3D Lya radiation transfer. II. Fitting the Lyman break galaxy MS 1512-cB58 and implications for Lya emission in high-z starbursts

0.29 MB·English

by  Daniel Schaerer

Astronomy&Astrophysicsmanuscriptno.cb58˙final (cid:13)c ESO2008
February2,2008
α
3D Ly radiation transfer. II. Fitting the Lyman break galaxy MS
α
1512–cB58 and implications for Ly emission in high-z starbursts
DanielSchaerer1,2,AnneVerhamme1
1 ObservatoiredeGene`ve,Universite´deGene`ve,51,Ch.desMaillettes,CH–1290Sauverny,Switzerland
2 Laboratoired’Astrophysique(UMR5572),ObservatoireMidi-Pyre´ne´es,14AvenueE.Belin,F–31400Toulouse,France
8
0 Receiveddate;accepteddate
0
2 ABSTRACT

n
Aims.To understand the origin of the Lyα line profile of the prototypical Lyman break galaxy (LBG) MS 1512–cB58 and other
a
J similarobjects.ToattemptaconsistentfitofLyαandotherUVpropertiesofthisgalaxy.Tounderstandthemainphysicalparameter(s)
responsibleforthelargevariationofLyαlinestrengthsandprofilesobservedinLBGs.
8
Methods.Using our 3D Lyα radiation transfer code (Verhamme et al. 2006), we compute the radiation transfer of Lyα and UV

continuum photons including dust. Observational constraints on the neutral gas (column density, kinematics, etc.) are taken from
]
h otheranalysisofthisobject.
p Results.TheobservedLyαprofileofMS1512–cB58isreproducedforthefirsttimetakingradiationtransferandallobservational
- constraints into account. The observed absorption profile is found to result naturally from the observed amount of dust and the
o relativelyhighHIcolumndensityN .RadiationtransfereffectsandsuppresionbydusttransformastrongintrinsicLyαemissionwith
H
r EW(Lyα)>∼60ÅintotheobservedfaintsuperposedLyαemissionpeak.WeproposethatthevastmajorityofLBGshaveintrinsically
t
s EW(Lyα)∼60–80Åorlarger,andthatthemainphysicalparameterresponsiblefortheobservedvarietyofLyαstrengthsandprofiles
a
in LBGs is N and the accompanying variation of the dust content. Observed EW(Lyα) distributions, Lyα luminosity functions,
[ H
andrelatedquantitiesmustthereforebecorrectedforradiationtransferanddusteffects.Theimplicationsfromourscenarioonthe
1 duty-cycleofLyαemittersarealsodiscussed.
v
Keywords.Galaxies:starburst–Galaxies:ISM–Galaxies:high-redshift–Ultraviolet:galaxies–Radiativetransfer–Line:profiles
7
8
1
1 1. Introduction thesampleofShapleyetal.(2003)cB58isfoundinthequartile
. (∼25%)ofLBGswiththestrongestLyαabsorption.Assucha
1 Discovered serendipitously by Yeeetal. (1996), the Lyman
representativeandgiventhequalityandamoutofobservational
0 Break Galaxy (LBG) MS 1512–cB58 (hereafter cB58) lo-
dataavailable,cB58isofparticularinterest.
8 cated at z ∼ 2.73 is strongly gravitationally magnified by the
0
foreground cluster MS 1512+36. It is by far the best stud-
: OurobjectivesaretoexamineiftheobservedLyαlinepro-
v ied LBG, which has been observed at many wavelengths (see
file and strength of cB58 can be understood,and if one is able
i Bakeretal. 2001, 2004; Bechtoldetal. 1997; Ellingsonetal.
X toobtainconsistentdiagnosticsfromtheLyαlineandfromthe
1996; Frayeretal. 1997; Nakanishietal. 1997; Pettinietal.
r 2002, 2000; Savaglioetal. 2002; Sawicki 2001; Teplitzetal. otherUVandbroadbandfeaturesusedinearlierpapers.Suchan
a
attemptiscarriedouthereforthefirsttimewithaLyαradiation
2004, 2000). In particular, rest-frame UV (Pettinietal. 2002,
transfercode(Verhammeetal.2006).OtherLBGswithvarying
2000),optical(Teplitzetal.2004,2000),andradio(Bakeretal.
strengthsofLyαemissionwillbeanalysedinasubsequentpaper
2001, 2004) observations have allowed to draw a fairly global
(Verhammeetal.2007).Inparticularwewishtoelucidatewhat
picture of this star-forming galaxy and its interstellar medium
(ISM):itisyoung(∼50–300Myr),massive(∼ 1010 M ),with causesthebroadLyαabsorptionandveryweaksuperposedLyα
⊙
emissionincB58andinotherLBGsshowingsimilarLyαspec-
asub-solarmetallicity(Z ∼ 2/5Z ),astarformationrate(SFR
⊙
∼24M yr−1)typicalofLBGs,anditissurroundedbyoutflow- tra (cf. Shapleyetal. 2003). Similarly we want to understand
⊙
ingmaterialatV ∼250kms−1. whatphysicalparameter(s)distinguishthedifferentsubtypesof
exp
LBGsshowinglargevariationsespeciallyinLyα.Finally,fitting
Thankstoitsapparentbrightnesstherest-UVspectraofthis
observed starburst spectra with detailed Lyα radiation transfer
galaxyare of comparablequality as the best studied localstar-
modelingshouldingeneralprovideinsightfortheuseofLyαas
bursts.Thishasinparticularmadeitpossibletodetectnumerous
adiagnosticindistantgalaxies.
stellar and interstellar (IS) lines, to study their kinematics, and
tousethemfordetailedUVlinefitstoconstrainitsstellarcon-
tent, age, star formation history etc. (e.g. deMelloetal. 2000; Theremainderofthepaperisstructuredasfollows.Themain
Ellingsonetal.1996;Pettinietal.2000).Apartfromitsbright- observationalpropertiesofcB58aresummarisedinSect.2.The
ness,magnifiedbyafactor∼30thankstogravitationallensing principles of our simulations and fit method are described in
(Seitzetal.1998),thepropertiesofcB58areempiricallyfound Sect. 3. In Sect. 4 we discuss the implicationsfromour results
to be typicalof LBGs (Shapleyetal. 2003). More precisely, in ontheunderstandingofLyαemissioninLBGs,andontheprop-
ertiesofthesegalaxies.Ourmainconclusionaresummarisedin
Sendoffprintrequeststo:[email protected] Sect.6.
