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Shock wave phenomena and plasma effects caused by Shoemaker-Levy 9 hypervelocity impact with Jovian atmosphere
Int. J. Impact Engng, Vol. 20, pp.431-442, 1997 © 1997 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0734-743X/97 $17.00+0.00
Pergamon
SHOCK WAVE PHENOMENA AND PLASMA EFFECTS CAUSED BY SHOEMAKER-LEVY 9 HYPERVELOCITY IMPACT WITH JOVIAN ATMOSPHERE A. V. IVLEV, V. E. FORTOV, and B. A. KLUMOV High Energy Density Research Center, Russian Academy of Science, 127412, Izhorskaya 13/19, Moscow, Russia
Summary-Impact of the Shoemaker-Levy 9 comet with Jupiter has been accompanied by a great number of various effects in the atmosphere, ionosphere and magnetosphere of the planet. Among the most interesting effects are bursts of radiation registered in a wide spectral range during the impact of cometary fragments, the generation of giant gaseous plumes and the formation of large-scale long-livingvortex structures in the Jovian atmosphere. In the present paper the main observational results obtained during about thirty minutes after the fragments collision with Jupiter are discussed; a unified physical model is suggested which explains consistently the basic observational data. INTRODUCTION In July 1994 the collision of the Shoemaker-Levy 9 comet (SL9) with Jupiter took place. SL9 impact has been accompanied by a great number of various effects in the atmosphere, ionosphere and magnetosphere of Jupiter. Among the most interesting effects are bursts of radiation registered in a wide spectral range during the cometary fragments impact, the generation of giant gaseous plumes, and the formation of large-scale long-living vortex structures in the Jovian atmosphere. Following encounter with Jupiter, many papers have appeared that consider theoretical aspects of this event. The main part of these papers are devoted to modelling gasdynamic processes during SL9 fragments braking in the atmosphere [1-6]. In the majority of these papers, methods of direct numerical modeling were used, which allowed a sufficiently accurate description of the braking and destruction of cometary fragments. However, an adequate description of large-scale gasdynamic processes caused by a powerful energy output during fragments braking has met serious numerical difficulties (for example, it is impossible to provide the sufficient space discretization for calculations in a three-dimensional region with a linear size of some 100 km). In order to describe large-scale effects, it is necessary to propose a semi-quantitative analytical model, in which the results of numerical calculations of fragments braking are taken as the input data. The analysis of the results obtained by using both numerical and analytical models enables comparison with observational data and gives preference for one of the initial models. In this paper the main observational results obtained during about thirty minutes after the fragments collision with Jupiter are discussed; a unified physical model is suggested which explains consistently the basic observational data.
ANALYTICAL
M O D E L OF T H E SL9 I M P A C T W I T H J U P I T E R
Fig. 1 shows a typical dependence of the comet energy output along the trajectory on the altitude. These curves were obtained using a simple hydrodynamic model [7] that describes the body deformation assuming the constancy of its volume (without ablation) under the 431
A.V. IVLEVet al.
432
action of aerodynamic drag force. The difference of the results of this simple model from data obtained using numerical modeling of braking and destruction of cometary fragments with different form, density and strength [4] turns out to be not very significant until the moment when strong evaporation and destruction of the fragment material begins. There is nothing specially surprising in that the simple model [7], which reduces to four ordinary differential equations, provides the acceptable accuracy of description. At an early stage of the fragment motion in atmosphere, when aerodynamic load does not noticeably affect its motion and does not lead to a significant deformation of the nucleus, the amount of thermal energy liberated per unit trajectory length is directly proportional to the atmospheric density which depends exponentially on the altitude. Therefore, at high altitudes dE/dh =constp(h), which is clearly seen in Fig. 1.
d E erg/cm ~
~9(h), g/cm3
dh
1021
10 -3
4km
km 10-s
1019
0.5kin
1017
I
-200
i
-100
10-7
I
I
I~
0
100
200
"~ ~
I
h, km 300
Fig. 1. The thermal energy dE/dh released per unit trajectory length as a function of the altitude. The solid lines correspond to results of calculation of braking of fragments with different sizes according to the model [7] and the dashed line represents the Jovian atmosphere density height profile. The angle of entrance of fragments is 45 ° . As the fragments move down, the mass of captured atmospheric gas increases rapidly and, when it becomes comparable to the fragment mass the stage of notable braking begins. This occurs at altitudes corresponding to the following density of the ambient gas:
Di cos 0 Ps~P
3/x
'
(1)
where 0 ~ ~r/4 is the slant angle of the fragment with respect to the local vertical line, pi is the fragment material density and Di is its diameter. The ram pressure at these altitudes far exceeds the strength limit for the cometary material, so the fragment strength does not affect significantly the shape of dE/dh. The scale height A in the Jovian atmosphere depends strongly on the altitude h above the level where the pressure of the ambient gas p = 1 bar and the corresponding density is p = p0 = 1.7 x 10 .4 g/cm 3. At altitudes where p > 1 bar the density changes according to the law p = p0(1 - h/A) 2"27, h <_O, A ..~ 75 km; for p _< 1 bar p = p0 e x p ( - h / A ) , h >_ 0, A _~ 23 km (see, e.g., ref. [81). Assuming the cometary fragment density pi ~.- 1 g/cm a (which corresponds to the density of ice), the diameter Di ~- 2 km, we find that the fragment undergoes most braking at the ambient gas density ps -~ 2 x 10 .3
Shock wave phenomena and plasma effects caused by SL-9 comet
433
g/cm 3 and pressure ps "~ 35 bar. This corresponds to the altitude hs --- -140 km in the Jovian atmosphere and agrees well with a maximum of dE/dh for a fragment 2 km across (see Fig. 1). Also seen from the plot, when approaching the maximum, an increase of dE/dh becomes more and more rapid (relative to the atmospheric density increase). This is due to the fact that increasing aerodynamic loads at the stage of strong braking lead also to significant plastic deformation of the fragment, thereby significantly increasing its crosssection. For this reason, the ratio of dE/dh to the atmospheric density near the maximum of energy output turns out to be an order of magnitude greater than that at the early stage of braking. The difference of numerical modeling data from the results of the simple model [7] described above is that in this case the maximum of dE/dh proves to be somewhat shifted toward the region of higher altitudes (and densities, respectively). This is connected with the fact that at late stages of braking the nucleus is completely destroyed and partially evaporated, which is not taken into account in the model [7]. This leads to a faster increase of the cometary nucleus cross-section. In addition, Rayleigh-Taylor and Kelvin-Helmholtz instability start to develop on the liquid surface [9], which also increases the fragment's cross-section and leads to even sharper growth of dE/dh curve. Thermal energy released during the braking of cometary fragments leads to a strong shock wave (SW) generation. As follows from [10], the mean fragment size is about 1-3 km which, for the relative impact velocity of vi ~- 60 km/s, corresponds to the kinetic energy of order 102s - 103o erg. The pressure beyond the SW front caused by such an enormous energy release will exceed very much the pressure of the ambient atmosphere [30]. In other words, the SW intensity will be so high that the ratio of densities after and before the
wave passage will be equal to a limiting value 7 + 1 where 7 is an effective adiabatic index 7-1' of the atmospheric gas. Therefore to describe the initial stage of the SW expansion we take the self-similar solution for the strong cylindric explosion problem [11] using the fact, noted above, that at the early stage of the fragment braking the ratio -~enters the only dimensionless parameter of the problem r p
-~-£-t
p(h) (which
) is constant (r is
the radius of the cylindric SW and t is time). The nonsimultaneous energy release along tile line of motion of the fragment cannot affect significantly the results of semi-qualitative considerations. Indeed, to the moment of time ~-s = A/vi <_0.5 s, which the fragment takes to fly the distance A (where the time is counted beginning from the moment of passing a given point by the fragment), the front radius rD of the cylindric SW is equal to A(D~/64A) 1/4 according to [11]. Since Di _~ 1-4 km and A _> 25 km, the value of rD turns out to be appreciably smaller than A but larger than Di. In addition, the duration of the existence of the cylindric SW (which is about
dE
16pc
, where cs m: 1 km/s is the sound speed
in the Jovian atmosphere) exceeds the time ~-~ by more than an order of magnitude. For these reasons, the use of self-similar solution of the problem of a strong cylindric explosion on a time-scMe t > ~-~ is well justified for our estimations. It is easy to verify that our initial assumption that the SW is strong at early stages of expansion is correct. For this, it is sufficient to compare the atmospheric pressure p with the mean pressure PD after the SW front, which is approximately equal to the energy released per unit length dE/dh, divided by the a r e a S D of a circle with radius r D. The area is S D ,.o ~rD~(A/4Di)3/2/4 and the corresponding pressure is: 7 -
1 dE
(102 _
104)p.
(2)
At the stage of strong braking, when dE/dh begins increasing much faster than p(h), the use of the cylindric explosion approximation becomes incorrect. However, as is seen from Fig. 1, the space scale of the intensive energy release does not exceed A and the amount of energy liberated is of order of the initial kinetic energy of the fragment E0. Therefore, to describe the initial stage of motion of the SW resulted from energy release in the given region, we use a solution of the strong point-like explosion problem [11,12]. Using the total momentum and energy conservation law for the whole system (the moving fragment material plus the
A.V. IVLEVet al.
