Origin of Phobos grooves: Testing the Stickney Crater ejecta model

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Origin of Phobos grooves: Testing the Stickney Crater ejecta model Kenneth R. Ramsley a, b, *, James W. Head a a b

Department of Earth, Environmental and Planetary Sciences, Brown University, Providence, RI, USA School of Engineering, Brown University, Providence, RI, USA

A R T I C L E I N F O

A B S T R A C T

Keywords: Phobos grooves Phobos boulders Stickney crater Rolling boulders Bouncing boulders Testing the model

The model of Wilson and Head (1989, 2005, 2015) interprets the grooves of Phobos as the product of sliding, rolling, and bouncing ejecta boulders from the Stickney Crater impact. To test the model of Wilson and Head (1989, 2005, 2015) we apply a dynamical physics simulation to a three-dimensional shape model of Phobos and systematically assess six specific objections to the rolling boulder model. Our simulation calculates the motions of Stickney Crater ejecta boulders under the influence of Mars gravitation, the post-Stickney-impact desynchronized rotation of Phobos and altered orbit of Phobos, a spherically symmetrical gravity field of Phobos, and a collision system that simulates the effects of surface friction. We also take the orbital history of Phobos into account and test the rolling boulder model at three semimajor axes greater than the present day (10,000 km, 12,000 km, and 14,000 km). At a Phobos semimajor axis of 12,000 km, we find that boulder motions are generally consistent with observed grooves – specifically 1) Test boulders travel in linear/parallel patterns that are consistent with observed grooves, including grooves that are not radially aligned with Stickney Crater; 2) test boulders drift into suborbital flights over the trailing hemisphere of Phobos and do not travel on the surface of Phobos in this region; 3) grooves inside Stickney Crater are produced by Stickney ejecta boulders that return to Stickney Crater; 4) boulders that travel around Phobos >180
from Stickney Crater crosscut the motions of other boulders that travel >180
from Stickney; 5) at boulder ejection velocities ≲6 m/s, test boulders moving in contact with Phobos typically follow the contours of local terrain. We also find that 6) a spike of Stickney secondary impacts likely destroyed missing groove-producing boulders and removed grooves with widths ≲80 m; 7) with respect to the motion of test boulders, the two possible pre-Stickney-impact tidal-lock orientations of Phobos produce the same boulder motion effects; and 8) where our 12,000 km semimajor axis testing model is consistent with observed grooves, this supports a ~150 Ma prediction for the age of Phobos grooves and Stickney Crater.

1. Introduction Our study tests the model where Phobos grooves are produced by low-velocity ejecta boulders from the Stickney Crater impact event. (Head and Cintala, 1979; Wilson and Head, 1989, 2005; 2015; Duxbury et al., 2010; Head and Wilson, 2010; Hamelin, 2011). The central focus of the model includes a prediction of sliding, bouncing, and rolling boulders, and for simplicity, we refer to the model as the rolling boulder model or the model of Wilson and Head (2015). Our report focuses on the construction, operation, and implications of our software-based tests of the rolling boulder model. For a comprehensive description of the rolling boulder model, we refer the reader to referenced literature. For an overview of Phobos grooves, see Fig. 1 and its associated narrated video, Movie-S1 in supplementary online material. Supplementary video related to this article can be found at https://

doi.org/10.1016/j.pss.2018.11.004. Suggesting that the origin of Phobos grooves remains an unresolved topic of investigation, Wilson and Head (2015) list numerous published models, observations, and interpretations – summarized as follows: (1) Original primary layering (Veverka and Duxbury, 1977). (2) Drag forces generated during satellite capture (Pollack and Burns, 1977). (3) Tidal distortion (Soter and Harris, 1977). (4) Impact fracturing (Fujiwara and Asada, 1983). (5) Impact fracturing accompanied by degassing (Thomas et al., 1979). (6) Impact fracturing accompanied by regolith drainage (Thomas et al., 1979).

* Corresponding author. Ground mail: Department of Earth, Environmental and Planetary Sciences, Brown University, Box 1846, Providence, RI, 02912, USA. E-mail address: [email protected] (K.R. Ramsley). https://doi.org/10.1016/j.pss.2018.11.004 Received 31 March 2018; Received in revised form 2 November 2018; Accepted 9 November 2018 Available online xxxx 0032-0633/© 2018 Elsevier Ltd. All rights reserved.

Please cite this article as: Ramsley, K.R., Head, J.W., Origin of Phobos grooves: Testing the Stickney Crater ejecta model, Planetary and Space Science, https://doi.org/10.1016/j.pss.2018.11.004

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Fig. 1. Panel (a) shows a view of the northern hemisphere of Phobos (Mars Express HRSC Image 401-20080729-5851-6-na-1b, orbit 5851, Neukum, 2008). Approximately 90% of Phobos grooves are 80–200 m wide, and are emplaced in linear/parallel associations up to 30 km long. Grooves 200–400 m wide are preferentially solitary, pitted, and typically less linear in their emplacement (Thomas et al., 1979; Murchie et al., 1989). Panel (b) shows the sub-Mars hemisphere, Panel (c) the leading orbital hemisphere, Panel (d) the trailing orbital hemisphere, and Panel (e) the anti-Mars hemisphere (base model, Thomas, 1997; texture map, Schrempp, 2011; overlaid groove map, Murray and Heggie, 2014; Visualization software, Celestia Software Development Team, 2011). See supplementary online material Movie-S1 for a 360
rotating overview.

displacement, and friction. Instead – consistent with a boulder's current velocity, collision angle, and the local morphology of Phobos terrain (or adjacent boulder) – the testing software includes a calibrated dampening factor that removes a portion of a boulder's total angular momentum at each collision event. Under the influence of the dampening factor, after a series of collisions, test boulders come to a halt at distances that are consistent with the model of Wilson and Head (2015). As a consequence of our simplified collision algorithm, we observe boulders skipping and bouncing more than sliding and rolling. Nonetheless, test boulders in moving contact with Phobos maintain a rudimentary level of contact that is generally consistent with continuous contact. In Section 2 of our report, we describe six objections that have been raised against the rolling boulder model of Wilson and Head (2015) (Murray and Heggie, 2014). In Section 3, we describe our testing system, its calibration, and our methods. As part of our calibration process, we discuss the modeling implications of the two potential pre-impact tidal lock orientations of Phobos (a present-day orientation, and an orientation rotated 180
from the present-day, Ramsley and Head, 2017). Further, we explain our choice to focus boulder-motion testing at a Phobos orbital altitude semimajor axis of 12,000 km. In Section 4, we conclude our report by discussing tests of the first five objections described in Section 2, and we assess the sixth objection based on previous work. In this report, we do not use the term “sesquinary craters” to describe impact craters on Phobos that are produced by ejecta that originates from Phobos and returns to Phobos from orbits around Mars (Nayak and Asphaug, 2016; Nayak, 2018). Instead, for nomenclature consistency with our previous reports (Ramsley and Head, 2013a, 2013b, 2017), we use the generic term “secondary craters.”

