Intergalactic Transmission and its Impact on the Lyα Line
aa r X i v : . [ a s t r o - ph . C O ] D ec Preprint typeset using L A TEX style emulateapj v. 11/10/09
INTERGALACTIC TRANSMISSION AND ITS IMPACT ON THE LY α LINE
Peter Laursen , Jesper Sommer-Larsen and Alexei O. Razoumov ABSTRACTWe study the intergalactic transmission of radiation in the vicinity of the Ly α wavelength. Simu-lating sightlines through the intergalactic medium (IGM) in detailed cosmological hydrosimulations,the impact of the IGM on the shape of the line profile from Ly α emitting galaxies at redshifts 2.5 to6.5 is investigated. In particular we show that taking into account the correlation of the density andvelocity fields of the IGM with the galaxies, the blue part of the spectrum may be appreciably reduced,even at relatively low redshifts. This may in some cases provide an alternative to the often-invokedoutflow scenario, although it is concluded that this model is still a plausible explanation of the manyasymmetric Ly α profiles observed.Applying the calculated wavelength dependent transmission to simulated spectra from Ly α emittinggalaxies, we derive the fraction of photons that are lost in the IGM, in addition to what is absorbedinternally in the galaxies due to dust.Moreover, by comparing the calculated transmission of radiation blueward of the Ly α line withcorresponding observations, we are able to constrain the epoch when the Universe was reionized to z . . Subject headings: intergalactic medium — radiative transfer — scattering — line: profiles INTRODUCTION
The past decade has seen a rapid increase in the useof Ly α as a cosmological tool. A plethora of physicalcharacteristics of young galaxies and the intergalacticmedium (IGM) that separate them manifest themselvesin the shape, the strength, and the spatial distributionof both Ly α emission and absorption lines.Since generally the evolution of astrophysical objectshappen on timescales much longer than a human life-time, numerical simulations are particularly well-suitedfor exploring the Universe. Many elaborate numericalcodes have been constructed to model the Universe onall scales, from dust agglomeration, over planetary andstellar formation, to simulations of cosmological volumes.Although these codes include a steadily increasing num-ber of physical processes, numerical resolution, etc., andalthough they are able to predict various observables,many of them fail to account for the fact that the ob-served light may be rather different from the light thatwas emitted. Once radiation leaves its origins, it maystill be subject to various physical processes altering notonly its intensity, but in some cases also its spatial andspectral distribution. If we do not understand these pro-cesses, we may severely misinterpret the predictions ofthe models when comparing to observations. This isparticularly true with regard to resonant lines like Ly α , Dark Cosmology Centre, Niels Bohr Institute, Uni-versity of Copenhagen, Juliane Maries Vej 30, DK-2100,Copenhagen Ø, Denmark; email: [email protected],[email protected]. Oskar Klein Centre, Dept. of Astronomy, Stockholm Uni-versity, AlbaNova, SE-10691 Stockholm, Sweden. Excellence Cluster Universe, Technische Universit¨atM¨unchen, Boltzmannstraße 2, 85748 Garching, Germany. Marie Kruses Skole, Stavnsholtvej 29-31, DK-3520 Farum,Denmark. SHARCNET/UOIT, 2000 Simcoe Street N., Oshawa ONL1H7K4, Canada; email: [email protected]. where its complicated path may take it through regionsof unknown physical conditions. In order to interpret theobserved Ly α lines correctly, it is crucial to have an un-derstanding of the physical processes that influence theshape and transmission of the line.Although the atomic processes regulating the individ-ual scatterings are always the same , the physical condi-tions governing different regions in space will have a largeimpact on the outcome. For example, photons producedby gravitational cooling are mostly born in low-densityregions, and may escape the galaxy more or less freely.These photons thus tend to have a frequency close to theline center. On the other hand, photons produced in thedense stellar regions will usually have to scatter far fromthe line center in order to escape, and thus tend to com-prise the wings of the spectrum. However, these photonsare also more vulnerable to dust, since their paths aremuch longer, and since also most of the galactic dustresides in these emission regions. Moreover, the veloc-ity field of the gas elements also has an effect on theobserved line profile. In particular macroscopic gas mo-tions, such as gas accretion or outflows caused by feed-back due to massive star formation, will skew the line(e.g. Dijkstra et al. 2006; Verhamme et al. 2006).While the history of theoretical Ly α radiative trans-fer (RT) dates back to the 1930’s (Ambarzumian 1932;Chandrasekhar 1935), the first practical prediction ofspectra emerging from a source embedded in neutral hy-drogen was given by Harrington (1973), and later gen-eralized by Neufeld (1990). Due to the high opacityfor a photon at the line center, in general the photonshave to diffuse in frequency and should hence escape themedium in a double-peaked spectrum. Although this As long the atom is not perturbed during the ∼ − seconds itis excited; this, however, can be safely ignored in most astrophysicalsituations. Laursen et al.has indeed been observed (e.g. Yee & De Robertis 1991;Venemans et al. 2005; Vanzella 2008), apparently mostLy α profiles from high-redshift galaxies seem to be miss-ing the blue peak. An immediate conclusion would bethat high-redshift, Ly α emitting galaxies (LAEs) are inthe process of massive star formation and thus exhibitstrong outflows. Indeed, this scenario has been invokedto explain a large number of LAE spectra, most convinc-ingly by Verhamme et al. (2008) who, assuming a centralsource and thin surrounding shell of neutral gas whilevarying its expansion velocity, temperature, and gas anddust column density, manage to produce nice fits to anumber of observed spectra.Although the thin expanding shell scenario hinges ona physically plausible mechanism, it is obviously ratheridealized. Furthermore, since most observations showonly the red peak of the profile, it seems to indicate thatmost (high-redshift) galaxies exhibit outflows. However,at high redshifts many galaxies are still forming, resultingin infall which would in turn imply an increased blue peak. Since this is rarely observed, in this paper we aimto investigate whether some other mechanism, such asIGM RT effects, could be responsible for removing theblue peak and/or enhancing the red peak.The present study complements other recent endeav-ors to achieve a comprehensive understanding of howthe Ly α line is redistributed in frequency and real space after having escaped its host galaxy (Iliev et al. 2008;Barnes & Haehnelt 2010; Faucher-Gigu`ere et al. 2010;Zheng et al. 2010a,b,c). Our cosmological volume is notas large as most of these studies, and although gas dy-namics are included in the simulations, ioniziation by UVradiation is calculated as a post-process rather than onthe fly. The reward is a highly increased resolution, al-lowing us to study the circumgalactic environs in greatdetail. Moreover, we inquire into the temporal evolutionof the IGM.The exploration of the high-redshift Ly α Universe israpidly progressing, gradually providing a census of thephysical properties of young galaxies, such as their lu-minosity functions, clustering properties, evolution, andcontents. Recent notable surveys have revealed hundredsof LAEs at high redshifts, from z ∼ . z ∼ . z ∼ . α line profile and amplitude throughout differentepochs is a step toward a more accurate interpretationof the observations.In the following section, we discuss qualitatively theimpact of the IGM on the Ly α line profile. In Section 3we then decribe the numerical simulations we have per-formed to study the effect quantitatively, the results ofwhich are presented in Section 4. We discuss our findingsin Section 5, and summarize in Section 6. THE INTERGALACTIC MEDIUM
