SILICATE DUST SIZE DISTRIBUTION FROM HYPERVELOCITY COLLISIONS: IMPLICATIONS FOR DUST PRODUCTION IN DEBRIS DISKS

Interplanetary dust particles with sizes between 1 and 100 μm have very short lifetimes as compared with the timescales of the solar system and other planetary systems. Radiation pressure and Poynting–Robertson drag remove these particles from planetary systems. The lifetime of micron-sized (μm) dust at 1 AU from the Sun is only several thousand years (Mann 2009). Therefore, sources of new dust particles are required to maintain the dust population. Fragments generated by high-velocity collisions between solid planetary bodies, such as asteroids, are believed to be one of the major sources of interplanetary dust particles.

Recent astronomical observations have shown that many stars have extensive circumstellar disks of dust particles. The A3V star Fomalhaut was one of the first main-sequence stars found to possess a circumstellar debris disk. Spectral energy distribution (SED) modeling estimated the slope of the dust-size distribution in the Fomalhaut's debris disk as roughly equivalent to the distribution expected for a collisional equilibrium cascade (Wyatt & Dent 2002). The slope of the dust-size distribution in the β Pictoris disk may be flatter than that expected for a collisional cascade (Vandenbussche et al. 2010). Meanwhile, Lisse et al. (2009) showed that the best-fit model of the size distribution for the HD172555 circumstellar disk producing an infrared sharp silica feature is dominated by a higher proportion of small particles than a purely collisional equilibrium distribution would suggest. It was also suggested that the steep slope of the size distribution for the HD172555 circumstellar disk is indicative of a fresh non-equilibrium source of material within the last 0.1 Myr. A hypervelocity collision (>10 km s⁻¹) between rocky bodies is a possible candidate for such a source.

So far, the data on the ejecta size or mass distribution of laboratory impact experiments of silicate rocks are very limited. Only narrow ranges of ejecta size, target material, and impact velocity have been explored. Impact fragmentation experiments on basalt and pyrophyllite blocks with polycarbonate projectiles at impact velocities of 70–990 m s⁻¹ were conducted, and mass distributions of recovered fragments larger than a few hundred micrometers were reported in detail (Takagi et al. 1984). In each of three fragment-mass regimes, the mass-distribution curve was fit by a power law

$$\begin{equation} N({>}\, m) \propto m^{ - \gamma + 1}, \end{equation} \tag{ 1 }$$

where N(> m) is the cumulative number of recovered fragments heavier than mass m, and the slope γ is a constant. They showed that although the slope of the mass distribution of the larger fragments changed with experimental conditions, the slope of that of the smallest fragments was almost constant; γ = 1.5–1.6 when the impact was moderate (in the P_I < 1 range), but γ increased gently to ∼2.0 with increased impact intensity (in the P_I > 1 range). Note that P_I corresponds to the ratio of the shock-generated pressure at the target's rear surface to the material strength. Disruption experiments on basalt targets with nylon projectiles fired at higher velocity (∼3.2 km s⁻¹) also yielded a value of γ ∼ 1.7 for millimeter-sized fragments (Nakamura & Fujiwara 1991).

Only a few experiments have been performed to determine the size distribution of smaller micron-scale fragments. Fine fragments (in the 1–70 μm range) captured by a Styrofoam board were analyzed in an experiment that shot a nylon projectile into a basalt target at an impact velocity of 3.85 km s⁻¹ (Asada 1985). The fine fragments were shown to obey a power-law size distribution

$$\begin{equation} n(a)da \propto a^{ - \beta } da, \end{equation} \tag{ 2 }$$

where n(a)da is the number of the fragments between sizes a and a+da. The slope β (= 3γ−2) was shown to be ∼3.0–3.5, which corresponds to γ ∼1.7–1.8 in Equation (1). Impact experiments with nylon projectiles onto basalt targets were also conducted at an impact velocity of ∼3.7 km s⁻¹ (Nakamura et al. 1994). The size distribution of fragments from a few to a few hundreds of microns, the velocity, and the ejection angle were investigated by counting penetration holes on aluminum foils or thin plastic films of different thicknesses placed near the target. The slopes of the fragment-size distributions were consistent with previous results. These two studies indicated that the slope of the size distribution found for millimeter-sized fragments remained constant down to the micron-scale regime.

Target material is a key parameter that can influence the resulting size distribution of dust-sized fragments. In an impact disruption experiment consisting of an aluminum projectile fired at a velocity of 4.45 km s⁻¹ at a target of Murchison CM2 carbonaceous chondrite meteorite, the slope of the cumulative mass–frequency distribution for the fragments detected by aluminum foils was almost flat for masses less than 10⁻⁶ g, corresponding to sizes of about 100 μm (Flynn et al. 2009). It is not clear whether the same size distribution observed for impacts with relative velocity less than 4 km s⁻¹ is expected for impacts with higher relative velocities. However, accelerating macroscopic projectiles to velocities higher than about 10 km s⁻¹ has been a major technological challenge. Consequently, the dust-production efficiency at such impact velocities has remained highly uncertain. In this study, we conducted impact experiments to study the ejecta-size distribution from a hypervelocity collision using a GEKKO XII-HIPER laser at the Institute of Laser Engineering of Osaka University in Japan (Kadono et al. 2010).

