Beamed Lyman Alpha Emission through Outflow-Driven Cavities

2.4 MB·

by  Christoph Behrens

Astronomy&Astrophysicsmanuscriptno.rev2˙arxiv (cid:13)c ESO2014
July4,2014
Beamed Lyα Emission through Outflow-Driven Cavities
C.Behrens1,M.Dijkstra1,2,3,andJ.C.Niemeyer1,
1 Institutfu¨rAstrophysik,Georg-AugustUniversita¨tGo¨ttingen,Friedrich-Hund-Platz1,D-37077Go¨ttingen
e-mail:[email protected]/[email protected]
2 MaxPlanckInstituteforAstrophysics,Karl-Schwarzschild-Str.1,85741,Garching,Germany
3 InstituteofTheoreticalAstrophysics,UniversityofOslo,Postboks1029,0858Oslo,Norway
e-mail:[email protected]
DraftJuly4,2014
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ABSTRACT
1
0
We investigate the radiative transfer of Lyα photons through simplified anisotropic gas distributions, which represent physically
2
motivatedextensionsofthepopular’shell-models’.Ourstudyismotivatedbythenotionthat(i)shellmodelsdonotalwaysreproduce

n observedLyαspectrallineprofiles,(ii)(typical)shellmodelsdonotallowfortheescapeofionizingphotons,and(iii)theobservation
a &expectationthatwindsaremorecomplex,anisotropicphenomena.WeexaminetheinfluenceofinclinationontheLyαspectra,
J relativefluxesandescapefractions.Wefindthefluxtobeenhanced/suppressedbyfactorsuptoafewdependingontheparameter
rangeofthemodels,correspondingtoaboostinequivalentwidthofthesameamplitudeifweneglectdust.Ingeneral,lowermean
2
optical depths tend to reduce the impact of anisotropies as is expected. We find a correlation between an observed peak in the –
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occasionallytriple-peaked–spectrumatthesystemicvelocityandtheexistenceofalowopticaldepthcavityalongthelineofsight.

Thiscanbeofimportanceinthesearchforionizingphotonsleakingfromhigh-redshiftgalaxiessincethesephotonswillalsobeable
]
A toescapethroughthecavity.
G Keywords.High-redshiftGalaxies–RadiativeTransfer
.
h
p
- 1. Introduction Recently however, NIR spectrographs have measured rest-
o frame optical nebular lines from galaxies at z ∼ 2 (where it is
tr ThereisampleobservationalevidencethatLyαphotonsscatter possible to detect Hα) and z ∼ 3 (where it is possible to de-
s through outflowing HI gas as they emerge from the interstellar tect [OIII]). The detection of these nebular lines constrains the
a
[ mediumofstarforminggalaxies.Inlocalgalaxies,gaskinemat- systemicvelocityofgalaxies,andthereforethespectralshiftof
icsoninterstellarscalesisoneofthekeyfactorsthatdetermines theLyαlinerelativetotheirsystemicvelocity(McLindenetal.,

2 whether Lyα photons escape (Kunth et al., 1998; Atek et al., 2011;Kulasetal.,2012;Hashimotoetal.,2013).Importantly,it
v 2008).Moreover,observedLyαspectrallinesinhigherredshift hasbeendemonstratedthathavingboththeshiftandthespectral
0 (z ∼ 3) galaxies have P-Cygni type profiles which consist of lineshapeposesachallengetotheshellmodelsforafractionof
6
a redshifted emission line and a blueshifted absorption trough, Lyαemittingsources,i.e.sincetheDopplerparameterbderived
8
whichareclearcharacteristicsofthepresenceofanoutflow(e.g. from this data seems not to fit the observed low-ionization ab-
4
. Shapleyetal.,2003).Theubiquitouspresenceofoutflowsisalso sorption(Kulasetal.,2012),althoughtheexactfractionofemit-
1 revealedbytheblueshiftedlow-ionizationmetalabsorptionlines ters problematic for the shell model is still debatable. There is
0 inalargefractionofLymanBreakGalaxies(LBGs).Thesesame alsoevidencefortheexistenceofholesintheHIdistributionof
4
LBGstypicallyexhibitaLyαemissionlinethatisredshiftedby someLAEsthatareonlypoorlyfittedbytheshellmodel(Chonis
1
∼ 2−3×theoutflowvelocityinferredfromtheabsorptionline etal.,2013).Hence,thereisincreasingobservationaldemandfor
:
v data,andstronglysuggestthatLyαphotonshavebeenscattered modelsthatgobeyondtheshellmodel.Moreover,fromaphys-
i byHIwithintheoutflow(e.g.Steideletal.,2010). icalpointofviewtheshell-modelisnotsatisfactorybecauseits
X
simple geometry does not capture the complex structure of the
r Modeling cold, outflowing interstellar gas is an extremely gasinoutflows.