As light travels through the expanding Universe, it getsredshifted, implying that wavelengths λ blueward of theLy α line center are eventually shifted into resonance. If,for a given wavelength, this happens in the vicinity of asufficient amount of neutral hydrogen, the spectrum ex-periences an absorption line (although strictly speaking the photons are not absorbed, but rather scattered outof the line of sight). This results in the so-called Ly α forest (LAF; Lynds 1971; Sargent et al. 1980).As the red part of the spectrum is only shifted far-ther away from resonance, IGM absorption tends toskew the line and not simply diminish it by some fac-tor. In most earlier studies of the line profiles of high-redshift galaxies, the IGM has either been ignored (e.g.Verhamme et al. 2006, 2008), taken to transmit the redhalf and remove the blue part (e.g. Finkelstein et al.2008), or to influence the line uniformly by a fac-tor e −h τ i , where h τ i is the average optical depth ofthe Universe (e.g. Bruscoli et al. 2003; Meiksin 2005;Faucher-Gigu`ere et al. 2008; Rykoff et al. 2009).Consider a source emitting the normalized spectrum F em ( λ ) ≡ λ . In an idealized, completely ho-mogeneous universe undergoing completely homologousexpansion (“ideal Hubble flow”) and with the absorptionprofiles having a negligible width, the observed spectrumwould simply be a step function, with F ( λ ) = F red = 1for λ > λ , and F ( λ ) = F blue < λ ≤ λ , where λ = 1216 ˚A is the central wavelength of the line. Threefactors contribute to make F differ from a step function:Firstly, the Ly α line is not a delta function, but has a fi-nite width, in some cases extending significantly into thered part of the spectrum. Secondly, the IGM is highly in-homogeneous, leading to large variations in F bluewardof λ — the LAF. If we consider the average effect ofthe IGM and let F be the average of many sightlines, F blue should still be a constant function of wavelength.However, in the proximity of galaxies the gas density ishigher than far from the galaxies; on the other hand, inthese regions the stellar ionizing UV radiation may re-duce the neutral gas fraction. Consequently, wavelengthsjust blueward of the line center may not on average besubject to the same absorption as farther away from theline. Regardless of which of the two effects — gas over-density or stronger UV field — is more important, thecorrelation of the IGM with the source cannot be ne-glected.Finally the expansion is not exactly homologous, sincepeculiar velocities of the gas elements will cause fluctua-tions around the pure Hubble flow. Considering againnot individual sightlines but the average effect of theIGM, these fluctuations are random and cancel out; onaverage, for every gas element that recedes from a galaxyfaster than the Hubble flow and thus causes an absorp-tion line at a slightly bluer wavelength, another gas el-ement does the opposite. Hence, the average transmis-sion in a “realistic” universe is the same as in a universewhere there are no peculiar velocities. However, in theproximity of overdensities, the extra mass results in a“retarded” expansion of the local IGM. When expansionaround a source is somewhat slower than that of the restof the Universe, on average matter in a larger region willbe capable of causing absorption, since the slower theexpansion, the farther the photons will have to travelbefore shifting out of resonance. The transmission function
This paper focuses on two different aspects of the in-tergalactic transmission. First, to see how the Ly α line isaffected by the IGM, we calculate a “transmission func-ntergalactic Transmission and its Impact on the Ly α Line 3tion” given by the average, normalized flux F ( λ ). Specif-ically, F is calculated by taking the median value in eachwavelength bin of many sightlines, originating just out-side a large number of galaxies (where “just outside” willbe defined later). The standard deviation is defined bythe 16 and 84 percentiles. From the above discussionwe may expect that F be characterized by a red part F red ≃
1, and a blue part F blue <
1, but with a non-trivial shape just blueward of the line center, since theIGM in the vicinity of the sources is different than farfrom the sources.
The average transmission
We will also examine the average transmission T = T ( z ) of the IGM, defined by first calculating for each in-dividual sightline the fraction of photons that are trans-mitted through the IGM in a relatively large wavelengthinterval well away from the line center, and then takingthe median of all sightlines (again with the 16 and 84percentiles defining the standard deviation). This quan-tity is sensitive to the overall ionization state of the IGM,and has therefore been used observationally to put con-straints on the so-called Epoch of Reionization (EoR; e.g.Becker et al. 2001; Djorgovski et al. 2001). A paramountpuzzle in modern cosmology is the question of when andhow the hydrogen, and later helium, was reionized. TheEoR marks a comprehensive change of the physical stateof the gaseous Universe, and to understand the cause, aswell as the course, of this phenomenon is a challengingtask. Besides being a compelling event in itself, it alsohas profound implications for the interpretation of ob-servations and theoretical cosmological models, not onlydue to the increased transparency of the IGM, but alsobecause of the accompanying rise in IGM temperature.One way of probing the EoR is by looking at the spec-tra of high-redshift quasars. The intrinsic spectrum of aquasar is characterized by broad emission lines; in partic-ular the Ly α line is very prominent. For larger redshiftsthe absorption lines of the LAF gets increasingly copious,until eventually all of the light blueward of Ly α is ab-sorbed, resulting in the so-called Gunn-Peterson trough(Gunn & Peterson 1965). Observations of a large num-ber of quasars show that the Universe was largely opaqueto radiation blueward of Ly α at z & SIMULATIONS
Laursen et al. (2009a,b) considered numerically theshape of the Ly α spectrum emerging from galaxies at z ∼ .
5, based on hydro/gravity galaxy simulations ofvery high resolution. In these studies, the RT was carriedout with Monte Carlo simulations, following individualphotons (or photon packets) as they scatter stochasti-cally out through the interstellar medium. Since highresolution is important for the Ly α RT, especially whentaking into account dust, the simulations were conductedin galaxies extracted from a fully cosmological, large vol-ume model, resimulated at high resolution, and inter-polated onto an adaptively refined grid. This Ly α RT A “resimulation” is performed by tracing the position of theparticles comprising a given galaxy back to the initial conditions,and then repeating the simulation at 8 or 64 times the originalmass resolution. evidently only predicts the spectrum of radiation thatone would observe if located in the vicinity of the galax-ies. In reality the radiation has to travel trough the IGM.At a redshift of ∼ how largean impact the IGM exerts on the radiation, full IGMRT has to be computed. Furthermore, at higher red-shifts where the IGM is generally more neutral and moredense, neglecting the effect would lead to severely erro-neous results.In principle this could be achieved by performing firstthe “galactic” RT in the high-resolution resimulationsand subsequently continuing the RT in the low-resolutioncosmological volume from the location of the individualgalaxies. However, although the physics of scatteringin galaxies and that of scattering in the IGM is not in-herently different, the difference in physical conditionsimposes a natural division of the two schemes: in thedense gas of galaxies, photons are continuously scatteredin and out of the line of sight, whereas in the IGM, oncea photon is scattered out of the line of sight, it is “lost”,becoming part of the background radiation. The prob-ability of a background photon being scattered into theline of sight, on the other hand, is vanishingly small.In order to disentangle galactic from intergalactic ef-fects, and, more importantly, to investigate the generaleffect of the IGM instead of merely the IGM lying be-tween us and a handful of resimulated galaxies, we takea different approach: the transmission properties of theIGM are studied by calculating the normalized spectrum F ( λ ) — the transmission function — in the vicinity ofthe Ly α line, as an average of a large number of sightlinescast through the cosmological volume, and originatingjust outside a large number of galaxies. Cosmological simulations
A standard, flat ΛCDM is assumed, with Ω m = 0 . Λ = 0 .
7, and h = H /
100 km − Mpc − = 0 . ab initio hydro/gravity simulations (Sommer-Larsen et al. 2003;Sommer-Larsen 2006). The code used in these simula-tions is a significantly improved version of the TreeSPHcode, which has been used previously for galaxy for-mation simulations (Sommer-Larsen et al. 2003). Themain improvements over the previous version are: (1)The “conservative” entropy equation solving scheme(Springel & Hernquist 2002) has been implemented, im-proving shock resolution in SPH simulations. In partic-ular, this improves the resolution of the starburst-drivengalactic superwinds invoked in the simulations. (2) Non-instantaneous gas recycling and chemical evolution, trac-ing the ten elements H, He, C, N, O, Mg, Si, S, Ca andFe (Lia et al. 2002a,b); the algorithm invokes effects ofsupernovae of type II and type Ia, and mass loss fromstars of all masses. (3) Atomic radiative cooling de-pending both on the metal abundance of the gas andon the meta-galactic UV background (UVB), modeledafter Haardt & Madau (1996), is invoked, as well as asimplified treatment of radiative transfer, switching offthe UVB where the gas becomes optically thick to Ly- Laursen et al.man limit photons on a scale of 0.1 kpc (Sommer-Larsen2006). The simple scheme for UVB RT is supplementedby a more elaborate post-process ionizing UV RT scheme,as described in Section 3.2.The simulation volumes were selected from two darkmatter (DM) only cosmological simulations of box length10 h − Mpc, set up at z i = 39 using identical Fouriermodes and phases, but with rms linear fluctuations ona scale of 8 h − Mpc, σ , equal to either 0.74 or 0.9, re-spectively, bracketing the latest WMAP -inferred valueof ∼ DM particles, andhave been used previously for galaxy resimulations (e.g.Sommer-Larsen et al. 2003; Sommer-Larsen 2006, note,however, that in these simulations, σ = 1 . h − Mpc (about half thevolume of the original DM-only simulation), and in thisregion all DM particles were split into a DM particle anda gas (SPH) particle according to an adopted universalbaryon fraction of f b = 0 .
