Pressure Support vs. Thermal Broadening in the Lyman-alpha Forest II: Effects of the Equation of State on Transverse Structure

0.68 MB·English

by  Molly S. Peeples

Mon.Not.R.Astron.Soc.000,1–??(2009) Printed25January2010 (MNLATEXstylefilev2.2)
α
Pressure Support vs. Thermal Broadening in the Lyman- Forest II:
Effects of the Equation of State on Transverse Structure
0
Molly S. Peeples1⋆, David H. Weinberg1, Romeel Davé2, Mark A. Fardal3, Neal Katz3
1
0 1DepartmentofAstronomyandtheCenterforCosmologyandAstro-ParticlePhysics,TheOhioStateUniversity,Columbus,OH43210
2 2UniversityofArizona,StewardObservatory,Tucson,AZ85721
3DepartmentofAstronomy,UniversityofMassachusetts,Amherst,MA01003
n
a
J

3 25January2010
2

] ABSTRACT
O
Weexaminetheimpactofgaspressureonthetransversecoherenceofhigh-redshift(26z64)
C Lyman-αforestabsorptionalongneighboringlinesofsightthatprobethegasJeansscale(pro-
. jected separation∆rp 6500h- 1kpccomoving;angularseparation∆θ.30′′). We compare
h
predictionsfrom two smoothed particle hydrodynamics(SPH) simulations that have differ-
p
ent photoionization heating rates and thus different temperature-densityrelations in the in-
-
o tergalacticmedium(IGM).We alsocomparespectracomputedfromthegasdistributionsto
r thosecomputedfromthepressurelessdarkmatter.Thecoherencealongneighboringsightlines
t
s is markedlyhigher for the hotter, higher pressure simulation, and lower for the dark matter
a spectra. We quantifythis coherenceusingthe flux cross-correlationfunctionand the condi-
[
tionaldistributionoffluxdecrementsasa functionoftransverseandline-of-sight(velocity)
2 separation.Sightlinesseparatedby∆θ.15′′areidealforprobingthistransversecoherence.
v Higherpressuredecreasestheredshift-spaceanisotropyofthefluxcorrelationfunction,while
0 higher thermal broadeningincreases the anisotropy. In contrast to the longitudinal(line-of-
5 sight) structure of the Lyα forest, the transverse structure on these scales is dominated by
2 pressureeffectsratherthanthermalbroadening.Withtherapidrecentgrowthinthenumber
0
ofknownclosequasarpairs,pairedline-of-sightobservationsofferapromisingnewrouteto
.
0 probetheIGMtemperature-densityrelationandtesttheunexpectedlyhightemperaturesthat
1 havebeeninferredfromsinglesightlineanalyses.
9
0 Keywords: cosmology:miscellaneous—intergalacticmedium—methods:numerical
:
v
i
X
r 1 INTRODUCTION 1995; Hernquistetal. 1996) and associated analytic descriptions
a
(Rauch&Haehnelt 1995; Reisenegger&Miralda-Escude 1995;
The 1.5.z.6 intergalactic medium (IGM) is most commonly
Bi&Davidsen1997;Huietal.1997),inwhichmostLyαabsorp-
studied via the Lyman-α forest, which arises from Lyα absorp-
tionarisesinacontinuouslyfluctuatingmediumoflowdensitygas
tion of neutral hydrogen along the line of sight to some dis-
ratherthaninasystemofdiscreteclouds.Morerecently,observa-
tant source (e.g., a quasar). Most of the information we have on
tionsofpairshavebeensuggestedaswaysofinvestigatingmeasur-
the nature of the IGM is from sightlines piercing physically dis-
ingthecosmological constantviatheAlcock&Paczynski(1979)
tinct regions of the IGM. Absorption features have finite widths,
effect(McDonald&Miralda-Escudé1999),thematterpowerspec-
but from individual sightlines it is difficult to separate the con-
trumonsmallscales(Vieletal.2002),andtheIGMtemperature-
tribution of bulk velocities (Hubble flow and peculiar velocities)
densityrelation.Itisonthelastofthesethatwefocusinthispaper.
from those of thermal broadening. Close quasar pairs can break
Theoretical models predict that the low density IGM should
this degeneracy by probing the transverse structure of the IGM.
haveapower-law“equationofstate,”
In the mid-1990s, several studies of quasar groups and lensed
quasars definitively showed that the absorbing structures are co- T =T(1+δ)α, (1)
0
herent over hundreds of kpc(Bechtoldetal. 1994; Dinshawetal.
