1. Crater models and possible scaling law
G. Cremonese, P. Borin, E. Martellato, F. Marzari, M. Massironi

2. Scientific Motivation
determination of the projectile size
hints on the asteroid composition and structure
Cremonese G., Martellato E., Marzari F., Kuhrt E., Scholten F., Preusker F., Wünnemann K., Borin P., Massironi M., Simioni E., Ip W., and the OSIRIS team, 2012, PSS special issue, in press.
determination of the scaling law

3. iSALE Simplified Arbitrary Lagrangian Eulerian Features :
multi-rheology, multi-material extension of the SALE hydrocode
Amsden et al., 1980;
Melosh et al., 1992; Ivanov et al., 1997; Collins et al., 2004; Wünnemann et al., 2006
Features :
Regular structured mesh
Explicit finite-difference solution algorithm
Artificial viscosity for shock capturing
Multi-material advection scheme
ANEOS and Tillotson equation of state routines
Custom deviatoric strength model developed specifically for impacts in geologic materials
An efficient porous algorithm
Fast and efficient output data read/write/compression algorithms
My group is perfoming numerical modelling by using iSALE, that is an extension of the SALE hydorcode developed by Amsden.
iSALE is characterized by a number of features, including:
up to three target materials
various equations of state & constitutive models
a porous-compaction model

4. North Polar Crater Cluster
Massilia
d = 24 km

5. Lutetia and the projectile
The overall asteroid’s dimensions are (126 ± 1) × (103 ± 1) × (95 ± 13) km3 along the principal axes of inertia (Sierks et al., 2011). Hence, in our hydrocode simulations, we modeled Lutetia as a sphere with mean radius of 50 km and a density of (3.4 ± 0.3) g/cm3 has been derived. We have chosen a dunite composition because it is a reasonable approximation of the chemical composition of the rocky material found in bodies in the inner Solar System (Davison et al., 2010) and it is similar in density to the one calculated for Lutetia. The projectile is assumed of dunitic composition as well our target to conveniently reducing the number of materials in the model, and a porosity of 30% was set. The adopted porosity is found to be a mean value for the C taxonomic class asteroids (cfr. Fig. 4, Britt et al. 2002), which represents the larger class of objects relative to the heliocentric distance where Lutetia is orbiting (Mothé-Diniz et al., 2003).

6. iSALE input parameters

7. Massilia
Massilia is the largest crater observed on Lutetia. The DTM shows an elliptical shape having 47 km and 55 km as shorter and larger axis. The shorter axis is perpendicular to the terminator, we have assumed that is not completely visible, as the terminator does not make possible to trace the rim beyond it or it has been eroded. In addition, an impact with a largely inclined direction to justify the crater elliptical shape is very unlikely. We did not consider an average DTM profile for the comparison with the resulting simulation, but we have assumed the longest axis as the diameter of 55 km.

8. NPCC-d: comparison between DTM (black line) and iSALE (dashed line) profiles

9. Massilia: comparison between DTM (black line) and iSALE (dashed line) profiles

10. Conclusion
The high density of the body combined with the clues on its collisional history indicates that Lutetia is probably an intact planetesimal and not an evolved rubble pile. This hypothesis is reinforced by the lack of a collisional family around the asteroid. It is also noteworthy that the good match we find between hydrocode simulations and observations is obtained assuming that the body is compact without a crust.

11. Scaling Law
A wide range of general scaling laws are available that can be used for the age determination They strongly depend upon target/impactor material, bulk structure and impact conditions Our work consists on deriving a scaling law for Lutetia thanks to a specific exploration of the relation between crater diameter and projectile size using the hydrocode iSALE

12. depth/diameter ratio for Lutetia taken from Vincent et al
depth/diameter ratio for Lutetia taken from Vincent et al., 2012, PSS special issue, in press.

13. INPUT PARAMETERS Parameters Projectile Lutetia Density 2.319*103 Kg/m3
Material
Dunite
Velocity
4.3*103 m/s -
Porosity
30%

14. PRELIMINARY RESULTS Projectile radius (m) Resolution (m)
Crater diameter (km)
p/D
900
200
12.8
0.125
1200
240
16.32
0.191
1500
300
17.4
0.241
1800
360
21.6
0.250