434
captured atmospheric gas), it is easy to obtain the temporal dependence of the thermal energy released at the stage of strong braking [13]: E ( t ) __ e - l E o + (1 - e - ' ) E o 1
(3)
+ tits"
The time is counted from the moment when the fragment reaches atmospheric layers with a density of order ps, and its strong braking begins. Since this occurs at altitudes lower than 1-bar level, where A _~ 70 km, then Ts _~ 1 s. Thus, in a time period to of order of several r~ an energy close to Eo is released, so one should substitute E = Eo, p = ps and t _> to into the self-similar parameter, which is r(p/Et2) 1/s in the case of a point-like explosion. The use of the point-like explosion model to describe the SW evolution on time-scales t _> to is well justified, as the diameter of the spherical front of the wave (at the fragment energy E0 ~ 103o erg) will be of order 100 km to this moment according to [11] i.e. larger than A and much larger than Di. THE
OBSERVATIONAL
DATA
OBTAINED
DURING
THE
SL9
IMPACT
Observations of Jupiter during impact of the cometary fragments were performed at the Galileo spacecraft at different wavelengths including IR, visible light, and the UV-region. The impact of many fragments was accompanied by bursts of radiation which were detected by the Galileo. Fig. 2 and 3 show light curves obtained at different wavelengths with the P P R [14] and SSI [15] Galileo instruments. The data presented are a small portion of the results obtained by the Galileo during the whole period of observations; nevertheless, characteristic features of these results are clearly seen in the plots presented. At first, the most prominent is a sharp increase in the radiation intensity from the background level to a maximum during the first 1-2 s. This feature is typical for almost all light curves obtained by the Galileo. Subsequent behavior of the light curve turns out to be strongly wavelength-dependent. In addition, the behavior of light curves obtained for some fragments at the same wavelength differs significantly from that of all other fragments.
3xlO.l Itensi,Wcm, i2nm-
L 2~10 -is
+G lxlO -Is
Q1 I
I
0
20
"
I
40
"
i
*Y
]" 60 Time, s
Fig. 2. Light curves obtained by Galileo spacecraft (with the P P R device) for some impacts [14] at the wavelength ~ = 945 nm. The dashed curve corresponds to the analytical solution (6).
435
Shock wave phenomena and plasma effects caused by SL-9 comet
Temporal dependencies of the emission intensity obtained with the P P R (Fig. 2) at /~ = 945 nm for different fragments are identical in shape to each other, whereas for these bursts with a higher maximum intensity duration is longer. After the sharp intensity increase, a specific "plateau" with a duration of 10-15 s appears, after which a more smooth, nearly linear decrease down to the background level begins. The total duration of emission is 30-40 s for different fragments, except for the Q1 fragment I light curve. This curve shows at least four clear outbursts of emission.
150
== 100 ~D
CD
50
0
10
I
I
20
30
I 40
50
60 Time, s
Fig. 3. Light curves obtained by Galileo spacecraft (with the SSI device) for some impacts [15] at the wavelength A = 0.89 #m. A special place is taken by the SSI data obtained at a wavelength of A = 0.89 #m (Fig. 3). After a sharp increase of the radiation intensity, an equally strong decrease begins. This drop is accompanied by either some decrease in intensity during 10-15 s (fragment K), after which the light curve behaves similar to the case of the P P R light curve, or the fast drop leads to the emission decrease down to the background level for a short time interval of less than l0 s. This behavior of light curves was discovered for fragments N and W impact (in the latter case the measurements were done at a wavelength ~ = 0.56 #m). An explanation for such a strange behavior of light curves is given in the next section. One of the most impressive results obtained by the Hubble Space Telescope (HST) are images of luminous features that arose above the Jupiter limb shortly after the impact of many large fragments, whereas the impact site itself is on the dark side of the planet and is not yet seen from Earth 2. These features are usually referred to as "plumes" or "ejecta". This ejecta was discovered after the impact of ten largest nuclei [16], which enables us to reconstruct a picture of this phenomenon and to consider the ejecta as a typical effect that accompanies the impact. Impacts of small-size fragments did not lead to noticeable 1Each fragment of the SL9 Comet was labelled with a letter. 2Fragment's impacts occured at the side of Jupiter invisible from Earth. Typical angle of the impact site was about 6-8 degree behind the limb
436
A.V. IVLEVet al.
observational consequences, therefore we focus on the effects caused by large fragments more than one km across. The series of images obtained by HST clearly demonstrates all main stages the ejecta passed in most cases. At first, a short outburst appeared with a duration less than one minute, followed by some decrease of the glow. Then, the luminous spot above the limb became gradually larger during 4-5 min, after which its growth in size increased. The luminous ejecta attained a size of some tens thousand km, and the altitude above the limb was about 3000 km [17]. After other 5-7 min the spot of ejecta became decreasing in size and after about 10 min desappeared completely. At the same time, at altitudes of 200-300 km above the limb, an extended relatively weakly shining belt appeared, which corresponded to enormous spots, bright in methane bands, that arose on the Jovian surface after the impact sites had rotated to be seen from Earth. We give a description of these spots and discuss their possible nature in the next section.
2.0 1.5 1.0
i
~0
0.5
Pcl Pc2
i"
0.0
,
-0.5 05:27
I
I
I
I
I
05:33
05:39
05:45
05:51
05:57
Time, UT Fig. 4. Light curves obtained at Mauna Kea observatory during the R fragment impact at the wavelength I = 2.3 #m [19]. The dashed line corresponds to solution (9). Observations during the fragment's impacts allowed to obtain a big number of light curves in the visible and IR bands. Fig. 4 shows the light curve taken at I = 2.3 #m with telescope at Mauna Kea Observatory [19] during the R fragment impact. This light curve is typical in the sense that it contains all common features with other light curves. The first outburst of emission was relatively weak and very short and its duration less than a few tens of seconds. After the first outburst, the second, much stronger one followed in many light curves (but not in all!); the intensity far exceeded the background level. In the literature it is accepted to denote the first two maxima by the term "precursor", or briefly Pcl and Pc2. About five minutes after the Pcl emerges, the intensity of radiation begins to increase rapidly, which indicates the beginning of the so-called "main event" in the light curve. It should be noted that the time interval between the Pcl appearing and the main event beginning is of about 5-6 min almost for each of the light curves obtained. The main event duration in the typical light curve is of the order of ten minutes, after which a "plateau" appears in the curve. The duration of this "plateau", as well as its intensity relative to the main event, varies strongly depending on wavelength and fragment. For example, the "plateau" intensity in the H fragment light curve (~ = 10 #m) is about one tenth of the main event intensity, whereas the "plateau" in the R fragment light curve ( t = 2.3 #m) has a relative intensity one order of magnitude lower.
Shock wave phenomena and plasma effects caused by SL-9 comet INTERPRETATION
437
OF T H E O B S E R V E D D A T A
T h e i n t e r p r e t a t i o n of d a t a o b t a i n e d on t h e G a l i l e o s p a c e c r a f t . In order to understand the source of emission registered at the Galileo spacecraft, as well as to explain the form of the light curves, we consider physical processes occurring beyond the SW front as the wave weakens. The temperature T/ behind the front of a high intensity is proportional to the square the wave velocity D. Since the velocity D depends on the front radius rf as oc r71 in the case of cylindric symmetry and e< rj 3/2 in the case of spherical symmetry, Tf drops rapidly enough down to a few 1000 degrees. At the same time, the temperature increases very rapidly toward the explosion center: T ~_ (r//r)2~-z~-+-~Tf. Thus, beyond the SW front a region of hot ionized atmospheric gas emerges; if its density (of about 90% of the Jovian atmosphere consists of hydrogen) is sufficiently high, this region is optically thick. Using the Unzold-Kramers formula [20] for the total absorption coefficient in ionized gas, we are able to estimate an upper boundary of the atmosphere beyond which the shock-wave-heated gas can not be optically thick; this altitude is about 200 km above the 1-bar level. The optically thick gas beyond the SW front radiates with a transparency temperature Topt [20], which is determined from the condition that the inverse absorption coefficient corresponding to a given temperature coincides in order of magnitude with a space scale of the temperature changing. Topt is directly proportional to the ionization potential I and depends logarithmically on the gas density; in the case of hydrogen plasma, Topt ~15000 K. The gas layer with the temperature Topt moving after the SW front cools down primarily due to radiation; this leads, as the SW relaxes, to the formation of a temperature jmnp and a radiation cooling wave [20] moving toward the explosion center with a velocity with respect to the expanding gas: u
~-
27 - 1 N - 1 crT4p~
'~Top~
P
,
(4)
N
where 5Topt ~- kTopt/I [20]. As follows from (4), the cooling wave velocity u depends exponentially on altitude. At tile early stage of braking which, for fragments more than one kilometer across, continues up to the upper boundary of cloudy cover (p _ 0.3 bar) the velocity u is some 10 km/s. The cylindric SW velocity becomes comparable with u at about one second after the SW appearance; the cooling wave radius ropt attains then a maximum value and is nearly equal to the SW radius rf -- 30-40 km. After this the gas bulk velocity beyond the SW front becomes smaller than u, so the cooling wave radius (and, hence, the area of emitting surface) begins decreasing. Therefore, the time during which an effective emission occurs from a region heated up higher than the cylindric SW clouds may be estimated as not exceeding r / / u ~_ 5-6 s. Here the maximum emission region moves along the line of impact after the fragment by remaining at a some distance from it. Obviously, this separation is determined by the time during which the radiative cooling wave radius ropt reaches a maximum value. Since the duration of this emission proves relatively short, dense atmospheric gas heated up during the early braking stage is sometimes called the meteor track. The emission of gas heated up below the cloudy layer will be; screened for a few seconds until the impact-induced heating evaporates aerosols that form the cloudy cover and the expanding SW leads to the formation of a sufficiently big hole in the cover. Therefore this emission can be time-delayed by 1-2 s from the meteor track radiation. Simultaneously with the hole expansion, a strong braking of the fragment begins at altitudes corresponding to the atmospheric pressure of p = ps -~ 10 bar and a SW emerges for which we use the pointlike explosion model. The radiation cooling process in this case will not differ qualitatively form the cylindric explosion example considered above; however, the cooling wave velocity at altitudes corresponding to a maximum energy release level will be an order of magnitude less and the duration of efficient emission from this region will be about 40-50 s. This region restricted by the cooling wave front ropt is often referred to as a fireball 3 3The term "fireball" is used to describe the region of a hot emitting gas produced by an atmospheric nuclear explosion. As the radiation and gasdynamic processes occurring in the region of most energy release during a comet, impact are mmllar to those during the nuclear explomon, it IS used term fireball
438
A.V. IVLEVet al.
