lambda/2$)
retarder-waveplate rotated at sixteen different position angles between
$0^{\circ}-337.5^{\circ}$ in steps of $22.5^{\circ}$. The final value of
polarisation of a given night is the weighted average of the set of
observations of that night. Finally, we observed high polarisation stars,
BD+64106 and HD204827, and zero polarisation star, BD+284211, on a number of
the NOT observing nights. Comparing our measurements to literature values, we
calculated the instrumental polarisation in both the R- and B-filters, which
we used to calibrate our data. This step was not necessary for VLT
observations as measurements of standard stars are already part of the
calibration plan of the instrument.

The DART spacecraft impacted Dimorphos at 23:14 UT on September 26th, 2022.
Our observations span a period from about one month before to almost four
months after the impact, with a number of the VLT observations being made
hand-in-hand with spectropolarimetric observations (Bagnulo et al., 2023)—this
has been indicated in the observing log. Considering the entire observing
campaign, we have observed the asteroid system in three stages. (i) Pre-
impact, when the system remained unperturbed and the surface properties are
those resulting from the previous collisional history of the system. (ii)
Immediate post-impact, characterised by a large ejected dust cloud that
persisted for several weeks, influencing polarimetric measurements. As time
passed, the cloud dispersed, giving rise to an extensive tail, marking the
third and final stage of observation. (iii) Long-term post-impact, possibly
representing a “new” system to that of its pre-impact state.

Throughout the campaign, we observed Didymos-Dimorphos on six pre-impact and
29 post-impact nights using various filters and covering a phase angle range
of approximately $7-76^{\circ}$. With FORS2, we used the broadband filters
b_HIGH, v_HIGH, R_SPECIAL, and I_BESS (B-, V-, R-, and I-filter hereafter)
centred around 440 nm, 557 nm, 655 nm and 768 nm, respectively. With ALFOSC,
we used the B_BES and R_BES filters (B- and R- hereafter) centred around 440
nm and 650 nm. In total, we have accumulated 148 measurements: 67 in the B
filter, 4 in the V filter, 74 in the R filter, and 5 in the I filter. This
large number is a consequence of the observations being repeated 2-4 times in
each filter during each night with NOT. As mentioned, the final recorded value
of polarisation is calculated as the weighted average of these repeated
observations. Therefore, we have ended up with 30 measurements in the B filter
and 33 in R.

##  3 Data Reduction

###  3.1 Data Pre-Processing

All data reduction processes were performed using dedicated, original Python
scripts. Prior to any scientific reduction, bias and flat-field corrections
were applied to all frames. For each observing night, a master-bias image was
generated from a series of zero-exposure frames and a master-flat was created
for each filter using the median of a series of exposures of a uniform light
source. Twilight (sky) flats were used for FORS2 while dome flats were used in
the case of ALFOSC. For each observing night, the corresponding master-bias
was subtracted from each science frame, which was then divided by its
corresponding master-flat image. To ensure data quality, all files were
carefully inspected and those in which the asteroid photocentre passed in
front of a background star were discarded, as well as their corresponding
pair.

Figure 1: The polarimetric growth curves of imaging polarimetric VLT data of
Didymos-Dimorphos in BVRI filters, i.e, the polarisation is measured in
apertures of increasing size (pixel radii, where 0.125“/pixel). The colour of
each curve represents an observing epoch and phase angle, indicated on the
right. The pixel scale varied from epoch to epoch due to the changing
asteroid-observer distance ($\Delta$). Thus, all curves have been scaled to
the same distance scale (horizontal axis). The values reported in Table 1 and
Figure 2 are those integrated in an aperture radius equivalent to 100 km (0.1
($10^{3}$ km) on the x-axis). A number of the curves are spurious at larger
radii due to the contamination of background stars: 2022-Oct-25 in the B
filter, 2022-Oct-20 in the R filter, and 2022-Sep-28 in the I filter. These
spurious signals have been left unshaded.

###  3.2 Polarimetry

To study the polarimetric behaviour of Didymos-Dimorphos, we measured the
reduced Stokes parameters (Shurcliff, 1962), $P_{Q}$ and $P_{U}$ using the so-
called beam-swapping technique (Bagnulo et al., 2009). For this, we first
measure the reduced Stokes parameters in the instrument reference system as:

$\begin{split}P_{Q}^{\prime}&=\frac{1}{2}[D(\phi=0^{\circ})+D(\phi=90^{\circ})],\\\
P_{U}^{\prime}&=\frac{1}{2}[D(\phi=22.5^{\circ})+D(\phi=112.5^{\circ})],\end{split}$
(1)

where

$D(\phi)=\left(\frac{f^{\parallel}-f^{\perp}}{f^{\parallel}+f^{\perp}}\right)_{\phi}-\left(\frac{f^{\parallel}-f^{\perp}}{f^{\parallel}+f^{\perp}}\right)_{\phi+45\arcdeg}$
(2)

and $f^{\perp}$ and $f^{\parallel}$ are the fluxes measured in the
perpendicular and parallel beam, respectively, obtained with the retarder
waveplate at the position angle $\phi$. Where applicable, we transformed the
Stokes parameters into the reference direction perpendicular to the scattering
plane, and hence, the reference system of the target using the equation:

$\begin{split}P_{Q}&=\phantom{-}\cos(2\chi)P_{Q}^{\prime}+\sin(2\chi)P_{U}^{\prime},\\\
P_{U}&=-\sin(2\chi)P_{Q}^{\prime}+\cos(2\chi)P_{U}^{\prime},\end{split}$ (3)

Here, $\chi={\rm PA}+\Phi+90^{\circ}$ and $\Phi$ is the angle between the
asteroid-north celestial pole direction and the asteroid-Sun direction. After
this transformation, we expect all the polarisation to be in $P_{Q}$ while
$P_{U}$ is expected to be zero within uncertainties for symmetry reasons.
Further, the Null $N_{Q}$ and $N_{U}$ parameters, which are calculated by
subtracting the second $D(\phi)$ expression in Eq. 1 rather than adding it,
can be used as as an additional quality check for our measurements. Again, the
Null parameters should be zero within uncertainty (Bagnulo et al., 2009).

In this study, we performed aperture polarimetry and generated polarimetric
maps. In both cases, the initial step was to accurately determine the position
of the asteroid photocentre in both the $f^{\perp}$ and $f^{\parallel}$ beams.
This was accomplished using the DAOStarFinder Python package, which uses point
spread function (PSF) estimation for source detection. Next, we measured the
flux of the target in the parallel and perpendicular beams in a circular
aperture, while the background sky level was measured in a region of the CCD
free from background stars and the dust cloud and tail resulting from the
impact. The $f^{\parallel}$ and $f^{\perp}$ fluxes of the frames of each
position of the retarder waveplate ($0,22.5^{\circ}$…), once corrected for
background sky, were then combined using Eq. 1 and transformed with Eq. 3 to
obtain the final values of the reduced Stokes parameters.

###  3.3 Maps

With the VLT data, we generated both polarimetric and imaging maps. The
polarimetric maps were obtained in a similar manner to that of aperture
polarimetry, but this time, the entire $f^{\perp}$ and $f^{\parallel}$ beams,
background subtracted, were combined (while aperture polarimetry extracts a
numerical value only). The photocentres of the two beams of each waveplate
angle ($0,22.5,45^{\circ}$, etc.) were aligned and merged using Eq. 1 and 3.
The resulting maps allow one to view the spatial distribution of the
polarisation of the asteroid system. In the context of the DART mission, these
maps are of particular interest as they make it possible to investigate small
scale structures within the ejected dust cloud and tail, and track their
spatial and temporal evolution. It is important to note that even minor
misalignments, in the order of a few pixels, can give rise to spurious
structures near the photocentre which may be misinterpreted as real variations
in polarisation. Similarly, we co-added the two beams of all waveplate angles
to create high S/N (signal-to-noise) imaging maps. These deep images provide a
detailed view of the asteroid system and, hand-in-hand with the polarimetric
maps, contribute to a better understanding of the overall features and
characteristics of the ejected material.

