Probing Reionization with Intensity Mapping of Molecular and Fine Structure Lines

0.32 MB·English

by  Yan Gong

DRAFTVERSIONJANUARY17,2011
PreprinttypesetusingLATEXstyleemulateapjv.08/22/09
PROBINGREIONIZATIONWITHINTENSITYMAPPINGOFMOLECULARANDFINESTRUCTURELINES
YANGONG1,ASANTHACOORAY1,MARTAB.SILVA2,MARIOG.SANTOS2,PHILLIPLUBIN3
DraftversionJanuary17,2011
ABSTRACT
We propose observations of the molecular gas distribution during the era of reionization. At z 6 to 8,
12CO(J=1- 0)lineintensityresultsinameanbrightnesstemperatureofabout0.5µKwithrmsfluctu∼ationsof
1
0.1µKat1to10Mpcspatialscales,correspondingto30arcminuteangularscales. Thisintensityfluctuations
1
can be mapped with an interferometer, similar to existing and planned 21-cm background experiments, but
0
operating at 12 to 17 GHz. We discuss the feasibility of detecting the cross-correlation between HI and
2
∼
CO moleculargassince sucha cross-correlationhastheadvantagethatitwillbe independentofsystematics

n andmostforegroundsin eachofthe 21-cmandCO(1- 0)line experiments. Additionalinstrumentstunedto
a higher-ordertransitionsof the CO moleculeor an instrumentoperatingwith highspectral resolutionat mm-
J
wavelengths targeting 158 µm CII could further improve the reionization studies with molecular gas. The

4 combined21-cmandCOlineobservationshasthepotentialtoestablishtherelativedistributionofgasinthe
1 inter-galactic medium and molecular gas that are clumped in individual first-light galaxies that are closely
connectedtotheformationofmassivestarsinthesegalaxies.
]
O Subjectheadings:cosmology:theory—diffuseradiation
C
h. 1. INTRODUCTION Intermsofpotentialspectrallinesofinterest,thelineinten-
p Recentlytherehasbeenagreatdealofinterestintheevolu- sityoftheJ=1to0transitionof12COhasbeenusedasaway
- tionoftheintergalacticmediumathighredshifts(z>6)and toestablishthegasmassofstar-forminggalaxiesbothatlow
o (e.g.,Downes&Solomon1998)andmedium(e.g.,Greveet
specifically,thereionizationhistoryoftheUniverse. Mostof
r al.2005)redshifts.IndividualCOlineobservationsnowexist
t thisinterestissparkedbyexistingmulti-wavelengthobserva-
s tionsthatsuggestacomplexreionizationhistory,withastrong outtoz=5.3(e.g.,Riechersetal. 2010),whichissignificant
a giventhatthehighest21-cmlineemissionfromagalaxycur-
[ possibilityforextendedandhighlyinhomogeneousperiodof
reionization. Observationsofthe21-cmspin-fliplineofneu- rentlymeasuredisatzof0.24(Lahetal. 2007;seeChanget

1 tralhydrogenare currentlyconsideredto be one ofthe most al.2010for21-cmintensityvariationsofthekindwepropose
v promisingprobesoftheepochofreionization(e.g.,Madauet atz 0.9). InadditiontotheCOlines, wealsofindthatthe
∼
2 al. 1997;Loeb&Zaldarriaga2004;Gnedin&Shaver2004). finestructureCIIline, withobservationsin themmrangeof
9 thespectrum,couldbeastrongprobeofreionizaion.
Giventhe lineemission, leadingto afrequencyselectionfor
8 ThisLetterisorganizedasfollows: inthenextSection,we
observations,the21cmdataprovidesatomographicviewof
2 outlinethecalculationrelatedtothestrengthoftheexpected
thereionization(Santosetal. 2005;Furlanettoetal. 2004a).
. signalfromreionization,Section3presentsresultsrelatedto
1 Itisalsoausefulcosmologicalprobe(Maoetal.2008;Santos
0 &Cooray2006;McQuinnetal. 2006;Bowmanetal. 2007). apotentialCObrightnesstemperaturefluctuationexperiment
1 Hereweproposespectrallineintensitymappingassociated that target 1-0 transition, and Section 4 discusses the cross-
1 with molecular gas during the era of reionization as an ad- correlationwiththe21-cmbackground.
