JENAM 2011, July 8, 2011. S2-9

Cavities as a source of outbursts from comets

Sergei I. Ipatov 1Catholic University of America, USA.

2Space Research Institute, Moscow, Russia

(siipatov@hotmail.com, http://faculty.cua.edu/ipatov/) This presentation can be found on http://faculty.cua.edu/ipatov/jenam2011cavities.ppt

Introduction• On July 4, 2005 370 kg 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 20-35o. 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.

• The values of the projection of the velocity vle of the leading edge of the dust cloud of ejected material onto the plane perpendicular to the line of sight were about 100-200 m/s for observations made 1-40 h after impact.

• Jorda et al. (2007) concluded that particles with d<2.8 μm represent more than 80% of the cross-section of the observed dust cloud. The velocities discussed in our presentation correspond mainly to particles with d<3 μm, which probably constitute not more than 7% of the total ejected material.

• The total mass of ejected dust particles with diameter d less than 2, 2.8, 20, and 200 μm was estimated to be about 7.3×104–4.4×105, 1.5×105–1.6×105, 5.6×105-8.5×105, and 106-1.4×107 kg, respectively.

• Our studies were based on analysis of the images made by Deep Impact (DI) cameras during the first 13 minutes.

The main aims of our studies: Time variations in velocities and relative amount of material ejected from Comet 9P/Tempel 1. The role of a triggered outburst in the ejection. Excessive ejection in a few directions (rays of ejected material). Cavities in comets as sources of outbursts. 2

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, 771.953

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.

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 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 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 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

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 at several moments in 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. 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 for which velocities vmodel at te are the same as velocities vexpt=c×(t/0.26)-α of particles at the edge of observed bright region at time t.

The values of vyobs and vxobs are based on analysis of local minima and maxima of plots on the previous slide.

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 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

Calculations of the relative rate of ejection

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 Lr

2h, 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=c∙Lr∙t-α.

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Relative rate of ejection at different times te 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 vexpt=c×(t/0.26)-α. At 1<te<3 and 8<te<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.) There was a local maximum of the rate at te~10 s with typical projections of velocities vp~100 m/s, and there was a sharp decrease of rte at te~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.

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Relative amount fev 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=vexpt=c×(t/0.26)-α for five pairs of α and c. fev=1 for material ejected before the time te803 of ejection of particles located at the edge of the bright region

in an image made at t=803 s. At velocities of several tens of meters per second, the model amount is greater than for theoretical estimates. For theoretical models, 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).

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‘FAST’ and ‘SLOW’ OUTBURSTS• 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). • The ‘fast’ outburst could be caused by ejection of material under gas pressure.

The ‘slow’ outburst ejection could be similar to the ejection from a ‘fresh’ surface of a comet and could be noticeable at 30-60 min after the formation of the crater. • The jump of the contribution of the DI outburst to the brightness of the DI cloud

began at te~8 s. The ejection rate at te=10 s was greater by a factor of 1.4 than that obtained at the supposition that the previous decrease in the rate was prolonged with the same exponent. This factor may characterize the increase of the role of the outburst in the ejection of small particles if at that time veo~ve.

•There could be a sharp decrease in the outburst at te~60 s.•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 because typical sizes of particles ejected at the outburst probably were smaller than those ejected at the normal ejection. 11

Velocities of ejected particles•Projections of velocities of most of observed material ejected at te~0.2 s were

about 7 km/s. Analysis of DI observations that used different approaches showed

that at 1<te<100 s the time variations in the projections vp of characteristic velocity onto the plane perpendicular to the line of sight can be considered to be approximately proportional to te

-α with α~0.7-0.75.

•For the VExp model with vp proportional to te-α at any te>1 s, the fractions of

observed material ejected (at te≤6 and te≤15 s) with vp≥200 and vp≥100 m/s were estimated to be about 0.1-0.15 and 0.2-0.25, respectively, if we consider only material observed during the first 13 min.

•The ‘fast’ outburst with velocities ~100 m/s probably could last for at least several tens of seconds, and it could significantly increase the fraction of particles ejected with velocities ~100 m/s, compared with the estimates for the VExp model and for the normal ejection.

•Destruction, sublimation, and acceleration of particles did not affect much on our estimates of velocities because we considered the motion of particles along a distance of a few km during not more than a few minutes.

•During the considered motion of particles with initial velocities vp≥20 m/s, the increase of their velocities due to the acceleration by gas did not exceed a few m/s. 12

Cavities with material under gas pressure

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 below a considerable fraction of a comet’s surface. Internal gas pressure (e.g. due to the sublimation of the CO ice and/or to the crystallization of amorphous ice) and the material in the cavities can produce natural and triggered outbursts and can cause splitting of comets. •The outburst ejection of material from a cavity could be greater for a specific direction. Therefore, its role in the direction from the place of ejection to the brightest pixel could be greater than in the total ejection rate. 13

Location of the upper border of the main excavated cavity

•Our estimates testify in favor of the location of the upper border of the main excavated cavity at a depth dcav~5-10 meters. For example, at time teb=8 s, the depth of a crater dcr=df×dh×(teb/Te)γ ≈12 m for df=150 m, dh=0.25, Te=400 s, and (Te/teb)γ=10γ=2; for the same data and df=100 m, dcr≈8 m. For theoretical models (Holsapple & Housen 2007), radius of a crater is proportional to te

γ, where γ is about 0.25-0.4. For small cavities excavated at te=1 s, the value of dcr (~4-6 m) was smaller by a factor of 8γ (i.e. by about a factor of 2) than at te=8 s.

•The distance dcav between the pre-impact surface of the comet’s nucleus and the upper border of the cavity could be smaller than dcr because the excavated cavity could be located at some distance from the center of the crater (not below the center). On the other hand, due to cracks caused by the impact, the outburst from the cavity could begin before excavation of the upper border.

•The distances from the upper borders of large cavities to the surface of a comet of about 5-10 m, and sizes of particles inside the cavities of a few microns are in a good agreement with the results obtained by Kossacki and Szutowicz (Icarus, 2011, v. 212, 847-857).

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Conclusions • At time of ejection te~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 vp~100 m/s. At 1<te<3 s and

8<te<50 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.

• At te~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 te~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 below a considerable fraction of comet’s surface. The upper boarder of relatively large cavities can be located at about 5-10 meters below the surface of the comet. 15

Results of our studies are presented in the below papers:[1] Ipatov S.I. and A’Hearn M.F., The outburst triggered by the Deep Impact collision with Comet Tempel 1, Mon. Not. R. Astron. Soc., 2011, v. 414, N 1, 76-107. http://faculty.cua.edu/ipatov/di-mnras.pdf, http://arxiv.org/abs/0810.1294.[2] Ipatov S.I., Cavities as a source of outbursts from comets (Chapter 3), In “Comets: Characteristics, Composition and Orbits”, Nova Science Publishers, 2011, in press, http://faculty.cua.edu/ipatov/cavities.pdf , http://arxiv.org/abs/1103.0330 .

[3] Ipatov S.I. and A'Hearn M.F., Deep Impact ejection from Comet 9P/Tempel 1 as a triggered outburst, Proc. IAU Symp. S263 "Icy bodies in the Solar System“, Cambridge University Press, 2010, pp. 317-321. http:/faculty.cua.edu/ipatov/di-iau.pdf , http://arxiv.org/abs/1011.5541 .

A full list of Ipatov’s publications (and copies of most of them) can be found on http://faculty.cua.edu/ipatov/list-publications.htm .• AcknowledgementsThis research was supported in part by NASA through the American Astronomical Society's Small Research Grant Program. 16