NHK カルチャー講座「惑星科学最前線 ～多様な衛星の多様な起源～」第１回

NHK カルチャー梅田教室にて、衛星形成に関する講座を行ってきました。そのときに用いた講演資料です。

Transcript

1. 2020೥9݄13೔ɹNHKΧϧνϟʔകాڭࣨ@Zoom ࿭੕Պֶ࠷લઢ ɹʙଟ༷ͳӴ੕ͷଟ༷ͳىݯʙ ژ౎େֶ Ӊ஦෺ཧֶڭࣨɹࠤʑ໦وڭ
2. ଠཅܥͷߏ੒ϝϯόʔ ஍ٿܕ࿭੕
   ɹɹਫ੕
   ɹɹۚ੕
   ɹɹ஍ٿ
   ɹɹՐ੕ ڊେΨε࿭੕
   ɹɹɹ໦੕
   ɹɹɹ౔੕ ڊେණ࿭੕
   ɹɹఱԦ੕
   ɹɹւԦ੕ খఱମʢখ࿭੕
   ଠཅܥ֎ԑఱମ
   ΦʔϧτͷӢʣ (c) ikachi.org
3. ਫ੕ ۚ੕ ஍ٿ Ր੕ يಓ௕൒ܘ [AU] 0.39 0.72 1 1.52 ެసपظ [೥] 0.241 0.615 1 1.881 ࣭ྔ [஍ٿ = 1] 0.055 0.82 1 0.11 ൒ܘ [km] 2440 6052 6378 3396 ີ౓ [kg/m3] 5430 5240 5520 3930 Ӵ੕ͷ਺ 0 0 1 2 ஍ٿܕ࿭੕ͷੑ࣭
4. ໦੕ ౔੕ ఱԦ੕ ւԦ੕ يಓ௕൒ܘ [AU] 5.2 9.6 19.2 30.1 ެసपظ [೥] 11.86 29.46 84.02 164.7 ࣭ྔ [஍ٿ = 1] 317.8 95.2 14.5 17.2 ൒ܘ [km] 71490 60270 25560 24760 ີ౓ [kg/m3] 1330 690 1270 1640 Ӵ੕ͷ਺ 72 53 27 14 ڊେΨε࿭੕ɾණ࿭੕ͷੑ࣭
5. ଠཅܥͷ୅දతͳӴ੕ͨͪ (c) Wikipedia
6. ༷ʑͳӴ੕ܗ੒࿦ • δϟΠΞϯτΠϯύΫτʢ݄ɾΧϩϯʣ • प࿭੕ԁ൫ʢΨϦϨΦӴ੕ɾλΠλϯʣ • Ϧϯάʢڊେ࿭੕ͷنଇӴ੕ͷҰ෦ʣ • ั֫ʢڊେ࿭੕ͷෆنଇӴ੕ɾτϦτϯʣ • ະ֬ఆʢՐ੕Ӵ੕ɾఱԦ੕Ӵ੕ʣ • ଠཅܥ֎ͷӴ੕ܗ੒࿦ʹ޲͚ͯ
7. ༷ʑͳӴ੕ܗ੒࿦ • δϟΠΞϯτΠϯύΫτʢ݄ɾΧϩϯʣ • प࿭੕ԁ൫ʢΨϦϨΦӴ੕ɾλΠλϯʣ • Ϧϯάʢڊେ࿭੕ͷنଇӴ੕ͷҰ෦ʣ • ั֫ʢڊେ࿭੕ͷෆنଇӴ੕ɾτϦτϯʣ • ະ֬ఆʢՐ੕Ӵ੕ɾఱԦ੕Ӵ੕ʣ • ଠཅܥ֎ͷӴ੕ܗ੒࿦ʹ޲͚ͯ
8. ଠཅܥͷ୅දతͳӴ੕ͨͪ (c) Wikipedia
9. ݄ ɾਓྨ͕߱Γཱͬͨ།Ұͷ஍ٿ֎ఱମ
   ɾ஍ٿ͔Βͷڑ཭ɿສLN
   ɾ൒ܘɿLNʢ஍ٿͷഒʣ
   ɾ࣭ྔɿºLHʢ஍ٿͷഒʣ
   ɾ஍ٿʹৗʹಉ͡໘Λ޲͚͍ͯΔ
   ɾද໘͸ແ਺ͷΫϨʔλʔʹ෴ΘΕ͍ͯΔ ද ཪ (c) Wikipedia (c) Takayuki Yoshida
10. ݄ͷىݯઆ ั֫આ ෼྾આ ૒ࢠઆ ݪ࢝஍ٿ͕ߴ଎ճసʹΑΓ;͘ΒΈ
    ͦͷҰ෦͕ͪ͗Ε݄͕ͯ஀ੜ ஍ٿيಓ෇ۙͰͷඍ࿭੕ͷूੵʹΑΓ
    ஍ٿͱ͸ಠཱʹ݄͕ܗ੒ ஍ٿͱ͸ผͷ৔ॴͰ࡞ΒΕ݄͕ͨ
    ஍ٿͷۙ͘Λ௨ͬͨͱ͖ʹัΒ͑ΒΕͨ ߴ଎ճస͕೉͍͠
    
    ֯ӡಈྔ͕େ͖͗͢Δ ݄ͷ಺෦ߏ଄͕આ໌Ͱ͖ͳ͍
    
    ݄Λ࢒ͤͳ͍ ั֫֬཰͕௿͍
    
    Խֶత੍໿Λຬͨͤͳ͍
11. δϟΠΞϯτΠϯύΫτઆ [Hartman & Davis, Icarus, 1975] [Cameron & Ward, LPI Conference, 1976] (c) Wikipedia
12. ڊେఱମিಥʹΑΔԁ൫ܗ੒ [Canup & Asphaug, Nature, 2001] © Natsuki Hosono ݪ࢝஍ٿʹՐ੕αΠζͷ ݪ࢝࿭੕͕িಥ ඈͼࢄͬͨഁย͕஍ٿͷ
    पғʹԁ൫Λܗ੒ ͜ͷഁยΛࡐྉʹͯ͠
    ݄͕ܗ੒͞ΕͨͷͰ͸ʁ
13. Roche radius, whereas Fig. 3 is a rather extended disk case (run 9). The extension of a disk is indicated by Jdisk /Mdisk , where Jdisk is the total angular momentum of the starting disk. For the disks in Figs 2 and 3, Jdisk /Mdisk are0:692 GM!aR and 0:813 GM!aR , respectively. Figure 3 The same snapshots as in Fig. 2 but for run 9 of a more extended disk (J disk =M disk ¼ 0:813 GM ! a R ). At t ¼ 1,000 the largest moon mass is 0.71M L. [Ida et al., Nature, 1997] FIG. 2. Snapshots of the circumterrestrial disk projected on the R–z plane at t = 0, 10, 30, 100, 1000TK for runs (a) 29a centered at the coordinate origin stands for Earth. Circles represent disk particles and their size is proportional to the physic [Kokubo et al., Icarus, 2000] N ମܭࢉʹΑΔ݄ܗ੒ܭࢉ
14. ݄ܗ੒γϛϡϨʔγϣϯ ਺ϲ݄ʙ਺೥Ͱɺͻͱͭͷ݄͕Ͱ͖Δ [Sasaki & Hosono, ApJ, 2018] [Simulation by Natsuki Hosono]
15. “CAIʢଠཅܥ࠷ݹ෺࣭ʣܗ੒͔Β໿3,000ສ೥ޙ ݪ࢝஍ٿʹՐ੕αΠζͷݪ࢝࿭੕͕ࣼΊিಥ͠ ඈͼࢄͬͨϚϯτϧ෺࣭͕प࿭੕ԁ൫Λܗ੒͠ ͦΕΒ͕໿਺೥͔͚ͯूੵ݄͕ͯ͠஀ੜͨ͠”
16. ݄ܗ੒ʹؔ͢Δ੍໿৚݅ (1) ஍ٿʔ݄ܥͷ֯ӡಈྔʢLtotal ͕อଘʣ (2) ஍ٿΑΓ௿ີ౓ʢίΞ͕খ͍͞ʣ[Hood & Zuber, 2000] (3) شൃੑݩૉ͕ڧ͘ރׇ [Jones & Palme, 2000] (4) ද໘͕େن໛༹༥Λܦݧ [Warren, 1985] (5) ࢎૉಉҐମൺ͕஍ٿͱ΄΅Ұக [Wiechert et al., 2001] [Touboul et al., 2007] (6) ೉شൃੑݩૉͷಉҐମൺ͕஍ٿͱ΄΅Ұக (7) Si ಉҐମൺ͕஍ٿͱ΄΅Ұக [Armytage et al., 2012] (8) W ಉҐମൺ͕஍ٿͱ΄΅Ұக [Touboul et al., Nature, 2015]
