© ESO, 2015

1. Introduction

On 6 August 2014 the European spacecraft Rosetta (Glassmeier et al. 2007) encountered its target comet 67P/Churyumov-Gerasimenko (hereafter 67P) and became the first artificial satellite of a cometary nucleus. Rosetta carried the lander spacecraft Philae on board (Bibring et al. 2007), which on 12 November 2014 successfully landed on the surface of 67P at a heliocentric distance of 2.99 AU (Biele et al. 2015). One of the scientific instruments on board Philae is the Dust Impact Monitor (DIM) which is part of the Surface Electric Sounding and Acoustic Monitoring Experiment (SESAME; Seidensticker et al. 2007).

Comet 67P is a short-period comet with a present orbital period of about 6.6 years and aphelion and perihelion distances at 5.68 AU and 1.24 AU, respectively. What we know about 67P before the arrival of Rosetta was summarized by Lamy et al. (2007). Nucleus images recently taken by the cameras on board Rosetta show an irregularly shaped body with a size of about 4 km that consists of two lobes connected by a short depression, and a wide diversity in surface morphology (Thomas et al. 2015).

In situ investigations of comets 1P/Halley, 81P/Wild 2, and 9P/Tempel 1 showed that micrometer-sized particles dominate the dust population in their comae within several hundred kilometers of their nuclei (McDonnell et al. 1991; Tuzzolino et al. 2004; Economou et al. 2013). The existence of larger millimeter- to centimeter-sized particles in cometary comae is also shown by meteor streams that can be attributed to individual comets (Jenniskens 2006). Particles up to tens of centimeters were reported from the flyby of the Deep Impact spacecraft at comet 103P/Hartley 2 (A’Hearn et al. 2011).

Fig. 1 Rosetta lander Philae. The DIM sensor is visible at the top. Drawing ESA/ATG medialab.

Earth-based observations performed before Rosetta’s arrival indicate that particles in the size range from 10 μm to 1 mm, or possibly even larger, may exist in the coma of 67P (Tozzi et al. 2011). Millimeter-sized particles also exist in the dust trail (Agarwal et al. 2007), and recent investigations with Rosetta revealed millimeter- to centimeter-sized particles in the close vicinity of the nucleus of 67P (Rotundi et al. 2015). Although a significant fraction of these large particles move more slowly than the escape speed near the cometary nucleus, escaping particles in this size range may contribute considerably to the nucleus’ total mass loss.

The DIM sensor is mounted on the top side of Philae (Fig. 1) and measures submillimeter- and millimeter-sized particles hitting piezoelectric sensor plates. It measures dynamical data such as flux and the directionality of the impacting particles. The mass and speed of the particles can be constrained assuming particle density and elastic properties (Seidensticker et al. 2007).

DIM was operated for a total of 280 min before the separation of Philae from Rosetta; for a total of 35 min after the separation when Philae was descending to its nominal landing site on the surface of 67P, named Agilkia; and for 280 min at the final landing site, named Abydos. The goal of the DIM measurements at 67P was to determine the abundance and the particle size distribution in the submillimeter to millimeter size range in order to constrain the mass loss from the comet in the form of large dust particles. Measurements of the temporal variability in the dust flux were foreseen and were aimed at diurnal and seasonal variations in dust release from the cometary surface close to Philae’s landing site. Furthermore, the material properties of the detected particles were to be constrained with DIM.

In Sect. 2 we give a brief overview of Philae’s mission to comet 67P. Section 3 describes the DIM instrument and its operation on board Philae, and in Sect. 4 we present the DIM dust measurements at comet 67P. In Sect. 5 we analyze the data and in Sect. 6 we discuss our results. Finally, in Sect. 7 we summarize our conclusions.

2. Philae mission

The Rosetta spacecraft was launched on 2 March 2004. After swing-bys at Earth and Mars, and flybys at the asteroids S˘teins and Lutetia, Rosetta arrived at its target comet 67P in mid 2014. The spacecraft was brought into an orbit about the comet’s nucleus on 6 August 2014, with an initial altitude of 100 km. Until mid October 2014 the orbit was reduced stepwise to 10 km.

Rosetta carried the lander spacecraft Philae on board which attempted the first ever landing on a cometary nucleus. Philae was separated from Rosetta on 12 November 2014 at 08:35:00 UTC. At that time Rosetta was at a distance of 22.7 km from the comet’s barycenter, corresponding to an altitude of about 20.5 km from the surface (Biele et al. 2015). During the descent, Philae was rotating about its + Z axis. After a seven-hour descent, Philae reached the comet surface and made its first touchdown at 15:34:04 UTC at the Agilkia landing site. The touchdown speed relative to the comet surface was 1.0 m s^-1.

Owing to failures of its anchoring mechanism and active descent system, Philae did not come to rest at Agilkia. Instead, the spacecraft bounced and continued its journey across the surface of 67P. It came to rest about two hours later at 17:31:17 UTC (Biele et al. 2015). The final landing site, Abydos, is approximately 1.2 km from Agilkia and, to date, Philae’s location is only known with an uncertainty of approximately 21 × 34 m² (Kofman et al. 2015).

At Abydos, Philae encountered very low ambient temperatures varying from 90 K to 130 K between night and day (Spohn et al. 2015). The insolation of Philae’s solar arrays lasted only for about 1.5 h per comet day (comet rotation period 12.4043 ± 0.0007 h after its 2009 perihelion; Mottola et al. 2014). The low temperatures, the short solar insolation period, as well as images of Philae’s environment taken by the cameras on board (Bibring et al. 2015) that show cliffs and walls a few meters away indicate that Philae came to rest in some type of cavity. Philae may be tilted by approximately 90° with its instrument balcony (-X side) pointing to the ground (Bibring et al. 2015, cf. Fig. 1).

Philae was successfully operated from battery power during its nominal mission at Abydos which lasted for about 56 h. All instruments on board were operated during this period, including DIM. When the batteries were exhausted, Philae went into hibernation because the insolation of the solar arrays was too low for the continuing operation of the spacecraft. During the following months, the comet was approaching the Sun and passed through its perihelion on 13 August 2015, leading to a gradual increase in the insolation. On 13 June 2015 contact with Philae was established again, opening the possibility for extended measurements at the comet surface that were never foreseen for Philae, i.e., during the highest activity phase of 67P.

Fig. 2 Detail of Philae. The DIM cube with its three active sensor sides is visible at the top. The housing of the SD2 drill is also indicated.

3. Dust Impact Monitor

The piezoelectric sensors of DIM are mounted on a cube of about 7 cm side length. Three sides of the cube are covered with sensors, the other three sides are either closed by aluminum plates or left open for harness access. The DIM cube is mounted on the top side of Philae, and the three active sensor sides point in the +X, +Y, and +Z directions in the Philae coordinate system (Fig. 2). Each of the active DIM sides is divided into three equally sized segments that carry rectangular piezoelectric sensors made of PNZT7700 (Pb, Ni, Zi, Ti; hereafter PZT). The size of each segment is 50 × 16 × 1 mm³. Adding all nine active segments gives a total sensor area of about 70 cm². More details of the DIM sensor can be found in Seidensticker et al. (2007) and Flandes et al. (2013, 2014).