15, in line with recent esti-mates. The cosmological regions resimulated thus had acomoving volume of about 1500 Mpc , contained about17 million particles in total, and were resimulated withan open boundary condition using the full hydro/gravitycode. The numerical resolution of these cosmological res-imulations was hence the same as that of the individualgalaxy formation simulations of Sommer-Larsen et al.(2003), reflecting the very considerable increase in com-puting power since then.The masses of SPH, star and DM particles were m gas = m ⋆ = 7 . × and m DM = 4 . × h − M ⊙ , andthe gravity softening lengths were ǫ gas = ǫ ⋆ = 380 and ǫ DM = 680 h − pc. The gravity softening lengths werekept constant in physical coordinates from z = 6 to z =0, and constant in comoving coordinates at earlier times.The choice of stellar initial mass function (IMF) af-fects the chemical evolution and the energetics of stel-lar feedback processes, in particular starburst-drivengalactic superwinds. Motivated by the findings ofSommer-Larsen & Fynbo (2008), a Salpeter (1955) IMFwas adopted for the simulations presented in this paper. Ionizing UV radiative transfer
The Haardt & Madau UVB field becomes negligible at z ≥ z re = 6. To comply with the results of WMAP, whichindicate a somewhat earlier onset of the ionizing back-ground, we ran an additional set of models, in whichthe UVB intensity curve was “stretched” to initiate at z re = 10. In the following, Model 1, 2, and 3 refersto simulations using ( z re , σ ) = (10 , . z re = 10 will be referred to as “early”reionization, while z re = 6 will be referred to as “late”reionization. In Sections 4.1 and 4.3 we study the differ-ences between these models.A realistic UV RT scheme(Razoumov & Sommer-Larsen 2006, 2007) was em- http://lambda.gsfc.nasa.gov/product/map/current/ ployed to post-process the results of the hydrodynamicalsimulations using the following approach: First, thephysical properties of the SPH particles (density,temperature, etc.) are interpolated onto an adaptivelyrefined grid of base resolution 128 , with dense cellsrecursively subdivided into eight cells, until no cellcontains more than ten particles. Around each stellarsource, a number of radial rays are constructed andfollowed through the nested grid, accumulating photore-action number and energy rates in each cell. Rays aresplit either as one moves farther away from the source,or as a refined cell is entered. These reaction rates areused to compute iteratively the equilibrium ionizationstate of each cell.In addition to stellar photons, we also accountfor ionization and heating by LyC photons origi-nating outside the computational volume with theFTTE scheme (Razoumov & Cardall 2005) assuming theHaardt & Madau UVB, modified to match the particularreionization model.Since the relative ratio of H i , He i , and He ii densitiesvaries from cell to cell, the UV RT is computed separatelyin three frequency bands, [13 . , .
6[ eV, [24 . , .
4[ eV,and [54 . , ∞ [ eV, respectively. In each cell the angle-averaged intensity is added to the chemistry solver tocompute the ionization equilibrium. Galaxy selection criteria
Galaxies are located in the simulations as describedin Sommer-Larsen et al. (2005). To make sure that agiven identified structure is a real galaxy, the followingselection criteria are imposed on the sample:1. To ensure that a given structure “ i ” is not just asubstructure of a larger structure “ j ”, if the centerof structure i is situated within the virial radius of j , it must have more stars than j .2. The minimum number of star particles must be atleast N ⋆, min = 15. This corresponds to a minimumstellar mass of log( M ⋆, min /M ⊙ ) = 7 . V c = p GM vir /r vir must be V c ≥
35 km s − .The IGM in the vicinity of large galaxies is to some ex-tend different from the IGM around small galaxies. Themore mass gives rise to a deeper gravitational poten-tial, enhancing the retarded Hubble flow. On the otherhand, the larger star formation may cause a larger bub-ble of ionized gas around it. To investigate the differencein transmission, the sample of accepted galaxies is di-vided into three subsamples, denoted “small”, “interme-diate”, and “large”. To use the same separating criteriaat all redshifts, instead of separating by mass — whichincreases with time due to merging and accretion — thegalaxies are separated according to their circular veloc-ity, which does not change significantly over time. Thethresholds are defined somewhat arbitrarily as V = 55km s − (between small and intermediate galaxies) and V = 80 km s − (between intermediate and large galax-ies). The final sample of galaxies is shown in Figure 1,which shows the relation between stellar and virial mass,and the distribution of circular velocities.ntergalactic Transmission and its Impact on the Ly α Line 5
Fig. 1.—
Left:
Scatter plot of virial masses M vir vs. stellar masses M ⋆ for the full, unfiltered sample of galaxies. The colors signifyredshift, with more red meaning higher redshift (exact values are seen in the right plot’s legend). The data points of Model 1, 2, and 3are shown with triangles , plus signs , and crosses , respectively. The galaxies that are rejected are overplottet with gray crosses, with dark , medium , and light gray corresponding to rejection criterion 1, 2, and 3, respectively. Right:
Distribution of circular velocities V c for theaccepted galaxies in Model 1. The distributions for Model 2 and 3 look similar, although Model 2 has more galaxies (see Table 1). TABLE 1Number of galaxies in the simulations
Model z re σ z Total Small Intermediate Large1. 10 0.74 2.5 343 207 80 563.5 309 138 127 443.8 283 125 119 394.3 252 102 115 354.8 225 111 86 285.3 201 98 85 185.8 154 75 62 176.5 121 70 44 72. 10 0.9 3.5 405 207 128 704.3 384 165 150 694.8 341 150 129 625.3 324 145 125 545.8 277 121 106 506.5 252 126 92 343. 6 0.74 3.5 325 162 122 413.8 318 165 117 364.3 293 150 110 334.8 250 138 84 285.3 204 101 85 185.8 160 75 67 186.5 126 69 50 7
Note . — “Small”, “intermediate”, and “large” galaxies aredefined as having circular velocities V c <
55 km s − , 55 kms − ≤ V c <
80 km s − , and V c ≥
80 km s − , respectively. The exact number of galaxies in the three models stud-ied in this work is seen in Table 1.
