The formation of gas dwarfs and rocky planets a case for the new - - PowerPoint PPT Presentation

Exoplanets in Lund, May 2015 Slide 1

NBI / STARPLAN

Åke Nordlund

Niels Bohr Institute and Centre for Star and Planet Formation (STARPLAN) University of Copenhagen

The formation of gas dwarfs and rocky planets

University of Copenhagen

– a case for the new DISPATCH Code

Exoplanets in Lund. May 2015 Slide 2

This talk is about two – related – potential break-throughs: A new, unified, scenario for planet formation Is it possible, perhaps even likely, and possible to demontrate, that all types of planets – gas giants, gas dwarfs & rocky planets form in basically the same way?

 Very rapidly, and directly via pebble accretion in proto-atmospheres, rather than via the round-about way via planetesimals

A new, exa-scale ready concept for supercomputing How can one harness the immense computing power of the forth-coming exascale era (approaching 1018 floating point

• ps per sec)?

 The new DISPATCH code introduces a completely new approach to extreme scaling  With it, hypotheses about planet formation can be put to decisive tests

NBI / STARPLAN

Exoplanets in Lund. May 2015 Slide 3

So, who am I to make such bold claims?  I make [extreme] supercomputer models, in e.g

• solar physics – magnetic flux emergence & coronal heating
• kinetic modeling – particle acceleration
• star formation & protoplanetary disks – cf. ADS (Padoan et al, …)
• planet formation – just starting …

 Hall marks:

• realistic models, in agreement with observations – no ‘idealized models’
• three dimensions – no 2-D / 1-D / 0-D
• full radiative transfer – no flux limited diffusion (the ‘look-alike’ method)

NBI / STARPLAN

Exoplanets in Lund. May 2015 Slide 4

Important recent observational findings – mostly from Kepler:  The most common exoplanets are ‘gas dwarfs’ (aka ‘mini Neptunes’)

• We just happen to not have any in our solar system

 Migration is much less pronounced than most predictions

• As evidenced by the statistically very minor signature of resonances

 Close-in exoplanets are common, but hard to explain

• Were they formed in situ, or by migration?

 Many exoplanet systems have Titius-Bode laws

• But with different exponents

NBI / STARPLAN

Exoplanets in Lund. May 2015 Slide 5

The most common exoplanets are ‘gas dwarfs’ (aka ‘mini Neptunes’)

[ ‘gas dwarf’ is a better name than ‘mini-Neptune’ ] We happen to not have any in our solar system – had we had them, the theory of planet formation might have taken a different track (earlier than will happen now ;-)

NBI / STARPLAN

Exoplanets in Lund. May 2015 Slide 6

Mean motion resonances leave only very weak Kepler signatures

NBI / STARPLAN

Exoplanets in Lund. May 2015 Slide 7

Other important facts/constraints on planet formation  Jupiter must have once had a more massive atmosphere

• Evidenced by its chemical abundance pattern

 Earth (and Mars) probably once had more massive atmospheres

• Evidenced by Rayleigh fractionation patterns of their inert gases

 Planets plobably received major mass contributions from chondrules

• Evidenced by similar isotopic fingerprints

 The asteroids must have formed at most a few 105 years after t=0

• Evidenced by differentiation of small bodies (revised 26Al abundance)

NBI / STARPLAN

Exoplanets in Lund. May 2015 Slide 8

All of these facts can be consistently explained in a scenario where

 Planets – even rocky planets

• form directly, via pebble accretion, and ..
• where pebbles = chondrules: the result of hefty ‘thermal processing’ of

dust

• remaining dust = chondrite matrix, chondrules ‘dressed’ with dust rims

 Planet embryos are surrounded by ‘proto-atmospheres’

• atmospheres with outer BCs = disk pressure
• they go away – mostly – when the disk BCs go away

 Proto-atmospheres make chondrule accretion much more efficient

• increasing the cross sections and capture efficiencies

NBI / STARPLAN

Exoplanets in Lund. May 2015 Slide 9

All of these facts can be consistently explained in a scenario where

 Planets – even rocky planets

• form directly, via pebble accretion, and ..
• where pebbles = chondrules: the result of hefty ‘thermal processing’ of

dust

• remaining dust = chondrite matrix, chondrules ‘dressed’ with dust rims

 Planet embryos are surrounded by ‘proto-atmospheres’