1994; Fangetal. 1996;Charltonetal.1997;Crotts&Fang1998; withdensergasbeinghotterthanlessdensegas(α>0,Katzetal.
D’Odoricoetal. 1998). These observations provided critical sup- 1996;Miralda-Escudéetal.1996;Hui&Gnedin1997).Although
port for the physical picture of the Lyα forest then emerg- thistemperature-density(T-ρ)relationisdifficulttomeasure,mul-
ing from cosmological simulations (Cenetal. 1994; Zhangetal. tipleobservationssuggestthatithasahighernormalizationanda
shallowerslopethanthatexpectedusingthemoststraightforward
assumptions about photoionization heating (Schayeetal. 2000;
⋆ E-mail:[email protected] McDonaldetal.2001;Theunsetal.2002;Boltonetal.2008).Be-
2 Peeples et al.
causethedegreeofsmall-scaletransversecoherenceissetbythe
Jeans length, andtheJeans length depends on thetemperatureof
thegas,studying thetransversestructureof theLyαforest might
giveinsightintotheIGMT-ρrelation(J.Hennawi,privatecommu-
nication,2007).InPeeplesetal.(2009,hereafterPaperI),weshow
thatwhilethermalbroadeningandpressuresupportbothaffectthe
longitudinalstructureoftheLyαforest,thermalbroadeningdom-
inates.Inthispaperweinvestigatetheeffectsofthetemperature-
densityrelationviapressuresupportandthermalbroadeningonthe
transversesmall-scalestructureoftheLyαforest.
ThegastemperatureaffectstheJeanslengthλ (andtheco-
J
movingJeanslengthλ )via
J,comv
π
λ ≡ c (2)
J srGρ
⇒λ = (1+z)σ H- 1 5π 3 Ω (1+z)3(1+δ) - 1/2
J,comv th 0 r 3 (cid:20)8π m,0 (cid:21)
= 782h- 1kpc (3)
σ Ω (1+δ) 1+z - 1/2
× th m,0 ,
(cid:16)11.8kms- 1(cid:17)(cid:20)(cid:18)0.25×(1+0)(cid:19)(cid:18)1+3(cid:19)(cid:21)
where 1 + δ ≡ ρ /ρ¯ is the gas overdensity and c =
gas b s
[5kT]/[3m] =σ 5/3 is the speed of sound in an ideal gas
th Figure1.Distributionofparticlesinthetemperature-overdensityplanefor
pexpressed as a multpiple of the 1-D thermal velocity σth, which thefiducialsimulationatz=2.4,withthreeimposedtemperature-density
wehavenormalizedtocorrespondto104K(Miralda-Escudéetal. relationsover-plottedaslabelled,aswellasthetemperatureandoverden-
1996; Schaye 2001; Desjacques&Nusser 2005). While thermal sitydistributionsforthefiducialandH4simulations.ThehotterH4gasis
broadeningaffectstheobservedIGMbysmoothingtheLyαforest preferentiallylessdensethanthelowerpressurefiducialgasandpressure-
in one-dimension (namely, along the line of sight), pressure sup- lessdarkmatter.
portsmoothsthephysicalgasdistributioninallthreedimensions.
Therefore,whilewefoundinPaperIthatσ dominatesthelongitu-
th
analyses.WenotethatPaperIincludesanextensivediscussionof
dinalLyαforeststructure,weexpectλ todominatethetransverse
J
thephysicalstructureoftheLyαforestinthesesimulations,soin
structure.Oursimulationsindicatethatthe“effective”Jeanslength
this paper we will focus only on those issues relevant to quasar
intheLyαforestissmallerthanthatgiveninEquation(3)byafac-
pairobservations.Alldistancesaregivenincomovingcoordinates
torofafew,probablyowingtoacombinationofgeometricfactors,
unlessotherwisestated.
theuniverseexpanding onthesametimescaleasthegasevolves,
andthecontributionofdarkmattertothegravitationalforces(see
alsoGnedin&Hui1998).