IGM radiative transfer
The IGM RT is conducted using the code
IGMtrans-fer . For the RT we use the same nested grid used for The code can be downloaded from the following URL: . the ionizing UV RT. The transmission properties of theIGM are studied by calculating the normalized spectrum F ( λ ) in the vicinity of the Ly α line, as an average ofa high number of sightlines cast through the simulatedcosmological volume.The resulting value of F ( λ ) at wavelength λ for a givensightline is F ( λ ) = e − τ ( λ ) . (1)The optical depth τ is the sum of contributions from allthe cells encountered along the line of sight: τ ( λ ) = cells X i n H I ,i r i σ ( λ + λv || ,i /c ) . (2)Here, n H I ,i is the density of neutral hydrogen in the i ’thcell, r i is the distance covered in that particular cell, v || ,i is the velocity component of the cell along the line ofsight, and σ ( λ ) is the cross section of neutral hydrogen.Due to the resonant nature of the transition, the largestcontribution at a given wavelength will arise from thecells the velocity of which corresponds to shifting thewavelength close to resonance.Although no formal definition of the transition from agalaxy to the IGM exists, we have to settle on a defini-tion of where to begin the sightlines, i.e. the distance r from the center of a galaxy. Observed Ly α profiles resultfrom scattering processes in first the galaxy and subse-qently the IGM, and regardless of the chosen value of r ,for consistency “galactic Ly α RT” should be terminatedat the same value when coupling the two RT schemes. Ingalactic Ly α RT, individual photons are traced, while inIGM RT we only consider the photons that are not scat-tered out of the line of sight. Hence the sightlines shouldbegin where photons are mainly scattered out of the lineof sight, and only a small fraction is scattered into theline of sight. Since more neutral gas is associated withlarger galaxies, as well as with higher redshift, clearly Laursen et al. r depends on the galaxy and the epoch, but measuring r in units of the virial radius r vir helps to compare thephysical conditions around different galaxies. In Section4.1 we argue the a reasonable value of r is 1 . r vir , andshow that the final results are only mildly sensitive tothe actual chosen value of r .At a given redshift, F ( λ ) is calculated as the median ineach wavelength bin of 10 sightlines from each galaxy inthe sample (using 10 sightlines produces virtually iden-tical results). The number of galaxies amounts to severalhundreds, and increases with time (cf. Table 1). The sim-ulated volume is a spherical region of comoving diameter D box , but to avoid any spuriosities at the edge of theregion only a 0 . D box sphere is used. Due to the limitedsize of the volume, in order to perform the RT until asufficiently short wavelength is redshifted into resonancethe sightlines are allowed to “bounce” within the sphere,such that a ray reaching the edge of the sphere is re-“emitted” back in a random angle in such a way that thetotal volume is equally well sampled. Note however thatin general the wavelength region close to the line that isaffected by the correlation of the IGM with the source isreached well before the the first bouncing.The normalized spectrum is emitted at rest wavelengthin the reference frame of the center of mass of a galaxy,which in turn may have a peculiar velocity relative tothe cell at which it is centered. This spectrum is thenLorentz transformed between the reference frames of thecells encountered along the line of sight. Since the ex-pansion of space is approximately homologous, each cellcan be perceived as lying in the center of the simulation,and hence this bouncing scheme does not introduce anybias, apart from reusing the same volume several timesfor a given sightline. However, since the sightlines scatteraround stochastically and thus pierce a given region fromvarious directions, no periodicities arise in the calculatedspectrum.To probe the average transmission, the sightlines arepropagated until the wavelength 1080 ˚A has been red-shifted into resonance, corresponding to ∆ z ≃ .
1. Inthis case the sightlines bounce roughly 30 (20) times at z = 2 . RESULTS
In the following sections, Model 1 is taken to be the“benchmark” model, while the others are discussed inSection 5.5.
The Ly α transmission function Figure 2 shows the calculated transmission functions F ( λ ) at various redshifts. Indeed, a dip just bluewardof the line center is visible at all redshifts. The resultsin Figure 2 were calculated as the median of sightinesemerging from all galaxies in the sample. Of course alarge scatter exists, since each sightline goes through verydifferent regions, even if emanating from the same galaxy.Figure 3 shows the scatter associated with F for threedifferent redshifts. The equivalent transmission functionsfor the z re = 6 model are shown in Figure 4. While athigh redshifts the z re = 6 model clearly results in a muchmore opaque universe, at lower redshifts the transmissionproperties of the IGM in the different models are moresimilar, although at z = 3 .
5, the z re = 10 model stilltransmits more light. To see the difference in transmission around galaxiesof different sizes, Figure 5 shows transmission functionfor three size ranges (defined in Section 3.3). Since thedistance from the galaxies at which the sightlines startis given in terms of virial radii, sightlines emerging fromsmall galaxies start closer to their source than for largegalaxies, and since at lower redshifts they tend to be clus-tered together in the same overdensities as large galaxies,this results in slightly more absorption. However, the dif-ference is not very significant. Effect on the spectrum and escape fraction
In Figure 6 the “purpose” of the transmission functionis illustrated: the left panel shows the spectrum emergingfrom a galaxy of M vir = 4 . × M ⊙ and Ly α luminosity L Ly α = 4 . × erg s − , calculated with the MonteCarlo Ly α RT code
MoCaLaTA (Laursen et al. 2009a).Its circular velocity of 42 km s − characterizes it as asmall galaxy. The spectrum which is actually observed,after the light has been transferred through the IGM,is shown in the right panel. Although on average theeffect of the IGM is not very large at this redshift, asseen by the solid line in the right panel, due to the largedispersion in transmission (visualized by the gray-shadedarea) at least some such galaxies will be observed with asubstantially diminished blue peak.In general, the larger a galaxy is the broader its emit-ted spectrum is, since Ly α photons have to diffuse far-ther from the line center for higher column densities ofneutral gas. If dust is present, this will tend to narrowthe line (Laursen et al. 2009b). Larger galaxies tend tohave higher metallicities and hence more dust, but thelines will still be broader than the ones of small galaxies.The galaxy used in Figure 6 is quite small. In Figure 7we show the impact of the IGM on the nine simulatedspectra from Laursen et al. (2009b), spanning a rangein stellar masses from ∼ to ∼ . For comparison,typical LAEs have stellar masses of M ⋆ /M ⊙ ∼ -10 (Gawiser et al. 2006; Lai et al. 2007; Finkelstein et al.2007; Nilsson et al. 2007, obtained from SED fitting).Besides altering the shape of the emitted spectrum, theIGM also has an effect on another quantity of much inter-est to observers, namely the observed fraction f obs of theintrinsically emitted number of Ly α photons. Since thebulk of the emitted Ly α photons is due to young stars,the total Ly α luminosity of a galaxy may be used as aproxy for its star formation rate (SFR), one of the mainquantities characterizing galaxies. Assuming case B re-combination, L Ly α can be converted to a total H α lumi-nosity L H α (through L H α = L Ly α / .
7; Osterbrock 1989),which in turn can be converted to an SFR (through SFR= 7 . × − L H α / (erg s − ) M ⊙ yr − ; Kennicutt 1998).The above conversion factors assume that none of theemitted light is lost. If dust is present in the galaxy afraction of the emitted photons will be absorbed (possi-bly making the LAE observable in FIR; see Dayal et al.2010a). This can be corrected for if the color excess E ( B − V ) is measured, assuming some standard extinc-tion curve. However, this assumes that both the H α andLy α radiation are simply reduced by some factor corre-sponding to having traveled the same distance throughthe dusty medium. But since the path of Ly α photonsis increased by resonant scattering, this may be far fromntergalactic Transmission and its Impact on the Ly α Line 7
Fig. 2.—
Normalized transmission F ( λ ) at wavelengths around Ly α , for different redshifts given by the color. In the left panel, thevertical axis is linear, while in the right it is logarithmic, emphasizing the transmission at high redshifts. Fig. 3.—
Transmission F for z = 3 . left ), 5.8 ( middle ), and 6.5 ( right ) in Model 1, i.e. with σ = 0 .
74 and z re = 10. The shaded regionindicates the range within which 68% of the individual calculated transmission functions fall. Fig. 4.—
Same as Figure 3 for Model 3, i.e. with z re = 6. While at high redshifts a much more neutral IGM than in the z re = 10 modelcauses a severe suppression of the Ly α line, by z = 3 . Laursen et al.
Fig. 5.—
Transmission F for z = 3 . left ), 5.8 ( middle ), and 6.5 ( right ), for three different size categories of galaxies; small ( dotted ),intermediate ( dashed ), and large ( solid lines ). Although slightly more absorption is seen in the vicinity of smaller galaxies, the transmissionfunctions are quite similar for the three size ranges. Fig. 6.—
Illustration of the effect of the IGM on the observed Ly α profile emerging from a galaxy at z ∼ .
