The line-of-sight proximity effect in individual quasar spectra

1.1 MB·English

by  Aldo Dall'Aglio

Astronomy&Astrophysicsmanuscriptno.7088 c ESO2008
(cid:13)
February2,2008
∗
The line-of-sight proximity effect in individual quasar spectra
AldoDall’Aglio, LutzWisotzki, andGa´borWorseck
AstrophysikalischesInstitutPotsdam,AnderSternwarte16,D-14482Potsdam,Germany
Received.../Accepted...
8
ABSTRACT
0
0
Weexploitasetofhighsignal-to-noise( 70),low-resolution(R 800)quasarspectratosearchforthesignatureoftheso-called
2 proximity effect in the H Lyα forest. O∼ur sample consists of 17∼bright quasars in the redshift range 2.7 < z < 4.1. Analysing

n the spectra withthe fluxtransmission technique, we detect the proximity effect in the sample at high significance. Weuse thisto
a estimatetheaverageintensityofthemetagalacticUVbackground, assumingittobeconstantoverthisredshiftrange.Weobtaina
J valueofJ =(9 4) 10 22 ergcm 2s 1 Hz 1sr 1,ingoodagreementwithpreviousmeasurementsatsimilarz.Wethenapplythe
− − − − −
8 sameprocedure±toin×dividual linesofsight,findingasignificantdeficitintheeffectiveopticaldepthclosetotheemissionredshift
1 ineverysingleobjectexceptone(whichbyadifferentlineofevidencedoesneverthelessshowanoticeableproximityeffect).Thus,
we clearly see the proximity effect as a universal phenomenon associated with individual quasars. Using extensive Monte-Carlo
] simulationstoquantifytheerrorbudget,weassesstheexpectedstatisticalscatterinthestrengthoftheproximityeffectduetoshot
h noise(cosmicvariance).Theobservedscatterislargerthanthepredictedone,sothatadditionalsourcesofscatterarerequired.We
p rule out a dispersion of spectral slopes as a significant contributor. Possible effects are long time-scale variability of the quasars
- and/orgravitationalclusteringofLyαforestlines.Wespeculateonthepossibilityofusingtheproximityeffectasatooltoconstrain
o individualquasarages,findingthatagesbetween 106 and 108 yrsmightproduceacharacteristicsignatureintheopticaldepth
r profiletowardstheQSO.Weidentifyonepossible∼candidatef∼orthiseffectinoursample.
t
s
a Keywords.diffuseradiation–intergalacticmedium–quasars:absorptionlines
[

2
v 1. Introduction notedbyCarswelletal.(1982)andwaslaterbaptised‘Inverse’
7 (Murdochetal.1986)or‘ProximityEffect’Bajtliketal.(1988,
6 The multitude of absorption lines seen in the spectra of high hereafterBDO88).Itsprimeapplicationhasbeensofarthepos-
7 redshift quasars gives important information about the state of sibility to derive an independent estimate of the UVB inten-
1 matterintheuniverse,tracingthephysicalconditionsofthein- sity, by measuring the reduction of column densities (against
. tergalacticmedium(IGM)atvariousepochs.Itiscommonlybe-
1 the global evolution of absorption line density increasing with
0 lieved that for column densities up to NH 1017.5cm−2, the redshift) and combining this with the QSO luminosity at the
≈
8 absorbersare in photoionisationequilibrium with a metagalac- Lymanlimit,assumedtobeknown.Thebestconstraintsonthe
0 tic ultraviolet background field (UVB), composed of the inte- UVBusingtheproximityeffectstemfromthecombinedanaly-
v: gral over all sources of UV radiation (essentially, star-forming sisoflargequasarsamples(Cookeetal.1997;Scottetal.2000;
galaxiesandquasars).High-resolutionspectraoftheLymanfor-
i Liske&Williger 2001), yielding mostly valuesconsistent with
X estprovidenotonlyaratherdetailedstatisticalcharacterisation
theabovequotedothermethods.However,theuncertaintiesare
oftheabsorberpropertiessuchaslinenumberdensitiesaswell
r still substantial. Besides the problem that a limited number of
a astemperatureanddensitydistributions(e.g.,Kimetal.2001), linesofsightalwayssuffersfrom‘cosmicvariance’,theremay
but also physical parameters such as H and He photoioni-
alsobesystematicbiases.Inparticular,ifQSOsresideinintrin-
sation rates (Rauchetal. 1997; Fardaletal. 1998), which di-
sicallyoverdenseenvironmentsthenthesignatureoftheproxim-
rectly relate to the intensity of the UVB, as described recently ityeffectwillappearweakerthanpredicted(Loeb&Eisenstein
by Boltonetal. (2005) invoking hydrodynamical simulations.
