Cosmic density field reconstruction from Ly-alpha forest data

0.68 MB·English

by  Simona Gallerani

Mon.Not.R.Astron.Soc.000,1–??(2011) Printed27January2011 (MNLATEXstylefilev2.2)
α
Cosmic density field reconstruction from Ly forest data
S. Gallerani1, F. S. Kitaura2,3, A. Ferrara2
1INAF-OsservatorioAstronomicodiRoma,viadiFrascati33,00040MontePorzioCatone,Italy
2ScuolaNormaleSuperiore,PiazzadeiCavalieri7,56126,Pisa,Italy
3Ludwig-MaximiliansUniversitatMunchen,Scheinerstr.1,D-81679,Munich,Germany
1
1
27January2011
0
2

n ABSTRACT
a Wepresentanovel,fastmethodtorecoverthedensityfieldthroughthestatisticsofthetrans-
J
mitted flux in high redshift quasar absorption spectra. The proposed technique requires the

6 computationof the probabilitydistribution functionof the transmitted flux (PF) in the Lyα
2 forestregionand,asasoleassumption,theknowledgeoftheprobabilitydistributionfunction

ofthematterdensityfield(P∆).Weshowthattheprobabilitydensityconservationoftheflux
O] and matter density unveils a flux-density (F −∆) relation which can be used to invert the
Lyα forest without any assumption on the physical properties of the intergalactic medium.
C
Wetestourinversionmethodatz =3throughthefollowingsteps:[i]simulationofasample
.
h ofsyntheticspectraforwhichP∆isknown;[ii]computationofPF;[iii]inversionoftheLyα
p forest through the F −∆ relation. Our technique, when applied to only 10 observed spec-
- tracharacterizedbya signal-tonoise ratioS/N ≥ 100providesanexquisite(relativeerror
o ǫ∆ .12%in&50%ofthepixels)reconstructionofthedensityfieldin&90%ofthelineof
r
t sight.Wefinallydiscussstrengthsandlimitationsofthemethod.
s
a
Keywords: cosmology:large-scalestructure-intergalacticmedium-absorptionlines
[

2
v
8
1 INTRODUCTION lenght of theIGM(Cenet al.1994; Petitjean,et al.1995; Zhang
2
2 etal.1995;Hernquistetal.1996;Miralda-Escude’etal.1996).As
6 The ultraviolet radiation emitted by a quasar can suffer resonant aconsequence ofthisresult,theLyαforesthasbeenproposedas
. a powerful method to study the clustering properties of the dark
1 Lyαscatteringasitpropagatesthroughtheintergalacticneutralhy-
matter density field and to measure its power spectrum (Croft et
1 drogen.Inthisprocess,photonsareremovedfromthelineofsight
al.1998;Nusser&Haehnelt1999;Pichonetal.2001;Rollindeet
0 resultinginanattenuationofthesourceflux,theso-calledGunn-
1 Petersoneffect(Gunn&Peterson1965).Atz 3,theneutralhy- al.2001;Zhanetal.2003;Vieletal.2004;McDonaldetal.2005;
v: drogennumberdensityissufficientlysmallto∼allowtoresolvethe Zaroubietal.2006;Saittaetal.2008;Birdetal.2010).
In thispaper, we focus our attention on the reconstruction of the
i wideseriesofabsorptionlines,whichgiverisetotheso-calledLyα
X density field along the line of sight (LOS), which represents the
forest in quasar absorption spectra. Initially, the absorption lines
starting point for the dark matter power spectrum measurement.
r observedinquasarspectrawerebelievedtobeproducedbyanin-
a Wepresentanovel,fastmethodtorecoverthedensityfieldalong
tergalacticpopulationofpressure-confinedclouds,photoionizedby
theLOStowardsz 3quasarwhichcanbeconsideredalternative
theintegratedquasarflux(Sargentetal.1980).Nowadayabsorbers ∼
and/or complementary to the existing techniques in the literature
oftheLyαforestaregenerallyassociatedtolarge-scaleneutralhy-
mentionedabovewhichwillbefurtherdiscussedinthiswork.
drogendensityfluctuationsinthewarmphotoionizedIGM.