• atmospheres with outer BCs = disk pressure
• they go away – mostly – when the disk BCs go away

 Proto-atmospheres make chondrule accretion much more efficient

• increasing the cross sections and capture efficiencies

NBI / STARPLAN

 For an early version of this scenario, see the proceedings of IAU Symposium 276 (ÅN, 2011)  Similar ideas have since been advanced by others, mainly in the context of gas giants

• Guillot+14
• Johansen+15
• Levison+15

Exoplanets in Lund. May 2015 Slide 10

No planetesimals ! It’s important to understand that this scenario does not go the route via planetesimals. It assumes that  There is a dominating accreter in every X% radius interval

• This would explain Titius-Bode
• … ‘the winner takes it all’ … inside-out

 The most extreme fluctuation wins (Hopkins 2013…2015), be it

• just turbulence (Pan & Padoan, 2011...14)
• streaming- and magneto-rotational instability (Johansen et al)
• combinations (possibly gravity-assisted) of the above

 Rapid growth is due to pebble accretion in proto-atmospheres

• Cf. recent papers by Chris Ormel et al (2015)
• see also recent abstract by Hal Levison et al (2014..15)

NBI / STARPLAN

Exoplanets in Lund. May 2015 Slide 11

Proto-atmospheres (Hunten 1979, …, Lammer et al. 2014) Proto-atmospheres inevitably occur around objects in a gaseous disk:  A normal atmosphere (e.g. Earth’s current) is hydrostatic, with essentially zero pressure outside  A proto-atmosphere has a finite pressure outside

• that makes a lot of difference: exponential depence on embryo mass!
• the equations are exactly the same, but with a finite external BC

 All planet-embryos in gaseous disks have proto-atmospheres

• they would in fact be humongous if the atmospheres were cold
• but accretion by pebbles make them hot, which saves the day

NBI / STARPLAN

Exoplanets in Lund. May 2015 Slide 12

How can this be tested in a realistic setting?  The range of scales involved is enormous:  The answer is Adaptive Mesh Refinement (AMR), but only if it’s limitations can be circumvented

NBI / STARPLAN

Scale physical relative

Scale height of Earths current atmosphere 8 km 1 Scale height of a proto-atmosphere 600 km 102 Earth radius 6400 km 103 Hill radius 235 RE 105 Scale height of accretion disk at 1 AU, 100K 1000 RE 106 Distance to the Sun 23000 RE 107 Size of the solar system 100 AU 109 Size of the prestellar core 10 000 AU 1011 Size of the a star forming region 50pc=108 AU 1015

Exoplanets in Lund. May 2015 Slide 13

How can this be tested in a realistic setting?  The range of scales involved is enormous:  The answer is Adaptive Mesh Refinement (AMR), but only if it’s limitations can be circumvented

NBI / STARPLAN

Scale physical relative

Scale height of Earths current atmosphere 8 km 1 Scale height of a proto-atmosphere 600 km 102 Earth radius 6400 km 103 Hill radius 235 RE 105 Scale height of accretion disk at 1 AU, 100K 1000 RE 106 Distance to the Sun 23000 RE 107 Size of the solar system 100 AU 109 Size of the prestellar core 10 000 AU 1011 Size of the a star forming region 50pc=108 AU 1015

Exoplanets in Lund. May 2015 Slide 14

How can this be tested in a realistic setting?  The range of scales involved is enormous:  The answer is Adaptive Mesh Refinement (AMR), but only if it’s limitations can be circumvented

NBI / STARPLAN

Scale physical relative

Scale height of Earths current atmosphere 8 km 1 Scale height of a proto-atmosphere 600 km 102 Earth radius 6400 km 103 Hill radius 235 RE 105 Scale height of accretion disk at 1 AU, 100K 1000 RE 106 Distance to the Sun 23000 RE 107 Size of the solar system 100 AU 109 Size of the prestellar core 10 000 AU 1011 Size of the a star forming region 50pc=108 AU 1015

Exoplanets in Lund. May 2015 Slide 15

How can this be tested in a realistic setting?  The range of scales involved is enormous:  The answer is Adaptive Mesh Refinement (AMR), but only if it’s limitations can be circumvented

