Metallicity of the intergalactic medium using pixel statistics: III. Silicon

0.47 MB·English

by  Anthony Aguirre

Draftversion February2,2008
PreprinttypesetusingLATEXstyleemulateapjv.7/15/03
METALLICITY OF THE INTERGALACTIC MEDIUM USING PIXEL STATISTICS:
III. SILICON.1
Anthony Aguirre2,Joop Schaye3,
Tae-Sun Kim4,5, Tom Theuns6,7, Michael Rauch8, Wallace L. W. Sargent9
Draft versionFebruary 2, 2008
ABSTRACT
We study the abundance of silicon in the intergalactic medium by analyzing the statistics of Si IV,
C IV, and H I pixel optical depths in a sample of 19 high-quality quasar absorption spectra, which
we compare with realistic spectra drawn from a hydrodynamical simulation. Simulations with a
4
constant and uniform Si/C ratio, a C distribution as derived in Paper II of this series, and a UV
0
background (UVB) model from Haardt & Madau reproduce the observed trends in the ratio of SiIV
0
2 and CIV optical depths, τSiIV/τCIV. The ratio τSiIV/τCIV depends strongly on τCIV, but it is nearly
independent of redshift for fixed τCIV, and is inconsistent with a sharp change in the hardness of the
n
UVBatz ≈3. ScalingthesimulatedopticaldepthratiosgivesameasurementoftheglobalSi/Cratio
a
(usingourfiducialUVB,whichincludesbothgalaxyandquasarcontributions)of[Si/C]=0.77±0.05,
J
with a possible systematic error of ∼ 0.1dex. The inferred [Si/C] depends on the shape of the UVB
3
(harder backgrounds leading to higher [Si/C]), ranging from [Si/C]≃ 1.5 for a quasar-only UVB, to
1
[Si/C]≃ 0.25 for a UVB including both galaxies and artificial softening; this provides the dominant

uncertainty in the overall [Si/C]. Examination of the full τ /τ distribution yields no evidence
2 SiIV CIV
forinhomogeneityin[Si/C]andconstrainsthe widthofa lognormalprobabilitydistributionin[Si/C]
v
4 to be much smaller than that of [C/H]; this implies a common origin for Si and C. Since the inferred
6 [Si/C]dependsontheUVBshape,thisalsosuggeststhatinhomogeneitiesinthehardnessoftheUVB
6 are small. There is no evidence for evolution in [Si/C]. Variation in the inferred [Si/C] with density
0 depends on the UVB and rules out the quasar-only model unless [Si/C] increases sharply at low
1 density. Comparisons with low-metallicity halo stars and nucleosynthetic yields suggest either that
3 our fiducial UVB is too hard or that supermassive Population III stars might have to be included.
0 The inferred [Si/C], if extrapolated to low density, corresponds to a contribution to the cosmic Si
/ abundance of [Si/H]= −2.0, or Ω ≃ 3.2×10 7, a significant fraction of all Si production expected
h Si −
p by z ≈3.
- Subjectheadings: cosmology: miscellaneous—galaxies: formation—intergalacticmedium—quasars:
o
absorption lines
r
t
s
a 1. INTRODUCTION con(Songaila & Cowie 1996),andoxygen(Schaye et al.
:
v 2000a)inthediffuse intergalacticmedium(IGM).These
Observationalstudies using high-resolutionquasarab-
i metals constitute an important record of star formation
X sorption spectra have firmly established the presence of
and of the feedback of galactic matter into the IGM.
heavy elements such as carbon (Cowie et al. 1995), sili-
r This paper is the third in a series employing the
a
1 BasedonpublicdataobtainedfromtheESOarchiveofobser- statistics of pixel optical depths to study the enrich-
vations from the UVES spectrograph at the VLT, Paranal, Chile ment of the IGM. The basic technique – pioneered
and on data obtained at the W. M. Keck Observatory, which is by Cowie & Songaila (1998, see also Dav´e et al. 1998
operatedasascientificpartnershipamongtheCaliforniaInstitute
and Songaila 1998) and later employed by Ellison et al.
ofTechnology,theUniversityofCalifornia,andtheNationalAero-
nautics andSpace Administration. TheW. M.Keck Observatory (1999, 2000) and Schaye et al. (2000a) – was developed
wasmadepossiblebythegenerousfinancialsupportoftheW.M. and extensively tested using cosmologicalhydrodynami-
KeckFoundation. calsimulationsbyAguirre,Schaye&Theuns(2001;here-
2 Department of Physics, University of California at after Paper I). The technique was then generalized and
Santa Cruz,1156 High Street,Santa Cruz, CA 95064;
appliedto19high-qualityspectrainordertomeasurethe
[email protected]
3 School of Natural Sciences, Institute for Advanced Study, full distribution of carbon as a function of redshift and
EinsteinDrive,PrincetonNJ08540; [email protected] gas density in Schaye et al. (2003; hereafter Paper II).
4 European Southern Observatory, Karl-Schwarzschild-Strasse
See Aracil et al. (2003) and Pieri & Haehnelt (2003) for
2,D-85748GarchingbeiMu¨nchen,Germany
5 Institute of Astronomy, Madingley Road, Cambridge CB3 other recent studies applying the pixel method to C IV
0HA,UK and OVI.