##  4 Results

###  4.1 Aperture Polarimetry

Table 1:  Observing log. $\Delta$T indicates the time to/from the DART impact, $\Delta$ is the asteroid-observer distance, the scale is the km covered by 1” at each $\Delta$ value, $\alpha$ is the phase angle of the asteroid system at the time of the observation, INSTR is the instrument used for each observation, and $P_{Q}$ is the Stokes $Q$ parameter measured in the the BVRI filters, rotated to the direction perpendicular to the scattering plane. *VLT indicates spectropolarimetric measurements published in Bagnulo et al. (2023) which we have included for completeness. DATE |  $\Delta$T | $\Delta$ | Scale | $\alpha$ | INSTR |  $P_{Q}$(%)
---|---|---|---|---|---|---
YYYY-MM-M-DD |  | (AU) | (km) | $(^{\circ})$ |  | B | V | R | I
2022-Aug-19 | -38d 20h 39m | 0.20 | 145 | 20.68 | NOT |  |  -0.19$\pm$ | 0.08 |
2022-Aug-23 | -34d 21h 28m | 0.18 | 130 | 21.50 | VLT |  0.18$\pm$ | 0.08 |  0.17$\pm$ | 0.07 |  -0.05$\pm$ | 0.09 |  -0.1$\pm$ | 0.06
2022-Aug-28 | -29d 20h 25m | 0.16 | 116 | 23.29 | *VLT |  0.34$\pm$ | 0.05 |  0.27$\pm$ | 0.05 |  0.24$\pm$ | 0.05 |  0.24$\pm$ | 0.05
2022-Sep-07 | -19d 15h 44m | 0.12 | 87 | 29.86 | *VLT |  1.26$\pm$ | 0.05 |  1.15$\pm$ | 0.05 |  1.07$\pm$ | 0.05 |  1.04$\pm$ | 0.05
2022-Sep-09 | -17d 21h 02m | 0.12 | 87 | 31.41 | NOT |  1.42$\pm$ | 0.36 |  |  1.25$\pm$ | 0.09 |
2022-Sep-13 | -13d 20h 44m | 0.11 | 79 | 35.34 | NOT |  2.27$\pm$ | 0.25 |  |  1.7$\pm$ | 0.08 |
2022-Sep-17 | -9d 16h 54m | 0.09 | 65 | 39.99 | *VLT |  2.89$\pm$ | 0.05 |  2.59$\pm$ | 0.05 |  2.47$\pm$ | 0.05 |  2.46$\pm$ | 0.05
2022-Sep-21 | -05d 20h 04m | 0.09 | 65 | 44.91 | NOT |  4.03$\pm$ | 0.1 |  |  3.16$\pm$ | 0.05 |
2022-Sep-23 | -03d 18h 56m | 0.08 | 58 | 47.68 | NOT |  4.27$\pm$ | 0.09 |  |  3.55$\pm$ | 0.05 |
| -03d 19h 49m |  |  |  | *VLT |  4.30$\pm$ | 0.05 |  3.79$\pm$ | 0.05 |  3.61$\pm$ | 0.05 |  3.59$\pm$ | 0.05
2022-Sep-26 | -15h 49m |  |  | 52.25 | *VLT |  5.24$\pm$ | 0.05 |  4.63$\pm$ | 0.05 |  4.39$\pm$ | 0.05 |  4.35$\pm$ | 0.05
2022-Sep-27 | +04h 47m | 0.08 | 58 | 53.48 | VLT |  4.76$\pm$ | 0.03 |  4.30$\pm$ | 0.03 |  4.09$\pm$ | 0.02 |  4.04$\pm$ | 0.02
| +05h 37m |  |  |  | *VLT |  4.56$\pm$ | 0.05 |  4.16$\pm$ | 0.05 |  3.98$\pm$ | 0.05 |  4.01$\pm$ | 0.05
| +09h 54m |  |  |  | VLT |  4.65$\pm$ | 0.03 |  4.22$\pm$ | 0.02 |  4.04$\pm$ | 0.04 |  4.03$\pm$ | 0.04
2022-Sep-28 | +01d 09h 59m | 0.08 | 58 | 55.04 | *VLT |  4.88$\pm$ | 0.05 |  4.43$\pm$ | 0.05 |  4.25$\pm$ | 0.05 |  4.27$\pm$ | 0.05
| +01d 10h 30m |  |  |  | VLT |  |  4.41$\pm$ | 0.04
2022-Sep-30 | +03d 04h 38m | 0.07 | 50 | 58.21 | NOT |  5.34$\pm$ | 0.14 |  |  4.59$\pm$ | 0.06 |
| +03d 08h 30m |  |  |  | *VLT |  5.39$\pm$ | 0.05 |  4.86$\pm$ | 0.05 |  4.65$\pm$ | 0.05 |  4.65$\pm$ | 0.05
2022-Oct-01 | +04d 05h 36m | 0.07 | 50 | 59.53 | NOT |  5.63$\pm$ | 0.11 |  |  4.79$\pm$ | 0.05 |
| +04d 08h 59m |  |  |  | *VLT |  5.63$\pm$ | 0.05 |  5.1$\pm$ | 0.05 |  4.87$\pm$ | 0.05 |  4.84$\pm$ | 0.05
| +04d 09h 19m |  |  |  | VLT |  5.9$\pm$ | 0.03 |  |  5.02$\pm$ | 0.03 |
2022-Oct-02 | +05d 05h 12m | 0.07 | 50 | 61 | NOT |  5.96$\pm$ | 0.07 |  |  4.96$\pm$ | 0.03 |
2022-Oct-03 | +06d 06h 17m | 0.07 | 50 | 62.43 | NOT |  6.24$\pm$ | 0.18 |  |  5.18$\pm$ | 0.04 |
2022-Oct-04 | +07d 05h 14m | 0.07 | 50 | 63.83 | NOT |  6.65$\pm$ | 0.11 |  |  5.35$\pm$ | 0.06 |
| +07d 08h 21m |  |  |  | VLT |  6.60$\pm$ | 0.03 |  |  5.67$\pm$ | 0.03 |
2022-Oct-07 | +10d 09h 17m | 0.07 | 50 | 67.75 | VLT |  7.17$\pm$ | 0.04 |
2022-Oct-08 | +11d 04h 58m | 0.07 | 50 | 68.86 | NOT |  7.25$\pm$ | 0.12 |  |  6.21$\pm$ | 0.05 |
2022-Oct-11 | +14d 05h 28m | 0.07 | 50 | 71.87 | NOT |  8.18$\pm$ | 0.19 |  |  6.6$\pm$ | 0.06 |
2016-Oct-17 | +20d 04h 38m | 0.08 | 58 | 75.56 | NOT |  8.38$\pm$ | 0.29 |  |  6.84$\pm$ | 0.14 |
2022-Oct-20 | +23d 06h 54m | 0.09 | 65 | 76.27 | VLT |  8.75$\pm$ | 0.04 |  |  6.82$\pm$ | 0.05 |
2022-Oct-21 | +24d 04h 49m | 0.09 | 65 | 76.34 | NOT |  8.83$\pm$ | 0.83 |  |  6.99$\pm$ | 0.18 |
2022-Oct-24 | +26d 09h 01m | 0.09 | 65 | 76.16 | *VLT |  9.08$\pm$ | 0.05 |  7.91$\pm$ | 0.05 |  7.47$\pm$ | 0.05 |  7.37$\pm$ | 0.05
2022-Oct-25 | +28d 08h 44m | 0.10 | 72 | 75.98 | VLT |  8.2$\pm$ | 0.06 |  |  6.93$\pm$ | 0.1 |
2022-Oct-26 | +29d 06h 55m | 0.10 | 72 | 75.73 | NOT |  8.87$\pm$ | 0.33 |  |  7.13$\pm$ | 0.3 |
2022-Oct-31 | +34d 05h 02m | 0.11 | 79 | 73.85 | NOT |  8.77$\pm$ | 0.2 |  |  7.04$\pm$ | 0.11 |
2022-Nov-16 | +50d 03h 46m | 0.14 | 101 | 62.36 | NOT |  6.54$\pm$ | 0.28 |  |  5.03$\pm$ | 0.12 |
2022-Nov-24 | +58d 07h 26m | 0.16 | 116 | 54.52 | VLT |  5.14$\pm$ | 0.04 |  4.46$\pm$ | 0.06 |  4.42$\pm$ | 0.05 |  4.28$\pm$ | 0.06
2022-Dec-02 | +66d 02h 47m | 0.18 | 130 | 46.09 | NOT |  3.68$\pm$ | 0.22 |  |  3.06$\pm$ | 0.07 |
2022-Dec-16 | +80d 03h 12m | 0.21 | 152 | 29.73 | NOT |  1.24$\pm$ | 0.28 |  |  0.93$\pm$ | 0.09 |
2022-Dec-17 | +81d 07h 13m | 0.21 | 152 | 28.29 | VLT |  |  0.83$\pm$ | 0.05 |
2022-Dec-24 | +88d 08h 55m | 0.23 | 166 | 20.17 | VLT |  0.01$\pm$ | 0.05 |  |  -0.18$\pm$ | 0.05 |
2022-Dec-28 | +92d 06h 55m | 0.25 | 181 | 15.72 | VLT |  |  -0.51$\pm$ | 0.05 |
2023-Jan-03 | +98d 08h 09m | 0.27 | 195 | 9.88 | VLT |  |  -0.76$\pm$ | 0.06 |
2023-Jan-11 | +106d 05h 01m | 0.31 | 224 | 6.55 | NOT |  -0.52$\pm$ | 0.6 |  |  -0.47$\pm$ | 0.24 |
2023-Jan-19 | +114d 03h 09m | 0.36 | 261 | 10.41 | NOT |  -0.82$\pm$ | 0.37 |  |  -0.83$\pm$ | 0.18 |

