Suite of Hydrodynamical Simulations for the Lyman-Alpha Forest with Massive Neutrinos

1.8 MB·

by  Graziano Rossi

Astronomy&Astrophysicsmanuscriptno.rossi_etal_2014 (cid:13)cESO2014
June23,2014
Suite of hydrodynamical simulations for the Lyman-alpha forest
with massive neutrinos
⋆
GrazianoRossi1,2 ,NathaliePalanque-Delabrouille1,3,ArnaudBorde1,MatteoViel4,5,ChristopheYèche1,JamesS.
Bolton6,JamesRich1,Jean-Marc LeGoff1
1CEA,CentredeSaclay,Irfu/SPP,F-91191Gif-sur-Yvette,France
2DepartmentofAstronomyandSpaceScience,SejongUniversity,Seoul,143-747,Korea
3LawrenceBerkeleyNationalLaboratory,Berkeley,CA94720,USA
4 4INAF,OsservatorioAstronomicodiTrieste,viaG.B.Tiepolo11,34131Trieste,Italy
1 5INFN/NationalInstituteforNuclearPhysics,viaValerio2,34127Trieste,Italy
0 6SchoolofPhysicsandAstronomy,UniversityofNottingham,UniversityPark,NottinghamNG72RD
2
June23,2014
n
u
J ABSTRACT

0
2 ThesignatureleftinquasarspectrabyneutralhydrogenintheUniverseallowsconstrainingthesumoftheneutrinomasseswitha
bettersensitivitythanlaboratoryexperimentsandmayshednewlightontheneutrinomasshierarchyandtheabsolutemass-scaleof
] neutrinos.Constraintsoncosmologicalparametersandonthedarkenergyequationofstatecanalsobederivedfromajointparameter
O estimationprocedure.However,thisrequiresadetailedmodelingoftheline-of-sightpowerspectrumofthetransmittedfluxinthe
Lyman-α(Lyα)forestonscalesrangingfromafewtohundreds ofmegaparsecs, whichinturndemandstheinclusionandcareful
C
treatmentofcosmologicalneutrinos.Tothisend,wepresenthereasuiteofstate-of-the-arthydrodynamicalsimulationswithcolddark
h. matter(CDM),baryonsandmassiveneutrinos,specificallytargetedformodelingthelow-densityregionsoftheintergalacticmedium
p (IGM) asprobed by theLyαforest at high-redshift. Thesimulations spanvolumes ranging from(25h−1Mpc)3 to(100 h−1Mpc)3,
- andweremadeusingeither3×1923 ≃21millionor3×7683 ≃1.4billionparticles.Theresolutionofthevariousrunswasfurther
o enhanced,sothatwereachedtheequivalentof3×30723 ≃87billionparticlesina(100h−1Mpc)3boxsize.Thechosencosmological
r parametersarecompatiblewiththelatestPlanck(2013)results,althoughwealsoexploredtheeffectofslightvariationsinthemain
t
s cosmological and astrophysical parameters. We adopted a particle-type implementation of massive neutrinos, and consider three
a degeneratespecieswithmasses m =0.1,0.2,0.3,0.4,and0.8eV,respectively.Weimprovedonpreviousstudiesinseveralways,
ν
[ in particular with updated routinPes for IGM radiative cooling and heating processes, and initial conditions based on second-order
Lagrangianperturbationtheory(2LPT)ratherthantheZel’dovichapproximation.Thisallowedustosafelystartourrunsatrelatively
2
lowredshift(z=30),whichreducedtheshot-noisecontaminationintheneutrinocomponentandtheCPUconsumption.Inaddition
v
toprovidingtechnicaldetailsonthesimulations,wepresentthefirstanalysisofthenonlinearthree-andone-dimensionalmatterand
4
flux power spectra from these models, and characterize the statisticsof the transmitted flux in the Lyα forest including the effect
6
ofmassiveneutrinos.InsynergywithrecentdatafromtheBaryonAcousticSpectroscopicSurvey(BOSS)andthePlancksatellite,
4
andwithagridofcorrespondingneutrino-lesssimulations,ourrealizationswillallowustoconstraincosmologicalparametersand
6
neutrinomassesdirectlyfromtheLyαforestwithimprovedsensitivity.Inaddition,oursimulationscanbeusefulforabroadervariety
.
1 ofcosmologicalandastrophysicalapplications,rangingfromthethree-dimensionalmodelingoftheLyαforesttocross-correlations
0 between different probes, studying theexpansion historyof theUniverseincluding massive neutrinos, and particle-physicsrelated
4 topics.Moreover,whileoursimulationshavebeenspecificallydesignedtomeettherequirementsoftheBOSSsurvey,theycanalso
1 beusedforupcomingorfutureexperiments–suchaseBOSSandDESI.
:
v Key words. large-scale structure of Universe – cosmology: theory, observations, numerical simulations, intergalactic medium,
i neutrinos–methods:numerical
X
r
a
1. INTRODUCTION encestherein),asprimordialmassiveneutrinoscompriseasmall
portionofthedarkmatter(DM)andthereforemustsignificantly
Neutrinoscience has receiveda boostof attentionrecently,be-
alter structure formation. Potentially, combining cosmological
cause the breakthrough discovery in particle physics over the
andparticlephysicsresults,itisexpectedthatwewillbeableto
last decade that neutrinos are indeed massive. However, at the
determinetheabsolutemassscale ofneutrinosin theverynear
present time we only know their mass differences, because so-
future,andsolveoneofthekeyquestionsinneutrinophysicsto-
lar, atmospheric, reactor, and accelerator observations of neu-
day–namely,thenatureoftheirmasshierarchyandperhapsthe
trinooscillationsaresensitiveonlytodifferencesinthesquares
originofmass.
of neutrino masses, requiring that there be at least one species
with mass m ≥ 0.06 eV. On the other hand, cosmology offers Neutrino physics also provides one of the best exam-
a unique ‘laboratory’ with the best sensitivity to the neutrino ples of the interplay between particle physics and cosmol-
mass (see for example Lesgourgues & Pastor 2012, and refer- ogy/astrophysics. For instance, the measurement of neutrino
masses could point to a new fundamentaltheory, of which the
⋆ e-mail:[email protected] standard model (SM) is the low-energy limit (Lesgourgues &
Articlenumber,page1of22
A&Aproofs:manuscriptno.rossi_etal_2014
Pastor 2006) – hence calling for new physics beyond the SM. high-redshiftUniverse,becauseitisataredshiftrangeinacces-
Inaddition,astrophysicalneutrinofluxescanbeexploitedtotest sible tootherLSSprobesandspansa wide intervalin redshift.
the SM, with experiments of neutrino decays, oscillations, and For this reason, it was recently possible, for instance, to detect
searchesfornonzeroneutrinoelectromagneticmoments. forthefirsttimethebaryonacousticoscillation(BAO)signaldi-
In a cosmological context, the effect of massive neutrinos rectlyfromtheLyαforest(Buscaetal.2013;Slosaretal.2013).