Each particle impact onto one of the piezoelectric sensor plates generates an electric pulse that is registered with the instrument electronics. The output signal can be approximated by a damped sine wave, and the measured signals are analyzed by the Hertzian theory of contact mechanics (Hertz 1882; Johnson 1985). The amplitude and the width of the first half-sine pulse are used to derive particle properties such as the reduced modulus and the mass. To calibrate the instrument signals, we performed a large number of drop experiments with particles made of different materials, including water ice as a cometary analogue material (Flandes et al. 2013, 2014).

3.1. DIM impact measuring values

Two parameters, impact duration T_c and peak voltage U_m, are derived from the signal curve by the instrument electronics. These values are transmitted to Earth (Flandes et al. 2013).

To distinguish noise or false events from real dust impacts, we use the term “impact” for true dust impacts only, and we use the term “noise”, “false event”, or “long event” for all other registered events (cf. Sect. 3.3 for a definition of these event types). The simple term “event” is used in a general sense, referring to both real dust impacts and all other types of registered events. In addition, we use the term “false signal” for events that are characterized by the instrument software as true dust impacts but for which we know by other means that they cannot be due to dust impacts. The instrument software is not able to distinguish between false signals and dust impacts. We use the term “dust” as a synonym for both ice or dust particles.

3.1.1. Impact duration

The impact duration is derived from the number of counts of a 20 MHz clock. The conversion between impact duration on a logarithmic scale to microseconds is given by Eq. (A.1) in Appendix A.

The false and long events are identified by using algorithms specified by Péter & Lucás (2001), see also Sect. 3.3. These events are defined according to the measured impact duration. They are counted with an onboard counter and only their total numbers are transmitted to Earth. The impact durations are transmitted for true dust impacts, but not for false or long events.

3.1.2. Peak voltage

The instrument provides the peak voltage of a single dust impact after logarithmic amplification. The amplifier transfer function of the DIM flight model is given by Eq. (A.2) in Appendix A, and a fixed logarithmic scaling is used for storage as given by Eq. (A.3).

The transfer characteristics of the logarithmic DIM amplifier can vary with time. It was regularly checked by a calibration procedure (cf. Sect. 3.2).

3.1.3. Event time

In addition to the impact duration and the peak voltage of a signal, the time in UTC when the event occurred is also stored for up to 350 events transmitted in Burst Continuous Test2 mode (not in Burst Continuous mode; see Sect. 3.2 for a description of these measurement modes).

3.2. DIM operational modes

DIM can be operated by telecommands from the Earth. Before any DIM measurement is started, a few operations have to be performed to guarantee that DIM is working properly. We can only give an overview here; more details about the DIM operation can be found in Fischer (2012).

After DIM is switched on (A) a power check is performed to verify that the supply voltages are within predefined limits, then (B) electronic noise is measured on the DIM amplifier (with the DIM sensor disconnected). Starting from a very low value, the detection threshold (the margin; see Sect. 3.4) is increased by steps of 10 dB until no further false event is detected. The rates of false events typically encountered in flight were such that the margin was set to 30 dB or 40 dB (cf. Tables 1 and 2). This means that a true dust impact must have an amplitude of at least approximately 0.1 mV or 0.25 mV, respectively, to overcome the threshold of the amplifier (Krüger et al. 2012). In the next step (C), a DIM sensor test checks whether all three sensor sides are operational. An electrical pulse (approximately 5 V for 10 μs) is applied to each sensor side and the response is registered in the same way a dust impact would be measured. Finally (D), the electronics performs a DIM calibration – two test pulses are applied to the logarithmic amplifier – to re-calibrate the transfer characteristic of the logarithmic amplifier and to check the time measuring (T_c) circuit. Pulse height and duration are 1 mV and 8 μs for low level, and 100 mV and 20 μs for high level, respectively.

The results of the calibration procedure were supposed to be used to re-calibrate the amplifier transfer function in the data evaluation on Earth. However, it was discovered after launch that the high-level value is in saturation for temperatures below + 20 °C so that this re-calibration procedure could not be applied. We therefore used the amplifier transfer function measured before launch throughout the data evaluation presented in this paper, which is given by Eq. (A.2). The uncertainty caused by this deficiency is taken into account in our error estimation (cf. Sect. 3.6).

After successful execution of the steps listed above, DIM was ready to measure dust impacts. Two measurement modes were used to measure dust at the comet. Single events on one sensor side can be registered in the so-called Burst Continuous (BC) Mode. The measured peak amplitude U_m and the impact duration T_c are stored in a compressed way: they are scaled to a logarithmic scale U_m and T_c according to Eqs. (A.1) and (A.3), and the counts for impacts or false signals with a particular [U_m, T_c] combination are stored in memory cells of different sizes depending on the expected frequency of such events (regular characters U_m and T_c denote the raw uncompressed data; bold characters U_m and T_c denote the compressed logarithmic values). Each BC measurement starts with a 10 s instrument warm-up period, which is not included in the measuring time.

In addition to the BC mode (which delivers the [U_m,T_c] matrix), the instrument can be operated in a so-called Burst Continuous Test2 mode (BCT2). Similar to the BC mode, the BCT2 mode delivers U_m and T_c for each individual impact. Here the raw uncompressed data are transmitted instead of the compressed logarithmic values, as well as the event time when the impact or false signal was registered. The number of data sets for impacts that can be stored and transmitted to Earth in BCT2 mode is limited to 350.

3.3. Measurement of single impacts

A DIM measurement consists of a series of single-event measurements. Each of these measurements detects and evaluates one event by comparing the amplified sensor signal U_out with the detection threshold voltage U_thr (cf. Sect. 3.4). The underlying assumption is that the initial part of the dust impact signal can be approximated by the first half of a sine wave. An impact should thus show up as a voltage that crosses the threshold voltage upwards, followed by a second crossing of the threshold voltage downwards. The period between the two threshold crossings defines the impact duration T_c.

If the amplified sensor signal crosses the detection threshold too early (less than 1 ms after the single-event measurement was initialized), the event is classified as a false event, otherwise it is accepted as the beginning of a potential real impact. The measurement is stopped after 0.5 ms. The event is ruled out as a long event, if no second threshold crossing is detected during the measurement duration. A true dust impact is thus characterized by its occurrence later than 1 ms after the initialization of the measurement and by a duration of less than 0.5 ms.

Regardless of the event type (dust impact, false, or long event), an adjustable dead time, the so-called sensor signal decay time (Flandes et al. 2013), is included after the end of each single event measurement. It was set to 5 ms for all measurements. Apart from the signal decay time, several waiting and latency periods are added to the total duration of a single impact measurement. All latency periods add up to a total instrument dead time of approximately 10 ms (Fischer 2014).