2 DanielSchaerer,AnneVerhamme:3DLyαradiationtransfer.II.cB58andimplicationsforLyαinhigh-zstarbursts
2. ObservationalconstraintsfromcB58 a young age is the underabundance of N and the Fe-peak ele-
mentsintheISMofcB58(Pettinietal.2002),givingtheupper
ThemainpropertiesofcB58ofrelevanceforthe presentpaper limit age <∼ 300 Myr, the timescale for the release of N from
aresummarisedinwhatfollows.
intermediate-massstars.
2.1.RedshiftandISMoutflowproperties
2.3.Extinction/dustcontent
DirectobservationsofphotosphericlinesbyPettinietal.(2002,
ThepreciseamountofextinctionincB58remainsunclear.While
2000) assign the systemic redshift at zUV = 2.7276+−00..00000013. Pettinietal. (2000) estimated Es(B−V) = 0.29fromtheirUV
Teplitzetal. (2004) determine zHII = 2.729±0.001 from rest- spectralfitting,andTeplitzetal.(2000)calculatedE (B−V) =
frame optical emission lines(Hα, [N ], [O ] and Hβ) of the g
0.27fromthe H /H ratio, Bakeretal. (2001) used fourmeth-
α β
counterarc “A2”, in agreement with their earlier determination
odsincludingacorrectionofthevaluederivedfromtheBalmer
fromthemainimageofcB58.TheCOemissionlinedetermina- decrementobtaining values from E (B−V) = 0.042 to 0.236.
tionbyBakeretal.(2004)isz =2.7265+0.0004. s
CO −0.0005 Here Es and Eg refertothecolorexcessofthestellarlightand
The interstellar absorption lines and Lyα absorption are the nebulargasrespectively,which are related by E (B−V) =
blueshiftedby∼ 250kms−1 withrespecttothegalaxyredshift, 0.44E (B−V) if the Calzetti law (Calzettietal. 200s0) applies.
g
determined by its photospheric lines. The small Lyα emission FromthisweconcludethatE (B−V)∼0.10–0.54,andweadopt
g
peak on top of the absorption (see e.g. Fig. 4) is redshifted by ameanvalueofE (B−V)∼0.3forsimplicity.
∼ 300 km s−1(Pettinietal. 2002). Both are evidence for large- g
scaleoutflowingmediumaroundthestar-forminggalaxy.
Interestingly,andincontrasttothepropertiesseenintheav- 2.4.Starformationrate,mass,andmetallicityofcB58
erage LBG spectra of Shapleyetal. (2003) and spectra of in-
ThestarformationrateestimatedfromtheUVluminosityL
dividualz ∼ 3 LBGs observed by Tapkenetal. (2007), Lyα is is SFR ∼ 40 M yr−1 (Pettinietal. 2000) after correct1i5n0g0
UV ⊙
redshifted in cB58 by a similar amountas the interstellar lines
forreddeningandgravitationalmagnification(assumingamag-
areblueshifted,insteadofbeingredshiftedby∼ +2×V with
exp nification factor µ = 30, cf. below). Adopting a lower extinc-
respectto thestellar lines(orby ∼ 3×V fromthe ISlines).
exp tion,basedontheBalmerdecrement,Bakeretal.(2004)derive
As discussed by Verhammeetal. (2006) the latter behaviouris SFR =23.9±0.7M yr−1fromHα.
naturallyexplainedbyasphericallysymmetricexpandingshell Hα/Hβ ⊙
The velocity dispersion measured from nebular and CO
withconstantvelocity,wheretheemergingLyαphotonsmostly emissionlinesaresimilar:σ =81kms−1(Teplitzetal.2000),
originatefromscatteringonthebacksideoftheshellwherethey andσ = 74±18km s−1H(IBIakeretal. 2004). The dynamical
gainredshiftof∼2×V .ThesmallerredshiftofLyαindicates CO
exp mass deducedfromthese values, giventhe physicalsize of 2.4
alreadyempiricallyadeviationfromthissimplesymmetry.This kpc of the galaxy (Seitzetal. 1998), is M ∼ 1.×1010 M .
willbesubstantiatedbelow.Howtypical/frequentsuchvelocity dyn ⊙
The mass of the gas deduced from the CO column density is
shiftsarecannotbeassertedfromtheavailabledata,represent- M =(6.6±5.8)×109M (Bakeretal.2004).
ingmostlystackedspectra.Thiswillrequiremanyhighquality gas 4.3 ⊙
Themetallicityderivedfromtheinterstellarabsorptionlines
spectra of individualLBGs. However, only the Lyα shape, not
and from the ionised region are compatible: Z ∼ 2/5 Z
IS ⊙
line shifts, is the criterion used to classify cB58 in the quartile
(Pettinietal.2002)andZ ∼1/3Z (Teplitzetal.2000).
withLyαabsorption. HII ⊙
ThelowionisationISMabsorptionlinesyieldconsistentlya
velocitydispersionb = 70kms−1(Pettinietal.2002).Theneu- 2.5.Gravitationallensing
tral hydrogen column density of the outflow is determined by
Lensing reconstructionshows that the primary image of cB58,
VoigtfittingoftheLyαabsorptionwings;N =(7.0±1.5)×1020
H anarcwhosespectrumwillbeusedhere,ismagnifiedby3.35–4
cm−2 and N = 6+1.4 × 1020 cm−2 is obtained by Pettinietal.
H −2. mag overall, i.e. a magnification factor µ ∼ 22–40 (Seitzetal.