Figure 1 shows the polarisation measured as a function of aperture radius
increasing in steps of one pixel, i.e., the polarimetric growth curves, of the
VLT data. Each data point of these curves represents an increase of one pixel
in aperture radius. The asteroid-observer distance ($\Delta$), and hence, the
pixel scale varied throughout the observing campaign. Taking this into
account, we have scaled all growth curves to the same distance scale. The plot
shows a mix of both flat and slightly varying growth curves. In the case of
point sources, such growth curves are typically used to determine the most
appropriate aperture radius for measurements, as the polarisation reaches an
asymptotic value with increasing aperture (Bagnulo et al., 2011, 2016).
Variations with aperture size are likely due to the passing of background
stars whose flux contaminate measurements. For extended objects, however, such
variations may be indicative of properties intrinsic to the object, reflecting
a dust environment which varies with photocentric distance. These curves will
be particularly useful when analysing the polarimetric maps.

Table 1 reports the numerical values measured from aperture polarimetry. The
VLT values have been integrated in an aperture radius equivalent to 100 km
(0.1 on the horizontal axis of Figure 1). The recorded NOT measurements are
the weighted averages of the repeated observations (two to four times in each
filter) of each night. For smaller $\Delta$ values ($0.07-0.09$ AU), we chose
aperture radii corresponding to 100 km as we did with our VLT measurements.
When $\Delta$ is larger, aperture radii of 100 km corresponded to a pixel
radii smaller than 5 pixels. We, therefore, opted for larger radii to assure
sufficient flux in the aperture. The flat polarimetric growth curves from
2022-0ct-25 forward assure us that a choice of a larger aperture radius in the
NOT observations should not change the value in polarisation. For
completeness, we have included the spectropolarimetric measurements by Bagnulo
et al. (2023) in the table, indicated with an asterix (*VLT). These
observations use a rectangular aperture fixed to a 2” slit width, thus,
covering a larger area than the imaging polarimetric measurements.

Figure 2: The polarimetric phase curves of Didymos-Dimorphos in the BVRI filters. The vertical blue line indicates the phase angle of the asteroid system at the time of the DART impact ($\sim 53.2^{\circ}$). The SpPol data points refer to the spectropolarimetric measurements taken with the VLT by Bagnulo et al. (2023), while the ImPol data points refer to the imaging (aperture) polarimetric measurements taken with the VLT and NOT (this study). In each plot, the black symbols and curve represent pre-impact measurements and their best fit, while the coloured symbols and curve represent post-impact measurements and fit. The shaded area around the curves (where applicable) represents $1\sigma$ of the fit. In the case of the ImPol measurements, the open and filled data points are measurements taken when the phase angle was increasing ($\rm{d}\alpha/\rm{d}t>0$) and decreasing ($\rm{d}\alpha/\rm{d}t<0$, after $\alpha$ peak at $76.34^{\circ}$ on 2022-Oct-21), respectively. Figure 3: The difference between the calculated pre-impact curve and the measurements of the degree of linear polarisation, i.e., the value of the pre-impact curve minus the value of data points between phase angles $30-65^{\circ}$. The symbols are as those in Figure 2. Table 2:  Numerical values according to the best fit of the pre- and post-impact fits of the polarimetric phase curve. $P(\alpha_{\rm{Impact}}$) is the value of polarisation at the impact phase angle, $53.2^{\circ}$, while $\Delta P(\alpha_{\rm{Impact}}$) is the difference between the pre- and post-impact values, $\alpha_{0}$ is the inversion angle, h is the slope of the curve at $\alpha_{0}$ and $\rho_{v}$ is the geometric albedo calculated from Eq. 5. | Pre-Impact | Post-Impact | Pre-Impact | Post-Impact
---|---|---|---|---
| B | R
$P(\alpha_{\rm{Impact}}$) (%) | 5.40$\pm$ | 0.09 | 4.73$\pm$ | 0.02 | 4.42$\pm$ | 0.06 | 4.05$\pm$ | 0.01
$\Delta P(\alpha_{\rm{Impact}}$) (%) | 0.68 $\pm$ 0.09 | 0.37 $\pm$ 0.06
$\alpha_{0}$ (${}^{\circ})$ | 20.0$\pm$ | 0.1 | 20.2$\pm$ | 0.1 | 21.9$\pm$ | 0.1 | 21.1$\pm$ | 0.1
h | 0.10$\pm$ | 0.07 | 0.09$\pm$ | 0.01 | 0.11$\pm$ | 0.06 | 0.10$\pm$ | 0.01
| $\rm{V_{B}}$ | $\rm{V_{R}}$
$P(\alpha_{\rm{Impact}}$) (%) | 4.86$\pm$ | 0.09 | 4.26$\pm$ | 0.02 | 4.66$\pm$ | 0.06 | 4.25$\pm$ | 0.02
$\Delta P(\alpha_{\rm{Impact}}$) (%) | 0.61 $\pm$ 0.09 | 0.40 $\pm$ 0.06
$\alpha_{0}$ (${}^{\circ})$ | 20.0$\pm$ | 0.1 | 20.2$\pm$ | 0.1 | 21.5$\pm$ | 0.1 | 21.1$\pm$ | 0.1
h | 0.09$\pm$ | 0.08 | 0.08$\pm$ | 0.01 | 0.12$\pm$ | 0.05 | 0.11$\pm$ | 0.01
$\rho_{v}$ | 0.23$\pm$ | 0.20 | 0.26$\pm$ | 0.03 | 0.18$\pm$ | 0.10 | 0.19$\pm$ | 0.02

###  4.2 Polarimetric Phase Curve

Figure 2 shows the polarimetric phase curve of Didymos-Dimorphos in all four
BVRI filters, with values obtained from aperture polarimetry plotted as a
function phase angle, along with the results from Bagnulo et al. (2023). The
pre-impact and post-impact data and fits are distinguished with black and
coloured points and curves, respectively. Over the course of the entire
observing run, the phase angle ranged between $\sim 7$ and $-76^{\circ}$. The
phase angle peaked around half way through the observing run (2022-Oct-21)
after which the phase angle decreased until reaching a minimum (2023-Jan-11).
Consequently, several measurements were taken at very similar phase angles,
but months apart, corresponding to the asteroid system’s different stages with
respect to the DART impact. We have distinguished these data points with open
($\rm{d}\alpha/\rm{d}t>0$) and filled ($\rm{d}\alpha/\rm{d}t<0$) data points
for clarity. For example, around phase angle $52-54^{\circ}$, the system was
observed immediately before (T-15hr), immediately after (T+5hr) and months
after (T+58d) the impact. This extensive data set allows us to study the
immediate as well as the long term effects of the DART impact.

The best fits of pre- and post-impact data have been calculated with the
linear-exponential empirical model suggested by Muinonen et al. (2009):

$P(\alpha)=A(\rm{e}^{-\frac{\alpha}{B}}-1)+C\alpha,$ (4)

where $\alpha$ is the phase angle, and $A,B,C$ are free parameters which shape
the curve and are derived by least-square fitting. In the case of the V and I
filters, there was insufficient data to calculate the post-impact best fit. To
better study the differences between the pre- and post-impact polarimetric
phase curves (of R and B filters only), we calculated the values of the best
fits at the impact phase angle ($53.2^{\circ}$), the inversion angles
$\alpha_{0}$, and the slope of the curves at $\alpha_{0}$ in Table 2. In the
context of asteroid polarimetry, Umov’s law describes the empirical inverse
correlation between the polarisation and the geometric albedo of the
scattering surface—darker surfaces polarise light to a higher degree than
brighter surface. A consequence of the Umov effect is the direct relation
between the slope h of the polarimetric phase curve at the inversion angle
$\alpha_{0}$ to the geometric albedo $\rho_{v}$. Zellner & Gradie (1976)
showed that the polarisation phase curve can be used to derive the albedo
using two empirical relations:

