ModelinggalaxyredshiftspacedistortionsforWFIRST

NickHandUCBerkeleyMarch3,2016

withUrosSeljak,YuFeng,andGrigorAslanyan

GalaxyclusteringwithWFIRST

theul'mategoal:measureexpansionhistoryandgrowthratewithsub-percentlevelprecision

Andersonetal.2014 PlanckCollabora'onXIII2015

BAOasstandardruler redshiHspacedistor'ons

UncertaintiesintheforecastingofRSDconstraints

•smallscalescontaminatedbynon-lineareffects,buthavegreatersta's'calprecision

•theore'calsystema'csimplicitlyforecastedthroughvalueofkmax

source:Weinbergetal.2013

RSDconstraintshavegreatpotential

source:Wangetal.2010

•needfullP(k)analysistofullycaptureinforma'on

•factorof~3improvementindarkenergyFOMwhenusingfullP(k)shapemeasurements(assumingGR)

•fullshapeanalysisprovidesinforma'ononneutrinomassesandexpansionthroughAPtest

NickHand,UCBerkeley March3,2016

AnewschemeformodelingRSD

1.ApproximateN-bodysolverwithhaloforma'onmodelthatisbothsufficientlyfastandaccurateenoughtoextractgalaxysta's'cs

2.Physicalmodelforgalaxy-haloconnec'onthatisgeneralenoughtoavoidthemanyunknownaspectsofgalaxyforma'on

3.Simultaneouslysampletheposteriordistribu'onandemulatetheslowevalua'onofthedatalikelihood

NickHand,UCBerkeley March3,2016

FastPM:fastsimulationsofhalos

•anapproximatepar'clemeshN-bodysolverthatenforcesthecorrectlarge-scalelineargrowthateach'mestep

•wriXenfromscratchtoexhibitstrong-scaling—nearlylinearscalingwiththenumberofCPUsallowsforfastsimula'ons

•benchmarkswith10'mestepsproducehalocatalogsthatareveryclosetotheexact(N-body)solu'on

•simula'onsledbyYuFengatUCBerkeley,withpublica'oncomingsoon

findtheprojectongithub:hXps://github.com/rainwoodman/fastpm

NickHand,UCBerkeley March3,2016

preferredconfigura'ontakes~100CPU-hours—>typicallyO(1min)

Fengetal.2016(inprep.)

FastPM:fastsimulationsofhalos

NickHand,UCBerkeley March3,2016

FastPM:benchmarksforhalocatalogs

transfer(P

1/P 2)1/2

Fengetal.2016(inprep.)

atz=0

thegalaxy-haloconnection:HODformalism

•flexibleenoughtoimmunizeconstraintsagainstgalaxyforma'onuncertain'es:

1. velocitybiasforcentrals/satellites2. centralgalaxyincompleteness3. satelliteprofileuncertain'es4. assemblybias—>decoratedHODs(seeHearinetal.2015,

1512.03050)5. others?

•simplifiedHOD-modelingalreadysuccessfulinextendingRSDconstraintstosmallerscales:Reidetal.2014,Guoetal.2014.

•populateFastPMhalocatalogsusingasmanyfeaturesasneededusingHalotools soHware(ledbyAndrewHearin)

Halotools:hXps://github.com/astropy/halotools

0.2 0.4 0.6 0.8 1.0k (h/Mpc)

−0.5

0.0

0.5

1.0

1.5

2.0

Pgg ℓ)(,2/PEH

ℓ)((k)

satellitefrac'on

fromsimulationtoclusteringobservables

•fastpowerspectrummeasurementsviaFFTsvianbodykit• popula'on+powerspectrumstepstakeO(seconds)

nbodykit:hXps://github.com/bccp/nbodykit

monopole

quadrupole

todo:tailortoWFIRSTvolume,HODmasses,observa'onaleffects,etc

NickHand,UCBerkeley March3,2016

CombiningthepieceswithCosmo++ emulator

•acombinedsamplerandemulatorfordatalikelihoodusingtrainingsetofexactresultsproducedduringsamplingprocedure

•robusterrorcontrolofemula'onerrorsthatarepropagatedtoposteriorprobabilitydistribu'on

•exactsolu'oncomputediferrormodelpredictsanunacceptableemula'onerror

•“learn-as-you-go”:updateserrormodelandtrainingsetgivennew,exactsolu'ons

Aslanyanetal.2015,1506.01079hXps://github.com/aslanyan/cosmopp

NickHand,UCBerkeley March3,2016

ledbyGrigorAslanyanatUCBerkeley

appliedtoCMBlikelihoodsin1506.01079

Aslanyanetal.2015

CombiningthepieceswithCosmo++ emulator

Conclusions

• RSDanalysescanprovidepowerfulconstraintsondarkenergyandGeneralRela'vitytestswithWFIRST,iftheore'caluncertain'escanbecontrolled

• keychallenge:accuratemodelingofnon-lineareffectsandgalaxyforma'onphysicsonsmall-scales

• developingasimula'on-basedRSDmodelthatisbothcomputa'onallytractableandsufficientlyaccurate

1. FastPMsimula'onsproducehalocatalogsinO(minutes)2. HODpopula'onandpowerspectrumes'ma'onin

O(seconds)3. Combinethesestepsinlearn-as-you-goemulatorto

simultaneouslysampletheposteriorandemulatethenon-lineargalaxypowerspectrum

NickHand,UCBerkeley March3,2016

FastPM:benchmarksforhalocatalogsstochas'city

Fengetal.2016(inprep.)

~0.18dexscaXerinhalomasscorrespondsto:stochas'city~0.10,0.18,0.22in1012,1013,1014Msun/hhalos

NickHand,UCBerkeley March3,2016

ModelingassemblybiaswithdecoratedHODs

NickHand,UCBerkeley March3,2016

thecurrentstatusofgrowthrateresults

bestuncertaintyonfσ8(z=0.57)is~8%,fipngtokmax=0.24h/Mpc

Gil-Marinetal.2015

NickHand,UCBerkeley March3,2016

BAOsystematicsarewell-controlled

simula'onsindicatereconstruc'oneliminatessystema'cstothe~0.1%level

BAOsh

i1

source:Mehtaetal.2011

NickHand,UCBerkeley March3,2016

nbodykitsoftwaretools

•pythontoolsforN-bodysimula'ons+LSSsurveys

•parallelizedwithMPIanddesignedtorunonsuper-computers

•availabletools/features:

•periodicandwindowedpowerspectra

•correla'onfunc'ons

•FOFhalofinder

•sub-halofinder

•runningabovealgorithmsinparallelacrossnodesinbatchmode

availableatgithub.com/bccp/nbodykit