17. ratio of 9:1 and a total mass of 1.05 ME (Canup, 2004). Both the impactor and the target are assumed to be differentiated bodies with a 30 wt% iron core and a 70 wt% silicate mantle. In these low-velocity collisions, the impactor loses kinetic energy during its grazing collision with the target, before it is dispersed into a disk around the target. The resulting proto-lunar disk is therefore mainly composed of impactor material. We will call this the ‘‘canonical scenario’’. When the assumption that no mass is lost is dropped however, the collisional angular momentum is no longer tightly constrained, as lost mass also carries away angular momentum. The total collisional angular momentum can therefore be con- siderably higher than the final angular momentum in the Earth–Moon system. With this additional degree of freedom, new regions in the collision parameter space be- come feasible. Apart from the disk mass, another interesting quantity is the origin of the mate- rial which ends up in the proto-lunar disk, especially for the silicate part. We call the fraction of target silicate to total silicate material in the disk fT ¼ ðMsilc targ =Msilc tot Þdisk ð1Þ where Msilc targ and Msilc tot denote the mass of the silicate fraction of the disk derived from the target, and the total disk mass, respectively. If we define a similar target-derived silicate fraction for the post-impact Earth, we can deduce a deviation factor dfT ¼ Msilc targ  . Msilc tot  disk . Msilc targ  . Msilc tot  post-impact Earth À 1 ð2Þ which directly reflects the compositional similarity between the silicate part of the proto-lunar disk and the silicate part of the post-impact Earth. Isotopic measurements show (Wiechert et al., 2001; Zhang et al., 2012) a strong isotopic similarity between the silicate fractions of today’s Moon and Earth. Assum- ing isotopic heterogeneity of the pre-impact bodies, this suggests that either the material of the bodies mixed during the collision or re-equilibrated their isotopic signatures after the collision. Either scenario is represented by a dfT $ 0 between to- day’s Earth and the Moon. The value of dfT right after the impact thus serves as a starting point, from which a re-equilibration mechanism leads to todays value of dfT $ 0. In a typical simulation of the canonical scenario, only about 30% of the disk material and 90% of the material of the post-impact Earth is derived from the target (the proto-Earth) respectively (Canup, 2004), yielding a dfT of À67%. 4. Results The new class of collisions presented here falls into the broad regime of slow hit-and-run collisions (Asphaug et al., 2006) with impact velocities between 1.20 and 1.40 vesc . Hit-and-run occurs up to half the time for collisions with impact colors. In the canonical scenario, the impactor grazes around the target’s mantle and is deformed. Due to the low impact velocity, material supposed to end up in or bit around the Earth must not be decelerated too strongly in order to retain enough velocity to stay in orbit. This is only achieved for the parts of the impactor mantle most distant to the point of impact, and some minor part of the target’s mantle. Bu if impact velocity is increased from 1.00 (cA08) to 1.30 vesc (cC01), parts from dee- per within the target mantle receive the right amount of energy for orbit insertion while the outer regions of the target mantle, retain too much velocity and leave the system, thereby removing mass and angular momentum. Both processes work to wards increasing the target material fraction in the proto-lunar disk. While in run Fig. 1a. Five snapshots from the 30° impact angle and 1.30 vesc impact velocity case (cC06) showing cuts through the impact plane. Color coded is the type and origin o the material. Dark and light blue indicate target and impactor iron; Red and orange show corresponding silicate material. The far right shows