1995;Rollindeetal. 2005).Anotheruncertaintyis thepossibly
Independently, the UVB has been successfully synthesised by
limitedlifetimeofquasars.Ontheotherhand,theproximityef-
combiningtheobservedquasarluminosityfunctionandtheUV
fectmayalsobeusedtoderiveconstraintsonthisimportant,but
emission from galaxies (although the latter is still very uncer-
largely unknown astrophysical quantity (e.g., Pentericcietal.
tain)withthepropagationofdiffuseradiation(Haardt&Madau
2002).
1996).
InthevicinityofstrongUVsourcessuchasbrightquasars, In this paper we present an exploitation of new observa-
the H photoionisation rate should locally increase, further re- tionalmaterialintermsoftheproximityeffect(Sect.2).Rather
ducingthe density of residualneutralhydrogen.This enhances than the traditional line counting we use the more sensitive
the transparency of the IGM to H ionising radiation and flux transmission statistic to search for proximity effect signa-
should become observable as a weakening of the Lyman for- tures, augmentedby extensive Monte-Carlosimulationsto cal-
est absorption near such sources. Such an effect has first been ibrate the systematic and statistical errors(Sect. 3). We deliver
our results in Sections 4.1 and 5. Firstly we briefly present an
Sendoffprintrequeststo:A.Dall’Aglio,e-mail:[email protected] analysis of the combined sample of 17 QSO spectra and de-
Based on observations collected at the European Southern rive an estimate of the UV backgroundintensity. Secondly we
∗
Observatory,Paranal,Chile(Programme070.A-0425) demonstrate that the effect is measurable on single sightlines
2 A.Dall’Aglioetal.:Theline-of-sightproximityeffectinindividualquasarspectra
Fig.1. Example of a quasar spectrum taken
fromthedataset (HE0940 1050, z = 3.088).
−
In the upper panel the flux density in units of
erg cm 2 s 1 Å 1 as function of wavelength
− − −
ispresentedwiththeuncorrected(dottedline),
corrected (long-dashed line) continuum level
and the noise of the spectrum (dashed-dotted
line).Inthelowerpanelthefittedtransmission
isshowningraywhilethecorrectedcontinuum
isplottedinblack(SeeSect.2.1and3.2.3for
details).Inbothpanelstheverticaldottedline
representtheemissionredshift.
(Willigeretal. 1994; Luetal. 1996; Savaglioetal. 1997), not 0.1. For those spectra taken in clear to photometric condi-
onlystatisticallyinlargesamples(Bajtliketal.1988;Scottetal. tions (6 in total), the corrected magnitudesmatched the values
2000;Liske&Williger2001). from Ve´ron-Cetty&Ve´ron (2006) within δVmag 0.1. The
≤
The effect can actually be systematically detected in each V magnitudes of the remaining objects, after slit loss correc-
singleQSOofoursample(withonespecialcasethatisdiscussed tion, were systematically lower than the Ve´ron-Cetty&Ve´ron
separately).Wespeculateaboutthepossibilitiestodetectsigna- (2006) values by not more than 0.3 mag. Since those data
turesoffinitequasaragesbyvirtueoftheproximityeffect. were taken in relatively poor sky conditions, we adopted the
Throughout this paper, we assume a flat Λ Universe with Ve´ron-Cetty&Ve´ron(2006)valuesandassociatedlargeruncer-
Ω =0.3andΩ =0.7andH =71kms 1Mpc−1. tainties(δVmag 0.3).
m Λ 0 − −
≤
2. Data
2.3.Systemicquasarredshifts
2.1.Observationsanddatareduction
Our spectra cover a sufficient range in wavelength so that we
OurdatawereobtainedattheESO-VLTUT4(Yepun)inservice could measure the redshift of each quasar from more than one
modebetweenOct2002andApr2003.WeusedFORS2inlong emissionline.AllmeasuredredshiftsarecompiledinTable2.In
slitspectroscopymodewiththe600Bgrism,coveringtherange orderto adopta systemic redshiftwe used low-ionisationlines
3315–6360Å. A longitudinal atmospheric dispersion corrector whenever possible (Gaskell 1982; Tytler&Fan 1992). For ob-
(LADC) was used to account for differential refraction effects. jectswherethiswasunfeasible,weusedtheredshiftfromhigh-
With a slit width of 1 , the resolution is 800 (4Å FWHM). ionisation lines with a statistical correction, determined from
′′
Table 1 summarisesthe observationsfort∼he fullsample. In to- the average shift between Si+O and Si+O]. The agree-
tal we observed17 QSOs, always fully coveringthe Ly Forest mentbetweenSi+OandCestimatesisgenerallygood,even
spectrumbetweentheLyαandLyβemissionlines. though the second line is usually very weak and rather broad.