isessentiallytwofold.Firstly,neutrinoscontributetotheexpan- Thiswill be evenmore so with future surveys,such as eBOSS
sionrateduringtheradiationepochasoneofN neutrinos(with (Comparatetal.2013)andDESI(Schlegeletal.2011).
eff
N theeffectivenumberofneutrinospecies;arecentconstraint The Lyα forest is particularly well suited to constrain neu-
eff
from the Planck data is N = 3.36 ± 0.34 – see Ade et al. trinomasses,sincemassiveneutrinosleavearedshift-andmass-
eff
2013)and later as a nonrelativisticcomponentof matter. Com- dependent signature in the one-dimensional flux power spec-
paredwithmasslessmodels,thismodifiesthetimingofmatter- trum because the growth of cosmological structures on scales
radiation equality and the distance-redshift relation. Secondly, smallerthantheneutrinofree-streamingdistanceissuppressed.
aftertheybecomenon-relativistic,neutrinosparticipateinstruc- Todetectthiseffect,carefulmodelingoftheline-of-sight(LOS)
tureformation,butonlyonscalesgreaterthanthefree-streaming powerspectrumofthetransmittedLyαfluxisrequired.Pioneer-
scale.Becauseofthesetwoeffects,modelswithneutrinomasses ing work along these lines has been carried out by Croft et al.
greaterthan0.1eVgivepredictionsdifferentfromstandardcold (1998, 2002), Zaldarriaga, Hui & Tegmark (2001), Viel et al.
darkmatter(CDM)scenarioswithacosmologicalconstant(i.e., (2004,2006,2010),Seljaketal.(2005),McDonaldetal.(2006),
LCDMmodels),whichgenerallyincorporateaminimalneutrino Seljak,Slosar&McDonald(2006),andKim&Croft(2008).In
massof0.06eV. particular,McDonaldetal.(2006)andSeljaketal.(2006)used
Hence, while the most recent results from the cosmic mi- a sample of 3035 moderate-resolution forest spectra from the
crowavebackground(CMB),suchasdatafromthePlancksatel- SDSS to measure the one-dimensionalflux power spectrum at
lite(Adeetal.2013),theAtacamaCosmologyTelescope(ACT; z=2.2−4.2.Theyplacedconstraintsonthelinearmatterpower
Sieversetal.2013)ortheSouthPoleTelescope(SPT;Houetal. spectrumandonneutrinomasses,whileVieletal.(2010)stud-
2012),and fromthe large-scalestructure(LSS) as in the Sloan iedtheimpactofmassiveneutrinosinthetransmittedLyαflux.
Digital Sky Survey (SDSS; York et al. 2000, Eisenstein et al. Atpresent,themostprecisemeasurementoftheLyαfluxpower
2011)or in the WiggleZsurvey(Drinkwateret al. 2010;Blake spectrum comes from the Baryon Acoustic Spectroscopic Sur-
etal.2012)areconsistentwiththeΛCDMmodeldominatedby vey(BOSS;Dawsonetal.2013),withasampleofforestspectra
a dark energy(DE) component,with baryonsconstitutingonly almost two ordersof magnitudelarger than in previousstudies
4.5%ofthetotalmatter-energycontent,apureCDMscenariois (Palanque-Delabrouilleetal.2013).TheseLyαforestmeasure-
stillunsatisfactoryandincomplete–sinceevenasmallamount ments supplementthose obtained from the populationof lumi-
of neutrinos can significantly impact structure formation. Im- nousredgalaxies(LRGs),andconsiderablyextendtheredshift
provingourknowledgeofcosmologicalneutrinosisessentialfor rangethatcanbestudied.
anaccurateandconsistentminimalcosmologicalmodel,andthe TheLyαforestalsooffersoneofthestrongestreportedcon-
presentstudyisaneffortinthisdirection. straints on neutrino mass when combined with WMAP 3-year
Incosmology,neutrinoshavebeenstudiedwithalargenum- CMBdata(i.e. m < 0.17eVat95%CL;Seljaketal.2006),
ν
ber of probes and complementary techniques. The most direct buttheconstrainPtdependsonthenormalizationoftheobserved
way is through the analysis of the CMB radiation, because for LSS power spectrum relative to the CMB power spectrum;us-
thecurrentmasslimitstheirprimordialsignaturedoesnotvanish ing recent data from the Planck satellite instead of those from
althoughneutrinosarestillrelativisticatthetimeofrecombina- WMAP, the previous constraints are weakened. Nevertheless,
tion(Lesgourgues&Pastor2006).Whiletheoverallsensitivity current neutrino mass limits are on the verge of distinguishing
ofmassiveneutrinosimpactstheCMBtemperaturepowerspec- betweenanormal(onespecieswithm ∼ 0.06eV)andinverted
trumverymarginally,thereare non-negligibleconsequencesin (two species with m ∼ 0.06 eV) hierarchy, and in the near fu-
the polarizationmapsthroughtheearlyintegratedSachsWolfe turethedegeneracyofneutrinomasseswillberemovedbycom-
(ISW)effect(Hinshawetal.2013),anddistinctsignaturesfrom biningcosmologicalresultswithatmosphericandsolarneutrino
thegravitationallensingoftheCMBbyLSS–bothintempera- constraints.Forexample,thecombinationofPlanckCMBdata,
tureandpolarization(seeforinstanceSantosetal.2013orBat- WMAP9-yearCMBpolarizationdata(Bennettetal.2013),and
tye&Moss2013).Othermethodsforquantifyingtheimpactof a measurement of BAO from BOSS, SDSS, WiggleZ, and the
massive neutrinos involve baryonic tracers of the LSS cluster- 6dFgalaxyredshiftsurvey(Jonesetal.2009)producesanupper
ing of matter, and high-redshift surveys. Examples include the limit of m < 0.23 (95% CL), while a more aggressive use
ν
measurement of the three-dimensional matter power spectrum of galaxyPclustering into smaller scales and the nonlinearclus-
obtainedfromgalaxysurveys,Lyman-α(Lyα),or21cmprobes teringregimecanleadtostringentconstraints(Zhaoetal.2012;
wherethe underlyingtracer is neutralhydrogen(HI),the study Riemer-Sørensenetal.2013).
of galaxy clusters via the Sunyaev-Zel’dovich(SZ) effect, and However,thevalidityofthecurrentlimitsonneutrinomasses
the characterization of the cosmic shear through weak lensing dependson the assumption that there are no systematic offsets
(Kaiser 1992; Jain & Seljak 1997; Zaldarriaga & Seljak 1998; between estimates of the matter power spectrum obtained with
Abazajian&Dodelson2003). differentmethods; according to Viel et al. (2010), these uncer-
Whilemosttechniquesusedincosmologytoconstrainneu- tainties are not reflected in the quoted measurement errors. To
trino masses are based on the CMB or on galaxy clustering, this end, one needs to gain a better understanding of the char-
fewerstudiesinvolvetheLyαforest–thatis,theabsorptionlines acteristicsignaturesofmassiveneutrinosinthepowerspectrum
in the spectra of high-redshift quasars, that are due to neutral across differentredshift slices, and be in controlof the various
hydrogenin the interveningphotoionizedintergalacticmedium systematicsinvolved,especiallyatlowerredshifts(z=2−4)and
(IGM).ThankstodatafromtheSDSS(Yorketal.2000),thesta- atsmallscales(1−40h−1Mpc)–wherethenonlinearevolution
tisticalpoweroftheLyαforesthasgreatlyincreased,sothatitis of density fluctuations for massive neutrinos is non-negligible.