the situation at the time of impact. At 0.52 h, it can be seen how the impactor ploughs deep through the targets mantle and pushes considerable amount of target material into orbit. A spiral arm of material forms and gravitationally collapses into fragments. The oute portions of the arm mainly consist of impactor silicates and escapes due to having retained a velocity well above escape velocity. The silicate fragments further inward are stronger decelerated and enter eccentric orbits around the target. The impactor’s iron core also looses much of its angular momentum to the outer parts of the spiral arm and re-impacts the proto-Earth. (For interpretation of the references to color in this figure legend, the reader is referred to the web version o this article.) A. Reufer et al. / Icarus 221 (2012) 296–299 297 ༷ʑͳ݄ܗ੒γφϦΦ [Reufer et al., Icarus, 2012] with less angular momentum. angular momentum by add- pactors generated successful wer-spinning planets. Because m is carried away with debris giant impacts, the spin period ases. Thus, the spin state of d to be near fission before or ming impact in our scenario entry in Table 1). However, is near the stability limit. Our candidate Moon-forming events have more than double the kinetic energy of previous scenarios, and the impact velocities were suf- ficient to substantially vaporize silicates (33). As a result, the silicate atmosphere and vapor-rich disk are more massive and hotter than found in previous work (34). At the resolution of the simulations, the projectile-to-target mass ratio is uniform from the atmosphere to the Roche radius. f the rth’s mpact or at −0.3 spin- f 2.3 Gray oche w of ower down spin enote and Earth e disk terial arth’s mpact e S1). view de- lue), and ensity ne of which 38 SCIENCE www.sciencemag.org on November 25, 2012 www.sciencemag.org Downloaded from [ Ć uk & Stewart, Science, 2012] into a single moon at an orbital distance of about 3.8R⊕ , where R⊕ is Earth’s radius (19, 20), MM MD ≈ 1:9 LD MD ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2:9GM⊕R⊕ p   − 1:1 − 1:9 Mesc MD   ð1Þ where Mesc is the mass that escapes from the disk as the Moon accretes. To estimate MM , we used Eq. 1 and made the favorable assumption that Mesc = 0. We tracked the origin (impactor versus tar- get) of the particles in the final planet and the disk. To quantify the compositional difference be- tween the silicate portions of the disk and planet, we define a deviation percentage dfT ≡ [FD,tar /FP,tar − 1] × 100 (2) where FD,tar and FP,tar are the mass fractions of the silicate portions of the disk and of the planet derived from the target’s mantle, respectively (21). Identical disk-planet compositions have dfT = 0, whereas a disk that contains fractionally more impactor-derived silicate than the final planet has dfT < 0, and a disk that contains fractionally less impactor-derived silicate than the final planet has dfT > 0. Prior impact simulations (1–3, 14, 15) that consider g ≡ Mimp /MT ≈ 0.1 to 0.2 produce disks with −90% ≤ dfT ≤ −35% for cases with MM > ML , where ML is the Moon’s mass. Results with larger impactors having g = 0.3, 0.4, and 0.45 are shown in Figs. 1 and 2 and Table 1. As the relative size of the impactor (g) is increased, there is generally a closer compositional match be- tween the final disk and the planet. For g ≥ 0.4, some disks have both sufficient mass and an- gular momentum