The origin of intergalactic metals around Lyman-break galaxies

a r X i v :a s t r o -p h /0504160v 1 6 A p r 2005

Draft version February 2,2008

Preprint typeset using L A T E X style emulateapj v.6/22/04

THE ORIGIN OF INTERGALACTIC METALS AROUND LYMAN-BREAK GALAXIES

Cristiano Porciani 1and Piero Madau 2

Draft version February 2,2008

ABSTRACT

Theoretical and observational arguments suggest that the intergalactic medium (IGM)might have been polluted with metals produced by early star formation.In this scenario,Lyman-break galaxies (LBGs)at redshift z =3are likely to be surrounded by old metal bubbles,relics of an era when the characteristic mass of galaxies was small and gas retainment more di?cult.We ?nd that pregalactic enrichment of the IGM from 108?1010M ⊙dwarf galaxies at 6

Subject headings:cosmology:theory –galaxies:high-redshift –intergalactic medium –quasar:ab-sorption lines

1.INTRODUCTION

Quasar absorption lines constitute a fossil record that holds the clues to the exchange of mass,metals,and en-ergy between active galactic nuclei,protogalaxies,and the intergalactic medium (IGM).The distribution of metals in the IGM is highly inhomogeneous,with a global cosmic abundance at z =3of [C/H]=?2.8±0.13for gas with overdensities 0.3<δ<100(Schaye et al.2003).The epoch at which this cosmic enrichment occurred is uncertain,and so is the nature of the galaxies responsible for seeding the IGM with nuclear waste.The extent of metal pollution seem to require galaxy-scale out?ows to overcome the gravitational potential of their host halos,and enriched material to be ejected far away from the density peaks where large galaxies form,gas cools,and star formation takes place.

Observationally,C IV absorbers and Lyman-break galaxies (LBGs)at z ≈3are found to be spatially cor-related (Adelberger et al.2003,hereafter ASSP).The mean number of LBGs within a comoving distance r

from a detectable C IV system (N CIV ～>10

11.5

cm ?2)equals one for r =r 1=2.4h ?1Mpc.This is much smaller than the value expected for a random distribu-tion (r 1?3.9h ?1Mpc,ASSP).Stronger C IV systems seem to be even more closely associated with LBGs

(r 1～<0.5h ?1Mpc for N CIV ～>10

13.5

cm ?2).At the same time,the Ly αabsorption produced by the IGM within ～0.5h ?1Mpc from an LBG appears to be sys-tematically reduced with respect to random locations.Moreover,high-resolution spectra reveal that LBGs have high star formation rates and strong winds with out?ow velocities exceeding several hundred kilometers per sec-ond.All these facts led ASSP to argue that metal-rich “superwinds”from LBGs are responsible for distributing

1

Institute for Astronomy,ETH Z¨u rich,8093Z¨u rich,Switzer-land;porciani@phys.ethz.ch.

2Department of Astronomy &Astrophysics,University of Cal-ifornia,Santa Cruz,CA;pmadau@https://www.360docs.net/doc/ba18930542.html,.

the product of stellar nucleosynthesis on Mpc scales.In this Letter we argue that this interpretation may be an oversimplication of a far more complex physical picture.The starting point of our investigation is the fact that LBGs are highly biased tracers of the under-lying mass-density ?eld.The observed clustering am-plitude suggests that LBGs reside in dark-matter halos with mass M >1011.5±0.3M ⊙at z =2.9(Porciani &Giavalisco 2002;Adelberger et al.2005).In hier-archical cosmogonies,these halos are expected to form within overdense regions (extending for a few Mpc)which are likely to be pre-enriched by subgalactic objects at much higher redshifts.The ejection of supernova debris from the shallow potential wells of collapsed,rare den-sity ?uctuations is,in fact,expected to lead to an early era of metal pollution and preheating in biased regions of the IGM (e.g.Tegmark et al.1993;Madau et al.2001;Scannapieco et al.2002;Thacker et al.2002).We show that pregalactic enrichment from 108?1010M ⊙dwarf galaxies at 6

2.BASIC THEORY

The properties of the dark-matter halo population as a function of redshift can be approximately computed with the excursion-set formalism (Bond et al.1991).In this approach,the halo mass function n (M,z )is determined by following the random walk of the linear density con-trast,δ,as a function of spatial resolution (parameterized by the mass variance,S )and measuring the rate with which di?erent trajectories ?rst upcross a given thresh-old value,t c =δc (z )/D (z ).Here δc is the linear over-density of a top-hat perturbation at collapse (δc =1.686in a Einstein-de Sitter universe)and D (z )is the linear growth factor of density perturbations,normalized such

2Metals in the IGM

that D (z =0)=1.