(7) Impact fracturing followed by regolith drainage (Horstman and Melosh, 1989). (8) Ejecta emplacement and secondary cratering associated with the Stickney event (Head and Cintala, 1979; Wilson and Head, 1989, 2005; 2015; Duxbury et al., 2010; Head and Wilson, 2010; Hamelin, 2011). (9) Crater ejecta from Mars intersecting Phobos to form secondary impact chains (Murray, 2011; Murray et al., 1992, 1994, 2006; Murray and Iliffe, 1995, 2011; Murray and Heggie, 2014; Ramsley and Head, 2013a, 2013b). (10) A combination of several of these processes (Illes and Horv
arth, 1980). (11) Additional observations and interpretations (Duxbury and Veverka, 1979; Head, 1986; Avanesov et al., 1989, 1991; Duxbury, 1989; Murchie et al., 1991, 2013; Murray, 2010).

1.1. Introducing our testing system and report Within a comprehensive system of gravity, orbital motion, and Phobos rotation, our software-based testing model simulates the motion of Stickney Crater ejecta boulders and their interactions with a texturemapped shape model of Phobos placed in orbit around Mars (Phobos shape model – Thomas, 1997; Phobos texture map – Schrempp, 2011; overlaid groove map – Murray and Heggie, 2014). Depending on a test boulder's velocity, rotation, intersection angle, and the morphology of local terrain (or an adjacent boulder) – a collision between a moving boulder and the local surface of Phobos (or another boulder) alters a test boulder's elevation, velocity, rotation, and direction-of-motion azimuth. Central to our testing model, the Blender/Bullet physics system (Blender Foundation Development Team, 2016) was chosen for its ability to simulate a complex three-dimensional gravity field, and further offers a way to visualize three dimensional objects in motion. Where our 20-sided D 1200 m test boulders subtend six degrees of Phobos surface area, the Thomas (1997) shape model of Phobos offers sufficient surface resolution. (See Section 3.2.4 where we discuss our decision to test the rolling boulder model using D 1200 m test boulders). Our testing model does not include factors of regolith compression,

2. The rolling boulder model and six objections 2.1. Grooves from low-velocity Stickney Crater boulder ejecta The rolling boulder model is based on observations of lunar groovelike features that terminate in emplaced boulders – observed for example in the mountainsides at the Apollo 17 landing site (Schmitt and

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2.2.1. Grooves not radially aligned to Stickney Crater If grooves were produced by Stickney Crater boulder ejecta, groove patterns that are proximal to Stickney Crater should radiate from Stickney in a pattern that is focused on the center of Stickney. However, when we observe the 'Northern Family' pattern of grooves that is located to the northeast of Stickney Crater (Fig. 3a), grooves follow parallel lines that are generally orthogonal to the rim of Stickney (Thomas et al., 1979; Murray and Heggie, 2014).

Cernan, 1973). To address the mechanics of boulders in motion across the surface of Phobos, the lunar boulder model is calibrated to the Phobos environment (Wilson and Head, 1989, 2005, 2015). Specifically, the rolling boulder model proposes a mechanism where Stickney Crater impact ejecta boulders D ~100–400 m, exit from Stickney and travel at velocities along the surface of Phobos that are less than the escape velocity from Phobos (3–8 m/s, depending on boulder-motion azimuths and the slope angles of local terrain). According to the rolling boulder model, boulders that exit Stickney Crater with velocities of 3–8 m/s retain sufficient kinetic energy to travel in continuous contact with the surface of Phobos to distances of up to 20 km. As a consequence of this motion – through a mechanism of regolith compression and displacement – sliding, rolling, and bouncing boulders emplace linear and pitted tracks – the “grooves” of Phobos (Wilson and Head, 1989, 2005; 2015; Schr€ apler et al., 2015; Omura and Nakamura, 2017). Based on the irregular shape of Phobos and its complex gravitational and rotational environment, the rolling boulder model also predicts that ejecta boulders with initial velocities of 3–8 m/s alternate between periods of travel in contact with the surface of Phobos and periods of suborbital flight above the surface. At the higher end of the 3–8 m/s velocity range (and greater velocities), ejecta boulders may fail to return from their suborbital flights and drift into orbits around Mars (Fig. 2). All Stickney Crater ejecta that exits from Phobos that does not achieve a solar orbit or collide with Mars or Deimos, stochastically returns to Phobos with velocities that are approximately equal to their exit velocities. Through a mechanism of high-velocity secondary impacts, lowervelocity regolith compression and gardening, and collisions with in situ boulders, returning Mars-orbiting ejecta modifies the post-impact surface of Phobos (Wilson and Head, 1989, 2005; 2015; Ramsley and Head, 2013b; 2017; Nayak, 2018).