3.4. Margin

The DIM electronics can detect an event if the amplified signal voltage exceeds an adaptive threshold value U_thr. The detection threshold U_thr is the sum of an adjustable margin and a signal average. The margin can be increased in steps of 10 dB in the range 10–70 dB. Each step changes the threshold voltage by approximately 0.3 V. The signal average is determined by the DIM electronics with a time constant of approximately 1 s. It varies slowly with impact properties and frequency, aiming at covering a wide range of event voltage levels. Measuring values for the respective sensor side of the signal average are transmitted to Earth if sampling of average values is commanded.

3.5. Electronics ageing

The performance of the DIM instrument electronics has been regularly checked since Rosetta’s launch in 2004. So-called payload checkouts of the instruments on board were performed approximately every six months between 2004 and 2011, and again in 2014. No such procedures were executed between 2011 and early 2014 when Rosetta was in hibernation.

During these checkouts the DIM operational procedures described in Sect. 3.2 were executed. They did not reveal any ageing of the instrument electronics, except a deficiency in the calibration procedure (D) described in Sect. 3.2. We therefore conclude that the performance of the DIM electronics remained stable during the entire Rosetta mission.

3.6. Temperature dependence

Operational periods when the DIM electronics noise was measured and sensor tests were performed during flight showed no significant temperature dependence (operational procedures B and C in Sect. 3.2). On the other hand, a strong correlation between calibration measurements (operational procedure D in Sect. 3.2) and the estimated DIM electronics temperatures could be observed: between −40 °C and + 30 °C the impact durations for the high calibration peaks decreased by 8%, and those of the low calibration peak by 20%. The low calibration peak amplitudes varied within ± 4% and showed a non-monotonous dependence as a function of the electronics temperature. High calibration peak amplitudes were not included in the analysis since the values were saturated in a wide temperature range. The temperature dependence of the system, to a large extent, can be attributed to the temperature dependence of the logarithmic amplifier.

4. Dust measurements at comet 67P

Before the launch of Rosetta, DIM was designed to measure dust particles after Philae had landed on the surface of the cometary nucleus. Measurements before the separation from Rosetta and during Philae’s descent were not foreseen, and were added later on in the planning process of the mission.

Fig. 3 Philae trajectory close to the surface of comet 67P on 12 November 2014. The trajectory is shown in the comet fixed coordinate system. The position of Philae at the time of the single particle detection is illustrated. The vector $\hat{{n}}$ represents the normal to the +Y side of DIM. For the nucleus shape we used the ESA Engineering Model CSHP_DV_096_01__00161.ROS.

Fig. 4 Altitude of Philae above the nucleus surface and distance from the comet’s barycenter, respectively, as a funtion of time during the descent to the nucleus of comet 67P. The time t = 0 refers to Philae’s separation from Rosetta on 12 November 2014; 08:35:00 UTC. Gray vertical bars indicate the operational periods of DIM.

4.1. DIM operation

After Rosetta arrived at comet 67P on 6 August 2014 and before Philae was released on 12 November 2014, DIM was operated three times, namely on 16 and 17 October 2014 and on 12 November 2014 (Tables 1 and 2, measurements 1 to 29). When Philae was connected to Rosetta, the DIM sensor was strongly shielded by the Rosetta structures. Only the DIM +X sensor side was operated in these time intervals because it was the least obscured side (Sect. 4.3). DIM was operated in BCT2 mode for a total of 280 minutes. No dust impact and only very few false signals were registered.

When Philae was descending to its first touchdown point Agilkia on 12 November 2014, DIM was operated in BCT2 mode for a total of 35 min. Measurements were taken sequentially with all three sensor sides (Table 2, measurements 30 to 41). The descent trajectory of Philae close to the nucleus and the altitudes of the DIM measurement periods are shown in Figs. 3 and 4.

Before Philae landed on 67P the entire operational procedures performed on board during the descent were tested with the Philae Ground Reference Model (GRM) at Deutsches Zentrum für Luft- und Raumfahrt (DLR) in Cologne, which is a twin of the Philae spacecraft in space. During these tests a high rate of false signals was registered with the DIM electronics. This noise occurred only when insolation of the solar arrays was simulated, i.e., the signals were due to cross-talk (Hirn et al. 2015). Therefore, we expected a similarly high rate of false signals for the measurements with the DIM flight model during Philae’s descent to the nucleus surface on 12 November 2014.

To suppress these signals, we operated the instrument with an increased margin setting for a few of the measurements during the descent: one measurement sequence was performed with margin 40 dB from 08:38 UTC to 08:46 UTC, while this sequence was repeated with a margin of 50 dB from 08:50 UTC to 08:57 UTC. A high rate of false signals was indeed registered during a few of the measurement periods with the lower margin setting, while the higher margin effectively prevented the occurrence of false signals. The higher margin setting raised the detection threshold of the instrument to somewhat larger particles (cf. Sect. 5.3) so that only particles with impact signals in excess of about 1 mV could be measured. As occurred during the GRM tests performed earlier, the false signals were likely caused by Philae’s solar energy generators (cf. Sect. 4.2).

At the final landing site, Abydos, DIM was operated in BC mode for a total of 280 minutes on 13 and 14 November 2014. Here, all three sensor sides were operated sequentially. Only a few false signals were recorded (Table 3, measurements 42 to 71).

Fig. 5 All detected events (false signals plus dust impacts) in the [Um,Tc] diagram. Vertical and horizontal histograms indicate the numbers of detected events.

4.2. Dust impact identification

Reliable identification of false signals in the data set is a prerequisite for the analysis of dust at 67P based on the DIM measurements. In order to characterize the behavior of the instrument with respect to false signals, we analyzed DIM data obtained with both the Philae GRM, as well as the data from the DIM Flight Model (FM) on board Philae.

4.2.1. Signal distribution in the [U_m, T_c] diagram

The measured impact durations T_c and signal amplitudes U_m can be used to characterize false events in the DIM data set. The false signals recorded with the GRM instrument during ground tests were found to show a behavior very similar to those measured with the flight instrument on board Philae. Therefore, we concentrate our analysis on the flight data in the following.

We show the distribution of the measured signals in the [U_m,T_c] diagram in Fig. 5. The false signals cluster in a very limited region in the [U_m,T_c] plane. They mostly occur with very short impact durations up to about 1.5 μs, and amplified signal amplitudes 1300 mV ≲ U_out ≲ 1700 mV. A second group of false signals showed impact durations of approximately 3.4 μs and signal amplitudes U_out ≈ 1800 mV. Clearly separated from this region we detected one single event with a contact duration of 61 μs, and a signal amplitude of 2070 mV.

We never detected false signals with such a large impact duration, neither during the GRM tests nor in earlier FM data. Laboratory experiments performed with ice spheres of about 0.6 mm radius yielded impact durations below 6 μs (Flandes et al. 2014). However, such a large impact duration could be obtained during laboratory experiments with porous particles (see Sect. 5.2). We therefore interpret this event as a true dust impact. It was registered with the DIM +Y sensor side on 12 November 2014, 14:43:47 UTC during measurement number 40.

4.2.2. Temporal behavior of false signals

During some measurement periods when Philae was descending to the nucleus surface, false signals occurred with a relatively high frequency up to 110 s^-1 (Table 2). Very similar signal frequencies were also recorded during tests with the Philae GRM due to cross-talk.