The spectrawerereducedusingIRAFstandardprocedures. For Q 0000 26 only the asymmetric Lyα line with strong as-
−
Each exposurewas bias-correctedand flat-fielded, cosmic rays sociated absorption was covered by our spectrum; for this ob-
were marked using a κ-σ clipping algorithm, and the images ject we adopted the redshift from Schneideretal. (1991). For
were finally sky-subtracted. The extracted spectra were cali- Q 0347 383our corrected value is in agreementwith the esti-
−
bratedinwavelengthandfluxandcorrectedforvacuumandhe- mationdonebySteidel(1990).
liocentricshifts.Thegalacticextinctionwastakenintoaccount
assuming the E(B V) estimations by Schlegeletal. (1998),
−
togetherwith the Cardellietal. (1989) extinctioncurveassum- 2.4.Quasarcontinuum
ingR = 3.1.Thetwoexposuresavailableforeachtargetwere
V
coaddedwithinversevarianceweights,yieldingatypicalsignal- Theanalysisofabsorptionlinesrequiresa normalisationtothe
to-noiseratio(S/N)of 70intheLymanforest. QSOcontinuum.Weexploredtwotypesofcontinuumestimates:
∼ (i)aglobalpowerlaw(f(ν) να),excludingemissionandab-
∝
sorption regions,used to estimate the quasar flux at the Lyman
2.2.Quasarmagnitudes limit;(ii)amorelocalestimatethatalsoincludesthebroademis-
sion lines as quasi-continuum. For this task we developed an
An evaluation of the proximity effect relies on the accurate
automaticalgorithm,followingtheworkbyYoungetal.(1979)
knowledgeof quasar fluxes. Even though absolute spectropho-
and Carswelletal. (1982), which perform a cubic spline inter-
tometry is compromised by intrinsic quasar variability, we
polationbasedonadaptiveintervalsalongthespectrumwithre-
reached reasonable accuracy in almost all spectra (See Tab. 1
specttothecontinuumslope.Thepointsforthesplineinterpo-
for details). We accounted for slit losses modelling a gaussian
lationwerechosenstartingfromaregularsamplingofthespec-
point spread function with FWHM given by the average see-
trumwithabinningthatbecomesfinerwhenevertheslopeofthe
ing during the observations. Centering the 1 arcsec slit on the
computedcontinuumexceedsagiventhreshold.Thisisdonein
Gaussian centroid,we correctedfor the flux falling outside the
ordertobetterreproducethewingsofemissionlines.
slit in all our spectra. In addition to our data, we used images
obtained at ESO-VLT UT1 (Antu) in Nov 2004 under photo- In Sect. 3.2.3 below we assess the expected errors (aris-
metric conditions, covering 3 of our fields and SDSS infor- ing mainly from line crowding) associated with this process.
mation for 4 quasars yielding consistency to within δVmag Figure1showsasamplequasarspectrumtogetherwiththeesti-
≤
A.Dall’Aglioetal.:Theline-of-sightproximityeffectinindividualquasarspectra 3
Table1.Logofobservations.
QSO Vmag z Exp.Time Seeing Airmass SkyConditiona Obs.Date Ref.Mag
em
(s) (arcsec)
CTQ0247 17.4 3.025 750 1.29 1.07 CL,WI Dec.8,2002 4
CTQ1005 18.4 3.205 1500 1.13 1.21 TN Jan.9,2003 3
CTQ0460 17.5 3.139 900 1.45 1.10 PH Dec.23,2002 4
H0055 2659 17.5 3.665 600 1.34 1.02 CL,WI Dec.8,2002 4
−
HE0940 1050 16.4 3.086 600 0.86 1.12 TN,TK Nov.26,2002 3
−
HE2243 6031 16.4 3.010 600 1.02 1.24 CL,PH Nov.9,2002 4
−
HE2347 4342 16.7 2.885 600 0.77 1.06 PH Nov.10,2002 1
−
PKS2126 15 17.0 3.285 600 0.97 1.20 PH Oct.29,2002 4
−
Q0000 26 18.0 4.098 600 1.31 1.03 TN,CL Nov.7,2002 4
−
Q0002 422 17.2 2.767 600 1.39 1.45 TK,TN Oct.14,2002 3
−
Q0347 383 17.7 3.220 800 1.45 1.15 TN Jan.9,2003 1
−
Q0420 388 16.9 3.120 600 1.37 1.06 CL,WI Dec.8,2002 1
Q0913+−0715 17.8 2.787 800 1.45 1.18 TN Jan.9,2003 2
Q1151+0651 18.1 2.758 900 0.94 1.17 TN,CL Jan.25,2003 2
Q1209+0919 18.5 3.291 1500 0.78 1.80 CL,TN,TK Jan.1,2003 2
Q1223+1753 18.1 2.945 900 0.66 1.35 TN,CL Jan.25,2003 2
Q2139 4434 17.7 3.214 800 0.85 1.33 TN Apr.30,2003 3
−
aLegend:PH-Photometric,CL-Clear,TN-Thincirrus,TK-Thickcirrus,WI-Windy.