(2002) and Savaglioetal. (2002) respectively. Absorption pro-
1998). Approximately only a fraction 0.5–0.66 of the source
file line fitting shows that at least ∼ 2/3 of the low ionisation
is imaged into the cB58 arc according to Bakeretal. (2004);
materialisfoundatV = −265kms−1,withabparameterof70
Seitzetal. (1998). However, the fact that cB58 follows all the
kms−1(Pettinietal.2002).
samescalingrelations(amongLyαequivalentwidth,interstellar
The outflow of cB58 is located well in front of the stars
absorption line strengths, extinction etc. Shapleyetal. (2003))
and coversthem almost completely, since it absorbs almost all
obeyed by unlensed LBGs, shows that the spectrum is not an
the UV lightfromthe backgroundstars. Indeed,Savaglioetal.
unrepresentativesliceofthegalaxy.
(2002)findonlyasmallresidualmeanfluxabovethezerolevel
in the core of the Lyα absorption feature, whereas it is black
forPettinietal.(2002).Heckmanetal.(2001)estimateanareal 3. FittingtheLyαspectrumofcB58
coveringfactorforopticallythickgasof98%fromtheresidual
intensityatthecoreoftheCλ1335line. 3.1.Observations
We use the normalised rest-frame UV spectrum from
Pettinietal.(2002),obtainedwiththeEchelleSpectrographand
2.2.Ageandstar-formationhistoryofcB58
Imager(ESI)ontheKecktelescopeIIata resolutionof58km
UV spectral fitting, including detailed stellar line profile fits, s−1, and kindly made available to us by Max Pettini. We have
consistently indicate ages of >∼ 20–100 Myr and favour con- also examined the UVES spectrum taken with the VLT from
stant star formation over this timescale (deMelloetal. 2000; Savaglioetal. (2002). Except for slight differences in the nor-
Ellingsonetal. 1996; Pettinietal. 2000). Such an age is also malisationthespectrashowaverygoodagreement(cf.Fig.2).
consistentwiththeobservedstellarmassandstarformationrate The former spectrum is used subsequently for our line profile
(Bakeretal.2004).Anotherindependentargumentinfavourof fitting.
DanielSchaerer,AnneVerhamme:3DLyαradiationtransfer.II.cB58andimplicationsforLyαinhigh-zstarbursts 3
Table1.Inputparametersofthe“standard”cB58modelforthe ineifconsistentsolutionscanbeobtained.ThevalueforFWHM
radiationtransfercode istakenfromtheobservedHαline(σ ).
HII
For the spherical shell (1), the emergent spectrum is com-
V =V 255kms−1 puted by integration over the entire volume. This assumes
exp front
Vback free that the shell is unresolved and completely integrated within
NH 7.0×1020cm−2 the spectroscopic aperture, which corresponds to ∼ 2 kpc
b 70kms−1 (Seitzetal. 1998). For the slabs (2), the emergent spectra are
E (B-V) 0.3
g computed taking the photons emitted within an opening angle
FWHM(Lyα) 80kms−1
oftypically60degreesintoaccount.Theresultsdependlittleon
EW(Lyα) free
theexactopeningangle.
AllmodelshavebeencomputedusingtheMonteCarlo(MC)
radiation transfer code MCLya developed by Verhammeetal.
3.2.LyαplusUVcontinuummodeling
(2006).Thecodetreatsthescatteringoflineandcontinuumpho-
To fit the observations we use our 3D Monte Carlo (MC) ra- tonsintheLyαlineandtheadjacentcontinuum,aswellasscat-
diationtransfercodeMCLya(Verhammeetal.2006).Thecode teringandabsorptionbydust.InpracticeonehighstatisticsMC
solvesthetransferofLyαlineandadjacentcontinuumphotons simulationisrunforeachsetofparameterslistedaboveassum-
includingthedetailedprocessesofLyαlinescattering,dustscat- ingaconstant(flat)inputspectrum.Bykeepingtraceofthere-
teringanddustabsorption. lationbetweentheinputfrequencybinofthephotonsandtheir
For simplicity, and given empirical evidence in favour of a emergentfrequency,simulationsfor arbitraryinputspectra can
fairlysimplegeometryinz∼3LymanBreakGalaxies(hereafter be generated a posteriori in an interactive manner. This avoids
LBG) discussed by Verhammeetal. (2006), we first adopted a unnecessarytransfercomputationswithoutresortingtoanysim-
simple“super-bubble”modeltoattemptfittingtheobservedLyα plifyingassumption.Forcomparisonwiththeobservations,the
lineprofile.Theassumed“standard”geometryisthatofanex- theoreticalspectrumisfinally convolvedwith a gaussianto the
panding,spherical, homogeneous,and isothermal shell of neu- instrumentalresolution.
tralhydrogensurroundingacentralstarburstemittingaUVcon- Simulations for multi-slab geometries (3) have been com-
tinuumplusLyαrecombinationlineradiationfromitsassociated putedbycombiningtheresultsfromasingleslabMCcomputa-
H  region. The homogeneity and a covering factor near unity tionsinanumericalfashion,modifyingappropriatelytherelative
arealsosupportedbytheobservations(cf.Sect.2).Takinginto velocityshifts of the slabs and openinganglesof the emerging
accountdeviationsfromaconstantexpansionvelocityisneces- radiation. This allows fast, interactive fitting, without resorting
sary to reproducethe observedLyαprofile of cB58,as already e.g.toapproximateanalyticfits(cf.HansenandOh2006).
indicatedfromtheempiricalevidencediscussedearlier.
3.2.2. SyntheticstarburstspectraintheLyαregion
3.2.1. Radiationtransfermodeling
When spatially integratedgalaxy spectra are considered,it is a
The following geometries have been adopted: 1) a spherically priorinecessarytoincludebothstellarandnebularlinesinfitsof
symmetric expandingshell with velocity V , 2) a foreground observedspectra.AstheregionaroundLyαisgenerallynotcon-
exp
slabmovingtowardstheobserverwithvelocityV =V ,and sideredandnotincludedordiscussedinmostevolutionarysyn-
front exp
3) two parallelslabs with differentvelocitiesV and V = thesiscodes,weherebrieflyexaminethebehaviourofthisspec-
back front
V respectively to mimic a shell like geometry allowing for tral range. To do so we use the evolutionary synthesis models
exp
velocity variationsbetween the frontand the back of the shell. ofSchaerer(2003)(hereafterS03)complementedbytherecent
ThevalueofV istakenfromtheobservations.V isafree modelsofDelgadoetal. (2005) includinghighspectralresolu-
exp back
parameter. tionstellaratmospheres,kindlymadeavailabletousbyMiguel
The other model parameters are: the velocity dispersion Cervin˜o.Onlythemainingredientsofthesemodelsetsshallbe
given by the Doppler parameter b, the H  column density N , summarisedhere.