: ditionalprobeduringtheformationoffirst-lightgalaxies. In
v
i particular,westudytheJ=1to0transitionofthe12CO(car- 2. THECO(1-0)SIGNAL
X bonmonoxide),whichhasarest-wavelengthof2.61mm.Our For a galaxy at a given redshiftthe CO(1-0) luminosityis
r suggestion extendsthe initial work on this topic by Righi et takentoberelatedtotheH contentandthemetallicityofthe
a al. (2008;see also Basu etal. 2004). Insteadof theangular gas (Obreschkow et al. 20209b). A key input here is the re-
power spectrum, which is dominated by CMB anisotropies lation between CO(1-0)luminosity, L , and the halo mass.
CO
at tens of arcminute scales, we propose spectral line inten- While such a relation is expected it also has a large scatter
sity mapping leading to the three-dimensional power spec- coming from differences in the gas content, at a fixed halo
trum (see also Visbal & Loeb 2010). An additional probe mass, dueto variationsin thehaloagesata fixedmass; The
of reionization is useful since the first-generation21-cm ex- gasinolderhalosismorelikelytobedepletedmorethanthe
perimentsareexpectedtobenoise-dominatedandtheobser- youngerones with older halos containing more stars. How-
vationscould,inprinciple,beaffectedbyvarioussystematics ever,forsufficientlylargevolumes,wewillbeaveragingover
andresidualforegrounds. Asecondprobeofthereionization manygalaxiessothat,sothethemeanrelationanditsscatter
epochprovidingthree-dimensionalinformationcanbecross- canbequantified. Thisissimilartotheluminosity-halomass
correlatedwith the 21-cmspectralline measurementsto im- relationforopticallightwhichhasallowedstatistics such as
provetheoverallunderstandingofreionization. the conditional luminosity functions to be constructed and
improve the halo modeling beyond the simple halo occupa-
1Department ofPhysics&Astronomy, University ofCalifornia, Irvine, tionnumber(e.g.,Yangetal. 2004;Cooray&Milosavljevic
CA92697
2CENTRA,InstitutoSuperiorTéecnico,Lisboa1049-001,Portugal 2005b;Cooray2006).
3Department of Physics & Astronomy, University of California, Santa Here we make use of the numerical simulations of
Barbara,CA Obreschkow et al. (2009d) that are available as part of the
2
Figure1. Left: TheLCO(Mhalo)relationforCO(1-0)luminosityasafunctionofthehalomassMhaloatz=7. Thelinesshowsthemeanrelation(thickcenter
line)and±1σrelation(thinlines)giventhescatter(seetextfordetails).Thedotsshowthemeanofthescatterwhenbinnedto150logarithmicintervalsinhalo
mass.Right:TherelationneutralhydrogenmasscontentinindividualgalaxiesMHIvs.thehalomassMhaloatz=7.
SKA SimulatedSkies website4. Thissimulationis based on
the galaxy catalog from De Lucia & Blaizot (2007) which
post-processed the Millennium dark matter simulation with
semi-analytical models of galaxy formation. It captures the
gasastrophysics,especiallyHIandH andallowforthecos-
2
mic evolution of these two phases of the cold hydrogengas
(see,Obreschkowetal. 2009b;2009cfordetails). Theyalso
constructedavirtualskyfieldwithHIandCOlineluminosi-
ties for each of the galaxies, calculated from a combination
of the neutral and molecular hydrogen gas masses and the
metallicity of each galaxy. Using the online tools we made
a query with a four degree observing cone containing more
than5 105galaxiesateachofz=7.