It is not difficult to obtain the equation of motion for the fireball surface [21]. In the case of a point-like explosion, the equation and its solution have the form: d?`opt 2 2 ?'opt dt - 5 7 + 1 t
u~,
(5)
where ~ = s~+11)usto/?`o;T = t/to; ro is the radius of a layer with temperature Tort at the moment to, i.e. the initial radius of the cooling wave (for the fragment with energy E0 ~ 103° erg the radius r0 -~ 40 kin). Radiation will escape the cloudy cover through a hole whose diameter is equal to the diameter d of the cylindric SW, which is relatively weakened at this moment. The value of d is a few D~(A/4D~) 3/4 and the intensity of emission I~ is proportional to fi ~_ d2/h 2 ~ ~, where h~ is the altitude of explosion relative to the 1-bar level. Thus, the radiation intensity, which may be detected at Galileo, is determined by the following equation: 5 ( t ) ~ 8~ckTopt ?`o~(t)fl, ° ~ R~ (6) where R j a ,.o 1.5 astronomical unit (A.U.) is a distance between Jupiter and the Galileo. Fig. 2 demonstrates the dependence Ix(t) according to (6). This dependence, which corresponds to the diameter Di -- 3 km (or energy E0 ~- 3 x 1029 erg) provides a good approximation to the light curve obtained during the L fragment impact. Using (1) and (4), it is shown that the fireball emission duration is proportional to D TM and the maximum intensity I ~ ~ o( D~ 3. The sizes of the G and H fragments obtained using the latter relation were found to be 2.6 km and 2.2 kin, respectively. The possible absorption of radiation at the wavelength ,~ =945 nm in the Jovian atmosphere, as well as multiple diffuse scattering by aerosol particles inside the hole formed, may lead to the actual fragment sizes being larger than those obtained by using (6). It is impossible to estimate the size of the Q1 fragments, because the corresponding light curve consists of a sequence of relatively weak peaks apparently caused by the fragment splitting into several small-size fragments during its impact on to Jupiter. An interesting feature of equation (6) is that the intensity Ix(t) proves to be dependent on the fragment size only, but not on its density pi, as according to (1) the density p~ at the altitude of explosion is proportional to pi. Since the real density of a fragment may differ significantly from 1 g/cm 3 it is difficult to calculate the fragment energy (for example, in paper [22] the density of fragments is estimated to be pi ~ 0.2 g/cm3). Thus, the model considered well describes the P P R light curves. The SSI light curves obtained at the wavelengths ~ = 0.89 #m (see Fig. 3) and )~ = 0.56 #m are exceptions. The first maximum in the light curves for the K and N fragments is apparently connected to the meteor track emission. However, a time interval between the first maximum and the second longer outburst can not be explained by the hole expansion in the cloudy cover, because the corresponding time delay is shorter than 1-2 s. Most probably, this time interval is caused by the absorption of fireball radiation by methane molecules, which are present in the atmosphere with an abundance of a few tenth percent; the vertical optical depth in atmosphere, caused by absorption in strong bands of CH4 at the wavelengths )~ = 0.89 #m and 0.56 #m, becomes equal to unity at the pressure level < 0.3 bar [23], i.e. practically at the upper cloud boundary. Methane molecules start dissociating efficiently at temperatures Tdis~ ~--4000-5000 K, so the region comprised by the cylindric SW front can be subdivided into three conditional regions: (a) 0 < r < ?`opt: the region of optically thick meteor track; (b) ropt <_ 7" <_ ?`di~: the region of transparency at given wavelengths (radius ?`diss corresponds to the temperature Td~); (c) ?`di.~ < r < r]: the region beyond the SW front with a temperature inside not exceeding Tdi~. For radiation at wavelengths corresponding to CH4 absorption bands, only region (b) is transparent; for radiation at other wavelengths at which observations were performed, regions (b) and (c) are transparent. The temperature increases from the SW front towards the explosion center according to a power law, so when the SW relaxes and 7"] << Top~ but the cooling wave radius ?`opt still does not start decreasing, we obtain that r] - ?`opt >> r d ~ -- ropt, i.e. the (c) region is much larger than that of the (b) region. For this reason, the fireball emission at wavelengths )~ = 0.89 #m and 0.56 #m could
Shock wave phenomena and plasma effects caused by SL-9 comet
439
be detected on Galileo only after the cooling wave has made the meteor track "transparent" along the total height from the transparency boundary of the atmosphere in the methane bands up to some conditional boundary with the fireball, where the pressure is p~pp~. The coefficient of the emission absorption is proportional to pressure, so the condition for the fireball emission to begin escaping through the meteor track ("transparent" up to the level puppet) is equivalent to the condition that the ratio of the pressure inside the fireball and the pressure p~pp~ is of order of e. The time interval tt~ during which the meteor track becomes transparent is tt,. ~ u -1 ~ Puppet. Therefore, the total duration of the fireball emission and the time tt~ must be also of the same order, which is actually the case. According the mechanism proposed, small-size fragments may cause only short radiation outbursts from the meteor track located above the boundary of atmospheric transparency in methane bands. As mentioned above, the duration of the fireball emission is proportional to D~ 4, so for small fragments (such as N) it must be about four times shorter than for the K fragment, i.e. of order 10 s. The duration of the meteor outburst then will not depend on the fragment size, because this duration is determined only by the time of the fragment motion from the altitude of about 200 km down to the boundary of transparency in methane bands and by the duration of the meteor track glowing at this level. T h e i n t e r p r e t a t i o n of t h e d a t a o b t a i n e d on E a r t h a n d f r o m n e a r - E a r t h spacecrafts.
In order to explain the origin of the third outburst on the light curves obtained on Earth (see Fig. 4) we consider the part of the SW that propagates upwards in the direction of decreasing atmospheric density, which formed at the stage of strong atmospheric braking of the fragment. Once the distance travelled by the SW matches with the height-scale A, the inhomogeneity of the atmosphere begins to affect the propagation velocity D. First the SW velocity decreases with distance R from the site of explosion as D (x R - 3 1 2 e ul2A [25] and attains a minimum D,~i~ at R -~ 3A. As was shown in [8] (for an explosion at an altitude of hs -~ -100 km, ps ~ 10 bar, E0 -~ 1029 erg), the SW start to accelerate from a level of ~ 1 bar where the velocity D~i~ -~ 5 - 6 km/s. At this stage D -~ D,~i~e (R-3a)/~ [26], where a depends on the isentropic index "7 (for example, c~ ___ 4.9 for "7 = 5/3, and c~ _~ 6.5 for ~ = 1.2). The temperature of the shock-compressed gas T is proportional to D 2 and Tmi~ = T,,n(D,~i,~, 7) ~- 2000 K. Notice that the shock-compressed gas starts expanding and cooling adiabatically immediately after the SW passage. The characteristic cooling time after shock compression increases with time from several seconds (just after the SW passage) to a few tens seconds at a late stage of the cooling [26]. When the temperature behind the SW front reaches a few thousand degrees, a large number of chemical compounds, which are usually absent in the Jovian atmosphere, begin forming. In addition to hydrogen, tile unperturbed atmosphere contains a few percent of helium, a few tenths percent of CH4, NH3, NH4SH and H20, which form three consecutive layers of the cloud cover. In paper [27], the results of numerical calculations of the equilibrium chemical composition of gas heated up to temperatures of order several thousand degrees are presented. The maximum temperature in all calculations did not exceed Tdis~ --- 5000 K, because at high temperatures an intensive dissociation of nearly all chemical compounds begins. At lower temperatures, in the hot gas such compounds as CO, NH, CH, HCN, CN, N2, CS, CH4, etc. start forming. Here the carbon monoxide is especially notable, whose molecular composition is at a level of 10 .3 over all temperature range. Our interest to chemical compositions appearing in the shock-heated gas is caused by some of these molecules contributing effectively to the optical thickness. Therefore in the case of a sufficiently high density the shock-compressed gas can radiate as a black body. Now we turn to a detailed discussion of the third peak - so-called main event shown in Fig. 4. By comparing series of the plume images obtained by HST with the corresponding light curves, it can easily be seen that the processes of expanding and decreasing of the glowing ejecta correlate well with the periods of the intensity increasing and decreasing. In addition, according to the spectral observations, the radiation temperature of the main event decreased monotonically with the radiation intensity growth, by varying from about 1000 K at the moment of the main maximum appearance to a few hundred degrees near the intensity maximum [28]. The radiation spectrum during the intensity growth is almost continuous and is well described by a Planck type distribution function in the frequency
440
A.V. IVLEVet al.