to yield the Moon and nearly identical silicate compositions to that of the final Fig. 1. An SPH simulation of a moderately oblique, low-velocity (v∞ = 4 km s–1) collision between an impactor and target with similar masses (Table 1, run 31). Color scales with particle temperature in kelvin, per color bar, with red indicating tempera- tures >6440 K. All particles in the three-dimensional simulation are overplotted. Time is shown in hours, and distances are shown in units of 103 km. After the initial impact, the plan- ets recollided, merged, and spun rapidly. Their iron cores migrated to the center, while the merged structure developed a bar- type mode and spiral arms (24). The arms wrapped up and finally dispersed to form a disk containing ~3 lunar masses, whose silicate composition dif- fered from that of the final planet by less than 1%. Because of the near symmetry of the colli- sion, impactor and target material are distributed approximately proportion- ately throughout the final disk, so that the disk’s dfT value does not vary ap- preciably with distance from the planet. Fig. 2. Compositional differ- ence between the disk and final planet (dfT ) (Eq. 2) produced by simulations with (A) g = 0.3 and (B) g = 0.4 (triangles) and 0.45 (squares) versus the pre- dicted mass of the moon that would accrete from each disk (MM ) (Eq. 1) scaled to the final planet’s mass (MP ). There is a change in y axis scales between the two plots. Gray, purple, dark REPORTS on November 25, 2012 www.sciencemag.org Downloaded from [Canup, Science, 2012] ༷ʑͳ G.I. γφϦΦ ͕ఏҊ͞Ε͍ͯΔ͕ ͲΕ΋શͯͷ੍໿৚ ݅Λຬ͓ͨͯ͠Βͣ ܾఆଧ͕ແ͍
18. ௒ߴΤωϧΪʔিಥ ஍ٿͷϚϯτϧ͸ G.I. Ͱ͍ͬͨΜશͯৠൃͨ͠ʂʁ [Wang & Jacobson, Nature, 2016]
19. ෳ਺ճͷিಥʹΑΔ݄ܗ੒ NATURE GEOSCIENCE DOI: 10.1038/NGEO2866 ARTICLES a −60 −45 −30 −15 0 15 30 45 60 V imp /V esc V imp /V esc 1.0 1.4 2.0 3.0 4.0 1.0 1.4 2.0 3.0 4.0 M moon M moon 1.0 0.5 0.1 9 5 2.4 1 0 10 20 30 40 50 60 b 1.0 0.5 0.1 9 5 2.4 1 10 20 30 40 50 60 Impact angle, (°) β |δf T | (%) |δf T | (%) a L imp /L EM L final /L EM −4 −2 0 2 4 M sat /M moon 10−2 10−1 100 b 1.0 1.5 2.0 2.5 3.0 |δf T | < 10 Graze and merge Hit and run Partial accretion / max = 0.00 ω ω / max = 0.25 ω ω / max = 0.50 ω ω NATURE GEOSCIENCE DOI: 10.1038/NGEO2866 ARTICLES a −60 −45 −30 −15 0 15 30 45 60 V imp /V esc V imp /V esc 1.0 1.4 2.0 3.0 4.0 1.0 1.4 2.0 3.0 4.0 V imp /V esc 1.0 1.4 2.0 3.0 4.0 M moon M moon M moon 1.0 0.5 0.1 9 5 2.4 1 0 10 20 30 40 50 60 b 1.0 0.5 0.1 9 5 2.4 1 0 10 20 30 40 50 60 c 1.0 0.5 0.1 9 5 2.4 1 10 20 30 40 50 60 Impact angle, (°) β −60 −45 −30 −15 0 15 30 45 60 Impact angle, (°) β |δf T | (%) |δf T | (%) |δf T | (%) a L imp /L EM L final /L EM L imp /L EM −4 −2 0 2 4 M sat /M moon 10−2 10−1 100 b −6 −4 −2 0 2 4 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 |δf T | < 10 Graze and merge Hit and run Partial accretion / max = 0.00 ω ω / max = 0.25 ω ω / max = 0.50 ω ω Figure 4 | Final satellite mass and system angular momentum. a, Mass of the formed satellite using equation (2) as a function of impact angular momentum for !