nowemergingasaverypromisinganduniquewindowintothe Particularly for the Lyα forest, constraints on neutrino masses
Articlenumber,page2of22
G.Rossietal.2014: Lyman-αforestandmassiveneutrinos
are onlylimitedby thesystematic accuracywith whichwe can laterwasitrealizedthatthenumerousabsorptionfeaturesinthe
makethesetheoreticalpredictions.Thisisonlypossiblethrough spectraofhigh-redshiftquasars,bluewardsoftheredshiftedres-
more and more sophisticated numericalsimulations, where the onant1215.67Åemissionline,directlytracetheunderlyingdark
fullhydrodynamicaltreatmentisperformedatscaleswherenon- matter fluctuations (Cen et al. 1994; Bi et al. 1995; Zhang et
lineareffectsbecomeimportantforthe neutrinocomponent;so al. 1995;Hernquistet al. 1996;Miralda-Escudeet al. 1996;Bi
far,onlyahandfulstudiesintheliteraturehaveaddressedthese & Davidsen 1997; Hui, Gnedin & Zhang 1997; Theuns et al.
aspectsfortheLyαforestinsomedetail.Giventhatcurrentand 1998). Clearly, since hydrogenmakes up most of the baryonic
plannedexperimentssuchasBOSS,eBOSSandDESIwillpro- densityoftheUniverse,the Lyαforestisalso a directtracerof
videexcellent-qualitydatafortheLyαforest(seealsotherecent thebaryonicmatterdistributionoverawiderangeofscalesand
American2013report‘CosmicFrontierVision’,andinparticu- redshifts–i.e.k∼0.1−10hMpc−1;1≤z≤6.
larConnollyetal.2013),itisnowtimelytodesignandperform Since then, considerable progress has been made toward a
accurate numerical simulations capable of reproducing the ef- thorough understanding of the nature of these absorption fea-
fectsofmassiveneutrinos. tures and of the properties of the IGM. We now have observa-
The present study aims at filling this gap by presenting a tional evidence that at high redshift the IGM contains the ma-
suite of state-of-the-art hydrodynamical simulations with cold jority of baryonspresentin the Universe(Petitjean et al. 1993;
darkmatter,baryonsandmassiveneutrinos,specificallytargeted Fukugitaetal.1998),ishighlyionizedbytheultra-violet(UV)
for modelingthe low-densityregionsof the IGM as probedby backgroundproducedbygalaxiesandquasars,andbecomesin-
theLyαforestathigh-redshift.Inadditiontoprovidingtechnical creasingly neutral from z = 0 to z = 7 (Mortlock et al. 2011).
details on the simulations and on the improvementsmade with Theoverallphysicalpicturethatemergesisrelativelysimple:the
respecttopre-existingliterature,weshowheremeasurementsof IGMprobedbytheLyαforestconsistsof mildlynonlineargas
the simulated nonlinear three- and one-dimensionalmatter and density fluctuations; low column-density absorption lines trace
fluxpowerspectra,andcharacterizethestatisticsofthetransmit- the filaments of the cosmic web; high column-density absorp-
tedfluxintheLyαforestinpresenceofmassiveneutrinos.This tion lines trace the surrondings of galaxies; the gas traces the
isthefirstofaseriesofpapersdedicatedtoquantifytheeffects dark matter, and is photoionized and photoheated by the UV-
of massive neutrinos in the Lyα forest across different redshift background. Although metals are present in the IGM (Cowie
slices and at nonlinear scales. In addition, we are planning to et al. 1995; Schaye et al. 2003; Aracil et al. 2004), stirring of
makethesimulationsavailabletothescientificcommunityupon the IGM due to feedback from galaxies or active galactic nu-
request;hence,thepresentworkmayserveasaguideforadirect clei (AGNs) does not significantly affect the vast majority of
useofthesimulationsandoftheproductsprovided. the baryons (Theuns et al. 2002; McDonald et al. 2005). Pho-
The layout of the paper is organizedas follows: in Section toionization heating and expansion cooling cause the gas den-
2,webrieflyoutlinethetheorybehindthemodelingoftheLyα sity(ρ)andtemperature(T)tobecloselyrelated,exceptwhere
forest,alongwiththemostcommonlyusednumericaltechniques mildshocksheatthegas(seeSchayeetal.2000),sothatinlow-
available.InSection3,wefocusonneutrinoscienceandonthe density regions a simple redshift-dependent polytropic power-
implementation of massive neutrinos in cosmological N-body lawtemperature-densityrelationholds(Katz,Weinberg&Hern-
simulations and explain the method of our choice. In Section quist1996;Hui&Gnedin1997):
4,wepresentournovelsuiteofhydrodynamicalsimulationsand
ρ γ(z)−1
provideseveraltechnicaldetailsonthecodeusedfortherun,ini- T(z)=T (z) , (1)
0 ρ
tial conditions, optimization strategies and performance, along (cid:16) 0(cid:17)
withvariousimprovementsandadescriptionofthepipelinede- where T and ρ are the corresponding gas mean temperature
0 0
velopedtoextractthesyntheticLyαtransmittedflux;intheap- and density, while the parameter γ depends on redshift, reion-
pendix,wealsodescribeasanitycheckweperformedtoensure izationhistorymodel,andspectralshapeoftheUVbackground.
thatwecorrectlyrecoverthelimitofmasslessneutrinos.InSec- Itisinterestingtoaddressthemodificationstothissimplerela-
tion 5, we presentthe first analysis of our suite of simulations, tioncausedbymassiveneutrinos,andwereturntothisissuein
whereinparticularwecomputethethree-andone-dimensional Section5.