range considered. This shows that the cause of tile main maximum appearance on the light curves is the radiation from the hot expanding gas ejected into the upper atmosphere. Let us consider the processes occurring at a late cooling stage of the gas ejected into the upper atmosphere. Until the temperature of expanding gas exceeds Tdi,s (the corresponding SW velocity D _> 12 km/s), all complex chemical compositions are dissociated and the gas is optically transparent. At this stage, the gas moves upwards almost inertially and in about a minute after the SW passage the gas can be seen directly from Earth. The maximum altitude H,~=~ the ejected gas reaches is determined by the initial velocity acquired at the moment of the SW passage and is approximately Hm~,: ~- D2/2g ~- 3000 km. The gas expansion is described by a self-similar solution [26]. According to [26], the expansion is quasi-one dimensional at the beginning and the gas concentration changes according to the law n c v (t/tz) -1, where tl is the characteristic expansion time at the late cooling stage. This time depends on the explosion altitude; for the layer considered tz -~ 20 - 30 s [8]. The scale length of inhomogeneity AL of the layer increases as AL --~ A(t/t~). The temperature decrease is determined by the adiabatic expansion only, which becomes three-dimensional with time: rt cx: t -3, T cx: rt"r-1 o( t -3('r-I). When the temperature of the optically transparent gas decreases to 2000-3000 K, the molecular compounds that are capable of absorbing effectively the IR radiation begin to form, which results in a rapid increase in the gas optical thickness. The cooling from temperatures 5000-7000 K to 2000-3000 K occurs during a period of time of order (5 - 10)tz -~ 200 - 300 s. Therefore, the SW leads to the ejection of the hot atmospheric gas into altitudes of some thousand km. As a result of the adiabatic expansion, the gas which is directly seen from Earth becomes optically dense about 4-5 min after the fragment impact and has a temperature of T -~ 2000 - 3000 K by this time. The absorption coefficient of the hot gas ~ may be estimated using the expression [20]: &. ~-- -
mc kT
~_.fiNiexp
\
Uf
]
,
(7)
where e, m are the electron charge and mass, f i - is the oscillator force, N i - is the concentration of molecules that absorb IR radiation, hw is the photon energy and Ei is the energy of the excited level. At temperatures of some thousand degrees the absorption in the gas is due to electron transitions to low vibration levels of the upper electron state. As the temperature decreases, the absorption due to transitions to the upper vibration levels prevails and the absorption coefficient is also dependent exponentially on temperature. Using (7) we may estimate the optical depth rovt of the heated gas. Assuming Ni >_ 1018 ca~-a, E~ _ 1 aB, To - 2000 K, f i ~ 10-4 we obtain: %pt ~ tCwZ2X "" 10a - 1 0 4 ~> 1. Therefore, the initial thickness of the optically dense layer is Lo ~- Alnropt ~- 10A ~-, 250 km, and the initial transverse size of the layer is do ~- 2rcA ~_ 150 km [25]. To estimate the radiation flux from the surface of the expanding gas, we need to determine how the thickness and cross-size of the optically dense region change. The thickness L of the optically dense layer is obtained fi'om the transparency condition: ~,AL ~ 1. The absorption coefficient may be estimated as: ~c~oc~ ~
exp
-~-
,
where E~:: is some effective excitation energy of the oscillatory transition, z is the coordinate (relative to the moving gas mass center) and so n o< e x p ( - - Z / A L ) . Substituting AL(t) and T ( t ) into the transparency condition yields the equation for dependence of the thickness L on time:
(
L({) __ L0i 1 - ~oo (5 - 3~/)lni +
kTo
,8,
where t = t/t~, t > 1. The radiation intensity of the expanding gas ejected into the upper atmosphere (at the limit hw < k T ) is given by the following expression:
(9)
Shock wave phenomena and plasma effects caused by SL-9 comet
441
The cross-size of the emitting region increases proportionally to t, with the characteristic expansion time te ~- do/c~ ~- 20 - 30 s, where Cs is the sound speed, and thickness changes as follows. At the beginning of expansion when the temperature is sufficiently high and Boltzmann's factor e x p ( - E ~ H / k T ) plays no decisive role, the thickness L of the emitting layer increases and, in spite of the temperature decrease, the radiation intensity increases. As the temperature decreases, Boltzmann's factor begins dominating and, in spite of expansion, the thickness L start decreasing and a "collapse" of the emitting region occurs. From (9) we determine the duration of emission:
t~d-~
[
1
1+ AE~ H-hw
For the parameters given above, t~=d = t~=dtt ~-- 500 -- 1000 s. Fig. 4 shows the radiation intensity curve obtained using the model described. The calculated outburst duration is about ten minutes, which agree with the main maximum duration observed in the light curve.
Note that the model suggested explains easily the following observational result [17] namely that the maximum altitudes reached by the gas ejected during different fragment impacts was nearly the same, at Hm,x -~ 3000 km. In fact, the temperature of the gas ejected is strongly dependent on the SW velocity. The initial temperature of the gas pushed out by the SW with the velocity D = 12 - 14 km/s somewhat exceeds Tails (T -~ 5000 - 7000 K) and the maximum ejection altitude is H,~,x ~- D ~ / 2 g ~- 2500 - 3500 km. Such a gas being initially transparent, becomes optically dense at late cooling stages. However, if the initial temperature of the gas ejected is significantly higher than Tai~, this means that the gas is being ejected from sufficiently high altitudes (h _> 150 km over the 1 bar level) and its initial density is fairly small. At a late stage of the expansion of such a gas, when its temperature reaches 2000-3000 K, its density is too small to provide the optical depth ropt _> 1. Similarly, the gas ejected with a relatively small initial temperature (T _< 3000 K) cools down rapidly enough to become optically transparent as well. After 15-20 minutes from the cometary fragments impact, the formation of a "plateau" observed on the light curves. In the radiation spectrum during the phase when tlhe intensity is decreasing and the "plateau" formation (fragments K, C [28], and H [29]) some absorption lines of It2, NH3, CH4, CO and of some other species have been found. The temperature of some of these elements is of order a few hundred degrees, whereas the temperature of CO and NH3 is estimated as 1500-3000 K. The appearance of the first group of lines is due to exponential dependence of the molecular absorption cross-section on temperature and hence, during the cooling, the gas ejected inlo the upper atmosphere remains sufficiently optically thick only near the absorption maximum and becomes transparent at other wavelengths. Tile appearance in the spectrum of the secondary group lines and the formation of the "plateau" seems to be caused by the radiation from the hot upper atmosphere. Heating of tile atmosphere is caused by the ejected and falling back gas, since according to calculations [24], the fallback on to the atmosphere gas heats it up to temperatures of some thousand degrees at altitudes of 250-350 km over the 1-bar level. This hypothesis is also favored by the fact that the time of the plateau formation and of the appearance of sharp CO and NH3 lines with a temperature of some thousand degrees well correlates with moments of the fragment impact sites crossing the limb. Paper [24] assumed that the heated atmospheric layer radiates as a black body, but simple estimates show that the optical depth of such a layer is very small and the heated gas is thus a volume emitter. For this reason, despite a high temperature of the gas, the radiation intensity proves to be appreciably less than tile equilibrium one and contributes insignificantly into the flux observed compared with the main maximum level. In many papers the main maximum in the light curves is interpreted as the radiation of the atmosphere heated by the falling gas. In addition to the arguments given above, the mechanism of the atmosphere heating by falling gas cannot explain the main maximum appearance for one more reason. As seen from Fig. 4, the time-delay t~ between the moment of the fragment impact and the beginning of the main maximum is about t6 -~ 300 s, which is typical for most fragments except for fragments Q1 and Q2 which produced unusual light curves at the impact moments as well (see Fig. 2). The results of numerical hydrodynamic modeling show that the braking of falling gas and the subsequent atmosphere heating occur
442
A.V. IVLEVet al.
at altitudes of hbr _< 300 km over the 1-bar level. By the moment t = t~ after the fragment impact, the heated atmospheric gas is far behind Jupiter's limb (for example, for the H fragment a distance hllrab between the impact site and the line of direct seeing from Earth is about 700 km > hbr). Therefore, the heated atmospheric gas cannot be a reason of the main m a x i m u m appearance in the IR light curves. Moreover, the model [24] is very sensitive to the impact site angle behind the limb, since in this case the time t6 should correlate u n d o u b t e d l y with this angle. This correlation is not found, and in contrast, in the case of the C fragment impact for which the angle of incidence behind the limb was one of the highest (hlimb >_ 1000 km) and the time t6 turned out to be one of the smallest (about 250 s). |n paper [24] only the IR curve for R fragment was analyzed: among all the fragments for which the detailed light curves were obtained at different wavelengths, this fragment had a m i n i m u m angle of incidence behind the limb of about 4.8 °. Therefore, the R fragment impact site emerged on the visible side of Jupiter at about the same time when a strong heating of the atmosphere by fallback gas began. It appears t h a t the R fragment light curve was chosen in [24] just for this reason, to illustrate the model of the atmosphere heating by fallback gas. CONCLUSION In this paper, an a t t e m p t is m a d e to generalize, describe from unified positions the most impressive results obtained during the SL9 comet impact with Jupiter in July 1994. The interpretation proposed for light curves taken by Galileo, HST and some ground-based observatories provides a key to understand the details of physical processes under way during the cometary fragment impact, as well as to find the penetration depth into the atmosphere and energy of a typical fragment. The model of the explosion inside an inhomogeneous atmosphere explains the most spectacular effects of the collision.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.