=0.25!max rotation. The colours correspond to di￿eren collisional regimes (hit and run—impactor escapes partially intact; graze and merge—impactor impacts the target twice; partial accretion—addition of mass to the target). b, The final angular momentum of all the systems that created a satellite. The di￿erent styles of markers represent di￿erent initial rotations. The darker horizontal lines represent the initial planetary angular momentum value with colours corresponding to the colours of the markers. Disks containing <100NSPH were omitted. −60 −45 −30 −15 0 15 30 45 60 V im V imp /V esc 1.0 1.4 2.0 1.0 1.4 2.0 3.0 4.0 V imp /V esc 1.0 1.4 2.0 3.0 4.0 M moon M moon 0 10 20 b 1.0 0.5 0.1 9 5 2.4 1 0 10 20 30 40 50 60 c 1.0 0.5 0.1 9 5 2.4 1 0 10 20 30 40 50 60 Impact angle, (°) β −60 −45 −30 −15 0 15 30 45 60 Impact angle, (°) β −60 −45 −30 −15 0 15 30 45 60 Impact angle, (°) β %) |δf T | (%) |δf T | (%) Figure 3 | Disk properties in the angle–velocity phase space. a–c, Initial planetary rotation rate !=0.10!max (a), !=0.25!max (b) and !=0.50!max (c). The marker size corresponds to disk mass and the colour to the compositional di￿erence between the silicates in the final planet and disk. For comparison, the grey circles in the upper left corner represent a disk mass of 0.1, 0.5 and 1 MMoon. Markers are shifted horizontally according to the mass ratio, from left to right (9, 5, 2.4, 1%). The grey dots indicate disks that have an iron content larger than the estimated lunar core mass of 0.1Mmoon. Disks containing <100 smoothed particle hydrodynamics (SPH) particles were omitted. retrograde impactors often fail to form a disk with enough angular momentum to accrete a moonlet. Fi th m co an o th in an m h F ro g er d th p H p m im m re a [Rufu et al., Nature Geo., 2017] 20 ճఔ౓ͷিಥͰܗ੒͞Εͨ moonlets ͷूੵ িಥதͷ previous moonlets ͷ҆ఆੑʹ͍ͭͯ͸ෆ໌
20. d e - e a - n # d proto-Earth proto-Earth impactor impactor magma ocean vapor jet (a) (b) Fig. 4. Schematic drawing of processes of ejection of materials upon a giant impact. (a) A case where the proto-Earth does not have a magma ocean. (b) A case where the proto-Earth has a magma ocean. R h A B C Fig. 3. A schematic diagram showing possible paths of materials ejected at a certain height. Only a fraction of materials goes to the orbit (shaded region) from which the Moon was formed. The fate of ejected materials depends on the ratio h/R and materials with only for modest value of h/R and velocity will become the source of the Moon. 2 e n e n n- s, ϚάϚΦʔγϟϯ஍ٿ΁ͷ G.I. ஍ٿͷϚάϚΦʔγϟϯ͕બ୒తʹ݄ԁ൫ʹ෼഑ʂ [Hosono et al., Nature Geo., 2019]
21. Canup (2004) Kokubo et al. (2000) Giant Impactʢ໿1೔ʣ ݄ͷܗ੒ʢ໿1݄ʣ ʁ Pahlevan & Stevenson (2007) ݄ԁ൫ͷྫྷ٫ਐԽ ʢ50೥ʙ100೥ʣ ຊདྷ͸݄ԁ൫ͷਐԽաఔΛ௥͏ඞཁ͕͋Δ͕ ௕࣌ؒͷܭࢉΛߦ͏͜ͱ͕Ͱ͖ͣෆՄೳͩͬͨ ݄ԁ൫ͷਐԽաఔΛܭࢉ [Sasaki & Hosono, 2018, 2020 submitted]
22. 222 Therefore, exploration of this region may address some fundamental questions, such as on the nature of the lunar mantle, the cause of the greater crustal thickness on the farside, and how farside maria differ from site. The boundary between impact ejecta and underlying basalt is clearly identifiable, and there is potential evidence of excavated deep mafic material, which could reveal the mineralogy of the lunar mantle. China. 3China Aerospace Science and Technology Corporation, Beijing, China. 4Institute of Tracking and Communication Technology, Beijing, China. 5National Space Science Center, Chinese Academy of Sciences, Beijing, China. 6China Academy of Space United States China Soviet Union/Russia Elevation (m) –9,178 –6,178 –3,178 –178 2,822 5,822 8,822 CHANG'E-4/YUTU 2 CHANG'E-3/YUTU SURVEYOR 7 APOLLO 16 APOLLO 11 SURVEYOR 5 SURVEYOR 6 APOLLO 14 APOLLO 12 SURVEYOR 3 SURVEYOR 1 Apollo 17 Apollo 15 LUNA 16 LUNA 20 LUNA 24 LUNA 23 LUNA 9 LUNA 13 LUNA 17/LUNAKHOD 1 LUNA 21/LUNAKHOD 2 0° 30° N 60° N 90° N 30° S 60° S 0° 30° N 60° N 30° S 60° S 90° S 0° 30° N 60° N 90° N 30° S 60° S 0° 30° N 60° N 30° S 60° S 90° S Nearside Farside Fig. 1 | Distribution of manned and unmanned landings on the Moon to date. Data (https:/ /go.nature.com/2tT27ez) laid over a digital elevation model from Chang’e-2. China’s Chang’e-4 is the first lander on the lunar farside. NATURE GEOSCIENCE | VOL 12 | APRIL 2019 | 222–223 | www.nature.com/naturegeoscience ݄୳ࠪɿ͍ͭʹ݄ͷཪଆ΁ தࠃͷ୳ࠪػʮᇲᇝ̐߸ʯ͕݄ͷཪଆΛॳ୳ࠪ