matter and flux powerspectra, focusingon the imprintof mas- ThegasoftheIGMisgenerallyassumedtobeinphotoion-
siveneutrinos.WeconcludeinSection6,wherewesummarize ization equilibriumwith the UV background,and it can be de-
ourmainachievementsandexplainhowwewillusethesimula- scribed by an optical depth τ(z) that depends on the evolving
tions presentedhereto constrainneutrinomasses directly from photoionizationrate (Peebles 1993).The optical depthfor Lyα
theLyαforest,withimprovedsensitivity. absorptionisproportionaltotheneutralhydrogendensity(Gunn
& Peterson 1965), which – since the gas is in photoionization
equilibrium–canalsobeexpressedas
2. MODELINGTHELYMAN-ALPHAFOREST
ρ β
InthissectionwebrieflysummarizethebasictheoryoftheLyα τ= A , (2)
ρ
forestasacosmologicalprobeandthemostcommonlyusednu- (cid:16) 0(cid:17)
mericaltechniquesformodelingthe low-densityregionsof the whereβ=2.7−0.7γandAdependsonredshift,baryondensity,
IGM.Inparticular,wefocusonthespecificrequirementsneces- temperatureatthemeandensity,Hubbleconstant,andphotoion-
sarytoaccuratelyreconstructtheLyαtransmittedflux. izationrate.Whiletheopticaldepthisatracerofthematterdis-
tributiononscaleslargerthantheJeanslengthofthephotoion-
ized IGM, it is more conventionalto use the mean transmitted
2.1.Lyαforest:overviewandchallenges fluxF¯ instead,anddefineaneffectiveopticaldepthτ sothat
eff
The observational discovery of the Lyα forest traces back to τ =−lnF¯. (3)
Lynds(1971),althoughthe actualexistenceof an ionizedIGM eff
was already postulated back in the 1960s (Bahcall & Salpeter Thepreviousexpressioncontainstheuncertaintiesintheinten-
1965;Gunn&Peterson1965).However,onlysometwentyyears sityoftheUVbackground,themeanbaryondensity,andother
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parametersthatsetthenormalizationoftherelationbetweenop- mayprovideasuperiorresolutionofthelow-densityregionsof
tical depth and density of the gas. Measurements of the mean theIGMandmoreaccuratetreatmentsofshocks,butatahigher
transmissionandofitsevolutionallowonetoconstrainthebasic computational cost. For more details on hydrodynamicaltech-
cosmological parameters (see Jenkins & Ostriker 1991; Hern- niquesrelevanttothisstudy,seeKatzetal.(1996).
quistetal.1996;Rauchetal.1997;Rauch1998;McDonald& Both approacheshave been successfully used to model the
Miralda-Escude2001).Thegasdensityisalsocloselyrelatedto Lyα forest at low- and high-redshift and to obtain quantitative
thatoftheDMonlargescales,whileonsmallscalestheeffects estimatesoftheclusteringamplitudeandconstraintsoncosmo-
of thermal broadening and Jeans smoothing must be included. logicaland astrophysicalparameters. The numberof dedicated
FormoredetailsonthephysicsoftheIGManditspotentialfor studieshasincreasedinrecentyears,sincetheforestisemerging
cosmology,seeMeiksin(2009). asa keyprobeofthe hydrogenreionizationepoch.A long,but
Dynamicalandthermalprocessesare essential in modeling stillincompletelistofrelevantnumericalworksincludesGnedin
the Lyα forest: therefore, the effects of baryon pressure, non- & Hui (1996,1998),Croftet al. (1998,1999,2002),Huiet al.
linear evolutionof density perturbations,thermaland chemical (2001),McDonaldet al. (2000,2001,2005),Meiksin & White
evolutionsuch as adiabaticcoolingdueto the expansionof the (2001), Gnedin & Hamilton (2002), Zaldarriaga et al. (2001,
Universe, UV background photoionization heating, as well as 2003),Seljaketal.(2003),Bolton&Haehnelt(2007),Vieletal.
Compton and recombination cooling need to be taken into ac- (2003,2004,2010,2012),Crainetal.(2009),Bolton&Becker
count. For instance, the Lyα flux power spectrum depends not (2009),Schayeetal.(2010).
only on the DM distribution, but also on the thermal state of The importance of having full hydrodynamicalsimulations
the IGM, and on feedback effects due to star formation and cannot be stressed enough. To provide an example, McDonald
AGNs. Hence, a full hydrodynamical modeling including ef- et al. (2005) used hydrodynamical simulations extended with
fects of galaxy formationphysicsis necessary.While there ex- hydro-particle-mesh (HPM) realizations to analyze the SDSS
ist several numerical challenges in simulating the Lyα forest, Lyα forest power spectrum and infer the corresponding linear
along with a series of physical mechanisms still poorly under- theorypowerspectrum.However,theirHPMsimulations–cali-
stood, today we do have the computationalcapability of carry- bratedbyalimitednumberofhydrodynamicalruns–werefound
ing out full hydrodynamical treatments, as we perform in this tobediscrepantbyupto20%whencomparedwithfullhydro-
work.Despite hydrodynamicuncertainties,hierarchicalmodels dynamicalsimulations, with respectto the statistical properties
ofstructureformationarenowcapableofreproducingalmostall oftheLyαfluxdistribution(Vieletal.2006).Hence,whileus-
the aspects of the Lyα forest. We also note that once the spec- ingapproximatenumericalcalculationsiscertainlyattractivebe-
trumismodeledasa continuousphenomenon,thereisnoneed causecomputationallylessdemanding,acompletehydrodynam-
to resolveeverysingle feature(Weinbergetal. 1999,2003),so ical treatment is mandatoryto reach the precision that data are
thattheforestcanbestudiedwithrelativelymoderateresolution nowbeginningtoshow.
spectra. Beforemovingontothetreatmentofmassiveneutrinos,we
stressthatthedevelopmentofprogressivelymoresophisticated
numericalsimulationsisanareaofrapidprogress–particularly
2.2.Hydrodynamicalsimulationsinanutshell
crucialforarealistic modelingoftheLyαforest.With increas-
Therapidprogressmadeinourtheoreticalunderstandingofthe ingcomputationalpower,thereiscurrentlylessmotivationtouse
Lyαforestismainlyduetothe improvedabilitytosimulateall approximationmethods–althoughmoreworkisneededtoun-
thephysicaleffectsthatimpacttheIGMmoreandmorerealisti- derstandamultitudeofcomplexbaryonicprocesses.Thisiseven
cally–thankstostate-of-the-artcomputationalfacilities.Infact, moresowhenmassiveneutrinosareincludedinthepicture,and
while the forest has been traditionally studied using a variety thescopeofthepresentworkisto addmoreknowledgein this
of analytical techniques such as the Zel’dovich approximation direction.
(Doroshkevich & Shandarin 1977; McGill 1990; Hui, Gnedin
& Zhang 1997; Matarrese & Mohayaee 2002), the lognormal
approximation(Hamilton 1985;Coles & Jones 1991;Bi 1993; 3. IMPLEMENTINGMASSIVENEUTRINOS
Bouchet et al. 1993;Kofman et al. 1994;Gnedin & Hui 1996;
Bi & Davidsen 1997; Viel et al. 2002), or semi-analytic mod- Inthissectionwefirstprovideasyntheticoverviewoftheeffects
els (Balian & Schaeffer 1989; Bernardeau & Schaeffer 1992, ofmassiveneutrinosincosmology–focusingontheLyαforest;
1999; Valageas, Schaeffer & Silk 1999; Pichon et al. 2001), it in particular,we presentthe expectedlinear predictionsfor the
is only with hydrodynamicalsimulations that the interplay be- matterpowerspectrainpresenceofmassiveneutrinos,withthe
tweengravityandgaspressureonthestructureofthephotoion- set of cosmologicalparametersadoptedin oursimulations. We
ized IGM can be modeled self-consistently – so that most of thenbrieflydescribehowneutrinosareimplemented.InSection
the observed properties of the Lyα forest are successfully re- 5,thelinearpredictionsshownherearecomparedwithnonlinear
producedandtheuncertaintiesinthetheoreticalmodelingover- measurementsobtainedfromoursimulations.
come.