×
TheL (M)fromeveryhaloatz 7fromthissimulation
CO
∼
isshownin the leftpanelofFigure1 withthe shadeof gray
darker in the regionswhere the halo density is higher. Typ-
ically we find one galaxy per halo at these redshifts. The
lines show the result of averaging the total L from the
CO
halos for each of 150 logarithmic bins of halo mass. Mo-
tivated by parameterization of optical luminosity and halo
mass (Cooray & Milosavljevic 2005a), we use a relation of
the form L (M)=L (M/M )b(1+M/M )- d to describe the
CO 0 c c
meanrelationanddeterminethefourfreeparametersA, b, c
andd. Atz=6,7,and8,theseparameterstakethevaluesof
3L.05=41.301×1,130.06,6.120×111,20.60,4.01×01110M6⊙L,⊙a,nbd=d2=.42,.28.,63,.24.,83,.3M,cre=- F8.igTuhree628..3T%heCb.iLa.s(a1nσd)barreigahltsnoessshotewmnpienragtruereenodfaCshOedlinlienefso.rTzh=e6b,ia7sahnads
spec×tively. × × noadditionaluncertaintyastheuncertaintyinLCO(M)relationisachangein
UsingtheaboverelationbetweenL andhalomassM as theoverallamplitudeatagivenmassandnotashapechange(see.eq.2).
CO
afunctionofredshift,wecanwritethemeanintensityofthe
CO(1-0)lineas
I¯CO=ZM∞mindMddMn (z,M)LC4Oπ(Dz,2LM)y(z)D2A, (1) mInoavbionvgedyis(zta)n=ced,χν/disνth=eλoCbOs(e1rv+ezd)2f/rHeq(uze),nwcyh,eλreχ=is2t.h6emcom-
CO
where we take Mmin =108(M⊙/h) as the minimum mass of istherestframewavelengthoftheCO(1-0)line.
thedarkmatterhalosthatcanhostgalaxies(tobeconsistent Thesignalis expectedto containspatial variationsaround
withmassscale ofatomicHydrogencoolingora virialtem- theaverageintensityduetopoissonfluctuationsinthenumber
peratureof104K(Loeb&Barkana2001),dn/dMisthehalo ofhalos(shotnoise)andcorrelationswiththeunderlyingdark
mass function(Sheth & Tormen1999),D is the luminosity matter density field which will enhance the fluctuations by
L
distance,andD isthecomovingangulardiameterdistance. a factor of (1+b(z,M)δ), with δ being the density contrast
A
of this dark matter field. The intensity of the CO(1-0) line
4http://s-cubed.physics.ox.ac.uk can be written as a function of the spatial location ICO(x)=
3
Figure3. Leftpanel: thedimensionlessautopowerspectrumandtheshotnoisepowerspectrumforCOlineatz=7. The68.3%C.L.(1σ)isshowningreen
thinlines.Middlepanel:thedimensionlessautopowerspectrumandtheshotnoisepowerspectrumfor21-cmemissionatz=7.Theautoandshotnoisepower
spectrumofthegalaxies∆Gand∆shotaresosmallcomparedwith∆IGM,that∆totisdominatedby∆IGM. Thebluelineswitherrorbarsmakeuseofnoise
H HG H H H
powerspectrum(shownbythebluedashedline)correspondingtothedesignofLOFAR.Rightpanel: thedimensionlesscrosspowerspectrumandshotnoise
powerspectrumforCOlineand21-cmemissionatz=7. ThebluesolidlineistheerrorfromLOFAR.The68.3%C.L.(1σ)isshowninredthinlines. The
long-dashedmagentalinesinthemiddleandrightpanelsaretheresultsfromthesimulationof21-cminSantosetal.(2010)forcomparison.
I¯ [1+b δ(x)]withbiasb givenby atredshiftz(Maoetal. 2008)is
CO CO CO
bCO(z)= RM∞mind∞MdddMMnLdCnOLb(z,M), (2) T¯bIGM=c(z)x¯H(cid:18)T¯s- T¯TsCMB(cid:19)(mK). (5)
RMmin dM CO Here x¯H is the mean neutral hydrogen fraction, that we as-
whereb(z,M)isthehalobias(Sheth&Tormen1999). sume x¯ 1- x¯ where x¯ is the mean ionized fraction, and
H i i
In Figure 2, we show both the mean signal and the halo wesetx¯ ≡=0.3and0.7atz=7and8respectively(Maoetal.
biasasafunctionoftheredshiftduringreionization.Forsim- H ¯
2008). The T is the averagedspin temperature of the IGM,
plicity,wehaveconvertedthemeanintensityofthesignalto s ¯
andweassumeT T here. Theparameterc(z)(defined
s CMB
Rayleigh-Jeansbrightnesstemperature.Atz 6,thesignalis ≫
inSantosetal. 2008)is
∼
atthelevelof0.2to1.5µK,withthelargerangecomingfrom
theSisnccaettethreinmtheaenLiCnOte(Mns)itryeliastciohna.llengingtomeasureasitre- c(z)=23(cid:18)0h.7(cid:19)(cid:18)Ω0.b0h22(cid:19)(cid:18)Ω0.1h5211+0z(cid:19)1/2(mK), (6)
quires absolute measurements we discuss the feasibility of m
measuring anisotropies of the CO line intensity. The total whereΩ isthebaryondensityparameter.