23. ଠཅܥͷ୅දతͳӴ੕ͨͪ (c) Wikipedia
24. ਫۚ஍Ր໦౔ఱւ້ 9 ೥݄೔
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27. ͭͷ࿭੕ͱͭͷ४࿭੕ ࿭੕ ४࿭੕ ਫ ۚ ஍ Ր ໦ ౔ ఱ ւ ້Ԧ੕ ΤϦε έϨε ϚέϚέ ೥݄ ϋ΢ϝΞ ೥݄   ࠓޙ΋૿͑ΔՄೳੑ͋Γ (c) Wikipedia, NASA
28. ້Ԧ੕ͱӴ੕Χϩϯ (c) Wikipedia (c) NASA
29. [Canup, Science, 2005] e f d 100 75 50 25 0 –100 –75 –50 –25 Longitude (°) 0 60 120 180 240 300 360 Latitude (°) Latitude (°) d = 0 km (Surface) d = 200 km 0 0.2 0.4 Area fraction (T > Tpost ) 0.5 0.3 0. 0 30 60 90 –30 –60 –90 30 60 90 –30 –60 –90 0 43.6 h tion of a Charon-sized satellite and elongated post-impact heated area near Pluto’s equator. The results Table 1) are shown. Both the target and the impactor were undifferentiated bodies with rock mass ratios (f r nd initial potential temperatures (T 0 ) of 150K. The impactor-to-target mass ratio was 0.35. The impact vel ້Ԧ੕ͷӴ੕Χϩϯͷܗ੒ [Sekine et al., Nature Astron., 2017] ້Ԧ੕΁ͷ Giant Impact ʹΑΔӴ੕ͷ “ั֫”
30. ͭͷ࿭੕ͱͭͷ४࿭੕ ࿭੕ ४࿭੕ ਫ ۚ ஍ Ր ໦ ౔ ఱ ւ ້Ԧ੕ ΤϦε έϨε ϚέϚέ ೥݄ ϋ΢ϝΞ ೥݄   ࠓޙ΋૿͑ΔՄೳੑ͋Γ (c) Wikipedia, NASA
31. ϋ΢ϝΞͷӴ੕ɾϦϯάܗ੒ ਤ 1.3 খఱମͷিಥʹΑͬͯϋ΢ϝΞͷࣗస͕Ճ଎͠෼྾͢Δ༷ࢠΛࣔͨ͠ N ମγϛϡϨʔγϣϯͷ݁Ռɻ ʢOrtiz et al. 2012ʣ [Sumida,…, Sasaki, ApJ, 2020]
32. ༷ʑͳӴ੕ܗ੒࿦ • δϟΠΞϯτΠϯύΫτʢ݄ɾΧϩϯʣ • प࿭੕ԁ൫ʢΨϦϨΦӴ੕ɾλΠλϯʣ • Ϧϯάʢڊେ࿭੕ͷنଇӴ੕ͷҰ෦ʣ • ั֫ʢڊେ࿭੕ͷෆنଇӴ੕ɾτϦτϯʣ • ະ֬ఆʢՐ੕Ӵ੕ɾఱԦ੕Ӵ੕ʣ • ଠཅܥ֎ͷӴ੕ܗ੒࿦ʹ޲͚ͯ
33. ଠཅܥͷ୅දతͳӴ੕ͨͪ (c) Wikipedia
34. ໦੕ͷΨϦϨΦӴ੕ ΠΦ Τ΢ϩύ Ψχϝσ ΧϦετ (c) Wikipedia ΨϦϨΦɾΨϦϨΠ
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    ைࣚྗ͕ΤωϧΪʔݯ͔ʁ (c) Wikipedia
36. Τ΢ϩύʹ͸஍ٿ֎ੜ໋ͷՄೳੑʁ ಺෦ʹӷମ ঢ় ͷਫΛ࣋ͭ ੜ໋͕ଘࡏ͢Δ͔΋ʂʁ ද໘ͷණʹ͸
    ແ਺ͷͻͼׂΕ͕ଘࡏ (c) NASA ಺෦ʹӷମ ঢ় ͷਫΛ࣋ͭ (c) Wikipedia (c) ౦ژༀՊେֶ
37. ֎ଆͷڊେͳ̎Ӵ੕ ൒ܘɿLN
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38. ӷମϝλϯͷބ͕ଘࡏ ද໘ʹ͸ੴ΍ණմ (c) Wikipedia ౔੕ͷڊେӴ੕λΠλϯ
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40. ڊେΨε࿭੕ͷܗ੒ ݪ࢝࿭੕ʹԁ൫Ψε͕๫૸తʹྲྀೖ
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41. Ψεั֫ʹΑΔڊେΨε࿭੕ܗ੒ ݪ࢝࿭੕͸ॏྗʹΑΓपғͷԁ൫ΨεΛั֫
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42. प࿭੕ԁ൫಺ͰӴ੕͕ܗ੒ (c) ໊ݹ԰େֶ
43. 26 24 ATURE|Vol 441|15 June 2006 ARTICLES We now consider the implications of this limiting mass for the total mass of the resulting satellite system. Consider an inflow that persists for a time exceeding that needed for a satellite of mass mcrit to form. Within a given annulus in the disk, a satellite grows to a mass ,mcrit before being lost to type I decay, but in a comparable timescale to its loss another similarly massive satellite grows in its place (because t1 < tacc ). In this way, the disk is regulated to contain a total mass in satellites, MT , comparable to a distribution of mass mcrit objects across the inflow region. For (H/r) and f that are approximately constant across the disk, the predicted satellite system mass fraction is: MT MP   ¼ ðrC RP ðmcrit=MP Þ Dr dr <3:5 1 Ca   4=9 H r   10=9 a f   1=3 1 ðQtGf Þ1=9 ,2:5 £ 1024 1 x 3:5 Ca   4=9 H=r 0:1   10=9 a=f 3 £ 1025   1=3 ð3Þ similar to the observed satellite systems. Here we assume rC . . RP; where