## 2. Model constructionWe shall estimate the dust production rate of hypervelocity impacts
on EKOs by interstellar dust. The surface condition of the target is
an important parameter in the cratering process. Since the escape
velocity of EKOs is small (less than about cm
s ## 2.1. Model for a hard surface of ice materialThe first model assumes that EKOs have a hard surface of ice
material. In previous works, impact experiments onto water ice targets
were performed to investigate the crater volume (e.g., Lange &
Ahrens 1987; Frisch 1992; Eichhorn & Grün 1993). Frisch
(1992) used particles with masses g to
g for the projectile, while Lange & Ahrens
(1987) applied a particle mass of 8 g for the projectile. On the
other hand, Eichhorn & Grün (1993) used smaller particles
with masses between g and
g as the projectiles. The data of Eichhorn
& Grün (1993) is appropriate for the study of craters
produced by the impacts of interstellar dust grains, which have an
average mass of about g (Grün et al. 1993
). Eichhorn & Grün (1993) compared their results with those
obtained by Frisch (1992) and Lange & Ahrens (1987), and gave an
expression for the crater volume
[cm where [g cm Since the impact velocity is sufficiently high (26 km
s It should be noted that some of the excavated material may melt or vaporize. According to Melosh (1989), the ratio of the mass of melted material to the mass of the projectile is given by where is the specific internal energy for
melting the target material. Substituting erg
g Impact ejecta with velocity smaller than the escape velocity of the target body would eventually fall back and deposit on the surface. The amount of escaping ejecta depends on the velocity distribution of excavated material and on the gravity of the target body. Unfortunately, the velocity distribution of icy ejecta has not yet been investigated in previous impact experiments onto icy targets. Therefore, the amount of ejecta escaping from the icy target bodies is estimated in the following way. When the target is composed of hard materials, the effect of material strength dominates the cratering process; this is referred to as the strength regime (e.g., Housen et al. 1983). According to Housen et al. (1983), the volume of ejecta with velocity higher than can be expressed in the strength regime by: where Substituting into Eq.(5), we obtained, From the definition of , where is the minimum velocity of the ejecta. From Eqs.(6) and (7), we obtained, Substituting Eq.(3) into Eq.(8), we obtained the total mass of ejecta with velocities higher than the escape velocity of target body, as If we assume that the EKO with g
cm From the observations by the Ulysses spacecraft, the flux of
interstellar grains We set minimum velocities ranging from 10 cm s ## 2.2. Model for a layer of icy particlesThe second model assumes that the surfaces of EKOs are covered by a layer of icy particles. We note that if the size of the particles is sufficiently larger than that of the interstellar dust grain, the impact by the latter produces a crater on the surface of an individual particle. This process can then be treated as the hard surface case presented in Sect. 2.1. On the other hand, if the layer of particles is composed of fine grains which are smaller than the interstellar dust grains, an impact crater will be produced in the layer of the particles. This case shall be examined in the following. Gravity dominates over material strength for cratering in a layer of particles; this is generally referred to as the gravity regime (Housen et al. 1983). Therefore the cratering process is not sufficiently affected by the properties of the target material. Hence we assume that the cratering process in icy particles is similar to that of sand targets. Housen et al. (1983) formulated the distribution of velocity in
the lower velocity ( m s where In this study we estimate the impact ejecta from target bodies with
radii ranging from hundreds of m to hundreds of km, with corresponding
escape velocities from about tens of cm s According to Schmidt & Holsapple (1982), the crater radius
where where We have assumed that the porosity of particles was 0.5 (Yen &
Chaki 1992) and the bulk density was 0.5 g cm whilst the lower estimate is Substituting Eq.(10) into Eqs.(17) and (18), and using the value of
In both cases we quote the power index to 3 significant figures. © European Southern Observatory (ESO) 1998 Online publication: December 8, 1997 |