IAU GA, RIO, Symp. 263, #495
Deep Impact Ejection from
Comet 9P/Tempel 1 as a
triggered outburst
Sergei I. Ipatov
Catholic University of America, USA. The work was initiated at University of Maryland
(siipatov@hotmail.com, http://faculty.cua.edu/ipatov/, http://www.dtm.ciw.edu/ipatov)
and Michael F. A’Hearn
University of Maryland, College Park, USA
The file with this presentation can be found on
http://faculty.cua.edu/ipatov/present.htm
(http://faculty.cua.edu/ipatov/rio2009-deep-impact.ppt )
See http://arxiv.org/abs/0810.1294 for details
Abstract
Time variations of velocities and relative amount of material ejected from Comet
Tempel 1 are studied [1-2] based on analysis of the images made by Deep Impact (DI)
cameras during the first 13 minutes after the collision of the DI impactor with the comet.
The rate of production of observed ejected material and velocities considered correspond
mainly to small (with diameter d<3 micron) icy particles, and our conclusions were made
only for observed small particles. The rate had a peak at ejection time te~0.6 s. At 1<te<3 s
and 8<te<40 s, the estimated rate of ejection was essentially greater than for theoretical
monotonic exponential decrease. Such difference was caused by that the impact was a
trigger of an outburst. At the time te~10 s corresponding to a local maximum of ejection
rate, the direction from the place of ejection to the brightest pixel quickly changed by
about 50 degrees, a considerable excessive ejection (rays of ejected material) to a few
directions began, and typical projections vp of velocities onto the plane perpendicular to
the line of sight were ~100-200 m/s. The sharpest rays were caused by material ejected at
te~20 s. In particular, there were excessive ejections, especially in images at t~25-50 s
after impact, in directions perpendicular to the direction of impact. Directions of excessive
ejection could vary with time. A sharp (by a factor of 3) decrease of the ejection rate at
te~60 s could be caused by a decrease of the outburst. The outburst could take place at
te~10 min because the rays were still observed close to the place of ejection in images at
t~500-700 s. Most of the ejected mass and crater volume could be caused by typical
cratering, but a considerable fraction of observed mass of the DI cloud could be due to
small particles ejected at the triggered outburst. Projections of velocities of most of
observed material ejected at te~0.2 s were about 7 km/s. As the first approximation, the
characteristic velocity of ejection at te~1-60 s can be considered to be proportional to te in
the power of -0.75 or -0.7, but the decrease of velocity could differ from this exponential
dependence. The fractions of observed material ejected (at te<6 s and te<15 s) with
vp>200 m/s and vp>100 m/s were estimated to be about 0.07 and 0.2, respectively, if we
consider only material observed during the first 13 min. These estimates are in accordance
with the previous estimates (100-200 m/s) of projection of velocity of the leading edge of
the DI dust cloud based on various ground-based observations and observations made by
space telescopes. The work was supported by NASA DDAP grant NNX08AG25G. [1] Ipatov
S.I., A'Hearn M.F., 2009, LPSC XL, 1022. [2] Ipatov S.I., A'Hearn M.F., 2009,
http://arxiv.org/abs/0810.1294 .
Introduction
• The mass of impactor was 370 kg. Impact speed was 10.3 km/s. The Deep Impact
collision with comet 9P/Tempel 1 was oblique: between 25o and 35o deg from the
surface horizontal.
• Moving particles were accelerated by gas. They can be sublimated and
fragmentated.
• Our studies of projections vp of velocities on the plane perpendicular to the line
of sight and relative amounts of particles ejected from Comet 9P/Temple 1 were
based on the images made by the Deep Impact cameras during the first 13
min after the impact. We considered velocities v of the particles that give the
main contribution to the brightness of the cloud of ejected material, i.e.,
mainly of particles with diameter d<3 μm.
• We analyzed the distances from a place of ejection to the levels of calibrated
physical surface brightness (CPSB, always in W m-2 sterad-1 micron-1) of a cloud
of ejected material on RADREV images.
