1. Session JD5 “From meteors and meteorites to their parent bodies”. August 23, 2012 Location of the Upper Border of the Main Cavity Excavated after the Deep Impact Collision Sergei I. Ipatov 1 Catholic University of America, Washington, DC, USA. 2 Space Research Institute, Moscow, Russia * Present address: Alsubai Est. for Scientific Studies, Doha, Qatar (siipatov@hotmail.com, http://faculty.cua.edu/ipatov/) This presentation can be found on http://faculty.cua.edu/ipatov/iau2012cavities.pptsiipatov@http://faculty.cua.edu/ipatov/http://faculty.cua.edu/ipatov/iau2012cavities.ppt

2. INTRODUCTION. Outburst. On July 4, 2005 370 kg Deep Impact impactor collided with Comet 9P/Tempel 1 at velocity of 10.3 km/s (A’Hearn et al. 2005). It was an oblique impact, and the angle above the horizon was about 20-35 o. Evolution of the cloud of ejected material was observed by Deep Impact (DI) cameras, by space telescopes (e.g. Rosetta, Hubble Space Telescope, Chandra, Spitzer), and by over 80 observatories on the Earth. Ipatov & A’Hearn (2011) analysed images of the cloud of material ejected after this collision. Based on analysis of the images made by the DI cameras during the first 13 minutes, Ipatov & A’Hearn studied the process of ejection of material and concluded that, besides the normal ejection, there was a triggered outburst of particles with diameters mainly less than a few microns. The outburst was considerable at 8-60 s after the impact. It increased the duration of ejection and mean velocities of observed ejected particles (compared with the normal ejection). Mean velocities of small observed particles almost did not change with time t e after the impact (and were about 100 m/s) at 10<t e <20 s. Ipatov & A’Hearn (2011) supposed that the outburst was caused by the ejection of material from cavities containing dust and gas under pressure. Velocities of such `fast` outburst particles could be mainly ~100 m/s (such velocities were obtained at various observations of the leading edge of the DI cloud). 2

3. SeriesInstru- ment INTTIME, seconds Size, pixelsEXPIDIMPACTM, seconds min, max Ma (dif)MRI0.051464×649000910, 90009100.001, 5.720 MbMRI0.31024×10249000942, 900106777.651, 802.871 Ha (dif)HRI0.1512×5129000910, 90009450.215, 109.141 HbHRI0.61024×10249000931, 900100239.274, 664.993 Hc (dif)HRI0.6512×5129000927, 900094227.664, 86.368 HdHRI0.11024×10249000934, 900096150.715, 251.525 HeHRI0.51024×10249001017, 9001036719.805, 771.95 3 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.

4. 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. 4

5. 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 even close to the place of ejection. It shows that the outburst could continue up to ~10 min. Considerable excessive ejection to a few directions (some rays) began approximately at the same time t e ~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 t e ~20 s. The upper-right excessive ejection (perpendicular to the direction of impact) began mainly at t e ~15 s (though there was some ejection at t e ~2 s), could reach maximum at t e ~25-50 s, could still be considerable at t e ~100 s, but then could decrease, though it still could be seen at t e ~400 s. The value of t e ~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 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. 5

6. Time variations in sizes L (in km) of regions inside contours of CPSB=const. The number after a designation of the series in the figure legend shows the value of brightness of the considered contour. The curves have local minima and maxima that were used for estimates of velocities of particles at several moments in time. Based on the supposition that the same particles correspond to local maxima (or minima) of L at different CPSB (e.g., to values L 1 and L 2 on images made at t 1 and t 2 ), we calculated the characteristic velocities v=(L 1 -L 2 )/(t 1 -t 2 ) of ejected particles at time of ejection t e =t 1 - L 1 /v. 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. 6

7. Typical projections v model of velocities (in km/s) on the plane perpendicular to the line of sight at time t e of ejection for the model for which velocities v model at t e are the same as velocities v expt =c×(t/0.26) -α of particles at the edge of observed bright region at time t. The values of vy obs and vx obs are based on analysis of local minima and maxima of plots presented on the previous slide. The distance from the place of ejection to the edge was used to find the dependence of t on t e. As the first approximation, the characteristic velocity of particles at t e >1 s can be considered to be proportional to t e -0.75 or t e -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 vymin and vxmin show the minimum velocities of particles needed to reach the edge of the bright region (in an image considered at time t) from the place of ejection moving in y or x-direction, respectively. 7