Klumov B.A. et al., Uspekhi Fizicheskih Nauk, 164(6), 617 (1994). Ahrens T.J. et al., Geophys. Research Lett., 21, 1087 (1994). Takata T. et al., Icarus, 109, 3 (1994). Boslough M.B. et al., Geophys. Research Left., 21, 1555 (1994). Mac Low M.M. and Zahnle K., Astrophys. lournal, 434, L33 (1995). Zahnle K. and Mac Low M.M., Icarus, 108, 1 (1994). Grigoryan S.S. Kosmicheskie Issledovaniya 6,875 (1979). Gryaznov V.K. et al., Earth, Moon and Planets, 66, 99 (1994). Crawford D.A. et al., Shock Waves, 4, 47 (1994). Weaver H.A. et al., Science, 263,787 (1994). Sedov L.I. Similarity and Dimensional Methods in Mechanics, Academic Press, New York (1958). Fortov V.E, Ivlev A.V. and Klumov B.A.. JETP Lett., 62,772 (1995). Fortov V.E., Ivlev A.V. and Klumov B.A., Icarus, in press. Martin T.Z. et al., Science, 268, 1875 (1995). Chapman C.R. et al., Geophys. Research Lett., 22, 1561 (1995). Beatty J.K. and Levy D.H., Sky ~' Telescope, 10, 18 (1995). Hammel H.B. et al., Science, 267, 1288 (1995). Nicholson P.D. et al, Geophys. Res. Lett., 22, 1617 (1995). Graham J.R. et al., Science, 267, 1320 (1995). Zel'dovich Y.B. and Raizer Y.P., Physics of Shock Waves and High-Temperature Hydrodinamic Phenomena, Academic Press, New York (1967). Ivlev A.V., Klumov B.A. and Fortov V.E.,JETP Lett., 61,431 (1995). Sekanina Z., Proceeding ESO SL9 Workshop, 43, February 13-15, Garching, Germany (1995). West R.A. et al., Science, 267, 1296 (1995). Zahnle K. and Mac Low M.M., J. Geophys. Res., 1996, in press. Kompaneets A.S. Soy.Phys. Dokl., 5, 46 (1960). Raizer Y.P. Prikl. Matem. i Tehn. Fiz., 4, 49 (1964). Borunov S., Drossart P. and Encrenaz Th., Proceeding ESO SL9 Workshop, 275, February 13-15, Garching, Germany (1995). Meadows V. and Crisp D., Proceeding ESO SL9 Workshop, 239, February 13-15, Garching, Germany (1995). Herbst T.M. et al., Proceeding ESO SL9 Workshop, 119, February 13-15, Garehing, Germany (1995). Ivlev A.V., K|umov B.A. and Fortov V.E., JETP Lett., 60,491 (1994).
Pergamon
SHOCK WAVE PHENOMENA AND PLASMA EFFECTS CAUSED BY SHOEMAKER-LEVY 9 HYPERVELOCITY IMPACT WITH JOVIAN ATMOSPHERE A. V. IVLEV, V. E. FORTOV, and B. A. KLUMOV High Energy Density Research Center, Russian Academy of Science, 127412, Izhorskaya 13/19, Moscow, Russia
Summary-Impact of the Shoemaker-Levy 9 comet with Jupiter has been accompanied by a great number of various effects in the atmosphere, ionosphere and magnetosphere of the planet. Among the most interesting effects are bursts of radiation registered in a wide spectral range during the impact of cometary fragments, the generation of giant gaseous plumes and the formation of large-scale long-livingvortex structures in the Jovian atmosphere. In the present paper the main observational results obtained during about thirty minutes after the fragments collision with Jupiter are discussed; a unified physical model is suggested which explains consistently the basic observational data. INTRODUCTION In July 1994 the collision of the Shoemaker-Levy 9 comet (SL9) with Jupiter took place. SL9 impact has been accompanied by a great number of various effects in the atmosphere, ionosphere and magnetosphere of Jupiter. Among the most interesting effects are bursts of radiation registered in a wide spectral range during the cometary fragments impact, the generation of giant gaseous plumes, and the formation of large-scale long-living vortex structures in the Jovian atmosphere. Following encounter with Jupiter, many papers have appeared that consider theoretical aspects of this event. The main part of these papers are devoted to modelling gasdynamic processes during SL9 fragments braking in the atmosphere [1-6]. In the majority of these papers, methods of direct numerical modeling were used, which allowed a sufficiently accurate description of the braking and destruction of cometary fragments. However, an adequate description of large-scale gasdynamic processes caused by a powerful energy output during fragments braking has met serious numerical difficulties (for example, it is impossible to provide the sufficient space discretization for calculations in a three-dimensional region with a linear size of some 100 km). In order to describe large-scale effects, it is necessary to propose a semi-quantitative analytical model, in which the results of numerical calculations of fragments braking are taken as the input data. The analysis of the results obtained by using both numerical and analytical models enables comparison with observational data and gives preference for one of the initial models. In this paper the main observational results obtained during about thirty minutes after the fragments collision with Jupiter are discussed; a unified physical model is suggested which explains consistently the basic observational data.
ANALYTICAL
M O D E L OF T H E SL9 I M P A C T W I T H J U P I T E R
Fig. 1 shows a typical dependence of the comet energy output along the trajectory on the altitude. These curves were obtained using a simple hydrodynamic model [7] that describes the body deformation assuming the constancy of its volume (without ablation) under the 431
A.V. IVLEVet al.
432
action of aerodynamic drag force. The difference of the results of this simple model from data obtained using numerical modeling of braking and destruction of cometary fragments with different form, density and strength [4] turns out to be not very significant until the moment when strong evaporation and destruction of the fragment material begins. There is nothing specially surprising in that the simple model [7], which reduces to four ordinary differential equations, provides the acceptable accuracy of description. At an early stage of the fragment motion in atmosphere, when aerodynamic load does not noticeably affect its motion and does not lead to a significant deformation of the nucleus, the amount of thermal energy liberated per unit trajectory length is directly proportional to the atmospheric density which depends exponentially on the altitude. Therefore, at high altitudes dE/dh =constp(h), which is clearly seen in Fig. 1.
d E erg/cm ~
~9(h), g/cm3
dh
1021
10 -3
4km
km 10-s
1019
0.5kin
1017
I
-200
i
-100
10-7
I
I
I~
0
100
200
"~ ~
I
h, km 300
Fig. 1. The thermal energy dE/dh released per unit trajectory length as a function of the altitude. The solid lines correspond to results of calculation of braking of fragments with different sizes according to the model [7] and the dashed line represents the Jovian atmosphere density height profile. The angle of entrance of fragments is 45 ° . As the fragments move down, the mass of captured atmospheric gas increases rapidly and, when it becomes comparable to the fragment mass the stage of notable braking begins. This occurs at altitudes corresponding to the following density of the ambient gas:
Di cos 0 Ps~P
3/x
'
(1)
where 0 ~ ~r/4 is the slant angle of the fragment with respect to the local vertical line, pi is the fragment material density and Di is its diameter. The ram pressure at these altitudes far exceeds the strength limit for the cometary material, so the fragment strength does not affect significantly the shape of dE/dh. The scale height A in the Jovian atmosphere depends strongly on the altitude h above the level where the pressure of the ambient gas p = 1 bar and the corresponding density is p = p0 = 1.7 x 10 .4 g/cm 3. At altitudes where p > 1 bar the density changes according to the law p = p0(1 - h/A) 2"27, h <_O, A ..~ 75 km; for p _< 1 bar p = p0 e x p ( - h / A ) , h >_ 0, A _~ 23 km (see, e.g., ref. [81). Assuming the cometary fragment density pi ~.- 1 g/cm a (which corresponds to the density of ice), the diameter Di ~- 2 km, we find that the fragment undergoes most braking at the ambient gas density ps -~ 2 x 10 .3
Shock wave phenomena and plasma effects caused by SL-9 comet
433
g/cm 3 and pressure ps "~ 35 bar. This corresponds to the altitude hs --- -140 km in the Jovian atmosphere and agrees well with a maximum of dE/dh for a fragment 2 km across (see Fig. 1). Also seen from the plot, when approaching the maximum, an increase of dE/dh becomes more and more rapid (relative to the atmospheric density increase). This is due to the fact that increasing aerodynamic loads at the stage of strong braking lead also to significant plastic deformation of the fragment, thereby significantly increasing its crosssection. For this reason, the ratio of dE/dh to the atmospheric density near the maximum of energy output turns out to be an order of magnitude greater than that at the early stage of braking. The difference of numerical modeling data from the results of the simple model [7] described above is that in this case the maximum of dE/dh proves to be somewhat shifted toward the region of higher altitudes (and densities, respectively). This is connected with the fact that at late stages of braking the nucleus is completely destroyed and partially evaporated, which is not taken into account in the model [7]. This leads to a faster increase of the cometary nucleus cross-section. In addition, Rayleigh-Taylor and Kelvin-Helmholtz instability start to develop on the liquid surface [9], which also increases the fragment's cross-section and leads to even sharper growth of dE/dh curve. Thermal energy released during the braking of cometary fragments leads to a strong shock wave (SW) generation. As follows from [10], the mean fragment size is about 1-3 km which, for the relative impact velocity of vi ~- 60 km/s, corresponds to the kinetic energy of order 102s - 103o erg. The pressure beyond the SW front caused by such an enormous energy release will exceed very much the pressure of the ambient atmosphere [30]. In other words, the SW intensity will be so high that the ratio of densities after and before the
wave passage will be equal to a limiting value 7 + 1 where 7 is an effective adiabatic index 7-1' of the atmospheric gas. Therefore to describe the initial stage of the SW expansion we take the self-similar solution for the strong cylindric explosion problem [11] using the fact, noted above, that at the early stage of the fragment braking the ratio -~enters the only dimensionless parameter of the problem r p
-~-£-t
p(h) (which
) is constant (r is
the radius of the cylindric SW and t is time). The nonsimultaneous energy release along tile line of motion of the fragment cannot affect significantly the results of semi-qualitative considerations. Indeed, to the moment of time ~-s = A/vi <_0.5 s, which the fragment takes to fly the distance A (where the time is counted beginning from the moment of passing a given point by the fragment), the front radius rD of the cylindric SW is equal to A(D~/64A) 1/4 according to [11]. Since Di _~ 1-4 km and A _> 25 km, the value of rD turns out to be appreciably smaller than A but larger than Di. In addition, the duration of the existence of the cylindric SW (which is about
dE
16pc
, where cs m: 1 km/s is the sound speed
in the Jovian atmosphere) exceeds the time ~-~ by more than an order of magnitude. For these reasons, the use of self-similar solution of the problem of a strong cylindric explosion on a time-scMe t > ~-~ is well justified for our estimations. It is easy to verify that our initial assumption that the SW is strong at early stages of expansion is correct. For this, it is sufficient to compare the atmospheric pressure p with the mean pressure PD after the SW front, which is approximately equal to the energy released per unit length dE/dh, divided by the a r e a S D of a circle with radius r D. The area is S D ,.o ~rD~(A/4Di)3/2/4 and the corresponding pressure is: 7 -
1 dE
(102 _
104)p.