$\begin{split}\log(\rho_{v})&=C_{1}\log(h)+C_{2},\\\
\log(\rho_{v})&=C_{3}\log(P_{\rm{min}})+C_{4},\end{split}$ (5)

where $C_{1},C_{2},C_{3},C_{4}$ are constants that may be obtained from
fitting. We used values $C_{1}=-1.111\pm 0.031$ and $C_{2}=-1.781\pm 0.025$ as
suggested by Cellino et al. (2015) to calculate the geometric albedo in this
study. These constants, however, have been calculated and calibrated according
to V-band polarimetric data. Therefore, we first converted our R- and B-band
measurements to the V-band before using the above expression to calculate the
geometric albedo. According to the spectropolarimetric measurements of Bagnulo
et al. (2023), the ratio between measurements in the V- and R-bands are nearly
constant with phase angle, i.e.
$(P_{Q}(\rm{V})-P_{Q}(\rm{R}))/P_{Q}(\rm{R})\sim 0.05$, as well as between the
V- and B-bands, $(P_{Q}(\rm{V})-P_{Q}(\rm{B}))/P_{Q}(\rm{B})\sim 0.1$. Knowing
this, we approximate the polarisation in the V filter using

$\begin{split}P_{Q}(V_{R})&=0.05P_{Q}(R)+P_{Q}(R)\ ,\\\
P_{Q}(V_{B})&=0.1P_{Q}(B)+P_{Q}(B)\ .\end{split}$ (6)

In Table 2, we have recorded the properties of the $\rm{V_{R}}$ and
$\rm{V_{B}}$ polarimetric phase curves, as well as our calculated values of
the geometric albedo. We measured a sharp drop in polarisation immediately
after the impact. According to the best fit curves, this drop was
approximately $0.7$ p.p. and $0.4$ p.p. in the B and R filters, respectively.
In the following days and weeks the polarisation increased with phase angle as
expected, but remained lower than the extrapolated pre-impact polarisation. We
observed some scattering in values around the peak phase angle, the reason for
which is still unclear. This scattering appears more pronounced in the B
filter compared to the R filter due to the generally higher value of
polarisation in the blue. After the peak phase angle ($76^{\circ})$, the
polarisation decreased as the phase angle decreased, again remaining at a
lower level compared to the pre-impact system. In particular, the data points
around phase angle $52-54^{\circ}$ are of particular interest. In Figure 3, we
plotted the difference between the fit of the pre-impact data and the observed
polarisation in the BVRI filters around phase angles $30-65^{\circ}$. We focus
on these phase angles only due to the unreliability of the pre-impact fit at
larger and smaller phase angles. This plot highlights that the polarisation
appears to remain lower than the pre-impact level even months after the
impact. The similarity of the pre- and post-impact data points at small phase
angles (approaching $20^{\circ}$) is due to the viewing geometry of the
polarimetric phase curve. We cannot compare the negative polarisation branch
of the pre- and post-impact data sets due to lack of data.

Overall, our measurements are in good agreement with spectropolarimetric
measurements by Bagnulo et al. (2023). The observations in that study,
however, only cover the pre-impact and early post-impact stages of the DART
impact. The new data presented here is specially suitable to establish
whether, months after the impact, the polarisation characteristics of Didymos-
Dimorphos came back to the pre-impact situation or if they were still affected
by the dust ejecta. We conclude that the change in polarisation induced by
DART lasted long after the impact, when the majority of the initial dust
ejecta is expected by most to have dispersed. We explore some explanations for
this finding in the Discussion section.

###  4.3 Imaging Maps

Figure 4 displays the imaging maps in the B- and R-filters created from the
VLT data. Each row represents maps from a given epoch and phase angle, shown
in the text boxes. The panels to the left of the maps indicate the north (N),
east (E), anti-solar ($-\odot$) and velocity ($v$) directions. The bottom five
panels are plotted with a distance scale double to that of the upper seven
panels. The maps have been plotted in a logarithmic scale for display purposes
and those that appear blank (black) are due to the absence of data in a given
filter on a given date. The presence of background stars appear as bright,
sometimes elongated, spots in the maps.

Our observations reveal effects of the DART impact consistent with findings
from HST (Li et al., 2023) and MUSE (Opitom et al., 2023) observations. At
T+4.8hr, the ejected material forms a cone-shaped cloud in the eastern
hemisphere that engulfs the entire asteroid system. Several linear features
are apparent in these initial images and become more defined in subsequent
observations. The most pronounced of these features, found in the northern and
south-eastern directions, are the edges of the ejecta cone. Similarly, faint
“clumps” of material are visible moving radially away from the asteroid. At
T+9.9hr, the first signs of tail formation appear, extending up to 1500 km in
length. By T+4.4d, the tail had stretched out beyond 5000 km and continued to
grow with time, eventually extending beyond 10 000 km as more material was
pushed towards the anti-solar direction by solar radiation pressure.

At T+7.3d and T+10.4d, faint linear features in the direction parallel to the
tail appear within the dust cloud. These features likely arise from the
natural separation of particles of different size caused by radiation
pressure, where smaller particles are accelerated more efficiently than larger
particles (Li et al., 2023). By T+23.3d, most of the material forming the dust
cloud has dissipated, while the tail remains. From this point, little
variation is found except for the gradual attenuation of the intensity of the
tail.

Figure 4: Imaging maps of VLT data of Didymos-Dimorphos in the B and R
filters. The phase angle and date of each observation are indicated in each
row. The north (N), east (E), anti-solar ($-\odot$) and velocity ($v$)
directions are given in the panels to the left of the maps. Panels are left
blank (black) in cases where there is no data. Background stars appear as
aligned and sometimes elongated bright spots (e.g. 2022-Oct-20, B filter).
Figure 5: Polarimetric maps of VLT data of Didymos-Dimorphos in the B and R
filters. The colour of each pixel represents the value of polarisation as
given in the colourbar. Pixels with values outside the $(-2,10)$ % range have
been set to white. The phase angle, date of each observation, and value
measured from aperture polarimetry ($P_{Q}$) are indicated in each row. The
north (N), east (E), anti-solar ($-\odot$) and velocity ($v$) directions are
given in the panels to the left of the maps. Panels are left blank in cases
where there is no data. Gaps in the tail and the spurious tail of 2022-Oct-20
(R filter) are due to background stars.

Figure 6: (a) The same polarimetric maps as in Figure 5, but with dynamic
colour scales. The scale of each panel has been set to $P_{Q}$ $\pm 2$ %,
where $P_{Q}$ is the value measured from aperture polarimetry and is indicated
in each panel. The grid indicates the photocentre of the asteroid system. (b)
Quality checks of 2022-09-27a polarimetric maps. From left to right: $P_{Q}$
map with $(-2,10)\%$ scale, $dP_{Q}$ map, $N_{Q}$ (Null) map, $P_{U}$ map,
$N_{U}$ map. The latter three maps are plotted with absolute values. A
colourbar is given for each column.

###  4.4 Polarimetric Maps

Figure 5 displays the polarimetric maps in the B- and R-filters created from
VLT data. Again, each row represents an observing epoch, with directional
labels (north, east, anti-sunward, and velocity vector) in the panels to the
left of the maps. The colour of each pixel represents the value of
polarisation as given in the colourbar to the right of the plots. The scale of
the colourbar has been set to the same scale as the polarimetric phase curve
(dark blue at $-2\%$ to dark red at $10\%$). For viewing purposes, all pixels
whose value lays outside this range has been set to white. The polarisation
value measured from aperture polarimetry is indicated by $P_{Q}$ in a text box
of each plot. The same polarimetric maps are also presented in Figure 6, but
this time the scale has been set to $P_{Q}$ $\pm 2\%$ in each plot. For
example, since $P_{Q}$ $=5\%$ in the R-filter on 2022-Oct-01, the maximum
value in this plot will be $7\%$ (red) and the minimum will be $3\%$ (blue),
while pixels with values outside this range appear in white. The reason for
plotting the polarimetric maps in this manner is to increase the contrast and
enhance any variability in polarisation. A grid has been included in these
maps to indicate the photocentre. Same as before, the maps that appear blank
are due to absence of data and the presence of background stars create some
spurious signals. Figure 6 shows an example of some of the quality checks we
have performed for our polarimetric maps. In particular, they show the
uncertainty map of $P_{Q}$ i.e. $dP_{Q}$, as well as the $N_{Q}$ (Null),
$P_{U}$ and $N_{U}$ maps, using data from 2022-Sep-27a in both the B- and
R-filters as an example. The latter three maps have been plotted in absolute
values. The scale of each panel corresponds to the colourbar in the centre of
its column. As expected, the $P_{U}$ and Null maps oscillate around zero,
while the uncertainty of $P_{Q}$ increases significantly with photocentre
distance. Although not displayed, we assured the accuracy of our other
polarimetric maps with such quality checks.

