www.elsevier.com/locate/newastrev

New Astronomy Reviews 50 (2006) 58–63

Lya radiative transfer in a multi-phase medium

Matthew Hansen, S. Peng Oh *

Department of Physics, University of California, Santa Barbara, CA 93106, USA

Available online 13 December 2005

Abstract

Hydrogen Lya is our primary emission-line window into high redshift galaxies. Surprisingly, despite an extensive literature, Lya radi-ative transfer in the most realistic case of a dusty, multi-phase medium has not received detailed theoretical attention. We investigate Lyaresonant scattering through an ensemble of dusty, moving, optically thick gas clumps. We treat each clump as a scattering particle anduse Monte-Carlo simulations of surface scattering to quantify continuum and Lya surface scattering angles, absorption probabilities,and frequency redistribution, as a function of the gas dust content. This atomistic approach speeds up the simulations by many ordersof magnitude, making possible calculations which are otherwise intractable. Our fitting formulae can be readily adapted for fast radiativetransfer in numerical simulations. With these surface scattering results, we develop an analytic framework for estimating escape fractionsand line widths as a function of gas geometry, motion, and dust content. Our simple analytic model shows good agreement with fullMonte-Carlo simulations. We show that the key geometric parameter is the average number of surface scatters for escape in the absenceof absorption, N0, and we provide fitting formulae for several geometries of astrophysical interest. We consider two interesting appli-cations: (i) Equivalent widths. Lya can preferentially escape from a dusty multi-phase ISM if most of the dust lies in cold neutral clouds,which Lya photons cannot penetrate. This might explain the anomalously high EWs sometimes seen in high-redshift/submm sources. (ii)Multi-phase galactic outflows. We show the characteristic profile is asymmetric with a broad red tail, and relate the profile features to theoutflow speed and gas geometry. Many future applications are envisaged.� 2005 Elsevier B.V. All rights reserved.

Keywords: Radiative transfer; Lyman alpha; Resonant scattering; Multi-phase

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 592. Lya surface scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593. Analytic multi-phase transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

1387-6

doi:10.

* CoE-m

4.1. Lya equivalent widths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 604.2. Multi-phase outflows. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5. Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

473/$ - see front matter � 2005 Elsevier B.V. All rights reserved.

1016/j.newar.2005.11.004

rresponding author.ail address: peng@physics.ucsb.edu (S. Peng Oh).

M. Hansen, S. Peng Oh / New Astronomy Reviews 50 (2006) 58–63 59

1. Introduction

The hydrogen Lya line is our primary emission line win-dow on the high-redshift universe. It is almost invariablycrucial in securing redshift-identifications for the highestredshift galaxies. Besides yielding redshifts, the shape ofthe line profile, equivalent width, and offset from otheremission/absorption lines also encode information aboutthe geometry, kinematics and underlying stellar populationof the host galaxy. Because of the numerous factors whichcontribute to Lya radiative transfer, the interpretation ofsuch features is fraught with complexity. Due to the tre-mendous potential returns for interpreting some richdata-sets, it is crucial to strive for a more detailed theoret-ical understanding of Lya emission line features.

Neufeld (1991) and Charlot and Fall (1993) emphasizedthe importance of the geometry and multi-phase nature ofthe ISM in affecting the observed Lya line. For instance, ifthe dust survives primarily in cold neutral clouds, Lya pho-tons scatter off the clouds and spend most of their time inthe intercloud medium, whereas continuum photons prop-agate unhindered into the clouds and suffer greater extinc-tion. The clumpiness of the ISM is well-established and itmust be taken into account in radiative transfercalculations.

This contribution to these proceedings represents a firstattempt at numerically investigating Lya radiative transferincorporating both the effects of dust and gas clumping,along with several applications relevant to high redshiftgalaxies.

2. Lya surface scattering

Multi-phase radiative transfer typically involves photonpropagation through an optically thin inter-cloud medium,and repeated scattering off optically thick clouds. In a full-blown Monte-Carlo simulation, the latter consumes by farthe lion�s share of computational time. This is extremelyinefficient: the same scattering/absorption problem offcloud surfaces is being solved over and over again for eachphoton. A better approach is to consider each cloud as ascattering/absorbing particle with its own radiative transferproperties (for other applications of this viewpoint, seeNeufeld, 1991 and Varosi and Dwek, 1999).

