### preamble small = font-size:26px; novsp = text-align:left;margin-bottom:0em; novsphi = text-align:left;margin-bottom:0em;color:#3b91ff darkbg = #444444 #hicolor = #29d hicolor = #70a comment = color:red;font-size:22px;font-style:italic;text-align:center; annotate = font-size:24px;background-color:rgba(255,225,225,0.9);color:black;border:4px dashed red; envS = par|style|$small, eqn|opts|d180, eqi|opts|d180, div|style|$small envW = par|style|$small, eqn|opts|d180, eqi|opts|w,d180, div|style|$small ### start === :: background=trappistI-system-red vvv 72% p :: *FORMATION* :: style=color:rgba(255,255,255);font-size:90px and :: style="color:rgba(255,255,255); *DYNAMICS* :: style=color:rgba(255,255,255);font-size:90px p :: of the :: style=color:white;text-align:center;margin-bottom:1em;margin-top:1em; h1 :: TRAPPIST-1 planets :: style="color:rgba(255,255,255);" div :: style=color:white p :: *Chris Ormel* \n Department of Astronomy, Tsinghua University, Beijing, China :: style=color:white img :: DoAlogo-official div :: style=color:white;margin-top:-0.0em p :: with p :: *Shuo Huang* (Tsinghua University); *Djoeke Schoonenberg* (Amsterdam) \n *Beibei Liu* (Zhejiang University); *Caroline Dorn* (Univ. Zürich) p :: 21.09.22 Ringberg meeting Inside \n :: style=color:white;margin-top:1em;$small vvv border=1% img :: qrcode-ringberg :: style=height:400px p :: \N :: style=margin-top:1.5em; img :: Shuo2018_small :: style=height:230px imb :: Shuo Huang :: style=color:white img :: djoeke :: style=height:230px imb :: Djoeke Schoonenberg :: style=color:white vvv 100% #a :: http://astro.tsinghua.edu.cn/~cormel/Presentations/TrappistI/2020sjtu.html :: http://astro.tsinghua.edu.cn/~cormel/Presentations/TrappistI/2020sjtu.html === :: background=trappistI-system-red :: nest=new h2 :: Contents :: style=color:white *1 Observations ::: style=color:white;font-size:70px * Scenario * Statements * Conclusions === :: nest=new h2 :: TRAPPIST-1 vvv 70% * TRAPPIST-1 star properties: **- mass = 0.089 M_{Sun}_ ** 0.05% L_{Sun}_ ** red dwarf (spectral type M8) ** distance of 12.1 pc (40 ly) ** age 7.6 ± 2.2 Gyr p :: :ads:BurgasserMamajek2017:VanGrootelEtal2018:a: :: style=$small * TRAPPIST = *Tra*nsiting *P*lanets and *P*lanetes*i*mals *S*mall *T*elescope img :: trappist-instrument :: style=height:300px img :: trappist-beer1 :: style=height:300px vvv img :: trappist1-location-aquarius :: style='width:500px' img :: trappist1-sun-jupiter :: style='width:500px' === :: nest=cont h2 :: Discovery TRAPPIST-1 system img :: GillonEtal2017fig1a arr :: sw:3.5,col:#e00 :: pos=lb(.31,.29) imc :: pos=lb(.224,.29) :: \N arr :: sw:3.5,col:#e00 :: pos=lb(.14,.292) imc :: pos=lb(.226,.292) :: \N imc :: pos=lb(.22,.23) :: P_{c}_ :: style=color:red imb :: Combined space (Spitzer) and ground (TRAPPIST) observations. :ads:GillonEtal2017:a: vvv 60% div :: style=text-align:left * From the lightcurve monitoring, we obtain: **- the relative brightness → radius ** the transit interval durations → period \** of all seven planets :: style=text-align:right vvv === :: background=$darkbg :: nest=cont h1 :: TRAPPIST 1 system vvv 30% p :: irradiation received by TRAPPIST-1 planets very similar as inner solar system ----- p :: style=$small :: → planets ordered after amount of radiation received from the star. IoA/Amanda Smith vvv 37% img :: trappistI-solarsys-irradiation :: style=height:700px vvv img :: trappist1e-poster :: style=height:700px === :: repeat=7 :: nest=new h2 :: Observational properties TRAPPIST-1 planets vvv 35% !=2 * planet *radii* from lightcurve dips !=2 * planet orbital periods very precisely !=2 * system is ultra-compact ==1,3,4,5,6 * planets are all *in resonances* ==1,3,4,5,6 * inner planets (b,c,d) are in higher order (weaker) resonances >=4 * mass of the planets through transit timing variations :: ==4 style=color:$hicolor >=6 * composition and/or internal structure ==2 img :: conjunction ==2 imb :: resonances occur when planets have conjunctions at the same point in the orbit. vvv ==0 vid :: trappist1-orbits :: opts=a :: style=max-height:700px ==0 imb :: :ads:GillonEtal2017:a: ==2 * Formally resonances are defined in terms of a two-body *resonance angle*: ==2 eqn :: \phi_\mathrm{res} &= (j+1)\lambda_2 -j\lambda_1 -\varpi_2 \\ :: ==2 &= j(\lambda_2 -\lambda_1) +(\lambda_2 -\varpi_2) \\ :: ==2 &= M_2 \qquad \qquad \qquad \qquad \qquad \qquad (\lambda_2=\lambda_1) ==2 p :: style=$small :: for a first-order resonance. We can also define one wrt ==2 eqi :: \varpi_1. :: opts=d180 ==2 Dynamically, the system is in resonance when the resonance angle librates. ==2 * However, ==2 eqi :: \varpi_i ==2 cannot be measured for the TRAPPIST-1 planets (_e_ too low) ==2 * Solution: combine two 2BR angles into a new angle w/o :: opts=f ==2 eqi :: \varpi_i ==2 eqn :: \phi_\mathrm{12;2} &= (j+1)\lambda_2 -j\lambda_1 -\varpi_2 \\ :: ==2 \phi_\mathrm{23;2} &= (k+1)\lambda_3 -k\lambda_2 -\varpi_2 \\ :: ==2 \Rightarrow \Phi_{123} &= (k+1)\lambda_3 -(k+j+1)\lambda_2 +j\lambda_1 ==1,3,5 tab :: style=font-size:28px; ==1,3,5 | | b | c | d | e | f | g | h :::: opts=H ==1,3,5 radius (Earth) | | 1.12 | 1.10 | 0.79 | 0.92 | 1.05 | 1.13 | 0.76 ==5 mass (Earth) | | 1.3 | 1.3 | 