H
and the dust absorption optical depth τ at Lyα wavelength. TheS03modelsbasicallyincludesimplifiednon-LTEmodel
a
We assume that dust and H  are uniformly mixed. As dis- atmospheres for massive stars (> 20 M ), and LTE line blan-
⊙
cussedinVerhammeetal.(2006),τ relatestotheusualextinc- ketedKuruczatmospheresotherwise.TheDelgadoetal.(2005)
a
tion E(B−V) ≈ (0.06...0.11)τ , where the numericalcoeffi- modelsincludeinparticulartheoreticalhighspectralresolution
a
cientcoversattenuation/extinctionlawsofCalzettietal.(2000), libraries,andallmassivestarsaretreatedwiththeplaneparallel
Seaton(1979) andsimilar. Herewe assume E(B−V) = 0.1τ . non-LTEblanketedTLUSTYcode(LanzandHubeny2003).In
a
The values for these parameters, summarised in Table 1, are bothcasesthesamestellartracksandmetallicities,summarised
takenfromtheobservationsofcB58(Sect.2).Notethatwesup- in S03, have been used. With respect to the Lyα region these
posethatthecolorexcessmeasuredforthenebulargasisrepre- modelsrepresentthemostup-to-datecomputations.Theonlyre-
sentativeforthedustopticaldepthseenbytheLyαphotons. strictionisthatthesecomputationsdonottreatthestellarwinds
Thespectrumofthecentralpointsourceisdescribedbythe ofthehotteststars,whichleadstosomemodificationsofthein-
stellar continuum around Lyα, either a flat continuum or syn- trinsicLyαlineprofileofthesestars.However,unpublishedtest
theticstarburstspectradescribedbelow,andthenebularrecom- computations (Martins 2000) show that these effects are small
bination line, described by its equivalent width EW(Lyα) and or negligible compared to the underlyingLyα absorption from
fullwidthathalfmaximumFWHM(Lyα).Althoughinprinciple thebulkofBandAstarsandcomparedtotheexpectednebular
theequivalentwidthoftheintrinsicLyαemissionisdetermined emission.ThisisalsoconfirmedbyLeitherer(2007).
by the stellar population,i.e. can be predicted by the synthetic In Fig. 1 we show the spectra predicted by these two syn-
spectra,EW(Lyα)iskeptasafreeinputparameterfortheradia- thesis over the spectral range centered on Lyα. The spectra,
tiontransfermodeling.Theresultingfitvalueswillsubsequently computed for instantaneous bursts with ages 0.1, 10, and 50
becomparedtovaluesexpectedfromsynthesismodelstoexam- Myr at solar metallicity and for a Salpeter IMF with an up-
4 DanielSchaerer,AnneVerhamme:3DLyαradiationtransfer.II.cB58andimplicationsforLyαinhigh-zstarbursts
Fig.1. Predicted stellar spectra around Lyα from the synthesis Fig.2. Observed spectra of cB58 from Pettinietal. (2002)
models of S03 (blue and red low-resolution curves), and the (black) and Savaglioetal. (2002) (red) compared to the high-
high-resolution models of (Delgadoetal. 2005) in black and resolution synthesis models of (Delgadoetal. 2005) for solar
green.Computationsforsolarmetallicityburstsofages0.1,10, metallicityburstsofages0.1,10,and50Myr(inmagenta,green
and50Myrareshownfromtoptobottom.Thegreenlineshows and blue from top to bottom). Apart from small differences in
the equilibrium spectrum reached for constant star formation, the normalisationthe two observedspectra are very consistent.
as the red dashedline for the S03 model.All spectra are in F Thecomparisonwiththemodelsillustrateshowtheshapeofthe
λ
units, normalisedarbitrarily at 1280Å. The main photospheric red wing of Lyα can be clearly used to exclude bursts of ages
line identifications are indicated at the top (cf. text). Note the largerthan10–50Myr.
excellentoverallagreementof the two independentmodels,al-
lowingareasonabledescriptionofthebroadabsorptionaround
Lyα. oramoreconstantstarformationhistoryarethereforerequired.
Ofcourse,otherUVspectrallinessuchasthewellknownSi
andClines,aresensitivetoageandstarformationhistory(cf.
Leithereretal.1995).
per mass cut-off of 100 M , are normalised arbitrarily at 1280
⊙ As other parts of the UV spectrum (see e.g. Leithereretal.
Å. The high-resolution spectra allow the identification of the
1999), the detailed integrated spectrum in the Lyα region de-
main(photospheric)spectrallines,whicharetheCmultiplet
pendsalsosomewhatonmetallicity(cf.Fig.3).Themainreason
centered at 1175.6 Å, Si  multiplets at λλ 1193.3,1194.5and isthesystematicshiftoftheaveragestellareffectivetemperature
1260.4,1264.7,the Si  multiplet λλ 1206.5,1207.5,and C  with metallicity for a given age. In consequence similar spec-
λ1247.4. The position of the N  multiplet λλ 1238.8,1242.8 tra of burstscan be obtainedatdifferentmetallicities, provided
formed in the winds of early type stars (not included in the some age shift is allowed for. Despite the detailed metallicity
presentmodels)isalsoindicated. differences,whichcanbeaccountedforbyusingtheappropriate
ThetemporalbehaviouroftheLyαprofileinaburstcanbe highresolutionspectra,theoverallbehaviouroftheshapeofthe
sketchedasfollows:forages<∼10MyrtheLyαabsorptiondeep- Lyαprofileremainsquiteindependentlyofmetallicity,ascould
ensbutremainsrelativelynarrow.Atolderages,whenstarswith beexpected.
