The missing metals problem: II. How many metals are in z ~ 2.2 galaxies?

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by  N. Bouche

Mon.Not.R.Astron.Soc.000,1–5(0000) Printed4February2008 (MNLATEXstylefilev2.2)
The missing metals problem: II. How many metals are in
z ≃ 2.2
galaxies?
Nicolas Bouch´e1⋆, Matthew D. Lehnert1, C´eline P´eroux2
1Max Plank Institut fu¨r extraterrestrische Physik, Giessenbachstraße, D-85748 Garching, Germany
2European Southern Observatory, Karl-Schwarzschild-Str 2, D-85748 Garching, Germany
6
0
0
2 Accepted —.Received—;inoriginalform—

n
a
J ABSTRACT
In the context of the “missing metals problem”, the contributions of the UV-selected
9
z ≃ 2.2 “BX” galaxies and z ≃ 2.5 “distant red galaxies” (DRGs) have not been

2 discussedpreviously.Here weshowthat:(i)DRGs onlymakeamarginalcontribution
v to the metal budget (∼ 5%); (ii) BX galaxies contribute as much as 18% to the
8 metal budget; and (iii) the K-bright subsample (K <20) of the BX sample (roughly
9 equivalent to the ‘BzK’ selected samples) contributes roughly half of this 18%, owing
6 both to their larger stellar masses and higher metallicities, implying that the rareK-
1 brightgalaxiesatz >2 area majorsourceofmetals in the budget. We showedin the
1
firstpaper ofthis series that submm galaxies(SMGs) brighterthan 3 mJy contribute
5 ∼5%(.9%asanupperlimit)tothemetalbudget.AddingthecontributionofSMGs
0
and damped Lyα absorbers,to the contribution of UV selected galaxies, implies that
/
h at least30%of the metals (in galaxies) have been accountedfor atz ≃2. The cosmic
p metal density thus accounted for is ρZ,galaxies ≃ 1.3×106 M⊙ Mpc−3 or in terms of
o- the closure density, ΩZ =9.6×10−6. This is a lower limit given that galaxies on the
r faint-endoftheluminosityfunctionarenotincluded.Anestimateofthedistributionof
st metalsinlocalgalaxiesasafunctionluminositysuggeststhatgalaxieswithluminosity
a <L⋆ contributeabouthalfofthe totalmassofmetals.Ifthemetalsingalaxiesatz∼2
: are similarly distributed then faint galaxies alone cannot solve the ‘missing metals
v
i problem.’ Galaxy populations at z∼2 only account for about 50% of the total metals
X
predicted.
r
a Key words: cosmology:observations—galaxies:high-redshift—galaxies:evolution
— galaxies:abundances
1 INTRODUCTION movingmetal density is:
For a given initial mass function (IMF), the total expected ρZ,expected = 4.0×106 M⊙ Mpc−3, (1)
amount of metals ρ formed at a given time t is
Z,expected
simply the integral of the star formation history (SFH) (Bouch´eet al.2005;Pettini2003)usingtheSFHparameter-
or star formation rate density (SFRD; Lilly et al. 1996; ized (in a LCDM cosmology) either as in Cole et al. (2001)
Madau et al.1996;Giavalisco et al.2004;Hopkins2004,and or by a constant star formation rate (SFR) beyond z = 2.
others): i.e., ρ = ρ˙ (t)× < p >, where < p > is Equation 1 is about 25% of thez =0 metals.
Z,expected ⋆ z z
the mean stellar yield (Songaila et al. 1990). Madau et al. Atredshiftsz≃2−3,ourknowledgeofthecosmicmetal
(1996) found that < p >= 1 or 2.4% using a Salpeter budget is still highly incomplete, contrary to the situation
z 42
IMFextendingfrom0.1to125M⊙ 1 andthetypeIIstellar atredshift z =0(e.g. Fukugita& Peebles2004).Untilvery
yields(forsolar metallicity) p (m)from Woosley & Weaver recently,it was thought that only a small fraction (20%) of
z
(1995). After integrating the SFH over the redshift z range thebudgetisactuallyaccountedforwhenoneaddsthecon-
from 4 to 2 (or 1.75 h−1 Gyr), we find that the total co- tributionoftheLyαforest (NHi =1013−17 cm−2),damped
70 Lyα absorbers (DLAs) (NHi > 1020.3 cm−2), and galaxies
such as Lyman break galaxies (LBGs) (Pettini et al. 1999;
⋆ E-mail:[email protected] (NB) Pagel 2002; Pettini 2003; Wolfe et al. 2003).
