2015年度前期 第２回衝突勉強会 テーマ：氷天体におけるイジェクタサイズ分布 Secondary craters from large impacts on Europa and Ganymede Ejecta size-velocity distributions on icy world, and the scaling of ejected blocks Kelso N. Singer , William B. McKinnon , L.T. Nowicki Icarus 226 (2013) 865-884 神⼾⼤学 理学研究科 M2 松榮 ⼀真 Outline of this study ² 本研究では、EuropaとGanymedeの巨⼤クレーターの解析を⾏った Ø ２次クレーターを調べることで、イジェクタのsize-velocity distribution(SVD)を詳細に 調べることが可能 Ø ejection velocity, ejection position, mass of material ejected, number of fragment (Alvarellos er al.2002, Housen and Holsapple, 2011) ² 本研究のアウトライン 1. イントロダクション 2. 今回調べた３つクレーターの２次クレーター場とカウンティング⽅法 3. 重⼒⽀配域における２次クレーターを形成したイジェクタ破⽚サイズと速度の⾒積も り⽅法 4. SVDの上限を決定した結果とスケーリング則から求めることのできる関係式との⽐較 5. 氷衛星の結果を岩⽯天体との結果と⽐較 6. 本研究の結果を踏まえ、氷衛星に存在する1.5次クレーターのサイズの⾒積もり 7. まとめ Introduction ² 2次クレーター ² 1.5次クレーター (Zahnle et al.2008) ヒル圏 ヒル圏 ejecta ² Europa上の直径＜1kmのクレーターの95%は２次クレーター (Bierhaus et al.2005) Ø ２次クレーターの空間分布はランダムであるため、クレーターカウンティングによる地表 ⾯年代決定に影響がでる Ø ⼩天体or彗星の衝突と⾒分けることが難しくなるため b ² 2次クレーターを1次クレーターとカウントすると、 Ns ∝ D クレーター年代を過⼤評価することがある 累 Ø ⼩さなクレーターの累積個数が⼤きくなる 積 a 個 Ns ∝ D Ø クレーターカウンティングによる年代決定するた 数 めには、１次クレーターと２次クレーターを⾒分 ける必要がある クレーター直径 Introduction ² １次クレーターと2次クレーターの⾒分け 1. １次クレーター近傍 Ø ２次クレーターの数密度は、１次クレーターからの距離とともに減少 Ø 形状が不規則 Ø ２次クレーターの特徴 chain ｰ clustersやradial chainsを形成 cluster 2. １次クレーター遠⽅ Ø 形状は円形で、空間分布がランダム Ø １次クレーターと区別することは難しい １次 ² 氷衛星上でのクレーターのSVDについて調べた研究が少なくあまりわかっていない Ø 破⽚のSVDは⼩さなクレーターの分布に寄与する (Zahnle et al.2008, Bierhaus et al.2012) Ø 岩⽯天体(⽔星・⽉・⽕星)でのSVDは調べられている ntroduction I STROM StromET AL.: CRATER et al.1981 POPULATIONS ON GANYMEDE AND CALLISTO 8671 I [ I [ I I [ • [ I I I I I I I ] I I [ I [ [ I [ ets. We tend to favor the latter explanationfor the following ² 岩⽯天体と氷天体の違い reasons.Figures 11 through 12 show that sevendifferent cra- ⽉の⾼地 ter curves,representing vastly different densities,on different terrains and even on different satellitesall possessthis steep- Ø Ganymede l ⽉と を⽐較 l l slope index (•-4.7) distribution function. Furthermore, as I pointed out earlier, even though older cratersup to about 100 • l ｰ Ganymedeでは⼤きなクレーターが少ない km diameter have been degraded,i.e., fiat floors at about the -I - Lunar Highlands--. - level of the surroundingterrain, their rim sharpnessis more or （D>100km） ｰ 50<D<100kmでベキ〜­３ Callisto lesspreserved, suggesting that relaxation is not very effective at totally obliteratingcraters. If the paucity of cratersin this n-' GanymedeGanymedecratered ----Callisto diameter range was solely due to obliteration by relaxation, Ø 天体表層の違い then one would expect a very different distribution function 0 between,for example, fresh craterspreserved over long time ｰ ⽉：岩⽯質地殻 Ganymede：氷質地殻 -2- % - periodsin rigid ice, and degradedcraters perhaps formed at a time when the ice was better able to flow. Therefore the ob- LunarPost- t / served large variations in crater densities,but similarities in ｰ 標的物質の強度が異なる ⽉の海 slopeamong the many different terrains, ages,degradational classes,and even satellites,argue againstthis diameter range being solely the result of equilibrium. Furthermore, the ab- ² 衝突後の破⽚サイズ senceof palimpsestson Callistosuggests that the presentlyob- servedcrater populationformed when the icy crust was rigid Ø 氷の強度は岩⽯より⼩さいため、氷のSpall破⽚は岩⽯ enoughto retain the cratersbasically intact, with a minimum -:3- J - of obliteration due to plastic relaxation of the ice. The con- 2. I0 I00 I000 clusionis that it is basicallya