6 Institute for Computational Cosmology, Department of Most studies of the enrichment of the IGM have fo-
Physics, University of Durham, South Road, Durham, DH1 3LE, cused on C IV absorption because it is strong and lies
UK
7 University of Antwerp, Universiteits plein 1, B-2610 Antwer- redwardof the Lyα forest. Moreover,as shownin Paper
pen,Belgium II,ratiosofCIVandHIopticaldepthscanbeconverted
8 Carnegie Observatories, 813 Santa BarbaraStreet, Pasadena, into carbon abundances using an ionization correction
CA91101
9 DepartmentofAstronomy,CaliforniaInstituteofTechnology, that is neither very large, nor very sensitive to the tem-
Pasadena,CA91125 perature and density of the absorbing gas. While mea-
2 Aguirre et al.
surements of the distribution of carbon provide impor- tails and tests. Section 3.1 contains a brief overview of
tant information on the mechanism by which the IGM the method. Readers who wantmore detail would bene-
was enriched, relative abundance information is crucial fit from also reading sections 3.2– 3.4 which summarize
for identifying the types of sources responsible for the the method, making reference to the relevant sections of
enrichment. Papers I and II, and noting the changes to the method
PreviousstudieshaveestablishedthepresenceofSiIV used in Paper II.
absorptionintheIGMatz ∼2−5andhaveusedsimple
3.1. Overview
ionization models to infer that their data is consistent
with Si/C exceeding the solar ratio by a factor of a few For each QSO spectrum, we first recover the optical
(Songaila & Cowie 1996; Songaila1998; Songaila2001; depths due to H I Lyα (λ = 1216 ˚A) absorption in all
Boksenberg, Sargent & Rauch 2003). The observed ra- pixels in the Lyα forest region. Then we recover the
tiosofSiIV/CIVhavealsobeenusedtostudytheshape opticaldepth in pixels at the correspondingwavelengths
andevolutionoftheionizingUVbackground(UVB),but ofmetallinessuchasSiIV(λλ1394,1403),SiIII(λ1207),
with conflicting results: while Songaila (1998) sees an and C IV (λλ1548,1551) and correlate the (apparent)
abrupt change in Si IV/C IV column density ratios at opticaldepth in one transitionwith thatin another. We
z ≃ 3, Boksenberg et al. (2003) see no evidence for any dothisbybinningthepixelsintermsoftheopticaldepth
evolution. of the most easily detected transition, e.g., C IV, and
Thispaperpresentsmeasurementsoftherelativeabun- plottingthemedianopticaldepthoftheothertransition,
dances of silicon and carbon in the IGM, obtained by e.g., Si IV, against it. A correlation then indicates a
comparingthe statistics ofSiIV,CIV,andHI pixel op- detection of Si IV absorption; see the bottom curve in
ticaldepthsinasampleof19high-qualityquasarspectra the left-hand panel of Fig. 2 for an example. By doing
to synthetic spectra obtained using a cosmological, hy- the same for percentiles other than the 50th (i.e., the
drodynamical simulation. Our primary goal is to mea- median) we obtain information on the full probability
suretheoverallSi/Cabundanceratiointhegasforwhich distribution of pixel optical depths (see the other curves
SiIVabsorptionisdetected,givenamodelfortheextra- inthepanel). Inthiswayalargequantityofinformation
galactic ionizing UVB. In doing so, we also obtain some can be extracted from each observed spectrum.
informationonhow muchthe distributionofsiliconmay By comparing the observed optical depths with those
differ from that of carbon (beyond an overall difference obtained from synthetic spectra generated using a hy-
inthenormalization),aswellasconstraintsontheshape drodynamical simulation, we make inferences about the
and the evolution of the UVB and on the thermal state distribution of silicon. For each observed spectrum, we
of the absorbing gas. generate a large set of spectra drawn from the simula-
We have organized this paper as follows. In §§2 and 3 tionandprocessthemtogivethemthe samenoiseprop-
we briefly describe our sample of QSO spectra and our erties, wavelength coverage, resolution, etc., as the ob-
methodology (both of which are discussed at length in served spectrum. We do this for each of several UVB
Paper II). In §4 we first show results for our best QSO models; for each model the simulations include a carbon
spectrum, Q1422+230,as an illustration of the method. distribution as measured in Paper II for that assumed
We then give measurements (using the full sample) of UVB, and some value of [Si/C],10 with ionization bal-
the τ /τ ratio, from which we infer the relative ances computed using the CLOUDY package11 (version
SiIV CIV
abundance of silicon to carbon ([Si/C]) for our fiducial 94;see Ferland et al. 1998and Ferland 2000for details).
UVB model (which is, as in Paper II, a re-normalized We analyze these simulated spectra in exactly the same
versionof that given for galaxies and quasarsby Haardt mannerastheobservedones,andcomparethesimulated
& Madau 2001, hereafter HM01). Next we give results and observed pixel optical depth statistics.
for other UVB models, and discuss to what extent our The UVB models we employ are those in Paper II
datacanconstraintheUVBshapeandevolution,andthe (§ 4.2). Allare basedonthe models ofHaardt&Madau
variationsin[Si/C].Wethengiveandinterpretmeasure- (2001; see also 1996)12, but renormalized (by a redshift-
ments of τ /τ and τ /τ (which help constrain dependent factor) so that the simulated spectra match
SiIV HI SiIII SiIV
the thermal state of the absorbing gas). We discuss and ourmeasurement(PaperII)oftheevolutionofthemean
interpret our results in §5, and conclude in §6. Lyαabsorption. Ourfiducialmodel,“QG”,includescon-
tributions from both galaxies (with a 10% escape frac-
2. OBSERVATIONS tionforionizingphotons)andquasars;“Q”includesonly
Weanalyzeasampleof19high-quality(6.6kms 1 ve- quasars;“QGS”is anartificiallysoftenedversionofQG:
−
locity resolution, signal-to-noise ratio [S/N] > 40) ab- itsflux hasbeen reducedbya factoroftenabove4 Ryd.
sorption spectra of 2.1 ≤ z ≤ 4.6 quasars. The sam- Model “QGS3.2” is like model QG for z < 3.2 and like
ple is identical to that of Paper II. It includes four- model QGS for z ≥ 3.2 and was constructed to crudely
teen spectra taken with the UV-Visual Echelle Spectro- model the possible evolution of the UVB if He II was
graph(UVES, D’Odorico et al. 2000) on the Very Large suddenly reionized at z =3.2.
Telescope(VLT)andfivetakenwiththeHighResolution
3.2. Recovery of pixel optical depths
Echelle Spectrograph (HIRES, Vogt et al. 1994) on the
Keck telescope. See Paper II (§ 2) for a description of
the sample and data reduction. 10Allabundancesaregivenbynumberrelativetohydrogen,and
solarabundance aretaken tobe(Si/H)⊙ =−4.45and (C/H)⊙ =
3. METHOD −3.45(Anders&Grevesse1989).
11 Seehttp://www.nublado.org.
Thebasicmethodemployedissimilartothatdescribed 12 The data and a description of the input parameters can be
in Papers I and II, to which we refer the reader for de- foundathttp://pitto.mib.infn.it/∼haardt/refmodel.html.