2.2.2. Absence of grooves on the Phobos trailing hemisphere If boulders are rolling on the surface of Phobos, it would be a reasonable expectation to observe boulder tracks on every surface of Phobos. In particular, if we assume that boulders would preferentially roll downhill, boulder tracks should be a common feature across the lower elevations of Phobos, including the trailing hemisphere – a persistently low-elevation region of Phobos. In fact, only solitary grooves populate the peripheral margins of the trailing hemisphere, and much of the trailing hemisphere displays a 'zone of avoidance' where grooves are generally missing (Murray et al., 1992, 1994; 2006; Murray and Heggie, 2014) (Fig. 1b, d, e, 4a). 2.2.3. Grooves inside Stickney Crater Superposed geological features typically post-date underlying units. Consequently, grooves that are observed inside Stickney Crater must be younger than Stickney Crater, and the Stickney impact must be an event that predates the grooves (Murray and Heggie, 2014) (Fig. 5a). 2.2.4. Grooves that crosscut other grooves In the same manner as the superposition of grooves inside Stickney Crater (Section 2.2.3), individual and families of grooves crosscut at many intersecting locations on Phobos (Thomas et al., 1979; Murchie et al., 1989; Murray and Heggie, 2014). For example, Fig. 6a and c highlight pitted tracks that crosscut the Northern Family of grooves. The geological principle of superposition suggests an initial event that emplaced the Northern Family of grooves followed by later events where the pitted grooves crosscut the previously emplaced Northern Family

2.2. Objections to the rolling and bouncing boulder model Six objections have been raised by Murray and Heggie (2014) where they cast doubt on the rolling boulder model:

Fig. 2. This schematic diagram illustrates the trajectories of sub-orbital, orbital, and super-orbital ejecta from an impact crater on Phobos and the geometry of the interaction of ejecta blocks with the regolith surface of Phobos. Transient crater stages and various ejecta properties in relation to their positions inside the transient crater cavity are also diagramed (from Wilson and Head, 2015). 3

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Fig. 3. Panel (a) indicates a portion of the Northern Family of grooves – a groove pattern with little radial association with Stickney Crater (Mars Express HRSC Nadirchannel image, orbit 7926, Neukum, 2010). Panels (b) and (c) show two 82-boulder test runs one hour after the Stickney impact (Phobos in a 12,000 km semimajor axis orbit). The motion of exiting test boulders strongly aligns with grooves across a wide region northeast to southeast of Stickney. However, few test boulders immediately align with the Northern Family. The annotated oval in Panel (c) indicates a leading group of boulders that launched to the south and southwest of Stickney, and in Panel (d), six hours after the Stickney impact ≳14 boulders travel along the surface of the model in a pattern that strongly aligns with the Northern Family shown in Panel (a). To view a video of test runs shown in this figure, see supplementary online material Movie-S2.

Fig. 4. Panel (a) is centered on the trailing orbital hemisphere of Phobos (base model: Thomas, 1997; texture map, Schrempp, 2011; overlaid groove map: Murray and Heggie, 2014. Visualization software: Celestia Software Development Team, 2011). The annotated oval in Panel (a) indicates a region where no grooves are observed – a 'zone of avoidance' (Murray et al., 1992, 1994; 2006; Murray and Heggie, 2014). Panel (b) combines screen captures from our testing model and shows the fate of a single boulder ejected to the east of Stickney Crater (15-min increments of travel). At first, the boulder travels along the surface of Phobos. When the boulder encounters a persistent decrease in topographical elevation, it drifts into suborbital flight around Phobos, and during its suborbital flight, the boulder travels above the 'zone of avoidance. After nearly one hemisphere of suborbital flight, the boulder returns to Phobos and continues to travel on the surface. For a moving view of this test run, including a magnified portion of a video where we see the boulder drift into suborbital flight, see supplementary online material Movie-S3.

2.2.5. Morphologically consistent grooves inside preexisting craters Boulder-motion calculations that are based on static models of Phobos and the present-day orbit of Phobos suggest that boulders in motion across the surface of Phobos should skip rim-to-rim across preexisting impact craters. However, Phobos grooves are observed to modify preexisting crater rims, sloping walls, and floors with little change in groove

pattern. According to Murray and Heggie (2014), assuming separate events, a single rolling-boulder process could not have emplaced both the Northern Family of grooves and grooves that crosscut the Northern Family.

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Fig. 5. Panel (a) shows two grooves on the southeast floor and rim of Stickney Crater (Mars Express HRSC image H3769_0004 in Mercator projection, orbit 3769, Neukum, 2006). Panel (b) combines screen captures from our testing model and shows the fate of a single test boulder that is ejected to the east of Stickney Crater (10-min increments of travel). In this test, the boulder exits from Stickney, travels to the east, drifts into suborbital flight, and alternates between suborbital flights and traveling motions in contact with the surface of Phobos. Approaching the conclusion of its motion around Phobos, the test boulder slides down the western crater rim of Stickney, across the crater floor, and comes to rest on the eastern crater rim. For a moving view of this test run, including a magnified video segment where the test boulder travels through Stickney Crater, see supplementary online material Movie-S4.

Fig. 6. Panels (a) and (c) show grooves on Phobos that crosscut the Northern Family (Mars Express HRSC Nadir-channel image, orbit 7926, Neukum, 2010). Panels (b) and (d) show test boulders from our model that are inserted with slightly differing launch vectors (10-min increments of travel). The test boulders travel mostly in suborbital flights around Phobos before engaging the surface of Phobos to the east of Stickney. The boulder in Panel (b) travels to the north of Stickney and follows the groove indicated in Panel (a), and the boulder in Panel (d) moves in suborbital flight over Stickney and travels in a path to the northeast of Stickney following the groove indicated in Panel (c). For a moving view of these test runs, see supplementary online material Movie-S5.

our testing methods. To our knowledge, the six objections to the rolling boulder interpretation listed in Section 2.2 have not been tested with a system that includes a digital shape model of Phobos or a physics model that simulates the entire dynamical system of Phobos immediately following the Stickney impact – including the desynchronized rotation of Phobos (Ramsley and Head, 2017).

morphology across the entire crater surface (Murray and Heggie, 2014) (Figs. 1a, 5a and 6a, 6c). 2.2.6. Missing groove-producing boulders Rolling boulders D ~100–400 m should remain at the end of their boulder-produced grooves (Murray and Heggie, 2014) or briefly orbit Mars before returning to the surface of Phobos (Ramsley and Head, 2013b, 2017). However, in currently available image coverage, no boulders are observed at the end of a Phobos groove (Murray and Heggie, 2014), and very few boulders D ≳ 100 m are observed anywhere on Phobos (Thomas, 1979, 1998; Thomas et al., 2000; Basilevsky et al., 2014).

