Simulating the Universe Christine Corbett Moran, Irshad Mohammed, Manuel Rabold, Davide Martizzi, Doug Potter, Aurel Schneider Oliver Hahn, Ben Moore, Joachim Stadel
Outline - N-body codes: where do we stand? - accuracy - new solvers? - Challenges in Modified Gravity calculations. - f(r) and MOND - predictions - Simulating baryonic effects. - feedback processes - the physics of clusters & groups - baryons as a nuisance
N body simulations: the state of affairs EUCLID requires 1% accuracy up to k=10 h/mpc in the theory. Different codes have different systematic effects (time integration). GADGET3 large scale force with Fourier convolution and Particle Mesh small scale force with tree code (multipole direct space convolution) PKDGRAV3 large and small scale force with (fast multipole) tree code periodic BC using Ewald summation (use of GPU acceleration) RAMSES Particle Mesh with Adaptive Mesh Refinement Direct Poisson solver with Multigrid acceleration Ongoing Euclid CosmoSim WG project identical GADGET initial conditions and output files code comparison beyond the 1% barrier
Systematic effects in N body codes Schneider et al. 2015 in prep. linear non-linear
Comparing to the Cosmic Emulator Schneider et al. 2015 in prep. Heitmann et al. 2014
Comparing to the Cosmic Emulator Dark Sky simulation (Skillman et al. 2014)
Beyond N body codes? The Vlasov approach Hahn & Angulo (2015), Hahn, Abel, Kaehler (2013)
Cosmological simulations with modified gravity Viable models show small deviations (1-10%) with LCDM. Motivated theoretically by dark matter (e.g MOND) or dark energy (e.g. f(r)). A fully developed theory is required with at least: time evolution of the expansion factor (homogeneous universe) self-consistent initial random fluctuations viable weak-field limit for the dynamics of the matter MOND (AQUAL): a non-linear Poisson equation MOND (QUMOND): 2 standard (linear) Poisson equations f(r) model: a non-linear Poisson equation and a standard linear Poisson solver
Cosmological simulations with modified gravity Challenges for simulations with modified gravity models direct or Fourier convolution approach not valid anymore non-linear field solvers are slow and converge poorly non-linear multigrid techniques; Raphson-Newton iterations MLAPM with f(r) solver on AMR (Zhao, Li, Koyama 2011) ECOSMOG: f(r) field solver for the AMR code RAMSES (Li et al. 2012) MG-GADGET: f(r) models for the GADGET code (Puchwein et al. 2013) Phantom of RAMSES: QuMOND for the RAMSES code (Lüghausen et al. 2014) RAyMOND: AQUAL (and QuMOND) for the RAMSES code (Candlish et al. 2015)
Simulations with f(r) modified gravity model Lombriser et al. 2012
Simulations with f(r) modified gravity model Zhao, Li & Koyama (2011)
Zoom simulations with f(r) model strong (F4) Corbett medium (F5) weak (F6) ΛCDM Corbett Moran et al. 2014
Zoom-in simulations with f(r) models Corbett et al. (2014)
Baryonic effects are too difficult to model (18%) Very low efficiency of gas conversion into star. Small mass galaxies are dominated by stellar feedback. Large mass galaxies are governed by AGN feedback. Stellar-to-halo mass ratio Moster et al. (2010) Dekel & Silk (1986) Silk & Rees (1998)
Dark matter cusp-to-core transformation Excellent fit of the dark matter profile with a pseudo-isothermal profile de Blok et al. (2001)
Galaxy formation in groups and clusters
Adiabatic hydrodynamics: 10% accuracy? Rabold et al. in prep.
Feedback models from SMBH in massive ellipticals - Thermal feedback (Sijacki et al. 2007; Booth & Schaye 2010; Teyssier et al. 2010): thermal bombs - Radiative feedback (Choi et al, 2012, 2014; Vogelsberger et al. 2013): dust-absorbed UV radiation from the accretion disk. - Jet feedback (Omma et al., Cattaneo & Teyssier, Dubois et al. 2010, Choi et al. 2014): injection of momentum in a jet-like geometry. - Cosmic ray feedback (Pfrommer at al. 2010; Oh et al, 2013): heating from Alfven waves excited by CR-induced instabilities. - Bubble feedback (Sijacki et al. 2007): buoyantly rising bubble with initial radius close to 50 kpc These models are related to the quasar mode (thermal, radiative) or to the radio mode (jet, CR, bubbles) of AGNs. Cosmological simulations with zoom-in or periodic boxes and around 1 kpc resolution.
The effect of baryons on the halo mass Martizzi et al. 14 Martizzi et al. 14 RAMSES code
Central galaxy stellar mass Martizzi+14
Central galaxy stellar mass distribution Martizzi et al.14 Kravtsov et al.14
The effect of baryons on the halo mass Vogelsberger et al. 14 Genel et al. 14 AREPO code
Analytical halo model for the matter power spectrum For each halo, we consider analytical models for each of the 3 components: gas, dark matter and the central galaxy Using simple analytical profiles, we apply the halo model methodology to compute the power spectrum. Main ingredients are: - mass of the central galaxy : abundance matching - size of the central galaxy : 0.015 of the viral radius - total gas mass versus total halo mass : free parameter - adiabatic contraction for CDM White (2004), Zhan & Knox (2004), Rudd et al. (2008), Guillet et al. (2010), Semboloni et al. (2011), van Daalen et al. (2011) Good agreement with the zoom-in simulations of Martizzi et al. (2014)
A simple model for the effect of AGN feedback Mohammed et al. (2015) Semboloni et al. (2011)
A simple model for the effect of AGN feedback
Cosmological parameters estimation Mock weak-lensing observation with 3 redshift bins (EUCLID-like) Mohammed et al. (2015) increase max. multipole
Beating down baryonic effects? Mohammed et al. (2015)
Conclusions - N-body codes are 1% accurate below k=1 Mpc/h; 5% accurate between 1 and 10 Mpc/h. Do we need higher-order accurate N-body solvers? Something else? - Modified gravity solvers are getting more and more popular. Still slow and fragile. - Simulations with baryons are not even 10% accurate! - Massive variations between codes and feedback models! - AGN feedback models (when properly calibrated) can reproduce reasonably well the main properties of groups and clusters. - The effect of baryons reaches 10% (deficit) at k=20 Mpc/h. More? - Cosmological parameters could in principle be fitted with 1% accuracy down to 1 arcmin if one uses an unbiased model.