Silicon in the IGM 3
After continuum fitting the spectra (Paper II, §5.1,
step 1), we derive H I Lyα optical depths τ for each
HI
pixel between the quasar’s Lyα and Lyβ emission wave-
lengths, although we exclude regions close to the quasar
to avoidproximity effects (Paper II, §2). We use higher-
order Lyman lines to estimate τ if Lyα is saturated
HI
(i.e., F(λ) < 3σ(λ), where F and σ are the flux and
noise arrays, see Paper I, §4.1; Paper II, §5.1, step 2).
ForeachHIpixelwethenderivethecorrespondingSiIV
(andCIV)opticaldepthsτ (andτ ),correctingfor
SiIV CIV
self-contaminationandremovingcontaminationbyother
lines (Paper I, §4.2). In addition, we recover Si III opti-
caldepths τ , correctingfor contaminationby higher-
SiIII
order H I lines (Paper I, §4.2). We thus have four sets
of correspondingpixel opticaldepths that may be corre- Fig. 1.— Ionization correction factor, [Si/H]−log(τSiIV/τHI),
lated with each other. as afunctionof temperature and hydrogen number density. Solid
(dashed) contours are for the UVB model QG (Q) at z =3. The
hatched region indicates the temperature range containing 90%
3.3. Generation of simulated spectra of the particles at the given density. For both backgrounds, the
This study makes extensive comparisons between our ionizationcorrectionincreasesrapidlyfornH<10−4cm−3.
set of observed spectra and those generated from a cos-
mological simulation. The same simulation was used in
PapersI(§3)andII(§4.1),towhichthereaderisreferred depth lead to large errors in the recovered silicon abun-
for details. Briefly, the simulation uses a smoothed par- dance. Rather than applying ionization corrections to
ticle hydrodynamics code to model the evolution of a thedata,wethereforeconcentrateondirectlycomparing
periodic, cubic region of a (Ω ,Ω ,Ω h2,h,σ ,n,Y) = the predictions of our hydrodynamicalsimulation to the
m Λ b 8
(0.3,0.7,0.019,0.65,0.9,1.0,0.24) universe of comoving observedspectra. Usingthemeasurementsofthecarbon
size 12h 1 Mpc, down to redshift z = 1.5 using 2563 distribution obtained in Paper II, we find the value of
−
particles for both the colddark matter and the baryonic [Si/C] that best fits the data.
components. The UVB used in the simulation was cho- Foreachobservedquasarwegenerate50corresponding
sen to match(and only affects) the IGM temperature as simulated spectra with the same noise properties, wave-
measured by Schaye et al. (2000b). length coverage, pixelization, instrumental broadening,
SyntheticspectraaregeneratedasdescribedinPapers and excluded regions. We apply to the simulated spec-
I (§3)andII (§4.1),bycomputing the ionizationbalance trathesameautomatedcontinuumfittingroutineaswas
for each particle using an assumed uniform UVB, then usedfortheobservations(PaperII,§5.1,step1;seealso
passing random sightlines through the snapshots of the PaperI,§4.1)toreduceanydifferencesinthecontinuum
simulation box and patching these sightlines together to fitting errors between simulated and observed spectra.
form one long spectrum. Transitions due to CIII, CIV, Before generating the spectra, we first impose a car-
N V, Si III, Si IV, O VI, Fe II, and 31 Lyman lines of bondistributioninthesimulationthatisconsistentwith
HI are included. The spectra also include noise, instru- the measurements presented in Paper II. In that paper
mental broadening and pixelization chosento match the we found that for a given overdensity and redshift, the
observed spectra in detail. probabilitydistributionforthecarbonabundanceiswell-
describedby alognormalfunction, andwe presentedfits
3.4. Comparison of simulations and observations of the parameters of the distribution (i.e., the median
and the width) as a function of overdensity and redshift
Our simulations (Paper I, §5.1) and those of oth-
for four different UVBs (Paper II, Eqn. 8 and Table 2).
ers’(e.g.,Croft et al.1997;Schaye et al.1999)showthat
For the QG and Q ionizing backgrounds these fits are
there is a tight correlation between τ and the density
HI consistent with no evolution and we use the values for
and temperature of gas giving rise to the absorption. In
z = 3; for models QGS and QGS3.2 we use, for each
Paper II we used this predicted correlation to compute
quasar, the median redshift of the analyzed region. We
an ionization correction (i.e., the ratios of C IV/C and divide each simulation snapshot into 103 cubes, and as-
H I/H) in order to convert ratios of τ /τ into car-
CIV HI signthegasparticlesineachsectionacarbonabundance
bon abundances as a function of density (Paper I, §6;
of
PaperII,§5.1,step 5and§5.2). This method workswell
[C/H]=α+β(z−3)+γ(logδ−0.5)+s,
for C IV because the ionization correction varies slowly
withdensity(andthereforewithτ )inthedensityrange where s, which is the same for all particles in the sub-
HI
probedbytheLyαforest(n ∼10 6−10 3 cm 3). Un- volume, is drawn at random from a lognormal distribu-
H − − −
fortunately, this is not the case for Si IV: Fig. 1 shows tion with mean 0 and variance σ([C/H]) = 0.70, and δ
that while relatively insensitive to gas temperature, the is the overdensity of the particle. For QG, α = −3.47,
ionization correction factor, [Si/H]−log(τ /τ ), in- γ = 0.65, and β = 0; for Q, α = −2.91, γ = 0.17, and
SiIV HI
creasesdramaticallywithdecreasingdensity,from.102 β = 0 (see Paper II, Table 2 for values used for other
at an overdensity δ ≡ ρ/ρ¯∼ 10 (or n ∼ 10 4 cm 3 at UVBs). Silicon abundances are assigned by assuming a
H − −
z = 3) up to & 103 at δ ∼ 1. We find that this renders constant value of [Si/C]. (The assumption that silicon
ionization corrections as used in Paper II unreliable for tracks carbon perfectly is tested below.)