Traditionally, cosmological hydro-simulationscome in two
3.1.Revivalofneutrinoscience
basic flavors:smoothedparticlehydrodynamics(SPH;Gingold
&Monaghan1977;Lucy1977),andgrid-basedmethods;there Theimpactofmassiveneutrinoson theCMB andLSSwasin-
arealsomoresophisticatedcombinationsofthetwocategories. vestigated long ago (see for example Bond, Efstathiou & Silk
The SPH technique – adopted in this study – uses particles 1980; Klypin et al. 1993; Ma & Bertschinger 1995; Dodelson
to represent the baryonic fluid, employs an artificial viscosity et al. 1996; Hu, Eisenstein & Tegmark 1998; Hu & Dodelson
to simulate shocks (Springel & Hernquist 2002), and it is La- 2002;Abazajianetal.2005;Hannestad2005;Seljaketal.2006),
grangian in nature: this implies that the resolution is concen- andwitharenewedinterestquiterecently(e.g.Saitoetal.2008,
tratedinregionsofhigh-density.Ontheotherhand,grid-based 2009;Wong2008;Brandbygeetal.2008;Brandbyge&Hannes-
methodsuseagridofcellstorepresentthegasproperties,which tad 2009;Viel et al 2010;Marulli et al. 2011;Bird et al 2012;
Articlenumber,page4of22
G.Rossietal.2014: Lyman-αforestandmassiveneutrinos
free-streaminglengthequaltotheHubbleradius,andasanaddi-
tionalCDMcomponentwhentheybecomenon-relativistic.Sub-
sequently,massiveneutrinosaffectstructureformationby free-
streamingandbydelayingmatterdomination.Theseeffectscan
beparameterizedbytheirultimatefractionalcontributiontothe
matterdensity:
M
f =Ω /Ω , Ω h2 = ν , (6)
ν ν m ν 93.14eV
where h is the presentvalue of the Hubble constantin units of
100kms−1Mpc−1,M = m isthesumoftheneutrinomasses
ν ν
ofthethreespeciesconsidPered,andΩmisthematterenergyden-
sityintermsofthecriticaldensity.
Neutrinosinthemassrange0.05eV≤m ≤1.5eVbecome
ν
non-relativisticintheredshiftinterval3000≥z≥100,approxi-
matelyaroundz ∼2000(m /1eV)–duringthematterdomina-
nr ν
tionera;forthegivenmass-intervalsconsideredinthisstudy,all
ourrunsstartedwellinthenon-relativisticregime.Whenneutri-
nosarenon-relativistic,thereisaminimumwavenumber
k ∼0.018Ω1/2 mν 1/2hMpc−1 (7)
nr m 1eV
h i
abovewhichthephysicaleffectproducedbytheirfree-streaming
Fig.1.Lineartheorypredictionsforthematterpowerspectrawithmas- dampssmall-scaledensityfluctuations,whilemodeswithk<knr
siveneutrinos,normalizedbythecorrespondingcaseofmasslessneu- evolveaccordingtolineartheory.Thefree-streamingleadstoa
trinos.Thecosmologicalparametersconsideredarethoseusedforour suppressionof power on small scales; with increasing neutrino
simulations(seeSection4);theneutrinomassrangeisindicatedinthe mass, thissuppressionbecomesstrongerandits shapeandam-
figure. Different colors (andsimilar linestyles) show theevolution in plitude depend mainly on the total mass, but only weakly on
redshiftforz=0,2,4,respectively,asafunctionoftheneutrinomass. redshift(Bond, Efstathiou & Silk 1980). At scales k > 0.1 the
Theyellowareacorrespondstovaluesofk<k ,wherealinear
nr,Mν=0.8eV suppressionisconstant,whileat0.01< k < 0.1itgraduallyde-
descriptionfortheneutrinoevolutionissufficient;thegrayzonehigh-
creases to zero – with k expressed in units of h Mpc−1. When
lightstherangeofkapproximatelycoveredbytheone-dimensionalflux
k ≪ 0.01 (very large scales), the influence of neutrinos in the
powerspectrumobtainedfromtheLyαBOSSsurvey.
matterpowerspectrumbecomesnegligible.Alltheseeffectsare
clearlyseeninFigure1,whereweshowthelineartheorypredic-
Carbone et al. 2012; Hou et al. 2012; Lesgourgues & Pastor tionsfor the matter power spectra, whichinclude massive neu-
2012).Therenewedinterestismainlydrivenbythelargeamount trinos(Pk,Mν),normalizedbythecorrespondingcaseofmassless
ofcosmologicaldataavailabletoday,whichallowplacingcom- neutrinos (Pk,Mν=0). The cosmological parameters adopted are
petitivelimitsontheneutrinomass-scaleandhierarchy.Forin- thoseusedforoursimulationsandreportedinSection4;wecon-
stance, simply with the improvement of a factor of two from sider the followingneutrinomasses: Mν = 0.1,0.2,0.3,0.4,0.8
Seljak et al. (2006),one should be able to distinguish between eV. With different colors but similar line styles, we also show
a normalhierarchyandaninvertedone–a factwithinreachin the evolution in redshift for three significant intervals, namely
theverynearfuture,givenhigh-qualityupcomingsurveyssuch z=0(red),z=2(green),andz=4(blue).Allthevariouslinear
aseBOSSandDESI. predictionswerecomputedwiththeCAMBcode(Lewis,Challi-
The effects of cosmological neutrinos on the evolution of nor&Lasenby2000).Theyellowareainthefigurecorresponds
densityperturbationsinthelinearregimeiswellunderstood.In to values of k lower than knr for Mν = 0.8 eV (i.e., the most
whatfollows,we onlydiscussa few generalaspectsof cosmo- massive case considered here) obtained from (7), below which
logical neutrinos relevant for the Lyα forest, and refer to Les- a linear description for the neutrino evolution is sufficient. For
gourgues&Pastor(2006,2012)foramoreexhaustivetreatment. masses Mν < 0.8eV, the correspondingknr,Mν valuesare lower
Neutrinos decouple from the cosmic plasma before the than knr,Mν=0.8eV. The gray area in the same figure shows the
electron-positronannihilation(around∼ 1MeV),resultingina k-range approximately covered by the BOSS survey, relatively
subsequentneutrinotemperatureT thatislowerthanthephoton to the one-dimensional Lyα forest power spectrum. As can be
ν
temperatureT ,namely clearly seen, our primaryrangeof interest lies well outside the
γ
zoneinwhich a lineardescriptionwouldbe sufficient– forthe
T =(4/11)1/3T , (4) neutrinomassesconsideredinthisstudy;hence,afullnonlinear
ν γ
treatment of the neutrino component is mandatory. In Section
andanumberdensityn lowerthanthephotonnumberdensity: 5, we compare these linear predictions with the corresponding
ν
nonlinearevolutionsasafunctionofneutrinomassandquantify
3 4 thedeparturesfromlinearity;wealsodetermineatwhichkthese
n = N n , (5)
ν eff γ departuresaremaximized.