Aluminum and gold spheres of 80–250 μm in diameter were accelerated to velocities of 9–61 km s⁻¹ by laser ablation and shot into basalt (Kinosaki, Japan) and dunite (Horoman, Japan) blocks 15 mm on a side. The laser wavelength, energy, and pulse duration, were 1054 nm, 2800–8600 J, and 20 ns, respectively. At this facility, up to 12 laser beams irradiate from one direction, and the spot diameter of these laser beams was 100–200 μm. When the laser beam irradiation starts, a thin surface layer (∼1 μm) of the projectile sphere vaporizes and generates a high-temperature plasma. The expanding plasma accelerates the projectile. In this study, the ambient pressure was ∼10⁻⁴ Torr. Table 1 summarizes the experimental conditions. We observed the acceleration process of the projectiles using an X-ray streak camera to determine projectile velocity. Due to a problem with the X-ray streak camera, we could not measure the projectile velocity of Shot 33759. Therefore, the projectile velocity of the shot was estimated by the velocity of Shot 33764, the shot with similar impact conditions.

Aerogel blocks of 0.11 g cm⁻³ in density and 5 mm in thickness were deployed beside the target to capture target ejecta. These blocks were covered with an aluminum plate 0.5 mm in thickness with 3 mm diameter holes. To minimize the effect of the plasma on the aerogel blocks, we placed a copper plate 1 mm in thickness between the projectile and the aerogel blocks to act as a shield. We defined θ, ψ, l, and d as the ejection angle, the incident angle to the aerogel block, the distance between the projectile and the target, and the distance between the impact point and the analyzed region of the aerogel block, respectively. The distance between the projectile and target (l) was about 5 mm. The distance between the impact point and the aerogel surface (d) was 27.8–33.6 mm. Figure 1 shows the experimental configuration.

Zoom In Zoom Out Reset image size

Irregularly shaped surface depletions, i.e., craters, were formed on the targets in all shots. In Shot 33372 and Shot 33759, spallation of the target back surface occurred. Not only the target materials but also the projectile material (aluminum) and the shield material (copper) were captured on the aerogel surface. These materials cannot be distinguished under an optical microscope. Therefore, we analyzed the surface of the aerogel blocks using an electron probe micro analyzer (EPMA) (JEOL JXA-8900) in mapping mode (3.2 × 3.2 μm pixel⁻¹, 1024×1024 pixels) and counted the number of particles that contained elements typical of the target material (magnesium for dunite and calcium for basalt). The equivalent-area diameter was adopted as the particle diameter. The raw number of the particles was converted to the number per solid angle using the diameter of the hole region (3 mm), the distance between the target and the regions on the aerogel (d), and the angle of impact onto the aerogel (ψ). We captured the particles ejected at θ ∼ 61°–82°. Each area sampled by the 3 mm diameter region of aerogel surface corresponds to 0.09%–0.12% of the 2π solid angle. We obtained the cumulative size distribution of the ejecta ranging from 5 μm (corresponding to 2 pixels) to tens of microns in diameter. Figure 2 shows the size distribution of Shot 33370 as an example. The cumulative number of ejecta larger than 5 μm varied according to the ejection angle, θ , within one order of magnitude.

Zoom In Zoom Out Reset image size

Figure 3 shows the average size distribution of ejecta from the dunite targets. The size distribution varied with impact conditions such as size, velocity, and material composition of the projectile. Shot 33752 is the standard shot (bold solid line). The major variations from the standard shot parameters were the projectile size (Shot 33370), the impact velocity (Shot 33372), and the projectile material (Shot 33759). The slope of Shot 33370 is the steepest, and accordingly, the number of dust-sized ejecta (<10 μm) in Shot 33370 was the largest. The slopes of the cumulative ejecta-size distributions (−β + 1) between 5 μm and the largest ejecta are −2.2 ± 0.2 (0.34) for Shot 33752, −4.8 ± 0.3 (0.28) for Shot 33370, −3.8 ± 0.3 (0.99) for Shot 33372, and −2.5 ± 0.1 (0.55) for Shot 33759, i.e., values of β are from 3 to 6. Note that the numbers in the parentheses denote the scatter of the slope (1σ) over different ejection angles. Varying the material composition of the target had little effect on the ejecta-size distribution. The slopes are −3.5 ± 0.1 (0.27) in Shot 33364, −3.1 ± 0.1 (0.37) in Shot 33751, and −3.8 ± 0.2 (0.62) in Shot 33764, i.e., values of β ranged from 4 to 5. Most of the slopes were considerably steeper than those in previous laboratory studies, implying that a hypervelocity impact is more efficient at producing dust-sized particles. However, no clear trend between the slope index β and impact velocities was recognized within the data set of this study. Interestingly, the indicator of spatial fluctuation, i.e., the range of the slopes over different ejection angles (denoted by the numbers in parentheses), increased with the impact velocity of the aluminum projectiles. Therefore, the difficulty in determining a relationship between the experimental conditions and the slope index may be due to the small angular coverage of the aerogel detector, i.e., to spatial fluctuations in the ejecta-size distribution.