productionfunction. に⽐べ⼩さくなる CRATER DIAMETER- (km) Three important consequencesdevolve from these inter- Fig. l l. Curvesfor the craterpopulations measured on the heav- pretations.First, becauseof the similarityof the curvesfor the Ø 形成される２次クレーターのサイズが異なる可能性 ily crateredterrains of both Ganymedeand Callisto,with the lunar degradedand the fresh craters(over the range 30 to 130 kin) curve for reference. The differences between the Moon, Callisto and the processdegrading them must be nearly diameter-inde- Ganymedeare muchgreater than are the similarities.The Ganymede pendent. Second,although significantproportions of craters and Callistocurves are similar beyondabout 50 km diameter,but dif- have been degraded,the processwhich degradesthem is not fer substantiallyat smaller diameters. too effectivein totally obliteratingthem. If the degradational 本研究： but only degradeslarger craters.Figure 14 showsan area of processis crater relaxation,then it effectivelystops at a stress groovedterrain where the formationof new ice hasdestroyed EuropaとGanymede上の巨⼤クレーターのまわりの２次クレーターをカウンa large portion of the rims of severalcraters. Smaller ones,of course, would have been completely obliterated. The pro- i I [ i i [[ I i [ [ [ i i i ij i i i i i i i i posed preferential obliteration of small craters even on the ティングした cratered terrain may have been the result of an ancient epi- sodeof grooved-terrainformation (now hidden by the recra- / Ø tering) associatedwith the resurfacingor later crustalfreez- ! 岩⽯天体の、⽔星・⽉・⽕星の結果と⽐較 ! ing mentioned earlier. Alternatively, the formation of the LunarHighlands I Ø arcuatetroughs may have been responsiblefor the lossof the 氷天体におけるイジェクタ破⽚サイズと速度の関係を明らかにするsmaller craters. At diameters smaller than about 10 km the curve for the heavily cratered terrain on Ganymede turns up slightly. (D Gany Whether this is indicative of the primary crateringpopulation 0 or not, we cannot ascertainwithout comparablediameter cov- erageon Callisto.However, secondary craters of sufficientsize - 2 Gany - and perhapsof sufficientabundance to accountfor this upturn occur on Ganymede. At smaller diameters on Callisto the curvemay not be the productionfunction, but it setsan upper limit of about -3 for its slope.If an ancientepisode of obliter- Lunm ation, similar to that proposedfor Ganymede, operated on Callisto as well, then the production function could have an index more negativethan -3. In any case,it is far from the -•,2 I • • •,•1IO I I • i •j,Ioo , i i I I I IOOOI I -2.3 index observedon the terrestrialplanets. CRATER DIAMETER (km) All terrains on both Ganymede and Callisto show a de- Fig. 12. Comparisonof the crater populationson Ganymede's creasein slope index for cratersgreater than about 50 kin. groovedand heavily crateredterrains, with the lunar curve for refer- Two plausibleexplanations for this decreaseare: (1) a great ence.The groovedterrain is similar in slopeto the heavily cratered deal of crater obliteration due to crater relaxation in the icy terrainfor diametersabove 30 km, but at smallerdiameters a progres- crust,the vigor of the processincreasing with crater size [Par- sive loss of smaller craters has increasedthe slope index of the groovedterrain compared to that of the heavilycratered terrain. Also mentieret al., 1980],or (2) the curvesbasically represent the notice that the groovedterrains which were measuredare of at least