4 11
(cid:16) (cid:17)(cid:16) (cid:17)
Figure2presentsthedimensionlesslinearpowerspectraper
wheren isthedensityoftheCMBphotons,andthefactor3/4 componentwhenmassiveneutrinosareincluded,normalizedby
γ
comes from the difference between the Fermi-Dirac and Bose- thecorrespondingzero-neutrino-masscase.Thegeneralconven-
Einstein statistics. Moreover, they behave as additional radia- tion used in this paper sets ∆2 = k3P(k)/2π2, where the sub-
i i
tionwhileultra-relativistic,travelingatthespeedoflightwitha script i specifies the component considered. In detail, the left
Articlenumber,page5of22
A&Aproofs:manuscriptno.rossi_etal_2014
Fig.2.Dimensionlesslinearpowerspectrapercomponent inpresenceofmassiveneutrinos,normalizedbythecorrespondingcaseofmassless
neutrinos – as defined in the main text. The left panel shows the linear evolution of the CDM component, while the right panel displays the
correspondingbaryonicevolution.Thelinearevolutionofthetwocomponentsisverysimilar.Linestyles,redshifts,coloredareas,andneutrino
massrangesaresameasinthepreviousfigure.
Finally,Figure3showstheneutrinolineartransferfunctions
T (k)forthesamemassandredshiftrangesasconsideredbefore,
ν
witharbitrarynormalization.
Itisofconsiderableinteresttoinvestigatehowtheseeffects
propagate in the nonlinear regime, not only at the level of the
three-dimensionalmatterpowerspectrum,butalso fortheone-
dimensional Lyα flux power spectrum: we address these ques-
tionsinSection5.
3.2.Particleimplementationofmassiveneutrinos
Implementing massive neutrinos in cosmological N-body sim-
ulations is a delicate subject. Firstly, neutrinos can be treated
either as a fluid or as an ensemble of particles. Secondly, one
maydescribetheirevolutionwithlineartheoryorperformafull
nonlineartreatment;clearly,thesecondoptioncomeswithase-
riesofnumericalchallenges,inprimistheproblemofshotnoise
introducedbythehighthermalvelocitiesoftheneutrinocompo-
nent.
Severalattemptsalongtheselineshavealreadybeenmadein
theliterature,evenlongago(e.g.,White, Frenk& Davis1983;
Fig.3.NeutrinolineartransferfunctionsTν(k)forthesamemassand Klypin et al. 1993; Ma & Bertschinger 1994). More recently,
redshift ranges considered intheprevious figure; thenormalization is Brandbygeet al. (2008) described a simple method for includ-
arbitrary.TheyellowareaissameasinFigure1.
ingtheeffectofmassiveneutrinosinlarge-scaleN-bodysimula-
tions,usingahybridTreePMapproach,butneglectingallthehy-
drodynamics;theirfindingsalreadyshowedthatthesuppression
panelshowstheCDMlinearevolution,whiletherightpaneldis- ofpowerduetothepresenceofmassiveneutrinosisincreasedby
plays the evolution of the baryonic component; neutrino mass nonlineareffects.Subsequently,Brandbyge&Hannestad(2009)
ranges, redshifts, and line styles are the same as in Figure 1. modeledneutrinosasafluidwithagridmethod,andpointedout
Evidently, the linear evolution of the two components is very therelativebenefitsanddrawbacksofimplementingthe effects
similarandcloselycoupled,withslightdeparturesatincreasing ofneutrinosin the formofparticlesversusa grid-basedimple-
redshifts.Notealsotheremarkablesuppressionofpower(about mentation.Intheircode,thegravitationalforceduetoneutrinos
40%),causedsolelybya6%component. is calculated using the linearly evolved density distribution of
Articlenumber,page6of22
G.Rossietal.2014: Lyman-αforestandmassiveneutrinos
the neutrinos in Fourier space. Obviously, this technique elim- Table1.Basicparametersofoursimulations,commontoalltheruns–
ifnotspecifiedotherwise.
inates the Poisson noise at small scales introducedby an alter-
native particle representation, which results in higher accuracy
in regions where the effect of the nonlinear neutrino evolution Parameter Value
is mild. With this approacha seriesof computationalproblems
σ (z=0) 0.83
are avoided or drastically reduced, such as memory and CPU 8
time consumption– as one does notneed to store neutrinopo- n 0.96
s
sitions and velocities. In another study, Brandbyge & Hannes-
H [kms−1Mpc−1] 67.5
tad (2010) combined grid- and particle-based methods with a 0
hybrid technique to achieve good accuracy at small and large Ω 0.31
m
scaleswhilekeepingtheCPUconsumptionundercontrol:neu-
Ω 0.044
trinosarefirstdiscretizedonagrid,andsubsequentlypartofthe b
gridisconvertedintoN-bodyparticles,whenthethermalmotion Ω 0.69
Λ
of neutrinosdecreases to a few times the flow velocities in the
T (z=3)[K] 15000
simulation.Instead,Ali-Haïmoud&Bird(2013)usedadifferent 0
technique:theCDMcomponentisobtainedviaN-bodycompu- γ(z=3) 1.3
tations,whilethesmoothneutrinocomponentisevaluatedfrom
Startingredshift 30
that background by solving the Boltzmann equation linearized
withrespecttotheneutrinooverdensity.
Inthepresentwork,wechooseamoredirectandcomputa-
tionallyintensiveapproach–followingVieletal.(2010):neutri-
nosaremodeledasanadditionaltypeofparticleinthe N-body 4.1.Suiteofsimulationswithmassiveneutrinos
setup(ontopofgasandDM),andafullhydrodynamicaltreat-
We performed a total of 48 hydrodynamical simulations, both
mentiscarriedout,well-insidethenonlinearregime–including
with varying neutrino mass and fixed cosmological and astro-
theeffectsofbaryonicphysicswhichaffecttheIGM.Inparticu-
physicalparameters(groupI),orwithafixedneutrinomassand
lar,wemakenoapproximationsfortheevolutionoftheneutrino
slightvariationsinthebasiccosmologicalandastrophysicalpa-
component, nor interchange between grid- and particle-based
rameters(groupII)aroundwhatweindicateasthe‘best-guess’
implementations to save CPU time or speed up the computa-
run–thisisthereferencesimulationsetwithoutmassiveneutri-
tions.Theadoptedimplementationtechniqueisprimarilydriven
nos(butamasslessneutrinocomponent)andacosmologycom-
byourmaingoaltoaccuratelyreproduceallthemainfeaturesof
patiblewiththelatestPlanck(2013)results.Thebasicparame-
theLyαforest,atthequalitylevelofBOSSorfuturedeepLyα
terscommontoalltherealizationsarereportedinTable1.