Zoom In Zoom Out Reset image size

4.1. Dust-production Efficiency

The number of dust-sized ejecta probably depends on the initial peak pressure of impact, the volume of the isobaric region, and the properties of the target and projectile material, e.g., material strength. However, Figure 4 shows that the projectile kinetic energy (E_proj) and total surface area of ejecta down to 5 μm in diameter (X_s) can be approximated by a single power law,

$$\begin{equation} X_s [m^2 ] = (2.0 \pm 0.2) \times 10^{ - 6} E_{{\rm proj}} [J]^{0.66 \pm 0.13}, \end{equation} \tag{ 3 }$$

where a spherical surface area is assumed for each ejected particles.

Zoom In Zoom Out Reset image size

4.2. Circumstellar Debris Disk Around the HD172555

In collision cascades, the slope of the differential mass distribution for the dust (γ) is 11/6, assuming that the catastrophic disruption threshold (Q*) is independent of masses of the colliding bodies (Dohnanyi 1969; Tanaka et al. 1996). Q* is defined as the impactor kinetic energy per unit target mass required, given that the largest remnant mass is equal to the half the original target mass. In general, however, Q* is dependent on the mass of the target, M_t, and the mass dependence of Q* influences the size distribution. Kobayashi & Tanaka (2010) presented a model of the size distribution in a collision cascade that included the mass dependence of Q*,

$$\begin{equation} \gamma = \frac{{11 + 3p}}{{6 + 3p}}, \end{equation} \tag{ 4 }$$

where p is the slope of mass dependence of Q*,

$$\begin{equation} Q^* \propto M^p. \end{equation} \tag{ 5 }$$

The value of p in the strength regime was determined to be −0.135 by laboratory impact experiments on approximately centimeter-sized granite targets (Housen & Holsapple 1999). If this mass dependence of Q* can be extrapolated down to dust size (∼μm), the differential size distribution for the circumstellar dust in collision cascades would be n(a)da∝a^−3.68da. However, the best-fit model of the size distribution for the HD172555 circumstellar dust that produces the sharp silica feature is n(a)da∝a^{−3.95 ± 0.10}da with 0.1 < a < 1000 μm. We can conclude that this debris disk is dominated by a larger proportion of small dust particles than would be provided by a purely collisional equilibrium distribution from a collision cascade (Lisse et al. 2009). It is also suggested that the steep slope of this size distribution, which shows abundant dust particles, is indicative of a fresh source of material, such as a planetesimal-scale hypervelocity collision (>10 km s⁻¹) within the last 0.1 Myr. The steep slope of the ejecta-size distribution from the hypervelocity impact performed in this study supports the idea of a hypervelocity collision origin of the debris disk around HD172555. However, the large scatter in the size-distribution slope in this study hampers our ability to give a detailed estimate of the collision velocity, which in turn, restricts our ability to provide estimates of the orbital characteristics of the colliding bodies, from the dust-size distributions. Improvements in the data statistics and the development of a scaling model for dust-size distribution will assist us in answering these questions.

We conducted hypervelocity impact experiments to investigate the dust-production efficiency of such collisions in interplanetary space and in debris disks. Submillimeter-size aluminum and gold spheres were accelerated to 9–61 km s⁻¹ by laser ablation and shot into dunite and basalt targets. We analyzed the surfaces of aerogel blocks deployed near the targets using EPMA and counted the number of particles that contained target material. We derived the size distributions of the ejecta in the size range of from five microns to tens of microns in diameter. The total surface area of ejecta as small as 5 μm in diameter increased monotonically with projectile kinetic energy. The slopes of the ejecta-size distributions were considerably steeper than those reported from previous studies and steeper than the value expected for a purely collisional equilibrium distribution in a collision cascade. This suggests the possibility of a hypervelocity collision (>10 km s⁻¹) origin for the circumstellar disk observed around HD172555, which contains abundant small dust particles.

We thank C. Sekigawa and M. Umehara for assistance with EPMA analyses. This study was performed under the Joint Research Program of the Institute of Laser Engineering, Osaka University, Japan. This work was supported by grants-in-aid for science research (21244069) from the Japanese Society for the Promotion of Science (JSPS).