Disk Formation with Ambipolar Diffusion from Low- to High- Mass - - PowerPoint PPT Presentation

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Disk Formation with Ambipolar Diffusion from Low- to High- Mass - - PowerPoint PPT Presentation

May 19, 2023 204 likes •417 views

Disk Formation with Ambipolar Diffusion from Low- to High- Mass Star Formation Benot Commeron Centre de Recherche Astrophysique de Lyon Ugo Lebreuilly, Matthias Gonzlez, Patrick Hennebelle, Gilles Chabrier, Pierre Marchand, Jacques Masson,

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Disk Formation with Ambipolar Diffusion from Low- to High- Mass Star Formation

Benoît Commerçon

Centre de Recherche Astrophysique de Lyon Ugo Lebreuilly, Matthias González, Patrick Hennebelle, Gilles Chabrier, Pierre Marchand, Jacques Masson, Neil Vaytet

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Commerçon Benoît TagKASI 2018

State-of-the-art in 2008: ideal MHD

equatorial plane yz - plane

μ=5 Strong B Hydro B=0 μ=20 Weak B

Magnetic field dominates NO DISK, NO FRAGMENTATION

Magnetic braking catastrophe & Fragmentation Crisis (e.g., Hennebelle & Fromang 2008, Hennebelle & Teyssier 2008)

Commerçon et al. (2010)

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Commerçon Benoît TagKASI 2018

Late formation end of class 0, Menv<<Menv,0 (e.g., Machida & Hosokawa 2013)

  • Misalignment

no reason for the rotation axis and the magnetic field to be aligned (e.g., Hull et

  • al. 2013)

reduces magnetic braking efficiency (e.g. Hennebelle & Ciardi 2009, Joos et al. 2012, Li et al. 2013)

  • Turbulent diffusion

reconnection events fast with Ohmic diffusion only, collective effect at larger scale (e.g. Santos Lima et al. 2012, Joos et al. 2013, Seifried et al. 2013)

  • Non-ideal MHD

Ohm dissipation (Tomida et al. 2013, 2015, Machida et al.) Hall effect (Krasnopolsky et al. 2011, Tsukamoto et al. 2015, 2017, Wurster et

  • al. 2016, Marchand et al. 2018)

ambipolar diffusion (Tsukamoto et al. 2015, Masson et al. 2016)

  • Non-ideal MHD

Non-ideal effects:

  • rearrangement of magnetic field lines
  • reconnection
  • magnetic flux diffusion
  • … needs gas-grain chemistry

∂B ∂t r ⇥  u ⇥ BηΩJ ηH ||B||J ⇥ B+ ηAD ||B||2 J ⇥ B ⇥ B

  • = 0
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Commerçon Benoît TagKASI 2018

Equilibrium chemistry for non-ideal MHD

✓ Reduced chemical network dedicated to ionisation (based on the work by Umebayashi & Nakano 1990)

  • H, He, C, O, metallic elements (Fe, Na, Mg, etc..)
  • H+, H3+, He+, C+, molecular and metallic ions
  • bins in the dust grains size distribution (G, G+, G-)
  • dust evaporation at T>800 K
  • thermal ionisation of potassium (T>1000 K)
  • neutral elements have constant abundances
  • ✓ Goal: compute a 3D table of abundances
  • depends on temperature, density and CR ionisation
  • used on-the-fly in 3D calculations to compute resistivities

Marchand et al. (2016)

✓UMIST database for gas species

(McElroy et al. 2013)

✓Kunz & Mouschovias (2009) for

interactions with and between grains

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Commerçon Benoît TagKASI 2018

Marchand et al. (2016)

https://bitbucket.org/pmarchan/chemistry

Equilibrium chemistry for non-ideal MHD: results

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Commerçon Benoît TagKASI 2018

Marchand et al. (2016)

https://bitbucket.org/pmarchan/chemistry

Equilibrium chemistry for non-ideal MHD: results

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Commerçon Benoît TagKASI 2018

1/ Grain evaporation is the most important effect 2/ Needs at least 5 bins in dust grain size distribution to converge…

Marchand et al. (2016)

https://bitbucket.org/pmarchan/chemistry

Equilibrium chemistry for non-ideal MHD: results

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Commerçon Benoît TagKASI 2018

✓ Adaptive-mesh-refinement code RAMSES (Teyssier 2002) ✓ Non-ideal MHD solver using Constrained Transport (Teyssier et al. 2006, Fromang et al. 2006, Masson et al. 2012,2016, Marchand et al. 2018). In this work, just ambipolar diffusion with resistivity from equilibrium gas-grain chemistry (Marchand et al. 2016) ✓ Multifrequency Radiation-HD solver using the Flux Limited Diffusion approximation (Commerçon et al. 2011b, 2014, González et al. 2015). In this work, just grey ✓ Sink particles using clump finder algorithm (Bleuler & Teyssier 2014)