• Real velocity can be greater by a factor of 1.5-2 than the projection of velocity on
the plane perpendicular to a line of sight.
• If the same amount of material moves from distance D1 from the place of impact
to distance D2, then the number of particles on a line of sight (and so the
brightness) decreases by a factor of D2/D1.
• Ejected particles become cooler with time and so they become less bright.
3
Series of DI images considered. In each series, the
intergration time and the size of image were the same. For series Ma, Ha, and
Hc, we analyzed the differences in brightness between a current image and that before
the impact. These series are marked by “(dif)”. For other series, we analyzed the
brightness in current images.
Series
Instrument
INTTIME, Size, pixels
seconds
EXPID
min, max
IMPACTM,
seconds
min, max
Ma (dif)
MRI
0.0514
64×64
9000910, 9000910
0.001, 5.720
Mb
MRI
0.3
1024×1024
9000942, 9001067
77.651, 802.871
Ha (dif)
HRI
0.1
512×512
9000910, 9000945
0.215, 109.141
Hb
HRI
0.6
1024×1024
9000931, 9001002
39.274, 664.993
Hc (dif)
HRI
0.6
512×512
9000927, 9000942
27.664, 86.368
Hd
HRI
0.1
1024×1024
9000934, 9000961
50.715, 251.525
He
HRI
0.5
1024×1024
9001017, 9001036
719.805, 771.95
4
Variation of the relative brightness Br of the
brightest pixel with time t. For construction of the figures, we
took into account that due to not ideal calibration, maximum brightness on
images made at different exposure times, but at approximately the same
time, can differ by tens of percent. It is considered that Br=1 at t=4 s. Besides
peaks during the first second (e.g., at 0.6 s), there was an increase of
brightness after 10 s.
5
(a) The left figure. Coordinates x and y of the brightest pixel relative to the position of the
brightest pixel in the MRI image at t=0.001 s (the place of impact) at different times after the
impact.
(b) The right figure. The angle (in degrees) of the direction from the brightest pixel at
t=0.215 s (close to the place of ejection) to the brightest pixel at a current time. The angle
corresponding to the direction of the impact was about -60o.
A jump of direction of ejection in images at t~12-13 s and te~10 s.
6
Contours corresponding to CPSB (calibrated physical
surface brightness) equal to 1, 0.3, 0.1, and 0.03, for MRI
images from series Mb made 77.651 (a), 138.901 (b), 191.53 (c), 311.055 (d),
351.043 (e), and 410.618 s (f) after the impact.
7
Rays of ejected material
• The excess ejection of material to a few directions (rays of ejected
material) was considerable during the first 100 s, took place during
several minutes, and was still observed in images at t~500-770 s. It
shows that the outburst continued up to ~10 min.
• Considerable excessive ejection (the outburst triggered by the
impact) began approximately at the same time te~10 s when the
direction from the place of ejection to the brightest pixel changed,
the peak brightness began to increase, and there was a local peak of
the rate of ejection.
• The sharpest rays were caused by material ejected at te~20 s.
• The upper-right excessive ejection (perpendicular to the direction of
impact ) began mainly at te~15 s (though there was some ejection at te~2
s), could reach maximum at te~25-50 s, could still be considerable at
te~100 s, but then could decrease, though it still could be seen at te~400
s. The value of te~15 s is correlated with the changes of the direction to
the brightest pixel at t~12-13 s.
• The upper bump of the outer contours is clearly seen at 66<t<665 s,
especially, in at t~200-350 s. The direction from the place of impact to
this bump is not far from the direction opposite to the impact direction.
8
Time variations of sizes L (in km) of regions inside contours of
CPSB=const. The curves have local minima and maxima that were used for analysis
of time variations of velocities. Based on the supposition that the same particles correspond to
different local maxima (or minima) of L (e.g., to values L1 and L2 on images made at t1 and t2),
we calculated the characteristic velocities v=(L1-L2)/(t1-t2) at te=t1-L1/v.