a difficulttask,andpracticallyrequiressimulationstofullyresolve
the interstellar medium (see Dijkstra & Kramer, 2012, and ref- Goingbeyondtheshellmodelisclearlycomplicated:break-
erencestherein).ModelsofLyαemittinggalaxieshavethusfar ingsphericalsymmetrycausesthepredictedspectrallineshapes
employed a ‘subgrid’ model of scattering through the outflow, to depend on viewing angle. Moreover, departures from spher-
in which the outflow is represented by a spherical shell of HI ical symmetry introduce new parameters that significantly in-
gas(seeAhnetal.,2003;Verhammeetal.,2006,foradescrip- crease the volume of parameter space that can be explored. In
tionoftheshellmodel).Thissphericalshellisgeometricallythin this paper, we investigate Lyα transfer through non-spherical
(thicknessis10%oftheradiusoftheshell),andisparameterized models for winds that are still relatively simple & physically
(primarily)byanHIcolumndensity,anoutflowvelocity,anda motivated.Examplesofmodelswestudyinclude:(i)shellswith
dust optical depth. It has been demonstrated that these models holes,(ii)bipolarwinds,and(iii)socalled‘cavity’models(see
canprovidegoodfitstoobservedLyαlineshapes(Verhammeet §2.1-§2.3fordetails).Thefirsttwoclassesofmodelsapproach
al.,2008;Schaerer&Verhamme,2008;Vanzellaetal.,2010). asphericalshellmodelwheneithertheholebecomesarbitrarily
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C.Behrensetal.:BeamedLyαEmissionthroughOutflow-DrivenCavities
small,orwhentheanisotropicvelocitycomponentofthebipolar ‘cavity’modelsrepresentascenarioinwhichgasisoutflowing
model vanishes. Duval et al. (2013) have investigated different perpendiculartoagalacticdisk.Thispaperhastwomaingoals:
modifications of the shell model, namely statistically isotropic, (i)toinvestigatethevariationinfluxfordifferentviewingangles
dusty and clumpy shells. These models are in statistical sense which will give us an estimate for the expected boost in equiv-
stillisotropicandhavecoveringfactorsnear1,yieldingonlyfew alent width (EW) with respect to the isotropic case, and (ii) to
linesofsightthatareopticallythin,whilethemodelsdiscussed investigate whether there are robust observational spectral sig-
here have strong anisotropies with many optically thin lines of naturesoftheLyαlineforsightlinesthatgothroughacavity.
sight.Importantly,Duvaletal.(2013)(andLaursenetal.(2013)) The outline of this paper is as follows: in § 2 we introduce
havefocussedonstudyingboostsinEW,averagedoverallsight- ourmodels.In§3.1,wediscussandinterpretourresultswitha
lines.Laursenetal.(2013)pointsoutthattherecanbedepartures focusonindividualdust-freerealizationsofourmodelfamilies.
inthisboostfromtheaveragealongindividualsightlines,which In3.2and§3.3,weconsidertheinfluenceofdustandgeneralize
isthemainfocusofourwork. ourresultswithaparameterstudy.
Acommonpropertyofallourmodelsisthatthereexistsight-
lines through the wind which contain a very low (or zero) HI-
2. OurModelsandParameters
column density. Our wind models thus include possible escape
routes for ionizing photons (which clearly do not exist in the In order to investigate the variation of fluxes and spectra with
shellmodels).Thispropertyofourmodelsisimportant,andmo- viewingangle,wehavetobreakthesymmetryofthemodelsby
tivatedbyascenarioinwhichionizingphotonsescapeefficiently introducing anisotropic velocity and/or density fields. Like the
onlyalongafractionofsightlines.Thispictureismotivatedby shell model, our models are primarily motivated by situations
observations of LBGs for which outflowing low-ionization ab- wheregalacticwindsandotherfeedbackmechanismsdriveout-
sorption line systems, which trace ‘cold’ (T ∼ 104 K) gas, are flows,blowingoutorionizingneutralgas.Wetakeintotheac-
not always fully covering the UV-emitting regions1; For exam- count the asymmetry of such winds that are expected to occur
ple, Jones et al. (2013) find that the maximum low-ionization particularly in the transverse direction of the plane. This intro-
covering fraction for their z > 2 is 100% in only 2 out of 8 ducesananisotropyinthisdirection.Wedefinethe‘inclination’
galaxies (also see Heckman et al. 2011, who find evidence for as the angle between the z-axis and a unit vector towards the
a low covering factor of optically thick, neutral gas in a small observer. To quantify the anisotropy of fluxes and spectra, we
fractionoflowerredshiftLymanBreakAnalogues).Thiscover- define a set of observers, each observing photons within a cer-
ingfactorofcoldoutflowinggasdecreaseswithredshift(Jones tain angular bin. Bins are equally spaced in cos(θ) so that each
et al., 2012, 2013), which may explain that the escape fraction observer sees the same area of the unit sphere, meaning that in
ofionizingphotonsincreaseswithredshiftashasbeeninferred2 isotropic cases, all observers should detect an equal number of
independently by observations of the Lyα forest and the UV- photons.