alowerionisationdegreeintheiratmospheresdominate,theLyα It is also reassuring to note the good overall agreement of
becomes considerably stronger and broader. At > 50 Myr, not the two independent synthesis models, allowing a reasonable
shownhere,theredwingremainsbroad,whereasthefluxshort- descriptionofthe broadabsorptionaroundLyαevenwithlow-
wardofLyαdisappearsveryrapidly.Forconstant(ongoing)star resolution spectra. In any case predictionsfrom both synthesis
formationthespectrumreachesquiteshortly(over>∼10Myr)an models, as well as flat spectra, will be used below as input for
equilibriumwithaLyαlineprofilequitecloselyresemblingthat thecB58fitswiththeLyαradiationtransfercode.
ofa∼10Myrburst,asalsoshowninFig.1. The relative strengths of the stellar Lyα absorptionand ex-
The shape of the red wing of Lyα, up to ∼ 1240 Å, pro- pected intrinsic nebular emission is illustrated in Fig. 3, where
videsausefulconstraintontheageandstarformationhistoryof the predicted Lyα equivalent widths of these components are
the starburst. For bursts with ages >> 10 Myr the width of the plottedasafunctionoftimeforthecaseofinstantaneousbursts
stellar Lyα absorptionbecome so large, that a measurementof and for constant star formation, as well as for three different
the shape of its red wing can alreadybe distinctive,evenwith- metallicities. The behaviour of these quantities is as expected
outconsideringinterstellarLyαradiationtransfer.Forexample, from earlier computationsat solar metallicity (CharlotandFall
forthe case ofcB58shownin Fig. 2the observedLyαwingis 1993;Valls-Gabaud1993).Decreasingmetallicityincreasesthe
clearlylessbroadthantheburstmodelat50Myr.Youngerbursts nebularemissionandintroducesasmallageshiftinLyαabsorp-
DanielSchaerer,AnneVerhamme:3DLyαradiationtransfer.II.cB58andimplicationsforLyαinhigh-zstarbursts 5
Fig.3.PredictedLyαequivalentwidthsofthenebularemission Fig.4.PredictedLyαlineprofileforasymmetricsphericalshell
(EW(Lyα) > 0) and stellar absorption (EW(Lyα) < 0) for in- withconstantvelocity,theinputparameterssummarisedinTable
stantaneousbursts(solidandlong-dashedlines)andmodelswith 1, and EW(Lyα)=0, 10, 40 Å (green, blue, magenta respec-
constantstarformation(shortdashed,dotted,anddash-dotted). tively).Theinputspectrumisthereddottedline.Theobserved
Thelong-dashedlinesshowthetotalEW (nebular+stellar)for spectrumofcB58fromPettinietal.(2002)isshowninblack.
constant star formation, the dotted lines the stellar absorption
component.Threedifferentmetallicities,Z =0.02(solar,black),
0.004(red),and0.0004(blue)areshown.
tion. For constant star formation over ∼ 20–100 Myr or more,
oneexpectsinparticularEW(Lyα)∼60–100Å.
4. Results
Wenowdiscussthesimulatedspectraassumingdifferentgeome-
triesandtheirdependenceontheinputparameters.
4.1.Modelsforaconstantvelocityshell
The predicted Lyα line profile for a symmetric spherical shell
withconstantvelocity,computedwiththeinputparameterssum-
marisedinTable1andwithEW(Lyα)=0,10,and40Åiscom-
paredtotheobservedprofileinFig.4.Theinputspectrum,here
aflatcontinuumplusline,isalsoshownforillustration.
As expected from our earlier simulations (Verhammeetal.
2006), the global shape of the theoretic spectrum is similar to
theobservedone,consistingofabroaddampedabsorptionplusa
redshiftedasymmetricemissionlinecomponent,whosestrength
dependsonthestrength(EW)oftheinputline.Thenetabsorp- Fig.5. Observed (black) and predicted Lyα line profile for the
tionisduetodustabsorption,sincethecase consideredhereis singleforegroundslabmodel(blue).Theinputspectrum,shown
the integrated spectrum of a shell, where all scattered photons bythereddottedlinehasEW(Lyα)=40Å.
are observed. Scattering of photons out of the line of sight is
thereforenotpossible,henceanynetabsorptionmustbedueto
dust. The superposed emission peak results from the radiation ond the position of the predicted Lyα emission peak is found
transfer of the photons from the original (input) emission line, at too high positive velocities. The first problem can be solved
which are scattered and absorbed, and are able to escape only byincreasingthe columndensityof the shell. Asalreadymen-
thankstotheirredshiftacquiredonthebackoftheshell. tioned above, and first pointed out by Verhammeetal. (2006),
TwomainproblemsareimmediatelyclearfromFig.4.First anintegratedshellgeometrynecessarilyrequiresalargerN to
H
the predicted width of the absorption is unsufficient, and sec- reproducea simpleVoigtprofileofthesame widthasa slabof
6 DanielSchaerer,AnneVerhamme:3DLyαradiationtransfer.II.cB58andimplicationsforLyαinhigh-zstarbursts
thesamecolumndensity.Theseconddiscrepancywiththesim-
pleshellmodelcouldalsobeanticipated(cf.Sect.2),sincethe
redshiftedpeakofLyαisexpectedat2×V ,whereastheob-
exp
servationsshowthepeakaround∼ 300kms−1.Asthevelocity
shift of the Lyα peak is a fairly generic feature of symmetric
expandingshell models, it is clear that this discrepancycannot
be resolvedby changesofthe inputparameters,such as N , b,
H
E(B-V), etc. This has been confirmedby numerousmodel cal-
culations.
Note also that this model allows only for a fairly weak in-
trinsic Lyα emission with EW(Lyα) < 10 Å, much lower than
thevalueexpectedfromsynthesismodelsforthestarformation
historyderivedforcB58(cf.below).
4.2.Singleslabmodel
Giventhedifficultieswithasimpleshellmodelandthefactthat
the direct observational constraints on the outflow only relate
to cold material in front of the UV source, one could ask the
questionwhetherasinglemovingforegroundslab(withoutany
backscattering source) could explain the observations. In other
words this boils down to the question if the observed velocity
shiftof∼255kms−1 betweenstellarandinterstellarabsorption
Fig.6. Observed (black) and predicted Lyα line profile for the
linescouldbe enoughto allow fora partialtransmissionofthe
intrinsic Lyα line, such that it appears at velocities >∼ 250 km twoslabmodeldescribedinSect.4.3(blue).Theinputspectrum
s−1? The simpleanswerobtainedfrommanysimulationsis no. isshownbythereddottedline.