1: Worsecketal.(2007):PHconditions.
2: SDSS.
3: Ve´ron-Cetty&Ve´ron(2006).
4: Slitlosscorrectedonly.
matedlocalcontinuumandtheresultingtransmissionspectrum are isothermal, homogeneous, and randomly distributed along
(seeonlinematerialforthecompletesetofquasarspectra). theLOS,wefind
f (λ (1+z )) 1 d (z ,0) 2
ω= ν LL c L q (3)
3. Analysis 4πJ (1+z ) d (z ,z )
ν c L q c !
3.1.Thefluxtransmissiontechnique withz beingthecloudredshift,d (z ,0)theluminositydistance
c L q
oftheQSOasseenfromtheEarth,andd (z ,z )asseenfromthe
Thedistributionofabsorptionlinesalonga lineofsight(LOS) L q c
cloud. As clarified by Liske&Williger (2001), f (λ (1+z ))
towards a quasar is usually expressed as a function of red- ν LL c
is the flux at the Lyman limit which has to be weighted by a
shift z, column density NH, and Doppler parameter b in the
form d3n/(dzdNHdb) = η(z,NH,b). Due to our limited spec- bandwidth correction. We computed then the normalised opti-
cal depth (also called ξ) which is the deviation of the detected
tral resolution we could not perform single absorber analysis.
opticaldepthfromtheoneexpectedintheLyForest
We followedinsteadtheapproachproposedbyZuo(1993)and
Liske&Williger (2001) to link the line number density to the τ
ξ = eff =(1+ω)1 β. (4)
evolutionofthe effectiveopticaldepth.Theresultingevolution B(1+z)γ+1 −
dependsonredshiftas
In order to quantify the reduction of ξ close to a QSO we
τeff = B(1+z)γ+1 (1) need to know the parameters B and γ quantifying the redshift
evolutionoftheLymanforest.Thesevaluesaretypicallydeter-
where Bandγaresensitivetotheresolutionandthedetectable
minedfromhigh-resolutionspectroscopy.Kimetal.(2002)ob-
columndensityrangeandtheobservableeffectiveopticaldepth
tainedB = 0.0032andγ = 2.37,whichweusedasstartingval-
defined as the optical depth at the average transmission over a
uestocomputethenormalisedopticaldepthsforallQSOsover
predefinedwavelengthinterval:e−τeff =<e−τ >. thefullspectralrange.Thisresultedinslightlytoohighaverage
In orderto accountforlocalfluctuationsof the ionisingra-
ξoutsidetheproximityeffectzones,whereEq.1shouldholdand
diationfield,wefollowtheapproachbyBDO88whichassumes
produceameanξofunity.Wecorrectedthisslightmismatchby
interveningabsorberstobeinphotoionisationequilibriumwith
adjustingBuntilwereachedξ 1fortheLyαforestregion
ω 0
thelocalionisingfield;furthermoreanemptyspace,andnoflux inallspectra,excludingthepro→xim∼ityeffectzone.Thisresulted
attenuation except geometric dilution. The modification intro-
infinalnormalisationparameterofB=0.0041.Wewillquantify
ducedintheopticaldepththenbecomes
theimpactofdifferentnormalisationstrategieswhenpresenting
τ = B(1+z)γ+1(1+ω)1 β (2) theresultsfortheUVbackgroundinSect.4.1.Finallytheslope
eff −
ofthecolumndensitydistributionwassetthroughoutthepaper
where ω is the ratio between the photoionisation rates of the toβ=1.5(e.g.Huetal.1995;Kimetal.2002),ifnotexplicitly
quasarandthebackgroundandβtheslopeinthecolumndensity written.
distribution.AssumingaconstantUVBintherangeofredshifts Inordertorevealtheproximityeffect,wenowsearchedfor
of our sample, an equal spectral energy distribution of QSOs a systematic departureof the normalised opticaldepths ξ from
and background at ν > ν , and pure hydrogen absorbers that unityforlargevaluesofω.Theresultforourcombinedsample
LL
4 A.Dall’Aglioetal.:Theline-of-sightproximityeffectinindividualquasarspectra
Table2.Redshiftestimateswithassociatederrorsforthequasarsampleresultingfromdifferentemissionlines .
