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IAU GA, RIO, Symp. 263, #495 Deep Impact Ejection from Comet 9P/Tempel 1 as a triggered outburstSergei I. IpatovCatholic University of America, USA. The work was initiated at University of Maryland(firstname.lastname@example.org, http://faculty.cua.edu/ipatov/, http://www.dtm.ciw.edu/ipatov) and Michael F. A’Hearn University of Maryland, College Park, USAThe 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
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.  Ipatov S.I., A'Hearn M.F., 2009, LPSC XL, 1022.  Ipatov S.I., A'Hearn M.F., 2009, http://arxiv.org/abs/0810.1294 .
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.
Variation of the relative brightness Br of the brightest pixel with time t. Forconstruction 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.
(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.
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.
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.
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)-αof 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.
 Ipatov S.I., A'Hearn M.F., 2009, LPSC XL, 1022.
 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 Lrto the edge of the region is equal to dt=Lr/vexpt (where vexpt=vp=c×(t/0.26)-α), we found the time te=t-dt 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.
Relative rate of ejection at different times te of ejectionfor 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.
Relative amount fev of material ejected with velocities greater than vvs.vfor 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)-αfor 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.