Thisscenario, firstlytestedthrough analytical calculations (Bond
et al. 1988; Bi et al. 1992), has received an increased consensus
thankstothedetectionofaclusteringsignalbothalongindividual
(Cristianietal.1995;Luetal.1996;Cristianietal.1997;Kimetal.
2001)andclosepairsofquasarlinesofsight,resultinginanesti- 2 MODELLINGTHEFOREST
matedsizefortheabsorberswhichvariesbetweenfewhundredsof
LetusdiscretizetheLOStowardsadistantquasarinanumberof
kpc(Smetteetal.1992;D’Odoricoetal.1998;Rauchetal.2001;
pixelsN .ThetransmittedfluxduetoLyαabsorptionintheIGM
Becker et al. 2004) to few Mpc (Rollinde et al. 2003; Coppolani pix
atagivenpixeliiscomputedfromtheusualrelation
etal.2006;D’Odoricoetal.2006).Hydrodynamicalcosmological
simulationslendfurthersupporttothispicture,havingestablished F(i)=e−τ(i), (1)
theexistenceofatightconnectionbetweentheHIdensityfieldand
thedarkmatterdistribution,atleastonscaleslargerthantheJeans whereτ(i)istheLyαabsorptionopticaldepth:
(cid:13)c 2011RAS
2 S. Gallerani,F.S.Kitaura,A.Ferrara
Figure1.Leftpanel:Probabilitydistributionfunctionofthetransmittedfluxobtainedfrom10syntheticquasarabsorptionspectraatz = 3.Rightpanel:
Probabilitydistributionfunctionofthedensityfieldatz=3,aspredictedbythelognormalmodel.ThethicklineshowsP∆oftherecovereddensityfield.The
probabilityoffindingapixelcharacterizedbyatransmittedfluxaboveagivenFmax(cyanshadedregionontheleft-handpanel)isequaltotheprobabilityof
findinganoverdensitybelow∆b(cyanshadedregionontheright-handpanel).Analogously,theprobabilityoffindingapixelcharacterizedbyatransmitted
fluxbelowagivenFmin(grayshadedregionontheleft-handpanel)isequaltotheprobabilityoffindinganoverdensityabove∆d(grayshadedregionon
theright-handpanel).Inparticular,ateachpixelcharacterizedbyatransmittedfluxF∗itcanbeassociatedanoverdensity∆∗suchthateq.(8)issatisfied.In
thiscase,theprobabilityoffindingapixelcharacterizedbyatransmittedfluxFmin<F∗<Fmax(redhatchedregionontheleft-handpanel)isequaltothe
probabilityoffindinganoverdensity∆b<∆∗<∆d(redhatchedregionontheright-handpanel).
∆x Npix profile,sinceittakesintoaccountthethermalandthenaturalbroad-
τ(i)=cIα1+z(i) nHI(j)Φα[vH(i)−vH(j)], (2) eningoftheabsorptionline,respectively.Forlowcolumndensity
Xj=1 regions,astheonescorrespondingtoLyαforest,thermalbroaden-
wherecisthelightspeed,Iα istheLyαcrosssection,∆xisthe ingdominates,andtheVoigtfunctionreducestoasimpleGaussian
comovingpixelsize,z(i)istheredshiftofpixeli,ΦαistheVoigt 1 v (i) v (j) 2
ipsrothfielenefourtrtahlehLyydαrogtreannsfirtaicotnio,nv.HistheHubblevelocity1,andnHI Φα[vH(i)−vH(j)]= √πb(j)exp(−(cid:20) H b−(j)H (cid:21) ) ,(5)
ThecomputationofnHIgenerallyassumesthatthelowdensitygas whosewidthissetbythetemperature-dependentDopplerparame-
whichgivesrisetotheLyαforestisapproximatelyinlocalequi- terb(j)= 2k T(j)/m ,withk andm beingtheBoltzmann
B p B p
libriumbetweenphotoionizationandrecombination.Byneglecting
constantandtheprotonmass,respectively.