For Lya photons, clouds are extremely optically thickand have essentially the same radiative transfer propertiesas a semi-infinite slab. This eliminates detailed dependenceon the geometry of the cloud: all that matters is its dustcontent and the initial photon frequency. Using Monte-Carlo simulations of resonant Lya transfer through dustygas (Ahn et al., 2001), we derive fitting formulas for thenet absorption probability (the ‘‘cloud albedo’’) �c, the exit-ing photon angular distribution D(h), and the exiting pho-ton frequency redistribution R(xi,x), as a function of theinitial photon frequency xi and the gas composition. Withthese surface transfer formulae, radiative transfer throughregions containing opaque gas clouds can be quickly esti-

mated and/or simulated without performing any scatteringcalculations within the individual gas clouds. This allowsfor both vast speed-ups of Monte-Carlo simulations anda tractable analytic multi-phase radiative transfer analysis.

Based on the Monte-Carlos simulations, we show inHansen and Oh (2005) that �c mainly depends upon the sin-gle scattering albedo at the incident frequency, �i ” �(xi),

�c �2

ffiffiffiffi�i

p

1þ ffiffiffiffi�i

p ; ð1Þ

where �(xi) is defined by

�ðxiÞ ¼�d

1þ UðxiÞr0=rd; ð2Þ

where U(x) is the Voigt function normalized to U(0) = 1, r0is the Lya line center scattering cross-section, rd is the total(scattering + absorption) dust cross-section, and �d is thedust absorption albedo. Additionally, simulations of sur-face scattering show that the distribution of exiting anglesh is well fit by

DssðhÞ ¼ sin 2h. ð3ÞFor incident photons in the line wing, we find that the netfrequency redistribution is well approximated by a modifi-cation of the formula analytically derived by (Neufeld,1990)

Rðxi; x; aÞ ¼3

ffiffiffia

p

px2~x2i

a~x4i þ ðx3 � ~x3i Þ2; ð4Þ

where ~xi � xi � 2=xi and a = 45/2. This form for R(xi,x)breaks down once the dust content becomes large (approx-imately, rd J 10�20 cm2/H). As derived in Hansen and Oh(2005), generating an exiting frequency x that obeys thisdistribution is given by the formula

x ¼ ~x3i � ~x2iffiffiffia

ptanðpuÞ

� �1=3; ð5Þ

where u is a random number drawn from the intervalu 2 [0,1].

3. Analytic multi-phase transfer

Based on the surface scattering approximations found inSection 2, we derive in Hansen and Oh (2005) a flexibleanalytic approach to the escape fraction fe from a multi-phase gas, based on average number of cloud scatters forescape in the absence of absorption,N0. As shown in Han-sen and Oh (2005), the average number of cloud scattersfor escape with absorption included is given by

N ¼ �ð1� �cÞd

d�cln fe; ð6Þ

from which it follows that N0 � lim�c!0N. For 1-D radi-ative transfer in a finite slab with total optical thickness 2sand absorption albedo per scattering �, the escape fractionfrom the middle of the slab can be written as

fe ¼ 1= coshffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�ðs2 þ 2sÞ

p� �¼ 1= cosh

ffiffiffiffiffiffiffiffiffiffiffiffi2�N0

p� �; ð7Þ

60 M. Hansen, S. Peng Oh / New Astronomy Reviews 50 (2006) 58–63

where in this 1-D case one can show that the average num-ber of particle scatters in the absence of absorption isN0 ¼ 1

2ðs2 þ 2sÞ. By analogy to this 1-D escape fraction

formula, the escape fraction from a multi-phase gas canbe approximated by

fe ¼ 1= coshffiffiffiffiffiffiffiffiffiffiffiffiffiffi2�cN0

p� �ð8Þ

once one makes the multi-phase identification � ! �c andtakes N0 to be the average number of cloud scatters for es-cape when �c = 0. Thus, for any given multi-phase gaswhere surface scattering applies, the effect of the gas geom-etry is characterized by a single parameter, N0, while theeffect of dust is characterized by �c. In Hansen and Oh(2005), we compare this escape fraction formula to simula-tions for a variety of canonical multi-phase gas geometries,and find that this approximation for fe works quite well aslong as fe is not too small (approximately fe J 1%).

