IntroductionAstronomy is the science of understanding the universe by observing the light of distant objects in the Universe. Unfortunately, collisions don’t occur frequently enough to have astronomers observe such events. The NASA Deep Impact event occurred on July 4, 2005, and it successfully collided a 364 kg copper projectile into the surface of the 9/P Tempel 1 comet at a relative velocity of 10.3 km s-1. This is the first mission to ever examine the chemical composition and kinematics of a comet by observing the ejecta cloud from the collision. The event was observed by many ground and spaced based observatories. Surprisingly, the Monterey Institute for Research in Astronomy (MIRA) and the Hubble Space Telescope (HST), which used the Advanced Camera for Surveys (ACS) High Resolution Channel (HRC) were the only 2 observatories to successfully photometrically observe the event. These observations lead to surprisingly strict constraints on the mass and velocity distributions of the ejecta cloud.

Project and MethodsThis project attempts to model the impact using the data from the HST to resolve different interpretations of the event. Initially, the Deep Impact event was simulated on the computer by using the rapid prototyping programming language called QuickBasic. QuickBasic is fast at debugging, and easy to use, but it lacks the power to simulate the collision in fine detail. So, the QuickBasic program was translated to the more powerful FORTRAN programming language.

The code used the Monte Carlo method which simulated cloud distribution and evolution through the hour as imaged by the ACS. This included the effects of the optical distortions of the ACS and the photometry sampling techniques of the HST data reduction.

Computer simulations of the first 30 minutes of the ejecta cloud were used to decipher some of the more puzzling characteristics of the photometric light curves. The results of these simulations require complex cloud evolution within the smallest aperture observed by the Hubble Space Telescope. We simulated the collision in order to understand the physics of the photometric characteristics of the ejected cloud.

AcknowledgmentsI would like to thank my mentor, Bruce Weaver for all of the help that he gave me, and for all of the time he dedicated to me, Patrick McNeil, Joe Welch, and Andy Newton for giving me the opportunity to experience such a wonderful internship.This work has been supported by the Hartnell National Science Foundation STEP grant #0525444 and the Hartnell Department of Education Subaward with the Foundation of California State University Monterey Bay #5024701A-081120-5-A

ConclusionsResults from the computer simulations of the Deep Impact event support the conclusion that the optically thick sphere was only about 28 km in diameter 13 minutes after impact, expanding at ~36 m s-1 which would constrain the mass from the ejecta cloud to be about 2x107 kg as seen in Figure 5. The 28 km diameter opaque cloud is consistent with Feldman’s 40 km radius aperture photometric observation of the cloud not reaching a limit on brightness within the observed 13 minutes.

Furthermore, the estimated expansion velocity for the opaque cloud of ~36 m s-1 gives us a reasonable estimate of what the 20 different groups of astronomers would have calculated given better conditions and optics. Also, the extended image is presumed to be the lighter and faster particles separating themselves from the heavier and slower particles within the dense center, forming a non-opaque halo.

Alejandro CotaMonterey Institute for Research in Astronomy, Hartnell College, Salinas, California

Literature citedFeldmand, P.D. et al. Icarus 2007, 187, 113.Lisse, C.M., et al., Science 2006, 313, 635Walker, R.G., Weaver, Wm. B., Shane, W.W., Babcock, A., Icarus 2007, 187, 285

Figure 2. Large arrow points to place of impact.

ProblemThe 364 kg impactor collided with the comet at 10.3 m s-1 giving a total kinetic energy of 19 Gigajoules. Lisse (2006) calculated that 68.5% KE will go into accelerating the particles. The total mass of the ejecta can be calculated from an estimate of the particle size, density, and velocity. The black lines show the relationship between the kinetic energy, mass of the ejecta, velocity of the particles, and density of the particles. Experiments from 20 different groups of astronomers, including MIRA, Feldman, and Lisse estimate the velocity of the ejecta cloud to be 70 - 230 km s-1 giving us a total mass of about 106 kg. The orange graph represents the total mass of the optically opaque part of the cloud as a function of velocity as deduced from Fig.3 and Fig.4. For uniform particle size the intersection of the orange and black graphs constrains the velocity and total ejecta mass at 36 m s-1 and 2x107 kg.

Figure 7. Results of the aperture photometry as the ejecta cloud expands. The 400 km curve matches the data observed and shown in Fig.3. The MIRA observations show the rollover of the aperture photometry but the comet set before the HST could observe it.

Simulating the Ejecta Cloud for the NASA Deep Impact Experiment from MIRA and Hubble Space Telescope Observations.

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Figure 5. The intersection best represents the calculations of the ejected mass.

Figure 3. The R-band flux increases as the square of the radius (velocity x time). An optically thick sphere expanding at a constant velocity successfully models the concave portion of the light curve. The HST observations end at 13 minutes because the comet set for the HST.

Figure 4. A simple optically thick sphere expanding at constant velocity fit to the square root of the flux versus time concave portion of the light curve from Figure 3, 2 – 18 min after impact. This is consistent with an optically thick hemispherical ejecta cloud expanding at a constant velocity.

Figure 8. Normalized brightness distribution derived from Feldman's velocity distribution (Feldman, 2005, Fig.11) assuming equal partition of energy according to particle mass, giving an average particle radius as a distance from the comet. This predicts the particles on the outer edge of the expanding cloud, on average, will be smaller than those in the interior of the cloud.

Figure 6. My graphs illustrating the brightness of the explosion with a given radius. Each ACS pixel subtends 16 km at the comet.A) Theoretical representation of the inside portion of the impact with perfect optics. B) Theoretical image convolved with the measured ACS point spread function.C) 40 km radius aperture photometry of the observed ejecta cloud. D) 80 km radius aperture photometry of the observed ejecta cloud.

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Figure 8. My program created a contour plot showing the distribution of the total particle reflectivity. The reflectivity is the size (proportional to mass1/3 ) and number distribution. It uses probabilities derived from Feldman’s (2006) pre and post impact brightness distribution plots and then we interpret this to show a concentration of large particles close to the origin of impact and small particles at the edge.

Figure 1. MIRA photometric images of pre and post impact.