SiIV,becauseverysmallerrorsintheinferredHIoptical Foreachobservedandsimulatedquasarspectrum, op-
4 Aguirre et al.
Fig. 2.—SiIVoptical depths inbinsofτCIV (leftpanel)andτHI (rightpanel)forQ1422+230. Frombottom totop, thepointsarethe
median, 69th, 84th, 93rdand 97th percentiles. Solid lines represent predictions from simulations with h[C/H]i=−3.8+0.65δ, σ=0.70,
and [Si/C]=log5. For clarity, both observed points and simulatedlines are plotted withvertical offsets of (from bottom to top) 0.0, 0.5,
1.0,1.5,and2.0dex. Notethatfortherightpanelthespectrahavebeensmoothedby7.5kms−1 (see§4.3).
tical depths for pixels corresponding to absorption by a correlation.13 The error on τ for each realization is
min
H I, C IV, Si IV and Si III are extracted as described computedbybootstrap-resamplingthequasarspectrum.
in §3.2. We may then plot various percentiles (such as When the realizations are combined, the value of τ is
min
themedian)oftheτ distributionforeachbininτ . computedasthemedianamongtherealizations,andthe
SiIV CIV
The same procedure can be applied to correlate Si IV erroron this value is computed by bootstrap-resampling
with H I, or Si III with Si IV. For each C IV (or other) the realizations.
bin,errorsontheobservedpointsarecalculatedbyboot- The binned optical depth percentiles are then com-
strap resampling the spectrum, i.e., we divide the Lyα pared directly to the simulations, point by point. Be-
forest region of the spectrum into chunks of 5 ˚A which cause of slight differences in contamination, accuracy of
arebootstrapresampledtoformanewrealizationofthe continuum fitting, and noise, τ for a given QSO may
min
spectrum (see Paper II §5.1, step 3). We require that differ slightly from that of the simulations. Because we
in each bin there be at least five pixels above the per- do not want to compare noise with noise, we either: A)
centile being computed, and that at least 25 pixels and subtractτ frombothsimulationsandobservationsbe-
min
five chunks contribute to the bin so that the errors are fore comparing,14 or B) add a constant to the simulated
reliable; otherwise the point is discarded. For the sim- opticaldepths,chosentominimizethedifferencebetween
ulations we compute 50 synthetic spectra and each per- thesimulationsandobservationsforτ <τ ;inthiscase
HI c
centile in each bin is set equal to the median of the 50 we compare only points at τ ≥τ
HI c
realizations, with errors given by bootstrap resampling
the 50 simulated spectra. We require each bin of each 4. RESULTS
realization to have at least five pixels above the given Before presenting the results from our full sample,
percentile,andto haveatleastfivepixels andone chunk we illustrate the optical depth statistics by showing
contributing to the bin, and we discard medians com- some results from our QSO with the strongest signal,
puted with fewer than five acceptable realizations. Q1422+230.
For each percentile, the correlation disappears below
some CIV optical depth τ at a value τ that is deter- 4.1. Results for Q1422+230
c min
mined by noise, continuum fitting errors, and contam-
Fig.2showsseveralpercentilesofτ ,binnedaccord-
ination by other lines. These may be corrected for by SiIV
ingtotheircorrespondingopticaldepthinCIV(left)and
subtracting τ from the binned optical depths, thus
min HI(right)forQ1422+230. Thebottompointsaremedi-
convertingpointsatτ <τ intoupperlimits(PaperII,
HI c ans,andthenextfoursets(withverticaloffsetsof0.5,1.0,
section 5.1, step 4, and Fig. 4). For each realization, we
computeτmin asthegivenpercentileoftheopticaldepth 13 InPaperIIweusedfunctionalfitstodetermineτc. ForSiIV
for pixels withτHI <τc,where τc =0.01is chosenas the the correlations are generally less strong than for CIV and we fix
C IV or Si IV optical depth below which we never see τc “byhand”. ForbinsinτHI,weuseτc=1.
14AsinPaperII,wepropagatetheasymmetricerrorsforpoints
in which τmin has been subtracted by computing a fine grid of
errors(e.g.,±0.01σ,0.02σ,...).
Silicon in the IGM 5
1.5, and 2.0 dex) represent percentiles 69.146, 84.134,
93.319, and 97.725. These correspond to x=0, 0.5,1,1.5
and 2σ values of the cumulative gaussian probability
function f(x) = 1 x e t2/2σ2dt (so that, for exam-
√2π −
ple, a distribution of τ−∞ that is lognormal with width
RSiIV
1dexwouldgive1 dexhighermetallicityinthe84.134th
percentile than in the median). The solid lines are pre-
dictions from the simulations with [Si/C]= log5 = 0.70
uniformly, median C metallicity h[C/H]i=−3.8+0.65δ
and a width of σ([C/H]) = 0.70dex in the (lognormal)
metallicity distribution.15
The left panel shows that the simulations with the
QG UVB and [Si/C]=log5 match the observationsvery
well. This canbe quantifiedby computing, forallpoints
with logτ ≥logτ =−2.0, the χ2 difference between Fig. 3.— Predicted optical depth ratios logτSiIV/τCIV as a
CIV c functionofthetemperatureandthehydrogennumberdensity,as-
the simulated and observed data points.16 We obtain
suming a solar ratio of Si/C. Solid (dashed) contours are for the
χ2/d.o.f.=5.5/9,4.0/9,2.2/8,and7.4/7forthemedian, UV-backgroundmodelQG(Q)atz=3. Thehatchedregionindi-
0.5σ, 1σ and 1.5σ percentiles, respectively.17 The good catesthetemperaturerangecontaining90%oftheparticlesatthe
givendensity.
fit of the median indicates that a uniform [Si/C] ∼log5
modelfitswell(thoughslightlyhigher[Si/C]arefavored;
see below), and that the data do not require any strong
trend of [Si/C] with density (for which τ is a proxy). adjust for noise, contamination etc. (see § 3), then di-
CIV
Comparison of the higher percentiles can help constrain vide by the central value of the τCIV bin. These points,
scatter in τ /τ , which depends on the scatter in gathered from all QSOs, are rebinned by χ2-fitting, for
SiIV CIV
both [Si/C] and the ionization correction, and it is clear eachτCIV rangeindicatedinFig.4,aconstantleveltoall
thatthat simulationswith uniform[Si/C]andauniform of the points in the specified redshift range. The errors
UVB fit the observations well; this is quantified below represent 1- and 2-σ confidence intervals (∆χ2 = 2 and
using our full data sample. ∆χ2 =4).