LFofdrop-outgalaxies(e.g.Kuhlen&Faucher-Gigue`re,2012;
Robertsonetal.,2013).Finally,thepossibilitythationizingpho-
2.1. The’Bipolar’Model
tons escape highly anisotropically naturally explains the appar-
entlybimodaldistributionoftheinferredescapefractioninstar Here, we assume the wind to drive the expanding shell asym-
forming galaxies, in which a small fraction of galaxies have a metrically. This deforms the shell over time and displaces it
large fescandalargefractionpracticallyareconsistentwithhav- anisotropically. Likewise, the density evolves with inclination,
ing fesc = 0(Shapleyetal.,2006;Nestoretal.,2011;Vanzella becausemassconservationensuresthatthemasswithinasolid
etal.,2012). angle remains constant. We define the velocity at an angle θ to
FromaLyαtransferpoint-of-view,theexistenceoflowHI- be
column density channels can have major observational conse-
quences. For non-spherical gas distribution, Lyα generally es- v(r)=er(vbcos(θ)+vc) , (1)
capes anisotropically (see Laursen & Sommer-Larsen, 2007;
wheree istheunitvectorfromthecenterto r,v isthemagni-
Verhammeetal.,2012;Zheng&Wallace,2013,andreferences r b
tudeoftheanisotropicvelocitycomponentandv istheisotropic
therein),wherethefluxcanvarybyasmuchasafactorof> 10 c
component. At a given inclination cosθ, the shell will be dis-
depending on the viewing angle (Verhamme et al., 2012). We
placedbysomedistancesfromtheoriginalposition,
expect this anisotropy to be potentially more extreme in mod-
elsthatcontainlow-NHI sightlines,whichwerefertoas‘holes’ s=(vbcos(θ)+vc)t. (2)
and/or‘cavities’.Thesecavitiesmaycorrespondtoregionsthat
have been cleared of gas and dust by feedback processes (see Here,tissometimeparameterthatcontrolstheevolutionofthe
Nestor et al., 2011, 2013, who describe a simple ‘blow-out’ shell’sshape.Wecautionthereaderthatforourradiativetrans-
model). fer, we assume a steady state, e.g. t does not evolve during the
calculation. t is given in units of the simulation box crossing
InthispaperwestudyLyαtransferthroughsimplifiedmod-
time,e.g.sbecomestheboxlengthfort=1.Thedensitywithin
elsoftheISMwhichincludeoutflow-drivencavities.Ourmod-
theshellatagiveninclinationreads
els consist of several ‘families’. The ‘shells-with-holes’ and
‘bipolar-wind’modelscaneasilybeconnectedtothetraditional r2+rr +r2
shellmodels,whichmakesiteasiertointerpretourresults.The ρ=ρ i i o o , (3)
03s2+r2+rr +r2+3s(r +r )
i i o o i o
1 Acaveatisthatthecoveringfactorislessthanunityoverarange whereρ issomehydrogendensitydefinedsuchthatatt=0
ofvelocities.Coldgasmovingatdifferentvelocitiescancoverdifferent 0
partsofunresolvedUVemittingsources,anditremainspossiblethat N(cid:48) =ρ (r −r) . (4)
H 0 o i
thecoveringfactorintegratedovervelocityis1.
2 Thisredshiftevolutionappearstoberequiredinordertobeableto Wedenotethiscolumndensitywithanadditionalprimebecause
reionizetheUniverse(Kuhlen&Faucher-Gigue`re,2012). it is not the effective column density if t (cid:44) 0. In Fig. 1, this
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C.Behrensetal.:BeamedLyαEmissionthroughOutflow-DrivenCavities
Fig.1.Illustrationofthe’Bipolar’modelforthreedifferenttimeparameters.Arrowsindicatevelocityvectors,contoursthedensity
distribution. As the time parameter evolves from left to right, the anisotropy in the bulk velocity becomes visible in the density
distribution.
setupanditsdependenceonthetimeparameterisillustrated.In Table1.Summary:ModelParameters
practice,weparametrizev andv bythesumofbothv andthe
c b tot
fraction fbthatgoesintoparameterizingtheanisotropicvelocity Model ParameterSet
field Shell N ,v,b
H
Bipolar N(cid:48),b,v , f,t
H tot
ShellwithHoles N ,v,b,Ω
H
vb = fbvtot . (5) Cavity NH(cid:48)(cid:48),b,parametersoftheparabolae,vl
2.3. The’Cavity’Model
2.2. The’ShellwithHoles’Model
In a later stage, the galactic feedback might have completely
sweptawayorionizedthegasalongitspath,whileintheplane,
cold gas is still accreted. In an extreme scenario, this leads to
a quasi-static situation where a small region along the ±z-axis
is essentially evacuated. This model is somewhat similar to the
shellwithholesmodel,butduetothegaseoustorusaroundthe
cavity,thereisahighprobabilitythatphotonscomingfromran-
domanglesarescatteredsothattheyareeventuallyalignedwith
thez-axis.Here,ourdensityprofileisdescribedbytheintersec-
tion of two rotated parabolae, p (x) = a (|x| − b )2 + c and
1 1 1 1
p (x) = a (|x| − b )2 + c where x is the perpendicular dis-
2 2 2 2
tancefromthez-axis.Thedensityatapointatdistance x(cid:48) from
the z-axis and at a height h above the plane is non-zero when
h< p (x(cid:48))andh< p (x(cid:48)).
1 2
We define r to be the radius of the object at z = 0 and set
c
(cid:48)(cid:48)
NH = ρ.Welabelthecolumndensitywithtwoprimesbecause
rc
itisnotequivalenttothecolumndensitiesinthemodelsabove
sincetheeffectivecolumndensityseenbyaphotonemittedatan
Fig.2.Illustrationofthe’ShellwithHoles’model.Arrowsindi- initialangleθ0 willnon-triviallydependonthisangleduetothe
catevelocityvectors,contoursthedensitydistribution. shape of the density distribution (also see Fig. 3) Additionally,
weaddalinearvelocityfield
z
v=e v , (6)
Assuming a spherical expanding hydrogen shell around the zzmax l
emitter, in one limiting case the wind emerging from the ISM which is proportional to the height over the plane and parallel
might just blow off the cap of the spherical shell in the ±z- tothe±z-axis.z isthez-coordinateofthe’tip’ofthedensity
max
direction,carvingaconicalregionoutoftheshell.Acutthrough distribution.ThissetupisillustratedinFig.3.