0.39 | 0.69 | 1.0 | 1.3 | 0.33 ==1,3,5 period (days) | P_{i}_ | 1.5108 | 2.4219 | 4.0492 | 6.1010 | 9.2075 | 12.3524 | 18.773 ==1,3,5 period ratio | P_{i+1}_/P_{i}_ | 1.603 | 1.672 | 1.507 | 1.509 | 1.34 | 1.52 ==1,3,5 commensurability| | 8:5 | 5:3 | 3:2 | 3:2 | 4:3 | 3:2 ==1,3,5 three body res. | | | 2:-5:3 | 1:-3:2 | 2:-5:3 | 1:-3:2 | 1:-2:1 ==1,3,5 3BR angle Φ | deg | | 177 | 49 | -148 | -76 | 177 :::: style=border-bottom:2px solid black; ==1,3,5 sources: :ads:LugerEtal2017:AgolEtal2021:a: ::: opts=c7 ::: style=$small ==3 div :: env=$envS :: style=text-align:left;margin-top:1em; :: *Note*. A three-body resonance (3BR) angle is defined as a combination of two 2BR, e.g. ==3 eqn :: \phi_{bc;c} =&& 8\lambda_c -5\lambda_b -3\varpi_c \\ :: ==3 \phi_{cd;c} =&& 5\lambda_d -3\lambda_c -2\varpi_c ==3 p :: gives: ==3 eqn :: \Phi_\mathrm{bcd} = 2\lambda_b -5\lambda_c +3\lambda_d \approx 177^\circ ==4 img :: AgolEtal2021fig7 ==4 imb :: Best-fit TTV model (:ads:AgolEtal2021:a:) ==6 img :: AgolEtal2021fig12 :: style=max-height:700px ==6 imb :: :ads:GrimmEtal2018:AgolEtal2021:a: === :: repeat=6 :: nest=cont h2 :: Orbital resonances vvv <=3 p :: In resonance or not? ==0 vid :: orb1 :: opts=a ==0 rec :: ell:0.3,sw:0.0,col:#eee,fo:1.0 :: pos=bl(0.95,0.0) :: pos=bl(0.95,0.2) ==0 imb :: P_{2}_/P_{1}_ = 1.5 ==1,2 vid :: orb2 :: opts=a ==1,2 rec :: ell:0.3,sw:0.0,col:#eee,fo:1.0 :: pos=bl(0.95,0.0) :: pos=bl(0.95,0.2) ==1,2 imb :: P_{2}_/P_{1}_ = 1.59 ==2 imb :: The planets are still in resonance as the outer planet is precessing. Conjunctions still take place at apocenter ==3 img :: conjunction ==4 img :: lib-angle ==4 imc :: circulating :: pos=bl(0.6,0.2) :: style=font-size:30px;background-color:rgba(250,250,250,0.8);border:2px solid black ==4 imc :: librating :: pos=bl(0.6,0.7) :: style=font-size:30px;background-color:rgba(250,250,250,0.8);border:2px solid black ==4 imb :: circulating and librating two-body resonance (2BR) angles. ==5 img :: GalileanLaplace :: style=width:800px :: opts=f ==5 imb :: The three innermost Galilean Moons constitute an Laplace resonance -- :a:https://en.wikipedia.org/wiki/Orbital_resonance#Laplace_resonance (c) Wikipedia:a: ==5 imb :: In the Galilean system, there are two 2:1 2BR and one 3BR: ==5 eqi :: \Phi_\textrm{bcd} = 2\lambda_3 -3\lambda_2 +\lambda_1 \approx 180 \deg :: opts=d180 vvv border=2% <=2 * In an orbital mean motion resonance, the period ratios of the planets obey a _commensurability_: :: ==0 opts=f <=2 eqn :: \frac{P_2}{P_1} = \frac{j+o}{j} <=2 where _o_ is the order of the resonance <=2 p :: yet, this definition is insufficiently precise! :: style=color:$hicolor ==2 * resonances occur when planet conjunctions take place at the same point in the orbit ==2 p :: style=$small :: for example, at apocenter >=2 * a more precise definition is through the resonance angle >=2 eqn :: \phi_{12;i} =& (j+o)\lambda_2 -j\lambda_1 -o\varpi_i >=2 p :: env=$envS :: where _o_ is the order of the resonance, $$\lambda_i$$ is the mean longitude, $$\varpi_i$$ the >=2 longitude of pericenter, $$\lambda_i -\varpi_i$$ the mean anomaly of planet $$i$$. ==3 \n \n ← at conjunctions the resonance angle evaluates to $$ \phi_\mathrm{res} = o(\lambda_2 -\varpi_2) $$ and equals, for _o_=1, the mean anomaly at the point of the encounter. ==3,4 * Planets are said to be in resonance if the resonance angle is *librating*. ==4,5 p :: env=$envS :: For example, for the TRAPPIST-1 planets, we can write: ==4,5 eqn :: \phi_{bc;c} =&& 8\lambda_c -5\lambda_b -3\varpi_c \\ :: ==4,5 \phi_{cd;c} =&& 5\lambda_d -3\lambda_c -2\varpi_c ==4,5 * 2BR angles cannot be measured easily ==4,5 p :: style=$small :: When eccentricities are small (like for the TRAPPIST-1 planets) >=5 * A 3BR angle can be constructed from two 2BR: ==5 p :: env=$envS :: For example: >=5 eqn :: \Phi_\mathrm{bcd} = 3\phi_\mathrm{cd;c} -2\phi_\mathrm{bc;c} = 10\lambda_b -25\lambda_c +15\lambda_d >=5 p :: This angle no longer contains the (uncertain) longitude of pericenter >=5 * 3BR angles can be easily measured >=5 p :: style=$small :: When it librates, planets are in resonance === :: nest=cont h2 :: application: tidal expansion * The TRAPPIST-1 planets are (likely) tidally locked * Stellar tides remove energy from the system, but angular momentum is conserved * When is resonance, angular momentum is transferred to outer planets img :: Laplace imc :: pos=lb(0.2,0.55) :: total A.M. imc :: pos=lb(0.5,0.18) :: *b* imc :: pos=lb(0.5,0.44) :: *c* imc :: pos=lb(0.5,0.8) :: *d* imb :: In this example, tidal (eccentricity) damping only operates on planet b. The planets mutual spacing expands. === :: background=trappistI-system-red h1 :: Formation Model :: style=color:white === :: repeat=10 :: nest=new h2 :: Formation TRAPPIST-1 (schematic) vvv 60% ==0 img :: disk0 ==0 imc :: pos=tr(0.9,0.00) :: ~100 au :: style=color:$hicolor;font-size:32px ==1 img :: disk1 ==1 imc :: pos=tr(0.9,0.00) :: ~0.1 au :: style=color:$hicolor;font-size:32px ==2 img :: disk2 ==3 img :: disk3 ==4 img :: disk4 ==5 img :: disk5 ==6 img :: disk6 ==7 img :: disk8 ==8 img :: disk9 ==9 img :: disk10 ----- ==0 p :: style=$small :: see :ads:BirnstielEtal2012:LambrechtsJohansen2014:a:, ==0 