Comparisonbetweensimulatedandobservedτ ver- Theplottedlines indicatepredictionsfromthe simula-
SiIV
susτ (right)issomewhatlessstraightforward,asitde- tions for our different UVBs; our fiducial model, QG, is
HI
pends both on [Si/C] and on the assumed distribution shown in solid lines. For each background, we generate
of carbon. Encouragingly, we find that for Q1422+230 simulated τSiIV/τCIV points in the same way as we did
amodel withuniform[Si/C](and carbondistributionas for the observations,but averagingover50simulated re-
derivedinPaperIIfromthefullsample)fitstheobserved alizations as described in § 3.4. We then calculate a χ2
mediansfairlywell. Thepredictedhigherpercentilesare, betweenallvalidobservedoriginal(not rebinned)points
however,abitlow;thisispartlybecausetheQ1422+230 and the corresponding simulated points.18 Because we
CIVabsorbershappen toexhibit slightlymoremetallic- use 50 simulated realizations, the simulation errors are
ityscatter(≈0.81dex;seePaperII,§5.2)thanthelevel almost always negligible compared to the observed er-
derived from the full sample. rors,but they are still taken into account by calculating
In summary, the observed Q1422+230 Si IV optical the total χ2 using the formula:
depths, and their comparison to simulations show that:
1. A uniform [Si/C]∼ log5 is favored, 2. There is no χ2 = Xobs−Xsim −2+ Xobs−Xsim −2 −1,
evidenceforatrendof[Si/C]withdensity,3. Thereisno σ σ
evidenceforscatterinτSiIV/τCIV beyondthatincludedin Xi "(cid:18) obs (cid:19) (cid:18) sim (cid:19) # (1)
the simulation with uniform [Si/C] and a uniform UVB.
whereX ≡τ /τ andσ istheerrorinthisquantity.
SiIV CIV
We then add a constant offset to the simulated points
4.2. τ versus τ for the full sample
SiIV CIV (which corresponds to scaling [Si/C]) such that χ2 is
To place more quantitative constraints on [Si/C], test minimized. In each panel the lines connect the scaled,
forevolution,andmakeamoredetailedcomparisonwith rebinned simulation points.
several UVB models, we have combined the data points The first clear result is that there is a strong trend of
obtained from our entire sample.(These points are tab- log(τ /τ ) with logτ , from . −2 at logτ ∼
SiIV CIV CIV CIV
ulated in Table 1.) Figure 4 shows logτSiIV/τCIV versus −1.5 to & −1.0 at logτCIV & −0.5. This previously un-
logτCIV,inbins ofz. To generatethese points, webegin noted correlation is expected if [Si/C] is constant and
with τSiIV values binned in τCIV, as in Fig. 2. We then τCIV correlates with density, since (as shown in Fig. 3)
subtract from each the “flat level” τmin for that QSO to τSiIV/τCIV increases rapidly with gas density. As shown
by the simulation lines, this trend is reproduced in all
15ThesevaluesaretakenfromtheoverallsurfacefitsfromPaper redshift bins by the simulations for all of our UVB
II; h[C/H]i is evaluated at z = 3 and the small redshift evolution
models. Comparing the first three panels shows that
isneglected; σ([C/H])isevaluated atz=3andlogδ=0.75,with
bothδ-andz-dependences neglected. while τSiIV/τCIV correlates strongly with τCIV, there is
16Wetakeintoaccountbothsimulatedandobservederrors,and
adjustτmin ofthesimulationsasdiscussedin§3.4. 18 Even using 50 realizations, it may occasionally happen that
17 The rather low reduced χ2 values may indicate some corre- a simulated bins fails to have enough pixels for at least five re-
lation between neighboring points, but they largely result from a alizations, and so is undefined; in this case the observed point is
slightoverestimate oftheerrorsnearτc;seePaperII,§7. discardedaswell.
6 Aguirre et al.
Fig. 4.— Rebinned median log(τSiIV/τCIV) vs. logτCIV in cuts of z for the combined QSO sample. The first three panels show bins
centered at z = 2.0,3.0 and 4.0 with width ∆z = 1.; the bottom-right panel shows combined data from all redshifts. Lines represent
correspondingrebinnedsimulationpoints(witherrorssuppressed,andwith[Si/C]chosentominimizetheχ2)usingdifferentUVBmodels.