the density field of such a setup can be seen in Fig. 2. The
solidanglesubtendedbytheconicalholesintheshell,Ω,isthe
only new parameter in this setup and can be also parametrized 3. Results
by the angle θ as indicated in Fig. 2. As usual, we measure
H 3.1. FluxandSpectraforIndividualModels
thefrequencyofescapingphotonsinthedimensionlessquantity
x = ∆ν/ν ,where∆νisthephysicalfrequencycenteredonthe Inthissection,weshowresultsforthreeindividualrealizations
D
Lyαlinecenterandν istheDopplerfrequency. of our models. If not stated otherwise, we set the Doppler pa-
D
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C.Behrensetal.:BeamedLyαEmissionthroughOutflow-DrivenCavities
Fig.3. Illustration of the ’Cavity’ model with three different parameter sets for the parabolae that define the density distribution.
Arrowsindicatevelocityvectors,contoursthedensitydistribution.
rameterbto40km/sandinserttheLyαphotonswithaGaussian of the surface of the bipolar shell point towards the xy-plane.
distribution around the line center, where the width σ is set to Photons escaping the shell in these areas will most likely not
100 km/s. 107 photons were calculated for every realization to escape with a smallangle θ. Photons that doescape with small
ensure convergence. For the models presented here, we show angles most probably escape from the poles. This leads to en-
thecolumndensityandinitialopticaldepth(foraphotonatline hancedfluxatintermediateangles,becausephotonsescapingat
center)asafunctionofinclinationinFig.4. these angles can statistically escape at every point of the sur-
face, while those at small/large angles are confined to certain
areas.Thiscouldalsobedescribedasa’projectioneffect’.Our
3.1.1. Bipolar explanation is further supported by the fact that the effect be-
In the upper panel of Fig. 5, we show the flux as a function comesstrongerforabroaderinputspectrum.Thebluepartofthe
of viewing angle for a particular case of the bipolar model Gaussianissubjecttoscatteringsevenforphotonstraversingthe
(v = 200km/s, f = 0.5, N(cid:48) = 1020 cm−2,t = 0).Valuesare shellalongthez-axis.Thebroaderthespectrum,themoreblue
tot b H
giveninunitsofthecorrespondingisotropicdistributionamong photonsarescatteredatthepoles,redistributingtheirorientation
the observers. Let F = n/N be the relative flux an observer andfurtherenhancingmeasuredfluxatintermediateangles.
detects, where n is the number of photons received by the ob- ThespectrashowninthebottompanelsinFig.6againshow
serverandN thetotalnumberofphotonssimulated.Further,let a peak at x = 0 for observers looking down the z-axis (bottom
F = N/n be the relative flux assuming isotropy with n leftpanel).Foraninputspectrumwithawidthof100km/s,itis
0 bins bins
the number angular bins. The flux in these bins can be seen as slightlyshifted.Thiscanbeattributedtothesuppressionofthe
thefluxanobserverataspecificinclinationwouldobtain.F/F bluepartoftheinputspectrumduetoscatteringsintheoutflow-
0
measurestherelativefluxrelativetotheisotropiccase.Westress ingmaterial.Forsmallerwidths,thepeakisclearlycenteredat
that ssuming the object to be dust-free, this quantity is propor- x =0again.Forobserversaroundθ =40◦,theamplitudeofthe
tionaltotheEWoftheobservedLyαline. peak is lower. If we go to larger angles, the central peak van-
Since for the setup in Fig. 5 the time parameter is zero, the ishesandtheredpeakvisibleinallofthethreespectrabecomes
density field is equivalent to the isotropic shell model, but the dominant.
velocityfieldexhibitsananisotropy,loweringtheopticaldepth
alongthez-axisbyafactorof103 withrespecttolinesofsight
3.1.2. ShellwithHoles
within the xy-plane. As can be seen in the upper panel of Fig.
5 the flux variation is small, about 15% more photons escape Thedependenceoffluxandspectraforoneparticularcase(v =
at θ ≈ 0◦ than at θ ≈ 90◦. In the bottom panels of Fig. 5, 200 km/s, N = 1020 cm−2, Ω = 10%) of the shell with holes
H
weshowspectraobtainedatthreedifferentobservationsangles. modelisshownintheupperpanelofFig.7.
Horizontallinesinthetoppanelshowatwhichanglesthespectra AscanbeseeninFig.7,theobservedfluxdecreasesabruptly
whereevaluated.Fortheseparameters,theshapeofthespectrum atanangleof≈25◦,whichreflectstheangularsizeoftheholes
doesnotchangesignificantlywithobservationangle.Thethree in the shell. In the lower panels of Fig. 7, we show spectra of
differentlinesFig.5showtheresultsfordifferentinputspectra the photons in three different angular bins. Their positions are
with a width of 100/40/10 km/s (solid/dotted/dashed lines). As indicated by vertical lines in the upper panel. The bottom left
expected,anarrowinputspectrumleadstoahigherandnarrower spectrumshowsthespectrumforanobserverthatdirectlylooks
peakforsmallobservationangles.Thefluxdoesnotchangesig- “down the hole”. As expected, one can clearly identify the un-
nificantlywithrespecttothewidthoftheGaussian. processed,Gaussianinputcenteredaround x=0.Thespectrum
In Fig. 6, we show the same quantities for a more evolved in the bottom center shows a spectrum directly after the tran-
setup with t = 0.15 which will we will refer to as the ’late sition; the transition itself occurs so fast that we do not see it
bipolar’case.Here,thefluxdistributionshowsacounterintuitive occuring in one of the bins. The bottom right spectrum shows
trend; while flux is suppressed for large observations angles, it an observer at an angle of ≈ 67◦. Here, the peak at line center
isalsosuppressedforverysmallangles,leadingtoamaximum isclearlygone.Instead,thespectrummoreresemblestheorigi-
at around θ = 38◦. Detailed investigation shows that this is a nal shell case. We note that observers looking “down the hole”
geometricaleffectfromthedeformationoftheshell.Mostparts see a Lyα line that is not shifted. In this particular setup, ob-
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C.Behrensetal.:BeamedLyαEmissionthroughOutflow-DrivenCavities
107
Shell w/ Holes
106 Bipolar early
1.0
Bipolar interm.