thepresenceofhelium,andassumingthattheIGMishighlyion- p
Fromthesystemofequations(1)-(5)thecomplexrelationbetween
izedattheredshiftofinterestbyauniformultravioletbackground,
thetransmittedfluxF inquasarabsorptionspectraandtheunder-
thephotoionizationequilibriumconditionprovidesuswiththefol-
lying density field ∆ becomes evident. The determination of the
lowingrelation:
F ∆relationnotonlydependsontheparametersdescribingthe
−
nHI(j)= α[TΓ(j)]{n0[1+z(j)]3∆(j)}2 ∝∆(j)β, (3) hpihsytosircya,lbsutattaelsooftohneIthGeMco(Γnv;oTl0u;tiγo)n,io.ef.tohnetrheesuclotsinmgicnrHeIiowniizthatitohne
profileoftheabsorptionlines,whichinturnislinkedtothether-
with 1.5 < β < 2.0 (Hui & Gnedin 1997). In eq. (3), Γ is
malstateof thegasthroughtheDoppler parameter b.Inthenext
the photoionization rate of neutral hydrogen at a given redshift
Section,wedescribehowtheF ∆relationcanbeefficientlyin-
z(j), ∆(j) is the overdensity at the pixel j, n is the mean −
0 ferredfrom a statisticalanalysis of the transmittedflux inquasar
baryon number density at z = 0, and α[T(j)] T(j)−0.7 is
∝ absorptionspectra.
thetemperature-dependentradiativerecombinationrate.Forquasi-
linear IGM, where non-linear effects like shock-heating can be
neglected, the temperature can be related to the baryonic density
throughapower-lawrelation(Hui&Gnedin1997): 3 FLUX-DENSITYRELATION
T(j)=T ∆(j)γ−1, (4) Let us assume that the signal-to-noise ratiocharacterizing an ob-
0
servedquasarabsorptionspectrumissuchthatthemaximumflux
where T is the IGM temperature at the mean density at a given (minimum optical depth) which can be distinguished from full
0
redshiftz(j)whichdependsonthereionizationhistoryoftheUni- transmission is given by F (τ ), and that the minimum de-
max min
verse,suchastheslopeγoftheequationofstate,andΓ. tectableflux(maximumopticaldepth)isgivenbyF (τ ).By
min max
BesidesthenHIcomputation,thethermalstateoftheIGMaffects combiningeq.(2)-(3)-(4),itresultsthatτ = τ(z,β,Γ,T0,γ,∆).
theprofileoftheabsorptionlines.Infact,theVoigtprofilewhich Thismeansthat,atagivenredshiftz,foranyβ,andforanygiven
entersineq.(2)istheconvolutionofaGaussianandaLorentzian IGM thermal and ionization history, two characteristic overden-
sities do exist: [i] ∆ , where the subscript “b” means “bright”,
b
such that each Lyα absorber sitting on ∆ < ∆ would provide
b
1 ThevelocityofaLyαforestabsorberisgenerallygivenbythesumof τ(∆b) . τmin, i.e. full transmission of the quasar continuum
theHubble andthe peculiar velocities, i.e. v(i) = vH(i)+vpec(i). In (F >Fmax);[ii]∆d,wherethesubscript“d”means“dark”,such
thiswork,weneglect peculiar velocities andwediscussthis issueinthe that each overdensity ∆ > ∆d would provide τ(∆d) & τmax,
Discussionsection. thereforecompletelydepletingthefluxemittedbythesourceatthe
(cid:13)c 2011RAS,MNRAS000,1–??