surveys. As evident from Figure 1 (i.e., yellow versus gray ar-
For a given neutrino mass, we always performed a set of
eas),theone-dimensionalLyαforestdataprovidedbyBOSSlies
three simulations with different box sizes and number of par-
inak-rangewherenonlinearevolutionofcosmologicalneutrinos
ticles (their combinations determine the lowest and highest k-
cannotbeneglected:hence,anyattempttospeed-upcalculations
modesthatcanberesolved),whichareappropriateforthequal-
by using approximate linear solutions for the neutrino compo-
ityofBOSS;specifically,weadoptedaboxsizeof100h−1Mpc
nent would compromise our ability to accurately reproduce all
forlarge-scalepowerwithanumberofparticlespercomponent
the features of the forest. To this end, Viel et al. (2010) previ-
N = 7683(simulations‘a’inTables2and3),andaboxsizeof
ously compared particle and grid neutrino representations and p
foundthattheirdifferenceintermsofpowerspectraaremainly 25 h−1Mpc for small-scale power, in this case with Np = 7683
drivenbythefactthatthenonlinearevolutionatsmallscalesis or1923,respectively(simulations‘b’and‘c’inTables2and3).
not properly reproduced by the grid method; they also argued Extensiveconvergenceandresolutiontestsinsupportofourset-
thatonscalesrelevantfortheLyαforestitprovideshigheraccu- tingshavebeencarriedoutinBordeetal.(2014)–butseealso
racy to accountfor the nonlinearevolution rather than limiting Section5.1. Inparticular,thereasonbehindourspecificchoice
the descriptiontothe linearcase,despite theeffectofthePois- istheabilitytomatchthesensitivityoftheBOSSquasarcatalog
soncontributionontheneutrinopowerspectrumintroducedby (Paˆris et al. 2012) from Data Release 9 (Ahn et al. 2012), and
theparticle-basedmodeling.Thisfactalonewouldbesufficient is also related to the application of the splicing technique pro-
to justify our choice of the particle-based implementation for posedbyMcDonald(2003),whichallowscorrectingthe larger
neutrinos.Inaddition,wearenotlimitedbycomputationaltime boxsizesimulationforthelackofresolutionandthesmallbox
ormemorybecausewehaveaccesstostate-of-the-artcomputa- forthelackofnonlinearcouplingbetweenthehighestandlow-
tionalfacilitiestoperformacompletehydrodynamicaltreatment est k-modes; in this way, we are able to achieve an equivalent
–aswedescribenext. resolutionof3×30723≃87billionparticlesina(100h−1Mpc)3
boxsize–optimalalsoforeBOSSandDESI–withouttheneed
of running a single but computationally prohibitive numerical
simulation.
4. OURSIMULATIONS Whenwe includedmassiveneutrinoswealwayskeptΩΛ +
Ω fixedtogiveaflatgeometry(withΩ = Ω +Ω +Ω )
m m b ν CDM
Inthissectionwepresentournewsuiteofhydrodynamicalsim- andvariedtheadditionalmassiveneutrinocomponentΩ tothe
ν
ulationswithmassiveneutrinosandprovideseveraltechnicalde- detriment of Ω . Moreover,most of our runs were tuned to
CDM
tailsonthecodesusedfortheruns,theperformance,andthevar- haveσ = 0.83atz = 0byconstruction,whichistheobserved
8
iousoptimizationstrategies.We also brieflydescribethe work- Planck(2013)value.However,tocharacterizetheeffectofmas-
flowpipelineandthepost-processingproceduredevelopedtoex- siveneutrinoswithrespecttothecaseofmasslessneutrinos,we
tract the line of sight (LOS) and particle samples to accurately alsoran simulationswiththe initialspectralamplitude A fixed
s
modeltheLyαtransmittedflux. as in the best-guess, and therefore with values of σ changing
8
Articlenumber,page7of22
A&Aproofs:manuscriptno.rossi_etal_2014
Table2.Listofoursimulationsuite(groupI)–best-guess(BG)andneutrino(NU)runs∗.
Simulationset M [eV] σ (z=0) Boxes[Mpc/h] N1/3 Meanparticleseparation[Mpc/h]
ν 8 p
BGa/b/c 0 0.830 100/25/25 768/768/192 0.1302/0.0325/0.1302
NUBGa/b/c 0.01 0.830 100/25/25 768/768/192 0.1302/0.0325/0.1302
NU01a/b/c 0.1 0.830 100/25/25 768/768/192 0.1302/0.0325/0.1302
NU01-norma/b/c 0.1 0.810 100/25/25 768/768/192 0.1302/0.0325/0.1302
NU02a/b/c 0.2 0.830 100/25/25 768/768/192 0.1302/0.0325/0.1302
NU03a/b/c 0.3 0.830 100/25/25 768/768/192 0.1302/0.0325/0.1302
NU04a/b/c 0.4 0.830 100/25/25 768/768/192 0.1302/0.0325/0.1302
NU04-norma/b/c 0.4 0.733 100/25/25 768/768/192 0.1302/0.0325/0.1302
NU08a/b/c 0.8 0.830 100/25/25 768/768/192 0.1302/0.0325/0.1302
NU08-norma/b/c 0.8 0.644 100/25/25 768/768/192 0.1302/0.0325/0.1302
Table3.Listofoursimulationsuite(groupII)–neutrinocross-terms∗.
Simulationset M [eV] σ (z=0) Boxes[Mpc/h] N1/3 γ H n Ω T
ν 8 p 0 s m 0
γ+NU08a/b/c 0.8 0.83 100/25/25 768/768/192 1.6 67.5 0.96 0.31 15000
H +NU08a/b/c 0.8 0.83 100/25/25 768/768/192 1.3 72.5 0.96 0.31 15000
0
n +NU08a/b/c 0.8 0.83 100/25/25 768/768/192 1.3 67.5 1.01 0.31 15000
s
Ω +NU08a/b/c 0.8 0.83 100/25/25 768/768/192 1.3 67.5 0.96 0.36 15000
m
σ +NU08a/b/c 0.8 0.88 100/25/25 768/768/192 1.3 67.5 0.96 0.31 15000
8
T +NU08a/b/c 0.8 0.83 100/25/25 768/768/192 1.3 67.5 0.96 0.31 21000
0
∗a/b/cindicatethedifferentboxsizeandnumberofparticlesinthesimulation.
acrossredshifts;theseadditionalsimulationsaretermednormal- (groupI)–includingrunswithdifferentnormalizations–issum-
izedandareusedheretoquantifytheimpactofmassiveneutri- marizedinTable2;therealizationsindicatedasneutrinocross-
nosonthematterpowerspectrum;inmodelswithmassiveneu- terms (group II), in which we kept the neutrino mass fixed to
trinos, the power is suppressed on scales smaller than the free- be M = 0.8eV butvariedcosmologyandastrophysicsaround
ν
streaming scale when the normalization is fixed, as explained the best-guess, are listed in Table 3. To this end, we note that
previously. thereasonforproducingcross-termsismotivatedbythemulti-
dimensionalparameterestimationprocedureoutlinedin Vielet
Aside from the best-guess run, which only has a massless
al.(2010);inaforthcomingstudy,wewillapplythistechnique
neutrinocomponent,allourothersimulationscontainthreede-
toconstraincosmologicalparametersandneutrinomassesfrom
generate species of massive neutrinos implemented as a single
theLyαforestbycombiningresultsfromthesesimulationsand
particle-type, where M = 0.1,0.2,0.3,0.4,and 0.8 eV. To en-
ν BOSSLyαdata.