8. Calculations of the relative rate of ejection Considering that the time needed for particles to travel a distance L r to the edge of the bright region is equal to dt=L r /v expt (where v expt (t)=c×(t/0.26) -α ), we found the time t e =t−dt of ejection of material of the edge of the bright region considered at time t. The volume V ol of a spherical shell of radius L r and width h is proportional to L r 2 h, and the number of particles per unit of volume is proportional to r te ∙(V ol ∙v) -1, where v is the velocity of the material. Here r te corresponds to the material that was ejected at t e and reached the shell with L r 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 L r. Actually, the line of sight crosses many shells characterized by different r te, but as a first approximation we supposed that Br is proportional to r te (v∙L r ) -1. For the edge of the bright region, Br≈const. Considering v=v expt, we calculated the relative rate of ejection as r te = c ∙L r ∙t -α. 8

9. Relative rate of ejection at different times t e of ejection for the model in which characteristic velocities of particles constituting the edge of the observed bright region at time t are equal to v expt =c×(t/0.26) -α. At 1<t e <3 and 8<t e <60 s, the plot of time variation in the estimated rate rte of ejection of observed material was essentially greater than the exponential line connecting the values of rte at 1 and 300 s. (The exponential monotonic decrease in the rate is predicted by theoretical models.) At t e ~10 s there was an increase in the rate of ejection of particles (with typical projections of velocities v p ~100 m/s), and there was a sharp decrease in the rate rte at t e ~60 s. Such variations in rte can be mainly due to the triggered outburst. Our studies do not contradict to a continuous ejection of material during at least 10 minutes after the collision. 9

10. Relative amount f ev of observed material ejected with velocities greater than v vs. v for the model VExp in which characteristic velocities of particles at the edge of the observed bright region in an image at time t are equal to v=v expt =c×(t/0.26) -α for five pairs of α and c. f ev =1 for material ejected before the time t e803 of ejection of particles located at the edge of the bright region in an image made at t=803 s. Compared to theoretical models, there was an excess of ejection of particles at velocities of several tens of meters per second. For theoretical models, exponents of the velocity dependence of the relative volume f ev 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). 10

11. Acceleration of particles Hosapple & Housen (2007) supposed that ejected particles could be accelerated by the dust-gas interaction. Such acceleration could be important during time intervals of about several hours. Ipatov & A’Hearn (2011) made their conclusions basing on analysis of variations in brightness in images made during the first 13 minutes and considering distances R from a place of ejection between 1 and 10 km. They concluded that particles could not increase their velocities by more than a few m/s during not more than a few minutes, when the particles moved at R between 1 and 10 km. Ipatov and A’Hearn analysed the brightness of the DI cloud at such distances and did not consider a plume base at R<1 km as Richardson et al. (2007). In many DI images, the region corresponding to R<1 km consisted mainly of saturated pixels (in 8- bit images received from the DI spacecraft, the brightness of most saturated pixels equaled to 255). 11

12. Triggered outburst vs. a model of a layered target In our opinion, it is difficult to explain the time variations in the brightness of the DI cloud at 1<R<10 km without consideration of the triggered outburst with velocities of about 100 m/s. Several authors (e.g. Richardson et al. 2007) suppose that variation in brightness of the DI cloud was caused by variation in particle size distribution due to striking a layered target. In our opinion, the model of a layered target plays some role in explanation of the variation in brightness of the DI cloud, but it cannot explain all details of such variation (e.g., why at the same time ~10 s there was the jump in the direction from the place of ejection to the brightest pixel of the cloud image by 50 deg, the increase in the rate of ejection of small particles, and the increase in brightness of the brightest pixel; why at the same time of ejection t e ~60 s, there was the sharp decrease in the rate of ejection of small particles, and the direction from the place of ejection to the brightest pixel in an image returned to that at 1<t<12 s; why mean ejection velocities of observed particles were almost the same at t e ~10- 20 s, etc.). 12

13. Size of the Deep Impact crater Based on studies of ejecta plume, Richarson et al. (2007) concluded that a transient crater of not more than 85–140 m (but not less than 22–26 m) diameter, formed in not more than 250–550 s. Estimates of a crater diameter made by Busko et al. (2007) on the basis of analysis of DI images were about 150–200 m. Schultz et al. (2007) obtained a little wider range for the diameter: 130–220 m. On 2011 February 14, the Stardust spacecraft made photos of the crater formed after the DI impact. Peter Schultz et al. (2012) concluded that the diameter of the transient DI crater was about 150-200 m. Melosh and Richardson supposed that there is an approximately 50 meter diameter depression that most likely represents the DI crater. The crater size observed by Stardust spacecraft could be different from the transient crater size just after its formation. This is because the sublimation process as well as various modification processes changed the crater size after its formation. On the image made by the Stardust spacecraft (http://stardustnext.jpl.nasa.gov/Multimedia/popups/Tempel1ImageSite. html), the diameter of the brightest part of the ring zone of ejected material around the crater is about 90-100 m. The diameters of the inner and outer edges of the ring zone are ~60-70 m and ~130-140 m, respectively. The ring zone may correspond to ejected material, and the diameter of an excavation zone might not exceed 100 m. 13