Cosmicdensityfield reconstructionfromLyα forestdata 3
Figure2.Flux-densityrelationresultingfromflux/densityprobabilityconservationisshownfordifferentparametersdefiningtheIGMphysicalproperties,as
labelledinthefigures.Theblacksquaresrepresentresultsobtainedfrom10syntheticspectra,whilecolouredlinesdenotetheflux-densityrelationsresulting
bysolvingeq.(8).Intherightmostpanel,theflux-densityrelationisplottedforallthesetofparametersconsidered,whichprovidethesamemeanflux.
locationoftheabsorber(F <F ). of the baryonic density field and its correlation with the peculiar
min
Oneofthestatisticsadoptedtoanalyzequasarspectraistheprob- velocityfieldaretakenintoaccountadoptingtheformalismintro-
ability distribution function of the transmitted flux (P ), which duced by Bi & Davidsen (1997). To enter the mildly non-linear
F
quantify thenumber of pixels characterized by atransmittedflux regimewhichcharacterizestheLyαforestabsorbersweusealog-
between F and F +dF.Let us assume that at agiven overden- normalmodelintroducedbyColes&Jones(1991).
sity∆∗ itisassociatedauniquevalueofthetransmittedfluxF∗. The thermal and ionization state of the IGM are fixed in such
Inthiscase,∆ and∆ canbedefinedthroughtheprobabilityof a way that the mean transmitted flux simulated in a sample of
b d
findingapixelcharacterizedbyatransmittedfluxF >F ,and lines of sight is F¯ 0.72, as obtained from real data (Songaila
max
∼
F <F ,respectively.OnceP iscomputedfromobservedspec- 2004).Weadoptthefollowingsetofparameters:[i](Γ,T ,γ) =
min F 0
tra,∆ and∆ canbedeterminedfromthefollowingequations: (3.0,1.5,1.2); [ii] (3.2,1.5,0.6); [iii] (4.1,1.0,1.2), where Γ is
b d
reportedinunitsof10−12s−1,andT inunitsof104K.
1 ∆b 0
PF dF = P∆d∆, (6) We add observational artifacts to the synthetic spectra: first, we
ZFmax Z0 smooth each simulated spectrum to a resolution R=36000, com-
Fmin +∞ parabletotheoneofhigh-resolutionspectrographs (e.g.HIRES);
PF dF = P∆d∆, (7) then we add noise to get a signal-to-noise ratio S/N=100; finally
Z0 Z∆d we rebin the noisy synthetic spectra to R=10000, in order to re-
where P∆ is the probability distribution function of the density move small flux fluctuations. Starting from a sample of 10 LOS,
field. Analogously to eq. (6) and eq. (7), to each pixel character- wecomputetheresultingP forthecases[i],[ii],[iii].InFig.1,
F
ized by a transmitted flux Fmin < F∗ < Fmax an overdensity PFforthecase[i]isshownintheleftpanel,throughasolidline.
∆b <∆∗ <∆dcanbeassociatedsuchthat: WeassumethelognormalP∆whichhasbeenadoptedforthesyn-
Fmax ∆∗ thetic spectra simulations, and which is described by a Gaussian
PF dF = P∆d∆, (8) withmean= 0.28,andsigma= 0.48(Fig.1,rightpanel,solid
ZF∗ Z∆b line).Thechoi−ceofalognormalP isonlymadefortestingpur-
∆
or,equivalently, poses, but when dealing with real data any other, perhaps more
realistic, prescription for P can be implemented. For example,
F∗ ∆d ∆
PF dF = P∆d∆. (9) Miralda-Escude’etal.2000suggestedadifferentfunctionalform,
ZFmin Z∆∗ whoseagreement withdatahasnot yetfullyestablished(seedis-
Notethat eq. (6)-(7)-(8)-(9) are simplyobtained by imposing the cussioninBeckeretal.2006).