5. Without taking into accountthe IGM the two peaks are roughly equally high ( left panel ). However, when the spectrum is transmitted through the IGM characterizedby the transmission function F ( λ ) ( middle panel ), the blue peak is dimished, resulting in an observed spectrum with a higher red peak( right panel ). ntergalactic Transmission and its Impact on the Ly α Line 9
Fig. 7.—
Emitted spectra ( dotted lines ) from nine different simulated galaxies at ∼ solid lines with gray regions denoting the 68% confidence intervals ). Thetransmission functions appropriate for the given galaxy sizes have been used. In order to use the same ordinate axis for a given row, someintensities have been multiplied a factor indicated under the name of the galaxy. The numbers shown in gray are the corresponding galaxy’svirial mass in M ⊙ , its Ly α luminosity in erg s − , and its oxygen metallicity [O/H], respectively. the truth. Comparing the Ly α -inferred SFR with thatof H α (or UV continuum), the effect of scattering canbe constrained, as the quantity SFR(Ly α )/SFR(H α ;UV)will be an estimate of f obs . Using this technique, valuesfrom a few percent (mostly in the nearby Universe; e.g.Hayes et al. 2007; Atek et al. 2008; Hayes et al. 2010) to ∼ α , but not to Ly α . Dijkstra et al. (2007) estimated an-alytically the fraction of Ly α photons that are scatteredout of the line of sight by the IGM (at z ∼ . f IGM ∼ . T α ”). In that study, theintrinsic Ly α line profile is modeled as a Gaussian, the width of which is given by the circular velocity of thegalaxies, in turn given by their mass, and assuming thatno dust in the galaxies alters the shape of the line beforethe light enters the IGM.Since the transmission function is a non-trivial func-tion of wavelength, the exact shape and width of theLy α line profile is important. With the Ly α RT code
MoCaLaTA more realistic spectra can be modeled, andapplying the transmission function found in Section 4.1, f IGM can be calculated for the sample of simulated galax-ies. The transmitted fraction is not a strong function ofgalaxy size; on average, a fraction f IGM = 0 . +0 . − . ofthe photons escaping the galaxies is transmitted throughthe IGM, at the investigated redshift of z ∼ .
5. Theresults for the individual galaxies is given in Table 2.At higher redshifts the metallicity is generally lower,0 Laursen et al.
TABLE 2Ly α transmission fractions for nine simulatedgalaxies at z ∼ . V c f esc f IGM f obs S108sc 17 0 . ± .
02 0 . +0 . − . . +0 . − . S108 33 0 . ± .
02 0 . +0 . − . . +0 . − . S115sc 42 0 . ± .
03 0 . +0 . − . . +0 . − . S87 69 0 . ± .
01 0 . +0 . − . . +0 . − . S115 73 0 . ± .
05 0 . +0 . − . . +0 . − . K33 126 0 . ± .
02 0 . +0 . − . . +0 . − . S29 137 0 . ± .
03 0 . +0 . − . . +0 . − . K15 164 0 . ± .
02 0 . +0 . − . . +0 . − . S33sc 228 0 . ± .
02 0 . +0 . − . . +0 . − . Average . + . − . Note . — Columns are, from left to right: galaxyname, circular velocity V c in km s − , fraction f esc ofemitted photons escaping the galaxy (i.e. not absorbedby dust), fraction f IGM of these transmitted through theIGM, and resulting observed fraction f obs = f esc f IGM .Uncertainties in f esc represent varying escape fractionsin different directions, while uncertainties in f IGM rep-resent variance in the IGM. Uncertainties in f obs are cal-culated as ( σ obs /f obs ) = ( σ esc /f esc ) +( σ IGM /f IGM ) . leading to less dust and hence larger values of f esc . How-ever, the increased neutral fraction of the IGM scattersa correspondingly higher number of photons out of theline of sight, resulting in a smaller total observed frac-tion. Figure 8 and Figure 9 shows the impact of theIGM on Ly α profiles at z ∼ . z ∼ .
5, respec-tively, and Table 3 and Table 4 summarizes the ob-tained fractions. At these redshifts, for the six galax-ies for which the calculations have been carried outon average a fraction f IGM ( z = 5 .
8) = 0 . +0 . − . and f IGM ( z = 6 .
5) = 0 . +0 . − . of the photons is transmittedthrough the IGM, consistent with what was obtained byDijkstra et al. (2007). Probing the Epoch of Reionization
We now focus on a different topic, namely the RT inthe IGM far from the emitting galaxies. Measuring theaverage transmission in a wavelength interval bluewardof the Ly α line for a sample of quasars or other brightsources, one can ascertain the average transmission prop-erties and hence the physical state of the IGM. The in-terval in which the transmission is calculated should belarge enough to achieve good statistics, but short enoughthat the bluest wavelength does not correspond to a red-shift epoch appreciably different from the reddest. Fur-thermore, in order to probe the real IGM and not thequasar’s neighborhood, the upper limit of the wavelengthrange should be taken to have a value somewhat below λ .Songaila (2004) measured the IGM transmission in theLAFs of a large sample of quasars with redshifts between2 and 6.5, in the wavelength interval 1080–1185 ˚A. In Fig- TABLE 3Ly α transmission fractions for six simulatedgalaxies at z ∼ . V c f esc f IGM f obs K15g 63 0 . ± .
02 0 . +0 . − . . +0 . − . K15c 78 0 . ± .
02 0 . +0 . − . . +0 . − . K15b 88 0 . ± .
02 0 . +0 . − . . +0 . − . S29b 94 0 . ± .
01 0 . +0 . − . . +0 . − . S29a 96 0 . ± .
08 0 . +0 . − . . +0 . − . K15a 108 0 . ± .
05 0 . +0 . − . . +0 . − . Average . + . − . Note . — Same as Table 2, but for z = 5 . TABLE 4Ly α transmission fractions for six simulatedgalaxies at z ∼ . V c f esc f IGM f obs K15f 50 0 . ± .
03 0 . +0 . − . . +0 . − . K15e 62 0 . ± .
04 0 . +0 . − . . +0 . − . K15d 66 0 . ± .
02 0 . +0 . − . . +0 . − . K15c 76 0 . ± .
02 0 . +0 . − . . +0 . − . K15b 89 0 . ± .
03 0 . +0 . − . . +0 . − . K15a 108 0 . ± .
09 0 . +0 . − . . +0 . − . Average . + . − . Note . — Same as Table 2, but for z = 6 . ure 10 we compare the simulated transmitted fractionswith her sample. As is evident from the figure, an “early”reionization, i.e. with z re = 10 (Model 1 and 2), yields aslightly too transparent Universe, while a “late” reioniza-tion (Model 3) yields a too opaque Universe. Note thatthe log scale makes the z re = 6 data seem much fartheroff than the z re = 10 data. Convergence test
In Section 3.4 we stated that the sightlines should ini-tiate at a distance r from the centers of the galaxiesgiven by their virial radius. Figure 11 displays the cu-mulative probability distributions of the distance of thelast scattering from the galaxy center (calculated with MoCaLaTA ) for different redshifts and mass ranges,demonstrating that in most cases a photon will have ex-perienced its last scattering at the order of 1 r vir fromthe center of its host galaxy. For increasing redshift, thephotons tend to escape the galaxies at larger distancesdue to the higher fraction of neutral hydrogen, but thechange with redshift seems quite slow. Furthermore, ata given redshift the distinction between different galacticntergalactic Transmission and its Impact on the Ly α Line 11
Fig. 8.—
Same as Figure 7, but for z = 5 . Fig. 9.—
Same as Figure 7, but for z = 6 . Fig. 10.—
Comparison of observations ( black data points ) andsimulations ( colored data points ) of the transmitted flux bluewardof the Ly α line as a function of redshift. The three models arerepresented by the colors blue , green , and red for model 1, 2, and3, respectively. To highlight the significance of the improved UVRT, we show both the transmission in the “original” simulationwith the “pseudo”-RT ( crosses ) and with the improved UV RT( squares ). For details on the observations see Songaila (2004),from where the data are kindly supplied. size ranges appears insignificant (as long as r is mea-sured in terms of r vir ).Also shown in Figure 11 are the transmission curvesfor sightlines initiating at various distances r from thecenters of the galaxies. For very small values of r , asignificantly lower fraction is transmitted due to the highdensity of neutral gas. Around r ∼ r vir the change in F ( λ ) becomes slow, converging to F ( λ ) exhibiting nodip for r → ∞ .In summary, scaling r to the virial radius r vir of thegalaxies allows us to use the same value of r = 1 . r vir for all sightlines. DISCUSSION
The origin of the dip
In general, the effect of the IGM — even at relativelylow redshifts — is to reduce the blue peak of the Ly α line profile. At z ∼ .