cf. inside-out formation by :ads:ChatterjeeTan2017:a:. ==0 **- Assume a large, smooth disk ::: style=$small ==0 ** Pebble formation and drift is fast. Overall, the timescale to flush the disk ==0 eqn :: t_\mathrm{flush} \sim 10^{5\cdots 6}\,\mathrm{yr} :: opts=d180 ==0 p :: style=$small :: dependent on the extent of the disk. This sets the timescale for planet formation. ==1 p :: solid-to-gas ratio can be elevated at evaporation fronts, triggering streaming instabilities \n :ads:SchoonenbergOrmel2017:DrazkowskaAlibert2017:a: :: style=$small ==1 **- H_{2}_O vapor diffuses back across snowline ::: style=$small ==1 ** midplane dust:gas=1 exceeded ==1 ** planetesimal formation at iceline ==2 **- pebble accretion is very efficient in these inner regions (:ads:OrmelLiu2018:a:), ::: style=$small ==2 eqi :: \epsilon = 0.1 :: opts=d180 ==2 **- Planets cross when the migration timescale matches the growth timescale. We obtain a corresponding mass of ==2 eqn :: t_\mathrm{migr}=t_\mathrm{growth} \Rightarrow\quad M_\mathrm{cross} \sim 0.1\,M_\oplus :: opts=d180 ==2 p :: style=border:2px solid black;padding:5px; :: planet formation in rings modelled numerically (:ads:LiuEtal2019:SchoonenbergEtal2019:a:;Jiang & Ormel, subm.) ==3 **- ::: style=$small ::: After this mass, the planet migrates inwards and only accretes refactory pebbles (silicates) ==3 ** Pebble accretion is very efficient at small distances -- :ads:OrmelLiu2018:a: ==4 **- ::: style=$small ::: Pebble isolation _may_ (or may not) limit the final mass ==4 p :: The pebble isolation mass ==4 eqi :: h^3 M_\star \sim 1 M_\oplus :: opts=d180 ==4 p :: :ads:LambrechtsEtal2014:AtaieeEtal2018:BitschEtal2018:a: :: style=$small ==4 \** ==4 p :: style=border:2px solid black;padding:5px;margin-top:1em; :: I assume planets reached their observed masses at this stage and now focus on the dynamics ==5 **- ::: style=$small ::: In disks, planets can be trapped into first order (j+1:j) resonances ==5 **- The trapping halts at the inner cavity, due to strong torque reversal ==6 div :: env=$envS :: \N ==6 **- The expansion of the inner system is driven by the 1-sided Lindblad torque (2:1 resonance w/ disk). ==6 **- The 3BR resonance angle $$\Phi_\mathrm{bcd}$$ remains intact ==6 **- expansion completes before outer planets join the resonance chain ==7 div :: env=$envS :: \N ==9 div :: env=$envS :: \N ==9 **- tidal damping reduces eccentricities ==9 ** the system expands somewhat vvv border=2% >=0 *0 *dust* grows to pebbles; drift inwards >=1 * planetesimal formation triggered at H_{2}_O iceline. >=2 * Coagulation of planetesimals into planets in birthline ring :: ==2 style="color:$hicolor;" ==2 p :: The water contents is set :: style=$small >=3 * migration and accretion of *dry* pebbles :: ==3 style="color:$hicolor;" >=4 * planets reach their final mass; the process repeats at iceline :: ==4 style="color:$hicolor;" >=5 * planets pile-up at the inner cavity :: ==5 style="color:$hicolor;" >=6 * two inner-most planets fell into the cavity; enjoyed expansion :: ==6 style="color:$hicolor;" >=7 * higer-order resonances reached :: ==7 style="color:$hicolor;" >=8 * all resonances established in disk phase :: ==8 style="color:$hicolor;" >=9 * _limited_ tidal expansion :: ==9 style="color:$hicolor;" === :: background=trappistI-system-red h1 :: Statements :: style=color:white === :: repeat=3 :: nest=new :: ==2 background=$darkbg h2 :: 1. Single location origin (rings) vvv ==2 img :: AS209 ==0 img :: disk2 ==0 img :: disk4 ==1 img :: SchoonenbergEtal2019fig9-alt ==1 p :: :: style='font-size:24px;margin-top:0em;' ==1 blue dots: :: style='color:blue' ==1 model results by :ads:SchoonenbergEtal2019:a:; :: style='color:black' ==1 \n red crosses: :: style='color:red' ==1 inferred parameters from :ads:DornEtal2018:a:. ==1 \n *Note.*: Updated modelling now gives ice fractions down to 5% :ads:AgolEtal2021:a: vvv border=2% * The assembly belt model naturally explains *similar physical properties* of TRAPPIST-1 planets :: ==0 style=color:$hicolor p :: style=$small :: Statistics from detailed numerical modeling (involving N-body stochastics) match observations well * Composition remains hard to understand: :: ==1 style=color:$hicolor **- density low, if formed w/i iceline **- no evidence for copious amounts of H_{2}_O **- evaporation? Geophysical processes? >=2 ----- >=2 * Are rings manifestiation of planets _or_ planet formation factories? >=2 * Evidence for rings at H_{2}_O iceline? === :: repeat=2 :: nest=new h2 :: 2. Evidence for large-scale disk migration vvv img :: disk9 ==1 cir :: ell:1.0,sw:12.5,col:$hicolor,fill-opacity:0.0 :: pos=lb(0.36,0.09) :: pos=lb(0.43,0.09) vvv border=2% * The sequential formation (or growth) naturally explains trapping in j+1:j resonances p :: style=$small :: Disk trapping in higher-order resonances is hard (and unlikely) * Implies existence of an inner cavity radius :: ==1 :: style=color:$hicolor p :: style=$small :: "Last of the Mohicans" idea is terribly inefficient === :: nest=new :: repeat=2 ==0,2 h2 :: 3. Orbital expansion of the inner system ==0,2 vvv ==0,2 * Direct capture in disk in higher order resonances seems very unlikely.. ==0 p :: style=$small :: :ads:ColemanEtal2019:TeyssandierEtal2022:a: ==0,2 * Instead, hypothesize a two-step processes for inner planets (b,c,d): ==0,2 **1 Capture in 3:2 & 3:2 resonances ==0,2 ** *Expansion* to higher order resonances (8:5:3) ==0,2 * Motivation is that the (3-2)^2^ 3BR and the 8:5:3 3BR have *the same expression* for the 3BR angle: :: ==0 opts=f ==0,2 eqn :: \Phi_{bcd} = 2\lambda_b -5\lambda_c +3\lambda_d ==2 * But... full tidal expansion ==2 FAILS. :: style=color:red ==2 * Expansion operates only on inner system :: style=color:$hicolor ==0,2 vvv border=2% ==0 img :: sketch-shuo-adapted ==0 rec :: ell:0.06,sw:0.5,col:#fff,fill-opacity:1.0 :: pos=lb(0.0,0.8) :: pos=lb(1.0,0.8) ==0 rec :: ell:0.35,sw:0.5,col:#fff,fill-opacity:1.0 :: pos=lb(0.0,0.4) :: pos=lb(1.0,0.4) ==0 imc :: pos=rb(0.0,0.9) :: *observed \n configuration* :: style=color:black ==0 imc :: pos=rb(0.0,0.7) :: *Initial* :: style=color:magenta >=1 img :: HuangOrmel2022fig5 >=2 imb :: :ads:HuangOrmel2022:a: ==1 imc :: pos=lb(1.0,0.8) :: Arrows are the present period ratios :: style=$annotate ==1 imc :: pos=lb(0.5,0.8) :: b/c/d expands too little; \n h/g too much! :: style=$annotate ==1 imc :: pos=lb(0.2,0.35) :: eccentricities are off :: style=$annotate ==1 imc :: pos=lb(0.72,0.35) :: the c/d/e 3BR stays intact \n (in contrast to the observations) :: style=$annotate === :: nest=new :: repeat=4 h2 :: 4. Orbital expansion operated during disk phase vvv * Full tidal expansion fails ==0 p :: style=$small :: because the (wrong) c/d/e 3BR stays intact. >=1 * The inner and outer system may have been disconnected ==1 p :: style=$small :: :ads:PapaloizouEtal2018:a: >=1 p :: We consider this scenario unlikely :: ==1 style=color:$hicolor ==1 p :: style=$small :: it is very hard to explain such a configuration from planet formation perspective >=2 * Expansion of the inner planets must have happened during the disk phase :: ==2 style=color:$hicolor ==2 p :: style=$small :: Our idea is to fix planet d at the disk edge (and the outer planets as well) while expanding the b/c/d subsystem. >=3 * New problem arises: c/d/e can be trapped in different 3BR! >=3 p :: style=$small :: In particular, we find that the c/e/f 7:3:2 non-adjacent (!) 3BR (Φ_{2}_) is hard to overcome! >=3 \n Trapping planet c in the right 3BR is possible, but the likelihood low vvv border=2% <=2 img :: sketch-shuo-adapted ==0 rec :: ell:0.35,sw:0.5,col:#fff,fill-opacity:1.0 :: pos=lb(0.0,0.4) :: pos=lb(1.0,0.4) ==1 rec :: ell:0.15,sw:0.5,col:#fff,fill-opacity:1.0 :: pos=lb(0.0,0.28) :: pos=lb(1.0,0.28) ==2 imc :: pos=rb(0.0,0.25) :: *Our* :: style=color:orange <=2 imc :: pos=rb(0.0,0.7) :: *Full tidal* :: style=color:magenta ==1,2 imc :: pos=rb(0.0,0.5) :: *Papaloizou et al. (2018)* :: style=color:green <=2 imc :: pos=rb(0.0,0.9) :: *observed \n configuration* :: style=color:black ==2 imb :: Solutions to obtain the observed configuration (middle). :ads:PapaloizouEtal2018:a: envisions two separate systems, the inner experiencing tidal expansion and re-connection. In our model the expansion happens in the disk phase. ==3 img :: HuangOrmel2022fig9 ==3 imc :: pos=lb(0.5,0) :: style=$annotate :: the Φ_{4}_ 3BR is the present one. ==3 imb :: :ads:HuangOrmel2022:a: === :: repeat=5 :: nest=new h2 :: 5. Early Cavity Infall & Expansion ==3 vvv 30% >=4 vvv >=3 * The early cavity infall is advantageous: >=3 **1 the gas disk torques planet c naturally >=3 p :: style=$small :: Through the 2:1 Lindblad resonance (no free model parameter) >=3 ** The required planet formation interval time $$\tau_\mathrm{pl}$$ agrees with the form.model >=4 ** it works in a reasonably large part of the parameter space >=4 p :: style=$small :: high eccentricity-to-semi-major axis damping >=4 ** tidal expansion (after reaching $$\Phi_\mathrm{cde} = \lambda_c -3\lambda_d +2\lambda_e $$) works majestically... >=3 vvv border=2% <=3 img :: HuangOrmel2022fig13 ==0,1 rec :: ell:0.4,sw:0.5,col:#fff,fill-opacity:1.0 :: pos=lb(0.0,0.4) :: pos=lb(1.0,0.4) ==0 lin :: sw:3.5,col:#e00 :: pos=bl(0.9,0.47) :: pos=bl(0.8,0.47) ==0 arr :: sw:3.5,col:#d00 :: pos=lb(.47,.92) ==0 imc :: pos=lb(.41,.92) :: *2:1* :: style=color:red ==0 arr :: sw:3.5,col:#d00 :: pos=lb(.35,.92) ==0 imc :: pos=lb(.41,.92) :: \N ==0 arr :: sw:9.5,col:#d00 :: pos=lb(.30,.85) ==0 imc :: pos=lb(.35,.85) :: \N :: style=color:red ==0 imc :: pos=lt(.35,.25) :: Lindblad torque operating from 2:1 location \n drives the expansion :: style=color:red ==1,2 imc :: pos=bl(0.9,0.58) :: style=color:$hicolor :: Planets b and c fell in the cavity *early*, \n before the outer planets joined the resonance chain ==2 imc :: pos=bl(0.58,0.58) :: style=color:$hicolor :: Fueled by the disk repulsion, planets b and c migrated into the cavity before the outer planets arrived ==2 imc :: pos=bl(0.27,0.58) :: style=color:$hicolor :: ... avoiding trapping in 3BR :: opts=f ==4 img :: HuangOrmel2022fig14 ==4 imb :: :ads:HuangOrmel2022:a: -- for low C_{e}_ this model works in a large region of the parameter space (green symbols) === :: nest=cont img :: HuangOrmel2022fig12 imc :: pos=lb(1.0,0.8) :: Arrows are the present period ratios :: style=$annotate imc :: pos=lb(0.5,0.8) :: tidal expansion is weaker \n (low ecc of b,c) :: style=$annotate imc :: pos=lb(0.2,0.35) :: eccentricities agree \n after 2.5 Myr of simulation time! :: style=$annotate imc :: pos=lb(0.8,0.35) :: all 3BR consistent with observations :: style=$annotate === :: repeat=3 :: nest=new h2 :: 6. The TRAPPIST-1 planets form early (and fast) vvv ==0 img :: disk0 ==1 img :: disk2 ==2 img :: SchoonenbergEtal2019fig4-alt :: style=width:90%; ==2 imb :: :ads:SchoonenbergEtal2019:a: vvv border=2% p :: In our model, planets form fast: * planet formation time set by drift motions :: ==0 style=color:$hicolor p :: The timescale to flush the disk of pebbles is just :: style=$small eqn :: t_\mathrm{flush} \sim 10^{5\cdots 6}\,\mathrm{yr} >=1 * pebble accretion at/beyond H_{2}_O iceline equally fast :: ==1 style=color:$hicolor >=1 eqn :: t_\mathrm{growth} \sim \frac{3\times 10^4\,\mathrm{yr}}{\epsilon} \frac{M_\mathrm{pl}}{M_\oplus} ==2 ----- ==2 p :: The rapid formation explains ==2 * planet f/g in 4:3 resonance ==2 p :: style=$small :: They would otherwise end up in 3:2 -- :ads:HuangOrmel2022:a:. ==2 * trapping of planets in (3-2)^2^ b/c/d resonance === :: nest=new :: repeat=2 h2 :: other works vvv * Dynamicist tend to omit disk-planet interactions ==0 **- :ads:TamayoEtal2017:a: places the planets very close to their observed values; ::: style=$small ==0 ** :ads:PapaloizouEtal2018:a: points out the b/c/d system had to be isolated from the outer planets. ==0 However, they initialize system arbitrarily and do not discuss the viability of 3BR trapping in wrong resonances; ==0 ** :ads:BrasserEtal2022:a: find that stellar tidal damping only results in erroneous period ratios (like us). They also constrain ==0 eqi :: Q_T :: opts=d180 ==0 \** p :: style=border:2px solid $hicolor;margin-bottom:0.5em;padding:5px :: _we can only understand the dynamics from a formation context_ >=1 * Population synthesis approaches tend to neglect the dynamics >=1 **- :ads:ColemanEtal2019:MiguelEtal2020:a: need very massive disks, producing planets that are too wet. ::: style=$small >=1 ** :ads:BurnEtal2021:a: concentrates planetesimal in an inner, hot disk (this works). The planet masses are well explained (as we). >=1 ** None of these works match the 3BR angles. ==1 \** >=1 p :: style=border:2px solid $hicolor;margin-bottom:0.5em;padding:5px :: _dynamics of planet system contains clues about planet formation_ #* Finally, :ads:TeyssandierEtal2022:a: find a match to the TRAPPIST-1 dynamics using a PS approach #p :: env=$envS :: They find solutions that match observations are unlikely (due to randomized initial conditions). They conclude eccentricity damping is stronger than "standard" (like we do) vvv border=2% ==0 img :: TamayoEtal2017fig1a :: style=max-height:700px ==0 imb :: :ads:TamayoEtal2017:a: ==1 img :: BurnEtal2021fig19a ==1 imb :: :ads:BurnEtal2021:a: -- population synthesis approach starting with massive, hot inner disk. === :: nest=new h2 :: Tailored Model vvv 40% * Our disk model contains limited number of parameters → p :: style=$small :: Conduct N-body simulations with Rebound/Reboundx. :ads:ReinLiu2012:TamayoEtal2021:a:. REBOUND accounts for fiducial damping forces and an efficient symplectic integrator (WHfast) vvv border=2% img :: model-sketch :: style=border:2px solid $hicolor;padding:5px div :: env=$envS * disk migration is assumed to be *inward*, and *linear*, characterized migration timescale of a 1 Earth-mass planet $$t_{a,\oplus}$$. * ... migration reverses at the inner boundary to halt planets migration * eccentricity damping 1-1 related with s.m.a. damping, the ratio quantified by $$C_e$$. * (after disk dispersal) usual tidal damping, parameterized by tidal quality factor Q'. To accelerate the simulation damping is boosted artificially. === :: nest=new :: repeat=4 :: background=trappistI-system-red h2 :: Conclusions :: style=color:white div :: style=color:white;background-color:rgba(0,0,0,0.2) *1 The TRAPPIST-1 system inspires a great number of people (and will continue to do so) p :: style=$small :: The system is extremely rich, its properties very well defined, and it poses great opportunities to learn about planet formation >=1 * Formation at/near iceline explains similarity in planets' physical properties (masses and composition) >=2 * Planets' dynamical properties (3BR) far more constraining: >=2 **- b and c fell in the cavity early >=2 **- b/c/d system experienced orbital expansion _before_ disk dispersal >=3 * This allows us to constrain key planet formation parameters and concepts: >=3 **- nature of cavity >=3 p :: env=$envW :: position and strength of cavity "barrier" (A_{a}_); repulsion by the disk >=3 **- fast formation of these planets >=3 p :: env=$envW :: planet formation interval time $$\tau_\mathrm{pl} \approx 10^5\,\mathrm{yr}$$. >=3 **- migration rate slower than "standard" >=3 p :: env=$envW :: the disk eccentricity-to-semi-major axis damping parameter $$C_e \ll 1$$, cf. :ads:CharalambousEtal2022:TeyssandierEtal2022:a: -- this is somewhat at odds with planet migration theory >=3 **- internal properties of planets >=3 p :: env=$envW :: tidal quality parameter ($$Q/k_2 \gtrsim 200$$) for planet b. :ads:BrasserEtal2022:a: finds a similar value === end === h2 :: open questions * are there any TRAPPIST-1-like analogues? And how common are these systems? === :: repeat=3 :: nest=2 h2 :: TRAPPIST 1 vvv 50% p :: TRAPPIST = *Tra*nsiting *P*lanets and *P*lanetes*i*mals *S*mall *T*elescope >=1 p :: *TRAPPIST-1 properties:* :: style=$novsp >=1 * mass = 0.089 M_{Sun}_ >=1 * 0.05% L_{Sun}_ >=1 * red dwarf (spectral type M8) >=1 * distance of 12.1 pc (40 ly) >=1 * age 7.6 +- 2.2 Gyr >=1 \n :ads:BurgasserMamajek2017:VanGrootelEtal2018:a: :: style=$small >=2 p :: *TRAPPIST-1 contains seven planets!