20 105 Bipolar late
0
1 0.8 Cavity
× 104
]
2− 0.6 τ 103
m
c 102
[ 0.4
NH 101
0.2
100
0.0 10-1
0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90
θ [◦] θ [◦]
Fig.4.Neutralhydrogencolumndensity(left)andopticaldepth(right)ofphotonsstartinginthecenterofthesetupwith x=0for
realizationsofdifferentmodelsdiscussedinSec.3.1asafunctionoftheangleθbetweenthelineofsightanthethez-axis.Notethe
log-scalingintherightplot.
serving face-on will boost the flux and therefore the EW by a spectraalonewhetherornottheyarelookingdowntheholeor
factor of roughly 1.7 (assuming no scattering of the continuum notiftheinitiallineismuchnarrowerthan100km/s.Themax-
emission here). It is interesting that apart from the sharp tran- imumamplitudeofabroadGaussianisnotbrightenoughtobe
sition at the hole’s half opening angle, the spectrum does not distinguishedfromtherestofthespectrum.
evolve significantly. This can be seen by comparing the center Wenotethatincontrasttothelatebipolarmodel,wedonot
bottom and right bottom spectrum. We stress that both the flux seeasuppressionofthefluxatsmallanglesduetogeometrical
and the spectrum change very rapidly and are nearly constant effectsalthoughthedensityfieldinthiscaseisclearlydeformed
before and after the transition. Beyond the transition, the spec- aswell.Weattributethistothefactthatthedifferencesinoptical
trum resembles the normal shell case. Before the transition, it depthamongdifferentlinesofsightaremuchlargerthaninthe
consistsoftwocomponents,theinitialunscatteredspectrumand discussedbipolarsetup.Incontrasttotheshellwithholesmodel,
anothercontributionfromashell-likespectrum.Thelattercon- in this case the transition in the spectral shape and the flux is
tributioncomesfromphotonsthatmerelyscatterintothelineof not as rapid, but more smoothly. This is can be explained by
sight.Thisimpliesthatfordecreasingholeradiusthespectrum consideringthesmoothtransitionincolumndensityandoptical
asymptotestowardtheoriginalshellcase. depth as shown in Fig. 4, as well as by the fact that the escape
mechanismforthecavitymodelisdifferent(seebelow).
3.1.3. CavityModel
3.2. TheInfluenceofDust
IntheupperpanelofFig.8thefluxdistributionforonerealiza-
tion of the cavity model is shown. The model parameters here While not being the main focus of this paper, the influence
areN(cid:48)(cid:48) =1020 cm−2,v =200km/s,weusetheconfigurationil- of dust on the aforementioned phenomena is also of interest.
H l
lustratedintheleftplotofFig.3.Similartotheshellwithholes Therefore,wererantheindividualcasespresentedintheprevi-
model,wegetasharptransitionatsome“effectiveopeningan- oussectionswithvaryingdustcontent.Weintroduceddusttobe
gle”. Here, flux is suppressed up to a factor of 6 for observers proportionaltohydrogencontent,followingtheimplementation
looking edge-on, which as discussed above would also corre- given in Verhamme et al. (2006) with an albedo of 0.5 and an
spond to a boost/suppression of the EW by a factor of 3 with isotropicphasefunctionincaseofscatteringondust.Wequan-
respect to what one expects in an isotropic environment. When tifythedustcontentintermsoftheadditionalopticaldepthτD.
looking at the three spectra shown at the bottom of Fig. 8, one Similartothehydrogencolumndensity,τD isthedepththrough
noticesthatincontrasttotheshellwithholescase,thespectral theshellfortheshellwithholesmodel,theopticaldepthatt=0
propertiesdonotchangeabruptly.Theamplitudeofthepeaksis forthebipolarmodelsandtheopticaldepthintheplaneforthe
reduced with viewing angle, and the overall amplitude shrinks, cavitymodel.TheresultsareshowninFig.9,10,11,and12.All
but the input spectrum is not visible anymore at least for the runswereperfomedusinganinputspectrumofwidth100km/s,
fiducial case with an width of the input spectrum of 100 km/s andassumingb=40km/s.
(solid).Thereasonforthisdifferentbehaviouristhatwhileob- As expected, the dependence of the flux distribution on in-
servers near face-on position still see a significant fraction of clinationingeneralbecomeslargerforhigherdustcontent.For
photons that directly traversed the cavity, the amount of pho- the shell with holes case in Fig. 11, we see a boost in the flux
tons that merely scattered into the line of sight is much bigger. anisotropy by a factor of 3 with respect to the dust-free case:
Looking closely at the left and center spectra, one can see the photons not escaping through the holes are subject to destruc-
right shoulder of the Gaussian input spectrum. This modified tion by dust, so relatively the flux through the holes increases.
