Recent Abacus Simulations for DESI

Research Software Engineer
Scientific Computing Core

Flatiron Institute

October 12, 2023

Local Primordial Non-Gaussianity

Local-type primordial non-Gaussianity (PNG) is a modification to the primordial potential of the form
$$\Phi = \Phi_\mathrm{G} + f_\mathrm{NL}(\Phi_\mathrm{G}^2 - \langle\Phi_\mathrm{G}\rangle^2)$$
Local PNG is parameterized by $f_\mathrm{NL}$
To run an $f_\mathrm{NL}$ $N$-body simulation, the only modification is to the initial conditions
Unfortunately, the easiest way to implement this is
$$\tilde\Phi_\mathrm{G}(\mathbf{k}) \rightarrow \Phi_\mathrm{G}(\mathbf{x}) \rightarrow \Phi_\mathrm{G} + f_\mathrm{NL}\Phi_\mathrm{G}^2 \rightarrow \tilde\Phi(\mathbf{k})$$
Then ICs proceed as normal to generate displacements and velocities
Main computer cost is an extra backward and forward FFT
Main human cost is getting the units right

Implementation of f_NL can be found here: https://github.com/abacusorg/zeldovich-PLT/pull/8
- There's a failed idea in this PR to skip the extra FFTs via an application of the chain rule
Validation was performed on the power spectrum and bispectrum (specifically $dP/df_\mathrm{NL}$ and $dB/df_\mathrm{NL}$)
Compared against 2LPTPNG (labeled Gadget in the plots), and theory where known (to me)
Scale-dependent halo bias also has the right sign

Initial conditions power spectrum comparison

Three bispectrum triangle configurations were tested: equilateral, squeezed, and folded
Theory prediction is simple:
$$B_\Phi(k_1,k_2,k_3) = 2 f_{NL} P_\Phi(k_1)P_\Phi(k_2) + 2\ \rm{cyc.}$$ (from 2206.01619)
Abacus, 2LPTPNG, and theory all match for equilateral and folded
Abacus and 2LPTPNG match each other for squeezed, but do not match the theory prediction
Pylians3 code was used for bispectrum

10 simulations
- 5 f_NL values
- 2 phases each, ph000 & ph001
2 Gpc/h box (same as "base")
$1.5 \times 10^{10}\, \mathrm{M}_\odot/h$ particle mass (3.5x worse than "base", suitable for LRGs)
4096^3 particles
500 GPU node-hours each on Perlmutter
16 hours on 32 nodes, 1D decomposition
Final redshift of 0.3, matching DESI LRG selection

Name	f_NL	Phase	Full Outputs
pngbase_c000	{-100,-50,0,50,100}	ph000	Full
pngbase_c000	{-100,-50,0,50,100}	ph001	Partial

Checking for scale-dependent halo bias

Two high mass resolution simulations with outputs between z=5 and z=2
Abacus_DESI2_c000_ph300
- Larger volume
Abacus_DESI2_c000_ph310
- Better mass resolution
- Still running
2D domain decomposition
For reference, AbacusSummit base resolution was $2.1 \times 10^{9}\, \mathrm{M}_\odot/h$

Minor optimizations for high redshift
- Proper softening length is smaller and reaches 1/40th of the particle spacing at z=2
- Input linear power spectrum taken at z=2 (for ph310)

Implemented f_NL initial conditions for Abacus
- Any experts want to do additional validation on the ICs?
Ran 10 f_NL simulations
- Simulations are named "Abacus_pngbase_..."
2 high-redshift simulation for DESI-II studies
- Named "Abacus_DESI2_..."
- 1 finished and 1 running
Available now on NERSC, in the usual location:
$CFS/desi/cosmosim/Abacus
Requests for more simulations?
Special thanks: Martin White, Shadab Alam, Sandy Yuan, Daniel Eisenstein

By Lehman Garrison