surethatthevariousrealizationscorrectlyconvergewhen M =
ν
0eV,wealsoranasimulationsetwithaverylowneutrinomass, Allourrunsstartedatz = 30,withinitialconditionshaving
i.e.M =0.01eV–indicatedasNUbest-guess(seetheappendix thesamerandomseedandbasedonthesecond-orderLagrangian
ν
forasanitychecktest).Inaddition,weperformedaseriesofre- perturbationtheory(2LPT;Crocceetal.2006)insteadofonthe
alizationswith theneutrinomassfixedtobe M = 0.8eV,and Zel’dovichapproximation.Snapshots were producedat regular
ν
slightlyvariedthebasiccosmologicalandastrophysicalparame- intervalsinredshiftbetweenz = 4.6−2.2,with∆z = 0.2;fora
tersaroundthebest-guessreference.Specifically,weconsidered fewruns,wealsoreachedz=0.Weprovidevisualexamplesof
variations of ±0.05 in the amplitude of the matter power spec- oursnapshotoutputsatz = 2.2andz = 0inFigures4and5for
trumσ ,inthespectralindexoftheprimordialdensityfluctua- the gas (left panels), dark matter (central panels), and neutrino
8
tionsn , andin thematterdensitycontentΩ ,while we varied (rightpanels)components–whenpresent.Theuppertoppanels
s m
the Hubble constant H by ±5; regardingastrophysicalparam- are projectionsof the densityfield along the x and y directions
0
eters, we altered both T and γ, the former by ±7000 and the (andacross z) from our best-guessreferencesimulation, which
0
latterby±0.3.Thesuiteofsimulationswithbest-guesscosmo- onlycontainsmasslessneutrinos,withaboxsizeof25h−1Mpc
logicalandastrophysicalparametersandvaryingneutrinomass anda relativelylow resolutionN = 1923 particlespertype;in
p
Articlenumber,page8of22
G.Rossietal.2014: Lyman-αforestandmassiveneutrinos
GAS z =2.2 DARK MATTER z =2.2
20 Mν=0 eV 20 Mν=0 eV
h] h]
pc/ pc/
M M
y[ 10 y[ 10
0 0
0 10 20 0 10 20
x[Mpc/h] x[Mpc/h]
-8 -7 -6 -5 -7.5 -7 -6.5 -6 -5.5
log density log density
Mν=0.1 eV z =2.2 Mν=0.1 eV z =2.2 NEUTRINOS z =2.2
20 20 20 Mν=0.1 eV
h] h] h]
pc/ pc/ pc/
M M M
y[ 10 y[ 10 y[ 10
0 0 0
0 10 20 0 10 20 0 10 20
x[Mpc/h] x[Mpc/h] x[Mpc/h]
-8 -7 -6 -5 -7.5 -7 -6.5 -6 -5.5 -9.1 -9 -8.9 -8.8 -8.7
log density log density log density
Mν=0.4 eV z =2.2 Mν=0.4 eV z =2.2 Mν=0.4 eV z =2.2
20 20 20
h] h] h]
pc/ pc/ pc/
M M M
y[ 10 y[ 10 y[ 10
0 0 0
0 10 20 0 10 20 0 10 20
x[Mpc/h] x[Mpc/h] x[Mpc/h]
-8 -7 -6 -5 -7.5 -7 -6.5 -6 -5.5 -8.5 -8.4 -8.3 -8.2
log density log density log density
Mν=0.8 eV z =2.2 Mν=0.8 eV z =2.2 Mν=0.8 eV z =2.2
20 20 20
h] h] h]
pc/ pc/ pc/
M M M
y[ 10 y[ 10 y[ 10
0 0 0
0 10 20 0 10 20 0 10 20
x[Mpc/h] x[Mpc/h] x[Mpc/h]
-8 -7 -6 -5 -7.5 -7 -6.5 -6 -5.5 -8.1 -8 -7.9
log density log density log density
Fig.4.Visualexamplesofsnapshotsatz=2.2fromsimulationswithaboxsizeof25h−1MpcandaresolutionofN =1923 particlespertype.
p
Theuppertoppanelsarefullprojectionsofthedensityfieldinthe xandydirectionsacrosszfromourbest-guessreferencesimulationwithout
massiveneutrinos(butwithamasslessneutrinocomponent),whileindescendingordertheotherpanelsarefor M = 0.1,0.4,and0.8eV.Gas
ν
(leftpanels),darkmatter(centralpanels),andneutrino(rightpanels)components–whenpresent–areshown.TheaxisscalesareinMpc/h.The
variousplotsaresmoothedwithacubicsplinekernel,andboththeDMandneutrinocomponentsaretreatedinthesamewayasthegas.Seethe
textformoredetails.
Articlenumber,page9of22
A&Aproofs:manuscriptno.rossi_etal_2014
z =0 z =0
(cid:0)(cid:1) (cid:2)(cid:3)(cid:4)#(cid:5)(cid:3)$$(cid:6)(cid:4)
20 Mν=0 eV 20 Mν=0 eV
h] h]
pc/ pc/
M M
y[ 10 y[ 10
0 0
0 10 20 0 10 20
x[Mpc/h] x[Mpc/h]
-8 -7 -6 -5 -7.5 -7 -6.5 -6 -5.5
log density log density
Mν=0.1 eV z =0 Mν=0.1 eV z =0 NEUTRINOS z =0
20 20 20 Mν=0.1 eV
h] h] h]
pc/ pc/ pc/
M M M
y[ 10 y[ 10 y[ 10
0 0 0
0 10 20 0 10 20 0 10 20
x[Mpc/h] x[Mpc/h] x[Mpc/h]
-8 -7 -6 -5 -7.5 -7 -6.5 -6 -5.5 -9.1 -9 -8.9 -8.8 -8.7
log density log density log density
Mν=0.4 eV z =0 Mν=0.4 eV z =0 Mν=0.4 eV z =0
20 20 20
h] h] h]
pc/ pc/ pc/
M M M
y[ 10 y[ 10 y[ 10
0 0 0
0 10 20 0 10 20 0 10 20
x[Mpc/h] x[Mpc/h] x[Mpc/h]
-8 -7 -6 -5 -7.5 -7 -6.5 -6 -5.5 -8.5 -8.4 -8.3 -8.2
log density log density log density
Mν=0.8 eV z =0 Mν=0.8 eV z =0 Mν=0.8 eV z =0
20 20 20
h] h] h]
pc/ pc/ pc/
M M M
y[ 10 y[ 10 y[ 10
0 0 0
0 10 20 0 10 20 0 10 20
x[Mpc/h] x[Mpc/h] x[Mpc/h]
-8 -7 -6 -5 -7.5 -7 -6.5 -6 -5.5 -8.1 -8 -7.9
log density log density log density
Fig.5.Sameasinthepreviousfigure,butnowatz=0.
Articlenumber,page10of22