b
power spectrum of the CO(1-0) line involves two contribu- Weobtainthepowerspectrumofthe21-cmfluctuationsin
tions, the clustering term and the shot noise. Following the the IGM using the fitting formula of Mao et al. (2008) at
mean intensity and bias given above, the clustering power severalredshiftsduringreionization.Forcomparisonwealso
spectrumis considerthereionizationsimulationsofSantosetal. (2010).
PCclOus(z,k)=T¯C2Ob2COPδδ(z,k). (3) Thesesimulationshaveasmallerbubblesizeonaveragethan
the models of Mao et al. (2008). As we will discuss later,
¯
HereTCO isthemeantemperatureofCO line, Pδδ =Plin(z,k) while two models we consider give rise to the same 21-cm
where Plin is the linear power spectrum of the dark matter. power spectrum, they different significantly in terms of the
The shot niose power spectrum, due to discretization of the cross-correlation of CO and 21-cm brightness temperature
galaxies,is fluctuations.
SimilartotheIGMcalculationthemeanbrightnesstemper-
∞ dn L 2
Pshot(z)= dM CO yD2 . (4) atureof 21-cmemission fromthe galaxiescanbe calculated
CO Z dM(cid:18)4πD2 A(cid:19) through
Mmin L
T¯G=c(z) ρH(z) (mK), (7)
3. CROSSPOWERSPECTRUMOFCOLINEAND21-CMEMISSION b Xρ (z)
b
In order to calculate the expected strength of the correla- whereX =0.76isthehydrogenmassfraction,ρ (z)=Ω (1+
tionbetween21-cmandCOlineintensities,webrieflydiscuss b b
tchoenbsirdigerhttnweosssitgenmaplse,rtahteuruesvuaarlisaitgionnaslcinomthieng21fr-ocmmnsieguntaral.lgWaes z(M)3ρpcc/ish)th- 3e.baryondensityatzandρc=2.7752×1011M⊙/h
Weassumethatthetotalhydrogenmassinagivenpixelof
intheintergalacticmediumthatisnotdirectlycorrelatedwith
theexperimentonlydependsonthehalomasssothatthehy-
molecular gas in galaxies, and the remaining neutral gas in
individualgalaxies. Duringtheeraofreionizationthe21-cm drogenmassdensityρH isgivenbyρH= M∞mindMddMnMHI(M).
brightnesstemperaturefluctuationsareexpectedtobe domi- To obtain MHI(M) we used the same pRrocedure as before,
natedbythe IGM.Atlowerredshifts, Whilethe IGMsignal queryingthesimulationfromObreschkowetal. (2009d)and
is zero, a small 21-cm contribution still remains due to the adding the M from the galaxies in each halo. The result-
HI
neutralgasinindividualgalaxies. ing scatter plot is shown in the right panel of Figure 1 to-
Thedifferenceofthespatiallyaveragedbrightnesstemper- gether with the average in each mass bin (blue dots). The
atureof21-cmemissionintheIGMandtheCMBtemperature red line shows a fitting function to the average values using
4
MHI=10A×log10(M)+B,whereMisthehalomass,A=0.75,0.74 wave mode k and θ is the angle between k and the line of
and 0.75, and B=0.17, 0.23 and 0.07 for z=6, 7 and 8 re- sight). Typicallythis baselinedistributionwill bemorecon-
spectively. centrated around the core but for interferometers with high
Following the description related to the CO line intensity, filling factorswe can make the simplification that the distri-
themean21-cmbrightnesstemperatureistakentohavespa- bution is constant so that the required function for above is
tialvariationsTG(x)=T¯G(1+b δ(x)),whereb isthebiasof n()=λ2N2/πD2 with N as thenumberofelementsofthe
b b H H a max a
galaxiescontainingneutralhydrogen interferometerandD themaximumbaseline ofthe distri-
max
b (z)= M∞mindMddMnMHb(z,M). (8) batutaiogni.veNnokteisthjautstth(ePSer+roPrNi)n/√th(eNmm)e,awsuhreerdepPoSwiesrthspeescitgrunmal
H R ρH powerspectrumandNm isthenumberofmodescontributing
toagivenbinnedmeasurement. Inordertocountthesenum-
The clustering power spectrum of the 21-cm emission from
¯ berofmodes,weconsideragridinkspacewitharesolution
galaxies is then PHG(z,k)=(TbG)2b2HPδδ(z,k). Again, the shot givenby(2π)3/(yr2 FoV B), whichisset bythevolumeof
noisepowerspectrumfor21-cmemissionis · ·
the experiment(B is the bandwidth used in the analysis and
∞ dn M 2 FoVisthefieldofview).