For Ωm =0.25 and ΩΛ =0.75, the relation between angular 2 SIMULATIONS
separation∆θandcomovingtransverseseparationRatz=2–4is
approximately We use the same 2×2883 particle 12.5h- 1Mpc comoving
smoothed particlehydrodynamic (SPH)simulationsevolved with
1+z 0.6 R
∆θ≈4.4′′ × . (4) GADGET-2(Springel2005)asinPaperI;henceweonlypresenta
(cid:18) 4 (cid:19) (cid:18)100h- 1kpc(cid:19) basicdescriptionhere.ThroughoutweadoptaΛCDMcosmology
Lines of sight with angular separations of 3–10′′ are needed to of(Ωm,ΩΛ,Ωb,h,σ8,ns)=(0.25,0.75,0.044,0.7,0.8,0.95),which
probe the Jeans scale of the IGM. While this scale is just larger is in good agreement with the Wilkinson Microwave Anisotropy
than the cutoff for the typical Einstein radius of galaxy lenses Probe5-yearresults(Hinshawetal.2009).Thiscosmology leads
(Schneider,Kochanek,&Wambsganss2006),newsearchesforbi- toagasparticlemassof1.426×106M⊙,whichismuchlessthan
naryquasarsarerevealingsamplesofafewtodozenswith∆θ. the expected typical Jeans mass of ∼7×109M⊙. As a conver-
10′′(Hennawietal.2006,2009). gence test, we use a 2×1443 particle simulation that is other-
Thispaperisorganizedasfollows.In§2,wedescribetheSPH wise identical to our fiducial simulation. The distribution of par-
simulationsused,aswellastheartificialtemperature-densityrela- ticles in the temperature-density plane for our “fiducial” simula-
tionsweimposeonthegastoisolatetheeffectsofpressuresupport tion at z=3 is shown in Figure 1. The “H4” simulation has the
and thermal broadening. In §3 we discuss how the temperature- sameinitialconditionsasthefiducialone,buttheheatingratefrom
densityrelationaffectsthetransversecoherenceoftheLyαforest, photoionization by the UV background is four times higher than
withparticularfocusonfluxcross-correlationfunctionsandcondi- inthefiducialsimulation.Anobvious consequence ofthishigher
tionalfluxprobabilitydistributions.Wefindthat,asexpected,the heating rate is that the H4 gas has higher temperatures than the
transversecoherenceoftheLyαforestacrosscloselypairedsight- fiducialgas. Amoresubtleeffect,alsoshowninFigure1,isthat
linesisdominatedbytheamountofpressuresupportintheabsorb- the hotter gas has a larger Jeans length and is hence smoother,
inggas.Theseconclusionsaresummarizedin§4.InanAppendix with a smaller fraction of the gas at high overdensity. We there-
andassociatedelectronictables,weprovideLyαforestspectraex- fore adopt three artificial temperature-density relations to isolate
tractedfromoursimulationsatseveraltransverseseparationsthat theeffectsofpressuresupport,thermalbroadening,andtheunder-
canbeusedtocreatepredictionstailoredtospecificobservational lying overdensity distribution. As in Paper I, the fiducial and H4
Scaleof theTransverseLyman-α Forest 3
Figure2.A12.5×1×1h- 1Mpccomovingsectionofthefiducialsimulation,inHIdensity,with- 8<lognHI<0(notethattheaspectratiohasnotbeen
preserved).Thethreegreensightlinesareseparatedby100h- 1kpccomoving;atz=2.4,correspondingtoaprojectedseparationof4.9′′.
Figure3.Samplepaired lines ofsightatz=2.4separated by∆r=50,100,150,200,and250h- 1kpccomoving, fromtoptobottom,withthefiducial
simulationontheleftandtheH4simulationontheright.Withineachcolumn,theblackspectraarethesame(r=0).Thetop,middle,andbottomgreenspectra
correspondtothethreegreensightlinesinFig.2,withv=0correspondingtotheleft-handsideofFig.2.
temperature-density relationsmimictheonesfound inthose sim- whilefortheflatrelationwesetallthegastoT=2×104K,regard-
ulations, while the flat T =2×104K relation is used so that we lessofdensity.