* :: style=$novsp >=2 * 7 planets, all around 1 Earth radius >=2 * compact; 0.01 – 0.07 au; resonances, many close to 3:2 vvv ==0 img :: trappist-instrument ==0 \n ==0 img :: trappist-monk :: style="height:400px;" ==0 img :: trappist-beer1 :: style="height:400px;" ==0 p :: named after a Belgium monk order, famous for brewing their own beer :: style=$small ==1 img :: trappist1-location-aquarius :: style='width:500px' ==1 img :: trappist1-sun-jupiter :: style='width:500px' ==2 img :: GillonEtal2017fig1d ==2 imc :: :ads:GillonEtal2017:a: TRAPPIST-1 system === :: background=$darkbg :: nest=cont h2 :: TRAPPIST 1 detection vid :: trappist1-spitzer :: style='width:80%;' === :: background=$darkbg :: nest=cont img :: trappistI-solarsys-comparison :: style="width:80%;" === :: background=$darkbg :: nest=cont h1 :: TRAPPIST 1 system vvv 35% p :: conditions of TRAPPIST-1 planets very similar to inner solar system vvv 35% img :: trappistI-solarsys-irradiation :: style="width:100%" imc :: planets ordered after amount of radiation received from the star vvv img :: trappist1e-poster :: style="width:100%" === :: background=$darkbg :: nest=cont h2 :: Transit timing variations (TTV) vvv 60% vid :: ttv-animation-nasa * the interior planet (1) arrives earlier when it overtakes planet (2) :: opts=f :: style="margin-top:0px;" * ... (or later than average when they are further apart) :: opts=f * the magnitude of these _timing_ variations scales with the mass of the planets :: opts=f vvv p :: from the transit we obtain the sizes of the planets p :: but we can also get their masses through studying the variation in the time of the transits! p :: the mass and the radius constrain the composition === :: repeat=3 :: nest=new h2 :: Numerical modeling of the TRAPPIST-1 system p :: style='margin-top:-1em;' :ads:SchoonenbergEtal2019:a: :: style=$small <=1 * construct a planet _system_ formation model from A-Z \n <=1 * evolutionary timescales <=1 * model entire planet formation process <=1 \n dust --> pebbles --> planetesimals --> planets :: style=$small |==2tab :: style='font-size:32px;' |==2 code/method domain follows outputs :::: opts=H |==2L Lagrangian entire disk dust/pebble evolution planetesimals |==2N N-body iceline region planetesimal dynamics protoplanets |==2A Analytical inner disk planet growth,migration composition,mass planets ==1 ----- >=1 vvv 10% >=1 . >=1 vvv 80% >=1 img :: SchoonenbergEtal2019fig1 >=1 vvv #=== # #h2 :: overview "simple" 1D disk dust evolution models # #tab :: Work Approach Drift Collision comm. #Youdin & Shu (2002) analytical x #Birnstiel et al. (2012) analytical x x #Lambrechts & Johansen (2014) analytical x x #Ciesla (2005) Lagrangian x | #Krijt et al. (2016) Lagrangian x x | #Drazkowska et al. (2018) Eulerian x x +snowline #Schoonenberg et al. (2018) Lagrangian x x +snowline # === :: nest=cont h2 :: Lagrangian approach p :: style='margin-top:-1em;' :ads:KrijtEtal2016:SchoonenbergEtal2018:a: :: style=$small vvv 30% p :: *Follow _lifeline_ of batches:* :: style=$novsp * disk radius * mass * composition * porosity, etc. p :: *solve for...* :: style=$novsp img :: KrijtEtal2016eq13+14 * eqn :: t_\mathrm{drift} = f(m,r,t) * eqn :: t_\mathrm{growth} = f(m,r,t,\mathbf{\Sigma}) vvv img :: KrijtEtal2016fig2 imc :: Krijt et al. (2016) -- obtain surface density with _tripod_ method vvv === :: nest=cont h2 :: Schoonenberg's SPH method p :: style='margin-top:-1em;' Schoonenberg, Ormel, & Krijt (2018) :: style=$small vvv 60% img :: SchoonenbergEtal2018eq11 img :: SchoonenbergEtal2018fig2 vvv * particles different mass, compositions * 5 particles in the support Kernel * resample when relative distance exceeds 20% === :: nest=cont h2 :: Findings p :: style='margin-top:-1em;' Schoonenberg, Ormel, & Krijt (2018) :: style=$small vvv 60% img :: SchoonenbergEtal2018fig11 imc :: Schoonenberg et al. (2018) -- _Z_ = 0.02 vvv p :: model for first "burst" of planetesimal formation :: style='text-align:left;' * rapid disk evolution -> rapid formation :: opts=fh * planetesimals tend to form preferentially near snowline :: opts=fh * efficient for high Z, around low mass stars :: opts=fh vvv === :: repeat=5 :: nest=new h2 :: Adding planetesimal evolution vvv 40% p :: Developed an integrated numerical model combining three codes: :: style=$novsp >=1 * a *Lagrangian code* for the dust/pebbles, treating planetesimal formation >=1 \n :ads:SchoonenbergEtal2018:a: :: style=$small >=2 * an *N-body code* for the planetesimal dynamics/coaguation at the snowline >=2 \n Mercury, adapted by :ads:LiuEtal2019i:a: :: style=$small >=3 * an *Analytical code* to calculate pebble accretion