5, the effect is not strong enough tofully explain the oft-observed asymmetry, but at z & z = 3 .
5, however,this effect is overcome by the accretion of gas.Inspecting the dips in Figure 2, the minima are seen tobe located at roughly 50 km s − , almost independently of the redshift but becoming slightly broader with in-creasing z . At z = 3 .
5, the dip extends all the way outto 300–400 km s − . This corresponds to the central ab-sorption being caused by the IGM within ∼
150 kpc, andthe wings of the absorption by the IGM within ∼ z = 3 . ∼
150 kpc n H I is substantially higherthan the cosmic mean. Further away, the density is closeto the mean density of the Universe. However, as seen inFigure 12 the recession velocity of the gas continues tolie below that of the average, Universal expansion rate,and in fact does so until approximately 1 Mpc from thesource. Thus, the cause of the suppression of the blue wing ofthe Ly α line may, at wavelengths close to the line center(∆ λ ≃ / λ . α RT in the IGM at z = 5 . e − τ ,as has been done in previous models (e.g. Iliev et al.2008). They conclude that neglecting scattering effectsseverely underestimates the transmitted fraction. Whileit is certainly true that treating scattering processes asabsorption inside the galaxies is only a crude approxima-tion, once the probability of photons being scattered into the line of sight becomes sufficiently small, this approachis quite valid. In their analysis, Zheng et al. (2010a) starttheir photons in the center of the galaxies, which are re-solved only by a few cells (their dx being ∼
28 kpc inphysical coordinates and their fiducial galaxy having r vir = 26 kpc). Since the side length of our smallest cellsare more than 400 times smaller than the resolution ofZheng et al. (2010a), we are able to resolve the galax-ies and their surroundings in great detail, and we arehence able to determine the distance at which the e − τ model becomes realistic. Moreover, when coupling theIGM RT with Ly α profiles, we use the realistically cal-culated profile, whereas Zheng et al. (2010a) use a Gaus-sian set by the galaxies’ halo masses. Their line widths σ init = 32 M / km s − , where M is the halo massdivided by 10 h − M ⊙ , thus neglect broadening by scat-tering. This makes them much smaller than ours, whichare typically several hundred km s − . Note, however,that our relatively small cosmological volume and thefact that ionizing UV RT is performed as a post-processrather than on the fly may make our density field lessaccurate than that of Zheng et al. (2010a).The photons that are scattered out of the line of sightare of course not lost, but rather become part of a dif-fuse Ly α background. Since more scatterings take placein the vicinity of galaxies, LAEs tend to be surroundedby a low-surface brightness halo, making them look moreextended on the sky when comparing to continuum bands Since the cosmological volume is several Mpc across, exceptfor the galaxies lying close to the edge, the absorption takes placebefore the sightlines “bounce”, so in general there is no risk ofa sightline going through the same region of space before havingescaped the zone causing the dip. ntergalactic Transmission and its Impact on the Ly α Line 13
Fig. 11.—
Left:
Cumulative probability distribution of the distance r from the center of a galaxy at which the last scattering takes place(calculated with the Ly α RT code
MoCaLaTA (Laursen et al. 2009a)).
Thin solid lines represent individual galaxies at redshift 2.5 ( blue ),3.5 ( green ), and 6.5 ( red ), while thick solid colored lines are the average of these. Also shown, in black , are the average of three differentsize ranges at z = 3 .
5; small ( dotted ), intermediate ( dashed ), and large galaxies ( solid ). Right:
Resulting transmission function F ( λ ) for sightlines originating at various distances r /r vir from galactic centers, increasing in stepsof 0 . r vir and ranging from r = 0 . r vir to r = 5 r vir . The three different redshifts are shown in shades of blue , green , and red , for z = 2 . r to dark shades for high values of r . The transmissionfunctions corresponding to r = 1 . r vir are shown in black dotted lines. All results are for Model 1. Fig. 12.—
Average recession velocity v bulk of the IGM as a function of proper distance d from the centers of the galaxies in Model 1( solid black lines, with gray regions indicating the 68% confidence intervals). At all redshift, the expansion is retarded compared to thepure Hubble flow ( dashed line) out to a distance of several comoving Mpc. At high redshifts, however, very close to the galaxies outflowsgenerate higher recession velocities. Fig. 13.—
Average density n H I of neutral hydrogen as a function of proper distance d from the centers of the galaxies in Model 1( solid black lines, with gray regions indicating the 68% confidence intervals). While in general the density decreases with distance, at highredshifts ionizing radiation reduces n H I in the immediate surroundings of at least some of the galaxies, as seen by the small dip at ∼ r ∼ ∼ α lines to obtain the intrinsic line profiles,other than in a statistical sense. With a large sample,however, more accurate statistics on Ly α profiles couldbe obtained. Calculating the transmission functions asan average of all directions, as we have done in this work,assumes that observed galaxies are randomly oriented inspace, i.e. that there is no selection effects making moreor less luminous directions pointing toward the observer.For LAEs clustered in, e.g., filaments, the effect of theretarded Hubble flow may be enhanced perpendicular tothe filament, making the galaxies more luminous if ob-served along a filament than perpendicular to it (see Fig-ure 9 in Zheng et al. 2010b). Galactic outflows
As discussed in the introduction, at high redshiftsmany galaxies are still in the process of forming and areexpected to be accreting gas. In principle, this should re-sult in a blueshifted Ly α profile, but this is rarely seen.Evidently, IGM absorption is unable to always be thecause of this missing blue peak. On larger scales, massis observed to be conveyed through large streams of gas;the cosmic filaments. Although this has been seen onlytentatively on galactic scales, galaxy formation may beexpected to occur in a similar fashion. Indeed, numericalsimulations confirm this scenario (e.g. Dekel et al. 2009;Goerdt et al. 2010). Very recently, Cresci et al. (2010)reported on an “inverted” metallicity gradient in three z ∼ α profiles lacking the blue peakthan lacking the red peak.The fact that starbursts are needed to generate largeoutflows also imposes a bias on the observations; evenif outflows happen only during relatively short phases inthe early life of a galaxy (for LBGs, Ferrara & Ricotti(2006) found that a typical starburst phase lasts onlyabout 30 ± Transmitted fraction of Ly α photons Even though absorption in the IGM does not alter theline shape drastically at an intermediate redshift of 3.5,it reduces the intensity by roughly one-fourth, as seenfrom Table 2. This fraction is not a strong function ofthe size of a galaxy, but since the spectra emerging fromlarger galaxies tend to be broader than those of smallergalaxies, a comparatively larger part of the small galaxyspectra will fall in the wavelength region characterized bythe dip in the transmission function. Hence, on averagethe IGM will transmit a larger fraction of the radiationescaping larger galaxies.One-fourth is not a lot, but since it is preferentiallyblue photons which are lost, the spectrum may becomequite skewed when traveling through the IGM. The lostfraction f IGM is in addition to what is lost internally inthe galaxies due to the presence of dust. As mentionedin Section 4.2, dust tends to make the line profile morenarrow. For galaxies with no dust, the lines can be verybroad. In this case, f IGM will be slightly higher, since forbroad lines a relatively smaller part of the spectrum fallson the dip seen in F ( λ ). Note however that in general dis-tinguishing between dust absorption and IGM effects willbe rather tricky, if not impossible (see also Dayal et al.2010a).As expected, at higher redshifts the IGM is moreopaque to Ly α photon; at z = 5 . z = 6 . z = 6 . z = 5 .
8. However,as is seen from the gray area representing the 68% con-fidence interval, in some cases an appreciable fraction ofthe blue wing can make it through the IGM.