Moreprecisely,withtheobservedcolumndensity,bparameter,
E(B-V),andFWHM(Lyα)thetransmissionofLyαlinephotons
emitted at line center (V = 0) througha slab is negligible,and
hencenolineisformedontopofthebroadabsorptionlinepro-
file,independentlyoftheintrinsicLyαequivalentwidth.Thisis
showninFig.5.
Forenoughlinephotonstoescapetroughtheslabtheintrin-
sic emission line must be redshifted by > 200 km s−1, which
is larger than the possible redshift of ∼ 100 km s−1 found by
Teplitzetal.(2000)from10restframeopticalnebularemission
lines1.Inanycase,suchasolutionwouldrequirealargeintrinsic
Lyαequivalentwidth(EW(Lyα)>∼40Å)inagreementwiththe
resultsfoundbelow.
Hence the presence and position of the Lyα peak together
witharelativelylargeHIcolumndensitytestifiedbythedamped
absorptionexcludesmostlikelyapureforegroundslab.Toallow
fortheLyαtransmission,arecedingbackgroundscreenmustbe
presentso that the Lyα photonscan gain an additionalredshift
bybouncingofftheback,inasimilarfashionasinthespherical
shell.Suchasituationwillbesimulatednow.
4.3.Modelsfortwomovingslabs
To attempt reproducingthe observedLyα emission component
wenowassumeageometrywithtwoparallelslabs,oneinfront Fig.7. Same as Fig. 6 but using high resolution spectra from
andoneinthebackoftheUVandLyαsource.Whilethevelocity evolutionary synthesis models for the description of the stellar
andtheotherparametersoftheapproachingforegroundslabare continuum.Theinputspectrum,arbitrarilynormalised,isshown
fixedbytheobservations(cf.Table1),thevelocityV ofthe bythereddottedline.
back
recedingslabiskeptasafreeparameters.
A good fit to the observed spectrum of cB58 is found for
V ∼140kms−1,asshowninFig.6.ForthischoiceofV foregroundslab,andlowenoughtoproducethepeakattheob-
back back
the velocity shift of the receding slab is sufficient to allow a servedvelocityof∼300kms−1.Theemergentspectrumisbasi-
non-zerotransmissionofthereflectedLyαphotonsthroughthe callyindependentontheproperties(e.g.NH)ofthebackground
slab, which merely acts as a movingmirror.Thisis clear since
1 As pointed out by Pettinietal. (2002) this possible small reshift the spectrum reflected from a slab depends only on the ther-
couldwellbeduetouncertainties intheabsolutewavelengthcalibra- mal width b, and only weakly so (∝ b−1/2), as e.g. shown by
tion. HansenandOh(2006).
DanielSchaerer,AnneVerhamme:3DLyαradiationtransfer.II.cB58andimplicationsforLyαinhigh-zstarbursts 7
Interestinglythe valueofthe secondfreeparameter,the in- Bothdetailedanalysisoftherest-UVspectraofsomeLBGs
trinsicLyαequivalentwidthEW(Lyα),isrequiredtobe EW>∼ and broad band SED fitting of many LBGs yields typically
80 Å to reproduce the observed strength of the Lyα emission stellar ages of several hundred Myr and fairly constant or
peak. In our two slab model the solid angle under which the slowlydecreasingstarformationrates(cf.Papovichetal.2001;
receding“mirror”isseenbytheforegroundslabgovernsthere- Pentericcietal.2007;Shapleyetal.2001).Theseresultsandour
quired EW, since this controls the relative amount of photons analysisof cB58 indicate fairly longstar formationtimescales,
received from direct and reflected radiation at the back of the incontraste.g.tothesuggestionofFerraraandRicotti(2006).
foreground slab. The lower limit on EW(Lyα) given above is cB58 is part of the quartile of z ∼ 3 LBGs showing a
obtainedbyassumingasolidangleof2π.Theobservationsare Lyα dominated by absorption with faint or little Lyα emission
compatiblewitharbitrarilylargervaluesofEW(Lyα). (Shapleyetal. 2003). Therefore we can expect that these ob-
Insteadoftheflatcontinuumwehavealsoexaminedmodels jects behave in a similar way as cB58 and hence have much
using the more realistic synthetic spectra including stellar Lyα higherintrinsicLyαequivalentwidthsandhigherintrinsicLyα
absorptionpresentedabove(Sect.3.2.2)plusnebularLyαemis- luminosities. In other words observed distribution functions of
sionasinputfortheradiationtransfercalculations.Theresulting EW(Lyα) and the Lyα luminosity function must be strongly
Lyαprofile, shownin Fig. 7, is of similar qualityfor a slightly modifiedbyradiationtransferanddusteffects,andthefraction
lowerinputLyαequivalentwidthof>∼60Å. of objects with low EW(Lyα) (L(Lyα)) must be “artificially”
Fitsusingdifferentcombinationsofthecolumndensityand overestimated.
extinctioncouldbeexamined,giventheuncertaintyonthedust Takingradiationtransferanddustintoaccount,shouldthere-
opticaldepthdiscussedabove(cf.Sect.2).Usinge.g.lowerval- fore allow to reconcile observed Lyα strengths with relatively
ues of E (B − V) and our “standard” value for N leads to a long(≫ 50Myr) “dutycycles” of LBGs. In anycase, age dif-
g H
narrowerLyα absorptionprofile,which wouldrequirea higher ferencesbetween∼200and400MyrfoundbyPentericcietal.