conservationoftheflux/densityprobabilitydensities.Theinference Starting from the computed P and the assumed P , we solve
F ∆
of∆b,∆d,∆∗ onlydependsontheassumedP∆ andnotonany eq.(8),toestablishtheflux-densityrelationforeachofthesetof
assumptionconcerningthermalandionizationhistorieswhichare parametersconsidered.TheresultingF ∆relations2 areshown
−
howeverencodedintotheobservedP ,asweshowinthenextSec- through coloured lines in Fig. 2 for the case [i] (left-most panel,
F
tion.Bysolvingeq.(8),foreachobservedvalueofF∗ intermsof redline),[ii](middlepanel,greenline),[iii](right-mostpanel,blue
∆∗,theflux-densityrelationoftheLyαforestcanbereadilyde- line).Inthisfigure,thefilledsquaresandthesolidblacklinesrep-
rived. SuchF ∆relationcanbe usedtoinvert theLyαforest, resentthemeanfluxandtherelative1σ error,respectively,corre-
−
thereforeallowingtoreconstructthedensityfieldalongtheLOS. spondingtoagivenoverdensity,asobtainedfromoursimulations.
ItcanbeseenthattheresultingF ∆relationsobtainedbysolv-
−
ingeq.(8),agreeverywellwiththerelationbetweenthemeanflux
and the overdensities predicted by the simulations. However, our
4 INVERSIONPROCEDURE methoddoesnotmanagetotakeintoaccountthedispersionofthe
F ∆relations.
Wesimulatequasarabsorptionspectraatz =3throughthemodel −
describedintheprevioussection.Inparticular,forwhatconcerns
thebaryonicdensitydistributionalongtheLOSenteringineq.(3), 2 InthisworkweadoptthecosmologicalparametersprovidedbyKomatsu
weadopt themethod described byGallerani et al. (2006), whose etal.(2010).Uncertaintiesonthecosmologicalparametershavenegligible
mainfeaturesaresummarized asfollows.Thespatialdistribution effectontheflux-densityrelation.
(cid:13)c 2011RAS,MNRAS000,1–??
4 S. Gallerani,F.S.Kitaura,A.Ferrara
Thereasonforthisisduetoourassumptionofaone-to-onecorre-
spondence between thetransmittedfluxobserved atagivenpixel
iandtheunderlyingmatterdensityfieldatthecorrespondingred-
shiftz(i).Suchanassumptionwouldbevalidiftheprofileofthe
absorptionlineswouldbedescribedbyaDiracDeltafunction(i.e.
in the ideal case of an infinitely small natural broadening of the
line), and in the case of a cold IGM (i.e. in the ideal case of no
thermalbroadeningoftheline).Inthisidealcasethecrosssection
oftheLyαtransitionisdifferentfromzeroonlyincorrespondence
ofthepixeliforwhichwecomputetheopticaldepth.Inthereal
case,totheoptical depthof thepixel idocontributealsothead-
jacentpixels.Inparticular,thehigheristheIGMtemperature(i.e.
thelargeristhedopplerparameter),thelargeristhenumberofad-
jacentpixelsresponsiblefortheopticaldepthofthepixeli.There-
fore,anobservedvalueofthetransmittedfluxF∗atthepixelican
be produced by an isolated overdensity ∆ > ∆∗, as well as by
aclusteringofoverdensities∆ < ∆∗.Ourmethoddoesnottake
intoaccountthebroadeningoftheabsorptionlines,thereforeitcan
Figure 3. Top panel: Example of synthetic quasar absorption spectra
notprovidethedispersionintheF ∆relations;inthediscussion at z = 3 as obtained by adopt the following set of parameters: [i]
−
section, wewillanalyze theeffect of thislimitof our method on (Γ,T0,γ)=(3.0,1.5,1.2)(redline);[ii](3.2,1.5,0.6)(greenline);[iii]
thedensityfieldreconstruction. (4.1,1.0,1.2)(blueline),whereΓisreportedinunitsof10−12s−1,and
In Fig. 3, we show an example of the simulated density fieldfor T0inunitsof104 K.Bottompanel:Thedottedblacklinerepresentsthe
a random LOS (bottom panel, black line) and the corresponding distributionoftheoverdensitieswhichproducethetransmittedfluxshown
transmittedfluxes(toppanel)obtainedforforthecase[i](redline), inthetoppanel.Theredline(green/blue)showtherecovereddensityfield,
asobtainedbyinvertingthefluxdensityrelationcorrespondingtotheset
[ii](greenline),[iii](blueline).InthebottompanelofFig.3the
ofparameters[i][ii/iii].Themagentalineshowthecaseofahighquality
originallyadopted density field(blackline) iscompared withthe
(S/N=1000)spectrum.