With such high rates of false signals it might be asked whether DIM was able to detect any dust impacts in between the individual false signals. Here, a consideration of the dead time of DIM gives some insights. As described in Sect. 3.3, as a good approximation we consider the dead time to be 10 ms for both the detected and the false signals. Given that the total event rates during periods with the highest number of false signals are in the range 30 s^-1 to 110 s^-1, the detection of real impacts during these periods was extremely unlikely. We conclude that DIM was not able to detect any dust particles during these noisy periods. Hence, for estimations of dust fluxes (Hirn et al., in prep.), the use of the length of the quiet period when no false signal was recorded is preferable to the total length of the BCT2 measurement.

It should be noted that the single dust impact recorded on 12 November 2014, 14:43:47 UTC was measured during a BCT2 measurement with 100 s measurement time (Table 2, measurement 40). False signals were recorded only for 2 s after the start of this measurement, and the dust impact was measured 80 s later. No false signal was recorded in between. This clearly separates the dust impact from the false signals recorded in this measurement interval.

4.2.3. False events due to cosmic radiation

A potential source of false events can be hits by high-energy cosmic ray particles since PZTs show some sensitivity to high-energy radiation. Two major components of cosmic radiation can be distinguished: galactic cosmic rays (GCRs) originating from outside the solar system, and solar cosmic radiation. GCRs consist of energetic charged particles (86% protons, 12% alpha particles, and heavier ions and electrons typically in the energy range of 1 MeV to 10¹⁴ MeV). Solar cosmic radiation is composed of charged particles having a softer (eV to GeV) energy spectrum than GCRs. Most of the time the GCR component dominates, although during solar flares the flux of the solar cosmic radiation can be orders of magnitude higher.

High-energy radiation hitting the PZT can generate acoustic signals similar to mechanical impacts that could mimic a dust particle impact. Laboratory experiments with PZT ceramics showed that only bursts of penetrating ions, neutrons, or gamma-photons may cause a signal with a strength of approximately 1 mV (Miyachi et al. 2006, 2010; Adliene et al. 1985; Holbert et al. 2005). No single event was detected either with high-energy ions or high-energy photons, i.e., gamma rays. We can therefore exclude cosmic radiation as a source of false signals in our DIM measurements.

4.3. Detection geometry

Before the separation of Philae from Rosetta, the DIM sensor was heavily obscured by the structures of Rosetta and Philae (cf. Fig. 2). While the DIM +X sensor side was only partially obscured by the overhanging structures of Rosetta, the +Y sensor was almost entirely shielded, and the +Z sensor was completely covered. Therefore, only the +X sensor was operated before Philae’s separation.

After the separation from Rosetta the detection geometry was completely different. Figure 2 shows the DIM cube mounted on top of Philae. DIM is partially shielded by the Philae structures and the shielding differs for the three sensor sides. The +X side can only detect dust particles approaching from the +Z direction (top side of Philae), while Philae shields particles approaching from the –Z hemisphere entirely. The +Y side is partially shielded for particles approaching from the –Z hemisphere. Finally, the +Z side is partially shielded by the housing of Philae’s SD2 drill (light gray structure in Fig. 2), but it has the largest field of view of the three sensor sides (Hirn et al., in prep.).

After the separation from Rosetta, Philae was rotating about its Z axis so that the +X and the +Y sides of DIM scanned a complete circle during one Philae revolution, with an offset of 90° (cf. Fig. 2). Initially after the separation, Philae’s rotation period was about 5 min. After the landing gear was unfolded the rotation period increased to about 8.6 min. The landing gear was unfolded at about 08:41 UTC (R. Roll, priv. comm.), i.e., during DIM measurement 30 (Table 2).

5. Results and analysis

5.1. Dust detections

As described in Sect. 4.1, before and after the separation of Philae from Rosetta, the operational conditions of the DIM instrument differed. We therefore distinguish three measurement intervals and configurations:

• (1)

  Philae connected to Rosetta;

• (2)

  Philae’s descent to the comet surface (landing site Agilkia);

• (3)

  Philae at its final landing site Abydos.

5.1.1. Philae connected to Rosetta

DIM measurements on 16 and 17 October 2014 were taken at a distance of 9.6 km and 11.8 km from the nucleus barycenter, respectively, when Rosetta was orbiting the comet nucleus on an eccentric trajectory. A similar measurement was performed on 12 November 2014, about one hour before Philae’s separation from Rosetta, at a distance of 25.3 km (Meas. numbers 1 to 29; Tables 1 and 2). In all three cases only the +X sensor of DIM was taking measurements because the other sensor sides were strongly obscured (Sect. 4.3).

During these measurements the orientation of Rosetta was such that the DIM +X sensor was pointing within ± 10° perpendicular to the comet’s nadir direction and perpendicular to the direction of motion of Rosetta. With this orientation the DIM +X sensor could neither detect particles approaching radially from the nucleus nor particles on circular orbits about the nucleus. On the other hand, particles on highly bent ballistic trajectories or particles with highly eccentric orbits could have been detected by the DIM +X side. No dust impact was detected in this configuration during a total of about 280 min of measurement time.

5.1.2. Decent of Philae to the comet surface

Philae was separated from Rosetta on 12 November 2014 at 08:35:00 UTC, and during its seven-hour descent to the surface of the nucleus, all three DIM sensor sides were operated repeatedly with a total measuring time of 35 min (Table 2 and Fig. 4). During several of these periods the recorded rates of false signals were very high so that no dust impact was detectable between the noise events because of dead time of the instrument electronics (cf. Sect. 4).

Only one single dust impact was detected during the descent to the nucleus surface before the first touchdown at Agilkia. The particle was detected with the DIM +Y side at 14:43:47 UTC at a distance of 5.0 km from the barycenter of the nucleus, corresponding to an altitude from the nucleus surface of about 2.4 km. At this time Philae was at a latitude of 22° and a longitude of 346° in the comet fixed reference frame defined by Preusker et al. (2015), and the spacecraft’s velocity vector was [v_x,v_y,v_z] = [−0.817,−0.232,−0.434] (in m s^-1). The location of the particle detection with respect to the nucleus is shown in Fig. 3.

In order to constrain the particle dynamics from the DIM measurement, the velocity vector (i.e., impact direction and speed) has to be determined. Given that dust particles can hit each DIM sensor side from a wide range of impact angles from almost half a hemisphere, the impact direction is only little constrained (details of the DIM detection geometry will be discussed by Hirn et al., in prep.). In addition, the speed measurement is connected with a large uncertainty (Flandes et al. 2013, 2014). It is therefore impossible to determine the particle dynamics with high accuracy for a single detected particle.

The derivation of the impact direction of the particle is further complicated because Philae was rotating about its Z axis during the descent. Therefore, the +X and +Y sensors of DIM scanned an entire circle during one spin revolution of Philae. No information about the orientation of Philae during the descent was provided by the Philae Science Operations and Navigation Center (SONC) in Toulouse, France, at the time of this writing. Furthermore, attempts to determine the orientation from the magnetic field measurements of the Rosetta Magnetometer and Plasma Monitor (ROMAP) instrument on board Philae (Auster et al. 2015) led to inconclusive results for the interpretation of the DIM data. We attempted to derive the orientation of the DIM sensors as a function of time from the output signals of the solar arrays of Philae (Albin et al., in prep.). This analysis is still ongoing, and we therefore have to postpone a detailed discussion of the DIM detection geometry and the possible particle dynamics to a future publication.