14. CAVITIES CONTAINING DUST AND GAS UNDER PRESSURE IN COMET 9P/TEMPEL 1 It is considered (e.g. Croft 1980; Melosh 1989) that ejected material originates from an excavation cavity which has a geometry distinct from a transient crater. The excavation cavity and the transient crater have the same diameter d tc, but the depth d he of the excavation cavity is ~0.1d tc, or about one-third of the transient crater depth, and, in the case of simple bowl-shaped craters, about one-half of the depth of the final apparent crater. For example, d he ~10 m at d tc =100 m. For some craters, Croft (1980) considered the ratio d he /d tc to be in the range [0.09, 0.17]. For theoretical models (e.g. Holsapple & Housen 2007), during the most time of crater formation (except for initial and final stages), the diameter d c of a crater at time t e elapsed after the impact is proportional to t e γ, where γ is about 0.25-0.4. In their table 4, Holsapple & Housen (2007) considered models at 0.29≤γ≤0.36. 14

15. The depth of the DI crater at the beginning of excavation of the main cavity According to fig. 12 in (Holsapple 1993), diameter d c of a crater grows faster at the initial stage (which duration is usually less than 0.1T e, where T e corresponds to the end of the stage of proportionality of d c to t e γ ). Ipatov & A’Hearn (2011) concluded that outburst and excavation of a large cavity began at ~8 s after the DI collision. Supposing the diameter d c of a crater to be proportional to t e γ, we (Ipatov 2012b) estimated the lower limit of the depth, d cavDI, of the DI crater at the time of the beginning of excavation of the main cavity t eb =8 s as d cavmin =d he ×(t eb /T e ) γ. At d he =0.1d tc, the value of d cavmin equals d cmn =0.1d tc ×(t eb /T e ) γ. At t eb =8 s, the values of d cmn for three values of γ are presented in Table 1. The real value of d cavDI is greater by some value d h1 than d cmn because, during the short initial stage, the real growth of the crater is greater than that for the model used for calculation of the lower limit d cmn. We suppose that the difference d h1 can be about 1 m. In Table 1 we consider that d cavDI =0.1d tc ×(t eb /T e ) 0.3 +d h1, where d h1 =1 m. 15

16. Table 1. The distance, d cavDI, between the pre-impact surface of the comet and the upper border of the cavity excavated at t eb =8 s for several values of the diameter, d tc, of the DI transient crater and the time, T e, of formation of the crater. The minimum value, d cmn =0.1d tc (t eb /T e ) γ, of the distance at three values of γ is also given. The value of d cmn at γ=0.3 was used for estimates of d cavDI. d tc [m]50100150200 T e [s] 230330500660 d cmn [m] for γ=0.25 2.23.94.35.3 d cmn [m] for γ=0.3 1.83.34.35.3 d cmn [m] for γ=0.4 1.32.32.93.4 d cavDI [m] 3456 16

17. The depth of the DI crater at the beginning of excavation of the main cavity Based on the above estimates, we can suppose that d cavmin was probably not less than 3 m at d tc =100 m. During the intermediate stage of crater formation (when diameter d c of a crater is proportional to t e γ ), time usually increases by more than a factor of 10 (see fig. 12 in Holsapple 1993). Therefore, during the time interval [0.1T e, T e ] (we consider T e as the time that corresponds to the end of the stage of proportionality of d c to t e γ ) d c increases by a factor of 10 γ, where 10 γ is 1.8-2.5 at 0.25≤γ≤0.4. These estimates show that at t eb =8 s and T e >80 s (this inequality is fulfilled for the DI crater) the maximum value, d cavmax, of d cavDI does not exceed d he /10 γ +d h1, which is in the range [0.4d he +d h1, 0.56d he +d h1 ], that is d cavmax ≤0.056d tc +d h1 at d he /d tc =0.1 (e.g. d cavmax ≤0.05d tc +d h1 for γ=0.3). At T e =80 s and γ=0.3, the value of 0.05d tc is greater by about 2 and 5 m than the values of d cmn presented in Table 1 for d tc =100 m and d tc =200 m, respectively. Based on the values of d cavDI presented in Table 1, we concluded that the distance between the pre-impact surface of the comet and the upper border of the main excavated cavity is about 5-6 m for the estimates (150-200 m) of the diameter of the DI transient crater presented by Schultz et al. (2012). The estimated distance is 4 m for the diameter of 100 m. 17