3.1. Testing system Our testing system provides a three dimensional environment that tracks the positions and motion vectors of every object in the model: Mars, Phobos, and test boulders. In our testing system, Mars is a sphere, boulders are 20-sided polyhedral blocks, and Phobos is a shape-model produced by Thomas (1997) from NASA data, and textured with a terrain map produced by Schrempp (2011) and the groove map of Murray and Heggie (2014). Our testing system is assembled in Blender

3. Modeling system, calibration, limitations, and methods In this section we present our modeling system, its calibration, and

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boulder completed one orbit every 458.0 min. Confirming our Phobos gravitational setting, with a semimajor axis of 30 km, a test boulder orbits Phobos with a period of 644.6 min, and with a semimajor axis of 36 km, the orbital period is 847.3 min. Our gravitational model of Phobos does not vary according to the expected mass-distribution of Phobos. Instead, in our testing model, the gravitational effect is spherically and symmetrically centered at the geometrical center of the Thomas (1997) Phobos shape model. Comparing our symmetrically centered gravitational model of Phobos to the gravitational effect of the real-world planetary body of Phobos, it is likely that the effect of our spherical gravity model is slightly greater in the vicinity of lower topographical Phobos elevations, and slightly less in the vicinity of higher Phobos elevations.

software and the motions of test boulders are controlled with Blender's embedded Bullet physics engine (Blender Foundation Development Team, 2016). In view of how the generic version of Blender/Bullet software (Blender Foundation Development Team, 2016) is unable to process more than one source of gravity – we include a custom script that assigns three-dimensional gravity to test objects in the model. The script is able to process up to 84 objects – Mars, Phobos, and a maximum of 82 test boulders (See Blender Spherical Gravity Python Script in Supplementary Online Materials). A gravitational coefficient is assigned to each object in the testing model (a number used to assess the gravitational attraction among all objects). Using the assigned gravitational coefficient, during a test run, the custom script evaluates and updates the positions and motion vectors of every object in the model. Test runs are displayed on a computer screen and recorded for detailed study. During each test run, processing steps represent three seconds of elapsed time. Depending on the time duration of a test run, we record 8400–14,400 processing steps (7–12 h of elapsed time). Depending on the test altitude of Phobos (Section 3.2.1), during each processing step, Phobos travels around Mars 1.75 km, 1.89 km, or 2.07 km, and rotates 0.030
, 0.036
, or 0.045
. Relative to the motion of Phobos, during each processing step, test boulders typically travel ≲20 m across the surface of Phobos or ≲20 m in suborbital flight above Phobos.

3.2.3. Post-stickney impact Phobos rotation In the present day, we observe a rotational period of Phobos that is equal to its orbital period – a synchronous tidal lock. However, the Stickney impact desynchronized the tidal lock of Phobos and decreased its post-impact rotational period by approximately 20–30% (Ramsley and Head, 2017). Including this effect in our testing model, at an orbital semimajor axis of 10,000 km, our Phobos model rotates with a period of 400 min, at a semimajor axis of 12,000 km, 500 min, and at a semimajor axis of 14,000 km, 600 min. 3.2.4. Boulder diameters Our initial test runs inserted 82 boulders. Later testing focused on the fate of individual boulders. We initially planned to insert as many as 300 boulders D 100–400 m (boulder quantities and diameters that are consistent with the model of Wilson and Head, 2015). However, the Blender/Bullet physics engine (Blender Foundation Development Team, 2016) is unable to consistently detect collision events between the Thomas (1997) Phobos shape model and boulders D < 1200 m. Further, our configuration of the Blender/Bullet physics engine is unable to process more than 84 objects with spherical gravitational properties (82 boulders, Phobos, and Mars). Based on our boulder quantity and size limitations, we conducted our testing using a maximum of 82 test boulders D 1200 m (Figs. 3–6).

3.2. Testing system calibration and limitations 3.2.1. Phobos orbital period Over geological time, Phobos has orbited at greater altitudes above Mars than in the present day (Burns, 1972; Lambeck, 1979; Bills et al., 2005; Jacobson, 2010; Shi et al., 2011, 2013). Assuming that the Stickney Crater impact took place during the last 500 Ma (Ramsley and Head, 2017), we conducted test runs at three semimajor axis altitudes of Phobos that are greater than the present-day: 1) a semimajor axis of 10, 000 km  50 Ma, 2) a semimajor axis of 12,000 km  150 Ma, and 3) a semimajor axis of 14,000 km  500 Ma (orbital ages derived from Shi et al., 2011, 2013). Other than for the Earth, Blender/Bullet software (Blender Foundation Development Team, 2016) has no default gravitational settings for celestial bodies, and we calibrated the gravitation of Mars by placing Phobos in orbit around Mars while we adjusted the software's gravitational coefficient for Mars. Once calibrated, we observed an orbital period of 505.7 min for a semimajor axis of 10,000 km, and we confirmed this setting by observing orbital periods at semimajor axes of 12,000 km and 14,000 km (664.7 and 837.6 min). Where previous orbital eccentricities and inclinations of Phobos are unknown, and where, in the present-day, Phobos travels in a nearly circular and equatorial orbit, we initiate our testing at 10,000 km, 12,000 km, and 14,000 km semimajor axes with Phobos traveling in circular orbits and zero inclinations. Depending on the pre-Stickney-impact tidal-lock orientation of Phobos (see Section 3.2.9), the Stickney impact increased or decreased the orbital semimajor axis of Phobos by ~10 km and consequently altered the orbital period of Phobos by ~0.1% (Ramsley and Head, 2017). This slightly altered orbit of Phobos is included in our testing model.

3.2.5. Boulder friction The Phobos and boulder shape models in our testing system are constructed from rigid polygons. Consequently, we are unable to simulate regolith friction, compression, and displacement (as described by Wilson and Head, 1989, 2005, 2015; Schr€apler et al., 2015; Omura and Nakamura, 2017). To overcome this limitation, at each collision event, our collision system transfers a portion of momentum between the boulder and the surface of Phobos (or between colliding boulders). At the same time, the collision system applies a dampening factor that removes a portion of the boulder's momentum. Momentum-transfer and dampening-effects are informed by the boulder's relative velocity, its collision angle with Phobos (or another boulder), and the geometric morphology of colliding surfaces. At each collision event, a boulder changes its direction, alters its rotation, and after ~20 km of total surface contact with Phobos (consistent with Wilson and Head, 2015), it comes to a halt. 3.2.6. Boulder insertion method Boulders are inserted into the testing model and deflected over the Stickney Crater rim using a temporary cone-shaped object. The cone is designed to direct boulder motions over the crater rim at low velocities (typically ≲6 m/s). Once test boulders are underway, the temporary cone-shaped object is deleted from the model. In the same way that much of our testing system is empirically calibrated, the test boulder-insertion system is adjusted to inject as many boulders as possible with crater-exit velocities of 3–6 m/s.

