Adrian Jenkins
Institute for Computational Cosmology
Durham

Cosmological N-body simulations have grown rapidly in size over the last four decades
" N " AS A FUNCTION OF TIME
★
MII   Computers double their speed every 18 months
(Moore's law )
★
MXXL
N-body simulations have doubled their size every
16-17 months
Recently, growth has accelerated further.

The largest
N-body simulations cover a sizable fraction of the observable universe
DARK MATTER
CLUSTERING
ALONG THE
PAST LIGHT-
CONE OF THE
HUBBLE
SIMULATION
Evrard et al. (2001)
`Hubble-volume' simulation
Virgo Consortium (1999)
Λ CDM
1.000.000.000 particles m=2.2 x 10 12 M
⊙
/h

'Millennium' simulation
Springel et al. (2005)
Λ CDM
10.077.696.000 particles m=8.6 x 10 8 M
⊙
/h

Over 330 papers published using Millennium data.

R. Angulo, S. White, V. Springel, A. Jenkins,
C. Frenk, C. Baugh, S. Cole

New simulation aimed at exploring the connection between galaxy physics and large-scale structure.
Box: 3000 Mpc/h (216xMS & 27,000xM-II & 4xBOSS) ‏
Np: 6720 3 ~ 303 billion particles
“Millennium” Cosmology
Particle mass: 6.1x10
9 Mo/h
Softening: 10 kpc/h ; ICs: 2LPT
64 outputs (same spacing as the Millennium) ‏
Juropa/JSC
(70% of the 13 th largest cluster in the world)
1536 nodes; 2 quad-core procs and 24Gb of RAM

Exploring galaxy physics in di ff erent cosmologies. Angulo & White 2010
– Realistic mock catalogues for PanSTARRS, SDS-III/BOSS, BigBOSS, etc.
- The impact of galaxy physics in BAO/Growth factor measurements.
- Integrated Sachs-Wolfe e ff ect (with SA galaxies).
- Properties and assembly of massive superclusters
- Abundance and fate of high-z quasars
– 2pt and higher order large-scale clustering (up to 300 Mpc/h) ‏
– universality of halo bias and mass function
– Rare events, environmental e ff ects, etc
Large cosmological simulations are also useful for defining samples of objects for further study. For example the Aquarius project, GIMIC
(Crain et al 2009).

Millennium-II volume
6 May 2009

Substructures within substructures
There are substructures embedded within other structures.
We detect 4 generations

•   Particle physics candidates include the sterile neutrino ( ν s
) and the gravitino.
•   Both motivated by particle physics.
The ν s
(3 flavours) of Boyarsky,
Ruchayskiy, & Shaposhnikov(2009) as a solution to the flavour oscillations of
‘active neutrinoes. The gravitino could be the lightest supersymmetric particle
(Steffen 2006).
•   ν s
should decay into X-rays. Attempts made to detect this decay inside ultrafaint dwarf galaxies(Mirabal &
Nieto 2010, Mirabal 2010). As yet no conclusive detection reported
•   Other constraints from satellite galaxy abundance (Maccio & Fontanot 2010) and the Lyman
α
forest power spectrum (Viel et al 2005). Likely mass of ν s
~2keV.
Boyarsky et al 2009

•   Should include cut off in power spectrum and intrinsic particle
Wang & White
2007  velocities (latter ignored in most studies to date).
•   Results show far fewer dark matter substructures than in
CDM (Bode, Ostriker, & Turok
2001)
•   Suffer from top-down spurious fragmentation (Wang & White
2007)
•   We are simulating a Milky
Way-sized DM halo with the
ν s of Boyarsky, Ruchayskiy, &
Shaposhnikov (2009). Will repeat with a Cold-Warm mixture by the same authors.
Gao & Theuns 2007

Resimulating objects from MXXL

Setting phases for Gaussian random fields
•   The starting point for setting the phases for initial conditions based on Gaussian random fields is first to create a Gaussian white noise field.

•   Most cosmological and resimulation initial conditions can be considered as starting from a Gaussian white noise field which is specified in k-space. (e.g.
Hubble volume, Millennium, Aquarius). This is then transformed by Fourier methods into a real space Gaussian field with a specified power spectrum.
•   Salmon 1996 – advocated starting from a real space Gaussian white noise field, which is then convolved with an appropriate function to give the desired real space Gaussian field.
•   The GRAFICS-1/2 codes by Bertschinger starts with a real space white noise field. Resimulations made possible to refining regions of the white noise field.
•   Resimulations can also be set up starting from a k-space description.
e.g. the Aquarius simulations. GIMIC simulations. Difficult to create overlapping resimulations which are consistent.

Why change to using real space white noise fields?
•   For very large simulations e.g. MXXL, the k-space representation is very large (needing a 9216 3 FT) which makes creating resimulation initial conditions challenging.
•   A real space white field does not need to be evaluated everywhere at the highest resolution.
•   What is needed is a white noise field which can be defined everywhere at high resolution, and which can be resampled easily at as low a resolution as required.
•   Defining a shared white noise field would make it easier to share or publish initial conditions.

1.
Map the linear sequence from a pseudorandom number generator to an oct-tree level by level from top to bottom
2.
Use a generator where it is possible to rapidly access any part of the entire sequence.
For a sufficiently long pseudorandom number sequence can create initial conditions at what ever resolution is needed.

•   A disadvantage of the method is that the precise phase of any wave depends on which level of the oct-tree is used.
•   Can characterize this error by computating the power spectrum of the difference field between the true density field and the one obtained using the method - the difference power spectrum
•   Difference power spectrum has to be kept as small as possible.

Improving the accuracy of the reconstructed phases
•   Can choose what information is available to describe each white noise cell in the oct-tree
•   The more that is known about the white noise field within a cell, the more accurately the phases can be determined for a fixed number of oct-tree cells, but the more expensive the calculation of the white noise field becomes.

4
1
dV = I
1 cell
€
∫ cell
ρ x a y b z c dV = I abc
,0 ≤ a + b + c ≤ 1
27
8
€
∫ cell
ρ x a y b
cell z c
dV dV = I abc
,0
=
≤
I a ,
1 b , c ≤ 1 ∫ cell
ρ x a y b z c dV = I abc
,0 ≤ a , b , c ≤ 2
€

Real space multi-scale Gaussian white noise field has many advantages for making initial conditions.
Makes it easier to make resimulation initial conditions of regions drawn from large simulations like MXXL.
Allows consistent initial conditions in a volume that can be larger than the Hubble volume, and down to resolutions below the CDM free streaming scale.
I plan to make the white noise routines public. This would make it easier to communicate/publish initial conditions.
CAP …

Formed at the beginning of 2010. Two meetings so far.
Wide remit: including HPC, data curation, NGS, Hartree centre
STFC is required to provide input of HPC needs at the end of this year.
CAP is organising this. Currently working on an internal document. Aim is then to consult NUAP and FUAP panels next.
People:
Chair: Peter Clarke Astronomers: Adrian Jenkins, Mike Watson
Members from particle physics, nuclear physics, life sciences,
Daresbury.