The effect of partial ionisation in star formation James Wurster - PowerPoint PPT Presentation

The effect of partial ionisation in star formation James Wurster with Matthew Bate & Daniel Price 1 st Phantom Users Workshop Monash University, 23 February 2018

Non-ideal magnetohydrodynamics Ambipolar Diffusion (dissipative) Hall Effect log B (non-dissipative) Ohmic Resistivity (dissipative) log n Image credit: Tsukamoto et al (2017); 2 Adapted from Wardle (2007) see also: Braiding & Wardle (2012a,b)

Initial Conditions Ø Initial conditions: Ø 1 M sun of gas Ø Uniform density Ø Strong magnetic fields ( µ 0 = 5) Ø Ω .B < 0 (primary suite) Ø Ω .B > 0 (secondary suite) Ø Processes included: Ø Non-ideal MHD Ø Ohmic resistivity Ø Hall Effect Ø Ambipolar diffusion 3

Extreme Regimes: Ionisation Algorithms iMHD ζ 12 ζ 13 ζ 14 ζ 15 ζ 16 ζ 17 ζ 18 ζ 19 ζ 20 ζ 22 ζ 23 ζ 24 ζ 25 ζ 30 HD log density [g/cm 3 ] -15 -15.2 -15.4 500 AU -15.6 ρ max =10 -15 g cm -3 log density [g/cm 3 ] -12 -13 30 AU -14 ρ max =10 -12 g cm -3 log density [g/cm 3 ] -13 -14 -15 150 AU ρ max =10 -13 g cm -3 Ideal MHD 𝜂 = 10 -16 s -1 𝜂 = 10 -17 s -1 𝜂 = 10 -18 s -1 Hydrodynamic Ø Images are log(density). Ø Rows are ρ = 10 -15 g cm -3 , ρ = 10 -13 g cm -3 , ρ = 10 -12 g cm -3 4 Wurster, Bate & Price (2018b)

Extreme Regimes: Ionisation Algorithms iMHD ζ 12 ζ 13 ζ 14 ζ 15 ζ 16 ζ 17 ζ 18 ζ 19 ζ 20 ζ 22 ζ 23 ζ 24 ζ 25 ζ 30 HD log density [g/cm 3 ] -15 -15.2 -15.4 500 AU -15.6 ρ max =10 -15 g cm -3 log density [g/cm 3 ] -12 -13 30 AU -14 ρ max =10 -12 g cm -3 log density [g/cm 3 ] -13 -14 -15 150 AU ρ max =10 -13 g cm -3 Ideal MHD 𝜂 = 10 -16 s -1 𝜂 = 10 -17 s -1 𝜂 = 10 -18 s -1 Hydrodynamic Ø Images are log(density). Ø Rows are ρ = 10 -15 g cm -3 , ρ = 10 -13 g cm -3 , ρ = 10 -12 g cm -3 5 Wurster, Bate & Price (2018b)

Extreme Regimes: Ionisation Algorithms log density [g/cm 3 ] ρ max ideal MHD ζ cr =10 -13 s -1 ζ cr =10 -14 s -1 ζ cr =10 -15 s -1 ζ cr =10 -16 s -1 ζ cr =10 -17 s -1 ζ cr =10 -18 s -1 Hydro -12 =10 -12 g cm -3 -13 -14 log |B| -1 -2 -3 0 v r [km/s] -100 -200 v y [km/s] 50 0 -50 6 Wurster, Bate & Price (2018b)

Extreme Regimes: Ionisation Algorithms log density [g/cm 3 ] iMHD ζ 12 ζ 13 ζ 14 ζ 15 ζ 16 ζ 17 ζ 18 ζ 19 ζ 20 ζ 22 ζ 23 ζ 24 Hydro -12 -13 30 AU -14 ρ max =10 -12 g cm -3 log |B| -1 -2 -3 30 AU ρ max =10 -12 g cm -3 v y [km/s] 50 0 -50 30 AU ρ max =10 -12 g cm -3 0 v r [km/s] -100 -200 30 AU ρ max =10 -12 g cm -3 7 Wurster, Bate & Price (2018b)