The effects of the DART impact are apparent in polarised light. The material
ejected immediately after the impact polarises the light in an almost uniform
manner, with some small scale variations (i.e., fluctuations of red and blue)
at the edges where the dust cloud tapers. Despite this, these variations do
not appear as a clear gradient such as those in Rosenbush et al. (2017), so we
attribute these small scale variations to noise. This homogeneity is reflected
in the generally flat polarimetric growth curves of the first epochs in Figure
1. Compared to the imaging maps, the strong linear features found in the
northern and south-eastern directions (cone “edges”) are not as clearly
defined in the polarimetric maps. Instead, the material filling the entire
cone polarises light almost uniformly. This may be due to the fact that the
degree of linear polarisation is a relative quantity, which, in contrast to
brightness, does not depend on the number of particles but rather the physical
properties (size, shape, structure, composition). The tail is first visible at
T+9.9hr in polarised light, appearing as an extension of the dust cloud. As it
extends with time, it appears shorter in polarised light compared to the
imaging maps, again, due to diminishing brightness of the tail with distance.
A further consequence is the difficulty of measuring any variability of
polarisation within the tail. The spurious thick tail in R of 2022-Oct-20 is
due to the passing of background stars.

Despite the overall homogeneity of polarisation of the dust cloud, a feature
is visible at the photocentre in many of the polarimetric maps. This feature
is more obvious in Figure 6 where the degree of polarisation of the
photocentre is $\sim 0.5-1\%$ higher than the surrounding dust cloud. The
consistent alignment with the photocentre and its point-like appearance lead
us to believe that this features represents the asteroid surface. In other
words, the dust cloud is somewhat transparent to the asteroid surface in some
epochs and is opaque in others. As the majority of the dust cloud disperses
(around T+23.2d), a $\sim 1\%$ difference in polarisation persists between the
photocentre and the tail (except for the later epochs where the tail is too
faint to distinguish a gradient). This gradient suggests that the properties
of material on the surface of the asteroid(s) differ from those of the
material in the dust cloud and tail. These variations are also reflected in
the polarimetric growth curves of these epochs, where the polarisation peaks
at small apertures and gradually decreases with increasing aperture. As the
aperture size increases, more of the signal from the lower-polarised cloud and
tail is measured, bringing down the overall measurement of average
polarisation within the aperture. Interestingly, the asteroid surface is
visible in the B filter at just T+9.9hr, while it does not become visible in
the R filter until T+7.3d. This observation may have implications for
understanding the temporal evolution of the size distribution of the material
within the dust cloud. Finally, in the case that this interpretation is
correct, there is a possibility that the polarisation of the asteroid surface
is, in fact, higher than what we find in our measurements. Given that the
asteroid is sub-pixel and unresolved, its image becomes dispersed and diluted
with the surrounding cloud of particles. Thus, if the signal is contaminated
by the depolarising dust cloud, the polarisation of the asteroid surface could
exceed our measurements. This is difficult to confirm, however, without data
of higher spatial resolution.

##  5 Discussion

###  5.1 Drop in Polarisation I: Immediate Effects of DART

The most obvious effect of the DART impact is the dramatic drop in
polarisation immediately after impact. Based on this, we can safely assume
that particles different to those present on the original surface(s) (pre-
impact) are injected into the system. Importantly, they have a neutralising
effect on polarisation. For the interpretation of this results we turn to
light scattering theory, in particular, studies involving laboratory
experiments and computer simulations. In this context, studies can deal with
various particle size ($r$) to wavelength ($\lambda$) ratio. The Rayleigh
regime is valid for particles much smaller than wavelength ($r\ll\lambda$),
the resonance regime for particles of similar size to wavelength
($r\sim\lambda$), and the geometric-optics regime for particles much larger
than wavelength ($r\gg\lambda$). The rules of light scattering vary according
to these size regimes.

Several studies have shown that the value of maximum polarisation
($P_{\rm{max}}$ ) and its position on the phase curve ($\alpha_{\rm{max}}$ )
depend strongly on the scattering particle size. In the Rayleigh-resonance
regime ($r\ll\lambda$ or $r\sim\lambda$), $P_{\rm{max}}$ tends to increase as
particle size decreases. In the geometric optics regime ($r\gg\lambda$),
however, this rule is reversed: $P_{\rm{max}}$ increases with increasing
particle size. As the size of the particles increases into the geometric
optics regime, $\alpha_{\rm{max}}$ shifts towards larger phase angles. This
correlation is found, for example, in the laboratory experiments by Muñoz et
al. (2021) who studied the light scattering effects of particles over the full
size domain and found that $P_{\rm{max}}$ is approximately 20% higher and
shifts towards a larger phase angle for millimeter-sized pebbles compared to a
similar sample with particles in the $100\mu$m range. Further, the size
distribution of the overall sample affects the polarimetric properties. Both
Escobar-Cerezo et al. (2018b) and Frattin et al. (2022) found that
$P_{\rm{max}}$ and $\alpha_{\rm{max}}$ increased, while the negative
polarisation branch (NPB) almost disappears, when they sifted their sample to
remove small particles (up to tens of $\mu$m in radius). In other words, in
the geometric optical regime, it appears that the fraction of small particles
included in the overall sample with various particle sizes determines the
maximum degree of polarisation. This is in agreement with the findings of
light scattering simulations using Gaussian random sphere shapes by Liu et al.
(2015), who also concluded that small particles limit the maximum degree of
polarisation as the mean size of the particles moves into geometric optics
range.

Likewise, the colour of the scattering material affects the polarimetric
behaviour of the system. As noted by Umov (1905), darker surfaces polarise
light to a higher degree than brighter surfaces. Therefore, the maximum degree
of polarisation is dependent not only on the size of the particles but on
their refractive index. Laboratory measurements of low, moderate to highly
absorbing millimeter-sized compact particles reveal a direct correlation
between the imaginary part of the refractive index of the sample and the
maximum degree of polarisation (Muñoz et al., 2020). $P_{\rm{max}}$ is
significantly higher for highly absorbing particle (low albedo) than for the
low absorbing particle (high albedo), while $P_{\rm{max}}$ of the moderately
absorbing particle lies within the range of the other two samples. This may be
interpreted as being the result of multiple scattering, which randomises the
polarisation plane at each scattering and, consequently, neutralises the
polarising effects of single scattering (Sorensen, 2001).

The situation becomes more intricate when multiple variables are considered
simultaneously—disentangling their individual contributions and/or identifying
the dominant influencing factor (size, structure, compositions, etc.) on the
polarimetric properties is challenging. For example, in a study using
materials of various size distributions and compositions (hence, colour),
Frattin et al. (2019) found that the Allende meteorite sample presented the
lowest $P_{\rm{max}}$ value, despite its dark colour, lower than even the
samples whitest in colour. This result was attributed to the Allende sample
having the largest concentration of small particles, thus, reducing the value
of maximum polarisation. Further, a principal difficulty that arises in the
interpretation of astronomical observations with laboratory and computational
studies is the non-uniqueness of light scattering properties of different
particle groups. This is because the light scattering properties of various
particle types does not change drastically between the different types. For
instance, under single-scattering conditions, both small particles in the
Rayleigh regime ($r\ll\lambda$, where $r$ is the particle size) and large
particles in the geometric optics regime ($r\gg\lambda$) polarise light to a
high degree. The position of $P_{\rm{max}}$ for Rayleigh particles is
$90^{\circ}$, whereas it is shifted towards larger phase angles for
$r\gg\lambda$.