productionfunction with a deficiencyof impactingbodies in two ages,one being about as denselycratered as the heavily cratered this crater sizerange compared to that for the terrestrialplan- terrain, the other much less cratered. Sites and mapping methods ² GalileoとVoyager2 missionで得られた画像を⽤いた Ø ejecta blancketの外側に位置する２次クレーターをカウンティング Ø サイズと形状が周りの２次クレーターと⼤きく異なるクレーターは除外 K.N. Singer et al. / Icarus 226 (2013) 865–884 867 Table 1 Summary of primary and secondary crater field characteristics. Primary Primary Primary transient Diameter of primary Mosaic Number of Largest observed Fragment size for largest 1. Tyre-Europa a b c d crater diameter diameter (km) impactor (km) resolution secondaries secondary (km) secondary (m) 1 (km) (m pxÀ ) mapped Europa Tyre 38e 23 1.8 170 1,165 2.8 1160 e f (f Bierhaus et al.2005,2009) 直径が〜38kmで、⽐較的若くクレーターが少ない領域Pwyll 27 17 1.2 27, 21, 54 180 に位置する410 Ganymede Achelous 35g 21 1.9 180 630 2.7 1200 Ø Gilgamesh 585h 271 49.1 550 445 21.3 (18.6) 5760 (5000) ~175kma 中⼼から Sectionまで円形の溝が存在3. b 1 1 Assumes cometary impactors at 26 km sÀ (Europa) and 20 km sÀ (Ganymede) (Eq. (10)). c For Gilgamesh, the value listed is the largest crater likely to be a secondary, and in parentheses the largest crater in an unquestionable radial chain (see Fig. 4b). d Fragment sizes assume non-porous ice surface and gravity-regime scaling (Section 4). -1 -1 Ø e Schenk and Turtle (2009). 170mpx (~30mpx ) 画像に限りがあるがf Alpert and、 Melosh① (1999)解像度が. ②⾼解像度 g Schenk (2010). h Ø 1165 0.5-2.8kmSchenk et al. (2004). 868 K.N. Singer et al. / Icarus 226 (2013) 865–884 ① 個： from the secondary diameter we can estimate the fragment’s size. The inset in Fig. 5 illustrates the quantities described in the follow- Ø 375 ~180m ing section, and Table 2 lists all symbols and associated parameters ② 個： が最⼩ utilized. Fragment velocities were calculated from the range equa- tion for a ballistic trajectory on a planetary sphere: 2 =R g 1 tej sin h cos h p R 2R tanÀ ; 1 b p 2 2 ¼ 1 t cos h=Rpg ð Þ À ej ! where Rb is the measured ballistic range from the primary to each secondary, Rp is the radius of the planet or moon (see Table 2 for values), g is surface gravity, h is the ejection angle, and tej is the ejection velocity we solve for. There are several assumptions that go into this calculation. We do not know the exact launch point or ejection angle of each frag- ment. The ejection angle is assumed to be 45°, as laboratory exper- iments in a granular media show this to be a practical average value with some scatter ±15° (Cintala et al., 1999; Durda et al., 2012). There is a subtle aspect to this assumption, however, which will be returned to in Section 5. An approximate value of one-half of the transient primary crater radius (0.25Dtr) was used as the starting point for measuring the ballistic range to each secondary (we justify this in a later section). The transient crater represents Fig. 1. Europan impact basin Tyre (centered at 34°N, 147°W) and outline of high resolution mosaic shown in Fig. 2. Dashed circle indicates the equivalent rim of Tyre (38 km a nominal cavity shape as the excavation flow ceases but before 1 1 in diameter). Mosaic is 170 m pxÀ , from Galileo imagery. Mapped secondaries (n = 1165) indicated in yellow, with lower density to the eastFig. possibly 2. Portion indicating of high an oblique resolution mosaic of Tyre’s secondary field ( 30 m pxÀ ).