The number after a designation of the series in the figure legend shows the value of brightness
of the considered contour. For series Ma, we considered L as the distance from the place of
impact to the contour down in y-direction. For other series, we considered the difference
between maximum and minimum values of x for the contour.
9
Typical projections vmodel of velocities (in km/s)
on the plane
perpendicular to the line of sight at time te of ejection for the model when velocities
vmodel at te are the same as velocities vexpt=c×(t/0.26)-α of the edge of observed bright
region at time t. The distance from the place of ejection to the edge was used to find the
dependence of t on te. As the first approximation, the characteristic velocity at te>1 s
can be considered to be proportional to te-0.75 or te-0.7 (i.e. α~0.7-0.75; 0.71
corresponds to sand; 0.75, to the ejection mainly governed by momentum). The
values of vyobs and vxobs are based on analysis of local minima and maxima of
plots on the previous slide.
10
•
Models
of
ejection
Ejection of material from Comet Tempel 1 was studied based on analysis of the images made
by the Deep Impact cameras. Our studies presented in [1-2] and in this presentation
(including all the figures) were based on very simple calculations. Complicated models
depend on many factors, and we consider that it is better first to understand the general
features of the ejection. If we began our studies with complicated models, we could find at
what parameters, theoretical models better fits the observations, but might not understand the
role of the triggered outburst and that the DI ejection was far from the theoretical models.
• This year we began to construct and use more complicated models of ejections. The future
models will take into account several factors (including sublimation and destruction of
moving particles) and will simulate the observations of 3D cloud of ejected material. The
current model is still relatively simple, and it is a step to the construction of complicated
computer models of the DI ejection, which will allow one to understand better the process of
ejection and the role of different factors on the evolution and observable form of the ejected
cloud.
• A velocity of ejection is considered to be proportional to the time te of ejection in the power
of α. The time of ejection was divided into intervals corresponding to successive images. For
each interval (beginning from smaller times), based on the distances from the place of
ejection to the levels of brightness close to the place of ejection, we find the relative amount
dm of ejected material. Using also the distances to more far levels of brightness, we find α
that better fit the observations. As a result, we obtain the dependence of dm and α on te. The
preliminary results are in general accordance with the studies presented in [1-2].
[1] Ipatov S.I., A'Hearn M.F., 2009, LPSC XL, 1022.
[2] Ipatov S.I., A'Hearn M.F., 2009, http://arxiv.org/abs/0810.1294 .
11
The relationship between time of ejection and time when we consider the edge
of the bright region (left figure). Volume of the bright region (typically with
CPSB>3) at different times of images (right figure).
Considering that the time needed for particles to travel a distance Lr to the edge of
the region is equal to dt=Lr/vexpt (where vexpt=vp=c×(t/0.26)-α), we found the time te=tdt of ejection of material of the contour of the bright region considered at time t.
Based on the values of Lr, we calculated the values of the relative volume Vr=Lr3 of
material inside the bright region and the relative rate rte=Lr3×t-α of ejection (which is
proportional to Vr×vexpt(t)) for α=0.6, α=0.644, α=0.71, and α=0.75.
Based on these two figures, we obtain relationships of Vr and rte on te.
12
Relative rate of ejection at different times te of ejection
for the model in
which characteristic velocities of the edge of the observed bright region at time t are equal to
vexpt=c×(t/0.26)-α. The impact was a trigger of an outburst. At te~1-60 s the rate of ejection
was mainly greater than that for theoretical models, and instead of monotonic decrease of the
rate predicted by theoretical models, there was a local maximum of the rate at te~10 s with
typical projections of velocities vp~100-200 m/s. There was a sharp decrease of ejection
rate (and of the outburst) at te~60 s. Our studies do not contradict to a continuous ejection of
material during at least 10 minutes after the collision.