can study the effects of thermally-broadened pressure support in Ateachredshift—z=2,2.4,3,and4—weconsider200lines
theabsenceofoverdensity-dependentthermalbroadening.Weim- ofsightwithpairedsightlinesseparatedby∆r=50,100,125,150,
posethesetemperature-densityrelationsonthefiducialandH4gas 175, 200, 250, 300, 400, and 500h- 1kpc comoving for a total of
distributions,aswellasthefiducialdarkmatter,byassigningtem- 2200sightlinesperredshiftforeachoftheoverdensity–T-ρcom-
peraturesbasedsolelyonthelocalgas(ordarkmatter)overdensity, binationsdiscussedabove.Inallcasesweadjusttheintensityofthe
asdemonstratedinFigure1.ForthefiducialandH4relations,we UVbackgroundsothatthemeanfluxdecrementmatchesobserva-
setallgaswith1+δ>10toa“shocked”temperatureT=5×105K, tional estimates (see Paper I for details). In Table 1, we list the
4 Peeples et al.
Table 1. Observed mean flux decrements hDi ≡ h1- e- τi at z = 2.4,3, and 4 are from McDonaldetal. (2000); the z = 2 measurement is from
Faucher-Giguèreetal.(2008)withoutcorrectingformetalabsorption. Theobservedtemperature-density relations (T =T0[1+δ]α)atz=2.4,3,and4are
fromMcDonaldetal.(2001),withthez∼2measurementfromRicottietal.(2000).
z hDi observedT0[K] observedα fiducialT0[K] fiducialα H4T0[K] H4α ∆θat
100h- 1kpc
4.0 0.525±0.012 17400±3900 0.43±0.45 11700 0.54 28200 0.55 3.9′′
3.0 0.316±0.023 18300±1800 0.33±0.26 11000 0.57 25000 0.57 4.4′′
or18400±2100 0.29±0.30
2.4 0.182±0.021 17400±1900 0.52±0.14 10000 0.56 23000 0.57 4.9′′
or19200±2000 0.51±0.14
2.0 0.144±0.024 17700 0.32±0.30 8913 0.56 21380 0.57 5.4′′
adopted mean decrements and parameters for the observed, fidu- inherently smoother because they have more thermal broadening
cial,andH4temperature-densityrelations,aswellastheprojected thanthefiducialspectra.
angularseparationat100h- 1kpccomoving.
3.2 Cross-CorrelationFunctions
3 STRUCTUREOFTHEIGM&TRANSVERSELyα AcommonmethodforstudyingthetransversestructureoftheIGM
COHERENCE istolookatthefluxdecrementcross-correlationfunction,
hD (v)D (v+∆v)i
Togaininsightintotheeffectsoftemperatureonthetransverseco- ξ ≡ 1 2 , (7)
cross hDi2
herenceoftheLyαforest,welookathowpairedsightlinesdiffer
inthefiducialandH4simulationsin§3.1.Wethenquantifythese where D ≡ 1- F =1- exp(- τ) and the two sightlines are sep-
differencesbyexaminingtherelativechangesinthefluxdecrement arated by some ∆r (Miralda-Escudéetal. 1996; Rollindeetal.
cross-correlationfunctionin§3.2andtherelativetransversecoher- 2003). At ∆r=0, ξ is just the auto-correlation function. The
cross
ence of the conditional flux decrement probability distribution in cross-correlation functions for the z=2.4 fiducial and H4 sim-
§3.3. ulations at a range of ∆r are shown in the left-hand panels of
Figure 4. At small ∆r and ∆v, the gas in the fiducial simula-
tionhas ahigher ξ than thegasinthe H4simulation because
cross
3.1 Spectra thesmoother gasdistribution has lessrms density fluctuation. At
larger ∆r and ∆v, the H4 gas has a higher ξ owing to its
BeforedelvingintostatisticalmeasuresofthetransverseLyαfor- cross
greater coherence, as is visually evident in Figure 3. To quan-
est, it will be instructive to first consider the underlying physical
tify this relative change, ξ /ξ for the same selection of ∆r
structures.InFigure2,weshowasmallsectionofthefiducialsim- cross auto
is plotted in the right-hand panels of Figure 4. Although in real
ulationatz=2.4,wherebrighterregionscorrespondtohigherHI
spaceξ (∆r)=ξ (H∆r),invelocityspaceredshiftdistortions
densities.Theobservedtransmittedfluxiscalculatedassimply cross auto
preferentiallysuppresstheauto-correlationfunctionrelativetothe
F=e- τLyα, (5) cross-correlationfunction,causingξ >ξ forsomeregionsof
cross auto
parameterspace(McDonald&Miralda-Escudé1999;Marbleetal.
where τLyα is the optical depth to Lyα photons. As discussed in 2008b).Thehotter,higherpressure,H4simulationhasahigherrel-
detailinPaperI,
ativecoherence(largerξ /ξ )atsmall∆vthanthecolderfidu-
cross auto
τLyα ∝ nHI (6) cialsimulation.