Based on the conclusions from previous studies mentioned above, a possible,
but not exclusive, interpretation is that the ejected particles are smaller
and/or brighter than those present on the pre-impact surface. The continuing
discussion is based on this interpretation. High resolution images returned by
the camera onboard the DART spacecraft, Didymos Reconnaissance and Asteroid
Camera for Optical Navigation (DRACO), provided insight into the geological
composition of the pre-impact surface of Dimorphos. The imagery revealed that
the terrain consisted of sizable boulders in the order of tens of meters, as
well as smaller cobbles and pebbles (Daly et al., 2023; Barnouin et al.,
2023). A possible explanation is that that the impact of the DART spacecraft
caused the fragmentation of many of these larger elements and/or the ejection
of material from under the upper-most surface of Dimorphos. Identifying the
exact mechanism responsible for the change in particle size distribution,
however, is beyond the scope of this study. Although the phase angle range of
our measurements does not cover the maximum degree of polarisation, we can
infer from our measurements that $P_{\rm{max}}$ of the pre-impact system is
larger than that of the post-impact system. From this, we can conclude that
the drop in polarisation is (partly) due to the ejection of particles smaller
than those present on the original surface, although large enough to
scattering light in the geometric-optics regime. Furthermore, the slope of the
post-impact curve at the inversion angle is smaller than that of the pre-
impact curve. The smaller slope, and hence higher albedo, of the post-impact
data compared to the pre-impact data implies that the material ejected by the
impact is brighter than that of the original surface. We understand this to be
due to the effects of space weathering, which refers to the gradual alteration
of exposed surfaces via their interaction with the space environment. This
exposure encompasses various sources of energetic radiation (e.g., solar,
galactic, and magnetospheric, where applicable) and meteoroid-like objects
which can strike the surface. In the case of atmosphereless objects, one of
the consequences of space weathering is believed to be the darkening of the
surface (Hendrix & Vilas, 2019; Hasegawa et al., 2022; Zhang et al., 2022;
Escobar-Cerezo et al., 2018a; Penttilä et al., 2020, e.g.). This outer space-
weathered crust may act as a protective layer to the material below,
conserving its more-pristine nature. In this context, it is reasonable to
assume that the material below the surface of Dimorphos is brighter, and lower
in polarisation, than the outer dark layer. The closest and most obvious place
where the effects of space weathering is visible is the Moon. As far back as
1955, Gold (1955) recognised that material in and around impact craters,
including long ejecta streaks strewn across the surface, are brighter than the
surrounding material. Dynamic modelling of the cratering process show that
much of the material ejected by the DART impact comes from the inner layers of
the asteroid (Ferrari et al., 2022). Although not spatially resolvable, it is
possible that the DART impact ejecta left a footprint on the surface of
Didymos, while the surface of Dimorphos may be completely refreshed due to the
loss of a portion of the original material after impact. The removal of a
space-weathered surface layer is expected to rejuvenate the surface in such a
way as to increase its albedo, thus decreasing the polarisation.

###  5.2 Drop in Polarisation II: Long-term Effects of DART

Our monitoring campaign allows us to address whether the drop in polarisation
is limited to the immediate aftermath of the impact or if it persists as a
long-term phenomenon. After the Deep Impact mission for example, the
polarisation of Comet 9P/Tempel 1 returned to its pre-impact level within a
few days (Harrington et al., 2007; Hadamcik et al., 2007; Furusho et al.,
2007). The polarimetric maps of Didymos-Dimorphos show that the system was
engulfed by the ejecta dust cloud in the early weeks after the impact. The
aperture polarimetric measurements taken around this time are obviously
influenced by the still-present dust cloud made of smaller and/or brighter
material, hence, bringing down the value of polarisation. The maps at around
T+23.2d and T+28.3d, however, show that the majority of the dust cloud had
dissipated and, thus, observations from this point forward should be less
influenced by the ejecta. As discussed before, these dates also happen to
coincide with the maximum phase angle as viewed from Earth during this period
($\sim 76^{\circ}$). The decreasing phase angle allows us to measure and
compare the polarisation of the system at similar phase angles but different
stages in the context of the DART impact.

Figure 2 shows that the polarisation of the system in this long-term post-
impact stage, after the dissipation of the majority of the dust cloud,
continues to exhibit a lower level compared to the pre-impact state. However,
this difference may not be as drastic as observed immediately after the
impact. We are considering two potential explanations for this phenomenon.
Firstly, it’s possible that some remnants of the ejecta cloud, not currently
resolved by the VLT, remain in orbit within the system. This is highly likely
considering the presence of the dust tail — sustaining the tail for such a
long time would be impossible without large amounts of material remaining in
the system after the impact. Secondly, it’s possible that some of the fresh
ejecta has accumulated on the surfaces of Didymos and Dimorphos. In either
case, the presence of remaining fresh material within the system could
contribute to maintaining the lower level of polarisation. Depending on the
properties of the remaining material, it could also affect the magnitude of
the system. Graykowski et al. (2023) found that Didymos-Dimorphos faded back
to its ’normal’ brightness (Hv = 18.1) around 23 days post-impact. Comparing
to pre-impact measurements taken in the 2003 apparition, Pravec et al. (2023,
private communication) measure a marginal change (brightening) of the mean
(rotationally corrected) absolute magnitude H of just –0.061 magnitude that
they determined from their photometric measurements taken at solar phases from
6.6 to $28.3^{\circ}$ from 2022-Dec-17 to 2023-Jan-29. However, this
brightening has been detected at only 1.9-sigma level, not statistically
significant and could be attributed to an error or anomalous observation.

Using various methods to model the early collisional processes of material
within the ejecta, Ferrari et al. (2022) found that among all of the ejecta
fragments, 55% of particles are still in orbit after a week, 9% reaccumulate
on the surface of Dimorphos and 36% escape the system. The study does not
detail the reaccumulation of particles on the surface of Didymos and does not
run beyond one week. With Monte Carlo models, Moreno et al. (2023) provide a
characterisation of ejection geometric properties and ejecta dust properties
based on HST observations of Didymos-Dimorphos. They suspect that the
generation of the secondary tail is associated to reimpacting material on the
surface of Didymos. Their calculations show that up to $1.5\times 10^{6}$ kg
of material reimpact the surfaces of both Dimorphos and Didymos in the first
20 days following the impact, some of which may have settled permanently on
the surface. Further, any material still in orbit around this time will reside
in larger particles (but still smaller than the pre-impact surface,
considering the lower polarisation) as the smallest particle components will
have been removed by radiation pressure. Due to the small effective cross
section, this remaining mass will have very little effect on the total
brightness some weeks after the impact, hence in agreement with measurements
by Graykowski et al. (2023) and Pravec et al. (2023, private communication).
These findings lend support to our hypothesis that residual material from the
ejecta cloud still remain within the system at the time of our observations,
either in orbit or deposited on the asteroid surfaces.

###  5.3 Short-term Variations in Polarisation

Figure 7: The ratio between measurements of polarisation of Didymos-Dimorphos
(B- and R-filters) and the fit of the post-impact data at the corresponding
phase angle, phased according to the rotation period of Didymos (2.26 h). The
left panels show the original, individual measurements compared to the fit,
and the right panels show the weighted average of measurements grouped
together in steps of 0.1 rotation fractions. The symbols are as in Figure 2,
with the data points around phase angles $75-76^{\circ}$ highlighted in light
blue and yellow.

Across the polarimetric phase curve, some noticeable discrepancies are present
among polarisation measurements obtained at similar phase angles. While some
of these discrepancies are small, others exceed the estimated uncertainties
and are apparent both in comparisons between measurements taken using
different instruments and those obtained with the same instrument. These
observed discrepancies have several potential implications. On one hand, they
may indicate the presence of complex and variable physical processes occurring
in the aftermath of the impact event, such as evolution and expansion of the
ejecta cloud, changes in surface properties, or dynamical changes
(gravitational effects, solar radiation pressure, etc.) in the cloud. On the
other hand, they may be due to instrumental/data reduction effects or the
observing dynamics of the system. Here, we explore some of these
possibilities.

First, we consider differences between measurements taken with different
instruments. As visible from the polarimetric growth curves (Figure 1),
measurements taken in different apertures can yield different results. To
account for this, we systematically chose the pixel radii that best
approximated 100 km for the VLT data. For NOT data, again, we chose the pixel
radius closest to 100 km when possible. At larger asteroid-observer distances
($\Delta>0.1$ AU), however, our measurements were taken in larger radii, as
100 km corresponded to pixel radii smaller than 5 pixels. Considering this
only applies to pre-impact measurements, when the target is a point source,
and post-impact measurements beyond 2022-Oct-25 ($\rm{d}\alpha/\rm{d}t>0$),
when most of the dust cloud had dispersed, a larger aperture size should not
lead to significant differences compared to a 100 km aperture. Lastly, the
spectropolarimetric measurements cover a larger area than the imaging
polarimetric measurements. Despite this, these measurements are consistent
with our measurements within uncertainties in some cases, but not in others.

Second, we consider variations which may be intrinsic to the asteroid system.
On the night of the impact, two imaging- and one spectropolarimetric
measurement were taken with the VLT and exhibit considerable discrepancies.
These variations may be attributed to the dust environment at the moment of
the observations, which was likely rapidly evolving immediately after the
impact. Such rapid changes may have been mostly prevalent in the first days
following the impact. More puzzling are the discrepancies observed around
phase angle $75-76^{\circ}$, obtained more than 2 weeks after the impact,
which amount to $\sim 0.8-0.9$ p.p. in the B and R filters.