3.2.2. Phobos gravitation Repeating the calibration process described in Section 3.2.1, we placed our shape model of Phobos into a test environment with no external forces (no Mars, or any other perturbing body in the system). Alongside our model of Phobos, we inserted a single test boulder with a lateral velocity and allowed the gravity of Phobos to govern the motion of the boulder. Through a series of tests, we adjusted the software's gravitational coefficient for Phobos until the orbital period of the boulder matched the expected value for an unperturbed gravitational field of Phobos. When orbiting Phobos with a semimajor axis of 24 km, a test 6

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In summary, our testing of the objections listed in Sections 2.2.1-2.2.5 took place entirely at the 12,000 km semimajor axis altitude and a 0
present-day tidal lock orientation of Phobos (see results in Sections 4.1-4.5). Where objection 2.2.6 exceeds the scope of our testing system, based on previous work, objection 2.2.6 is discussed in Section 4.6.

3.2.7. Testing process To limit unconscious operator bias, our test boulder injection system is randomized by non-repeatable manually-operated startup steps. The boulder-injection process has three keyboard triggers: Trigger #1 initiates the gravitational engine and sets Phobos in motion, Trigger #2 accelerates the test boulders into Stickney Crater, and Trigger #3 removes the boulder insertion guide cone. The guide cone has the effect of directing test boulders over the rim of Stickney Crater and producing an initial traffic congestion of boulders in the vicinity of Stickney that randomly modifies boulder velocities, rotations, motion-elevation angles, and crater-exit azimuths. Once modeling parameters were calibrated, we made no further adjustments to the testing system. From this point forward, we conducted our study as a benchtop experiment, recording computer-screen-captured results as they were produced. Due to the underlying physics of our testing system, results from test-run-to-test-run produced generally similar patterns of boulder motions, yet because of how we manually initiated each test run, no two test runs were identical, and as a matter of modeling design philosophy, we were unable to 'manipulate dials and knobs' to produce a preferential result or precisely repeat a previous test run.

4. Test results and discussion In this section we address the six objections listed in Section 2.2. The first four objections are assessed through a discussion of specific tests. Our assessment of the fifth objection focuses on portions of supplementary online material Movies-S3 and -S4, and we discuss the sixth objection based on previous work. Supplementary video related to this article can be found at https:// doi.org/10.1016/j.pss.2018.11.004. 4.1. Objection 1: grooves not radially aligned to Stickney Crater Although test boulders exit Stickney Crater in a radial distribution pattern, the boulders almost immediately begin to travel with linear and parallel motions. In Fig. 3b, the motion of test boulders that exit from Stickney to the north and northeast of the crater generally align with the Northern Family of grooves in this region. In Fig. 3c, test boulders are moving in a pattern that aligns with grooves to the east of Stickney Crater. However, exiting boulders do not intersect the western portions of the Northern Family, and this initially suggests that Stickney boulders did not produce the western grooves of the Northern Family. Continuing to observe the fate of test boulders, approximately six hours after the Stickney impact (Fig. 3d), boulders that were launched to the south and southwest of Stickney have traveled above the southern and trailing hemispheres of Phobos, and while traveling across the surface of the northern hemisphere of Phobos, they follow a linear pattern that closely matches the observed Northern Family of grooves, including the western portion of the Northern Family. Supplementary video related to this article can be found at https:// doi.org/10.1016/j.pss.2018.11.004. Interpreting test runs shown in Fig. 3, we conclude that grooves to the north and northeast of Stickney were produced by boulders immediately exiting from Stickney, and grooves to the north and northwest of Stickney were produced by boulders that traveled over the southern and trailing hemispheres of Phobos before returning to the northern hemisphere of Phobos. Throughout this time, boulders were perturbed into linear and parallel motions, and while they traveled in contact with Phobos they consequently produced linear and parallel grooves. To view a video of test runs shown in Fig. 3, see supplementary online material Movie-S2.

3.2.8. Testing at Phobos 10,000 km, 12,000 km, and 14,000 km semimajor axes Three test runs were initiated at a Mars semimajor axis of 10,000 km, 17 test runs were initiated at a semimajor axis of 12,000 km, and 25 test runs at a semimajor axis of 14,000 km. In total, various configurations of our testing system were run 45 times. When we initiated test runs at a Phobos orbital semimajor axis of 10,000 km, the close proximity of Mars gravitation produced tidal forces in our testing model that rapidly removed boulders to orbits around Mars. On this basis, we discontinued testing at a semimajor axis of 10,000 km. When we initiated test runs at a Phobos orbital semimajor axis of 14,000 km, test boulders remained in the vicinity of Phobos, but their motions along the surface of the Thomas (1997) Phobos shape model did not follow the pattern of grooves that are observed in nature (Fig. 1). For this reason, we set aside our testing at a semimajor axis of 14,000 km, and attempted a third Phobos altitude: a semimajor axis of 12,000 km. When we initiated test runs at a Phobos orbital semimajor axis of 12,000 km, we observed boulder motions that are generally consistent with the observed grooves on Phobos. On this basis, we focused the remainder of our testing at the 12,000 km semimajor axis. The similarity of test boulder motions to the natural morphology of observed grooves on Phobos at a 12,000 km semimajor axis notionally suggests that Stickney boulders were produced when Phobos was orbiting Mars at a 12,000 km semimajor axis (~150 Ma – based on Shi et al., 2011, 2013). However, where we ran our testing model at three distinct semimajor axes, our study does not rule out the possibility of morphologically consistent grooves that are produced by Stickney boulders at semimajor axes of Phobos that we did not test.

4.2. Objection 2: absence of grooves on the Phobos trailing hemisphere The annotated oval in Fig. 4a highlights the 'zone of avoidance' (Murray et al., 1992, 1994; 2006; Murray and Heggie, 2014) – a region centered on the Phobos trailing hemisphere where grooves are not observed. Fig. 4b shows the motion of a test boulder launched with an initial velocity of ~4 m/s that remains in contact with the surface of Phobos until it encounters a substantial and continuing decrease in topographical elevation. Here, the boulder drifts into a suborbital flight over the trailing hemisphere of Phobos and avoids the zone of avoidance. Returning from its suborbital flight, the test boulder reengages the surface of Phobos. Prior to the continuing decrease in topographical elevation, the velocity of the boulder is sufficiently low to remain in contact with Phobos, and once in flight, the boulder drifts with sufficiently low velocity to return to Phobos. For a moving view, see supplementary online material Movie-S3. Similarly, Fig. 5b shows a second test boulder that exits from Stickney Crater at a lower velocity (~3 m/s) than the boulder in Fig. 4b (~4 m/s).