(2)
At the stage of strong braking, when dE/dh begins increasing much faster than p(h), the use of the cylindric explosion approximation becomes incorrect. However, as is seen from Fig. 1, the space scale of the intensive energy release does not exceed A and the amount of energy liberated is of order of the initial kinetic energy of the fragment E0. Therefore, to describe the initial stage of motion of the SW resulted from energy release in the given region, we use a solution of the strong point-like explosion problem [11,12]. Using the total momentum and energy conservation law for the whole system (the moving fragment material plus the
A.V. IVLEVet al.
434
captured atmospheric gas), it is easy to obtain the temporal dependence of the thermal energy released at the stage of strong braking [13]: E ( t ) __ e - l E o + (1 - e - ' ) E o 1
(3)
+ tits"
The time is counted from the moment when the fragment reaches atmospheric layers with a density of order ps, and its strong braking begins. Since this occurs at altitudes lower than 1-bar level, where A _~ 70 km, then Ts _~ 1 s. Thus, in a time period to of order of several r~ an energy close to Eo is released, so one should substitute E = Eo, p = ps and t _> to into the self-similar parameter, which is r(p/Et2) 1/s in the case of a point-like explosion. The use of the point-like explosion model to describe the SW evolution on time-scales t _> to is well justified, as the diameter of the spherical front of the wave (at the fragment energy E0 ~ 103o erg) will be of order 100 km to this moment according to [11] i.e. larger than A and much larger than Di. THE
OBSERVATIONAL
DATA
OBTAINED
DURING
THE
SL9
IMPACT
Observations of Jupiter during impact of the cometary fragments were performed at the Galileo spacecraft at different wavelengths including IR, visible light, and the UV-region. The impact of many fragments was accompanied by bursts of radiation which were detected by the Galileo. Fig. 2 and 3 show light curves obtained at different wavelengths with the P P R [14] and SSI [15] Galileo instruments. The data presented are a small portion of the results obtained by the Galileo during the whole period of observations; nevertheless, characteristic features of these results are clearly seen in the plots presented. At first, the most prominent is a sharp increase in the radiation intensity from the background level to a maximum during the first 1-2 s. This feature is typical for almost all light curves obtained by the Galileo. Subsequent behavior of the light curve turns out to be strongly wavelength-dependent. In addition, the behavior of light curves obtained for some fragments at the same wavelength differs significantly from that of all other fragments.
3xlO.l Itensi,Wcm, i2nm-
L 2~10 -is
+G lxlO -Is
Q1 I
I
0
20
"
I
40
"
i
*Y
]" 60 Time, s
Fig. 2. Light curves obtained by Galileo spacecraft (with the P P R device) for some impacts [14] at the wavelength ~ = 945 nm. The dashed curve corresponds to the analytical solution (6).
435
Shock wave phenomena and plasma effects caused by SL-9 comet
Temporal dependencies of the emission intensity obtained with the P P R (Fig. 2) at /~ = 945 nm for different fragments are identical in shape to each other, whereas for these bursts with a higher maximum intensity duration is longer. After the sharp intensity increase, a specific "plateau" with a duration of 10-15 s appears, after which a more smooth, nearly linear decrease down to the background level begins. The total duration of emission is 30-40 s for different fragments, except for the Q1 fragment I light curve. This curve shows at least four clear outbursts of emission.
150
== 100 ~D
CD
50
0
10
I
I
20
30
I 40
50
60 Time, s
Fig. 3. Light curves obtained by Galileo spacecraft (with the SSI device) for some impacts [15] at the wavelength A = 0.89 #m. A special place is taken by the SSI data obtained at a wavelength of A = 0.89 #m (Fig. 3). After a sharp increase of the radiation intensity, an equally strong decrease begins. This drop is accompanied by either some decrease in intensity during 10-15 s (fragment K), after which the light curve behaves similar to the case of the P P R light curve, or the fast drop leads to the emission decrease down to the background level for a short time interval of less than l0 s. This behavior of light curves was discovered for fragments N and W impact (in the latter case the measurements were done at a wavelength ~ = 0.56 #m). An explanation for such a strange behavior of light curves is given in the next section. One of the most impressive results obtained by the Hubble Space Telescope (HST) are images of luminous features that arose above the Jupiter limb shortly after the impact of many large fragments, whereas the impact site itself is on the dark side of the planet and is not yet seen from Earth 2. These features are usually referred to as "plumes" or "ejecta". This ejecta was discovered after the impact of ten largest nuclei [16], which enables us to reconstruct a picture of this phenomenon and to consider the ejecta as a typical effect that accompanies the impact. Impacts of small-size fragments did not lead to noticeable 1Each fragment of the SL9 Comet was labelled with a letter. 2Fragment's impacts occured at the side of Jupiter invisible from Earth. Typical angle of the impact site was about 6-8 degree behind the limb
436
A.V. IVLEVet al.
observational consequences, therefore we focus on the effects caused by large fragments more than one km across. The series of images obtained by HST clearly demonstrates all main stages the ejecta passed in most cases. At first, a short outburst appeared with a duration less than one minute, followed by some decrease of the glow. Then, the luminous spot above the limb became gradually larger during 4-5 min, after which its growth in size increased. The luminous ejecta attained a size of some tens thousand km, and the altitude above the limb was about 3000 km [17]. After other 5-7 min the spot of ejecta became decreasing in size and after about 10 min desappeared completely. At the same time, at altitudes of 200-300 km above the limb, an extended relatively weakly shining belt appeared, which corresponded to enormous spots, bright in methane bands, that arose on the Jovian surface after the impact sites had rotated to be seen from Earth. We give a description of these spots and discuss their possible nature in the next section.
2.0 1.5 1.0
i
~0
0.5
Pcl Pc2
i"
0.0
,
-0.5 05:27
I
I
I
I
I
05:33
05:39
05:45
05:51
05:57
Time, UT Fig. 4. Light curves obtained at Mauna Kea observatory during the R fragment impact at the wavelength I = 2.3 #m [19]. The dashed line corresponds to solution (9). Observations during the fragment's impacts allowed to obtain a big number of light curves in the visible and IR bands. Fig. 4 shows the light curve taken at I = 2.3 #m with telescope at Mauna Kea Observatory [19] during the R fragment impact. This light curve is typical in the sense that it contains all common features with other light curves. The first outburst of emission was relatively weak and very short and its duration less than a few tens of seconds. After the first outburst, the second, much stronger one followed in many light curves (but not in all!); the intensity far exceeded the background level. In the literature it is accepted to denote the first two maxima by the term "precursor", or briefly Pcl and Pc2. About five minutes after the Pcl emerges, the intensity of radiation begins to increase rapidly, which indicates the beginning of the so-called "main event" in the light curve. It should be noted that the time interval between the Pcl appearing and the main event beginning is of about 5-6 min almost for each of the light curves obtained. The main event duration in the typical light curve is of the order of ten minutes, after which a "plateau" appears in the curve. The duration of this "plateau", as well as its intensity relative to the main event, varies strongly depending on wavelength and fragment. For example, the "plateau" intensity in the H fragment light curve (~ = 10 #m) is about one tenth of the main event intensity, whereas the "plateau" in the R fragment light curve ( t = 2.3 #m) has a relative intensity one order of magnitude lower.
Shock wave phenomena and plasma effects caused by SL-9 comet INTERPRETATION
437
OF T H E O B S E R V E D D A T A
T h e i n t e r p r e t a t i o n of d a t a o b t a i n e d on t h e G a l i l e o s p a c e c r a f t . In order to understand the source of emission registered at the Galileo spacecraft, as well as to explain the form of the light curves, we consider physical processes occurring beyond the SW front as the wave weakens. The temperature T/ behind the front of a high intensity is proportional to the square the wave velocity D. Since the velocity D depends on the front radius rf as oc r71 in the case of cylindric symmetry and e< rj 3/2 in the case of spherical symmetry, Tf drops rapidly enough down to a few 1000 degrees. At the same time, the temperature increases very rapidly toward the explosion center: T ~_ (r//r)2~-z~-+-~Tf. Thus, beyond the SW front a region of hot ionized atmospheric gas emerges; if its density (of about 90% of the Jovian atmosphere consists of hydrogen) is sufficiently high, this region is optically thick. Using the Unzold-Kramers formula [20] for the total absorption coefficient in ionized gas, we are able to estimate an upper boundary of the atmosphere beyond which the shock-wave-heated gas can not be optically thick; this altitude is about 200 km above the 1-bar level. The optically thick gas beyond the SW front radiates with a transparency temperature Topt [20], which is determined from the condition that the inverse absorption coefficient corresponding to a given temperature coincides in order of magnitude with a space scale of the temperature changing. Topt is directly proportional to the ionization potential I and depends logarithmically on the gas density; in the case of hydrogen plasma, Topt ~15000 K. The gas layer with the temperature Topt moving after the SW front cools down primarily due to radiation; this leads, as the SW relaxes, to the formation of a temperature jmnp and a radiation cooling wave [20] moving toward the explosion center with a velocity with respect to the expanding gas: u
~-
27 - 1 N - 1 crT4p~
'~Top~
P
,
(4)
N
where 5Topt ~- kTopt/I [20]. As follows from (4), the cooling wave velocity u depends exponentially on altitude. At tile early stage of braking which, for fragments more than one kilometer across, continues up to the upper boundary of cloudy cover (p _ 0.3 bar) the velocity u is some 10 km/s. The cylindric SW velocity becomes comparable with u at about one second after the SW appearance; the cooling wave radius ropt attains then a maximum value and is nearly equal to the SW radius rf -- 30-40 km. After this the gas bulk velocity beyond the SW front becomes smaller than u, so the cooling wave radius (and, hence, the area of emitting surface) begins decreasing. Therefore, the time during which an effective emission occurs from a region heated up higher than the cylindric SW clouds may be estimated as not exceeding r / / u ~_ 5-6 s. Here the maximum emission region moves along the line of impact after the fragment by remaining at a some distance from it. Obviously, this separation is determined by the time during which the radiative cooling wave radius ropt reaches a maximum value. Since the duration of this emission proves relatively short, dense atmospheric gas heated up during the early braking stage is sometimes called the meteor track. The emission of gas heated up below the cloudy layer will be; screened for a few seconds until the impact-induced heating evaporates aerosols that form the cloudy cover and the expanding SW leads to the formation of a sufficiently big hole in the cover. Therefore this emission can be time-delayed by 1-2 s from the meteor track radiation. Simultaneously with the hole expansion, a strong braking of the fragment begins at altitudes corresponding to the atmospheric pressure of p = ps -~ 10 bar and a SW emerges for which we use the pointlike explosion model. The radiation cooling process in this case will not differ qualitatively form the cylindric explosion example considered above; however, the cooling wave velocity at altitudes corresponding to a maximum energy release level will be an order of magnitude less and the duration of efficient emission from this region will be about 40-50 s. This region restricted by the cooling wave front ropt is often referred to as a fireball 3 3The term "fireball" is used to describe the region of a hot emitting gas produced by an atmospheric nuclear explosion. As the radiation and gasdynamic processes occurring in the region of most energy release during a comet, impact are mmllar to those during the nuclear explomon, it IS used term fireball
438
A.V. IVLEVet al.
