DPS 2009, 20.06, October 6, 2009

Models of the ejection of material from Comet Tempel 1

caused by the Deep Impact experiment

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/dps2009-deep-impact.ppt or http://faculty.cua.edu/ipatov/

present.htm See http://arxiv.org/abs/0810.1294 for details

Series Instru-ment

INTTIME, seconds

Size, pixels EXPID IMPACTM, seconds

min, max min, maxMa (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, 771.952

We analyzed several series of DI images. In each series, the integration 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. Observed brightness of the cloud of ejected material was mainly due to particles with diameters d<3 micron, and we discuss mainly ejection of such particles.

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 a small increase of

relative brightness of the brightest pixel after 10 s.

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(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.

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Contours corresponding to CPSB (calibrated physical surface brightness) equal to 1, 0.3, 0.1, and 0.03, for series Mb.

Our studies were based mainly on analysis of distances from the place of ejection to such contours. The bumps on the contours correspond to rays of excessive ejection.

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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 to a few directions 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. These features could be caused by the outburst triggered by the impact.

• 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. 6

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 estimates of velocities at several moments of time. 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.

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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.

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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 [1-3] and in this presentation (including all the figures) were based on very simple calculations.

• Considering that the time needed for particles to travel a distance Lr to the edge of the bright region is equal to dt=Lr /vexpt (where vexpt(t)=c×(t/0.26)-α ), we find the time te=t−dt of ejection of material of the contour of the bright region considered at time t.

• The volume Vol of a spherical shell of radius Lr and width h is proportional to Lr2h, and the number

of particles per unit of volume is proportional to rte∙(Vol∙v)-1, where v is the velocity of the material. Here rte corresponds to the material that was ejected at te and reached the shell with Lr at time t. The number of particles on a line of sight, and so the brightness Br, are approximately proportional to the number of particles per unit of volume multiplied by the length of the segment of the line of sight inside the DI cloud, which is proportional to Lr. Actually, the line of sight crosses many shells characterized by different rte, but as a first approximation we supposed that Br is proportional to rte(v∙Lr)-1. For the edge of the bright region, Br≈const. Considering v=vexpt, we calculated the relative rate of ejection as rte=Lr∙t-α.

• Based on this dependence of rte on time t and on the obtained relationship between t and te, we constructed the plots of dependences of rte on te. These rates were used for construction of plots of the relative volume of ejecta launched before te vs. te and of the relative volume of ejecta with velocity vp>vmodel vs. vmodel .

• [1] Ipatov S.I., A'Hearn M.F., 2008, http://arxiv.org/abs/0810.1294 . • [2] Ipatov S.I., A'Hearn M.F., 2009, LPSC XL, 1022. • [3] Ipatov S.I., A'Hearn M.F., 2009, Proc. IAU Symp. 263, submitted. 9

Models of ejection

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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.We suppose that at distance L, brightness Br=rte/(L×ve), where L=(t-te)×cve×te

-α, and velocity of ejection ve=cve×te

-α . The time of ejection was divided into intervals corresponding to successive images. Using the formula for L, we find te corresponding to L3 on the image made at ti, where L3 is the value of L for CPSB=3 on the DI image. This value of te can be outside of (ti-1, ti), and it is used for calculation of rte=3L3×cve×te

-α. Calculations are made for many values of α from some interval, and cve is chosen to satisfy our estimates of ve at several te. The value of α at te is chosen in so that the ratio of model brightness at L3 and L1 is close to 3, where L1 is the value of L for CPSB=1 on the DI image. As a result, considering images made at different times (beginning from smaller times), we obtain the dependence of rte and α on te. The preliminary results are in general accordance with the previous studies.

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 1<te<3 s and 10<te<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 at te~60 s. Our studies do not contradict to a continuous ejection of material during at least 10 minutes after the collision.

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Relative amount fev of observed 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.

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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 or/and the normal ejection at te~60 s. Duration of the outburst (up to 30-60 min) could be longer than that of the normal ejection (a few minutes).

• 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 total ejected mass could be relatively small.

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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 ejection at te~60 s. Duration of the outburst (up to 30-60 min)

could be longer than that of the normal ejection (a few minutes). At the outburst, the ejection could be from entire surface of the crater, while the normal ejection was mainly from its edges. Material of the nucleus ejected during the first second could be more solid than that ejected after the first second. 14

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 0.13-0.15 and 0.22-0.25, 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 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 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 impact. Directions of excessive ejection could vary with time.

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