The significance of dust
The IGM calculations performed in this work are allneglecting the effect of dust. However, dust is mostly(although not completely) confined to the galaxies, es-pecially the central parts, and since by far the greatestpart of the distance covered by a given sightline is in thehot and tenuous IGM, one may expect this to be a fairapproximation.This anticipation was confirmed following the dustmodel of Laursen et al. (2009b). In short, dust densityscales with gas density and metallicity, but is reduced inregions where hydrogen is ionized to simulate the effect ofdust destruction processes. The factor n H I σ ( λ ) in Equa-tion (2) is then replaced by n H I σ ( λ ) + n d σ d ( λ ), where n d and σ d ( λ ) are the density and cross section of dust,respectively. The resulting decrease in transmission is atthe 10 − to 10 − level. “Early” vs. “late” reionization As is evident from Figure 10, although none of themodels really fit , the early and late reionization bracketthe observations. Model 1, with σ = 0 .
74 provides asomewhat better fit to the observations than Model 2with σ = 0 .
9. Due to the more clumpy structure of thelatter, galaxies tend to form earlier, rendering the IGMmore free of gas and thus resulting in a slightly moretransparent Universe. However, this should not be takento mean that the lower value of σ is more realistic, sincea higher σ could be accounted for by a (slightly) smaller z re .ntergalactic Transmission and its Impact on the Ly α Line 15Investigating the LAF is not the only way of prob-ing the EoR. The WMAP satellite detects the effectsof the Thomson scattering of cosmic microwave back-ground (CMB) radiation on free electrons. Since thenumber density n e of free electrons increases as the Uni-verse gets reionized, a signature of the EoR can be ob-tained by measuring the total optical depth τ e to Thom-son scattering. The latest results (Jarosik et al. 2010)give τ e = 0 . ± . z reion ∼ dt of time is dτ = n e ( z ) σ T c dt = n e ( z ) σ T c z ) H ( z ) dz, (3)where σ T is the Thomson scattering cross section. Thatis, given an electron density history, the resulting total τ e can be calculated by integrating Equation (3).Figure 14 displays the average comoving number den-sity n e of electrons as a function of redshift, as well as thecorresponding total optical depth τ e of electrons. The re-sults for Model 2 and Model 3 are shown; those for Model1 lie very close to those of Model 2. Going from largertoward smaller redshifts, both models are seen to be char-acterized by a roughly constant and very low density ofelectrons before reionization, then a rapid increase not at , but shortly after z re , and finally a slow decrease, dueto subsequent gas cool-out and resulting galaxy forma-tion. The rapid increase marking the EoR lasts approxi-mately 100 Myr. The difference in ionization history forthe pseudo- and the realistic UV RT schemes is not criti-cal, although in the latter the creation of ionized bubblesaround stellar sources causes a slightly earlier EoR thanthe pseudo-RT is able to, especially in Model 3 ( z re = 6).Also shown in Figure 14 is the corresponding τ e historythat would prevail in the hypothetical case of an instant reionization, where the Universe is fully neutral before,and fully ionized after, some redshift z reion fixed to makethe total τ e match the value measured by WMAP. In thismodel, no gas is assumed to be locked up in stars, and n e is thus given by n e ( z ) = (cid:26) z > z reion ψ Ω b ρ c (1+ z ) m H for z ≤ z reion , (4)where ψ = 0 .
76 is the mass fraction of hydrogen,Ω b = 0 .
046 is the baryonic energy density parameter(Jarosik et al. 2010), ρ c is the critical density of the Uni-verse, and m H is the mass of the hydrogen atom.As seen from the figure, not even the early reioniza-tion model is able to reproduce the optical depth probedby WMAP. However, for a model with an even earlierEoR, the transmission T of the IGM would be even far-ther off the observational data, as seen from Figure 10.In general, there seems to be a significant disagreementbetween the WMAP results and the QSO results con-cerning the redshift of the EoR. Many authors have triedto resolve this apparent discrepancy, e.g. Wyithe & Loeb(2003) and Cen (2003) who considered a double reioniza-tion, first at z ∼ z ∼ τ e of the z re = 10model is not entirely inconsistent with the WMAP-inferred value, being roughly 2 σ away. Furthermore, since only the total optical depth is measured by WMAP,the exact history of the EoR is obviously less certain.Generally, either an instant reionization must be as-sumed, or perhaps a two-step function to make the EoRslightly extended, and possibly with an additionally stepat z ∼ z = 10 . satel-lite has a much higher resolution and sensitivity; whenPlanck data become available, these issues may be solvedas much tighter constraints can be put on parameters like τ e (Galli et al. 2010). SUMMARY
Simulating sightlines through cosmological hydrosim-ulations, we have investigated the transmission throughthe IGM of light in the vicinity of the Ly α line. The highresolution of the cosmological simulations combined withthe adaptive gridding for the RT allows us to probe thevelcity field around the galaxies in great detail. Whileearlier studies (Zheng et al. 2010a) have shown that thisapproach of simply multiplying an e − τ factor on theintrinsically emitted Ly α line is a poor approximationfor the observed line profile and transmitted fraction,we have argued that when the circumgalactic environsare sufficiently resolved and combined with realisticallycalculated intrinsic Ly α lines, this approach should bevalid. Special emphasis was put on how Ly α line profilesemerging from high-redshift galaxies are reshaped by thesurrounding IGM. In general a larger fraction of the blueside of the line center λ is lost as one moves towardhigher redshifts. At z &
5, almost all of the light blue-ward of λ is lost, scattered out of the line of sight by thehigh neutral fraction of hydrogen. However, even at rela-tively low redshift more absorption takes place just blue-ward λ . A transmission function F ( λ ) was calculated,giving the fraction of light that is transmitted trough theIGM at various epochs. At all redshifts where some ofthe light blueward of λ is transmitted (i.e. at redshiftsbelow ∼ α profile is severely reduced, or lacking. Nevertheless, it isnot sufficient to be the full explanation of the numerousobservations of z ∼ α profiles showing only thered peak. The outflow scenario still seems a credibleinterpretation.Combining the inferred transmission functions withsimulated line profiles, the fraction of Ly α photons thatare transmitted through the IGM at z ∼ .
5, 5.8, and6.5 was computed, and was found to be f IGM ( z = 3 .
5) =0 . +0 . − . , f IGM ( z = 5 .
8) = 0 . +0 . − . , and f IGM ( z = Fig. 14.—
Left:
Volume averaged, comoving electron density n e / (1 + z ) as a function of redshift z for Model 2 ( green ) and 3 ( red ) whichhave z re = 10 and z re = 6, respectively. Both models are characterized by a quite sharp increase in n e shortly after the onset of the UVB.For Model 2 the EoR is seen to take place around z ∼ .
5, while for Model the EoR lies at z ∼ . Right:
Integrated optical depth τ e of electrons as a function of redshift z for the two models. The dark gray line with the associated lightergray
68% and 95% confidence intervals indicates the τ e history required to reach the optical depth measured by WMAP, if an instantreionization is assumed. As expected, none of the models are able to reach the 0 . ± .
015 inferred from the WMAP results, althoughthe z re = 10 model is “only” ∼ σ away. Since the n e data do not extend all the way to z = 0, a fiducial value of n e ( z = 0) = 1 . × − cm − has been used. The exact value is not very imporant, since the proper density at low redshift is very small. At low redshift, themodel curves lie slightly below the theoretical curve. This is due to a combination of the models including helium ionization, releasingmore electrons, and star formation and gas cool-out, removing free electrons. .
5) = 0 . +0 . − . , respectively. This is in addition to whatis lost internally in the galaxies due to dust. The stan-dard deviations were found to be dominated by sightline-to-sightline variations rather than galaxy-to-galaxy vari-ations.Considering the average fraction of light far from theline on the blue side transmitted through the IGM, andcomparing to the comprehensive set of observations ofthe LAF by Songaila (2004), we constrain the EoR tohave initiated between z re = 10 and z re = 6, correspond-ing the having ionized a significant fraction of the Uni-verse around z ∼ . z ∼ .