Table1. Recovered SiIVoptical depths
QSO logτCIV logτSiIV,−0.5σ logτSiIV,median logτSiIV,+0.5σ logτSiIV,+1σ logτSiIV,+1.5σ logτSiIV,+2σ
Q1422+230 -9.000 ··· ··· -3.047 0.088 -2.343 0.035 -1.959 0.031 -1.675 0.035 -1.354 0.047
Q1422+230 -3.900 -3.371 0.579 -2.530 0.153 -2.115 0.085 -1.898 0.071 ··· ··· ··· ···
Q1422+230 -3.700 ··· ··· -2.827 0.197 -2.183 0.092 -1.817 0.111 -1.622 0.105 ··· ···
Q1422+230 -3.500 ··· ··· -2.847 0.199 -2.308 0.076 -1.978 0.074 -1.765 0.049 ··· ···
Q1422+230 -3.300 ··· ··· -3.214 0.146 -2.492 0.114 -2.054 0.071 -1.786 0.127 -1.310 0.141
Q1422+230 -3.100 ··· ··· -2.879 0.139 -2.270 0.066 -1.918 0.058 -1.605 0.070 -1.326 0.072
Q1422+230 -2.900 ··· ··· -3.007 0.143 -2.361 0.049 -1.929 0.044 -1.583 0.082 -1.293 0.065
Q1422+230 -2.700 ··· ··· -2.936 0.110 -2.303 0.056 -1.954 0.039 -1.729 0.046 -1.482 0.064
Q1422+230 -2.500 ··· ··· -3.076 0.164 -2.306 0.052 -1.936 0.055 -1.661 0.044 -1.390 0.088
Q1422+230 -2.300 ··· ··· -3.127 0.160 -2.371 0.059 -1.985 0.043 -1.648 0.048 -1.402 0.069
Q1422+230 -2.100 ··· ··· -3.194 0.144 -2.409 0.047 -1.966 0.045 -1.691 0.041 -1.344 0.062
Q1422+230 -1.900 ··· ··· -3.050 0.090 -2.315 0.040 -1.974 0.039 -1.697 0.048 -1.450 0.075
Q1422+230 -1.700 ··· ··· -3.100 0.128 -2.318 0.059 -1.933 0.047 -1.647 0.050 -1.386 0.063
Q1422+230 -1.500 ··· ··· -3.037 0.230 -2.277 0.077 -1.882 0.068 -1.533 0.094 -1.221 0.121
Q1422+230 -1.300 ··· ··· -2.599 0.173 -2.024 0.125 -1.693 0.120 -1.421 0.104 -1.222 0.086
Q1422+230 -1.100 -3.610 0.606 -2.223 0.321 -1.678 0.213 -1.400 0.165 -1.194 0.143 ··· ···
Q1422+230 -0.900 -3.351 0.772 -1.773 0.439 -1.388 0.193 -1.195 0.121 -1.069 0.118 ··· ···
Q1422+230 -0.700 -1.873 0.313 -1.364 0.203 -1.156 0.102 -1.044 0.067 -0.930 0.095 ··· ···
Q1422+230 -0.500 -1.315 0.497 -1.063 0.270 -0.856 0.226 -0.545 0.225 ··· ··· ··· ···
Q1422+230 -0.300 -1.264 0.813 -0.928 0.450 -0.706 0.325 ··· ··· ··· ··· ··· ···
Q1422+230 -0.100 ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ···
Note. —Columns1and2containthequasarnameandtherecoveredCIVopticaldepthrespectively. Columns3and4containthe31stpercentileoftherecoveredSiIV
opticaldepthandthe1σerroronthisvalue. Theremainingcolumnsshowthesamequantitiesforhigherpercentiles(50th,69th,84th,93th,and98th). ACIVoptical
depthoflogτCIV=−9indicatesthatthecorrespondingτSiIV aretheτminvalues. Thecompleteversionofthistable,includingallquasars,isintheelectronicedition
oftheJournal. TheprintededitioncontainsonlydataforQ1422+230.
Silicon in the IGM 7
Fig. 5.—Rebinnedmedianlog(τSiIV/τCIV)vs. zincutsofτCIV forthecombinedQSOsample. Thefirstthreepanelsshowbinscentered
at logτCIV = −1.25,−0.75 and -0.25 with width 0.5dex; the bottom-right panel shows data for all τCIV combined. Lines represent
correspondingrebinnedsimulationpoints(witherrorssuppressed,andwith[Si/C]chosentominimizetheχ2)usingdifferentUVBmodels.
8 Aguirre et al.
orevolutioninthedistributionofτ –mayleadtoap-
CIV
Table2. Best fit[Si/C] andχ2/d.o.f. parentevolution in τ /τ . In our analysis,in which
SiIV CIV
we use small cuts in τ ,19 we see no evidence for evo-
CIV
UVBmodel bestfit[Si/C] χ2/d.o.f. lutionintheUVBbeyondthatinthesmoothlychanging
QQQQGGGSS3.2 0100....42476687+−+−+−+−00000000........1000000006558765 87665355....2867////111111115555 oQaQurGGTtrifihdoacearnitasdQailm,Qcmhuhalaomavndtiogineodelgnse.iaslnsws;isegionnefdtmifinepecedaslosn,ytatlahytsehszuQigm=GheeS3ra.32χ.c22oisntmhsdtoaiadsnnfeatelviatwonhrideetrhdutnbahinye-
form [Si/C]; but because the formation mechanism for
Si and C may be different this need not be the case.
We can, however, observationally constrain the scatter
little dependence on redshift. This can be seen more in [Si/C] by repeating our determination of it using dif-
clearly in the first three panels of Fig. 5, which show ferent percentiles in τ /τ . If the probability dis-
SiIV CIV
log(τSiIV/τCIV) versus z in bins of τCIV. There is no ev- tribution of [Si/C] for fixed τCIV is, like that of [C/H]
idence, in either the simulated or the observed points, and [Si/H] for fixed τ , lognormal, then we can di-
HI
for evolution in τSiIV/τCIV, except perhaps for a slight rectly constrain the width σ([Si/C]) of the distribution
increase in τSiIV/τCIV with increasing z at the highest bycomparing[Si/C]derivedfordifferentpercentiles. For
densities. the 69th, 84th, 93rd and 97th percentiles, we obtain
The observedtrendsinlog(τSiIV/τCIV)arereproduced [Si/C]=0.73+0.05, 0.64+0.07, 0.58+0.13, and 0.78+0.10, re-
0.06 0.07 0.04 0.14
well by the simulations. Because τSiIV/τCIV scales with spectively. T−his trans−lates into −a rough 2σ up−per limit
Si/C, the offset in τSiIV/τCIV obtained by minimizing of σ([Si/C]) . 0.04dex.20 As a rough test of this upper
the χ2 (Eq. 1) against the observations can be used limit,wehavegeneratedsimulatedspectrawithamedian
to compute the best fit [Si/C]. For our fiducial UVB [Si/C]=0.77 and the usual C distribution, but with a
model QG, the simulated spectra were generated with lognormalscatterin[Si/C]ofwidthσ([Si/C]). Ifweadd
[Si/C]=0.70, we find an offset of +0.07dex (implying theχ2 forthe69th,84thand93rdpercentilesforquasars
a best-fit [Si/C]=0.77) with χ2/d.o.f.=65.7/115. As we at z ≥ 3 (there is little useful information on the upper
foundinPaperIIandforQ1422+230above,thereduced percentiles from z < 3), we find χ2/d.o.f. = 198.0/185
χ2 is somewhat low; in Paper II we showed that his was forno scatterin[Si/C],andχ2 =198.2,203.4,and223.0
largely due to a slight overestimate of the errors at low- for σ([Si/C]) = 0.1,0.2,and 0.4 dex, respectively. Be-
τCIV. cause the percentiles are correlatedthese cannot be cor-
The fitted [Si/C] values and corresponding χ2/d.o.f., rectly translated directly into confidence limits; how-
arelistedinTable2,witherrorscomputedbybootstrap- ever they suggest that the data are compatible with
resamplingthequasarsusedintheχ2 minimization. For σ([Si/C]) = 0.1, but probably not with σ([Si/C]) = 0.2
our fiducial model, QG, the best fit [Si/C]= 0.77+00..0055. and almost certainly not with σ([Si/C]) = 0.4. Thus,
The quasar-only background Q (which is probabl−y too contrarytothelargescatterin[C/H],σ([C/H])≈0.7dex
hard; see Paper II) gives a higher values of [Si/C]= found in Paper II, there appears to be very little scatter
1.48+0.05, and the softer QGS and QGS3.2 backgrounds in [Si/C].