†
QSO zLyα zaSi+O zC zSi+O] zC ∆z zLit Reference
σz=0.003 σz=0.003 σz=0.005 σz=0.003 σz=0.003 zSi+O−zSi+O]
CTQ0247 3.008 3.025 3.021 3.016 3.008 0.009 3.020 1
CTQ1005 3.201 3.205 3.210 3.196 - 0.009 3.210 1
CTQ0460 3.134 3.139 3.135 3.128 - 0.011 3.130 1
H0055 2659 3.650 3.665 3.659 - - - 3.655 2
−
HE0940 1050 3.081 3.086 3.088 3.074 3.059 - 3.068 3
−
HE2243 6031 3.004 3.010 3.008 3.005 3.004 0.005 3.010 4
−
HE2347 4342 2.877 2.885 2.886 2.870 2.861 0.015 2.885 5
−
PKS2126 15 3.279 3.285 3.286 3.270 - 0.015 3.267 3
−
Q0000 26 4.100 - - - - - 4.098 6
−
Q0002 422 2.765 2.767 2.765 2.757 2.756 0.010 2.767 3
Q0347−383 3.213 3.220b - 3.209 - - 3.222 12
−
Q0420 388 3.117 3.120 3.120 3.109 - 0.011 3.110 2
Q0913+−0715 2.784 2.787 2.786 2.779 2.767 0.008 2.785 7
Q1151+0651 2.755 2.758 - 2.752 2.754 0.006 2.762 8
Q1209+0919 3.292 3.291 3.289 3.278 - 0.013 3.291 9
Q1223+1753 2.935 2.945 2.944 2.936 2.930 0.009 2.936 10
Q2139 4434 3.211 3.214 3.210 3.197 - 0.017 3.230 11
−
: Wavelength used to estimate the redshifts are: Lyα = 1215.67Å, Siii+Oi = 1305.77Å, Cii = 1335.30Å, Siiv+Oiv] = 1396.76Å,
† Civ=1549.06Å(Morton2003)
a: Takenassystemicredshift.
b: TheseredshiftswerecomputedfromtheaverageshiftbetweentheredshiftmeasurementsoftheSi+OandSi+O]emissionlines.The
averageredshiftshiftisabout0.011.
Ref: (1) Lopezetal. (2001), (2) Osmeretal. (1994), (3) Rollindeetal. (2005), (4) Lopezetal. (2002), (5) Reimersetal. (1997), (6)
Schneideretal. (1991), (7) Pettinietal. (1997), (8) Ve´ron-Cetty&Ve´ron (2006), (9) Storrie-Lombardi&Wolfe (2000), (10) Hewettetal.
(1995),(11)Hawkins&Veron(1993),(12)Steidel(1990).
is shown in Fig. 4, while Fig. 5 displays the run of ξ versus ω
for each individualQSO line of sight. Before we discuss these
resultswewanttobrieflydescribeourapproachtoquantifythe
statisticalandsystematicerrors.
3.2.Errorestimatesfromsyntheticspectra
3.2.1. Method
Realistic models of the Ly forest, as already developed by
Zhangetal. (1995), invoke the baryonic component in CDM
simulations to trace the absorption line properties along sight
linestowardsQSOs.However,inafirstapproximation,suchdis-
tributions can be considered as random processes, mathemati-
callygovernedbyPoissonstatistics. Followingthisassumption
we performed extensive Monte-Carlo simulations to study the
errorbudget,inparticularsystematicerrorsarisingfromlimited
spectralresolution.
Eachgivensimulatedlineofsightwaspopulatedwithlines
distributedusingdn/dz (1+z)γaslinenumberdensitydistribu-
tionleadingtoτ = B(∝1+z)γ+1.Thealgorithmcontinuestoadd
eff
absorptionfeatures until the effective optical depth reaches the
expectedvalueofτ usingthe bestfitconstraintby Kimetal.
eff
(2002)B=0.0032,γ=2.37.Thecolumndensitydistributionis
givenby f(NH)∝ NH−β wheretheslopeisβ∼1.5.TheDoppler Fig.2. Top panel: Average ratio between the fitted and input
parameter distribution is given by dn/db b 5exp b4/b4 continuum for the five sets of simulated QSOs. Bottom panel:
∝ − − σ
where b 24 km/s(Kimetal. 2001) is a parameterdepend- Standarddeviationprofilesrelativetotheabovesystematicbias.