Gaussian is gone far away form the transition, which leads to The same accounts for both the bipolar cases in Fig. 9 and 10,
negligible flux around x = 0, as can be seen in the right bot- although the effect is less strong. Interestingly, dust does not
tomplotofFig.8.Fornarrowerinputline,werecovertheinput strongly influence the cavity model as shown in Fig. 12 if one
spectrumagain.Weconcludethatwhilewegetalargefluxsup- compares tothe shellwith holescase. Surprisingly, the τ = 2
D
pressionforthissetup,observerscouldonlydistinguishfromthe just increases the flux boost by a factor ≈ 20%. Analysis of
5
C.Behrensetal.:BeamedLyαEmissionthroughOutflow-DrivenCavities
Bipolar Model - Early
1.15
1.10
0
F 1.05
/
F
1.00
0.95
a) b) c)
0.90
0 10 20 30 40 50 60 70 80 90
) Θ
3
−
10× a) b) c) 100 km/s
n ( 0.5 10 km/s 0.5
y bi 0.4 40 km/s 0.4
c
n
e 0.3 0.3
u
q
e 0.2 0.2
r
f
r
e 0.1 0.1
p

F0 0.0 0.0
/ 20 10 0 10 20 10 0 10 20 10 0 10
F
x x x
Fig.5. Top: Flux as a function of angle of observation for the shell with holes model. Units are chosen in a way so that a value
of1wouldcorrespondtotheisotropiccase.Bottom:Spectrumevaluatedatthreedifferentangularbins(indicatedbyverticallines
above).Resultsareshownforinputspectrawithawidthof100(blue,solid),10(green,dashed)and40(red,dotted)km/s.Spectra
arenormalizedtothetotalfluxintheangularbin.ModelparametersareN(cid:48) =1020cm−2,v =200km/s, f =0.5,t=0
H tot b
Bipolar Model - Late
1.10
1.05
0
F 1.00
/
F
0.95
a) b) c)
0.90
0 10 20 30 40 50 60 70 80 90
) Θ
3
− 0.8 0.8
0 a) b) c)
1×0.7 100 km/s 0.7
( 10 km/s
n 0.6 40 km/s 0.6
bi
y 0.5 0.5
c
n
e 0.4 0.4
u
q 0.3 0.3
e
r
f 0.2 0.2
r
e
p 0.1 0.1

F0 0.0 0.0
/ 20 10 0 10 20 10 0 10 20 10 0 10
F
x x x
Fig.6.SameasFig.5,butforthelatebipolarmodel.ModelparametersareN(cid:48) =1020cm−2,v =200km/s, f =0.5,t=0.15
H tot b
6
C.Behrensetal.:BeamedLyαEmissionthroughOutflow-DrivenCavities
Shell With Holes Model
2.0
1.5
0
F 1.0
/
F
0.5
a) b) c)
0.0
0 10 20 30 40 50 60 70 80 90
) Θ
3
−
0
1×1.4 a) b) c) 100 km/s 1.4
n ( 1.2 10 km/s 1.2
y bi 1.0 40 km/s 1.0
c
n 0.8 0.8
e
u
q 0.6 0.6
e
fr 0.4 0.4
r
pe 0.2 0.2

F0 0.0 0.0
/ 15 10 5 0 5 10 15 10 5 0 5 10 15 10 5 0 5 10
F
x x x
Fig.7.SameasFig.5,butfortheearlybipolarmodel.Modelparametersarev=200km/s,N =1020andΩ=10%,meaningthat
H
10%oftheshellissubtendedbytheholes.
Cavity Model
3.0
2.5
2.0
0
F
/ 1.5
F
1.0
0.5
a) b) c)
0.0
0 10 20 30 40 50 60 70 80 90
) Θ
3
− 3.0 3.0
0
1×a) b) c) 100 km/s
n ( 2.5 10 km/s 2.5
y bi 2.0 40 km/s 2.0
c
n
e 1.5 1.5
u
q
e 1.0 1.0
r
f
r
e 0.5 0.5
p

F00.0 0.0
/ 15 10 5 0 5 10 10 5 0 5 10 10 5 0 5 10
F
x x x
Fig.8.SameasFig.5,butforthecavitymodel.ModelparametersareN(cid:48)(cid:48) =1020cm−2,v =200km/s.
H l
7
C.Behrensetal.:BeamedLyαEmissionthroughOutflow-DrivenCavities
the spatial distribution with regard to the point of last scatter- Observers with θ > 42◦ Observers with θ < 42◦
ing of escaping photons show that most of the photons bounce 1.2 1.2
oftheinnertroughofthedensitydistributionwithoutpenetrating
deeply,somostphotonsdonotexperiencethedustopacity.This
1.0 1.0
escapemechanismalsopartlyexplainsthesmoothtransitionof
thespectra/fluxdistributionmentionedbefore.
y0.8 0.8
sit
3.3. ParameterStudy:PeakPositionversusObservation en
D
ToexAanmgilneethecorrelationofapeakatthesystemicvelocity(at ability 0.6 0.6
x=0)withlowinclination,weranasuiteofmodelswithdiffer- rob
entparameters.Wesetthewidthoftheinputspectrumto40km/s P0.4 0.4
here.Theparameterrangeforthethreedifferentmodelfamilies
isshownintable2.Intotal,weran272models,allwithoutdust.