NBI / STARPLAN

Scale physical relative

Scale height of Earths current atmosphere 8 km 1 Scale height of a proto-atmosphere 600 km 102 Earth radius 6400 km 103 Hill radius 235 RE 105 Scale height of accretion disk at 1 AU, 100K 1000 RE 106 Distance to the Sun 23000 RE 107 Size of the solar system 100 AU 109 Size of the prestellar core 10 000 AU 1011 Size of the a star forming region 50pc=108 AU 1015

Exoplanets in Lund. May 2015 Slide 16

Other AMR codes, with part of the solution AREPO and GIZMO use unstructured and meshless representations,

• respectively. Their representation has the important advantage (over

for example RAMSES), to respect Galilean invariance; i.e., their results are the same, independent of any bulk motion of the system under

• study. Main disadvantage: speed!

NBI / STARPLAN

Exoplanets in Lund. May 2015 Slide 17

Stepping on our own toes with traditional AMR codes  Static meshes, with hierarchical refinement

• Violate Galilean invariance – causing motion dependent diffusion
• Drastically limits the time step in supersonic flows; e.g. Keplerian flows
• Major efforts wasted on simply advecting properties across cells

 AMR levels must be evolved synchronously

• Requires near-perfect load balancing, which in practice is impossible
• Ghost cells need to be exchanged simultaneously everywhere

 Global time steps (with or without sub-cycling)

• Time step limited by worst cell out of billions

NBI / STARPLAN

Exoplanets in Lund. May 2015 Slide 18

The DISPATCH code – what’s in the name? The keys to the scaling properties are encoded in the name:  Using a DISPATCHer to lauch essentially independent processes, which are NOT forced to be locked together in time, NOR are they forced to exist in grid-locked arrangement !  The result is a number of DISconnected PATCHes, each of which has its own ‘task’ definition, which is responsible for its evolution. Especially two processes are crucial:

• 1. Downloading of boundary data, using MPI_Put/Get, without disturbing

the task that owns the data

• 2. Uploading of interior data, from patches that have higher quality data

NBI

Exoplanets in Lund. May 2015 Slide 19

DISPATCH breaks with traditions, to achieve unlimited scaling:  Allows asynchronous evolution of sub-domains (patches)  Allows moving patches – small Cartesian meshes with bulk motion  Allows local time steps; determined independently for each patch  Uses task-based scheduling, via OpenMP inside nodes  Uses neighborhood-limited MPI_Put/MPI_Get between nodes  Uses any preferred solver in patches, balancing speed against quality and ghost zone requirements

• Godunov, staggered-mesh, …
• This can include Multiple-Domain-Multiple-Physics
• e.g. PIC code for kinetic simulations inside MHD
• dust+gas dynamics = pebble accetion …

NBI / STARPLAN

Exoplanets in Lund. May 2015 Slide 20

Downloading and uploading info from other patches  Once all overlapping patches are in local memory we run through them, and always take data from them if they overlap with our ghost zones

• Rather than sort out exactly which sub-patch

comes from where, we just overlay them, in quality order

 Inside a patch proper, we only download data that has better quality (= refinement level)

• Later, we will define a more general measure of quality

than just “level of refinement”

NBI / STARPLAN

Exoplanets in Lund. May 2015 Slide 21

Ghost zones and communication  Boundary ghost zone values are ‘downloaded’

• from (possibly several) larger scale patches

 Interior values (fluxes and values) are ‘uploaded’

• from the interior of higher quality patches

 Intra-node down-/upload uses shared memory (OpenMP)

• with cubic interpolation in space and time

 Inter-node down-/upload uses MPI_Get/MPI_Put

• accesses memory in other MPI-processes directly – Remote Memory Access

 Collections are handled by linked lists

• Linked list are maintained in sorted order (e.g. by patch quality)

NBI / STARPLAN

Exoplanets in Lund. May 2015 Slide 22

Task based OpenMP/MPI for perfect load balancing

NBI

are are

A ‘task’ can be anything:

• a hydro/MHD patch
• ratiative transfer
• pebble dynamics
• pebble accretion
• planet evolution (thermal)
• planet orbital motion
• …

Exoplanets in Lund. May 2015 Slide 23

Refinement strategy in DISPATCH DISPATCH combines two strategies, and gets the best

• f both:

 When refining, we can choose a new patch size that is any size and resolution (no power-of-two constraint)  By letting the new patch move with the flow, we can typically delay the creation of more refined patches, AND reduce internal velocities

NBI / STARPLAN

Feature motion Patch motion

!

