Hydrocode Simulations

We carried out numerical simulations of impact cratering events on various planetary surfaces, using both two-dimensional (2D) and three-dimensional (3D) hydrocodes. Earlier studies were carried out using the 2D Eulerian hydrocode CSQ , developed at Sandia National Laboratories; (Thompson, 1979; 1985). By assuming axial symmery, CSQ is used to model vertical impacts. However, it is well known that the most probable impact angle is 45° (Gilbert, 1893; Shoemaker, 1962). Modeling the impact process in its full complexity, including the nonnormal impact angle of the incoming impactor, requires thus a fully 3D hydrocode, which is highly computation intensive. Because of this, the use of 3D hydrocodes has been sporadic; only recently have computer hardware advances allowed a more general use of 3D codes. We carried out oblique impact simulations for Mars and the Moon, using the 3D Eulerian hydrocode SOVA, developed at the Institute for Dynamics of Geospheres (Shu-valov, 1999). The code has been benchmarked in 3D simulations against the well-known hydrocode CTH (the latest hydrocode from Sandia National Laboratories; McGlaun et al., 1990). The results show similar shock melting and vaporization patterns in CTH and SOVA simulations (Pierazzo et al., 2001), with a better efficiency (faster runs for the same spatial resolution) for SOVA.

An important drawback with 2D simulations is that they tend to overestimate shock temperatures (and underestimate shock pressures) by at least a factor of 2, with possible excursions of up to an order of magnitude when compared to equivalent 3D simulations (Thomas and Brookshaw, 1997; Pierazzo and Melosh, 2000). This translates into a higher internal energy of the impact plume, resulting in a higher plume temperature and a larger fraction of the projectile material reaching escape velocity in 2D simulations. Therefore, results from 2D simulations (e.g., Chyba et al., 1990) can be considered conservative, in that they overall underestimate the amount of organic material surviving the impact and successfully delivered to the planetary surface.

The angle of impact affects shock intensity. Shock heating declines with increasing angle to the vertical (Chyba et al., 1990; Thomas and Brookshaw, 1997; Pierazzo and Melosh, 2000). Thus, simple 2D simulations underestimate the survivability of organic molecules compared to oblique impacts. In some cases, however, it is possible to correct ad hoc results of 2D simulations in a simplified approach that takes into account the effect of impact angle (Pierazzo and Chyba, 1999a; 2002).

In our simulations, hundreds of Lagrangian tracer particles were regularly distributed in half of the projectile (taking advantage of axial, for 2D, or bilateral, for 3D, symmetry). The tracers allow us to record the trajectories and thermodynamic histories of the projectile during the impact. Resolution plays an important role in the thermodynamic evolution of the impact event (Pierazzo et al., 1997); we kept the resolution of the 2D Eulerian mesh to 50 cells (2%) per projectile radius in all the simulations, substantially higher than that used in earlier simulations (e.g., Chyba et al., 1990; Thomas and

Brookshaw, 1997). The 3D simulations are much more computer intensive; therefore, our highest resolution in 3D runs is 20 cells per projectile radius. The thermodynamic state of the tracers was recorded every 0.005-0.01 seconds of simulation time.

The hydrocodes make use of the semianalytical equation of state ANEOS, a FORTRAN code designed for use with a number of hydrocodes (Thompson and Lauson, 1972). Utilizing valid physical approximations in different regimes, ANEOS uses the Helmholtz free energy to construct thermodynami-cally consistent pressures, temperatures, and densities. A major advantage of ANEOS over other analytical equations of state (e.g., the Tillotson EOS; see Melosh, 1989) is that it offers a limited treatment of phase changes. Asteroid impacts were modeled using granite (Pierazzo et al., 1997) and dunite (Benz et al., 1989) projectiles. Comets are "dirty iceballs," a combination of ice and silicate grains, but for simplicity in our modeling the comets are treated as pure water ice (Turtle and Pierazzo, 2001). Initial impact conditions varied depending on the planetary body of interest (Table 5.1). We used the granite ANEOS equation of state (Pierazzo et al., 1997) to model rocky targets, and the ice equation of state to model icy targets (Europa). In the oceanic impact

Table 5.1. Comparison of origin of life conditions on Earth, Mars, Europa, and the Moon, and summary of the properties important for the impact delivery hypothesis.

Earth

Mars

Moon

Europa

In situ organic production

Yes

Probable

Difficult

Difficult

Surface liquid water

Stable over geologic time

Stable for limited time

No (Dry formation?)

(Subsurface ocean?)

Surface gravity (m/s2 )

9.78

3.72

1.6

1.33

Escape velocity (km/s)

11.2

5

2.4

2

Likely impactor population

>90% asteroids

>90% asteroids

>90% asteroids

>90% J-F comets

Median impact velocity

(km/s)a

Asteroids

-15-17

-7.7

-12

Comets

-23

-15

-20

-26

aMedian impact velocities are from Chyba (1991) for Earth and Moon, from Olsson-Steel (1987) for comets on Mars, and from Zahnle et al. (1998) for Europa.

aMedian impact velocities are from Chyba (1991) for Earth and Moon, from Olsson-Steel (1987) for comets on Mars, and from Zahnle et al. (1998) for Europa.

simulations, a 3-km-deep ocean (using the equation of state for water) overlaid a granite crust. The simulations extended long enough for the projectile material to be released from the shock state and for the pressure and temperature to reach a plateau. Impact-related temperature histories (from tracer particles) were extracted from the hydrocode simulations. A good resolution of the shock wave generated by the impact is guaranteed by the high temporal resolution of the recorded histories.

The application of Eq. (5.1) to all the tracers' temperature histories provides a map of survival of amino acids in the projectile (assuming that amino acids are present). An example is shown in Fig. 5.2 for a comet impact on the Earth's ocean. The fraction of amino acids surviving the impact event is then obtained by integrating the survival fraction obtained through Eq. (5.1) over the volume of the projectile (see Tables 5.2, 5.4, and 5.5 for various planetary bodies). Amino acid survival depends strongly on the peak shock temperature and the postshock temperature experienced by the projectile. The peak shock temperature decreases away from the impact point, resulting in lower survival near the incident face of the projectile, where the shock temperatures are highest, as shown in Fig. 5.2. To maintain a conservative approach to the problem, we neglect the pressure contribution, P(t)V, in the exponent of Eq. (5.1). As discussed in Blank et al. (2001), the high pressures associated with shocks should retard the kinetics of reactions that involve the breaking of bonds, and therefore pyrolysis, associated with the very high shock temperatures. This occurs essentially because the activation volumes for bond breaking are positive (Asano and Le Noble, 1978). When introducing the pressure contribution in Eq. (5.1), we find that the estimated amino acid survival increases by up to an order of magnitude.

Aspartic acid

Aspartic acid

Fig. 5.2. Survival map for aspartic acid within a comet 2 km in diameter impacting the Earth's surface at 20 km/s. From Pierazzo and Chyba (1999a).

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