1 Madauetal. (1996) notes that the conversion is fairly insen- Over the last decade, numerous samples of z > 2
sitive to the IMF as long as the stellar population extends as a galaxies have emerged thanks to the increasing size and
powerlawtomassivestars,50-100M⊙. sensitivity of near-infrared detectors and to the availabil-
2 N. Bouch´e, M. D. Lehnert, C. P´eroux
ity of ultraviolet-sensitive instruments. On the one hand, The last piece of information needed to estimate the
the z = 3 Lyman break technique (e.g. Steidel et al. 1999) contributionoftheBXgalaxiestothemetalbudgetistheir
was extended to lower redshifts (z ∼ 1.5–2.5) using dif- metallicity. Few BXs have had their gas phase metallicities
ferent U GR colour criteria (Steidel et al. 2004). Samples published.Forinstance,Shapley et al.(2004)foundthatthe
n
selected in this way are referred to as ‘BX/BM’ galax- metallicities of7BXgalaxiesareclose tosolar,buttheme-
ies (Adelberger et al. 2004). Usingnear-infrared imaging to dianofamuchlargersampleappearstobeabouthalfsolar
select red galaxies with J − K > 2.3 colour, the Faint (Pettini 2005).
s
Infrared Extragalactic Survey (FIRES) (Franxet al. 2003; Using these estimates, we find that BX galaxies con-
van Dokkumet al. 2003) unveiled significant numbers of tribute:
galaxies at z ∼ 2.5 which they dubbed ‘distant red galax-
<Z >
ies’ (DRGs). The FIRES near-infrared selection includes ρZ,BX ≃3.8×105 0.5Z⊙ M⊙ Mpc−3 (2)
both passively evolving (PE) and reddened star-forming
(SF)galaxieswithE(B−V)>0.3(F¨orster Schreiberet al., to the cosmic metal density or about 10% of the expected
2004).TheK <20criterion (hereafter‘K20’;Cimattietal. metal density at z∼2 (equation 1).
2002) and in particular the B−z vs. z−K colour criteria BX galaxies with K-band magnitudes brighter than
(hereafter ‘BzK’; Daddi et al. [2004,2005]) also revealed a 20 (hereafter BX+K20) appear to be more evolved sys-
significant number of galaxies with 1.5 < z < 2.5 with a tems. Indeed, they seem to have higher stellar masses [<
range of star-formation histories includingboth SF and PE logM >= 11±0.6, Shapley et al. (2005)], and are more
⋆
galaxies. metal rich: their median metallicity is slightly below so-
This paper is the second in our series to estimate the lar [Z ∼ 4/5Z⊙, Pettini (2005)]. However, they are signif-
contribution of various galaxy populations at z ∼ 2 to the icantly rarer: their number density is a factor of 10 lower
total metal budget. In Bouch´e et al. (2005) (paper I), we [n∼1.7×10−4 h3 Mpc−3,Shapley et al.(2005)].Theout-
70
showed from current observations of z ≃2 submm galaxies come is that K -bright BX galaxies contribute significantly
s
(SMGs)thatSMGs(brighterthan3mJy)contain∼5%(and to themetal budget:
certainly .9%) ofthemetal budgetat z≃2.Inthispaper,
iwees dtoisctuhsesmtheetaclobnturdibguett.ioWneofwzil≃l s2h.o2wcotlhoautrcsoelloecutredsegleacltaexd- ρZ,BX,K<20 ≃3.0×105 <0.8ZZ>⊙ M⊙ Mpc−3 (3)
galaxies (‘BX’ galaxies) contribute significantly (∼ 18%) or8%oftheestimatedtotalmetaldensity(equation1).
to the metal budget. The K-bright (Ks < 20, hereafter These numbersare summarized in Table 1.
BX+K20) subsample contributes 8% to the metal budget, Unlike for the SMGs in paperI, we have not applied a
or almost half of the 18%. Since these samples are all mag- correction for the “duty cycle”, the fraction of cosmic time
nitude limited, we discuss likely contribution of the sample over which they meet the observational selection criteria.
ofgalaxiesatz∼2ifoneconsidersthefaintendofthelumi- ThedutycycleofBXscanbeestimatedfromthecomparison
nosity function using the metal-luminosity relation in local of the clustering strength to the observed number density
galaxies. Such an analysis suggests that galaxy populations (Adelberger et al. 2005). Adelberger et al. (2005) find that
atz∼2onlycontributeabout50%tothetotalmetalbudget. thedutycycleforthe“BM/BX”galaxiesis∼1.0,suggesting
In paper III, we will explore whether the remaining metals nocorrection to our estimate is required.
havebeenexpelledfromsmallgalaxiesintotheintergalactic
medium (IGM).