∝ T0 - 0.7(1+δ)2- 0.7α. plot ξWec/oξmparaesaawfuindcetriorannogfe∆ofrmaotd∆elvs=in2F0ikgmures-51,awthze=re2w.4e;
(cid:18)104K(cid:19) this cocrrorsesspaountods to taking a slice at ∆v=20kms- 1 in the right-
The three sightlines in Figure 2 give rise to the top, middle, and handpanelsofFigure4.ToelucidatewhethertheH4gasismore
bottomgreenspectraatz=2.4intheleft-handpanelofFigure3. strongly correlated because it has higher pressure, or because, as
Figure 3 shows how pairs of spectra become more dissimilar as shownindetailinPaperI,hottergashasmorethermalbroadening
theirtransverseseparation,∆r,increases,andhowthisdissimilar- andthereforelesssmall-scalestructure,wealsolookatarangeof
ity differs between the fiducial and H4 simulations. Spectral fea- T-ρrelationsandoverdensityfields.Inthisandinseveralofthefol-
turesremainingcoherent over largescalescorrespond tophysical lowingfiguresthelinetype(solid,dashed,ordotted)corresponds
structures that are parallel to the plane of the sky (see, e.g., the totheadoptedoverdensityfield,eitherthegasoverdensitiesfrom
structuresat400<v<600kms- 1),whilespectralfeaturesdisap- thefiducialsimulation(solidlines),thegasoverdensitiesfromthe
pearingfromonesightlinetothenextcorrespondtophysicalstruc- H4simulation(dashedlines)orthedarkmatteroverdensitiesfrom
turesthat aremore parallel tothelineof sight (see, e.g.,thefea- thefiducialsimulations.Thelinecolorcorrespondstotheadopted
tures at v<300kms- 1). In general, the H4 spectra remain more equationofstate,i.e.theT-ρrelation,eithertheartificialfittothe
similarthanthefiducialonesas∆rincreases;weaimtodetermine relationfromthefiducialsimulation(greenlines),thefittothere-
to what extent this relatively higher coherence owes to pressure lationfromtheH4simulation(redlines),or assuming aconstant
supportratherthantothefactthattheH4spectraareindividually temperatureofT =2×104K(bluelines).
Scaleof theTransverseLyman-α Forest 5
Figure4.Thecross-correlationfunctionξcross≡hD1(v)D2(v+∆v)i/hDi2
(left)andξcross/ξauto(right)forthefiducial(top)andH4(bottom)simula-
tionsforsixdifferent transverseseparations ∆r=50,100,150,200,and
250h- 1kpccomoving.Notethatthevertical scaleintheleftpanels does
notextendto0.
InFigure5,thethreechoicesfortheoverdensityfieldclearly oFfigthueretr5a.nNsvoerrmsealsiezpeadractrioosns-∆corrrfeolrat∆iovn=fu2n0ctkimonss-,1ξcartoszs/=ξ2au.4to.,Tahsealfiunnecttyiopne
separate into three distinct groups, with the highest-pressure H4
(solid,dashed,ordotted)denotestheadoptedoverdensityfieldandtheline
gas having the most transverse coherence and the zero-pressure colortheadoptedT-ρrelation(see§2fordetails).Thethickblacktickmark
darkmatterhavingtheleast.Evennon-thermallybroadenedspec- denotes∆r=H∆v.
tra(whichwehavenotplottedtoavoidvisualconfusion)showthe
samerelativedecreaseincoherencewithincreaseintransversesep-
arationasotherspectrawiththesameunderlyinggasdistributions. theresultsforthedarkmatter,fiducial,andH4overdensityfields.