The escape fraction depends upon the bulk cloudmotion due to the frequency dependence of �c (Eq. (1)).In Hansen and Oh (2005), we show that a good approxima-tion to the escape fraction results from using the r.m.s. fre-quency dispersion of the escaping photons, R, in order toestimate the ‘‘typical’’ cloud albedo �c. To this end, weinvestigated how R depends upon two generic types ofcloud velocity distributions: a Maxwellian distribution witha 1-D dispersion Vc, and a radial outflow with a constantspeed Vf. We focus on the generic case where the typicalbulk cloud speed (Vc or Vf) is much larger than the thermalDoppler speed of the atoms, in which case R is dominatedby the cloud motion. For the Maxwellian cloud velocitydistribution, a numerical investigation shows that the fre-quency dispersion R (in velocity units) upon escaping froma region with an average number of scatters N is wellapproximated by

R ¼ 2:2ffiffiffiffiffiffiN

pV c. ð9Þ

In Hansen and Oh (2005), we show how N can be esti-mated from N0 and the dust extinction cross-section rd.Thus, the escape fraction can be estimated for any multi-phase region given the geometric parameter N0 and thedust absorption parameters �d and rd.

4. Applications

The surface scattering approximations outlined in Sec-tion 2 and the analytic approach described in Section 3are applied in Hansen and Oh (2005) to two high-redshiftexamples of observational interest. First, the analytic meth-ods are used to show how the unusually larged Lya equiv-alent widths which are seen in many z > 4 sources canresult from multi-phase scattering effects. Second, the sur-face scattering approximations are used in simple simula-tions to show that multi-phase outflows naturallyreproduce the key features of the asymmetric, redshiftedLya emission line profiles seen in many high-redshiftsources.

4.1. Lya equivalent widths

Most Lya photons are produced in the HII regions sur-rounding sources of ionizing radiation, where roughly 2/3of the ionizing photons are converted into Lya photons(under case B recombination). Hence, in the absence ofradiative transfer effects, the equivalent width measuresthe number of ionizing photons emitted relative to theUV continuum near 1200 A. There are numerous examplesof high-redshift sources which have equivalent widthswhich are too large to be produced by conventional stellarpopulations. About �2/3 of the SCUBA submm galaxieswith accurate positions from radio detections have Lya inemission, many with equivalent widths too great for stellarsources (Smail et al., 2004). The mysterious Lya emitters atz � 3.1 observed by Steidel et al. (2000) have enormousLya fluxes, but no observed continuum. Finally, the LALAsurvey detects many high redshift z = 4.5, 5.7 sources withequivalent widths EW P 150 A significantly in excess ofany known nearby stellar population (Rhoads et al.,2003). An AGN origin is unlikely because follow-up obser-vations show no signs of the X-rays and high-ionizationlines expected for a type II quasar source (Wang et al.,2004; Dawson et al., 2004). Another possibility is that theLya emission is due to an extremely top-heavy populationof massive PopIII stars. However, there are no signs of thestrong HeII emission at 1640 A expected from metal-freestars (Dawson et al., 2004).

Another possibility for high Lya EWs, originally sug-gested by Neufeld (1991), is radiative transfer effects. Ifthe continuum is more absorbed than Lya photons duringthe escape from the host galaxy, then the equivalent widthof the transmitted spectra is larger than the equivalentwidth of the source. The initial and transmitted equivalentwidths are basically related by the ratio of Lya to contin-uum escape fractions,

EWout �f Lyae

f ctme

EWsrc; ð10Þ

where EWsrc is the source equivalent width and EWout isthe equivalent width for the escaping photons. In orderfor a ‘‘normal’’ starburst IMF with an intrinsic equivalentwidth of EWsrc � 150 A to produce an observed equivalentwidth of EWout J 300 A, then radiative transfer must ac-count for a ‘‘boost’’ by a factor of at least 2–3. For sourceswhere no continuum is observed, the continuum must bepreferentially extinguished by an even larger factor.