RP is the planet’s radius. Note that (MT /MP ) is insensitive to inflow rate through x, lacks a dependence on rC , and depends quite weakly on (a/f). Simulation results We model satellite growth and loss using a direct N-body accretion simulation19, modified to include interactions with a gas disk and ongoing mass inflow (Supplementary Methods). The solid inflow is mimicked by the addition of orbiting objects with random positions within the inflow region at a rate proportional to (Fin /f). Collisions are treated as inelastic mergers. Figure 2 shows results of three simulations involving a time- constant gas inflow rate but varied values for (a/f). Type I orbital decay acts as a negative feedback on the total mass contained in the satellite system, causing (MT /MP ) to oscillate about a value com- Figure 2 | Results of satellite accretion simulations with time-constant inflows. The total mass in satellites, MT , scaled to the planet’s mass, MP , is shown versus time scaled to tG ; MP =ðdM=dtÞ21; where dM/dt is the inflow rate. All three cases consider inflows having tG ¼ 5 £ 106 yr, rC ¼ 30RP , and gin ¼ 0, with the green, blue and red lines corresponding respectively to simulations with (a/f) ¼ 1026, 5 £ 1025 and 5 £ 1024. The inflow of solids causes MT to increase with time until objects of mass ,mcrit form (equation (2)). The orbits of the largest satellites then decay inward, and MT decreases in discrete steps as satellites are lost to collision with the planet. Solid inflow to the disk continues, leading to the growth of another generation of mass ,mcrit objects, and the cycle repeats. As (MT /MP ) depends on (a/f)1/3, the factor of 500 variation in (a/f) across these simulations yields about a factor of 10 spread in the characteristic system mass fractions. The long period oscillations in (MT /MP ) reflect the time needed to deliver mass sufficient to form mass mcrit objects; this period shortens as (a/f) (and therefore (mcrit /MP )) is decreased for a fixed tG . Shorter period variations result from the loss of individual objects. Dashed lines are predicted (MT /MP ) values (equation (3)). Equations (2) and (3) treat disk annuli independently but in actuality, as satellites formed in the outer disk migrate inwards they pass through interior zones and cannibalize material along the way. Migration- driven growth hastens their orbital decay, so that they are lost somewhat ARTICLES NATURE|Vol 441|15 June 2006 [Canup & Ward, Nature, 2006] ʙ 10-4 ≃ ≃ Ӵ੕ܥͱ࿭੕ͷ࣭ྔൺ͕΄΅౳͍͠ प࿭੕ԁ൫಺ͰͷӴ੕ͷ੒௕ͱ
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44. ໦੕Ӵ੕ܥͱ౔੕Ӵ੕ܥͷҧ͍ λΠλϯ ΠΦ Τ΢ϩύ Ψχϝσ ΧϦετ ؠੴ ؠੴ ණ ණ
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    ະ෼Խ dial ice-rock mixtures may display distinct degrees of internal differentiation. Impact- induced melting and/or intense tidal heating of Ganymede, locked in orbital resonances with the inner neighboring satellites Io and Europa, may have triggered runaway differ- entiation, but Callisto farther out from Jupiter ries and gradual unmixing of ice and rock may also play a role for incomplete differentiation of icy satellites. References and Notes 1. L. Iess et al., Science 327, 1367 (2010). 2. R. Jaumann et al., in Titan from Cassini-Huygens, R.H. Brown, J.-P. Lebreton, J. Hunter Waite, Eds. (Springer, New York, 2009), pp. 75–140. Inside Titan. Global gravity fi eld and sh pletely separated within Titan’s deep inte may contain a cold water-ammonia ocean water ice below (gray) and a fl oating ice/c images show that the extent of separation density that is predominantly affected by