Withineachoverdensity group,ξ /ξ increaseswithincreas- ForH∆r.20kms- 1(∆θ.10′′),theimpactofthermalbroaden-
cross auto
ingthermal broadening (e.g.,the imposed H4T-ρrelationyields ingonanisotropyisgenerallysmallerthantheimpactofpressure.
higherξ /ξ atall∆rthanimposingthefiducialT-ρ).How-
cross auto
ever,loweringtheresolutionleadstooffsetsfromthefiducialcase
byaboutthesameamountasimposingdifferentT-ρrelations.The
same trends are seen at z=2,3, and 4, as shown in Figure 6. In
general,wefindthisdelineationisclearerat10.∆v.30kms- 1
3.3 ConditionalFluxProbabilityDistributions
thanat∆v=0oratlargervelocityseparations.Thestarksepara-
tionbyoverdensitydistributionofthenormalizedcross-correlation The structure of one-point flux probability distribution function
functionasafunctionoftransverseseparationisaclearsignthat (PDF) depends on both the thermal history and current thermal
pressureplaysanimportant roleinthetransversestructureofthe state of the gas, leading to a complex relationship between the
Lyαforest. effects of pressure support and thermal broadening on the PDF
A common use for the flux decrement cross-correlation (Paper I). On the other hand, the interpretation of the condi-
function is to measure the anisotropy in the Lyα forest tional probability distribution function between paired sightlines
causedbyline-of-sightvelocitydistortions(Coppolanietal.2006; (Miralda-Escudéetal.1997)isrelativelystraightforward. Forex-
D’Odoricoetal.2006),suchasfortheAlcock&Paczynski(1979) ample, if for strongly absorbed pixels with 0.86D <1.0, the
1
test(Huietal.1999;McDonald&Miralda-Escudé1999).InFig- pixelsseparatedby∆vonasightline∆rawayaremorestrongly
ure 7, wecompare ξ (∆v=0,∆r) to the autocorrelation func- absorbed than randomly expected, then this might be a signature
cross
tionatthesamescale,ξ (H∆r),atz=2.4;highervaluesindicate of strong transverse coherence and thus a large Jeans length. In
auto
higher levels of anisotropy. As in Figure 5, the models separate Figure9 we plot the flux decrement difference probability distri-
into groups of overdensity, and the differences between our low- butions, p(D - D ),for∆v=0and∆r=150h- 1kpcand several
2 1
resolution and fiducial cases are comparable with imposing dif- binsofD ,forthefiducial,H4,andlowresolutiongasatz=2.4.
1
ferent T-ρ relationson thefiducial gas. Figure8 shows thesame BylookingatthePDFofthedecrementdifferences,wecaneasily
statistic for a smaller set of models at z=2, 3, and 4. As men- quantifythesimilarityoffluxdecrementpairs.Themorestrongly
tioned above, in real space ξ (∆r) = ξ (H∆r), but in (ob- thedistribution peaks around D =D , themore coherent are the
cross auto 2 1
served) velocity space, redshift distortions introduce anisotropy transversestructures.Whilethedifferencesbetweenthetwosimu-
(Marbleetal.2008b).Becausethermalbroadeningisaninherently lationsarenotdramatic,theH4modelisconsistentlymorestrongly
one-dimensionalanisotropicphenomenon,higherthermalbroaden- peaked around D =D , witha stronger signature at low D . For
2 1 1
ingleadstohigheranisotropy;weseethiseffectforeachoverden- mostchoicesofD ,thisdifferenceismuchmorepronouncedthan
1
sitydistributioninFigures7and8.Pressure,ontheotherhand,is thedifferencebetweenthefiducialandlow-resolutionsimulations,
athree-dimensionalinherentlyisotropicphenomenon:higherpres- indicatingthatour2883 particlesimulationsgiverobustresultsfor
surethereforeleadstolessanisotropy, asweseefromcomparing thisstatistic.