Pshot(z)= dM c(z) H . (9) Typically we will be interested on linear scales (k < 1.0
H ZMmin dM(cid:18) Xρb(z)(cid:19) h/Mpc) corresponding to a few arcminutes. Given the fre-
Thetotalpowerspectrumof21-cmemissionfollowsfroma quenciesinvolved,theneedforlargeFoV,andhighsensitivity
sum of shot-noise and clustering terms (see middle panel in to µK brightnesstemperaturefluctuationsleads to an exper-
figure3). imental setup that involves a total collecting area Atot =385
Thecrosspowerspectrumbetween21-cmandCOlinein- m2, bandwidth B=1 GHz with spectral resolution δν =30
tensitiesisPtot = PIGM +PG +Pshot ,whereweagainsep- MHzandinterferometerspacingsbetween0.7and25m. The
CO,H CO,H CO,H CO,H
aratethecontributionfromneutralhydrogenintheIGMand numberofelementsis1000witheachhavingareceiverwith
neutralhydrogenremaininginindividualgalaxies. Basedon systemtemperatureof20K.IntheleftpanelofFigure3, we
thediscussionrelatedto21-cmfluctuations,thecrosspower assumeatotalintegrationtimeof3000hourswhencalculat-
spectrumoftheCOlineand21-cmemissionintheIGMis ing the noise powerspectrum. For 21-cmnoise calculations
wemakeuseofasetupsimilartoLOFAR,thoughwenotethat
PCIGOM,H(z,k)=T¯CObCOc(z)[(1- ¯xi)Pδδ- x¯iPδxδ], (10) our calculations are not too different for an experiment like
MWA.ForexperimentalparametersrelatedtoLOFAR,were-
where Pδxδ(z,k) is the cross power spectrum for the ionized ferthereadertoHarkeretal.(2010).Thevalues(at150MHz)
fractionandthedarkmatter. TheIGMgasiscorrelatedwith
areA =5 104m2,T =490K(instrumentnoisetempera-
CO lines astheybothtracethe same underlyingdarkmatter tot × sys
ture),FOV=25deg2,bandwidthof8MHzwithδν=0.5MHz
densityfield.
andD =2000m. WetakeT =1000hours.
ThecrosspowerspectrumoftheCOlineand21-cmemis- max int
Fortheproposedexperimentalsetupthebrightnesstemper-
sioninindividualgalaxiesis
ature fluctuations can be detected with a cumulative signal-
PCGO,H(z,k)=T¯COT¯bGbCObHPδδ(z,k), (11) to-noiseratio thatleadsto morethan40σ confidence. How-
ever, CO(1-0) mapping could be impacted by foregrounds,
whiletheshotnoisepowerspectrumoftheCOlineand21-cm
including spectral lines associated with other molecules; In
emissioninthegalaxiesis
the case of other transitions of the CO lines, the contamina-
∞ dn L M tion for CO(1-0) measurements at z 6 to 8 is likely to be
PCshOo,tH(z)=ZMmindMdM4πCDO2LyD2Ac(z)XρbH(z). (12) mz ini1m3atlo; 1th7e. CThOe(2m-1o)stlisnigenfiofircaenxtamcop∼nlteammiunsattioornigsiwnailtlelifkroelmy
∼
4. DISCUSSION come from molecular transitions that have rest wavelengths
longward of the CO(1-0) line and thus coming from lower
In Figure 3, left panel, we show the brightness tempera-
redshifts. To avoid such contaminations and to improve the
ture power spectrum for the CO line at z= 7, while in the
overall study of reionization we suggest a cross-correlation
middlepanelweshowthe21-cmbrightnesstemperaturefluc-
between 21-cm brightness temperature fluctuations and the
tuationsatthe sameredshiftandin therightpanel,we show
COintensities.