5.1.3. Final landing site Abydos

All three sensor sides of DIM were operated at the Abydos landing site for a total of 280 min (Table 3). Only a few false signals and no dust impacts were recorded. The DIM health checks performed at Abydos did not indicate any non-nominal operation of DIM.

5.2. Particle properties

From the detected signal amplitude, U_m, and the impact duration, T_c, we can constrain the radius, R, and the impact speed, v, of the particle (Seidensticker et al. 2007; Flandes et al. 2013), ${\mathit{T}}_{\mathrm{c}}\mathrm{=}\mathrm{5.09}\hspace{0.17em}{\left(\frac{{\mathit{R}}^{\mathrm{5}}\hspace{0.17em}{\mathit{\rho }}^{\mathrm{2}}}{\mathit{v}\hspace{0.17em}{\mathit{E}}_{\mathrm{r}}^{\mathrm{2}}}\right)}^{\mathrm{1}\mathit{/}\mathrm{5}}$(1)and ${\mathit{U}}_{\mathrm{m}}\mathrm{=}\frac{\mathrm{3.03}\hspace{0.17em}{\mathit{d}}_{\mathrm{33}}\hspace{0.17em}{\mathit{E}}_{\mathrm{r}}^{\mathrm{0.4}}\hspace{0.17em}{\mathit{\rho }}^{\mathrm{0.6}}\hspace{0.17em}{\mathit{R}}^{\mathrm{2}}\hspace{0.17em}{\mathit{v}}^{\mathrm{1.2}}}{\mathit{C}}\mathit{,}$(2)where E_r is the combined reduced modulus of the PZT sensor, E_PZT, and the impinging particle E_p (see Flandes et al. 2013, for details).

From Eqs. (1) and (2) we define $\mathit{a}\mathrm{=}{\left(\frac{\mathrm{5.09}}{{\mathit{T}}_{\mathrm{c}}}\right)}^{\mathrm{5}}\left(\frac{\mathit{\rho }}{{\mathit{E}}_{\mathrm{r}}}\right)2$(3)and $\mathit{b}\mathrm{=}\frac{\mathrm{3.03}\hspace{0.17em}{\mathit{d}}_{\mathrm{33}}\hspace{0.17em}{\mathit{E}}_{\mathrm{r}}^{\mathrm{0.4}}\hspace{0.17em}{\mathit{\rho }}^{\mathrm{0.6}}}{{\mathit{U}}_{\mathrm{m}}\hspace{0.17em}\mathit{C}}\mathit{,}$(4)and solve for R and v, getting $\mathit{v}\mathrm{=}\frac{{\mathit{a}}^{\mathrm{1}\mathit{/}\mathrm{4}}}{{\mathit{b}}^{\mathrm{5}\mathit{/}\mathrm{8}}}$(5)for the impact speed, and $\mathit{R}\mathrm{=}{\left(\frac{\mathrm{1}}{{\mathit{a}}^{\mathrm{6}\mathit{/}\mathrm{5}}\hspace{0.17em}\mathit{b}}\right)}^{\mathrm{1}\mathit{/}\mathrm{8}}$(6)for the radius of the particle.

The piezoelectric constant, d₃₃; the capacitance of the PZT, C; and the reduced Young’s modulus, E_r, are known (see Flandes et al. 2013, 2014). These constants depend either on the properties of the PZTs, the properties of the impacting particles, or both. The parameter ρ is the bulk density of the particle. A summary of these constants is given in Table 4.

The U_m and T_c values are measured by the DIM electronics. However, as mentioned in Sect. 3, only the amplified output voltage (U_out) is stored and, therefore, U_m needs to be derived from the known amplifier transfer function of the DIM electronics, which is given by Eq. (A.2) in Appendix A.

From our calibration experiments, it was found that the U_m and T_c values recorded by the DIM electronics are sensitive to the shape of the signal produced by the particle impacts and to the margin set for the measurements. For the particle detected by DIM during the descent, U_out = 2070 mV and thus, from Eq. (A.2), U_m = 2.45 mV. Given the small input voltage and very long impact duration (T_c = 61 μs), we assume that the impacting particle is quite likely a porous conglomerate with reduced Young’s modulus larger than 10 MPa. This assumption is supported by calibration experiments performed with aerogel particles that have a bulk density of ρ ≈ 250 kg m^-3 and Young’s modulus E_p = 15 MPa. The signal amplitudes and impact durations measured with aerogel are consistent with the values recorded by the DIM electronics at the comet (see Appendix B for details). We therefore use the results from our experiments with aerogel particles to estimate the properties of the particle detected by DIM.

Fig. 6 Relationship between the impact speed v, radius R, and the Young’s modulus Ep of the particles. The curve was derived from Eqs. (1) to (6), given the detected values Um = 2.45 mV and Tc = 61 μs. The square highlights the case where Ep = 15 MPa (aerogel), which yields R = 0.98 mm and v = 1.95 m s-1. The Young’s modulus on a logarithmic scale is shown at the top. See text for details.

Figure 6 shows the relationship between v, R, and E_p, given the detected values U_m = 2.45 mV and T_c = 61 μs based on Eqs. (1) to (6). Estimations of the particle radius and speed are very sensitive to the values of E_p. If we simply assume that the detected particle have properties equal to those of the aerogel mentioned above, we can conclude that its radius and its impact speed are about 1 mm and 1.95 m s^-1 (the square in Fig. 6 highlights this case).

Nevertheless, in Flandes et al. (2013) we thoroughly discussed how the theoretical values deviate from the experimental data. We observed that, on average, the signal amplitudes U_m from the impacts could be underestimated by up to 30%, while the impact durations T_c could be overestimated by up to 50% (this can be seen in Table 5, see also Appendix B), which means that the real U_m values could be larger and the real T_c values could be shorter than the recorded ones. Furthermore, our experiments as well as our theoretical calculations show that T_c is correlated with the Young’s modulus of the material. This means that for a given impact speed the more elastic the material, the shorter the impact durations produced and vice versa. A similar effect applies to the voltage amplitude: for a given impact speed the more elastic the material, the more intense the voltage amplitude and vice versa. Thus, we conclude that for our detected particle the true values should be U_m> 2.45 mV and T_c< 61 μs, and thus, E_p> 15 MPa. Therefore, the derived radius of the particle should be a lower limit, R> 1 mm, and the derived speed should be an upper limit, v< 1.95 m s^-1, according to Fig. 6. Furthermore, the Young’s modulus of the nucleus surface may be as large as 500 MPa (Gibson & Ashby 1982), which implies an upper limit for the estimated particle radius of 2.3 mm and thus, a lower limit for the speed of 0.1 m s^-1. The comparison of the evaluated speed range with speeds measured at 67P for compact particles (Della Corte et al. 2015) and for fluffy particles (Fulle et al. 2015) is in agreement with a porous nature of the particle.