Porciani et al.(1998)have shown that the excursion-set formalism can be also used to derive the clustering prop-erties of dark-matter halos in the Lagrangian coordinate system (which gives the positions of proto-halo centers in the linear density ?eld,formally at z →∞).This is ob-tained accounting for the spatial coherence of the linear density ?eld and simultaneously following a number of correlated random walks associated with di?erent spa-tial locations.More recently,Scannapieco &Barkana (2002)generalized these results to halos collapsing at di?erent epochs.Here we use their analytical approxi-mation to compute the Lagrangian correlation function ξL (r L |M 1,z 1,M 2,z 2),between halos of mass M 1forming at z 1and halos of mass M 2forming at z 2>z 1.Hereafter,M 1>1011.5M ⊙will denote the mass of the host-halo of an LBG forming at z 1=3while the free-parameters M 2and z 2will characterize subgalactic halos collapsing at earlier epochs.

In order to compare theory and observations,one needs to compute the halo clustering properties in the Eulerian coordinate system (in which galaxies are ob-served).The mapping of halo positions from Lagrangian to Eulerian space depends on the gravity driven dy-namics of the background mass density ?eld (Catelan et al.1998).Consider the evolution of a spherically-symmetric shell of Lagrangian radius r L centered onto a halo of mass M 1?M 2.Its Eulerian position at red-shift z 1only depends on the mean overdensity ?(z 1)within it:r E =r L /[1+?(z 1)]1/3(for the sheared case see Catelan et al.1998).Using the spherical top-hat model it is possible to relate the non-linear density con-trast ?to its linearly extrapolated counterpart δ,as δ?δc [1?(1+?)?1/δc ]/D (z )(Pavlidou &Fields 2004).This implies r E =f (δ,r L )=r L [1?(D (z )δ/δc )]δc /3.What is the probability distribution of the linear over-density within a shell of given Lagrangian size centered onto an halo of mass M 1?This can be easily computed using the excursion-set model.The conditional probabil-ity that a trajectory assumes the value δwhen smoothed on the scale r L (corresponding to the mass variance s ),given that it will ?rst upcross the threshold t c (z 1)at the mass variance S (corresponding to the mass M 1),is

P (δ,s |δc ,S )=

W (δ,s )P 1(t c ?δ,S ?s )√

2s

?exp

?

(2t c ?δ)2

√

2S

(3)

denotes the probability distribution of ?rst upcrossings.The conditional probability distribution of r E given a Lagrangian separation can then be written as

P (r E |r L )=

t c

?∞

P (δ|r L )δD [r E ?f (δ,r L )]dδ=

3P (ˉδ

|r L )dr E

=4π ∞

R 1

P (r E |r L )n (M 2,z 2)[1+ξL (r L )]r 2

L

dr L ,(5)with R 1=(3M 1/4πˉρ)1/3the Lagrangian radius of the

halo of mass M 1and ˉρthe mean comoving density of the universe.For a population of halos with an extended range of masses at z 1,this becomes

dN 2

dr E

dM 1

4πr 2E N (M 2,z 1

) dN 2

Porciani &Madau

3

Fig. 2.—Left:Projected cross-correlation function between LBGs and C IV systems.Points with errorbars denote the observational data by ASSP,while the solid line shows our best-?tting model (which corresponds to χ2min =3.6).The shaded area indicates separations

smaller than the Eulerian radius of a 1011.5M ⊙halo,where our model does not hold.The inset shows the small-scale modi?cations due

to a ?nite bubble size.Right:Contour levels of the χ2function obtained by ?tting the data by ASSP with the model described in the text.Solid contour :?χ2=χ2?χ2min =2.3and 6.17(respectively marking the 68.3and 95.4per cent con?dence levels for two Gaussian variables).Long-dashed curve:set of points where D (z 2)1.15S (M 2)=2.9,which describes the location of the degenerate minimum.Light,short-dashed lines:set of points where the number density of C IV systems matches the observed value for di?erent values of r b [ranging from 50to 250comoving kpc (from bottom to top)and spaced by 50kpc].The shaded area marks the region where virialized gas cannot cool via excitation of hydrogen Ly α.

low mass systems at much higher redshifts ?Figure 1shows that LBGs form within overdense regions extend-ing for a few comoving Mpc.Assume that these biased regions have been already polluted by protogalaxies,i.e.that C IV systems are associated with metal “bubbles”that have been expelled from halos of mass M 2at some epoch between z 2and z 1.3Most of the bubbles lying in the vicinity of the formation site of an LBG will be driven by gravity towards the forming galaxy thus pro-ducing the observed spatial association (see bottom panel in Fig.1).