the cross-correlationbetween the two. In the case of 21-cm
Forthecross-correlation,weassumethatobservationswill
fluctuations,thesolidlinesshowthepredictionbasedonthe
beconductedinoverlappingareasontheskybyboththeCO
modelsofMaoetal. (2008),whilein dashedlineswe show
and 21-cmexperiment. Thisis a necessary featureof cross-
the predictionfromthe semi-numericalsimulationof Santos
correlation study leading to some coordinationbetween two
etal. (2010).
experiments. We reduce both datasets to a common, and a
To discuss the possibility of measuring the CO signal and
lower resolutioncube in frequencyand countthe total num-
the CO-21 cm cross-correlation we make use of a calcula-
berofcommonmodescontributingtoa givenbinink space
tion similar to the one used in 21-cm interferometers. Fol-
usingthesamemethodfornoisecalculationasbeforeforeach
lowing Santos et al. (2010), the noise power spectrum, P
N
of the experiments. Note that the error in a given pixel in k
for a given experimental “pixel” in Fourier space is given
by P (k,θ)= D2y(λ4T2 )/[A2t n D ksin(θ)/2π ] where A space can be written as (P2 +P P )/N , where N is
N A sys e 0 A e CO,H CO H m m
is the collecting area of one ele(cid:0)ment of the in(cid:1)terferometer the number of modes. Iqn Figure 3 right label we show the
(which could be a station), t0 is the total observation time cross-correlation power spectrum at z=7 and the expected
and the function n() captures the baseline density distribu- binnederrorsbyusing LOFAR andthe CO experimentwith
tion on the plane perpendicular to the line of sight, assum- parameters outlined in above. The overall uncertainties are
ing alreadyit is rotationallyinvariant(k is the moduliof the
5
dominatedbythe21-cmobservations. Forreference,wealso L /L 4100. With a rest wavelengthat158µm, obser-
CII CO
∼
show the prediction of the model by Mao et al. (2008) and vations are required over the frequencyrange of 210 to 270
fromthenumericalsimulationofSantosetal. (2010). While GHz (1.1 to 1.4mm). The rms fluctuations are expected to
thetwogiveasimilar21-cmfluctuationpowerspectrum,they be at the level of 102 to 103 Jy/sr at z 7 to 8 at tens of
differ significantly in terms of the cross-correlationwith the arcminuteangular scales. To probe reion∼izationfluctuations
CO emission. The difference is primarily related to the av- associatedwiththeCIIline,observationsmustbecarriedout
eragescaleofthereionizedbubblesizesandwefindthatthe insmallfrequencyintervalsof50MHzwithinstrumentspro-
cross-correlationsuchastheoneweproposehereismoresen- vidingangularresolutionofordertenarcminuteswithsurvey
sitivetoastrophysicsduringreionizationthanwith21-cmdata areasoforderafewtenssquaredegrees.Inafuturepaperwe
alone. hopetoreturntothescientificcaseofapotentialCIIexperi-
While our calculation and results are related to the CO(1- ment,sincesuchanobservationcanprobemultipleredshifts
0)transition,ourmethodcanbeextendedtoothertransitions withbothCIIandhigh-JCOlines.
and other molecules as well as long as a correction is made
for the ratio of line intensity between higher J transitions of
COandthe1-0line.Existingobservations,atlowtomoderate
redshifts,suggestavalueofabout0.6forJ=2to1luminosity WethankparticipantsoftheKavliInstituteforSpaceStud-
whencomparedto1-0luminosity. The2-1observationswill ies’ (KISS) Billion Years workshop for helpful discussions.
beoverthefrequencyrangeof25.5to32GHzforz 6to8. This work was supported by NSF CAREER AST-0645427
∼
The fine structure line CII has been detected in several at UCI. MGS and MBS acknowledges support from FCT-
of the high-z galaxies and existing studies indicate that PortugalundergrantPTDC/FIS/100170/2008.
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