Finally, we consider the possibility of the polarisation being modulated by
the rotation of Didymos or the eclipsing events of Didymos and Dimorphos.
Subtle but persistent spectral variability has been found in pre-impact
observations by Ieva et al. (2022) and De León et al. (2023, private
communication, preliminary result) which appear to be in sync with the
rotation of Didymos, hinting to compositional differences throughout the
surface. No post-impact variability has been reported thus far. Although we do
not have enough pre-impact data to search for rotational variability, we
tested it with our post-impact data. To do this, we phased the post-impact
data according to the rotation period of Didymos, 2.26 h (Pravec et al.,
2006), and the new orbital period of Dimorphos, 11.5 h (Daly et al., 2023),
and searched for a periodic variation with respect to the values predicted by
the global fit to all data points. The two to four observation repetitions in
each filter carried out on each observation night at the NOT proved especially
useful for this test. We excluded the data taken in the earliest days after
the impact but included the data from 2022-Oct-04 (T+7.3d) onwards, when the
asteroid surface is visible through the dust cloud according to the
polarimetric maps (Figure 6). We recognise that measurements taken around this
time may be influenced by the dust cloud, and hence, any changes in the dust
environment may lead to variations in the polarisation. However, we have
chosen to include them considering the small aperture sizes of the
measurements.

In the left panels of Figure 7, we have plotted the ratio between each
individual measurement of polarisation and the fit of the post-impact data (B-
and R-filters) at that given phase angle as a function of the rotational phase
of Didymos, where one full rotation corresponds to 2.26 h and the each 0.1
interval on the horizontal axis is approximately 13 minutes. We have plotted
the data according the mid-point of the observation and have plotted the
multiple NOT measurements of each night separately (as opposed to the weighted
average). We have highlighted the data points taken around phase angles
$75-76^{\circ}$, where the largest variations are found, with light blue and
yellow. In the right panels, we have plotted the weighted average of data
grouped together in 0.1 rotation fraction intervals. Considering the matching
trend in both the B- and R-filters, this plot shows marginal evidence of
variation of polarisation with rotation of Didymos. Further investigations and
observations are necessary to confirm this potential finding. If true, an open
question remains as to whether this variation is linked to compositional
differences of the pre-impact surface which have survived the impact, or due
to the potentially non-uniform settling of fresh ejecta on the surface of the
asteroid. We conducted the same test, phasing the data according to the
orbital period of Dimorphos (11.5 h), but did not find any correlation with
the discrepancies.

Overall, it is difficult to establish the exact reason for the discrepancies
in polarisation measurements. While some small discrepancies may be attributed
to instrumental or observational effects, others may provide valuable insights
into the nature of the ejected material, dust dynamics, and surface properties
of the asteroid system. Further investigations will be crucial in unraveling
the underlying cause of these observed discrepancies and their implications.
The future Hera spacecraft (Michel et al., 2018), targeted to rendezvous with
Didymos-Dimorphos in 2027 with the objective to study the asteroid system and
the outcome of the DART impact, will provide the information that will clarify
the situation.

###  5.4 Polarisation of the Ejecta-Cloud and Tail

Based on our polarimetric phase curve analysis, we conclude that the drop in
polarisation is caused by the ejection of particles of material smaller and/or
brighter than that on the original asteroid system. In a similar sense, one
would expect to see variations in polarisation within the dust cloud,
particularly in areas containing concentrations of particles of different
properties. The chosen colour scale for our polarimetric maps indicates that
regions with higher concentrations of larger particles would appear redder,
while areas with smaller particles would appear bluer. Despite this, only
minor features are discernible in these maps. Solar radiation pressure
naturally separates particles of different sizes, with smaller particles
generally being accelerated anti-sunward more efficiently than larger ones. We
observe evidence of this effect in the imaging maps at T+7.3d and T+10.4d,
where several linear features appear in the south-eastern ejecta cone “edge”
running parallel to the anti-solar direction. In the HST images, these
features are visible from T+4.7d. Consequently, an inhomogeneous distribution
of particles sizes should be present in this specific region of the cloud
around these dates. Similarly, the northern edge of the ejecta cone expands to
a wing-like shape with a sharp edge in the anti-solar direction, indicating a
cut-off in the largest particle size of the ejecta (Li et al., 2023).

Signs of this inhomogeneous mix of particles are visible solely in the B
filter polarimetric maps at T+4.4d (Figure 5). In particular, a clump-like
feature, appearing redder in colour than the surrounding area, emerges in the
south-eastern ejecta cone edge, implying a higher concentration of larger
particles in that region. This agrees with the notion that particles are
organised according to size, with smaller particles being blown in the anti-
solar direction and leaving behind the larger particles. The sharp northern
edge found in the imaging maps, however, is less evident in the polarimetric
maps. Further, these features are not obvious in any of the other maps. The
reason for this could be attributed to the S/N and/or the resolution of the
polarimetric measurements. Alternatively, it may be a result of the mixing of
particles of various sizes as these larger particles fall back towards the
system. As discussed, the concentration of large vs. small particles within an
overall sample has an effect on the polarimetric properties (Escobar-Cerezo et
al., 2018a; Frattin et al., 2022).

As for the tail in the polarimetric maps, it appears as an extension of the
dust cloud within the first ten days. In other words, we do not observe a
strong gradient between the ejecta cloud and tail. Further, our polarimetric
maps do not reveal any obvious features within the tail. This contrasts with
the findings of Opitom et al. (2023), who observe that the tail generally
appears redder in colour (associated with larger particles) compared to the
surrounding bluer dust cloud (associated with smaller particles) in their so-
called spectral-gradient maps. Again, the lack of a measurable polarisation
gradient between the dust cloud and tail or within the tail could be due to
the faintness, and hence low S/N, of the tail and/or the mixing of particles
of various sizes. Further analysis is required to better investigate the
polarisation of the dust tail.

Figure 8: Polarimetric phase curve of Didymos compared to S-type asteroids.
The main-belt asteroids are shown with filled, grey data points, while near-
Earth asteroids are shown in open, grey points. Same as Figure 2, the black
points and curve represent pre-impact data, while the blue, green, red and
pink points and fits represent the post-impact Didymos data (in the BVRI
filters, respectively). The solid data points represent observations that were
taken after the phase angle peak was reached on Oct 20. In the plot for the
V-filter, the majority of the Didymos-Dimorphos data points are values which
have been converted from the R-filter using Eq. 6.

###  5.5 Comparison with Other Asteroids

Based on previous observations, the physical characterization of Didymos-
Dimorphos has posed a puzzling challenge. First, visible spectroscopic
measurements by Binzel et al. (2004) classified the system as an Xk-type.
Later, spectroscopic measurements which extended into the near-IR range by de
León et al. (2006, 2010) classified it as an S-type. Dunn et al. (2013) found
that it is spectroscopically most consistent with L/LL-type ordinary
chondrites, which are among the most common meteorites to fall to Earth. More
recent observations by the James Webb Space Telescope (JWST) show that its
spectrum is most consistent with ordinary chondrite meteorites and is similar
to S-class asteroids (Rivkin et al., 2023). Polarimetric studies play an
important role in supporting and complementing taxonomic classifications based
on reflectance spectra. The detailed morphology of the polarisation phase
curve, including the values of $P_{\rm{min}}$, $\alpha_{\rm{min}}$
($P_{\rm{max}}$ and $\alpha_{\rm{max}}$ typically cannot be measured),
$\alpha_{0}$, and the slope of the curve at $\alpha_{0}$ (h), are highly
sensitive to the physical properties of each individual asteroid. Strong
analogies are found in the polarimetric phase curves of asteroids belonging to
the same taxonomic class and polarimetry has often proved useful in
identifying objects of rare classes (Belskaya et al., 2005; Cellino et al.,
2006; Gil-Hutton et al., 2008, e.g.).

For this study, we have compared the polarimetric phase curve of Didymos to
that of other asteroids using data from literature, primarily that accumulated
in the Asteroid Polarimetric Database (APD) (Lupishko, 2022) and the Calern
Asteroid Polarisation Survey (CAPS) (Bendjoya et al., 2022). Since most
observations in these databases were performed in the V-band, while the
majority of our observations were performed in the R-band, we converted our
measurements from R to V with Eq. 6, as discussed in Section 4.2. Figure 8
shows the polarimetric phase curve of Didymos compared to a number of S-type
asteroids: main-belt asteroids (3) Juno, (7) Iris, (8) Flora, (12) Victoria,
(14) Irene, (15) Eunomia, and (18) Melpomene; and near-Earth asteroids (NEAs)
(433) Eros, (1036) Ganymed, (1620) Geographos, (1627) Ivar, (1685) Toro, and
(4179) Toutatis. In the V-filter panel of this plot, $P_{Q}(V_{R})$ values
were used in epochs were $P_{Q}(V)$ measurements were not obtained—i.e. the
majority of the data points are those converted from the R-band to the V-band.
The main-belt and NEAs have been distinguished with filled and open data
points, respectively.

