1 Analysing Cosmological Simulations in the Virtual Observatory: Designing and Mining the Millennium...

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Analysing Cosmological Simulations in the Virtual Observatory:

Designing and Mining the Millennium Simulation Database

Gerard Lemson German Astrophysical Virtual Observatory (GAVO)ARI, HeidelbergMPE, Garching bei München

2 Garching, June 26, 2008

Acknowledgments

Alex Szalay Virgo consortium, in particular:

Volker Springel, Simon White, Gabriella DeLucia, Jeremy Blaizot(MPA, Munich, Germany),

Carlos Frenk, Richard Bower, John Helly (ICC, Durham, UK) Similar efforts/sites to Millennium Database

Durham (mirror of Millennium DB) Horizon/GalICS (Lyon) ITVO (Trieste)

GAVO is funded by the German Federal Ministry for Education and Research(BMBF)

Summary VO aims to provide access to remote data for use/analysis by 3rd

parties. Data analysis requires

advanced methods for analysis data

Data sets are often very large, often far away (makes them even larger!)

To analyse remote datasets, one needs to be able to bring the analysis to the data.

“Standard” approach using flat files and C/IDL/etc code sub-optimal To analyse very large datasets we also need advanced methods of

data organisation and data access Structured approach supported by relational database system allows

one to concentrate on science, iso worry about I/O optimisation etc And the questions can become pretty complex !

Case study: The Millennium SimulationSpringel V. et al. 2005 Nature 435, 629

Millennium Simulation

Virgo consortium Gadget 3 10 billion particles, dark matter only 500 Mpc periodic box Concordance model (as of 2004) initial conditions 64 snapshots 350000 CPU hours O(30Tb) raw + post-processed data

Post-processing data products complex and large Challenge to analyse, even locally! SimDAP-like approach required for remote access.

Intermezzo: Data Access is Hitting a Wall (courtesy Alex Szalay)

FTP and GREP are not adequate You can GREP/FTP 1 MB in a second You can GREP/FTP 1 GB in a minute You can GREP/FTP 1 TB in 2 days You can GREP/FTP 1 PB in 3 years SFTP much slower and 1PB ~2,000 disks

At some point you need indices to limit searchparallel data search and analysis

This is where databases can help

Analysis and Databases(courtesy Alex Szalay)

Much statistical analysis deals with Creating uniform samples -- data filtering Assembling relevant subsets Estimating completeness Censoring bad data Counting and building histograms Generating Monte-Carlo subsets Likelihood calculations Hypothesis testing

Traditionally these are performed on files Most of these tasks are much better done inside a

database

Advantages of relational databases Encapsulation of data in terms of logical structure, no

need to know about internals of data storage Standard query language for finding information Advanced query optimizers (indexes, clustering) Transparent internal parallelization Authenticated remote access for multiple users at same

Forces one to think carefully about data structure Speeds up path from science question to answer Facilitates communication (query code is cleaner) Facilitates adaptation to IVOA standards (ADQL)

Millennium Simulation Phenomenology Density field on 2563 mesh

CIC Gaussian smoothed: 1.25,2.5,5,10 Mpc/h

Friends-of-Friends (FOF) groups SUBFIND Subhalos Galaxies from 2 semi-analytical models (SAMs)

MPA (L-Galaxies, DeLucia & Blaizot, 2006; Bertone et al 2007) Durham (GalForm, Bower et al, 2006)

Subhalo and galaxy formation histories: merger trees Mock catalogues on light-cone

Pencil beams (Kitzbichler & White, 2006) All-sky (depth of SDSS spectral sample)

(Blaizot et al, 2005)

In preparation: Spectra for light cone galaxies

FOF groups, (sub)halos and galaxies

Time evolution: merger trees

Mock catalogues

Synthetic spectra (not yet available)

Hierarchy of Data Products

Density FieldMesh Cell

FOF Group Subhalo

SubhaloMergerTree

SAM Galaxy Merger Tree

Light ConeGalaxy

original

Tree relationships

Parent halo

SUBFIND result

Parent FOF group

Located in

Spectrum

Designing the Database Need a model for data, including relations between

different objects Model needs to support science: “20 questions”

(following Gray & Szalay)1. Return the galaxies residing in halos of mass between 10^13 and 10^14

solar masses. 2. Return the galaxy content at z=3 of the progenitors of a halo identified at

z=0 3. Return the complete halo merger tree for a halo identified at z=0 4. Find all the z=3 progenitors of z=0 red ellipticals (i.e. B-V>0.8 B/T > 0.5)5. Find the descendents at z=1 of all LBG's (i.e. galaxies with SFR>10

Msun/yr) at z=3 6. Find all the z=2 galaxies which were within 1Mpc of a LBG (i.e.