recovered ones, as obtained by applying the F ∆ relation to
−
the transmittedflux computed fromthe set of parameters [i] (red
line),[ii](greenline),and[iii](blueline).Thisfigureshowsthat
Asforlimit(2),thisisduetothefactthatweareconsideringbotha
themethodworksquitewell3forallthesetofparametersconsid-
maximumflux(F )whichcanbedistinguishedfromfulltrans-
ered,i.e.almostindependentlyfromthephysicalpropertiesofthe max
mission, and a minimum detectable flux (F ). As explained in
IGM.ThiscomesoutbythefactthattheF ∆relationsobtained min
− Sec.3,thesemaximumandminimumtransmittedfluxestranslate
by solving eq. (8) in terms of ∆∗ (coloured lines in Fig. 2) are intoaminimum(∆ )andmaximum(∆ )overdensitieswhichcan
notcompletelyindependentonthereionizationhistory,i.e.differ- b d
berecovered.Stateddifferently,incorrespondenceofthemostun-
entsetofparametersaffectsdifferentlytheP ,thereforeproviding
F derdense regions (∆ < ∆ ) we can only put an upper limit on
slightly different F ∆ relations. Thisisthe reason whyby in- b
verting the Lyαfore−st we can associate the same density fieldto the recovered density field, i.e. (∆ = ∆b); analogously, for the
mostoverdenseregions(∆ > ∆ )onlyalowerlimitocanbeset,
differentvaluesofthetransmittedflux,obtainingareconstruction d
i.e.(∆ = ∆ ). For afixed mean transmittedflux, themaximum
methodwhichisfreeofanyassumptiononthethermalandioniza- d
and minimum recoverable overdensities depend on IGM proper-
tionstateoftheIGM.Inthenextsectionwediscussthestrengths
ties, and are more sensitive4 to changes in γ than to T : [i/ii]
andthelimitsofourmethodinfurtherdetails. 0
(∆ ;∆ ) = (0.09;4.90); [iii] (∆ ;∆ ) = (0.11;3.90). Typi-
b d b d
caluncertaintiesonF atz = 3(< 10%,Songaila2004)im-
mean
pliessmallvariationson∆ and∆ .Forexample,inthecase[i]
b d
5 DISCUSSION a mean transmitted flux 10% higher [lower] than 0.72 results in
(∆ ;∆ )=(0.11;6.10)[(∆ ;∆ )=(0.08;3.82)].
From the bottom panel of Fig. 3, it is evident that the method is b d b d
Theexistenceof∆ and∆ allowsustorecoverthedensityfield
overallverysuccessful.Neverthelesssomeminordiscrepanciebe- b d
along&92%ofthesimulatedlinesofsight.Thisresultcanbefur-
tweentheoriginalandreconstructeddensityfieldremain.Inpartic-
therimprovedbyapplyingourmethodtoveryhighqualityspectra.
ular,thereconstructeddensityfieldis(1)smootherthantheorigi-
UptonowwehaveassumedaS/N = 100,whichmeansthatwe
nalone,and(2)itoverestimates(underestimates)theoriginalone
aresensitiveat1σleveltofluxvariationsuptotheseconddecimal
inthemostunderdense(overdense)regions.
digit. Therefore, we have considered F = 0.99 and F =
Theaccuracyloss(1)arisesfromtheadoptedassumptionofaone- max min
0.01.However,ifweconsiderhigherqualitydata(e.g.S/N=1000),
to-onecorrespondencebetweenthetransmittedfluxandthematter
theoriginaldensityfieldisbetterrecovered,sincethecompleteness
density.Asalreadydiscussedintheprevioussection,thisassump-
ofthesignal risesto& 98%,being(∆ ;∆ ) = (0.03;6.60). In
tion does not allow us to take into account the clustering of the b d
thiscase,weobtainareconstructedsignalcharacterizedbyarela-
densityfieldlocally,orequivalentlythethermalbroadeningofthe
absorptionlines.Thisresultsinareconstructeddensityfieldwhich
issmootherthantheoriginalone.