Exoplanets in Lund. May 2015 Slide 24

Performance In direct comparison with RAMSES, the speed factors are  Small patches, optimized for cache and vectorization: x3-5  Local time steps: x5-10  Essentially perfect load balancing: x2-3  Essentially perfect and unlimited MPI scaling; x2- increasing All together, a factor of 50-1000 faster, with advantage increasing with problem size

NBI / STARPLAN

Exoplanets in Lund. May 2015 Slide 25

DISPATCH summary: DISPATCH incorporates a number of concepts that are necessary for the exa-scale era:  Moving cartesian meshes

• size optimized for vectorization

 Asynchronous evolution

• local time step control

 Task-based scheduling

• ready-queue with prioritizations

 Modularity

• multi-physics ready
• pebble dynamics implemented (5h yesterday!): 50 nanosec / update!

NBI / STARPLAN

So, we now have a tool that can test whether the scenario works

Exoplanets in Lund. May 2015 Slide 26

The first DISPATCH experiment The aim is to study the competition between already existing embryos:  A fully realistic accretion disk

• Well resolved both vertically and radially
• With initial conditions from our RAMSES zoom-runs
• Radiative transfer will be implemented shortly (another 5h job ;-)

 Planet patches

• moving in Keplerian orbits
• with protoatmospheres represented by hierarchical meshes
• Rubics Cube (3x3x3 = 27 patches – then refine the innermost one)
• Rubics Revenge (4x4x4 = 64 pathes – refine the inner 2x2x2)

NBI / STARPLAN

Exoplanets in Lund. May 2015 Slide 27

Global disk simulation setup [ The number of cells and patches is reduced relative to production ]  Side view, showing also the side boundary layers needed to isolate the disk from periodic copies

• Disk gas density is shown

with log scaling

• The location of the two

planet embryos in the disk are indicated

NBI / STARPLAN

Exoplanets in Lund. May 2015 Slide 28

Global disk simulation setup [ The number of cells and patches is reduced relative to production ]  View from above the disk, with two planet embryo orbits

• The locations of the two embryos

are visible as small dots along their orbits

 The size of the 3D box is 4AU

• Patch hierarchies around each

embryo extend out beyond their Hill radii, with Keplerian motion in a disk (also built up by a number of patches)

NBI / STARPLAN

Exoplanets in Lund. May 2015 Slide 29

Global disk simulation setup – zoomed in [ The number of cells and patches is reduced relative to production ]  The innermost patch levels

• Note the Rubik’s

Cube (3x3x3) hierarchy

• Each patch is, for example,

a 16x16x16 resolution patch

• There is also a

Rubik’s Revenge (4x4x4 case)

 The smallest resolution element in the setup is ~1/16 of the planet embryo radius

NBI / STARPLAN

Log density

Exoplanets in Lund. May 2015 Slide 30

Animations [ The number of cells and patches is reduced relative to production ]  The initial proto-atmosphere structure is obtained by assuming hydrostatic pressure balance

NBI / STARPLAN

Final gas pressure profile, as resolved by the Rubik’s Cube hierarchy

Exoplanets in Lund. May 2015 Slide 31

Animations [ The number of cells and patches is reduced relative to production ]  The large size of the proto-atmosphere is illustrated by showing log gas density in a plane through the planet embryo (in white)

NBI / STARPLAN

Log density Log gas density

Exoplanets in Lund. May 2015 Slide 32

To sum up: You have a choice – you can believe that:  The only bodies that formed in the gaseous disk were

• Gas giants – everyone somehow believes in this without question
• Planetesimals – everyone also somehow believes in that!
• The planetismals were then laboriously gathered into rocky planets
• But what about gas dwafs then??

 All planets form in the gaseous disks

• There is a smooth continuum from rocky planets via gas dwarfs to giants
• They form directly, via pebble (=chondrule) accretion
• The process is assisted, very importantly, by early proto-atmospheres

NBI / STARPLAN

Exoplanets in Lund. May 2015 Slide 33

Take your pick – place your bets!

NBI / STARPLAN

And thank you for your attention !

We will know soon enough – thanks to DISPATCH!