σ ≃ h i
ing onthe averageamplitudeof the fluctuationsin the velocity
spaceoftheabsorbers(Hui&Rutledge1999).Eachabsorption
featurewasmodelledasaVoigtprofileandonceatransmission
spectrum was computed, we multiplied it by a QSO template
spectrumasdescribedinthenextsection.
A.Dall’Aglioetal.:Theline-of-sightproximityeffectinindividualquasarspectra 5
Fig.4.NormalisedOpticaldepthversusωpro-
file for the combined sample of 17 quasars,
binnedinstepsof∆logω=1.Thesignatureof
the proximity effect is clearly visible for both
continuum corrected and uncorrected profiles.
The curved lines arethe best fit of thesimple
photoionisationmodeltothedata,correspond-
ing toa UV background of log(J ) = 21.03
(solidline),inunitsof[ergcm 2sν1Hz−1sr 1],
− − − −
whilethegreenlong-dashedlinecorrespondto
thebestfittothecontinuum uncorrecteddata.
The horizontal line refers to the case of no
proximityeffect.
3.2.3. Systematicerrors:Continuumplacement
Foreachsimulatedspectrumwecomputedtheratiobetweenthe
fittedandtheinputcontinuum.Wethenaveragedtheratioover
allrealisationsateachemissionredshift.Theresultisshownin
thetoppanelofFig.2,forthefiveredshiftsadopted.Expectedly,
thehighestdeviationisalwaysinthewingsoftheLyαemission
line.Itcanalsobeseenthattheincreasinglinenumberdensity
with redshift causes a gradually growing systematic error. We
use this profiles to correct our automatic continuum estimates
and use the standard deviations shown in the bottom panel of
Fig.2ascontributiontotheuncertainties.Theeffectofthiscor-
rectioncanbeseeninalltheproximityeffectplotsasdifference
betweenthegreentrianglesandtheblackdotsinFig.4-5.
Fig.3.Statistical(shotnoise)uncertaintiesofthenormalisedop- Wenoteinpassingthatasecondsourceofsystematicerrors
tical depth close to a quasar, estimated from the Monte-Carlo would be the presence of metal line systems in the proximity
simulations. effectzone.Ourspectralresolutionisinsufficienttoidentifyin-
dividualmetal lines in the Lyman forest, and any such absorp-
tion present, but unaccounted for, will systematically increase
the normalisedopticaldepthξ and thustendto mask the prox-
3.2.2. QuasarSEDs imityeffect.
Wegeneratedasetof200artificialquasarspectralenergydistri-
butions(SEDs)viatheprincipalcomponentmethodasdescribed 3.2.4. Statisticalerrors
by Suzuki(2006).Each rest-frame quasar spectrum can be de-
We modelledthe statistical errorof the measuredopticaldepth
composedas f (λ) = µ(λ)+Σ(c p(λ))withameanspectrum
λ i· i along individual lines of sight as arising from Poissonian shot
µ,theprincipalcomponentspectra p andthecoefficientsc.We
i i noisedueto thelimitednumberofabsorbersineachsimulated
adoptedthe principalcomponentsby Suzukietal. (2005), who
spectrum.Foreachstackofsimulationswecomputedthemean
determinedµ and p at 1020 Å < λ < 1600 Å from 50 HST
i rf andstandarddeviationofξperlogωbin.Theresultsareshown
FOSspectraoflow-redshiftquasars.Thecoefficientsc areap-
i in Fig. 3, which demonstrates that the standard deviations σ
ξ
proximatelyGaussiandistributed(Suzuki2006).Aftergenerat-
are always considerably bigger than the continuum dispersion.
ingthe200SEDsbydrawingthec fromtheirGaussiandistri-
i However,recallthatwefullyaccountforbothrandomandsys-
butions,weconvolveditwiththeinstrumentalprofileandadded
tematicerrors.Asexpected,thestatisticalerrorsbecomebigger
randomGaussiannoisetoreproduceourobservations.
towardslowerredshiftsdue tothe smaller linenumberdensity.