4 Foraninvertedequationofstate[iii],∆bishigherand∆dislowerthan
inthecaseofa“regular”one.Infact,ascanbeseenfromFig.3,inthecase
3 Bycomputingtherelativeerrorǫ∆oftherecovereddensityfieldalong [iii](greenline),themostunderdenseregions(∆<∆b)tendtobemore
≥10linesofsight,wefindthat&50%ofthepixelsarecharacterizedby transmitting(F > Fmax)andthemostopaqueregions(∆ > ∆d)tobe
ǫ∆.0.12. evenmoreabsorbed(F <Fmin)
(cid:13)c 2011RAS,MNRAS000,1–??
Cosmicdensityfield reconstructionfromLyα forestdata 5
tiveerrorǫ . 12%in51%ofthepixels,12% < ǫ < 42%in thepropertiesoftheIGM(Γ;T ;γ)insuchawaythattheresulting
∆ ∆ 0
39%ofthepixels,and42%<ǫ <100%in10%ofthepixels. meantransmittedfluxmatchesobservations. Then,wehavecom-
∆
We finally compare our method with previously developed tech- putedP foreachparametersetconsidered.DifferentIGMprop-
F
niques.Oneoftheapproachesgenerallyadoptedinthedensityfield ertiesaffectdifferentlytheP ,henceresultinginslightlydifferent
F
reconstruction istodefineaphysical model relatingtheobserved F ∆relations.Thisprovidesareconstructionmethodwhichdoes
−
fluxtotheunderlyingdensityfieldandtheninvertthisrelation.As notrequireanyassumptiononthethermalandionizationstateof
showninSec.2,anymodel whichallowstopredictthetransmit- theIGM.Theproposedmethodisparticularlysuitablefortheex-
tedfluxresultingfromagivendensityfielddistribution,atagiven tractionoflargescalematterdensityfieldssignalsfromLyαdata,
redshift z,depends on several uncertain parameters (β,Γ, T γ). which represents the starting point for the detection of baryonic
0
Thisapproach hasbeen pioneered byNusser &Haehnelt (1999), acousticoscillationsthroughquasar absortionspectra(McDonald
hereafterNH99.Theseauthorshavedeveloped atechniquebased &Eisenstein2007;Slosaretal.2009;Kitauraetal.2010).Infact,
onamodeloftheLyαforest,whichallowstoreconstructtheden- thiskindofstudiesarebasedonthedensityfieldreconstructionon
sityfieldalongquasarsightlinesthroughaniterativemethod.Such scalessmallerthan0.1Mpcalongalargenumberoflinesofsight
techniqueallowstocorrectlytakeintoaccountthethermalbroad- morethan10Mpclong.Suchrequirementsarebeyondthecapabil-
eningoftheabsorptionlines,assumingthatbothT andγ,which ityofcurrentsimulations,whilecanbesatisfiedthroughourfast,
0
affecttheDopplerparameter,areknown. thoughapproximate,technique.
