Properties of the Pluto-Charon binary

Transcription

1 roperties o the luto-haron binary The orbital period, = ± days, and semi-major axis o haron s orbit, a = ± 8 km, imply a total mass M = ± g (S1). luto s motion relative to the system center o mass constrains the haron-to-luto mass ratio, q M /M, with recent HST observations (S) yielding q = 0.1 ± Radii and density estimates are 1151 ± 6 R (km) 1195 ± 5 and 1.83 ± 0.09 ρ (g/cm 3 ).05 ± 0.11 or luto, and 593 ± 13 R (km) 61 ± 1 and 1.59 ± 0.0 ρ (g/cm 3 ) 1.83 ± 0.18 or haron (e.g., S), indicating a haron that is comparably or less dense than luto. The luto-haron pair is tidally locked, so that the rotational angular velocity o both objects equals their mutual orbital velocity, ω (π/). The angular momentum o the system about its center o mass is L M M = ω M a + K M ωm q qωm a = a K R qk R ( 1 q) q + (1 + q) R + K M R. (S1) where K and K are the moment o inertia constants or luto and haron with K i I i /(M i R i ); or K, K > 0.3, the sum o the two spin terms is < % o L. Disk producing impacts Figure S1 shows the predicted q values vs. J or all o the disk-producing impacts. This is the most consistent scaling or these cases, and as J increases, the results converge to a relationship (dotted line) consistent with a planet rotating with period ~ T min, with the rest o the angular momentum partitioned into the disk. The angular

2 momentum in an object rotating at its stability limit is proportional to its moment o inertia constant, K, so that as K decreases, so too does the raction o the total angular momentum that can be accommodated by the planet. Thus or the disk-mode, orming a highly dierentiated central planet with a low K (as occurs or the IDI composition) increases the yield o orbiting material or a given set o collision parameters. Also shown on Fig. S1 (solid lines) are the limits possible or luto-haron over the range o system variable estimates. lanet-disk systems closest to the luto-haron region are produced by collisions with J imp > 0.4 and v imp ~ v esc, corresponding to oblique impacts (b > 0.8) o like-sized objects (γ ~ 0.5) and initial prograde spins that contribute signiicantly to the total impact angular momentum (10 to 5%). Somewhat higher impact speeds (1.1 (v imp /v esc ) 1.3) between dierentiated objects can produce disks, although they are contain a smaller raction o the planet s mass than their (v imp /v esc ) < 1.1 counterparts. As (v imp /v esc ) exceeds about 1. to 1.3 or an oblique impact, there is typically a rather abrupt transition (also seen in S3) to a non-accretionary event in which the majority o the impactor and the impact angular momentum escape. For IDI collisions with γ = 0.5, resulting disks were composed entirely o water ice, compared to initial objects that were 40% ice and 60% rock. Disks produced by collisions o SIM objects contained at average o 80% ice and 0% serpentine, compared to initial objects than were 50% serpentine and 50% ice. However we note that compositional granularity inherent to SH may tend to over-estimate dierentiation, and this could aect the disk compositions derived rom the collisions involving SIM objects.

3 0.1 Disks 0.08 q J 0.5; IDI; 1.0; no spin 0.5; IDI; 1.0; i10 0.5; SIM; 1.0; i10 0.5; SIM; 1.05; i10 0.5; IDI; 1.0; it10 0.5; IDI; 1.05; it10 0.5; IDI; 1.1; it10 0.5; SIM; 1.0; i7 0.5; SIM; 1.05; i7 0.5; IDI; 1.0; it7 0.5; IDI; 1.0; it7; HR 0.5; IDI; 1.05; it7 0.5; IDI; 1.0; i5 0.5; IDI; 1.0; i5; HR 0.5; IDI; 1.0; it5 0.5; IDI; 1.0; it5; HR 0.5; SIM; 1.0; it5 0.5; SIM; 1.0; i4 0.5; IDI; 1.0, it3 0.3; SER; 1.5; no spin 0.3; SER;.0; no spin 0.3; SER; 1.0; t5 0.3; SER; 1.0; t3 0.; IDI; 1.05; t5 0.; IDI; 1.0; it5 0.; IDI; 1.0; t3 0.; IDI; 1.05; t3 0.; IDI; 1.1; t3 0.; IDI; 1.; t3 0.; IDI; 1.0; it3 0.13; IDI;.0; t5 0.13; IDI;.5; t5 -low -high Tpl = Tmin Figure S1: Results o impact simulations that produced planet-disk systems. Simulation parameters are shown in the legend where the irst value is the ratio o the impactor to the total mass (γ), the second indicates the composition o the

4 colliding objects (see text), the third is the ratio o the impact velocity to the escape velocity, and the ourth is the pre-impact prograde spin period in hours or the impactor ( i ) and/or targer ( t ). The nominal resolution is 0,000 particles; 10,000 particle simulations are indicated with HR. Shown is the estimated satellite-to-planet mass ratio, q, (e.g., S4) vs. the normalized angular momentum o the inal bound system, J. The dotted line is the relationship between q and J or an IDI planet o mass M p rotating with a period equal to its minimum or rotational stability, together with a moon o mass M s qm p at a s = 1.a R, where a R is the Roche limit. Red and black solid lines rame the parameter regime consistent with the luto-haron system.

5 Table S1: arameters and results o impacts that yield disks with estimated 0.1 < q < 0.15* Run M T / M γ b v imp/ v esc J imp L s / L esc / M esc / L orb / M orb / J q L imp L imp M T L imp M T it * it it * it it it * it it it *Simulations here involved dierentiated objects with 40% water ice and 60% rock (with the rock composed o 30% iron and 70% dunite). The nominal resolution is N = 10 4 particles; runs with N = particles are starred. See text or variable deinitions. The pre-impact spin state o r r the objects is shown by the raction L / L ) = ( L L ) / L ; superscripts i and it ( s imp s imp imp correspond respectively to L s contained in the impactor or the impactor and target. Results shown are at approximately 4 hours post-impact. M orb and L orb are the disk mass and angular momentum, and J where M is the total system mass and L / GM R is the normalized inal bound system angular momentum, 3 R ( 3M / 4πρ) =. The inal column shows the predicted mass o a moon that would accumulate rom the resulting disk (e.g., S4). 1/ 3

6 S1. D. J. Tholen, M. W. Buie, in luto and haron, S. A. Stern, D. J. Tholen, Eds. (Univ. Arizona ress, Tucson, 1997), pp S.. B. Olkin, L. H. Wasserman, O. G. Franz, Icarus 164, 54 (003). S3.. B. Agnor, E. Asphaug, Astrophys. J. 613, L157 (004). S4. S. Ida, R. M. anup, G. R. Stewart, Nature 389, 353 (1997).