13
Relative amount fev of material ejected with velocities
greater than v vs. v for the model in which characteristic velocities of the edge
of the observed bright region at t are equal to v=vexpt=c×(t/0.26)-α for five pairs of α
and c. fev=1 for material ejected before te corresponding to the edge of the bright
region at t=803. At velocities of several tens of meters, the model amount is greater than
for theoretical estimates. Exponents of the velocity dependence of the relative volume fev of
material ejected with velocities greater than v, equal to -1, -1.23, -1.66, and -2, correspond to α
equal to 0.75, 0.71, 0.644, and 0.6, respectively. α=0.71 is for sand, and α=0.6 is for basalt.
14
Triggered outburst
• The rates and velocities of material ejected after the DI impact were
different from those for experiments and theoretical models. Holsapple and
Housen (2007, Icarus 187, 345-356) concluded that the difference was
caused by vaporization of ice in the plume and fast moving gas. In our
opinion, the greater role in the difference could be played by the outburst
triggered by the impact (by the increase of ejection of bright particles), and it
may be possible to consider the ejection as superposition of the normal
ejection and the triggered outburst. There was not only the increase of
velocities compared to theoretical models, but also there was the increase
of the rate of ejection.
• Due to the outburst, at te~1-60 s the rate of ejection was mainly greater
than that for theoretical models. During this time the fraction of ejected icy
particles could be greater than that at other time of ejection. The outburst
was maximum at time te of ejection ~10 s. There could be a sharp decrease
of the outburst at te~60 s.
• The increase of the fraction of icy material caused the increase of the
ejection rate and the initial velocities. Evaporation and sublimation of this ice
increased velocities of moving particles. The contribution of the outburst to
the brightness of the cloud could be considerable, but its contribution to the
15
ejected mass could be relatively small.
Conclusions
• Our studies of the projections vp of velocities of ejected material onto the plane
perpendicular to the line of sight and the relative amounts of particles ejected from
Comet 9P/Temple 1 were based on the images made by the Deep Impact cameras
during the first 13 min after the impact. We considered velocities of the particles that
give the main contribution to the brightness of the cloud of ejected material, i.e.
mainly of particles with diameter d<3 μm.
• There was a maximum of production of observed ejected
material at time of ejection te~0.6 s. There was a local maximum of
the rate at te~10 s with typical projections of velocities vp~100-200
m/s. At 1<te<3 s and 8<te<40 s the estimated rate of ejection of
observed material was essentially greater than that for theoretical
monotonic exponential decrease. Such difference was caused by
that the impact was a trigger of an outburst. There could be a
sharp decrease of the outburst at te~60 s. Our studies do not allow one to
estimate accurately the time of the end of ejection. They do not contradict to a
continuous ejection of material during at least 10 minutes after the collision. Material
of the nucleus ejected during the first second could be more solid than that ejected
16
after the first second.
Conclusions
•
•
Projections of velocities of most of observed material ejected at te~0.2 s were about 7 km/s.
As the first approximation, the time variations of characteristic velocity at 1 s < te < 60 s
can be considered to be proportional to te-0.75 or te-0.71, but they could differ from this
exponential dependence. The fractions of observed material ejected (at te≤6 s and te≤15
s) with vp≥200 m/s and vp≥100 m/s were estimated to be about 0.07 and 0.2,
respectively, if we consider only material observed during the first 13 min. These
estimates are in accordance with the previous estimates (100-200 m/s) of projection of
velocity of the leading edge of the DI dust cloud based on various ground-based
observations and observations made by space telescopes.
The excess ejection of material to a few directions (rays of ejected material) was
considerable during the first 100 s, and it was still observed in images at t~500-770 s.
It shows that the outburst continued after 60 s and could be at te~10 min.
Considerable excessive ejection began approximately at the same time te~10 s when
the direction from the place of ejection to the brightest pixel changed by 50o, the peak
brightness began to increase, and there was a local peak of the rate of ejection. The
direction from the place of impact to the brightest pixel was mainly close to the direction of
the impact in images made during the first 10-12 s, then quickly changed by about 50o, and
then slowly became closer to the direction of the impact. The sharpest rays were caused by
material ejected at te~20 s. In particular, there were excessive ejections, especially in
images at t~25-50 s after the impact, in directions perpendicular to the direction of the 17
impact. Directions of excessive ejection could vary with time.