Extreme Regimes: Ionisation Algorithms 10 7 ζ 18 ζ 24 iMHD ζ 19 ζ 25 HD 10 6 ζ 10 ζ 20 ζ 30 ζ 16 ζ 22 ζ 17 ζ 23 10 5 cpu time [h] 10 4 10 3 10 2 10 1 10 0 10 -17 10 -16 10 -15 10 -14 10 -13 10 -12 10 -11 ρ max [g cm -3 ] 8 Wurster, Bate & Price (2018b)

Collapse to stellar densities : Evolution of the density 9 Video available at https://www.youtube.com/watch?v=CgErHuWdcPw&t=3s

Collapse to stellar densities 10 0 10 0 ζ 12 iMHD ζ 14 ζ 12 10 -4 ζ 15 10 -2 ζ 14 ζ 16 ζ 15 n i /(n i +n n ) ζ 16 ζ 10 -8 10 -4 HD ζ ζ 10 -12 ρ max [g cm -3 ] ζ 10 -6 ρ max =10 -10 g cm -3 10 -16 10 0 10 -8 10 -4 10 -10 n i /(n i +n n ) 10 -8 10 -12 10 -12 10 -14 ρ max =10 -7 g cm -3 10 -16 24400 24600 24800 25000 25200 10 10 0 Time [yr] 10 6 10 -4 n i /(n i +n n ) 10 -8 10 4 10 -12 10 2 B max [G] ρ max =10 -4 g cm -3 ; dt sc =0 10 -16 10 0 10 0 10 -4 n i /(n i +n n ) 10 -8 10 -2 10 -12 10 -4 dt sc =0.5yr 10 -16 10 -18 10 -16 10 -14 10 -12 10 -10 10 -8 10 -6 10 -4 10 -2 10 0 10 10 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 Wurster, Bate & Price (2018a) ρ max [g cm -3 ] r [au]

ρ ρ ζ ζ Collapse to stellar densities: First hydrostatic core ζ ζ ρ max =10 -7 g cm -3 ρ max =10 -7 g cm -3 50 50 50 z [AU] z [AU] z [AU] 0 0 0 -50 -50 -50 ζ cr =10 -12 s -1 ζ cr =10 -12 s -1 ζ ζ 50 50 50 50 z [AU] z [AU] z [AU] 0 0 0 ζ ζ -50 -50 -50 ζ cr =10 -16 s -1 ζ cr =10 -16 s -1 -50 0 50 -50 0 50 -50 0 50 x [AU] x [AU] x [AU] Wurster, Bate & Price -2 0 2 -2 0 2 -2 0 2 11 11 (2018a) v y [km/s] log |B| [G] v r [km/s] ζ ζ ζ ζ

Collapse to stellar densities: Stellar core ζ cr =10 -16 s -1 ζ cr =10 -12 s -1 dt sc =17yr dt sc =0.5yr 28 au 28 au 7 au 7 au -5 0 5 -5 0 5 -5 0 5 -10 -5 0 5 10 v φ [km/s] v r [km/s] v φ [km/s] v r [km/s] 12 12 Wurster, Bate & Price (2018a)

ζ Collapse to stellar densities: Stellar core ζ dt sc =0.5yr 1 z [AU] 0 -1 ζ cr =10 -12 s -1 ζ 1 z [AU] 0 -1 ζ ζ cr =10 -16 s -1 -1 0 1 x [AU] -2 0 2 13 13 Wurster, Bate & Price (2018a) log |B|[G] ζ ζ

Conclusions Ø Modelled the collapse of a molecular cloud core through the first core to stellar densities; included Ohmic resistivity, ambipolar diffusion, the Hall effect Ø The coefficient of the Hall effect is similar to the ambipolar diffusion in the medium surrounding the core Ø High cosmic ray ionisation rates can reproduce ideal MHD collapses Ø Low cosmic ray ionisation rates can approximate hydrodynamicals collapses, but cannot reproduce them Ø Decreasing the cosmic ionisation rate increases the lifetime of the first hydrostatic core Ø The first and second hydrostatic cores become thermally ionised, but the accreting material is still only ionised by cosmic rays Ø The second core outflow is suppressed at low cosmic ray ionisation rates 14 j.wurster@exeter.ac.uk http://www.astro.ex.ac.uk/people/wurster/