5, respectively. Eventhough the “early” models of z re = 10 produces a slightlytoo transparent Universe when comparing to the LAF,the optical depth of electrons is too low when comparingto the observations of the CMB by the WMAP satellite, possibly indicating a too simplistic interpretation of theCMB polarization.We are grateful to Antoinette Songaila Cowie for let-ting us reproduce her observational data, to Andrea Fer-rara for helpful comments on the electron optical depth,to Zheng Zheng for pointing out errors and deficienciesin the first draft, and to the anonymous referee for com-ments leading to a substantially extended and better pa-per.The simulations were performed on the facilities pro-vided by the Danish Center for Scientific Computing.The Dark Cosmology Centre is funded by the DanishNational Research Foundation.PL acknowledges fundings from the Villum Founda-tion. REFERENCESAmbarzumian, V. A. 1932, MNRAS, 93, 50Atek, H., Kunth, D., Hayes, M., ¨Ostlin, G., Mas-Hesse, J. M.2008, A&A, 488, 491Barnes, L. & Haehnelt, M. G. 2010, MNRAS, 403, 870Bechtold, J., Crotts, A. P. S., Duncan, R. C., & Fang, Y. 1994,ApJ, 437, L83Becker, R. H. et al. 2001, AJ, 122, 2850Bi, H. & Davidsen, A. F. 1997, ApJ, 479, 523Bond, N. A., Feldmeier, J. J., Matkovi´c, A., Gronwall, C.,Ciardullo, R., & Gawiser, E. 2010, ApJ, 716, L200Bruscoli, M., Ferrara, A., Marri, S., Schneider, R., Maselli, A.,Rollinde, E., & Aracil, B. 2003, MNRAS, 343, L41Cen, R. 2003, ApJ, 591, 12Chandrasekhar, S. 1935, ZAp, 9, 267Cresci, G., Mannucci, F., Maiolino, R., Marconi, A., Gnerucci, A.,& Magrini, L. 2010 (arXiv:1010.2534)Dayal, P., Hirashita, H., & Ferrara, A., 2010, MNRAS, 403, 620Dekel, A., Birnboim, Y., Engel, G., Freundlich, J., Goerdt, T.,Mumcuoglu, M., Neistein, E., Pichon, C., Teyssier, R., &Zinger, E. 2009, Nature, 457, 451Dijkstra, M., Haiman, Z., & Spaans, M. 2006, ApJ, 649, 14 Dijkstra, M., Lidz, A., & Wyithe, J. S. B. 2007, MNRAS, 377,1175Dinshaw, N., Impey, C. D., Foltz, C. B., Weymann, R. J., &Chaffee, F. H. 1994, ApJ, 437, L87Djorgovski, S. G., Castro, S. M., Stern, D., & Mahabel, A. A.2001, ApJ, 560, L5Dunkley, J. et al. 2009, ApJS, 180, 306Fan, X., Carilli, C. L., & Keating, B. 2006, ARA&A, 44, 415Fang, Y., Duncan, R. C., Crotts, A. P. S., & Bechtold, J. 1996,ApJ, 462, 77Faucher-Gigu`ere, C.-A., Kereˇs, D., Dijkstra, M., Hernquist, L., &Zaldarriaga, M. 2010 (arXiv:1005.3041)Faucher-Gigu`ere, C.-A., Prochaska, J. X., Lidz, A., Hernquist, L.,& Zaldarriaga, M. 2008, ApJ, 681, 831Ferrara, A. & Ricotti, M. 2006, MNRAS, 373, 571Finkelstein, S. L., Rhoads, J. E., Malhotra, S., Pirzkal, N., Wang,J. 2007, ApJ, 660, 1023Finkelstein, S. L., Rhoads, J. E., Malhotra, S., Grogin, N., Wang,J. 2008 ApJ, 678, 655Fynbo, J. P. U., Møller, P., & Thomsen, B. 2001, A&A, 374, 443Fynbo, J. P. U., Ledoux, C., Møller, P., Thomsen, B. & Burud, I.2003, A&A, 407, 147 ntergalactic Transmission and its Impact on the Ly α Line 17
Galli, S., Martinelli, M., Melchiorri, A., Pagano, L., Sherwin, B.D., Spergel, D. N. (arXiv:1005.3808)Gawiser et al. 2006, ApJS, 162, 1Gnedin, N. Y. 2000, ApJ, 542, 535Gnedin, N. Y. Kravtsov, A. V., & Chien, H.-W. 2004, ApJ, 672,765Goerdt, T., Dekel, A., Sternberg, A., Ceverino, D., Teyssier, R.,& Primack, J. R. 2010 MNRAS, 407, 613Gronwall et al. 2007, ApJ, 667, 79Guaita, L. et al. 2010, ApJ, 714, 255Gunn, J. E. & Peterson, B. A. 1965, ApJ, 142, 1633Haardt, F. & Madau, P. 1996, ApJ, 461, 20Harrington, J. P. 1973, MNRAS, 162, 43Hayes, M., ¨Ostlin, G., Atek, H., Kunth, D., Mas-Hesse, J. M.,Leitherer, C., Jim´enez-Bail´on, E., Adamo, A. 2007, MNRAS,382, 1465Hayes, M., ¨Ostlin, G., Schaerer, D., Mas-Hesse, J. M., Leitherer,C., Atek, H., Kunth, D., Verhamme, A., de Barros, S., &Melinder, J. 2010 (arXiv:1002.4876)Hernquist, L., Katz, N., Weinberg, D. H., & Miralda-Escud´e, J.1996, ApJ, 457, L51Hibon, P., Cuby, J.-G., Willis, J., Cl´ement, B., Lidman, C.,Arnouts, S., Kneib, J.-P., Willott, C. J., Marmo, C.,McCracken, H. 2010, A&A, 515, 97Hui, L., Gnedin, N. Y., & Zhang, Y. 1997, ApJ, 486, 599Iliev, I. T., Shapiro, P. R., McDonald, P., Mellema, G., & Pen,U.-L. 2008, MNRAS, 391, 63Jarosik, N. et al. 2010, (arXiv:1001.4744)Kennicutt, R. C., Jr. 1998, ARA&A, 36, 189Komatsu, E. et al. 2009, ApJS, 180, 330Kroupa, P. 1998, MNRAS, 298, 231Kunth, D., Mas-Hesse, J. M., Terlevich, E., Terlevich, R.,Lequeux, J., & Fall, S. M. 1998, A&A, 334, 11Lai, K., Huang, J., Fazio, G., Cowie, L. L., Hu, E. M., & Kakazu,Y. 2007, ApJ, 655, 704Laursen, P. & Sommer-Larsen, J. 2007, ApJ, 657, L69Laursen, P., Razoumov, A. O., & Sommer-Larsen, J. 2009, ApJ,696, 853Laursen, P., Sommer-Larsen, J., & Andersen, A. C. 2009, ApJ,704, 1640Lia, C., Portinari, L., Carraro, G. 2002, MNRAS, 330, 821Lia, C., Portinari, L., Carraro, G. 2002, MNRAS, 335, 864Lidz, A., Oh, S. P., & Furlanetto, S. R. 2006, ApJ, 639, L47Lynds, R. 1971, ApJ, 164, L73Meiksin, A. 2005, MNRAS, 356, 596Mesinger, A. 2009 (arXiv:0910.4161) Miralda-Escud´e, J., Cen, R., Ostriker, J. P., & Rauch, M. 1996,ApJ, 471, 582Møller, P. & Warren, S. J. 1998, MNRAS, 299, 611Neufeld, D. 1990, ApJ, 350, 216Nilsson, K. K., Møller, P., M¨oller, O., Fynbo, J. P. U.,Michalowski, M. J., Watson, D., Ledoux, C., Rosati, P.,Pedersen, K., Grove, L. F. 2007, A&A, 471, 71Nilsson, K. K., Tapken, C., Møller, P., Freudling, W., Fynbo, J.P. U., Meisenheimer, K., Laursen, P., ¨Ostlin, G. 2009, A&A,498, 13Osterbrock, D. E. 1989,