column density. Quantifyingthe degeneraciesaround the solu- (2007) for LBGs with and without Lyα emission respectively,
tion found here is beyond the scope of this paper. In any case, cannotbethedirectcauseoftheobservedLyαdifferences.Ifour
itisquiteclearthatthemainconclusion,ahighcolumndensity scenarioalsoworksforLyαemitters(henceforthLAEs,i.e.Lyα
andtheneedforalargeintrinsicLyαequivalentwidth,mustbe selectedLBGs)andthesuppresionofLyαphotonsissufficient,
quiterobustwithrespecttothesedegeneracies.Thismustbethe it could explain the relatively low percentage of star-forming
casesinceahighcolumndensityisrequiredtocreatethebroad galaxieswithno/littleLyαemissionandhencereducetheneed
Lyα absorption (independently of the exact geometry), and in forshortstarburstepisodesinvokede.g.byMalhotraandRhoads
thiscasetheescapefractionofLyαphotons“injected”closeto (2002).Thiswouldthenalsohelptoreconcilethelowernumber
linecenterislowquiteindependentlyoftheexactdustcontent. densitiesof LAEs comparedto LBGs despite the agreementin
Insummary,weconcludethatwiththesimplegeometrycon- theirbias(Kovacˇetal.2007),
sidered here we are able to reproducefor the first time the ob- Itmay be reasonableto expectthatmostof the LBGs have
served Lyα profile of cB58 with a radiation transfer modelus- quiteverysimilarminimumintrinsicLyαequivalentwidthsof∼
ing all observed constraints on the outflow plus just two free 60–80Å determinedby constantstar formationover> 50–100
parameters,Vback andEW(Lyα).One of theinterestingconclu- Myr.LargerEWsareexpectedforobjectsdominatedbyyounger
sionsfromthisanalysisistoshowthattheobservedabsorption (<∼10–40Myr)populations(cf.Fig.3).LowerEWswouldthen
dominatedLyαlineprofileofcB58iscompatiblewithanintrin- be expected either in post-starburst objects or due to transfer
sicallyverydifferentspectrumwithastrong(EW(Lyα)>∼60Å) and dust effects. Since the outflow velocities of LBGs do not
Lyαemissionline.Radiationtransfereffectsandthepresenceof varystronglybetweensubsampleswithdifferentLyαstrengths2
dust transform the intrinsic starburst spectrum to the observed we proposethatthe mainfactorleadingto thediversityofLyα
one. strengthsinLBGsistheirHcolumndensityandconcomitantly
theirdustcontent3.
Thissuggestionis compatiblewith the observationalcorre-
5. Discussion:aunifyingscenarioforLyαemission lationsfoundbetweenE(B-V)andEW(Lyα)(e.g.Shapleyetal.
inLBGs 2003; Tapkenetal. 2007) and with the differences in extinc-
tion found by Pentericcietal. (2007) between two subsamples
As we have shown above the observed Lyα spectrum of cB58
ofz ∼ 4LBGs. Italsobroadlyagreeswith Lyαline profilefit-
is compatible with an intrinsically strong Lyα emission (with
ting of LBGs with strong Lyα emission, discussed in the next
EW(Lyα) > 60 Å). Hence this is compatible with the equiva-
paperofthisseries(Verhammeetal.2007).
lent width expected for a starburst with a constant star forma-
Given observed mass-metallicity relations (e.g. Erbetal.
tionrateover>50–100Myr,thetimescaleoverwhichEW(Lyα)
2006;Tremontietal.2004)itmaybequitenaturaltospeculate
reachesa constantequilibriumvalueof∼ 60–80Å fora “stan- thatthedifferenceinN anddustcontentisrelatedtothegalaxy
H
dard” IMF and metallicities comparable to that of cB58 (see
masstofirstorder.ThedataofShapleyetal.(2001)showsucha
Fig.3andSchaerer2003).ThereforetheobservedLyαstrength
trend.InthiscasemoremassiveLBGswouldbemoredusty,and
and profileare compatiblewith the star-formationhistoriesde-
henceshowlowerEW(Lyα),althoughtheycouldhaveidentical
rived from detailed modeling of the rest-UV properties, who
Lyαemissionpropertiesintrinsically.Suchatrendise.g.found
consistentlyfoundaconstantstarformationrateandagesupto
by Pentericcietal. (2007). The absenceof brightLBGs (in the
agesof∼20–100Myr(cf.deMelloetal.2000;Ellingsonetal.
1996; Pettinietal. 2000). Constant star formation over such
2 The expansion velocities determined by one third of the veloc-
timescales,insteadofanagedburstwhichwouldberesponsible
ity shift between the interstellar absorption lines and the Lyα peak,
foralowEW(Lyα),isalsophysicallymoreplausibleforobjects V ∼ 1/3∆(V ,V(Lyα)) is ∼ 160–260 km s−1 for the sample of
exp ISM
likecB58havinglargestarformationrates,largephysicalscales, Shapleyetal.(2003).
etc. Takinginto accountLyα radiationtransferand dustallows 3 Ifthedust-to-gasratioremainsconstant,bothN andthedustcon-
H
ustoreconcilethesediagnostics. tentincreaseinlockstep.
8 DanielSchaerer,AnneVerhamme:3DLyαradiationtransfer.II.cB58andimplicationsforLyαinhigh-zstarbursts
UV restframe) with high Lyα equivalent widths (in emission) prototypical Lyman break galaxy MS 1512–cB58 at z = 2.7.
reported in many papers (e.g. Andoetal. 2004; Shapleyetal. Since this is one of, if not the best studied LBG, and since it
2003;Tapkenetal.2007) wouldalso naturallybeexplainedby is part of the quartile of LBGs showing predominantly Lyα in
this fact, if the SFR correlates with mass, as observed for star absorption (cf. Shapleyetal. 2003), a detailed Lyα line profile
forminggalaxiesouttoz∼2(seeDaddietal.2007;Elbazetal. analysisincludingradiationtransferanddusteffectsis ofgreat
2007;Noeskeetal.2007). interest.