InordertoinvestigatehowdifferentQSOemissionredshifts Thesimulationresultswerethenusedtodescribeσ (ω,z)with
ξ
affected the error budget, we simulated quasars at five typical a simple polynomialparameterisation.Without introducingthe
redshifts z = 2.0, 2.5, 3.0, 3.5, 4.0, (denoted in Figs. 2–3 with proximity effect, the statistical error at high ω would be much
numbers 1, 2, 3, 4 and 5, respectively) and luminosities repre- largerduetocosmicvarianceonverysmallscale.
sentativeforoursample. In order to estimate the statistical error for the combined
We thennormalisedourspectraasperformedfortheactual analysisofthefullsamplewerananewsetofsimulations.Here
observations.These simulationscreated a database to quantita- wegenerated10randomlinesofsightwiththeemissionredshift
tivelyassessthetwodominantsourcesoferror:thelimitednum- of each of the 17 quasarsin the sample, andcomputedthe sta-
ber of absorbers per individualline of sight (cosmic variance), tistical scatterafter averagingoverthe 17contributionstoeach
andthemisplacementofthecontinuumbecauseof linecrowd- ωvalue.Wefoundσ tobeessentiallyindependentofωinthis
ξ
ing.Inthefollowingweconsiderbotherrorsourcesinturns. case.
6 A.Dall’Aglioetal.:Theline-of-sightproximityeffectinindividualquasarspectra
4. Theproximityeffectinthecombinedsample Table 3.Estimationsofthe UV background J(ν )/J⋆ (com-
LL 21
putedinunitsofergcm 2s 1Hz 1)fromdifferentmod−elparam-
4.1.AnewestimateoftheUVbackground − − −
eters(βandB)andbinsizes∆logω.
Figure 4 summarises the main results regarding the combined
sampleof17QSOspectra.Weseeahighlysignificantreduction
B=0.0032 B=0.0041
ofnormalisedopticaldepthsatlogω>0,i.e.forthezonewhere ∆log(ω) 0.7 1.0 0.7 1.0
photoionisation due to the local qua∼sar-induced radiation field
isexpectedtoprevailoverthemetagalacticUVbackground.As β=1.4 1.01 1.12 0.40 0.51
β=1.5 1.89 2.04 0.88 0.93
already demonstrated by BDO88, this turnover can be used to
β=1.6 2.83 3.01 1.19 1.41
constrainthemeanintensityoftheUVB.Weadoptedthefitting
formula
ω 1 β
F(ω)= 1+ −a21 − (5) laedaodpstetodξvωa→lu0e≃an1d.thWeevbaleulieebvyeKthiamttehteadl.is(c2r0e0p2a)nicsydbueetwtoeaencoomu-r
(cid:18) (cid:19) binationof line blendingand resolutioneffects. Our resultsare
withabeingthefreeparameterandω isthevalueofωrela-
21
tivetoareferencevalueoftheUVB, J−⋆ 10 21 ergcm 2s 1 sensitivetotheslopeofthecolumndensitydistributionβwhich
21 ≡ − − − sets the steepnessofξ(ω) in the BDO88 ionisationmodel.The
Hz 1sr 1.Wethenappliedastraightfor−wardχ2minimisationto
− − columndensitydistributionisverywellapproximatedbyasin-
searchforthebest-fittingvalueofa= J(ν )/J⋆ .
LL 21 gle powerlaw with β 1.5over10dex(Petitjeanetal. 1993).
Indoingthiscomputationwefoundthatthe−binsize∆logω ≃
However, it has been shown that the slope changes somewhat
has some moderate effect on the resulting best-fit value of the
with redshift (Kimetal. 2002). Since the lines are unresolved
UVB. If the data are merged with very small or even without
in our low-resolutionspectra, we fix a single power law distri-
anybinning,awillbebiasedtowardslowvaluesbecauseofthe
bution and varyits assumed value by ∆β = 0.1 to estimate the
substantialscatterinξ atverysmallω(forlog(ω) < 1.5),due
tothestrongeffectsofshotnoiseforthisnarrowlog∼(ω−)interval. robustness of our UVB measurements. The Doppler parameter
distributionhasnodirectimpactonourresultssincetheBDO88
Ontheotherhand,toolargebinswilltendtohidethesignature
modelsimplyassumesanisothermalHdistribution.
oftheproximityeffect,thusmaketheUVBappearstrongerthan
Table 3 summarises the dependence of our UVB estimates on
it really is. As a reasonable compromise we chose ∆logω =
model parameters. There is a substantial scatter in the estima-
1, upon which also Fig. 4 is based. An additional effect which
tionsandboth Bandβplayacentralrole.Thebinsizehasonly
tend to change the estimation of the UVB is the normalisation
asmall(butstilldetectable)effect.
used to compute ξ (see eq. 4). We address this problem with
twodifferentstrategies.We usethenormalisationbyKimetal.
(2002) and our normalisation(B = 0.0041)to reach ξ 1
ω 0 5. Theproximityeffectinindividuallinesofsight
for the combined set of Lyα forest regions. Tab. 3 summ→ar∼ises
our results revealing a maximal dispersion of about 0.9. We 5.1.Results
∼
decidetouseB=0.0041forourresults.
