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

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

State-of-the-art in 2008: ideal MHD Hydro μ =20 μ =5 B=0 Weak B Strong B equatorial plane Magnetic field dominates NO DISK, NO FRAGMENTATION Magnetic braking catastrophe & Fragmentation Crisis (e.g., Hennebelle & Fromang 2008, Hennebelle & Teyssier 2008) yz - plane Commerçon et al. (2010) Commerçon Benoît TagKASI 2018

Non-ideal MHD � Late formation � end of class 0, M env <<M env,0 (e.g., Machida & Hosokawa 2013 )  � ∂ B u ⇥ B � η Ω J � η H || B || J ⇥ B + η AD ∂ t � r ⇥ || B || 2 J ⇥ B ⇥ B = 0 � � Misalignment � no reason for the rotation axis and the magnetic field to be aligned (e.g., Hull et al. 2013 ) Non-ideal effects: � reduces magnetic braking efficiency (e.g. Hennebelle & Ciardi 2009, Joos et al. 2012, Li et al. 2013 ) - rearrangement of magnetic field lines � - reconnection � Turbulent diffusion - magnetic flux diffusion � reconnection events fast with Ohmic diffusion only, collective effect at larger - … needs gas-grain chemistry 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 ) � 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 + , H 3+ , 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 � � ✓ UMIST database for gas species � ( McElroy et al. 2013 ) � ✓ Kunz & Mouschovias (2009) for � interactions with and between grains � � ✓ 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) Commerçon Benoît TagKASI 2018

Equilibrium chemistry for non-ideal MHD: results https://bitbucket.org/pmarchan/chemistry Marchand et al. (2016) Commerçon Benoît TagKASI 2018

Equilibrium chemistry for non-ideal MHD: results https://bitbucket.org/pmarchan/chemistry Marchand et al. (2016) Commerçon Benoît TagKASI 2018

Equilibrium chemistry for non-ideal MHD: results https://bitbucket.org/pmarchan/chemistry 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) Commerçon Benoît TagKASI 2018

Radiation-magneto-hydrodynamics in RAMSES ✓ 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) + r · [ ρ u ] = 0 ∂ t ρ + r · [ ρ u ⌦ u + P I ] = � ρ r Φ � λ r E r + ( r ⇥ B ) ⇥ B ∂ t ρ u ⇣ ⌘ c λ ∂ t E T + r · [ u ( E T + P T ) � B ( B · u ) � E AD ⇥ B ] = � ρ u · r Φ � P r r : u � λ u r E r + r · ρκ R r E r ⇣ ⌘ + κ P ρ c ( a R T 4 � E r ) c λ + r · [ u E r ] = � P r r : u + r · ∂ t E r ρκ R r E r r ⇥ ( u ⇥ B ) � r ⇥ E AD = 0 ∂ t B � 1 Ambipolar EMF E AD = γ AD ρ i ρ [( r ⇥ B ) ⇥ B ] ⇥ B 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 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 � 𝜄 =40 ∘ • Rotationally supported disk formation ( R ~ 50 AU ) - consistent with obs. • P therm /P mag >1 within disks • vertical magnetic field => initial conditions for protoplanetary disks studies 𝜄 =0 Masson et al. 2016 Commerçon Benoît TagKASI 2018

1 M ⊙ : Turbulence and ambipolar diffusion •magnetisation & disk size does not depend on turbulence level, nor on the initial magnetic field μ =5 μ =2 amplitude Commerçon et al. in prep. Commerçon Benoît TagKASI 2018

1 M ⊙ : Turbulence and ambipolar diffusion •disk evolution does not depend on turbulence level 𝜄 =40 ∘ Subsonic Supersonic μ =5 μ =2 Convergence! Commerçon et al. in prep. Commerçon Benoît TagKASI 2018

100 M ⊙ : Massive dense core collapse (aligned) HYDRO AD mu=2 ✓ “Small” disk: R~300 AU ✓ Large disk: R~1000 AU ✓ No fragmentation ✓ Binary system: 24 and 13 M ⨀ ✓ Magnetic outflow ✓ Radiative outflow/bubble (1500 AU) Gonzalez et al. in prep. Commerçon Benoît TagKASI 2018

100 M ⊙ : Disks properties AMBI μ =2 AMBI μ =5 P therm >P mag HYDRO P therm <P mag ✓ disks are dominated by thermal pressure with AD (i.e. hydro disks) ✓ thick and magnetised disk with iMHD IMHD μ =2 Commerçon Benoît TagKASI 2018

100 M ⊙ : Magnetisation AMBI μ =2 AMBI μ =5 IMHD μ =2 ✓ B max reduced by > 1 order of magnitude by AD ✓ plateau @ B<1G ✓ similar to results found in low mass star Masson et al 2016 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 � Low-mass core - 1M ⊙ Massive core - 100 M ⊙ Hennebelle et al. (2016) Commerçon Benoît TagKASI 2018

Gas-dust dynamical coupling Drag force � Dust velocity � Gas velocity Stopping time (Epstein 1924) � � PhD work of Ugo Lebreuilly Coupling with the gas (Stokes number) @ CRAL Lyon If St<1, strong coupling If St>1, poor coupling Commerçon Benoît TagKASI 2018

Gas and dust mixture as a monofluid Multiple small dust species monofluid (Laibe and Price 2014c, Price & Laibe 2015) Approximation for small grains : St <1 Total density Dust ratio of species k Barycentre velocity Total energy of the mixture Lebreuilly, Commerçon & Laibe, submitted to A&A Commerçon Benoît TagKASI 2018

Collapse with dust and gas dynamical coupling Dust 1 nm Dust 0.1 mm Dust 1 nm Dust 0.1 mm 1000 AU Dust 0.5 mm Gas Dust 0.5 mm Gas Edge-on cut Mid-plane cut Lebreuilly et al., in prep. Commerçon Benoît TagKASI 2018