Fig. 7 Estimated detection range of DIM for porous ice particles. The curves are based on the mechanical properties of aerogel (bulk density of 250 kg m-3, average Young’s modulus of 15 MPa, and Poisson ratio of 0.2). Measurement boundaries are specified as dashed lines (see text for details).

Based on our analysis of the U_m and T_c values recorded by DIM during Philae’s descent and our aerogel experiments (Appendix B) we conclude that the detected particle was very likely porous, with a porosity of about 40%.

5.3. Detection threshold and sensitivity range

In order to estimate the sensitivity range of DIM, we assume a voltage range 0.2 mV <U_m< 15 mV. This is shown in Fig. 7 where each black solid curve represents the particle’s radius versus impact speed dependence for a constant signal amplitude U_m. The lowest possible voltage that can be recorded is determined by the margin (see Sect. 3.4) that is determined by the instrument setup before the measurement. The margin values allowed by the flight software are 0.1 (30 dB), 0.25 (40 dB), and 1.0 mV (50 dB), respectively, and are represented by continuous thick solid lines in Fig. 7. The corresponding impact durations that impacting porous particles could produce range from several tens to hundreds of microseconds. Furthermore, the DIM onboard electronics can only register impact durations up to a maximum value that is determined by the DIM operational mode (see Sect. 3.2 and Appendix A for details): the BC mode registers impact duration values up to 79 μs and the BCT2 mode up to 500 μs. These limits for the impact duration are represented by dashed lines in Fig. 7.

6. Discussion

The question arises of why DIM did not detect any dust impact at its final landing site Abydos. Two possible explanations are obvious. The first is shielding by ambient cliffs close to Philae. Reconstruction of Philae’s surroundings from the images taken by the CIVA cameras (Bibring et al. 2015) indicates that Philae ended up in some type of cavity. This is also in agreement with very low ambient temperatures ranging from 90 K to 130 K between night and day (Spohn et al. 2015). Furthermore, Philae is likely tilted by about 90° with respect to the local gravity vector. Reconstruction of the lander’s orientation indicates that the +Y sensor of DIM may be oriented towards open space while the +X and the +Z sensors are likely strongly shielded by cliffs that may be only a few meters away. The second explanation is the absence of cometary activity close to the landing site. The gas spectrometers on board Philae detected only a very low gas density (Goesmann et al. 2015; Morse et al. 2015), indicating that the landing site and its immediate vicinity were not active when DIM was taking measurements. Furthermore, owing to Philae’s operational constraints at Abydos, most of the DIM measurements were performed at night when the comet was likely not active (Table 3).

The Rosetta Lander Imaging System (ROLIS; Mottola et al. 2007) detected one single dust particle in the vicinity of Philae at Abydos (Schröder et al. 2015). The ROLIS field of view is oriented towards the bottom of Philae (–Z direction). The particle is seen in front of one of the cliff walls, implying that it must have been in the cavity close to Philae. This particle could have been swept up from the cometary surface when Philae came to rest at Abydos. However, the size of the particle cannot easily be determined, and no other particles were detected in the cavity. Additional particles are visible in ROLIS and CIVA images, however, very likely at much larger distances from Philae.

Many particles can also be seen in images taken by the cameras on board Rosetta. These observations allowed the detection of particles likely on bound orbits around the comet nucleus and also fast and outflowing particles that had diameters of up to 17 mm were detected (Rotundi et al. 2015). Dynamical simulations showed that the orbits of millimeter- to centimeter-sized particles are relatively unstable while objects of a few decimeters and larger in diameter may stay in orbit about the cometary nucleus for years, i.e., a full orbital revolution of the comet around the Sun (Fulle 1997).

The long impact duration measured by DIM during the single particle detection cannot be reproduced by impacts of compact particles in laboratory experiments. However, we were able to obtain a very long impact duration in experiments with aerogel particles that had a density of 250 kg m^-3 (see Appendix B), which indicates that the detected particle was likely a porous conglomerate.

The Cometary Secondary Ion Mass Analyzer (COSIMA) on board Rosetta also collected many porous particles in the size range up to a few hundred micrometers (Schulz et al. 2015). Most of these particles were collected at a distance between 10 km and 30 km from the cometary nucleus surface. The particles were very fragile so that many of them disintegrated during the collection process. The composition of these particles is not known yet, but they were not likely water ice particles.

The motion of particles under the influence of a very dilute gas has been studied by Tal (2014) using a Monte Carlo code. This code is similar to those described in Davidsson & Skorov (2004) and Davidsson et al. (2010). Tal (2014) investigated two general scenarios. The first was an ice patch (spot) at some particular temperature, and the second was a jet. In the first case the gas flow was uncollimated, while in the second case the particle motion was calculated for different degrees of collimation of the gas flow. Tal found that for a spot at 155 K, compact ice particles as large as 70 μm could be lifted from the surface. The gas drag force on a particle is proportional to its cross section, so for a spherical particle of radius a the drag force can be written as $\begin{array}{ccc}{\mathit{F}}_{\mathrm{drag}}\mathrm{=}\mathit{\alpha }{\mathit{a}}^{\mathrm{2}}\mathit{,}& & \end{array}$where α is some constant. The gravitational force on the particle is proportional to its mass. For a spherical particle this means that $\begin{array}{ccc}{\mathit{F}}_{\mathrm{grav}}\mathrm{=}\mathit{\beta \rho }{\mathit{a}}^{\mathrm{3}}\mathit{,}& & \end{array}$where β is another proportionality constant and ρ is the density of the particle material. The maximum radius of a liftable particle will be that for which the gravitational force on the particle exactly equals the drag force. In this case ${\mathit{a}}_{\max }\mathrm{=}\frac{\mathit{\alpha }}{\mathit{\beta \rho }}$(7)and the maximum radius of a liftable particle will be inversely proportional to the particle density.

Tal (2014) assumed particles with a density of 1000 kg m^-3, corresponding to water ice, but if the material is porous, these results must be adjusted. The porosity, p, is defined as the fraction of the volume that is void of mass. Thus, if a compact body of mass m occupies a volume V so that $\begin{array}{ccc}\mathit{\rho }\mathrm{=}\frac{\mathit{m}}{\mathit{V}}\mathit{,}& & \end{array}$then a body with mass m and porosity p will occupy a volume $\begin{array}{ccc}\mathit{V}\mathrm{=}\frac{\mathit{m}}{\mathrm{(}\mathrm{1}\mathrm{-}\mathit{p}\mathrm{)}\mathit{\rho }}\mathrm{=}\frac{\mathit{m}}{{\mathit{\rho }}^{\mathrm{\ast }}}\mathit{,}& & \end{array}$where ρ^∗ = (1−p)ρ is the effective density of the porous material. This is the density that must be used in Eq. (7) so that the maximum radius of a liftable particle will be proportional to ((1−p)ρ)^-1. These calculations assume that the trajectories of the gas molecules make random angles with the normal vector to the surface. However, if the gas is released as a collimated jet, the same gas production rate will provide a more efficient momentum transfer to the particle and somewhat larger particles will be lifted.