3.2.9. Pre-stickney-impact tidal lock orientation of Phobos Our testing also compared the two possible pre-Stickney-impact tidal lock orientations of Phobos. Due to the desynchronizing effect of the Stickney impact event, there is a ~50% chance that the pre-impact orientation of Phobos was offset ~180
from its 0
present-day orientation, and a ~50% chance that the orientation was similar to its presentday tidal lock (Ramsley and Head, 2017). In view of these two pre-impact tidal-lock possibilities, we expected to see a difference in the pattern of boulder motions when we tested the two potential orientations. However, the dynamic effect of forces on boulder-motions appears to be identically symmetrical at the 180
and 0
pre-impact orientations, and we observed no noticeable difference in boulder motions between the two orientations. On this basis, we discontinued testing at the 180
pre-impact tidal-lock orientation. 7

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by boulders and groupings of boulders that travel >180
around Phobos from Stickney to where they intersect the same local terrain at different times and azimuth angles of motion. Supplementary video related to this article can be found at https:// doi.org/10.1016/j.pss.2018.11.004.

The boulder in Fig. 5b drifts into a suborbital flight, skips once within the 'zone of avoidance', and once it leaves the vicinity of the trailing hemisphere, Fig. 5b boulder follows a series of episodic suborbital flights and traveling motions in contact with the Phobos surface. Where the boulder engaged the surface of Phobos within the 'zone of avoidance,' the collision produced a substantial bounce that prevented the boulder from rolling across the remaining surface of the zone (Movie–S3). This suggests that a slower-moving Stickney boulder may bounce within the zone to produce a collision-pit – but not a groove. The patterns of test boulder motions in Figs. 4b and 5b also strongly suggest that when a rolling boulder is moving across a generally uniform elevation, it will remain in contact with the Phobos surface (see Section 4.5), and when a rolling boulder encounters a persistent decrease in topographical elevation, it will drift into a flight above the surface of Phobos (Wilson and Head, 1989, 2005; 2015; Hamelin, 2011). The sense of boulders rising above the 'zone of avoidance' (Movie-S2 and -S3) is a consequence of two motion effects. The first of these motion effects is produced by the above-average topographical elevation of Stickney Crater, where the high elevation of the Stickney rim accelerates rolling boulders downhill away from the crater. In particular, to the east and northeast of Stickney, downhill-rolling boulders approach the ‘zone of avoidance’ with an additional ~2–4 m/s of forward velocity. The second motion effect takes place when boulders arrive at the rim of the zone. Here, they encounter a persistent drop in elevation. Combining both effects (the added boulder velocity and the rapid loss in terrain elevation) Stickney ejecta boulders arrive at the rim of the zone with sufficient forward velocity to drift into space following a ballistic trajectory that exceeds the elevation of the zone.

4.5. Objection 5: morphologically consistent grooves inside preexisting craters Our observations of boulder/Phobos surface interactions are derived from a study of magnified test-run videos. See supplementary online material Movies-S1 and -S3 to view the two magnified video segments. In summary: Movie-S1 – Before drifting into suborbital flight, this video shows a test boulder following the contours of local terrain. In our testing model, collisions are taking place between infinitely inflexible materials, and the nature of each collision is clearly abrupt and inconsistent with notions of boulders interacting with regolith. Nonetheless, the motion of the boulder suggests a tendency to follow the peaks and valleys of local terrain. Movie-S3 – Here we observe a close-up view of a boulder sliding into and through Stickney Crater. Contact with the crater rim and floor is continuous. Arguing against continuous rolling boulder surface contact with Phobos craters and other surface irregularities, a persistent reduction in elevation appears to terminate a boulder's surface contact ( Fig. 4a, 4b, 5b). However, as long as the topographical elevations of local terrain remain relatively uniform, and a boulder's Stickney Crater exit velocity is sufficiently low, a boulder will travel across relatively uniform terrain without losing contact with the surface, including contact with the generally muted craters of Phobos. Rolling boulder velocity appears to set strict limits on this process. Boulders that exit from Stickney Crater with velocities ≲6 m/s typically follow the local terrain of Phobos, whereas boulders that exit Stickney Crater with velocities ≳6 m/s are typically lost to orbits around Mars, and are consequently unavailable to skip across crater rims (Fig. 2). Where our testing model does not include sufficient parameters to properly test the compression and displacement of Phobos regolith, our model of boulder contact with the surface of Phobos is at most suggestive. However, where the motions of boulders appear to follow the irregular surface terrain of Phobos, we conclude that boulders passing through craters in continuous contact with Phobos is supported by our testing model. Nevertheless, an apparent contradiction remains: Unlike the motion of rolling boulders that maintain continuous contact with Phobos across the interior surfaces of craters, our testing model consistently predicts the ballistic flight of test boulders above the ‘zone of avoidance' with no contact other than a rare pit-producing bounce. Examining the apparent contradiction, we compare the motion of boulders passing through craters to boulders that approach and ballistically overfly the 'zone of avoidance,' and observe two key differences:

4.3. Objection 3: Grooves inside Stickney Crater Fig. 5a shows two grooves inside Stickney Crater. Fig. 5b shows the motion of a test boulder that travels ~360
around Phobos, reenters Stickney, and engages the rims, walls, and floor of Stickney. This motion strongly suggests that an ejecta boulder from Stickney Crater might potentially return to Stickney to emplace a groove inside Stickney in a process that concludes 6–8 h after the Stickney impact. The superposition of grooves inside Stickney Crater suggests an offset of time. However, as a fundamental principle of geological investigation, superposition does not rule out multiple processes that originate from a single event, or time-durations of complex single-origin events that take place over a period of hours. Where we observe few grooves emplaced inside Stickney Crater, it is likely that the reentry of Stickney boulders into Stickney Crater after traveling ~360
around Phobos is an unusual process. Nonetheless, without extensive investigation, we were able to discover viable launch vectors that predict superposed Stickney boulder motions inside Stickney Crater, and it is plausible that rolling boulders reentered Stickney to produce grooves inside the crater. 4.4. Objection 4: grooves that crosscut other grooves

1) Stickney Crater is located at a high topographical elevation (Fig. 1). For this reason, boulders roll downhill toward the zone, accelerate in transit, and arrive at the rim of the zone with velocities 2–4 m/s greater than their Stickney Crater rim exit velocities. 2) The 'zone of avoidance' is not a crater. It does have a leading rim, but instead of an immediately-present crater floor and immediatelypresent trailing wall and rim, boulders that arrive at the rim of the zone encounter a persistent drop in elevation. When a rolling boulder encounters the zone, it drifts into space following the lowest gravitypotential path until it intercepts a landform elevation that terminates the boulder's ballistic trajectory.