SFR>10Msun/yr) at some previous redshift.7. Find the multiplicity function of halos depending on their environment

(overdensity of density field smoothed on certain scale)8. Find the dependency of halo properties on environment

Data model features Each object its table

properties are columns each a unique identifier

Relations implemented through foreign keys, pointers to unique identifier column FOF to mesh cell it lies in Sub-halo to its FOF group galaxy to its sub-halo etc

Special design needed for Hierarchical relations: merger trees Spatial relations: multi-dimensional indexes required Support for random sample selection

Formation histories:Subhalo and Galaxy merger trees Tree structure

halos have single descendant halos have main progenitor

Hierarchical structures usually handled using recursive code inefficient for data access not (well) supported in RDBs

Tree indexes depth first ordering of nodes defines identifier pointer to last progenitor in subtree

Merger trees :select prog.* from galaxies des , galaxies prog where des.galaxyId = 0 and prog.galaxyId between des.galaxyId and des.lastProgenitorId

Branching points :select descendantId from galaxies des where descendantId != -1 group by descendantId having count(*) > 1

Spatial queries, random samples Spatial queries require multi-dimensional

indexes. (x,y,z) does not work: need discretisation

index on (ix,iy,iz) with ix=floor(x/10) etc More sophisticated: space filling curves

bit-interleaving/oct-tree/Z-Index Peano-Hilbert curve Need custom functions for range queries

(Implemented in T-SQL)

Random sampling using a RANDOM column RANDOM from [0,1000000]

The Millennium Database web site

SQLServer 2005 database Web application (Java in Apache Tomcat web server)

portal: http://www.mpa-garching.mpg.de/millennium/ public DB access: http://www.g-vo.org/Millennium private access: http://www.g-vo.org/MyMillennium MyDB

Access methods browser with plotting capabilities through VOPlot applet wget + IDL, R TOPCAT (3.1)

Usage statistics Up since August 2006 (astro-ph/0608019) ~225 registered users > 5 million queries > 40 billion rows ~130 papers, ~50% not related to Virgo consortium

(see http://www.mpa-garching.mpg.de/millennium )

Some science questions and their implementation as SQL

If time permits, in any case 1-1 demo possible.

Find light cone galaxies in a slice in redshift, RA and Dec

select ra,dec,redshift_obs from kitzbichler2006a_obs where redshift_obs between 1 and 1.1 and dec between -.05 and .0

Color-magnitude for random sample of galaxies

select mag_bdust, mag_bdust - mag_vdust as color, type from delucia2006a where snapnum=63 and random between 0 and 100 and mag_b < 0

Get merger tree for identified galaxy

select p.snapnum, p.x,p.y,p.z, p.stellarmass, p.mag_b-p.mag_v as color from delucia2006a d , delucia2006a p where d.galaxyid=0 and p.galaxyid between d.galaxyid and d.lastprogenitorid

Histogram of density field at redshifts 0,1,2,3; Gaussian smoothing 5 Mpc/h

select snapnum, .01*floor(f.g5/.01) as g5, count(*) as num from mfield f where f.snapnum in (63,41,32,27) group by snapnum,.01*floor(f.g5/.01) order by 1,2

FOF multiplicity function at redshifts 0,1,2,3,

select snapnum, .1*floor(log10(np)/.1) as lognp, count(*) as num from fof where snapnum in (63,41,32,27) group by snapnum , .1*floor(log10(np)/.1) order by 1,2

FOF mass multiplicity function, conditioned on density in environmentselect .1*floor(log10(fof.np)/.1)

as lognp, count(*) as num from mfield f , fof where fof.snapnum=f.snapnum and fof.phkey = f.phkey and f.snapnum=63 and f.g5 between 1 and 1.1group by .1*floor(log10(fof.np)/.1)order by 1

Thank you !

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