0.2 0.2
Sincecertainparametercombinationsleadtoweakanisotropies
inopticaldepthandcolumndensity,werestrictedouranalysisto
thoseforwhicheitherthefluxchangedbyatleast10%withre- 0.0 0.0
specttotheobservationangleand/orforwhichthehighestpeak 9 6 3 0 9 6 3 0
Shift from Line Center ∆x Shift from Line Center ∆x
inthespectrummovesatleast3unitsinfrequencydependingon
observationangle.Westressthatbytheseconditions,wedonot Fig.13.Distributionofthespectralpeakforourparameterstudy,
select only those models that already show the aforementioned see text for details. Left: Distribution of peak position for ob-
correlation, but all those models that show anisotropic spectra servers with θ > 42◦. Right: Distribution for observers with
and/orfluxesingeneral.Weendupwithatotalof179models. θ<42◦.
InFig.13,weshowthedistributionofthepeakpositionforthose
models.Intheleftpanel,thedistributionisshownforobservers
In spite of these complications: there are several results to
atangularpositionsθ > 42◦,whileintherightpanel,weshow
takeawayfromouranalysis:
thedistributionforobserverswithinθ<42◦.Forthelatter,there
isastrongpeakat x≈0.Whileforobserversabove42◦ thereis – In terms of the EW, we find boosts of up to ∼10% for the
a peak at the systemic velocity as well, it is much smaller than bipolar model, boosts of ∼2 for the shell with holes model
forobserversbelow42◦.Withinthescannedregionofparame- andafactorof∼3forthecavitymodel.Theinclusionofdust
terspace,wethereforefindacorrelationbetweenpeakshiftand enhancestheboostforthebipolar[shellwithholes]modelto
inclination.Forlowinclination,theprobabilitytoseeapeakat ∼15%[afactorof∼5.5].Forthecavitymodel,theinclusion
x ≈ 0isenhancedbyafactorofafew.Thistrendisconsistent ofdustincreasestheboosttoabout3.5.
in all our three model families, but stronger for the shell with – For all of the discussed models, we find a range of param-
holesandcavitymodels.ThissuggeststhataLyαspectrumwith eters for which there is a clear correlation between an ob-
apeakat∆x ∼ 0ismorelikely(thanrandom)tobeassociated served peak at a velocity shift of zero and an inclination
withasightlinepassingthroughaholeorcavity.Westressthat close to zero. This is intuitive, since when looking down a
due to the finite spectral resolution of observations, the peaks cavity,weexpecttoseetheunalteredspectrumoftheemit-
canbewashedout.Inthiscase,wedon’texpectadistinctpeak tingregion,notstronglyaffectedbyscatteringsininterven-
atsystemicvelocity,butafluxexcessnearthesystemicvelocity. inggas.Thiscanbeofpracticalimportancewhensearching
for ionizing flux leaking out of high-redshift galaxies, be-
causetheexistenceofsuchcavitieswillalsoallowionizing
4. Discussion&Conclusions
photonstoescapethegalaxy.Ourmodelssuggestthatthere
We performed Monte-Carlo radiative transfer simulations for is an increased probability to find ionizing photons leaking
the Lyα emission in three different families of models that are from LAEs for which the Lyα spectrum exhibitis a peak at
allinspiredbygalacticwindsandexpandingHIshells.Incon- systemicvelocity.Duetothefinitespectralresolutionofob-
trast to the shell models (e.g Verhamme et al., 2006), we have servations,thispeakmightbewashedoutandshowasflux
added anisotropic velocity and density components. While the excessnearthesystemicvelocity.Itisinterestingtonotethat
bipolar and shell with holes models are natural extensions to thispeakcorrespondstothethirdpeakinsomeofourbipolar
theisotropicshellmodels,thecavitymodelsaredesignedtobe andshells-with-holesmodels.Thatthisresultholdsupeven
moreextremewithlargeanisotropies(andreminiscentofawind whenthetotalchangeinfluxissmall;forthebipolarmod-
breakingoutofagalacticdisk). els,weseetheclearsignatureofsuchapeakeventhoughthe
We find that the anisotropies in our models lead to an totalfluxvariationisassmallas10%.
anisotropic escape of photons which is visible in the spectral Having such an observational diagnostic for sightlines go-
properties as well as in the flux as obtained for observers at ingthroughlowHIcolumndensitiesisimportant,asitmay
different angular positions. We generally find that the viewing provideanewwaytosearchforso-called‘Lymancontinuum
angle-dependence of the predicted spectrum is quite compli- leakers’:thesearchforthesegalaxieshasbeenhighlyineffi-
cated, with the flux in different peaks in the spectrum chang- cientasitrequiresdeepspectroscopicobservationsofgalax-
ing in some cases (see e.g. Fig. 10), but not in others (see e.g. ies,formostofwhichnoionizingfluxisdetected.Thusfar,
Fig. 9). Additionally, we find that the inclination effect due to only a handful of these galaxies have been discovered, and
anisotropicdensityandvelocityfieldscanbepartlycounteracted consequently the observational constraints on the escape of
bygeometricaleffects,e.g.forcontinouslydeformedshellslike ionizingphotonsfromstarforminggalaxiesareweakatbest.