RelevantfordeterminingtheLyαpropertiesarehowever,the Three different geometries were explored for the material
total H  column density and the relative dust to H  content. surrounding the central starburst; a spherically symmetric ex-
Assumingthelattertobeconstant4,theabovesuggestionwould panding shell with velocity V , a foregroundslab movingto-
exp
imply larger amounts of H  in more massive LBGs, known to wards the observer, and a geometry mimicing a shell with a
holdatleastinnearbygalaxies(Kennicutt1998).However,since lower velocity in the back. All available observational con-
theHresponsibleforshapingLyαisfoundinoutflowsitmay straintswereused(seeTable1).Inparticulartheseinclude:the
onlytraceafractionofthetotalneutralhydrogencontent.Hence velocityV ofthe foregroundmaterial, its Dopplerparameter
exp
the H  column density derivedfrom the Lyα fits may not be a b,columndensityN ,andtheobservedextinction.Thewidthof
H
goodtracerofthegasmass,andhencemaynotsimplyscalewith theintrinsicLyαemissionwastakenfromtheobservedFWHM
galaxymass.Correlatingtheoutflowpropertiesmorecloselyto ofHα.Thetwofreeparameterswere:theequivalentwidthofthe
those of the host galaxymayrequiredynamicalmodeling(e.g. intrinsicLyαemission,andthevelocityV ofthebackground
back
Blaizotandetal.2007;FerraraandRicotti2006). slab(ifapplicable).
While the “scenario”proposedheretoexplainthediversity Our radiation transfer calculations have confirmed what
ofLyαlinestrengthsinLBGsseemsconsistentwiththeobser- couldbeexpectedfromourearlierexpandingshellsimulations
vations,itremainstobetestedmoregenerally.LBGswithstrong and from the lower-than-usualobserved velocity shift between
Lyαemissionhavealsobeenstudiedwithourradiationtransfer the peak of “remnant” Lyα emission and the blue IS absorp-
models for this purpose and are broadly in agreementwith the tion lines (cf. Sect. 2.1); the Lyα line profile of cB58 cannot
scenarioproposedhere(Verhammeetal.2007).Alternativeex- bereproducedbyanexpandingshellwithisotropicconstantve-
planationshavealsobeenproposed.ForexampleShapleyetal. locity Vexp. Considering,however,a lower shell velocity in the
(2001)havefromempiricalevidencesuggestedageasthemain backallowedustoobtainexcellentfitstotheobservedLyαline
differenceinLBGs,whereyoungerobjectsaremoredusty,and profile.Interestingly,theinputspectrumrequiresafairlystrong
henceshowlessLyαemission.However,itisnotclearwhyolder Lyαemission,withalowerlimitofEW(Lyα)>∼60Å.Radiation
LBGs would contain less dust, especially since outflows, sup- transfer and the suppresion of photons by dust are responsible
posedly used to expel the dust, are ubiquitousin all LBGs and fortransformingsuchan inputspectrumintothe observedLyα
since precisely these outflowsare the location wherethe emer- absorptionprofilewithasuperposedfaintemissionpeak.Inthis
gent Lyα spectrum is determined. Also, why would younger waytheobservedLyαlinestrengthandprofilecanbereconciled
LBGsbemoremassivethanolderonesastheirdatawouldim- withthestrongintrinsicLyαemissionexpectedfromtheapprox-
ply ? FerraraandRicotti (2006) have proposedthat LBGs host imately constant star-formation history of cB58 derived from
short-lived (30± 5 Myr) starburst episodes, whose outflows – earlier detailed UV spectral analysis (cf. deMelloetal. 2000;
whenobservedatdifferentevolutionaryphases–wouldgiverise Pettinietal.2000).
totheobservedcorrelationsbetweenISlinesandLyα.However, In fact we suggest that cB58 and most other LBGs have
their conclusion may need to be revised since the “observed” intrinsically EW(Lyα) ∼ 60–80 Å or larger, and that the main
windvelocityversusSFRrelation(theirFig.1)isincorrectand physicalparameterresponsibleforthe observedvariety ofLyα
flatterthanassumed5.FurthermoretheagesobtainedfromSED strengthsandprofilesinLBGsisN andtheaccompanyingvari-
H
andspectralfitsofLBGsshowolderagesandfairlyconstantstar ation of the dust content (see Sect. 5). This explains not only
formationhistories,asalreadymentionedearlier. theabsorption-dominatedobjectcB58,butalsoobservedcorre-
InpaperIIIofthisseries(Verhammeetal.2007)wewillex- lationsbetweenE(B-V)andEW(Lyα)inLBGs, theabsenceof
amine how our models are able to explain variouscorrelations brightLBGswithstrongLyαemission,andothercorrelations.
observed among Lyα, IS lines, and other properties of LBGs Among the implications from our work are that observed
(Shapleyetal.2003)andLAEs.Furtherworkwillbeneededto EW(Lyα) distributions and Lyα luminosity functions must be
testthescenarioproposedhere,tounderstandmorepreciselythe correctedforradiationtransferanddusteffects.Furthermorerel-
relationsbetweenLBGsandLAEss,andtounderstandthelinks atively shortduty cycles, suggestedearlier in the literature,are
betweenstar-formation,hostgalaxy,andoutflowproperties. notrequiredtoexplainthevariationsobservedbetweendifferent
LBGtypes.Ourproposedunifyingscenariowillbedetailedfur-
therandsubjectedtoadditionaltestsinasubsequentpublication
6. Conclusions onasampeofLBGswithstrongLyαemission(Verhammeetal.
2007).Providingaclearerpictureofthephysicallinksbetween
A 3D Lyα and UV continuum radiation transfer code
theobservablesincludingLyαlinestrengthandprofile,andthe
(Verhammeetal.2006)hasforthefirsttimebeenappliedtothe
star-formation,hostgalaxy,andoutflowpropertiesandevolution
ofLBGsandLAEsremainsanobjectiveforthenearfuture.
4 Combining e.g.thedependence of thedust-to-gasratioonmetal-
licityO/HfromLisenfeldandFerrara(1998)withthemass-metallicity Acknowledgements. WethankMaxPettiniandSandraSavaglioforprovidingus
relationatz>∼2(Erbetal.2006),givesaverysmalldependenceofthe withtheirhighresolutionUVspectraofcB58,andMiguelCervin˜oforsynthetic
dust-to-gasratioongalaxianmass. high-resolutionspectra.ThisworkwassupportedbytheSwissNationalScience
5 Theyassume v = 1/2∆(V ,V(Lyα))insteadof theweaker de- Foundation.
w ISM
pendence v ∼ 1/3∆(V ,V(Lyα)) obtained from shell models and
w ISM
supportedbydirectmeasurementsofstellar,IS,andLyαvelocityshifts.
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