TheNH99inversionmethodhasbeenadoptedbyseveralauthors
tostudythepropertiesoftheIGMandtomeasurethematterpower
spectrum from the Lyα forest (e.g. Pichon et al. 2001; Rollinde ACKNOWLEDGMENTS
etal.2001;Zaroubietal.2006).However,ithasbeenrecognized
that uncertainties onβ, γ,and T resultin spurious biasesinthe SGacknowledgesaELTEBudapestPostdoctoralFellowship,and
0
recovereddensityfield(NH99;Pichonetal.2001; Rollindeetal. aSNSPisaVisitingScientistFellowshipwhichhavepartiallysup-
2001). The strong dependence of the matter power spectrum on ported this work. The authors thank the Intra-European Marie-
the IGM properties, as inferred from Lyα forest data, has been Curiefellowshipwithprojectnumber221783andacronymMCM-
alsoconfirmedbyBirdetal.(2010).Saittaetal.(2008)havepro- CLYMANforsupportingthisproject.
posed another possible approach to reconstruct the density field
through the transmitted flux in quasar absorption spectra, named
FLO(i.e.FromLinestoOverdensities). Alsointhiscase thepa- REFERENCES
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influence the quality of the recovery (NH99). However, we note
GalleraniS.,ChoudhuryT.R.&Ferrara,A.,2006,MNRAS,370,1401
thatthesamemethoddescribedinNH99forthereconstructionin
GunnJ.E.&PetersonB.A.,1965,ApJ,142,1633
realspacecanbeappliedtoourrecovereddensityfielditeratively. HernquistL.,etal.,1996,ApJ,457,L51
Weleavethistoafuturework.Wefinallynotethatsofarwehave HuiL.&GnedinN.Y.,1997,MNRAS,292,27
beenreferringtoquasar absorptionspectra. However,themethod KitauraF.S.,GalleraniS.,FerraraA.,2010,arXiv:1011.6233
proposedcanbeappliedtoGRBabsorptionspectraaswell. KomatsuE.etal.,2010,arXiv:1001.4538,acceptedforpublicationinApJS
McDonaldP.,EisensteinD.J.,2007,Phys.Rev.D.,76,6
McDonaldP.etal.,2005,atro-ph/0407377
Miralda-Escude’J.,CenR.,OstrikerJ.P.,RauchM.,1996,ApJ,471,582
6 CONCLUSIONS NusserA.,HaehneltM.,1999,MNRAS,303,197
PageM.J.etal.2007,ApJS,170,335
Anovel,fastmethodtorecoverthedensityfieldthroughthestatis- PetitjeanP.,Mu¨cketJ.P.,KatesR.E.,1995,A&A,295,L9
ticsofthetransmittedfluxinhighredshiftquasarabsorptionspec- PichonC.,etal.,2001,MNRAS,326,597
trahasbeenintroduced.Theproposedtechniquerequiresthecom- RauchM.,etal.,2001,ApJ,562,76
putation of the probability distribution function of the transmit- RollindeE.,PetitjeanP.,PichonC.,2001,A&A,376,28
ted flux(P ) inthe Lyαforest region and, asa soleassumption, RollindeE.,etal.,2003,MNRAS,341,1279
F
theknowledgeoftheprobabilitydistributionfunctionofthemat- SaittaF.,etal.,2008,MNRAS,385,519
SargentW.L.W.,etal.,1980,AJSS,42,41
terdensityfield(P ).Wehaveshownthattheprobabilitydensity
∆
SlosarA.,HoS.,WhiteM.,LouisT.,2009,JCAP,10,19
conservation of the fluxand matter density unveils aflux-density
SmetteA.,etal.,1992,ApJ,389,39
(F ∆)relationwhichcanbeusedtoinverttheLyαforest,with-
− SongailaA.,2004,AJ,127,2598
outanyassumptiononthepropertiesoftheIGM.
VielM.,HaehneltM.G.,SpringelV.,2004,MNRAS,354,684
Ourinversionmethodhasbeenthentestedatz=3throughasemi- ZaroubiS.,etal.,2006,MNRAS,369,734
analyticalmodeloftheLyαforestwhichadoptsalognormalP∆. ZhanH.,2003,344,935
Firstofallwehavesimulatedasampleofsyntheticspectravarying ZhangY.,AnninosP.,NormanM.L.,1995,ApJ,453,L57
(cid:13)c 2011RAS,MNRAS000,1–??