In this scenario,the projected cross-correlation func-tion between LBGs and the bubble centers is:

Ξ(r ⊥)r ⊥ ∞

r ⊥

r E ξ(r E )

S ?D (z 2)?0.425.In the

redshift interval 6

Figure 2also shows that the clustering data by ASSP cannot constrain r b .Winds from star-forming low-mass systems at z ～10are expected to sweep up regions of the IGM of comoving size r b <250kpc (Mori et al.2002;Furlanetto &Loeb 2003)while Ξhas been measured for separations r >0.3h ?1Mpc where the bubble size leaves no imprint.We thus constrain r b by comparing the ob-served mean number of C IV absorbers per unit redshift with the expectations from our model.From Songaila (2001),we infer that dN/dz ?8for C IV systems with N CIV >1013cm ?2at z ～3.2.This corresponds to a bubble size of the order of 100comoving kpc and im-plies that r b has to increase when one moves towards lower redshifts along the (M 2,z 2)degeneracy line (see Fig.2).Thus enriched out?ows of size r b =100kpc around 109M ⊙halos at z =9(or of size r b =200

kpc

4Metals in the IGM

around1010M⊙halos at z=6)might explain both the mean absorption-line density and the LBG–C IV cross-correlation observed at redshift3.

4.DISCUSSION

In hierarchical cosmologies,LBGs represent only the tail end of a larger population of pregalactic starbursts that formed at much higher redshifts.The metal pollu-tion of the IGM may then have started at early times, perhaps by the same sources responsible for hydro-gen reionization.In“pregalactic enrichment”scenar-ios,LBGs are expected to form within biased regions of the IGM(as indicated by their strong clustering), which are the sites of previous star formation and enrich-ment.In this Letter we showed that the LBG–C IV cross-correlation function measured by ASSP can be explained by out?ows from dwarf galaxies(108～1011.5M⊙,our model automatically reproduces also the observed cor-relation function of LBGs(Porciani&Giavalisco2002; Adelberger et al.2005).Contrary to previous beliefs, our results then indicate that the observed coincidence between LBGs and C IV systems does not necessarily im-ply that the metals observed in the IGM at z～3were driven out of massive LBGs by a superwind.

Typical LBGs seem to generate gas out?ows with ve-locities in the range0

It is fair to point out at this stage that the initial epochs of the galaxy formation process are currently only poorly understood.N-body+hydrodynamical sim-ulations of CDM cosmogonies have convincingly shown that the IGM is expected to fragment into bound struc-tures at early times,but are much less able to predict the e?ciency with which gravitationally collapsed objects lit up,reionized,and enriched the universe at the end of the “dark ages”.Still,from the arguments presented above, it would seem unwise to use the spatial association be-tween C IV absorbers and LBGs and draw far-reaching conclusions on the extent of galactic superwinds and the direct impact of LBGs on the Lyαforest.Uncovering the relative contributions of LBGs and young dwarfs to the pollution of the IGM may prove di?cult.Metals ejected during an early episode of star formation may be seen in absorption against bright background sources such as rare quasars or gamma-ray bursts at z～10 (Furlanetto&Loeb2003).This,however,requires high-resolution spectroscopy of faint sources in the near-IR and may have to wait for the James Webb Space Tele-scope.On the other hand,old wind bubbles may have dif-ferent abundance patterns than young winds from LBGs. As recently pointed out by Cen et al.(2004),the gaseous relics of an era when the characteristic mass of galaxies was small,gas retainment more di?cult,and metal recy-cling more limited,are expected to contain lower ratios of secondary(e.g.Nitrogen)to primary(e.g.Carbon, Oxygen)metals.For instance,theoretical yields from pair-instability SNe originating from massive Population III stars are characterized by large Si/C ratios(Heger& Woosley2002).Tests relying on measurements of relative metal abundances at high-z,however,are made imprac-tical by the uncertainties in the ionization corrections and the lack of information regarding the stellar initial mass function.

We thank Evan Scannapieco for providing an early set of Lagrangian correlations in tabulated form and an updated version of the Gemini code.Support for this work was provided by NASA grants NAG5-11513and NNG04GK85G,and by NSF grant AST-0205738and PHY99-07949(PM).

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