inthebipolarlate-typecases. Since this escape fraction plays a key role in the reioniza-
8
C.Behrensetal.:BeamedLyαEmissionthroughOutflow-DrivenCavities
Bipolar Model - Early with Dust
1.20
1.15
1.10
1.05
0
F
/ 1.00
F
0.95
0.90
0.85
a) b) c)
0.80
0 10 20 30 40 50 60 70 80 90
) Θ
3
0− 1.0 1.0
1× a) b) c) τd = 0
n ( 0.8 τd = 1 0.8
bi τd = 2
cy 0.6 0.6
n
e
u
q 0.4 0.4
e
r
f
r 0.2 0.2
e
p

0
F 0.0 0.0
/ 15 10 5 0 5 10 15 10 5 0 5 10 15 10 5 0 5 10
F x x x
Fig.9. Same as Fig. 5, but for three different optical depths in dust: τ =0 (blue, solid), 1(green, dashed), 2(red, dotted). Model
D
parametersareN(cid:48) =1020cm−2,v =200km/s, f =0.5,t=0.
H tot
Bipolar Model - Late with Dust
1.20
1.15
1.10
1.05
0
F
/ 1.00
F
0.95
0.90
0.85
a) b) c)
0.80
0 10 20 30 40 50 60 70 80 90
) Θ
3
−
0 a) b) c)
1×1.4 τd = 0 1.4
n ( 1.2 τd = 1 1.2
y bi 1.0 τd = 2 1.0
c
n 0.8 0.8
e
u
q 0.6 0.6
e
r
f 0.4 0.4
r
e
p 0.2 0.2

0
F 0.0 0.0
/ 15 10 5 0 5 10 15 10 5 0 5 10 15 10 5 0 5 10
F x x x
Fig.10.SameasFig.9,butforthelatebipolarmodel.ModelparametersareN(cid:48) =1020cm−2,v =200km/s, f =0.5,t=0.15
H tot
9
C.Behrensetal.:BeamedLyαEmissionthroughOutflow-DrivenCavities
Shell With Holes Model with Dust
7
6
5
04
F
/
F 3
2
1
a) b) c)
0
0 10 20 30 40 50 60 70 80 90
) Θ
3
−
0
1×1.4 a) b) c) τd = 0 1.4
n ( 1.2 τd = 1 1.2
y bi 1.0 τd = 2 1.0
c
n 0.8 0.8
e
u
q 0.6 0.6
e
fr 0.4 0.4
r
pe 0.2 0.2

F0 0.0 0.0
/ 15 10 5 0 5 10 15 10 5 0 5 10 15 10 5 0 5 10
F
x x x
Fig.11.SameasFig.9,butfortheshellwithholesmodel.Modelparametersarev=200km/s,N =1020andΩ=10%.
H
Table2.Summary:ExploredParameters
Model ParameterSet
Bipolar N(cid:48)=[1019,1020,1021cm−2],v =[100,200,300km/s], f=[0.25,0.5,0.75,1.0],t=[0,0.05,0.1,0.2]
H tot
ShellwithHoles N =[1019,1020,1021cm−2],v=[100,200,300km/s],Ω=[5%,10%,25%,30%]
H
Cavity N(cid:48)(cid:48)=[1019,1020,1021cm−2],v=[0,100,200,300km/s]
H l
tionprocess,itisimportanttofindobservationalsignatures ourshellmodelextensionsarenotstraightforwardsincethedif-
that may help us constrain this quantity (see also Nakajima ferentgeometrieshavestrongeffectsonthefluxdistribution.If
& Ouchi (2013) andJaskot & Oey (2013) who show that we quantify the anisotropies by the maximum deviation of the
galaxieswithhighOIII/OIIlineratiosaremorelikelytobe linecenteropticaldepthalonglinesofsightwithrespecttothe
sourcesthatleakionizingphotons). mean, as suggested by Zheng & Wallace (2013), then we find
– Especially for the cavity models, the observability of the muchsmalleramplitudesoftheinclinationeffectincomparison
peak at systemic velocity depends strongly on the width of to their solid sphere models. For example, in one of our bipo-
the input line since there are many photons near line cen- larmodels,theopticaldepthsalongdifferentlinesofsightmight
ter that are scattered into the line of sight of observers that differbyafactorof103,whilethefluxdoeschangeonlyby10%.
look down the cavity. Moreover, our simulations have infi- In Zheng & Wallace (2013), a difference of a factor of 2 in the
nitespectralresolution.Incontrast,thefinitespectralresolu- optical depth can lead to an enhancement in flux as large as a
tionofrealdatawashesoutthedetailedstructureoftheLyα factorof 2.Wehave confirmedthe sameenhancementin some
lines.BothpointssuggestthatlookingdownalowHIsight- of the models of Zheng & Wallace (2013) with our code. This
linedoesnotnecessarilygiverisetoadetectablepeakinthe suggeststhatthedeviationsintheopticaldepthdonottranslate
Lyαspectrumat x = 0.However,ouranalysisdoessuggest directlyintoanestimateofthefluxchangefordifferentgeome-
that if such a line is detected, then it may be indicative of tries.
havingalowHIcolumndensitysightlinetothegalaxy. Acknowledgements MD thanks the the Goettingen
– Dustingeneralenhancestheinclinationeffect,buttheinflu- Academy of Sciences and Humanities for awarding him a
ence differs by an order of magnitude or more between our Gauss-Professorship,andthekindhospitalityoftheInstitutefor
modelfamilies. AstrophysicsinGoettingen.
A preprint by Zheng & Wallace (2013) appeared recently
which also focussed on the escape of Lyα photons from
References
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10