As shown in Fig. 1, entire families of grooves crosscut each other, and in Fig. 6a and c, solitary grooves crosscut the Northern Family of grooves. The same way that principles of geological superposition inform our discussion of grooves inside Stickney Crater (Section 4.3), an observation of crosscutting grooves on Phobos is consistent with a single-origin for multiple instances of crosscutting grooves. As shown in Fig. 6, crosscutting grooves are produced by two test boulders that travel with sufficient distances to encounter previously emplaced grooves. In principle, where a boulder travels >180
around Phobos from Stickney Crater, it will begin to encounter previous boulder tracks that are emplaced by one or more boulders that also travel >180
from Stickney. From this we conclude that crosscutting grooves and crosscutting families of grooves – including a variety of intersecting angles and the apparent impression of multiple emplacement events – are produced

When comparing the morphological character of local Phobos craters to the 'zone of avoidance,' we conclude that our model properly predicts 8

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fact, measure the consequences of an impact spike that produced ~2.8–4.2 Ga. of apparent surface aging in a process that took place over a period of ≲1000 years following the Stickney impact (Dobrovolskis and Burns, 1980; Juh
asz et al., 1993; Hamilton and Krivov, 1996; Krivov et al., 1996; Ramsley and Head, 2013b; 2017; Basilevsky et al., 2014; Nayak, 2018). In view of the intense Stickney secondary impact spike and the deposition of Stickney regolith to a depth of 30–50 m, a mechanism exists to account for 'missing' Stickney boulders D ~100–400 m: Impacted by high-velocity Mars-orbiting Stickney ejecta, boulders were fragmented and buried within newly-produced regolith. According to Ramsley and Head (2017), the gardening effect of higher-velocity Mars-orbiting Stickney ejecta across the surface of Phobos began only after Phobos completed one full orbit following the Stickney impact. For this reason, during the first orbit of Phobos after the Stickney impact, there would have been no high-velocity secondary impacts to alter the fate of rolling boulders – the period of time when groove-producing boulders would have been in motion. Consequently, according to Ramsley and Head (2017), boulders had sufficient time to complete the emplacement of grooves before they were subsequently fragmented and buried by Stickney secondary impacts. With regard to the post-secondary-impact fate of the grooves, where the surface of Phobos was saturated with secondary impact craters ≲D 60 m, groove widths ≳80 m would have survived the impact spike, showing progressively less degradation at wider groove widths (Ramsley and Head, 2013b, 2017) ( Figs. 1a, 6a and 6c). In summary, Stickney ejecta boulders remain on Phobos. However, the intense spike of returning Stickney ejecta strongly suggests that large in-situ groove-forming boulders were fragmented and mixed into the regolith of Phobos (Soter and Harris, 1977; Thomas and Veverka, 1980; Thomas, 1998; Thomas et al., 2000; Ramsley and Head, 2013b; 2017; Basilevsky et al., 2013, 2014; 2015; Nayak and Asphaug, 2016; Nayak, 2018).

the motion of boulders through the interiors of Phobos craters and the ballistic flight of boulders that overfly the zone. 4.6. Objection 6: Missing groove-producing boulders Our discussion of the ultimate fate of Stickney boulders is based on previous work, and is unrelated to our Blender/Bullet testing system (Blender Foundation Development Team, 2016). According to the model of Wilson and Head (2015), after ~20 km of total surface contact, rolling boulders come to rest on the surface of Phobos. According to our testing model, once a boulder comes to rest, it remains on the surface of Phobos, and according to Ramsley and Head (2013b, 2017), if a boulder were subsequently dislodged from Phobos into an orbit around Mars, in almost every plausible circumstance, the boulder would return to the surface of Phobos. In high resolution imaging east of Stickney Crater, Thomas et al. (2000) observe a substantial concentration of Stickney ejecta boulders D ≲ 8 m, but they observe only one boulder large enough to produce a groove ≳80 m in width in accordance with Wilson and Head (2015). Even if boulders did not roll to produce Phobos grooves, Stickney boulders D ~100–400 m were nevertheless produced (Melosh, 1989; Wilson and Head, 2015), and where Stickney Crater produced hundreds of ejecta boulders D ~100–400 m (Ramsley and Head, 2017), we would expect to observe substantial evidence of boulders D ~100–400 m. Where are the missing D ~100–400 m Stickney Crater ejecta boulders? To address this question, we must consider events that took place throughout the ≲1000 years following the Stickney impact. Consistent with a typical crater formation process, Stickney Crater produced ejecta across a wide range of ejection velocities. Typically, smaller fragments were ejected at higher velocities and larger fragments at lower velocities (Melosh, 1989). Specifically, depending on the pre-impact tidal lock orientation of Phobos at the time of the Stickney impact (Section 3.2.9), 60% or 90% of Stickney ejecta returned to Phobos, and the balance was either launched to solar orbits or into the atmosphere of Mars (Ramsley and Head, 2013b, 2017). The remaining Stickney ejecta traveled in orbits around Mars with Phobos-relative velocities that were approximately equal to their crater ejection velocities from Stickney, including a portion of high-velocity fragments. During the ≲1000 years following the Stickney impact, highervelocity Stickney ejecta returned to Phobos to produce an intense impact spike that heavily reworked the entire surface area of Phobos (Ramsley and Head, 2017). In summary, the spike saturated the surface of Phobos with craters D ≲ 60 m (Hartmann and Gaskell, 1997; Murchie et al., 1989; Ramsley and Head, 2017) and produced new regolith with a global equivalent thickness of 30–50 m (Thomas, 1998; Thomas et al., 2000; Basilevsky et al., 2014; Ramsley and Head, 2017). Approximately 50% of the new Stickney-produced regolith deposit is Stickney primary ejecta, and the remaining 50% is ejecta from Stickney secondary impacts (Ramsley and Head, 2017). To help in visualizing the intensity of the Stickney Crater secondary impact spike on Phobos – across every km2 of Phobos – the spike produced an average of two secondary craters D 400–800 m, five craters D 200–400 m, 20 craters D 100–200 m, 50 craters D 50–100 m, 160 craters D 25–50 m, and thousands of craters D < 25 m (Ramsley and Head, 2017). In fact, in sum total, the flux of returning Stickney impact ejecta (including craters from returning secondary impacts) is sufficient to account for all Phobos craters D ≲ 0.6 km that are observed in the present day (Ramsley and Head, 2017; Nayak, 2018). Adding to evidence of an intense impact spike, Schmedemann et al. (2014) assume that Phobos craters that are located proximally to Stickney Crater and inside Stickney were produced by solar system flux. Based on an assumption of solar system flux, they calculate an age for Stickney of ~2.8–4.2 Ga. In view of the model of returning Stickney ejecta (Ramsley and Head, 2017; Nayak, 2018), Schmedemann et al. (2014), in