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50. M . g = 0.02 MJ Myr -1 M . d/M . g = 1 0 20 40 60 80 100 100 101 102 Relative velocity Δv [m s-1] Distance from the planet r [RJ] α = 10-4 50 m s-1 Δvdd Δvt Δvr 0 20 40 60 80 100 100 101 102 Distance from the planet r [RJ] α = 10-2 50 m s-1 Δvdd Δvt Δvr , Figure 5. Dust-dust relative velocities with different turbulence strength, α = 10−4 (left panel) and α = 10−2 (right panel). The other conditions are ˙ Md/ ˙ Mg = 1 and ˙ Mg = 0.02 MJ Myr−1 in both the panels. The black curves represent the dust-dust relative velocities (collision velocities). The red and blue curves represent the velocities induced by only the turbulence and their radial drift, respectively. The black dotted lines are the critical velocity of the fragmentation. Success
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            10-3 10-4 10-2 0.001 0.01 0.1 1      10-5 We found that the one of the condition for the satellites- imasl formation is ˙ Md/ ˙ Mg ≥ 1. However, this condition may be difficult to achieve. First, the dust particles tend to settle down toward the midplane, the inflow gas from the high altitude is likely to dust-poor gas (Tanigawa et al. 2012). This effect must depend on the conditions of the turbulence and the gas density of the region around the circumplanetary disk which the accretion gas comes from (Equations (15) and (10)). Second, the dust supply may not be enough to achieve ˙ Md/ ˙ Mg ≥ 1. The dust particles drift from the outer region of the protoplanetary disk (Sato et al. 2016). However, these particles have already grown to the pebbles (cm-sized parti- cles) until they reach around the gas planets like Jupiter, so that most of them should be dammed at the outer edge of ͦͷޙɿ༷ʑͳ໰୊఺ͷࢦఠ प࿭੕ԁ൫͸΄ͱΜͲͷ
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    ಛʹؠੴඍӴ੕͸ܗ੒ෆՄ Figure 4 but for the case of = 10−5. 40 1e-06 0.0001 0.01 1 100 5 10 15 20 25 30 35 40 Σ [g/cm2] r [RJ ] resents the surface densities at the given radius which have well-developed MRI turbulence at hat at only above 2H. Since we choose β0 = 105, βz < 2000 above 2.8H and well-developed densities in which we cannot find regions of Λ > 1 below 2.5H. The left panel is the result ains of a = 0.1 µm. With dust grains, the MRI-active region is smaller because of the lower v∞ )2 with y vesc 002). milar r, the (27) summarized in Figure 6. The surface densities which can sustain well-developed turbulence for z > 2H, z > 0.5H, and for the entire height at each radius are shown. The mid-plane plasma beta considered here is β0 = 105. If we choose larger β0 , the line Λ = 1 shifts higher which means the MRI-active region becomes smaller. On the other hand, if we choose smaller β0 , the region with βz > 2000 is smaller, and having large MRI-active regions becomes difficult. 5. DISCUSSION We find that when accounting for cosmic rays, X-rays, and radionuclides, circumplanetary disks are not likely to sustain [Shibaike,…, Sasaki, ApJ, 2017] [Fujii et al., ApJ, 2014]
51. ಺ଆͷӴ੕͸શͯམԼ
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    ໦੕Ӵ੕ܥΛ࠶ݱʂ ͞Βʹͦͷޙɿ৽ͨͳ෺ཧաఔͷఏҊ umber of ( ) 26 ( ) 27 Ogihara & 3:2 2×105 5×105 Shibaike et al. [Fujii & Ogihara, A&A, 2020] [Shibaike,…, Sasaki, ApJ, 2019]