Let us now estimate equivalent width boosts in ourmulti-phase model to see if this is possible. For anymulti-phase medium where the gas resides in clumps thatare very opaque to Lya, the surface scattering approxima-tions apply, and so the Lya escape fraction can be analyt-ically estimated as in Section 3. What about the continuumescape fraction? For simplicity, assume that each gas clumpis not opaque to dust extinction: sdc K 1, where sdc is the dustextinction (scattering + absorption) optical depth across a

Fig. 1. Lya/continuum escape fraction ratio. The Lya to continuum escapefraction ratio, f Lya

e =f ctme , as a function of the total dust absorption optical

depth sa�21 ¼ �drd�21N 21, assuming the temperature of the neutral phase is

�104 K. From top to bottom, N0 is (1,4,10), for bulk gas motions of50 km/s (solid lines) and 250 km/s (dashed lines), respectively. For theseparameters, the Lya escape fractions are f Lya

e ¼ ð0:94; 0:68; 0:38Þ andf Lyae ¼ ð0:81; 0:43; 0:18Þ, respectively, independent of the total dust opticaldepth sa. Most of the EW boost comes from the low escape fractions forcontinuum photons under optically thick conditions; very approximately,f ctme � expð�saÞ.

M. Hansen, S. Peng Oh / New Astronomy Reviews 50 (2006) 58–63 61

clump diameter.1 Since the self-shielding effect of clumpygas is therefore small for the continuum photons, the effec-tive dust distribution is approximately homogenous for thecontinuum radiative transfer. The escape fraction for aphotons injected in the middle of a homogenous medium,with an absorption albedo �d � 1/2, is approximately thatgiven by Eq. (7),

f ctme � 1= cosh

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�dððsdÞ2 þ 2sdÞ

q� �; ð11Þ

where sd ” Nrd is the average dust extinction optical depththrough a region with average HI column density N. Fig. 1shows how the ratio f Lya

e =f ctme varies as a function of N0

for a fiducial set of multi-phase gas parameters. A substan-tial ‘‘boost’’ in the transmitted equivalent width due toselective absorption of the continuum is quite reasonable,as long as two basic conditions are met: (1) there must beenough dust present to absorb a substantial fraction ofthe continuum; (2) this dust must be pre-dominantly lo-cated in dense neutral gas, so that the Lya photons areshielded from absorption. We turn to discussing the firstcondition.

The Lya escape fraction depends only weakly on theoverall dust content of the galaxy. In Fig. 1,f Lyae � 0:2–0:9 over a wide range of parameters, with theescape fraction decreasing with the number of surface scat-ters N0 and bulk gas motion Vc. On the other hand,because continuum photons are not shielded from dustby resonant scattering, they see the full optical depth ofdust absorption, and very approximately, f ctm

e � expð�saÞ.A significant boost in the equivalent width thereforerequires that sd P 1. If the average HI column densityacross the region is ÆNæ, then sd � 1 requires rd

�21 �1=hN 21i, where rd

�21 � rd=10�21 cm2=H and N21 ” N/1021 cm�2. A damped Lya type system with an average col-umn density ÆNæ � 1022 cm�2 would require a dust extinc-tion cross-section per hydrogen of rd � 10�22 cm2/H,which roughly corresponds to a metalicity of �1/10 solar.For sources in which these differential radiative transfereffects are taking place, the equivalent width should statis-tically have a positive correlation with the FIR flux. Thiscorrelation could potentially break down in more devel-oped galaxies at lower redshifts, where the Lya shieldingeffect of the HI can be broken by higher gas speeds in dee-per potential wells (rendering clumps optically thinner inLya), as well as the build-up/survival of dust in low densityinter-clump gas.