0.06
give−lowervalues than QG by ≈0.3−0.5dex. Note that Wemayalsosubdivideoursamplebyredshiftandden-
the QGS background is unrealistically soft at z ∼<3 (see sity to test the dependence of [Si/C] on these. First,
PaperII),buttheQGS3.2backgroundmaybeplausible. computing [Si/C] using only spectra that have a median
Because the τ /τ ratio depends on both [Si/C] absorption redshift med(z) > 3.0 (see Paper II, Table
SiIV CIV
and the shape of the UVB, its measurement can be 1) yields [Si/C]=0.76+0.05, versus [Si/C]=0.79+0.10 us-
0.07 0.08
used to study the evolution of the UVB under the as- ingthe spectrawith m−ed(z)<3.0. The [Si/C]v−alues in-
sumption that [Si/C] is constant. Songaila (1998, see ferredfromtheredshiftsubsamplesarealso(marginally)
also Songaila & Cowie 1996) has measured the median consistent for the Q and QGS UVBs, but inconsistent
Si IV/C IV ratio versus z for C IV systems of col- forQGS3.2;thelatterwouldimply ajump from[Si/C]=
umn density 5 × 1012cm−2 ≤ N(CIV) ≤ 1014cm−2 0.77+0.05 at z > 3 to [Si/C]= 0.32+0.08 at z < 3. This
and found evidence for strong evolution, as well as a is a−se0c.0o9nd way of seeing that our −da0.t1a3disfavors a sud-
sharp break in τ /τ at z = 3.0. This was inter-
SiIV CIV den change in UVB hardness near z =3, assuming that
preted as evidence for a sudden softening of the UVB
[Si/C] is constant.
at z > 3. However, in a recent study Boksenberg et al.
To test for variation in [Si/C] with overdensity δ we
(2003), in agreement with their earlier work and that
haverecomputed[Si/C]usingonly pixelswith τ corre-
HI
of Kim, Cristiani, & D’Odorico (2002) find no evolution
spondingto δ <20orδ >20(using the τ -δ conversion
in τSiIV/τCIV in their sample of 1012cm−2 ≤ N(CIV) . of Paper II, Fig. 2). We obtain [Si/C]H=I0.87+0.19 for
3×1014cm 2 absorbers. Asdiscussedabove(seeFig.5), 0.10
− the low-density sample, versus [Si/C]=0.73+0.03−at high
weseenoevidenceforevolutioninthemedianτSiIV/τCIV −0.05
stronger than that predicted by the simulations, in any
of our τ bins, or when all τ values are combined 19 In the bottom right panel of Fig. 5, we combine all τCIV
CIV CIV values. Although the observations and simulations should have
(Fig. 5, bottom-right). similarweightings by CIV, somedifferences may remainand the
Because τSiIV/τCIV varies by ∼ 1.5dex in correlation comparisonislessreliablethanifcutsinτCIV aremade.
with τ , its evolution is best assessed by using only a 20 This is only a rough error estimate as it assumes that the
CIV
points are fully independent, which does not hold because the
small window in τ ; otherwise evolution in the weight
CIV pointscorrespondtoaranking.
provided by each τ – whether due to selection effects
CIV
Silicon in the IGM 9
Fig. 6.— Median log(τSiIV/τHI) vs. logτHI in bins of z for the combined QSO sample. The first three panels show bins centered at
z = 2,3, and 4 with width ∆z = 1; the bottom-right panel shows combined data for all redshifts. The lines represent corresponding
simulationpoints(witherrorssuppressed)usingdifferent UVBmodels.
density. This difference could imply either that [Si/C] is able.
higher at low densities, or that the UVB is softer than The problems arising from differential line broaden-
we have assumed (see Fig. 3); but the effect is only sig- ing can be partially remedied by smoothing the spectra
nificant at the ≈1.3σ level. so that the minimal line widths of all species become
similar;experimentationshowsthatsmoothingthespec-
4.3. τ versus τ for the full sample
SiIV HI tra by convolvingthem with a Gaussianwith FWHM of
While the τ /τ ratios give the most direct con- ≈5−10 kms 1significantlyincreasesthestrengthofthe
SiIV CIV −
straints on [Si/C], it is also useful to examine τ /τ : signal, and a smoothing of 7.5 kms 1 has been adopted
SiIV HI −
comparingthesimulatedtotheobservedτ /τ ratios for the calculations shownin Figs.2 and6. Fig. 6 shows
SiIV HI
gives,inprinciple,asecondestimateof[Si/C].Thisinfer- logτ /τ versus logτ in bins of z for our combined
SiIV HI HI
ence, however, is less reliable than that from τ /τ sample. Lines again connect the corresponding simula-
SiIV CIV
for two reasons. First, it includes the uncertainty in tionpoints(withanoverallscalingtobestmatchtheob-
[C/H], which is largest at the relatively high densities servations) that reproduce the observed trends in z and
at which (because of the small SiIV/Si fractionat lower τ . The scalings correspond to best-fit [Si/C] values of
HI
densities) Si IV is best-detected. Second, Si absorption 0.97±0.08, 1.65±0.08, 0.25±0.07 and 0.48±0.09 for
lines have a much smaller thermal width than hydrogen QG, Q, QGS, and QGS3.2 respectively, slightly higher
lines, and are only observable in relatively high-density than the values found above using τ /τ . However,
SiIV CIV
gas (where Hubble broadening is small). This leads to asexplainedabove,these valuesdependonthe degreeof
significant differences between the Si IV-weighted and smoothing: for example, with no smoothing, we recover
HI-weighteddensities(seePaperII,§4.3,PaperI,§5.3), values≈0.1−0.3dexhigheryet. Sinceitisunclearwhich
i.e., the SiIV and HI absorption do note arise from ex- smoothing level gives the correct results, the inferences
actly the same gas. The effect of this is to skew (and of [Si/C] using τ /τ should not be relied on.
