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gadget_meeting

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gadget_meeting

  1. 1. Adaptive gravitational softening in GADGET Iannuzzi & Dolag (2011) and more
  2. 2. What softening is *Monaghan & Lattanzio 1985, A&A, 149, 135
  3. 3. What we need it for Depends on the kind of simulation one is performing: Collisional simulation - need softening to avoid divergences and reduce the computational time Collisionless simulation - need softening to reduce computational time and moderate the noise induced by the under-representation of the particles’ DF
  4. 4. Noise vs. Bias and the optimal h (Merritt 1996, AJ, 111, 2462) NOISEr = (Fr − Fr )2 BIASr = Fr −Fr,true ASEr = BIAS2 r +NOISEr = (Fr − Fr,true)2
  5. 5. Optimal h: does it always exist?
  6. 6. Adaptive softening (Price & Monaghan 2007, MNRAS, 374, 1347) Definition 4 3πh3ρ = mNngbs =⇒ h ∝ ρ−1/3 New Lagrangian Lgrav = N i=1 mi 1 2v2 i − Φ (ri , h(ri )) Equation of Motion dvj dt = − G N i=1 mi φij (hj ) + φij (hi ) 2 rj − ri |rj − ri | − G 2 N i=1 mi ζj Ωj ∂Wij (hj ) ∂rj + ζi Ωi ∂Wij (hi ) ∂rj
  7. 7. Adaptive softening (Price & Monaghan 2007, MNRAS, 374, 1347) Definition 4 3πh3ρ = mNngbs =⇒ h ∝ ρ−1/3 New Lagrangian Lgrav = N i=1 mi 1 2v2 i − Φ (ri , h(ri )) Equation of Motion dvj dt = − G N i=1 mi φij (hj ) + φij (hi ) 2 rj − ri |rj − ri | − G 2 N i=1 mi ζj Ωj ∂Wij (hj ) ∂rj + ζi Ωi ∂Wij (hi ) ∂rj
  8. 8. Adaptive softening (Price & Monaghan 2007, MNRAS, 374, 1347) Definition 4 3πh3ρ = mNngbs =⇒ h ∝ ρ−1/3 New Lagrangian Lgrav = N i=1 mi 1 2v2 i − Φ (ri , h(ri )) Equation of Motion dvj dt = − G N i=1 mi φij (hj ) + φij (hi ) 2 rj − ri |rj − ri | − G 2 N i=1 mi ζj Ωj ∂Wij (hj ) ∂rj + ζi Ωi ∂Wij (hi ) ∂rj
  9. 9. Adaptive softening (Price & Monaghan 2007, MNRAS, 374, 1347) Definition 4 3πh3ρ = mNngbs =⇒ h ∝ ρ−1/3 New Lagrangian Lgrav = N i=1 mi 1 2v2 i − Φ (ri , h(ri )) Equation of Motion dvj dt = − G N i=1 mi φij (hj ) + φij (hi ) 2 rj − ri |rj − ri | − G 2 N i=1 mi ζj Ωj ∂Wij (hj ) ∂rj + ζi Ωi ∂Wij (hi ) ∂rj
  10. 10. Adaptive softening (Price & Monaghan 2007, MNRAS, 374, 1347) Zeta ζi ≡ ∂hi ∂ρi N k=0 mk ∂φik(hi ) ∂hi Omega Ωi ≡ 1 − ∂hi ∂ρi N k=0 mk ∂Wik(hi ) ∂hi
  11. 11. Optimal h: fixed vs. adaptive softening
  12. 12. Correction term and energy conservation
  13. 13. Effects in a cosmological environment No analytical solution Keep the same power spectrum and increase the resolution Fixed 643 Fixed 1283 Fixed 2563 Adapt 643 Adapt 1283 Adapt+corr 643 Adapt+corr 1283
  14. 14. Mass functions
  15. 15. Correlation functions
  16. 16. The most massive halo M200 1015 M ; r200 2.4 h−1 Mpc; 3000, 21000, 160000 particles
  17. 17. The most massive halo M200 1015 M ; r200 2.4 h−1 Mpc; 3000, 21000, 160000 particles
  18. 18. The most massive halo: substructures
  19. 19. An “adaptive” mini-MillenniumII low-resolution version of the MillenniumII (Boylan-Kolchin et al. 2009) same power-spectrum, 125 times less particles mII mini-mII adaptive mini-mII
  20. 20. An “adaptive” mini-MillenniumII: mass function
  21. 21. An “adaptive” mini-MillenniumII: correlation function
  22. 22. Conclusions (I) adaptive softening lengths provide near-optimal softening with little dependance on Nngbs in order to retain energy conservation the equation of motion needs to be modified the use of adaptive softening in a cosmological simulation enhances the clustering of particles at small scales, anticipating the results obtained in higher resolution simulations
  23. 23. Hybrid simulations Fields sampled by particles of different masses: Collisionless species - to start with Hydrodynamical simulations - eventually Do we have an impact on two-body effects?
  24. 24. Hybrid collisionless simulation: evaporation of the light component from halos
  25. 25. Hybrid collisionless simulation: mass functions
  26. 26. Hybrid collisionless simulation: evaporation of the light component from halos
  27. 27. Hybrid collisionless simulation: evaporation of the light component from halos
  28. 28. Conclusions (II) simulations with equal-mass particles are well behaved in simulations with particles of different masses the effect of varying Nngbs on the correction term is only partially understood possible solutions may require non-immediate modifications of the method the use of adaptive softening (without correction) moderates the impact of two-body effects in hybrid simulations
  29. 29. Distribution of the softening lengths
  30. 30. Time bins
  31. 31. Dependence on the number of neighbours Inner density profile of a Hernquist sphere
  32. 32. Passive evolution of a bulge+halo system

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