4.2. Multi-phase outflows

We turn to discussing the effect of a multi-phase gas out-flow (or inflow) on the Lya emission line profile. The effectsof an outflowing shell (e.g. Tenorio-Tagle et al., 1999; Ahn

1 However, the total dust absorption optical depth across the entiregalaxy (many clumps) can be significantly greater than unity.

et al., 2003; Ahn, 2004) and a Hubble like expansion of auniform gas sphere (e.g. Loeb and Rybicki, 1999; Zhengand Miralda-Escude, 2002) on the Lya emission line is awell studied problem. In both the expanding shell andexpanding sphere scenarios, the generic effect is that a char-acteristic outflow speed Vf produces a redshifted emissionpeak at Vpeak � �Vf, with an asymmetric shape that hasa longer tail on the red side of the peak. The peak com-prises photons that reflect off the far side of the expandinggas, which Doppler shifts the frequency by a typicalamount � �Vf. However, in order for these singly back-scattered photons to escape, the intervening gas columndensity must be small enough for the photons to be trans-mitted, rather than be reflected a second time. In the restframe of the near-side shell, the singly back-scattered pho-tons have a frequency shift V

0peak � � 2Vf. We show inHansen and Oh (2005) that a non-negligible amount ofLya photons will be transmitted through a slab ifN 21 < Npt

21 � 0:05½V 2�2½ra�21�

�1. Setting V � �2Vf, we seethat an outflow with speed of 200 km/s will only allow anon-negligible amount of singly back-scattered photonsto be transmitted if the intervening column density isN 6 2 · 1020 cm�2. Observational estimates of the columndensity in galactic winds often exceed this, yet Lya is stilloften seen.

The main distinguishing feature of a multi-phase out-flow is that it allows photons of any frequency to escapeeven when the intervening gas column depth is very large,

-1600 -1400 -1200 -1000 -800 -600 -400 -200 0 200 400

Vesc

[km/s]

-1600 -1400 -1200 -1000 -800 -600 -400 -200 0 200 400

Vesc

[km/s]

-1600 -1400 -1200 -1000 -800 -600 -400 -200 0 200 400

Vesc

[km/s]

fC=1

fC=3

fesc

=0.69

fesc

=0.21

fesc

=0.05

fC=5

Flux

(ar

bitr

ary

units

)

Fig. 2. Outflowing clumps. The normalized emission profile as a functionof the velocity shift from line center. The thick lines are ra

�21 ¼ 1 while thethin lines (filled in) are dust free, ra = 0. The gas temperature is 104 K andthe outflow speed is 200 km/s. From top to bottom, each panel is adifferent covering factor: fC = 1, 3, 5. The escape fractions for the ra

�21 ¼ 1simulations are indicated. The delta function emission spike at Ve = 0 iscomposed of all the photons that escape freely without striking a clump.Exact line center photons are likely to scattered out of the line of sightbefore being observed.

62 M. Hansen, S. Peng Oh / New Astronomy Reviews 50 (2006) 58–63

N P Npt. As in the homogeneous gas outflow models withsmaller column densities N < Npt, we find that for multi-phase outflows, the emission peak is redshifted by �Vf.However, emission is still detectable even when N � Npt,as expected.

In particular, we investigated the emission profile fortwo basic types of multi-phase outflow geometries: an out-flowing shell with holes and an outflowing ensemble of gasclumps. In both cases, all surfaces were given a radiallyvelocity with constant speed. This choice is meant to reflectgalactic winds, where the gas reaches the asymptotic windspeed quickly. We placed a source of line center photonsin the center of the region. Since the regime of opticallythick gas has been given the least attention, we assume thatthe extreme case holds, where none of the photons pene-trate through the gas. In this limit the surface scatteringapproximations of Section 2 apply in the rest frame ofthe scattering surface. In order to distinguish the effectsof outflow from the effects of random bulk gas motion,we assume that there is no random bulk motion, so thateach gas surface has an exactly radial velocity, ~V

s ¼ V f r.To model outflowing gas clumps in a simple and efficient

way, we let a photon strike a gas cloud surface after trav-eling a mean free path ‘, where ‘ obeys a fixed exponentialdistribution: P(‘) = exp(�fc‘/R) where R is the radius ofthe region and fc is the mean number of clumps intersectedalong the radius. The outward normal to each surface istaken to be random with respect to the incident photon�s

direction. This is a good approximation to a randomarrangement of spherical clouds. In Fig. 2, we show howthe profile varies with the covering factor, for dust freegas ra = 0 and for a Milky Way type dust contentra�21 ¼ 1, where ra ” �drd. The inclusion of dust suppresses

photons which have redshifted far from line center (so theHI no longer shields them from the dust), and sharpens theline profile.