The Visible and Infrared Thermal Imaging Spectrometer (VIRTIS) on board Rosetta measured daytime surface temperatures between 180 and 230 K (Capaccioni et al. 2015). At these temperatures millimeter-sized compact particles can easily be lifted from the surface. For temperatures as low as 170 K, Tal (2014) found that sublimation from a spot could lift compact particles of 5.4 mm radius off the surface. Porous (fluffy) particles could be proportionately larger. In view of this, it is entirely consistent that the particle seen by the DIM instrument was lifted off the comet’s surface by sublimating water ice. While it is customary to use a total gas production rate instead of a temperature, this can be misleading if what is measured is the average value over a large area. In such a case local patches of activity can contribute much more gas (and drag) than would be expected from the average value, so that locally much larger particles can be lifted than would be expected from the average gas production rate.

The lifetime of a particle near the comet depends on its composition and albedo. Calculations of the lifetime of ice particles have been done by Beer et al. (2006). They find that pure ice particles larger than a few micrometers will survive for millions of years at around 3 AU. However, adding even a small amount of darker material sharply increases the heating rate so that micrometer-sized particles are only expected to survive for hours. In contrast, millimeter-sized particles of dirty ice could survive for many months. The results of Beer et al. (2006) are for compact ice particles. The rate of decrease in the radius a of the particle is given by $\frac{\mathrm{d}\mathit{a}}{\mathrm{d}\mathit{t}}\mathrm{=}\frac{{\mathit{P}}_{\mathrm{vap}}\mathrm{\left(}\mathit{T}\mathrm{\right)}}{\mathit{\rho }}\sqrt{\frac{\mathit{m}}{\mathrm{2}\mathit{\pi kT}}}\mathit{,}$(8)where P_vap is the vapor pressure, ρ is the density of the particle material, m is the mass of a molecule of particle material, k is Boltzmann’s constant, and T is the temperature of the particle. If the particle is porous, the mass density ρ must again be replaced by (1−p)ρ and the lifetime of the particle will be shortened proportionately. On the other hand, the lifetime of the particle will be greatly increased if it is composed of less volatile material such as organics or silicates.

Oblique impacts up to angles φ = 50° were examined in the course of the DIM calibration experiments reported by Flandes et al. (2013, 2014). The impact duration T_c increased by 5%, while the amplitude decreased by 20%, both following a cosine law. This entails that the parameter range for R expands by 10% towards lower values if analyzed as perpendicular impact. There are additional effects when the impact angles become so large that sliding friction and rolling of the particle sets in (Wu et al. 2003). These effects further decrease the perpendicular impact force and increase the contact time. With only one detected event, it is not possible to take these effects into account.

7. Conclusions

Measurements with the Dust Impact Monitor (DIM) on board Philae were obtained before the separation from Rosetta, during Philae’s descent to the nucleus surface, and at Philae’s final landing site Abydos. Our results can be summarized as follows:

• (1)

  DIM detected no dust before the separation of Philae fromRosetta during a measurement period ofabout 4.7 h. This ismost likely due to the unfavorable detection geometry of the DIMsensor and obscuration by the Rosetta spacecraft during thismission phase, which prevented the detection of particles ejectedradially from the nucleus.

• (2)

  One single dust impact was detected at an altitude of about 2.4 km during Philae’s descent to its nominal landing site Agilkia. This was very likely a porous particle with radius R ≈ 1 mm that hit the sensor with an impact speed v ≈ 2 m s^-1. The particle could have been lifted off the comet’s surface by sublimating water ice.

• (3)

  At Philae’s final landing site Abydos, DIM detected no dust particle during a total measurement period of 5 h. This may be due to the strong obscuration of DIM by the ambient cliffs, to the very low cometary activity at Abydos because most of the measurements were taken at night, or to other effects.

The particle detection at 2.4 km altitude is the closest dust detection ever performed by a dedicated dust instrument at a cometary nucleus. In June 2015 contact with Philae was established again, which may provide the possibility for additional DIM measurements at Abydos. The detection of more dust particles would allow us to better constrain the small scale properties of the cometary nucleus material.

Acknowledgments

SESAME is an experiment on the Rosetta lander Philae. It consists of three instruments CASSE, DIM and PP, which were provided by a consortium comprising DLR, MPS, FMI, MTA EK, Fraunhofer IZFP, Univ. Cologne, LATMOS and ESTEC. The contribution from MTA EK to the SESAME-DIM experiment was co-funded through the PRODEX contract No. 90010 and by the Government of Hungary through European Space Agency contracts No 98001, 98072, 4000106879/12/NL/KML and 4000107211/12/NL/KML under the plan for European Cooperating States (PECS). This research was supported by the German Bundesministerium für Bildung und Forschung through Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR, grant 50 QP 1302). Support by MPI für Sonnensystemforschung is gratefully acknowledged. A. Flandes was also supported by DGAPA-PAPIIT IA100114. We thank Lorenz Ratke and Benjamin Ignatzi (DLR Institut für Werkstoffforschung Köln) for providing us with aerogel samples for impact calibration experiments. We are grateful to Cynthia Volkert and Cornelia Mewes (Institute for Materials Science, University of Göttingen) for supporting us with measurements of the Young’s modulus of the aerogel particles. We thank the Rosetta project at ESA and the Philae project at DLR and CNES for effective and successful mission operations, and the GIADA team from providing us with predicted dust fluxes for DIM. We are grateful to an anonymous referee for helpful suggestions concerning the presentation of our results.

References

Appendix A: Impact parameters

Impact duration

The conversion between the number of counts n of the 20 MHz clock and the impact duration T_c in an internally defined logarithmic scale is given by ${{T}}_{\mathrm{c}}\mathrm{=}\mathrm{20}\mathrm{·}{\log }_{\mathrm{10}}\mathrm{(}\mathrm{2}\mathrm{·}\mathit{n}\mathrm{)}\mathrm{=}\mathrm{20}\mathrm{·}{\log }_{\mathrm{10}}\left(\frac{\mathrm{40}\mathrm{·}{\mathit{T}}_{\mathrm{c}}}{{\mathrm{10}}^{-6}\hspace{0.17em}\mathrm{s}}\right)\mathrm{·}$(A.1)The results of Eq. (A.1) are rounded to the nearest integer value. Impacts with T_c ≥ 70 are stored as if they were impacts with T_c = 70, thus impact durations larger than 79 μs cannot be distinguished in the BC mode.

Telemetry of the BCT2 mode also includes the counter value n. Therefore, this mode delivers impact durations of all accepted impacts with a time resolution of 0.05 μs.

The measuring range is limited by the clock frequency (20 MHz corresponding to a resolution of 50 ns; with 6 dB bandwidth) and depends on the operation mode. Thus, the following instrument limits have been specified: T_c,min = 100 ns, T_c,max,BC = 79 μs for BC mode and T_c,max,BCT2 = 500 μs for BCT2 mode.