It is not difficult to obtain the equation of motion for the fireball surface [21]. In the case of a point-like explosion, the equation and its solution have the form: d?`opt 2 2 ?'opt dt - 5 7 + 1 t
u~,
(5)
where ~ = s~+11)usto/?`o;T = t/to; ro is the radius of a layer with temperature Tort at the moment to, i.e. the initial radius of the cooling wave (for the fragment with energy E0 ~ 103° erg the radius r0 -~ 40 kin). Radiation will escape the cloudy cover through a hole whose diameter is equal to the diameter d of the cylindric SW, which is relatively weakened at this moment. The value of d is a few D~(A/4D~) 3/4 and the intensity of emission I~ is proportional to fi ~_ d2/h 2 ~ ~, where h~ is the altitude of explosion relative to the 1-bar level. Thus, the radiation intensity, which may be detected at Galileo, is determined by the following equation: 5 ( t ) ~ 8~ckTopt ?`o~(t)fl, ° ~ R~ (6) where R j a ,.o 1.5 astronomical unit (A.U.) is a distance between Jupiter and the Galileo. Fig. 2 demonstrates the dependence Ix(t) according to (6). This dependence, which corresponds to the diameter Di -- 3 km (or energy E0 ~- 3 x 1029 erg) provides a good approximation to the light curve obtained during the L fragment impact. Using (1) and (4), it is shown that the fireball emission duration is proportional to D TM and the maximum intensity I ~ ~ o( D~ 3. The sizes of the G and H fragments obtained using the latter relation were found to be 2.6 km and 2.2 kin, respectively. The possible absorption of radiation at the wavelength ,~ =945 nm in the Jovian atmosphere, as well as multiple diffuse scattering by aerosol particles inside the hole formed, may lead to the actual fragment sizes being larger than those obtained by using (6). It is impossible to estimate the size of the Q1 fragments, because the corresponding light curve consists of a sequence of relatively weak peaks apparently caused by the fragment splitting into several small-size fragments during its impact on to Jupiter. An interesting feature of equation (6) is that the intensity Ix(t) proves to be dependent on the fragment size only, but not on its density pi, as according to (1) the density p~ at the altitude of explosion is proportional to pi. Since the real density of a fragment may differ significantly from 1 g/cm 3 it is difficult to calculate the fragment energy (for example, in paper [22] the density of fragments is estimated to be pi ~ 0.2 g/cm3). Thus, the model considered well describes the P P R light curves. The SSI light curves obtained at the wavelengths ~ = 0.89 #m (see Fig. 3) and )~ = 0.56 #m are exceptions. The first maximum in the light curves for the K and N fragments is apparently connected to the meteor track emission. However, a time interval between the first maximum and the second longer outburst can not be explained by the hole expansion in the cloudy cover, because the corresponding time delay is shorter than 1-2 s. Most probably, this time interval is caused by the absorption of fireball radiation by methane molecules, which are present in the atmosphere with an abundance of a few tenth percent; the vertical optical depth in atmosphere, caused by absorption in strong bands of CH4 at the wavelengths )~ = 0.89 #m and 0.56 #m, becomes equal to unity at the pressure level < 0.3 bar [23], i.e. practically at the upper cloud boundary. Methane molecules start dissociating efficiently at temperatures Tdis~ ~--4000-5000 K, so the region comprised by the cylindric SW front can be subdivided into three conditional regions: (a) 0 < r < ?`opt: the region of optically thick meteor track; (b) ropt <_ 7" <_ ?`di~: the region of transparency at given wavelengths (radius ?`diss corresponds to the temperature Td~); (c) ?`di.~ < r < r]: the region beyond the SW front with a temperature inside not exceeding Tdi~. For radiation at wavelengths corresponding to CH4 absorption bands, only region (b) is transparent; for radiation at other wavelengths at which observations were performed, regions (b) and (c) are transparent. The temperature increases from the SW front towards the explosion center according to a power law, so when the SW relaxes and 7"] << Top~ but the cooling wave radius ?`opt still does not start decreasing, we obtain that r] - ?`opt >> r d ~ -- ropt, i.e. the (c) region is much larger than that of the (b) region. For this reason, the fireball emission at wavelengths )~ = 0.89 #m and 0.56 #m could
Shock wave phenomena and plasma effects caused by SL-9 comet
439
be detected on Galileo only after the cooling wave has made the meteor track "transparent" along the total height from the transparency boundary of the atmosphere in the methane bands up to some conditional boundary with the fireball, where the pressure is p~pp~. The coefficient of the emission absorption is proportional to pressure, so the condition for the fireball emission to begin escaping through the meteor track ("transparent" up to the level puppet) is equivalent to the condition that the ratio of the pressure inside the fireball and the pressure p~pp~ is of order of e. The time interval tt~ during which the meteor track becomes transparent is tt,. ~ u -1 ~ Puppet. Therefore, the total duration of the fireball emission and the time tt~ must be also of the same order, which is actually the case. According the mechanism proposed, small-size fragments may cause only short radiation outbursts from the meteor track located above the boundary of atmospheric transparency in methane bands. As mentioned above, the duration of the fireball emission is proportional to D~ 4, so for small fragments (such as N) it must be about four times shorter than for the K fragment, i.e. of order 10 s. The duration of the meteor outburst then will not depend on the fragment size, because this duration is determined only by the time of the fragment motion from the altitude of about 200 km down to the boundary of transparency in methane bands and by the duration of the meteor track glowing at this level. T h e i n t e r p r e t a t i o n of t h e d a t a o b t a i n e d on E a r t h a n d f r o m n e a r - E a r t h spacecrafts.
In order to explain the origin of the third outburst on the light curves obtained on Earth (see Fig. 4) we consider the part of the SW that propagates upwards in the direction of decreasing atmospheric density, which formed at the stage of strong atmospheric braking of the fragment. Once the distance travelled by the SW matches with the height-scale A, the inhomogeneity of the atmosphere begins to affect the propagation velocity D. First the SW velocity decreases with distance R from the site of explosion as D (x R - 3 1 2 e ul2A [25] and attains a minimum D,~i~ at R -~ 3A. As was shown in [8] (for an explosion at an altitude of hs -~ -100 km, ps ~ 10 bar, E0 -~ 1029 erg), the SW start to accelerate from a level of ~ 1 bar where the velocity D~i~ -~ 5 - 6 km/s. At this stage D -~ D,~i~e (R-3a)/~ [26], where a depends on the isentropic index "7 (for example, c~ ___ 4.9 for "7 = 5/3, and c~ _~ 6.5 for ~ = 1.2). The temperature of the shock-compressed gas T is proportional to D 2 and Tmi~ = T,,n(D,~i,~, 7) ~- 2000 K. Notice that the shock-compressed gas starts expanding and cooling adiabatically immediately after the SW passage. The characteristic cooling time after shock compression increases with time from several seconds (just after the SW passage) to a few tens seconds at a late stage of the cooling [26]. When the temperature behind the SW front reaches a few thousand degrees, a large number of chemical compounds, which are usually absent in the Jovian atmosphere, begin forming. In addition to hydrogen, tile unperturbed atmosphere contains a few percent of helium, a few tenths percent of CH4, NH3, NH4SH and H20, which form three consecutive layers of the cloud cover. In paper [27], the results of numerical calculations of the equilibrium chemical composition of gas heated up to temperatures of order several thousand degrees are presented. The maximum temperature in all calculations did not exceed Tdis~ --- 5000 K, because at high temperatures an intensive dissociation of nearly all chemical compounds begins. At lower temperatures, in the hot gas such compounds as CO, NH, CH, HCN, CN, N2, CS, CH4, etc. start forming. Here the carbon monoxide is especially notable, whose molecular composition is at a level of 10 .3 over all temperature range. Our interest to chemical compositions appearing in the shock-heated gas is caused by some of these molecules contributing effectively to the optical thickness. Therefore in the case of a sufficiently high density the shock-compressed gas can radiate as a black body. Now we turn to a detailed discussion of the third peak - so-called main event shown in Fig. 4. By comparing series of the plume images obtained by HST with the corresponding light curves, it can easily be seen that the processes of expanding and decreasing of the glowing ejecta correlate well with the periods of the intensity increasing and decreasing. In addition, according to the spectral observations, the radiation temperature of the main event decreased monotonically with the radiation intensity growth, by varying from about 1000 K at the moment of the main maximum appearance to a few hundred degrees near the intensity maximum [28]. The radiation spectrum during the intensity growth is almost continuous and is well described by a Planck type distribution function in the frequency
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A.V. IVLEVet al.