5. Conclusions

Our main technical, radiative transfer results are:

� With the aid of Monte-Carlo simulations, we study thescattering properties of Lya photons incident on an opa-que, dusty, moving cloud. We derive fitting formulas forthe absorption probability, frequency and angular redis-tribution functions of incident photons.

� These formulas can be incorporated into radiative trans-fer codes, affording a vast computational speed up, andmaking feasible otherwise intractable calculations.

� Analytically, a multi-phase gas geometry can be accu-rately characterized by a single number,N0, the numberof surface scatters in the absence of absorption. Otherfactors – such as the cloud radii distribution for fixedN0 – are generally unimportant.

� We derive analytic formulas for the Lya escape fractionand line widths.

� Several archetypal geometries are explored: randomlyplaced spherical clouds, randomly placed surfaces (anabstraction of the prior geometry), a shell with holes,and an open-ended, cylindrical cavity.

� Constant speed, radial, outflows are analyzed for bro-ken shells and random surfaces. The red-shifted peaksand widths are connected to the geometry and outflowspeed.

Our main results of direct observational relevance are:

� Lya can escape from multi-phase dusty galaxies for HIcolumn densities where it would be strongly quenchedin a single-phase medium.

� If most of the dust resides in a neutral phase which isoptically thick to Lya, the Lya equivalent width canbe strongly enhanced: while Lya photons typically scat-ter off such surfaces (which shield the dust), continuumphotons penetrate inwards and are preferentiallyabsorbed.

� When the characteristic bulk gas speed exceeds�100 km/s, the Lya line width is dominated by the gasmotion, and resonant scattering frequency redistribu-tion is sub-dominant effect.

� Multi-phase outflows generically produce Lya line pro-files that have the characteristic asymmetric shape seenin many starburst galaxies and Lya emitters.

� Multi-phase outflows can produce line widths severaltimes larger than the actual outflow speed.

M. Hansen, S. Peng Oh / New Astronomy Reviews 50 (2006) 58–63 63

The ISM of galaxies at both low and high redshift isalmost certain to be both dusty and multi-phase: metaland dust production begin very early, given the short life-time of massive stars, and thermal instability is almost inev-itable under galactic conditions. Nonetheless, despite anextensive literature, to the best of our knowledge this isthe first detailed numerical study of resonance-line radiativetransfer in a multi-phase dusty medium. The ground is sur-prisingly rich, and many future applications are envisaged!

References

Ahn, S., 2004. ApJ 601, L25.Ahn, S., Lee, H., Lee, H.M., 2001. ApJ 554, 604.

Ahn, S., Lee, H., Lee, H.M., 2003. MNRAS 340, 863.Charlot, S., Fall, S.M., 1993. ApJ 415, 580.Dawson et al., 2004. ApJ 617, 707.Hansen, M., Oh, S.P., 2005. MNRAS, in press, astro-ph/0507586.Loeb, A., Rybicki, G.B., 1999. ApJ 524, 527.Neufeld, D.A., 1990. ApJ 350, 216.Neufeld, D.A., 1991. ApJ 370, L85.Rhoads, J.E. et al., 2003. AJ 125, 1006.Smail, I., Chapman, S.C., Blain, A.W., Ivison, R.J., 2004. ApJ 616,

71.Steidel, C.C., Adelberger, K.L., Shapley, A.E., Pettini, M., Dickinson, M.,

Giavalisco, M., 2000. ApJ 532, 170.Tenorio-Tagle, G., Silich, S.A., Kunth, D., Terlevich, E., Terlevich, R.,

1999. MNRAS 309, 332.Varosi, F., Dwek, E., 1999. ApJ 523, 265.Wang et al., 2004. ApJ 608L, 21.Zheng, Z., Miralda-Escude, J., 2002. ApJ 578, 33.