SiIV HI
weaken) the correlation of τ with τ in a way that Thesamedifferenceinthermalwidthaffectsinferences
SiIV HI
depends on the H I column-density distribution. Unfor- using Si IV/C IV, but at a lower level; whether or not
tunately, as discussed by Theuns et al. (2002), the sim- we smooth by 7.5kms 1 changes the inferred [Si/C] by
−
ulation does not exactly reproduce the observed N(HI) ∼0.1dex, which is a reasonable estimate of the induced
distribution at the high-column density end (which is systematic error.
most importantfor the present study), so the “skewing”
may be somewhat different in observed and simulated
4.4. τ versus τ for the full sample
correlations,and render conclusions about [Si/H] unreli- SiIII SiIV
10 Aguirre et al.
Fig. 7.—PredictedopticaldepthratioslogτSiIII/τSiIVasafunc-
tion of the temperature and the hydrogen number density. Solid
(dashed) contours are for the UV-background model QG (Q) at
z = 3. The hatched region indicates the temperature range con-
taining90%oftheparticlesatthegivendensity.
A final correlation that we have examined is that
of τ /τ with τ . Fig. 7 shows the predicted
SiIII SiIV SiIV
τ /τ versus the temperature T and density n of
SiIII SiIV H
the absorbing gas. For high T, τ /τ becomes in-
SiIII SiIV
dependentofn ,anddeclines rapidlywithT. Thus,the
H
presence of Si III can be used to constrain the tempera-
ture of the gas providing Si IV absorption. In Paper II
a similar test was carried out using the τ /τ ratio,
CIII CIV
yielding the constraint T <105.0K.
Fig. 8 shows τSiIII/τSiIV versus τSiIV for our full sam- Fig. 8.— Ratios of median τSiIII/τSiV versus τSiIV in bins of z
ple, for three cuts in z. At logτ & −1.2 and for the full sample. The lines represent corresponding simulation
SiIV points(witherrorssuppressed)usingdifferentUVBmodels.
2.5 ≤ z ≤ 3.0 (where the data are particularly good)
−0.5 . τ /τ . 0.5, corresponding to a direct up-
SiIII SiIV
per limit of T . 104.9−105.1K for the bulk of the gas
giving rise to this SiIV absorption (the lower value per- We have shown that the pixel optical depth correla-
taining to the higher end of the τ range.) The sim- tions derivedfromour observedQSO spectra are consis-
SiIV
ulations give predictions that depend only very weakly tent, in detail, with spectra drawn from a hydrodynam-
on the UVB model and are in good agreement with the ical simulation with: 1) an assumed carbon metallicity
data, particularly at 2.5 ≤ z ≤ 3.0 (however note that distribution as derived in Paper II from measurements
at z &3.0 there is somewhat more SiIII absorption pre- of C IV absorption, 2) a uniform (rescaled) UVB model
dicted than observed for high τ ). Concentrating on taken from Haardt & Madau (2001), and 3) a constant
SiIV
the QG model, we find χ2/d.o.f. = 80.5/114 comparing and uniform [Si/C] value.
all simulated and observed points with logτ ≥−2.0. Wehaveusedthissuccesstodrawinferencesregarding
SiIV
Fitting an offset to the median logτ /τ ratios (as [Si/C]foreachofseveralmodelsoftheUVB.Beforeana-
SiIII SiIV
done above for τ /τ ) we find −0.32+0.14dex, in- lyzingtheseinferencesitisworthdiscussingsomeeffects
CIV SiIV 0.16
dicating that simulations predict somewh−at too much that bear on their robustness.
Si III absorption overall. We have repeated this exer-
ciseforthe16th,31st,69thand84thpercentilesinorder 5.1. Uncertainties
to fit the center and width σ([SiIII/SiIV]) of a lognor- UVB spectral shape: Our inference of [Si/C] obviously
mal distribution governing scatter in τSiIII/τSiIV beyond dependsontheassumedshapeandevolutionoftheUVB:
that present in the simulations. The fit obtained indi- the models used here produce a range 0.26 ≤ [Si/C] ≤
cates that overall the observed τSiIII/τSiIV ratio is lower 1.48. These models, however, span a range of possi-
by 0.15± 0.06dex than that for the simulations, with bilities that is larger than that allowed by independent
σ([SiIII/SiIV]) = 0.07±0.07dex. These results imply observations. The harder model Q, for example, was
thatmostofthe gasis coolenoughtobe consistentwith found in Paper II to produce a mean carbon abundance
the photoionization equilibrium assumed in the simula- thatincreaseswithdecreasingdensity,whichisprobably
tions,andthatthescatterinτSiIII/τSiIV issimilartothat unphysical. Likewise the softer model QGS was found
in the simulations. But they are also consistent with a to imply increasing [C/H] with z, also unphysical. The
(small) contribution by hotter gas to the observed SiIV modelQGS3.2,witha suddentransitionatz =3.2,pro-
optical depths. duced no problems in Paper II, but here we find that
the resulting predicted jump in τ /τ is disfavored
5. ANALYSISANDDISCUSSION OFRESULTS by our observations. Our fiduciSailIVmoCdIeVl QG appears