range considered. This shows that the cause of tile main maximum appearance on the light curves is the radiation from the hot expanding gas ejected into the upper atmosphere. Let us consider the processes occurring at a late cooling stage of the gas ejected into the upper atmosphere. Until the temperature of expanding gas exceeds Tdi,s (the corresponding SW velocity D _> 12 km/s), all complex chemical compositions are dissociated and the gas is optically transparent. At this stage, the gas moves upwards almost inertially and in about a minute after the SW passage the gas can be seen directly from Earth. The maximum altitude H,~=~ the ejected gas reaches is determined by the initial velocity acquired at the moment of the SW passage and is approximately Hm~,: ~- D2/2g ~- 3000 km. The gas expansion is described by a self-similar solution [26]. According to [26], the expansion is quasi-one dimensional at the beginning and the gas concentration changes according to the law n c v (t/tz) -1, where tl is the characteristic expansion time at the late cooling stage. This time depends on the explosion altitude; for the layer considered tz -~ 20 - 30 s [8]. The scale length of inhomogeneity AL of the layer increases as AL --~ A(t/t~). The temperature decrease is determined by the adiabatic expansion only, which becomes three-dimensional with time: rt cx: t -3, T cx: rt"r-1 o( t -3('r-I). When the temperature of the optically transparent gas decreases to 2000-3000 K, the molecular compounds that are capable of absorbing effectively the IR radiation begin to form, which results in a rapid increase in the gas optical thickness. The cooling from temperatures 5000-7000 K to 2000-3000 K occurs during a period of time of order (5 - 10)tz -~ 200 - 300 s. Therefore, the SW leads to the ejection of the hot atmospheric gas into altitudes of some thousand km. As a result of the adiabatic expansion, the gas which is directly seen from Earth becomes optically dense about 4-5 min after the fragment impact and has a temperature of T -~ 2000 - 3000 K by this time. The absorption coefficient of the hot gas ~ may be estimated using the expression [20]: &. ~-- -
mc kT
~_.fiNiexp
\
Uf
]
,
(7)
where e, m are the electron charge and mass, f i - is the oscillator force, N i - is the concentration of molecules that absorb IR radiation, hw is the photon energy and Ei is the energy of the excited level. At temperatures of some thousand degrees the absorption in the gas is due to electron transitions to low vibration levels of the upper electron state. As the temperature decreases, the absorption due to transitions to the upper vibration levels prevails and the absorption coefficient is also dependent exponentially on temperature. Using (7) we may estimate the optical depth rovt of the heated gas. Assuming Ni >_ 1018 ca~-a, E~ _ 1 aB, To - 2000 K, f i ~ 10-4 we obtain: %pt ~ tCwZ2X "" 10a - 1 0 4 ~> 1. Therefore, the initial thickness of the optically dense layer is Lo ~- Alnropt ~- 10A ~-, 250 km, and the initial transverse size of the layer is do ~- 2rcA ~_ 150 km [25]. To estimate the radiation flux from the surface of the expanding gas, we need to determine how the thickness and cross-size of the optically dense region change. The thickness L of the optically dense layer is obtained fi'om the transparency condition: ~,AL ~ 1. The absorption coefficient may be estimated as: ~c~oc~ ~
exp
-~-
,
where E~:: is some effective excitation energy of the oscillatory transition, z is the coordinate (relative to the moving gas mass center) and so n o< e x p ( - - Z / A L ) . Substituting AL(t) and T ( t ) into the transparency condition yields the equation for dependence of the thickness L on time:
(
L({) __ L0i 1 - ~oo (5 - 3~/)lni +
kTo
,8,
where t = t/t~, t > 1. The radiation intensity of the expanding gas ejected into the upper atmosphere (at the limit hw < k T ) is given by the following expression:
(9)
Shock wave phenomena and plasma effects caused by SL-9 comet
441
The cross-size of the emitting region increases proportionally to t, with the characteristic expansion time te ~- do/c~ ~- 20 - 30 s, where Cs is the sound speed, and thickness changes as follows. At the beginning of expansion when the temperature is sufficiently high and Boltzmann's factor e x p ( - E ~ H / k T ) plays no decisive role, the thickness L of the emitting layer increases and, in spite of the temperature decrease, the radiation intensity increases. As the temperature decreases, Boltzmann's factor begins dominating and, in spite of expansion, the thickness L start decreasing and a "collapse" of the emitting region occurs. From (9) we determine the duration of emission:
t~d-~
[
1
1+ AE~ H-hw
For the parameters given above, t~=d = t~=dtt ~-- 500 -- 1000 s. Fig. 4 shows the radiation intensity curve obtained using the model described. The calculated outburst duration is about ten minutes, which agree with the main maximum duration observed in the light curve.
Note that the model suggested explains easily the following observational result [17] namely that the maximum altitudes reached by the gas ejected during different fragment impacts was nearly the same, at Hm,x -~ 3000 km. In fact, the temperature of the gas ejected is strongly dependent on the SW velocity. The initial temperature of the gas pushed out by the SW with the velocity D = 12 - 14 km/s somewhat exceeds Tails (T -~ 5000 - 7000 K) and the maximum ejection altitude is H,~,x ~- D ~ / 2 g ~- 2500 - 3500 km. Such a gas being initially transparent, becomes optically dense at late cooling stages. However, if the initial temperature of the gas ejected is significantly higher than Tai~, this means that the gas is being ejected from sufficiently high altitudes (h _> 150 km over the 1 bar level) and its initial density is fairly small. At a late stage of the expansion of such a gas, when its temperature reaches 2000-3000 K, its density is too small to provide the optical depth ropt _> 1. Similarly, the gas ejected with a relatively small initial temperature (T _< 3000 K) cools down rapidly enough to become optically transparent as well. After 15-20 minutes from the cometary fragments impact, the formation of a "plateau" observed on the light curves. In the radiation spectrum during the phase when tlhe intensity is decreasing and the "plateau" formation (fragments K, C [28], and H [29]) some absorption lines of It2, NH3, CH4, CO and of some other species have been found. The temperature of some of these elements is of order a few hundred degrees, whereas the temperature of CO and NH3 is estimated as 1500-3000 K. The appearance of the first group of lines is due to exponential dependence of the molecular absorption cross-section on temperature and hence, during the cooling, the gas ejected inlo the upper atmosphere remains sufficiently optically thick only near the absorption maximum and becomes transparent at other wavelengths. Tile appearance in the spectrum of the secondary group lines and the formation of the "plateau" seems to be caused by the radiation from the hot upper atmosphere. Heating of tile atmosphere is caused by the ejected and falling back gas, since according to calculations [24], the fallback on to the atmosphere gas heats it up to temperatures of some thousand degrees at altitudes of 250-350 km over the 1-bar level. This hypothesis is also favored by the fact that the time of the plateau formation and of the appearance of sharp CO and NH3 lines with a temperature of some thousand degrees well correlates with moments of the fragment impact sites crossing the limb. Paper [24] assumed that the heated atmospheric layer radiates as a black body, but simple estimates show that the optical depth of such a layer is very small and the heated gas is thus a volume emitter. For this reason, despite a high temperature of the gas, the radiation intensity proves to be appreciably less than tile equilibrium one and contributes insignificantly into the flux observed compared with the main maximum level. In many papers the main maximum in the light curves is interpreted as the radiation of the atmosphere heated by the falling gas. In addition to the arguments given above, the mechanism of the atmosphere heating by falling gas cannot explain the main maximum appearance for one more reason. As seen from Fig. 4, the time-delay t~ between the moment of the fragment impact and the beginning of the main maximum is about t6 -~ 300 s, which is typical for most fragments except for fragments Q1 and Q2 which produced unusual light curves at the impact moments as well (see Fig. 2). The results of numerical hydrodynamic modeling show that the braking of falling gas and the subsequent atmosphere heating occur
442
A.V. IVLEVet al.
at altitudes of hbr _< 300 km over the 1-bar level. By the moment t = t~ after the fragment impact, the heated atmospheric gas is far behind Jupiter's limb (for example, for the H fragment a distance hllrab between the impact site and the line of direct seeing from Earth is about 700 km > hbr). Therefore, the heated atmospheric gas cannot be a reason of the main m a x i m u m appearance in the IR light curves. Moreover, the model [24] is very sensitive to the impact site angle behind the limb, since in this case the time t6 should correlate u n d o u b t e d l y with this angle. This correlation is not found, and in contrast, in the case of the C fragment impact for which the angle of incidence behind the limb was one of the highest (hlimb >_ 1000 km) and the time t6 turned out to be one of the smallest (about 250 s). |n paper [24] only the IR curve for R fragment was analyzed: among all the fragments for which the detailed light curves were obtained at different wavelengths, this fragment had a m i n i m u m angle of incidence behind the limb of about 4.8 °. Therefore, the R fragment impact site emerged on the visible side of Jupiter at about the same time when a strong heating of the atmosphere by fallback gas began. It appears t h a t the R fragment light curve was chosen in [24] just for this reason, to illustrate the model of the atmosphere heating by fallback gas. CONCLUSION In this paper, an a t t e m p t is m a d e to generalize, describe from unified positions the most impressive results obtained during the SL9 comet impact with Jupiter in July 1994. The interpretation proposed for light curves taken by Galileo, HST and some ground-based observatories provides a key to understand the details of physical processes under way during the cometary fragment impact, as well as to find the penetration depth into the atmosphere and energy of a typical fragment. The model of the explosion inside an inhomogeneous atmosphere explains the most spectacular effects of the collision.
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