efficiencies >=3 \n :ads:LiuOrmel2018:OrmelLiu2018:a: :: style=$small vvv ==0,4 img :: SchoonenbergEtal2019fig1 ==0,4 imc :: Schoonenberg et al. (2019) -- model overview ==3 img :: OrmelLiu2018fig4 :: style='height:700px;' ==3 imc :: Ormel & Liu (2018) -- fraction of pebbles accreted by planet, *3-body* calculations ==1 img :: SchoonenbergEtal2018fig5 :: style="width:80%;" ==1 imc :: Schoonenberg et al. (2018) -- Lagrangian model ==2 img :: SchoonenbergEtal2019fig4 :: style="width:80%;" ==2 imc :: Schoonenberg et al. (2019) -- *N-body* calculation ==4 vvv 99% ==4 p :: *Caveats*: :: style='margin-top:-1em;;margin-bottom:0em;text-align:left;' ==4 * No connection to star formation phase ==4 * No link to final dynamics === :: repeat=5 h2 :: Afterthoughts vvv 60% ==0 img :: SchoonenbergEtal2019fig9-alt ==0 p :: :: style='font-size:24px;margin-top:0em;' ==0 blue dots: :: style='color:blue' ==0 model results by :ads:SchoonenbergEtal2019:a:; :: style='color:black' ==0 \n red crosses: :: style='color:red' ==0 inferred parameters from :ads:DornEtal2018:a:. :: style='color:black' ==1 img :: trappist-timeline-assembly :: style='width:80%;' ==2 img :: PascucciEtal2016fig7 ==2 imc :: :ads:PascucciEtal2016:a: lack of planet-forming material for low-mass star? ==3 img :: Mulders2018fig7 ==3 imc :: :ads:MuldersEtal2018:a:, planet mass _vs_ stellar mass ==4 img :: planet-sys-designs ==4 imc :: planetet systems design #==4 img :: OrmelLiu2018fig6 #==4 imc :: Ormel & Liu (2018); _Top_: M_{★}_=1 M_{sun}_, h=0.03, η=10^-3^; _Bottom_: M_{★}_=0.1 M_{sun}_, h=0.05, η=3x10^-3^ :: style=$small ==5 vid :: trappistI :: opts=a ==5 \n :ads:OrmelEtal2017:a: :: style=$small vvv >=0 * *H_{2}_O fraction ~10% is special* :: style=$novsphi ==0 * too much to change by delivery, evaporation ==0 * hard to understand from theory ==0 * ... but result strongly depends on TTV measurement/modeling! >=1 * *Planets form very fast (~10^5^ yr)* :: style=$novsphi ==1 * Observational evidence for early formation? ==1 * Fast disk clearing for M-stars? ==1 \n :ads:SheehanEisner2017:TychoniecEtal2018:ManaraEtal2018:a: :: style=$small >=2 * *Scenario (only|especially) applicable to low mass stars?* :: style=$novsphi ==2,3 *- lack of building blocks for low-mass stars ==2,3 \n :ads:PascucciEtal2016:a: :: style=$small ==2,3 * many close-in planets around M-stars ==2,3 \n :ads:MuldersEtal2015:a: :: style=$small ==2,3 * Pebble accretion efficient for low-mass stars ==2,3 \n :ads:OrmelLiu2018:a: :: style=$small >=4 * *Scenario applicable to solar-type stars?* :: style=$novsphi ==4 * Kepler systems are thermal mass M ~ h^3^ M_{★}_ ==4 \n :ads:Wu2018:LiuEtal2019ii:a: :: style=$small ==4 * intra-system uniformity natural outcome of our model ==4 \n :ads:WeissEtal2018:a: :: style=$small >=5 * Intra-system uniformity natural #==3 * Role of giant planets to stop pebble flux? #==3 \n but close-in super-Earths and cold giants seem correlated #==3 (Bryan et al. 2017) :: style=$small ==4 h1 :: \n Thank you :: style=$novsphi #==0 style="color:$hicolor;" #==1 style="color:$hicolor;" === end === *1 Disk pebble flux: eqi :: \dot{M}_\mathrm{disk} = 2\pi R \Sigma_\mathrm{peb,0} v_R(\tau_s) * → $$ \Sigma_\mathrm{peb} $$. * MMSN model → $$ \rho_\mathrm{gas} $$. * but also $$ \Sigma_\mathrm{peb} = Z\rho_\mathrm{gas} \sqrt{2\pi} H_\mathrm{peb} $$ → $$ H_\mathrm{peb} = f(\dot{M}_\mathrm{disk}) $$ . * or... $$ H_\mathrm{peb} = ... H_\mathrm{gas} $$ → $$ \dot{M}_\mathrm{disk} $$. * or... $$ H_\mathrm{peb} = \sqrt{\alpha_z/(\alpha_z+\tau_s)} H_\mathrm{gas} $$. * accretion flux through Bondi sphere (_disk_ in 2D): eqn :: \dot{M}(r) = \sqrt{2\pi} H_\mathrm{peb} (2\pi r) \int \rho_\mathrm{peb} (r,\phi) v_r(r,\phi) d\phi * P.A. efficiency eqi :: \epsilon_\mathrm{PA} = \dot{M}_\mathrm{acc} / \dot{M}_\mathrm{disk} \n 2D expression, see :ads:LiuOrmel2018:a: \n $$ \epsilon_{2D} = f(\tau_s, M_p/M_\star, ..) $$. === :: repeat=4 :: nest=new h2 :: Formation TRAPPIST-1 (sketch) vvv ==0 img :: trappist-model-sketch-d ==0 imb :: Formation, then migration to the inner disk \n :ads:OrmelEtal2017:a:; :ads:SchoonenbergEtal2019:a: ==1 img :: HuangOrmel2022fig6 ==1 imb :: :ads:HuangOrmel2022:a: ==2 img :: HuangOrmel2022fig13 ==2 imb :: :ads:HuangOrmel2022:a: ==3 img :: tidal-expansion ==3 imb :: :ads:HuangOrmel2022:a: vvv border=2% *I Formation planets' physical properties **0 Formation at a single location in _factory mode_ ::: ==0 :: style=color:$hicolor p :: style=$small :: driven by pebble accretion, planets grow quickly and migrate inwards towards the disk inner edge \n The planets' physical properties are set at this stage * Planets' dynamical arrangements **1 Trapping into first-order MMR ::: ==1 :: style=color:$hicolor p :: style=$small :: through disk migration and trapping, the planets move into first-order MMR \n The c/d/e 3BR, however, is at odds with the observation ** Early cavity infall ::: ==2 :: style=color:$hicolor p :: style=$small :: planets b and c move into the cavity. The Lindblad torque on planet c causes them to move inwards. The timely arrival of planets e and f result planets to park in the observed 3BR ** Tidal expansion ::: ==3 :: style=color:$hicolor p :: style=$small :: the