In the remainder of this paper, we used Ω = 0.3,
M
ΩΛ =0.7, Ho =70 h70 kms−1 Mpc−1 and h=h100. 2.2 The contribution of DRGs
Rednear-infraredcolourselectionofgalaxies(suchasDRGs
with J − K > 2.3 Franxet al. 2003; van Dokkum et al.
s
2 THE METAL BUDGET AT Z ∼2.2 2003) was designed to discover large numbers of z ∼ 2.5
evolvedgalaxieswithastrongBalmerbreak.DRGsaremas-
2.1 The contribution of ‘BX’ galaxies
sivegalaxiesandincludebothheavilyreddenedSFgalaxies,
Using colour selection criteria similar to those of z = 3 andPEgalaxies(F¨orster Schreiber et al.,2004;Labb´e et al.
LBGs,Steidelandcollaboratorshaveconstructedlargesam- 2005).
ples of galaxies at z ≃ 2.2 (BX) and 1.7(BM). The me- The space density of DRGs is about 1 ×
dian redshifts of these samples are 2.22±0.34 (BX), and 10−4 h3 Mpc (Labb´eet al. 2005; Reddyet al. 2005).
70
1.70±0.34(BM), respectively (e.g. Adelberger et al. 2004). F¨orster Schreiber et al., (2004) found, from modelling the
The observed number density of BX and BM galax- spectral energy distributions (SEDs) of DRGs, that their
ies (n ) is somewhat higher than z = 3 LBGs. In- mean stellar mass is about 5 timeshigher thanz∼3LBGs,
BX/BM
deed,accordingtoAdelberger et al.(2005),nBX =(6±3)× or M⋆ ≃ 1×1011 M⊙(for a Salpeter IMF between 0.1 and
10−3 h3100 Mpc−3,andnBM =(5±2.5)×10−3 h3100 Mpc−3, 100 M⊙) and only varies by a factor of ∼2 depending on
whereasnLBG =(4±2)×10−3 h3100 Mpc−3.Wesummarize thestar formation history assumed.
these numbersin Table 1 for h70. van Dokkumet al. (2004) estimated the metallicity of
Shapley et al.(2005)derivedthestellarmasses(M )of a couple of DRGs from Keck NIRSPEC spectra. They
⋆
72 spectroscopically-confirmed z = 2.2±0.3 galaxies using foundthatthemetallicities, asdeterminedusing[NII]/Hα,
UVtomid-IRobservations.ThemeanM oftheirsampleis are high, 1-1.5 times the solar value. From the long slit
⋆
<logM >=10.3±0.5 for a Salpeter IMF extending from kinematics, van Dokkumet al. (2004) estimated that the
⋆
0.1 to 100 M⊙. dynamical masses are about ∼ 1 × 1011 M⊙, in agree-
The metals in BX galaxies 3
ment with the mass estimates using the SED modelling of onlyconsideredthebrightend(&L )ofthegalaxyluminos-
⋆
F¨orster Schreiber et al., (2004). ity function. One obvious criticism of our approach is that
Based on these published results, we find that the cos- given the limited depth of the selection images and the ob-
mic metal density contributed by DRGsis: viousincompleteness,couldthemetalshideinlowluminos-
ity/lowmassgalaxies? Whileitisdifficulttoestimatewhat
<Z >
ρZ,DRGs≃2×105 1Z⊙ M⊙ Mpc−3 (4) the contribution of the faint end of the luminosity function
mightbetothetotalmetalbudget,perhapsconsideringthe
or 5% of theexpected metal density (equation 1). localpopulationofgalaxiesmightbeusefulasaguide.Inthe
localUniverse,whilegalaxiesatthefaint-endoftheluminos-
ityfunctionaremorenumerousthantheluminousgalaxies,
3 DISCUSSION & CONCLUSIONS they are also more metal-poor (e.g., Tremonti et al. 2004).
For the local Universe, we estimate the contribution
Table 1 summarizes the observations discussed here. The of the faint-end of the luminosity function φ(L) using
properties of z=3 LBGs are listed for comparison. the well-known luminosity-metallicity (LZ) relation (e.g.