Peak voltage

The conversion between the signal generated by the piezoelectric sensors and the amplified signal is given by the amplifier transfer function of the DIM flight model (Péter 2002), ${\mathit{U}}_{\mathrm{out}}\mathrm{\left[}\mathit{V}\mathrm{\right]}\mathrm{=}\mathrm{3.61}\mathrm{+}\mathrm{0.59}{\log }_{\mathrm{10}}\left(\frac{{\mathit{U}}_{\mathrm{m}}}{{\mathit{U}}_{\mathrm{r}\mathit{,}\mathrm{1}}}\right)\mathit{,}$(A.2)where U_r,1 = 1 V is a reference voltage. The logarithmic amplifier was designed such that the maximum output voltage is U_out,max = 3 V. Equation (A.2) was determined by calibration procedures.

For storage of the DIM data a decibel scale relative to U_r,2 = 5.355 μV is used so that a 3 V output signal of the logarithmic amplifier corresponds to 85.4 dB in the input signal relative to the reference voltage U_r,2, which is arbitrary and is given by the development history of the DIM instrument. Hence, ${{U}}_{\mathrm{out}}\mathrm{\left[}\mathit{dB}\mathrm{\right]}\mathrm{=}\mathrm{20}\mathrm{·}{\log }_{\mathrm{10}}\left(\frac{{\mathit{U}}_{\mathrm{m}}}{{\mathit{U}}_{\mathrm{r}\mathit{,}\mathrm{2}}}\right)\mathrm{=}\mathrm{20}\mathrm{·}{\log }_{\mathrm{10}}\left(\frac{{\mathit{U}}_{\mathrm{m}}}{\mathrm{5.355}\mathrm{\times }{\mathrm{10}}^{-6}\hspace{0.17em}\mathrm{V}}\right)\mathrm{·}$(A.3)After some simple mathematics, Eqs. (A.2) and (A.3) can be transformed into ${{U}}_{\mathrm{out}}\mathrm{\left[}\mathit{dB}\mathrm{\right]}\mathrm{=}\mathrm{20}\mathrm{·}{\log }_{\mathrm{10}}\left(\frac{{\mathit{U}}_{\mathrm{m}}}{{\mathit{U}}_{\mathrm{r}\mathit{,}\mathrm{2}}}\right)\mathrm{=}\frac{{\mathit{U}}_{\mathrm{out}}\mathrm{-}\mathrm{0.5}}{\mathrm{0.03}}\mathrm{·}$(A.4)

Appendix B: Laboratory experiments with aerogel

Fig. B.1 Aerogel particles (bulk density, ρ ≈ 250 kg m-3) used in the impact experiments reported in Table 5.

Fig. B.2 Impact signals generated by the semi-spherical aerogel particle A (Fig. B.1A and Table 5, experiments A2 to A4). All curves except the gray one are smoothed in order to remove noise. The solid black curve (A2) and the gray curves are the same. The gray curve illustrates the noise of each signal.

In addition to the calibration experiments reported by Flandes et al. (2013, 2014), we performed impact experiments with a flight spare sensor of DIM at the Max-Planck-Institut für Sonnensystemforschung. We used high-density aerogel (bulk density ρ ≈ 250 kg m^-3 and Young’s modulus E_p = 15 MPa) which – to a first approximation – is a material whose density and Young’s modulus are close to porous ice.

The three aerogel particles shown in Fig. B.1 were released from a height of 4.5 cm (which corresponds to an impact speed of approximately 0.94 m s^-1) onto the center of the third PZT of the Z-side of a DIM flight spare sensor (normal impacts). These particles produced low impact amplitudes of a few millivolts as well as long contact durations of many tens of microseconds. These values are consistent with those recorded by the DIM onboard electronics during our particle impact. The values obtained during our impact experiments are shown in Table 5 and the signals generated by the almost spherical particle (Fig. B.1A) from the oscilloscope data are shown in Fig. B.2. In Flandes et al. (2013, 2014) we discuss in detail how the theoretical values deviate from the experimental data.

Appendix C: Error estimation

Columns (5) and (6) in Table 5 show the theoretically estimated particle diameter, D_t, and impact speed, v_t, calculated with Eqs. (5) and (6) and with the measured signal amplitude U_m and impact duration T_c (Cols. 3 and 4 in Table 5). The measured values do not represent a rigorous statistical analysis, but they show that the detected particle could be as porous as aerogel, having a density and Young’s modulus of the same order of magnitude as aerogel. The average estimated uncertainties of these values with respect to the measured signal amplitudes and impact durations (Cols. 3 and 4) are about 40% for the diameter and 50% for the speed. Furthermore, our analysis assumes that the impacting particles are spherical (cf. Sect. 5.2), which is certainly only a rough approximation. The shape plays a significant role as well, as can be seen in Table 5.

All Tables

All Figures

	Fig. 1 Rosetta lander Philae. The DIM sensor is visible at the top. Drawing ESA/ATG medialab.
In the text

	Fig. 2 Detail of Philae. The DIM cube with its three active sensor sides is visible at the top. The housing of the SD2 drill is also indicated.
In the text

	Fig. 3 Philae trajectory close to the surface of comet 67P on 12 November 2014. The trajectory is shown in the comet fixed coordinate system. The position of Philae at the time of the single particle detection is illustrated. The vector $\hat{{n}}$ represents the normal to the +Y side of DIM. For the nucleus shape we used the ESA Engineering Model CSHP_DV_096_01__00161.ROS.
In the text

	Fig. 4 Altitude of Philae above the nucleus surface and distance from the comet’s barycenter, respectively, as a funtion of time during the descent to the nucleus of comet 67P. The time t = 0 refers to Philae’s separation from Rosetta on 12 November 2014; 08:35:00 UTC. Gray vertical bars indicate the operational periods of DIM.
In the text

	Fig. 5 All detected events (false signals plus dust impacts) in the [Um,Tc] diagram. Vertical and horizontal histograms indicate the numbers of detected events.
In the text

	Fig. 6 Relationship between the impact speed v, radius R, and the Young’s modulus Ep of the particles. The curve was derived from Eqs. (1) to (6), given the detected values Um = 2.45 mV and Tc = 61 μs. The square highlights the case where Ep = 15 MPa (aerogel), which yields R = 0.98 mm and v = 1.95 m s-1. The Young’s modulus on a logarithmic scale is shown at the top. See text for details.
In the text

	Fig. 7 Estimated detection range of DIM for porous ice particles. The curves are based on the mechanical properties of aerogel (bulk density of 250 kg m-3, average Young’s modulus of 15 MPa, and Poisson ratio of 0.2). Measurement boundaries are specified as dashed lines (see text for details).
In the text

	Fig. B.1 Aerogel particles (bulk density, ρ ≈ 250 kg m-3) used in the impact experiments reported in Table 5.
In the text

	Fig. B.2 Impact signals generated by the semi-spherical aerogel particle A (Fig. B.1A and Table 5, experiments A2 to A4). All curves except the gray one are smoothed in order to remove noise. The solid black curve (A2) and the gray curves are the same. The gray curve illustrates the noise of each signal.
In the text