entire system, now connected through resonances, expands through tidal damping === :: repeat=7 :: nest=new h2 :: Pebble-driven formation -- Schematic p :: :ads:OrmelEtal2017 Ormel, Liu, Schoonenberg (2017):a: :: style=$small;margin-top:-1em;margin-bottom:1em;text-align:center vvv 55% ==0 img :: trappist-model-disk :: style=border:5px solid $hicolor; ==0 img :: trappist-model-sketch-a :: style=width:50%; ==1 img :: trappist-model-disk :: style=width:50%; ==1 img :: trappist-model-sketch-a :: style="border:5px solid $hicolor;" ==2 img :: snowline-sketch-Djoeke ==2 imc :: :ads:SchoonenbergOrmel2017:a: : growth by recondensation ==2 imc :: cf. :ads:StevensonLunine1988:CuzziZahnle2004:RosJohansen2013:DrazkowskaAlibert2017:a: ==3 vid :: iceline-buildup-sigma :: opts=a ==3 imb :: :ads:SchoonenbergOrmel2017:a: -- the release of water vapor from fast-drifting pebbles and re-condensation results in peak in the ice fraction ==4 img :: trappist-model-sketch-a :: style="width:50%;" ==1,5 img :: trappist-model-sketch-b :: style="width:50%;" ==4 img :: trappist-model-sketch-b :: style="border:5px solid $hicolor;" ==4,6 img :: trappist-model-sketch-c :: style="width:50%;" ==5 img :: trappist-model-sketch-c :: style="border:5px solid $hicolor;" ==5,7 img :: trappist-model-sketch-d :: style="width:50%;" ==6 img :: trappist-model-sketch-d :: style="border:5px solid $hicolor;" vvv border=2% >=0 * *dust* grow to >=0 pebbles; :: style=color:$hicolor; >=0 drift to inner disk ==0 p :: style=$small :: see :ads:BirnstielEtal2012:LambrechtsJohansen2014:a:, cf. inside-out formation by :ads:ChatterjeeTan2017:a:. ==0 **- Assume a large, smooth disk ::: style=$small ==0 ** Pebble formation and drift is fast.==0 p :: style=$small :: dependent on the extent of the disk. This, essentially, sets the timescale for planet formation >=1 * icy pebbles crossing snowline, enhance solids-to-gas ratio, trigger planetesimal formation ==1-3 p :: by streaming instability \n :ads:SchoonenbergOrmel2017:DrazkowskaAlibert2017:a: :: style=$small ==1 **- H_{2}_O vapor diffuses back across snowline ::: style=$small ==1 ** midplane dust:gas=1 exceeded ==1 ** planetesimal formation at iceline >=4 * planetesimals coagulate and protoplanet growth in birth ring (*wet* accretion) :: ==4 style="color:$hicolor;" ==4 **- the growth timescale by pebble accretion is ::: style=$small ==4 eqn :: t_\mathrm{growth} \sim \frac{3\times 10^4\,\mathrm{yr}}{\epsilon} \frac{M_\mathrm{pl}}{M_\oplus} :: opts=d180 ==4 **- pebble accretion is very efficient in these inner regions (:ads:OrmelLiu2018:a:), ==4 eqi :: \epsilon = 0.1 :: opts=d180 ==4 \n The water contents is set :: style=$small >=5 * migration and accretion of *dry* pebbles :: ==5 style="color:$hicolor;" ==5 p :: style=$small :: This happens when the migration timescale matches the growth timescale. We obtain a corresponding mass of ==5 eqn :: t_\mathrm{migr}=t_\mathrm{growth} \Rightarrow\quad M_\mathrm{cross} \sim 0.1\,M_\oplus :: opts=d180 ==5 p :: style=$small :: After this mass, the planet migrates inwards and only accretes refactory pebbles (silicates) >=6 * accretion ceases at _pebble isolation mass_ h^3^M_{★}_ :: ==6 style=color:$hicolor; ==6 p :: :ads:LambrechtsEtal2014:AtaieeEtal2018:BitschEtal2018:a: :: style=$small ==6 * The process repeats at H_{2}_O iceline :: style=color:$hicolor === :: nest=new :: repeat=4 h2 :: Pebble-driven formation -- Numerical p :: :ads:SchoonenbergEtal2019 Schoonenberg, Liu, Ormel, & Dorn (2019):a: :: style=$small;margin-top:-1em;margin-bottom:1em;text-align:center vvv ==0 vid :: SchoonenbergEtal2019 :: opts=a ==0 p :: style=$small ==0 orange: :: style='color:orange;' ==0 new pltsm.; ==0 *- - - -* :: style='color:blue;' ==0 : iceline ==1 img :: SchoonenbergEtal2019fig4-alt :: style=width:90%; ==2 img :: SchoonenbergEtal2019fig9-alt ==2 imb :: The synthetic planets (:ads:SchoonenbergEtal2019:a:) vs the observed planet properties (red error bars; now outdated!) ==3 img :: SchoonenbergEtal2019tab2-alt ==3 imb :: Schoonenberg, Liu, Ormel, Dorn (2019) ==3 div :: style=$small ==3 * lower alpha: smaller, wetter planets; higher alpha: similar results :: style='color:blue' ==3 * not too sensitive to accretion rate :: style='color:red' ==3 * higher disk mass: more massive, drier planets :: style='color:#00aa00' vvv * Follow the protoplanet growth around the iceline birth ring ==0 p :: style=$small :: using collisional N-body code w/ planetesimal dynamics and pebble accretion \n :ads:SchoonenbergEtal2019:a:, following :ads:LiuEtal2019:a: >=1 * numerical results by-and-large agree with the analytical scalings, but: >=1 **- planets do not _form_ 1 by 1, but face competitive accretion >=1 **- H_{2}_O fraction somewhat higher in the model >=2 * The iceline/pebble formation model explains: >=2 **- the planet composition >=2 **- the number of planets and the stochasticity in their properties (e.g., masses) >=2 **- planetesimal -> planet growth >=3 * Formation in rings may be more general... === :: background=$darkbg :: nest=cont img :: ALMA-dsharp-side imc :: pos=tl(0.1,0.1) :: style=color:white;font-size:42px :: Ringed Disks are found \n to be ubiquitous imc :: pos=tr(0,0.0) :: DSHARP survey