∂tρ + r · [ρu] = ∂tρu + r · [ρu ⌦ u + PI] = ρrΦ λrEr + (r ⇥ B) ⇥ B ∂tET + r · [u (ET + PT) B(B · u) EAD ⇥ B] = ρu · rΦ Prr : u λurEr + r · ⇣

cλ ρκR rEr

⌘ ∂tEr + r · [uEr] = Prr : u + r · ⇣

cλ ρκR rEr

⌘ + κPρc(aRT 4 Er) ∂tB

  • r ⇥ (u ⇥ B) r ⇥ EAD

=

Ambipolar EMF

EAD = 1 γADρiρ [(r ⇥ B) ⇥ B] ⇥ B

Radiation-magneto-hydrodynamics in RAMSES

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Commerçon Benoît TagKASI 2018

1 M⊙: Misalignment & ambipolar diffusion

  • formation of a plateau at B~0.1G
  • reorganisation of magnetic field lines (essentially

poloidal) => reduced magnetic braking

  • mass and radius of first core do not change
  • weaker outflows compared to ideal MHD
  • Masson et al. 2016
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Commerçon Benoît TagKASI 2018

1 M⊙: Misalignment & ambipolar diffusion

  • formation of a plateau at B~0.1G
  • reorganisation of magnetic field lines (essentially

poloidal) => reduced magnetic braking

  • mass and radius of first core do not change
  • weaker outflows compared to ideal MHD
  • Masson et al. 2016
  • Rotationally supported disk formation

(R ~ 50 AU) - consistent with obs.

  • Ptherm/Pmag>1 within disks
  • vertical magnetic field

=> initial conditions for protoplanetary disks studies

𝜄=40∘ 𝜄=0

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Commerçon Benoît TagKASI 2018

Commerçon et al. in prep.

  • magnetisation & disk size does

not depend on turbulence level, nor on the initial magnetic field amplitude

μ=5 μ=2

1 M⊙: Turbulence and ambipolar diffusion

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Commerçon Benoît TagKASI 2018

Commerçon et al. in prep.

Convergence!

  • disk evolution does not depend
  • n turbulence level

μ=5 μ=2 Subsonic Supersonic 𝜄=40∘

1 M⊙: Turbulence and ambipolar diffusion

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Commerçon Benoît TagKASI 2018

100 M⊙: Massive dense core collapse (aligned)

✓ Large disk: R~1000 AU ✓ Binary system: 24 and 13 M⨀ ✓ Radiative outflow/bubble (1500 AU) ✓ “Small” disk: R~300 AU ✓ No fragmentation ✓ Magnetic outflow

HYDRO AD mu=2

Gonzalez et al. in prep.

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Commerçon Benoît TagKASI 2018

HYDRO IMHD μ=2

✓ disks are dominated by thermal pressure with AD (i.e. hydro disks) ✓ thick and magnetised disk with iMHD

AMBI μ=2 AMBI μ=5

100 M⊙: Disks properties

Ptherm>Pmag Ptherm<Pmag

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Commerçon Benoît TagKASI 2018

100 M⊙: Magnetisation

✓ Bmax reduced by > 1 order of magnitude by AD ✓ plateau @ B<1G ✓ similar to results found in low mass star

AMBI μ=2 AMBI μ=5 IMHD μ=2

Masson et al 2016

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Commerçon Benoît TagKASI 2018

Magnetically regulated disk size with AD

  • very good agreement between the

analytical and experimental values

  • disk size does not depend on turbulence

level

  • weak dependance on the mass
  • Massive core - 100 M⊙

Hennebelle et al. (2016) Low-mass core - 1M⊙

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Commerçon Benoît TagKASI 2018

Gas-dust dynamical coupling

Drag force

  • Stopping time (Epstein 1924)
  • Coupling with the gas (Stokes number)

If St<1, strong coupling If St>1, poor coupling

Gas velocity Dust velocity

PhD work of Ugo Lebreuilly @ CRAL Lyon

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Commerçon Benoît TagKASI 2018

Gas and dust mixture as a monofluid

Multiple small dust species monofluid (Laibe and Price 2014c, Price & Laibe 2015)

Total density Barycentre velocity Total energy of the mixture Dust ratio of species k

Approximation for small grains : St <1

Lebreuilly, Commerçon & Laibe, submitted to A&A

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Commerçon Benoît TagKASI 2018

Collapse with dust and gas dynamical coupling

Mid-plane cut Edge-on cut Gas Gas Dust 0.5 mm Dust 0.5 mm Dust 0.1 mm Dust 0.1 mm Dust 1 nm Dust 1 nm 1000 AU

Lebreuilly et al., in prep.

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Commerçon Benoît TagKASI 2018

Conclusion

Disks are back! Disk size regulated by ambipolar diffusion

  • Magnetic fields cannot be neglected. Non-ideal MHD as well…
  • Magnetised models with AD compare well with observations
  • Grains of size >100 microns decouple dynamically during collapse
  • ➡ Dust evolution => impact on resistivity, opacity

➡ Second collapse: parameter study to determine the epoch of disk formation,

i.e. prior to/after the formation of the protostar

➡ Disks in a clustered environment