The polarimetric phase curve of Didymos-Dimorphos shows that it is generally
in good agreement with other S-type asteroids. The additional data in the V
band provided by Eq. 6 allow us to calculate a number of values in the
polarimetric phase curve of the post impact data which are considered as
indicative of the properties of the surface of asteroids. In particular, we
measure $P_{\rm{min}}=(-0.84\pm 0.10)\%$ at $\alpha_{\rm{min}}=(8.7\pm
0.09)^{\circ}$, and $\alpha_{0}=(21.4\pm 0.1)^{\circ}$ with a slope of
$h=0.11\pm 0.01$, and hence albedo of $\rho_{\rm{v}}=0.20\pm 0.02$. These
values are within the range of polarimetric phase curve parameters of S-type
asteroids, which are typically characterised by $P_{\rm{min}}\sim-0.5$–$-1\%$
around $\alpha_{\rm{min}}\sim 8^{\circ}$ and $\alpha_{0}$ in the range
$18-22^{\circ}$ (Gil-Hutton et al., 2008; López-Sisterna et al., 2019, e.g.).
The albedo of Didymos-Dimorphos, both pre- and post-imapact systems, is in the
brighter end of the typical albedo range of $0.1-0.28$ (mean $\sim 0.23$) for
S-type asteroids (DeMeo & Carry, 2013). Further comparison of the pre- and
post-impact system to other asteroids separately is challenging for a number
of reasons. (i) The lack of pre-impact data at small phase angles means we
cannot determine $P_{\rm{min}}$, an important quantity for distinguishing
different taxonomic classes. Thus, we cannot assess the effect of the DART
impact on the NPB. (ii) Most asteroids, other than NEAs, are only observable
up to phase angles $\sim 30-35^{\circ}$. It is only beyond this point,
however, that the pre- and post-impact fits diverge to a meaningful degree.
For this reason, we are particularly interested in comparing Didymos-Dimorphos
to other NEAs. (iii) The number of NEAs that have been observed in
polarimetric mode at large phase angles, especially $>53^{\circ}$, is very
small.

Since Didymos-Dimorphos was intially classified as an Xk-type, we also
compared the polarimetric curve to that of X-type asteroids. The polarimetric
phase curves of X-types, however, show high dispersion across large phase
angles ranges. This dispersion is likely due to the existence of many sub-
classes of X-type asteroids, which include objects classified as E-, M-, and
P-type in the Tholen (1989) taxonomy. Initially, these classes were described
as spectrally degenerate due to the absence of mineral absorption features in
their visible and near-infrared reflectance spectra. Instead, they were
differentiated solely based on their albedo. As the shape of the polarisation
phase curve is directly linked to the albedo, the polarisation of these
objects follow distinct curves which depend on their taxonomic classification.
Consequently, when plotted together, the resulting plot looks dispersed
(Cañada-Assandri et al., 2012). Although Didymos-Dimorphos shows a similar
polarimetric phase dependence as a small selection of X-type asteroids (e.g.
(92) Undina, (184) Dejopeja, (276) Adelheid, (1355) Magoeba and (2001)
Einstein, all of which have been observed at phase angles $<30^{\circ}$), we
cannot classify Didymos-Dimorphos as an X-type based solely on polarimetric
data. On the other hand, we can rule out that Didymos does not belong to the
C-type taxonomy, typically characterised by a much deeper NPB and steeper
slope (Cellino et al., 2015b), nor F-type, characterised by a smaller
inversion angle around $\sim 15^{\circ}$ (Devogèle et al., 2018b, e.g. (3200)
Phaethon), or V-type, characterised by a shallower NPB (Lupishko et al., 1988,
(4) Vesta ). We therefore conclude that, polarimetrically, Didymos-Dimorphos
resembles S-type asteroids the most, despite the general scattering of data
points at larger phase angles.

##  6 Summary

We monitored the Didymos-Dimorphos asteroid system in imaging polarimetric
mode from around one month before, up to four months after the impact of the
DART spacecraft. During this campaign, we have observed the system in three
stages: (i) pre-impact, (ii) immediately post-impact, when the dust cloud is
present, and (iii) long-term post-impact, when the dust cloud has dissipated
and left behind an extensive dust tail. We performed our observations with
FORS2 of the VLT in BVRI filters (mostly B and R) and ALFOSC of the NOT in B
and R filters. A number of the VLT observations were performed hand in hand
with spectropolarimetric observations also obtained with FORS2 (Bagnulo et
al., 2023). In total, we have obtained 30 observing series in the B filter, 4
in the V filter, 33 in the R filter and 5 in the I filter. Some of the
observations could be used to check for a modulation of the polarisation with
the rotation of Didymos, as well as with the orbit of Dimorphos. This study
includes aperture polarimetric measurements, imaging and polarimetric maps,
and hence, analysis of the polarimetric phase curve and spatial and temporal
evolution of the ejecta dust cloud in polarised light. Bagnulo et al. (2023)
observed a drop of polarisation following the impact, but could not assess
whether, after the ejecta cloud dissipated, the Dydimos-Dimorphos system came
back to the polarimetric behaviour observed prior impact. Our new data allows
us to establish the long-term, as well as the short-term, effects of the DART
impact on Didymos-Dimorphos.

We summarise our findings as follows:

  1. 1.

Immediate effects of DART: the most significant effect of the DART impact is
the dramatic drop in polarisation observed immediately after impact. This drop
suggests that the material ejected from the asteroid is different from that
present on the original surface. As a possible interpretation, we suggest that
the ejected particles are smaller and/or brighter than those on the pre-impact
surface, in agreement with Bagnulo et al. (2023).

  2. 2.

Long-term effects of DART: the drop in polarisation persists as a long-term
phenomenon, even after the majority of the dust cloud has dissipated. We
suspect that this is due to residual material from the ejecta cloud still
remaining in the system, either in orbit or deposited on the asteroid’s
surface.

  3. 3.

Ejecta-cloud and tail: a large dust cloud is ejected immediately after the
impact and persists for a number of weeks, eventually forming into an
extensive tail. Several features are apparent in the imaging maps, but are not
so obvious in the polarimetric maps. The dust cloud polarises light in an
almost-uniform manner and a gradient is found between the polarisation in the
dust cloud/tail and the surface of the asteroid.

  4. 4.

Variation in polarisation: some discrepancies among measurements taken at
similar phase angles are observed. We find marginal evidence that these
variations are linked to the rotation of Didymos, potentially implying
compositional differences on the surface of Didymos. Further investigations
are needed to confirm this possible finding. We have not found any correlation
between these discrepancies and the eclipsing events of the two asteroids.

  5. 5.

Polarimetric taxonomy: Didymos-Dimorphos resembles an S-type asteroid
according to its polarimetric phase curve.

In this paper, we provide quantitative measurements of the polarisation as
well as qualitative explanations to its implications with regards to the
properties of the dust (particle size and brightness). Future modelling
studies will provide more quantitative estimates of these parameters. Future
observations and analyses will also be essential to unravel the underlying
causes of the observed discrepancies and to gain a more comprehensive
understanding of the system behaviour.

## Acknowledgements

This work is based on observations made with European Southern Observatory
(ESO) telescopes at the La Silla Paranal Observatory under run ID 109.23GL and
Director Discretionary Time with run ID 110.259G, as well as observations made
with ALFOSC at the Nordic Optical Telescope (NOT) under proposal ID 66-020,
which is provided by the Instituto de Astrofísica de Andalucía (IAA) under a
joint agreement with the University of Copenhagen and NOT. NOT is owned in
collaboration by the University of Turku and Aarhus University, and operated
jointly by Aarhus University, the University of Turku and the University of
Oslo, representing Denmark, Finland and Norway, the University of Iceland and
Stockholm University at the Observatorio del Roque de los Muchachos, La Palma,
Spain, of the Instituto de Astrofísica de Canarias. Research by Zuri Gray is
funded by the UK Science and Technology Facilities Council (STFC). Geraint H.
Jones is grateful to STFC for partial support through consolidated grant
ST/W001004/1. Research by Karri Muinonen, Antti Penttilä, and Mikael Granvik
is supported by the Academy of Finland (Research Council of Finland) grants
No. 345115 and No. 336546. L. Kolokolova acknowledges support from NASA DART
PS Program, grant no. 80NSSC21K1131.

We are grateful to the referees for their thorough examination of the
manuscript and their insightful comments and suggestions.

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