Fromtheobservationsdiscussedabove,wefindthatthe Tremonti et al.2004;Garnett2002).Usingmass-to-lightra-
metal density in BX galaxies is: tios [M/L(L)] from Kauffmannet al. (2003), the z =0 LZ
<Z > relation(O/H(M)orZ(M))fromGarnett(2002)andφ(L)
ρZ,BX =3.8×105 0.5Z⊙M⊙ Mpc−3 , (5) from Driver et al. (2005), one can estimate the cumulative
metal density (R φ(L)M/L(L)Z(M)). Fig. 1 shows the cu-
or 10% of the metal budget, assuming a mean metallicity mulative Oxygen density M(O) at z = 0. The right axis
< Z > of one-half solar and the above co-moving space showsthetotalmetaldensityM(Z).The5th,50thand90th
densities. percentiles are shown. From Fig. 1, one sees that, at z =0,
Themoreevolvedsub-sampleoftheBXsources,namely 50%ofthemetalsareingalaxiesfainterthanL .Notethat
⋆
BX+K20 galaxies, are rarer (by a factor of 10), but more themetaldensityreaches∼2×107 M⊙ Mpc−3,closetothe
massive(byafactorof5),andmoremetalrich(byafactorof metal density obtained from integrating the SFH down to
2).Thus,theydoublethetotalcontributionof‘BX’galaxies z=0, i.e. ρZ,z=0=1.8×107 M⊙ Mpc−3,showing that the
tothemetalbudget.Themetaldensityofthissubsampleis: normalization must be approximately correct. Constraints
<Z > on the LZ relation at z > 2 are just becoming available
ρZ,BX+K20 =3.0×105 4/5Z⊙M⊙ Mpc−3 (6) (Savaglio et al. 2005; Erb et al. 2005, C.C. Steidel, private
communication).
or8%ofthemetalbudget.Thus,therareK-brightgalaxies
Based ontheselocal results, at least 50% ofthemetals
atz>2areamajor sourceofmetalsinthebudget.Weare
in galaxies are in objects on the faint-end of theluminosity
still far from closing the metal budget however. If we take function (L.L⋆). The limiting depths of the surveys that
these numbers at face-value, as much as 18% of the metals findz∼2 galaxies reach to or even beyond L⋆. Ifwe assume
could bein BX galaxies.
for simplicity that our numbers and estimates are appro-
Regarding the ‘BzK’ selection of z ∼ 2 galaxies priate for L⋆ and more luminous galaxies and that the z∼2
by Daddiet al. (2004), we note that the mean redshifts
galaxieshaveasimilarrelativefraction ofmetalsaboveand
for BzK/SF (star-forming) galaxies and BzK/PE (passive belowL⋆,itwouldsuggestthatweneedtocorrectourtotal
evolving) galaxies is < z >≃ 2±0.3 and 1.7±0.2, respec-
metalestimatebyaboutafactorof2.Thisislikelyanover-
tively(Reddyet al.2005).Focusingonthez>2subsample
estimateofthetruecorrectionnecessaryforthefaintendof
(i.e., BzK/SF), Reddyet al. (2005) showed that the ‘BX’
the luminosity function and shows that the total contribu-
selection criteria and that the ‘BzK/SF’ selection criteria
tiontothemetalbudgetisroughly60%orless.Inaddition,
overlapsignificantly(∼80%)toK =22.Wethereforeview
s this sum might also count some of the galaxy types twice,
these two populations (BX and BzK/SF) as two strongly
given that we effectively extrapolate to the faint end of the
overlappingsamples whichdonotrequireseparateanalyses
LF for each of the samples. Given these caveats, one can
of their contribution tothe metal budget at z∼2. easily account for ∼30—60% of the metal budget. We will
Havingnowconsideredasubstantialnumberofsamples
discussinpaperIIIthepossibility thattheremaining miss-
of galaxies selected at z∼2, we can now estimate the total
ing metals could have been ejected from small galaxies via
metalbudgetingalaxies.Wehaveestimatedthat5%(.9%)
galactic outflows intothe IGM.
of the metals are in z ∼ 2.4 SMGs (brighter than 3 mJy;
as shown in paper I), 18+5% in UV-selected and J −K-
selected galaxies, and 5% in DLAs (Pettini et al. 2003, and
ACKNOWLEDGMENTS
theforthcoming paper III).The resulting sum is:
Wethanktherefereeforapromptreport;M.Pettiniforin-
ρZ,galaxies ≃1.3×106 M⊙ Mpc−3 (7) teresting discussions and for sharing his results before pub-
or ∼33% of the expected metal density at z ≃ 2 (equa- lication; and N. F¨orster Schreiber for sharing her extensive
tion 1) 2. knowledge of DRGs.
However,equation7isalowerlimitgiventhatwereally
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