This project uses computer simulations to model observations of the 2005 Deep Impact collision with comet Tempel 1. The simulations aim to understand the physics behind the light curves observed by Hubble Space Telescope. The simulations suggest the optically thick ejecta cloud was about 28 km in diameter 13 minutes after impact and expanding at around 36 m/s, constraining the cloud's mass to approximately 2x10^7 kg. This mass and expansion velocity are consistent with independent estimates from observations by different astronomy groups.

1. Introduction
Astronomy 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 Methods
This 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.
Acknowledgments
I 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
Conclusions
Results 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 Cota
Monterey Institute for Research in Astronomy, Hartnell College, Salinas, California
Literature cited
Feldmand, P.D. et al. Icarus 2007, 187, 113.
Lisse, C.M., et al., Science 2006, 313, 635
Walker, R.G., Weaver, Wm. B., Shane, W.W., Babcock, A., Icarus 2007, 187, 285
Figure 2. Large arrow points to
place of impact.
Problem
The 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.
Minutes After Impact
0.0 5.0 10.0 15.0 20.0
[Flux(10-15
ergcm-2
s-1
Å-1
)]1/2
0.50
1.00
1.50
2.00
2.50
Aperture
Diameter
4.7"
8.7"
16.7"
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.
C D
BA
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.