6 Peeples et al.
Figure8.Normalized cross-correlation functions showingtheanisotropy
oftheLyαforest,ξcross/ξauto,asafunctionof∆v=H∆r,atz=4,3,and
2.ThemodelsaredenotedasinFig.5
InPaperIweshowedthatthefluxdecrementPDFsforeachof
theseT-ρrelationsarefairlydistinct,sosomeofthemodeldiffer-
encesin p(D - D )couldreflectdifferencesintheunderlyingflux
2 1
PDFs. We can remove this effect by converting from flux decre-
ment D to pixel rank R≡ p(<D), the fraction of pixels with a
fluxdecrement lowerthanD.Ofcourse, afullysuccessfulmodel
shouldreproducetheobservedPDF,butherewewishtofocuson
transversecoherenceand,therefore,removeanydifferencesinthe
PDFcaused by different temperature-density relations. Figure 10
showsthatspectrageneratedfromtheH4gashaverankdifference
distributionsmore strongly peaked around R - R =0 than spec-
2 1
Figure6.Normalizedcross-correlationfunctions,ξcross/ξauto,asafunction trafromthelowerpressure,fiducialgasspectra.Changingtheim-
ofthetransverseseparation∆rfor∆v=20kms- 1atz=4,3,and2,from
posedtemperature-density relationhaslesseffect onthedistribu-
toptobottom.ThemodelsaredenotedasinFig.5.Thethickblacktickmark
denotes∆r=H∆v. tionsthanchanging theunderlyinggasdistribution,implyingthat
(asexpected)pressureratherthanthermalbroadeningaccountsfor
the larger transverse coherence. In general, the larger coherence
appears at all redshifts, but it weakens with increasing ∆r. Non-
thermallybroadenedspectra(notshown)havebroaderR - R dis-
2 1
tributions,sothermalbroadeningdoesplaysomeroleintransverse
coherence. As with previous statistics, however, the lower reso-
lution spectra differ from the fiducial case by about as much as
spectrageneratedfromdifferentimposedT-ρrelations.Figure11
presentsthez=2.4predictionsingreaterdetailforthefiducialand
H4gas only, plottingfive ranges of R and comparing ∆v=0 to
1
∆v∼20kms- 1.Themodelsaremosteasilydistinguishedatsmall
∆vandatsmall∆r.
In general, the slope of the temperature-density relation is
much more difficult to observationally constrain than T because
0
mostmethodsformeasuringtheT-ρrelationaresensitivetoonlya
limitedrangeofτ andhence1+δ.Because(uptosaturation)we
HI
canlimitourselvestoaparticularrangeofopticaldepthandthus
1+δ whenusingconditionalrankdistributions,itmightbepossi-
bletousethistechniquetoconstraintheslopeofthetemperature-
density relation. We cannot test this possibility using our current
simulationsbecausethefiducialandH4temperature-densityrela-
tionshavesimilarslopesatallredshifts(seeTable1).
Figure7.Normalized cross-correlation functions showingtheanisotropy 4 CONCLUSIONS
oftheLyαforest,ξcross/ξauto,asafunctionof∆v=H∆r,atz=2.4.The Recentefficientsearchesforbinaryquasarshaveyieldedlargesam-
modelsaredenotedasinFig.5
plesofquasarswithangularseparationsof.10′′ (Hennawietal.
2006, 2009). The closely paired Lyman-α forest sightlines from
Scaleof theTransverseLyman-α Forest 7
Figure 9. Flux decrement difference probability distributions, p(D2- D1) v. (D2- D1), at z=2.4, for ∆v=0 and ∆r=150. The three columns show
D1∈[0.2,0.4)(left),D1∈[0.4,0.6)(middle),andD1∈[0.8,1.0](right),withfiducialinblack,H4inpurple(dotted),andthelowresolutionsimulationin
grey.
suchquasarpairsareidealforstudyingthesmall-scaletransverse investigation; we also thank Joe Hennawi and Eduardo Rozo for
structureoftheintergalacticmedium.Wehaveshownusingasetof helpful discussions and comments. Weare grateful to the anony-
smoothed particlehydrodynamic simulationswithdifferent equa- mousrefereeforthoughtfulsuggestionsonthetext.Thisworkhas
tions of state that the coherence of transverse structure at these been supported in part by NSF grant AST-0707985 and NASA
scalesisdeterminedprimarilybythelevelofpressuresupport,i.e. ADPgrantNNX08AJ44G.
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APPENDIXA: FORMATOFASSOCIATEDELECTRONIC
TABLES
Weprovideintheformofelectronictablesoursimulatedspectra,
theHIopticaldepthasafunctionofvelocityandtransversesepa-
ration,alongpairedsightlinesfromthefiducialandH4simulations