18. CAVITIES IN DIFFERENT COMETS The distance between the pre-impact surface of Comet 9P/Tempel 1 and the upper border of the largest excavated cavity equal to ~5 m, and sizes of particles inside the cavities of a few microns are in a good agreement with the results obtained by Kossacki & Szutowicz (2011). These authors made calculations for several models of the explosion of Comet 17P/Holmes. They concluded that the nonuniform crystallization of amorphous water ice itself is probably not sufficient for an explosion, which could be caused by a rapid sublimation of the CO ice leading to the rise of gas pressure above the tensile strength of the nucleus. In their models, the initial sublimation front of the CO ice was located at a depth of 4, 10, or 20 m, and calculations were finished when the CO pressure exceeded the threshold value 10 kPa. It was shown that the pressure of CO vapor can rise to the threshold value only when the nucleus is composed of very fine grains, a few microns in radius. Our estimates of location of cavities in Comet 9P/Tempel 1 and the studies of the initial sublimation front of the CO ice in Comet 17P/Holmes made by Kossacki & Szutowicz show that the upper borders of relatively large cavities containing dust and gas under pressure can be located at a depth of 3-20 m below surfaces of different comets. 18

19. Sources of gas pressure Therefore, probably, the more time a comet has spent close to the Sun, the greater are distances from the surface of the comet to the upper borders of cavities containing dust and gas under considerable pressure. It is usually considered that the main sources of gas pressure are the water ice sublimation, the sublimation of a more volatile ice such as CO or CO 2 at a lower temperature than required for water ice, and the crystallization of amorphous ice in the interior of porous nucleus. Other discussed potential mechanisms of outbursts include the polymerization of hydrogen cyanide HCN, the thermal stresses, the anneling of the amorphous water ice, and meteoritic impacts (see, e.g., Gronkowski & Sacharczuk 2010; more references are presented by Ipatov 2012a). The porous structure of comets provides enough space for sublimation and testifies in favor of existence of cavities. The projection of velocity of the leading edge of the DI cloud (onto the plane perpendicular to the line of sight) was about 100-200 m/s (see references in Ipatov & A’Hearn 2011) and is typical for outburst particles ejected from comets. According to Feldman et al. (2007), at the 2005 June 14 natural outburst from Comet Tempel 1, velocities of ejection were 60-145 m/s. Sarugaku et al. (2010) obtained that the dust cloud caused by the outburst from Comet 217P/LINEAR expanded at a velocity of 120-140 m/s. The similarity of velocities of particles ejected at the triggered and natural outbursts (~100 m/s) shows that these outbursts could be caused by similar internal processes in comets. 19

20. Conclusions At time of ejection t e ~10 s, there was a local maximum of the rate of ejection of observed particles (mainly with diameter d<3 μm) with typical projections of velocities v p ~100 m/s. At 1<t e <3 s and 8<t e <60 s the estimated rate of ejection of observed material was essentially greater than that for theoretical monotonic exponential decrease. Such difference could be caused by that the impact was a trigger of an outburst. At t e ~55-72 s, the ejection rate sharply decreased and the direction from the place of ejection to the brightest pixel quickly returned to the direction that was before 10 s. It could be caused by a sharp decrease of the outburst that began at t e ~10 s. Analysis of observations of the DI cloud and of outbursts from different comets testifies in favor of that there can be large cavities with material under gas pressure a few meters below a considerable fraction of comet’s surface. 20

21. Conclusions The upper border of the largest cavity excavated during ejection of material after the collision of the impact module of the Deep Impact spacecraft with Comet 9P/Tempel 1 could be located at a depth of about 5-6 metres below the pre-impact surface of the comet if the diameter of the DI transient crater was about 150-200 m, as presented by Schultz et al. (2012). The estimated depth was 4 m at the diameter equaled 100 m. The largest cavity excavated after the DI collision could be relatively deep because a considerable excess ejection lasted during ~50 s. These estimates of the depth are in accordance with the depth (4-20 m) of the initial sublimation front of the CO ice in the models of the explosion of Comet 17P/Holmes considered by Kossacki & Szutowicz (2011). Our studies testify in favour of that cavities with dust and gas under pressure located a few metres below surfaces of comets can be common. 21

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