5. Conclusions Our study assesses six objections (listed in Section 2.2) to the model of Wilson and Head (2015) – that the grooves of Phobos were produced by ejecta boulders from the Stickney Crater impact. We test four of the six objections with a model that simultaneously simulates three-dimensional gravitational forces of Mars and Phobos and the motions of Phobos and test boulders. We discuss a fifth objection based on close up observations of two test runs, and we examine a sixth objection based on previous work. We observe the rolling boulder model at two likely pre-impact tidal lock orientations of Phobos, and at three altitudes above Mars. On this basis we conclude the following: 1. Linear grooves that are not radially aligned with Stickney Crater are plausibly produced by Stickney ejecta boulders that are guided into linear and parallel motions by a complex system of gravitation and tidally desynchronized Phobos rotation. 2. The absence of grooves on the Phobos trailing hemisphere is plausibly produced by boulders that consistently drift into suborbital flights over the trailing hemisphere of Phobos. When approaching the trailing hemisphere of Phobos, rolling boulders encounter a persistent reduction in terrain elevation, and boulders overfly the trailing hemisphere following a ballistic trajectory. Our model therefore predicts that Stickney ejecta boulders would not emplace grooves within the 'zone of avoidance.' 3. Grooves inside Stickney Crater are plausibly produced by Stickney ejecta boulders that travel >360
around Phobos and return to Stickney Crater. The superposition of grooves inside the crater is produced by ejecta boulders that subsequently roll through Stickney Crater 6–8 h after the Stickney impact. 4. Grooves crosscutting other grooves are plausibly produced when two or more Stickney ejecta boulders engage the same surface of Phobos 9

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5.

6.

7.

8.

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after one or both have traveled >180
. The observed superposition of crosscutting grooves is due to Stickney boulders that intersect at the same latitude/longitude at different times after the Stickney impact, and differing angles of intersection are produced by boulders that arrive from differing azimuths of travel motion. Grooves inside craters are plausibly produced by boulders that exit from Stickney Crater with initial launch velocities ≲6 m/s. Boulders that exit the crater at ≲6 m/s generally follow the irregular terrain of Phobos, and boulders only drift from the surface of Phobos when they are initially launched with greater velocities, or they encounter a persistent drop in terrain elevation (such as the rim of the 'zone of avoidance'). Missing groove-producing boulders were plausibly removed in the years and centuries after the production of the grooves by an intense spike of returning secondary impacts from Stickney Crater that displaced and fragmented groove-producing boulders. In the present day, fragments of groove-producing boulders remain on Phobos – buried within a global equivalent deposit of Stickney regolith 30–50 m thick. Where the secondary impact spike saturated Phobos with craters ≲D 60 m, groove widths ≳80 m would have survived the spike, showing progressively less degradation with greater widths. The present-day synchronous tidal-lock orientation of Phobos compared to an orientation rotated 180
from the present day produces nearly identical boulder motion patterns in our testing model. Consequently, our testing model offers no evidence to establish the two most likely preStickney-impact tidal lock orientations of Phobos. Testing at a Phobos semimajor axis of 12,000 km produces boulder patterns that consistently align with the observed patterns of grooves on Phobos, suggesting an age for the grooves and Stickney Crater of ~150 Ma. However, we did not test the motion of boulders at semimajor axes >14,000 km. Consequently, our testing model does not rule out a matching pattern at greater (and more geologically ancient) Phobos altitudes.

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In summary, our study accounts for six objections to the model of Phobos grooves produced by rolling, sliding, and bouncing Stickney ejecta boulders raised by Murray and Heggie (2014). We also observe an overall character of Stickney boulder motions in our testing model that is generally consistent with the pattern of Phobos grooves, and we therefore conclude that the rolling boulder model (Head and Cintala, 1979; Wilson and Head, 1989, 2005; 2015; Duxbury et al., 2010; Head and Wilson, 2010; Hamelin, 2011) is both quantifiably and qualitatively plausible. Acknowledgments We gratefully acknowledge financial support from the NASA Solar System Exploration Research Virtual Institute (SSERVI) grant for Evolution and Environment of Exploration Destinations under cooperative agreement number NNA14AB01A at Brown University. We also sincerely appreciate the support of NASA grant (#1488322) for participation in the Mars Express Mission for the HRSC experiment (to JWH), and the spacecraft team mission scientists who have produced many of the images and measurements that underpin our study. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.pss.2018.11.004. References Avanesov, G.A., Bonev, B.I., Kempe, F., Bazilevsky, A.T., Boycheva, V., Chikov, K.N., Danz, M., Dimitrov, D., Duxbury, T., Gromatikov, P., Halmann, D., Head, J., Helfets, V.N., Kolev, V., Kostenko, V.L., Kottsov, V.A., Krasavtsev, V.M., Krasilov, V.A., Krumov, A., Kuzmin, A.A., Losev, K.D., Lumme, K., Mishev, D.N., M€ ohlmann, D., Muinonen, K., Murav'ev, V.M., Murchie, S., Murray, B., Neumann, W., Paul, L., Petkov, D., Petuchova, I., P€ ossel, W., Rebel, B., Shkuratov, Yu G., 10

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