The proximity effect is generally seen as a statistical phe-
AsbestfitvalueweobtainJ(ν ) = 9 4 10 22 ergcm 2
s 1 Hz 1 sr 1,orinlogarithmicunLitLs,logJ±(ν ×) =− 21.03+0.1−5. nomenon, which may or may not be detectable in individual
− − − LL − 0.22 spectra.ThehighS/Nofourspectramotivatedustosearchfor
Usingaslightlynarrowerbinsizeof∆logω=0.7lowersJ(−ν )
LL proximityeffectsignaturesineachofour17quasarspectra.The
byabout0.05dex.
basicapproachwasessentiallyidenticaltothatofthecombined
This estimate of the UVB intensity is in very good agree-
analysis.Computethemeannormalisedopticaldepthforagiven
ment with all recent measurements based on a wide range of
lineofsightwithinagivenbin∆logωandcheckwhetherξsys-
techniques and data sets. For example, Scottetal. (2000) ob-
tematicallydecreasesforlargevaluesofω.Wesetthesamenor-
tained J(ν )/J⋆ = 0.7+0.34, applying line count statistics on
LL 21 0.44 malisation for every object as for the combined analysis. The
morethanhund−redspectr−aat 1Å resolution.More similar to
ω scale was now fixed by assuming the value of the mean UV
∼
our approach, Liske&Williger (2001) used the flux transmis-
background intensity from the combined analysis. The results
sion statistic on 10 QSO spectra with 2 Å resolution and a are displayed in Fig. 5, one small panel per quasar. The error
S/N of ∼ 40, obtaining J(νLL)/J⋆21 = 0∼.35+00..3153. Not much has barsarenowofcoursedominatedbyPoissonianshotnoise,es-
yetbeenpublishedusinghighreso−lutionspec−tra.Giallongoetal. timatedfromthesimulationsasdescribedabove.Ineachpanel
(1996)obtainedJ(νLL)/J⋆21 =0.5±0.1andCookeetal.(1997) theexpectedrunofξwithωisshownasthedottedredline,as-
J(νLL)/J⋆21 =0.8+00..84,aga−inclosetoourvalueeventhoughthey sumingthatthemetagalacticUVbackgroundisconstantandhas
areallsm−aller(up−toafactorofabout2).Thisorderofmagni- thesamespectralshapeasthequasar.Wealsoshowtheprofile
tudeisalsoconsistentwithpredictionsbasedontheQSOlumi- beforethesystematiccontinuumcorrectionanditsbestfitmodel
nosityfunction(Haardt&Madau1996). (greentrianglesandline).
Figure5demonstratesthatinallexceptonecase,ξdecreases
substantially from left to right. Thus we can say that the prox-
4.2.Dependenceonmodelparameters
imityeffectisdetectedin16outofour17quasarspectra.Inthe
Concerningtheevolutionofτ intheLyforest(seeeq.1),we majority of spectra, the ξ-ω profile is even formally consistent
eff
regard only the normalisation B as variable. The slope γ has withthepredictionbasedonthecombinedanalysis.Inanumber
beenestimatedbyseveralauthorswithmuchhigheraccuracyin ofcasesthedataseemtobe(mildly)discrepantwiththepredic-
the pastyears(e.g.,Kimetal. 2001, 2002; Schayeetal. 2003). tion;wediscusssomeofthesecasesbelow.
We consider only two normalisations: a conservative one with We also applied the above fitting procedure to each spec-
B = 0.0032(Kimetal. 2002),whichreturnsa higherUVB es- trumseparately;theresultsofthatexerciseareshownasthesolid
timatesinceξ & 1,andB = 0.0041whichweadoptsinceit curvesinFig. 5. Table4 summarisesthe fitresults. Apparently
ω 0
→
A.Dall’Aglioetal.:Theline-of-sightproximityeffectinindividualquasarspectra 7
Fig.5.Searchforproximityeffectsignaturesinindividuallinesofsight,forall17QSOspectra.Eachpanelshowsthenormalised
opticaldepthξ versusω in the same way as Fig. 4, with the best-fitmodelof the combinedanalysis superimposedas dottedred
lines.ThesolidlinesdelineatethebestfittoeachindividualQSOasdescribedinthetext.ForCTQ0247wealsoplotthebestfit
excludingthestrongabsorptionatz 3.014(purplecurve).Thepanelsaresortedinorderofdecreasingstrengthoftheproximity
effect(horizontaldisplacementofsol∼idanddottedlines).HE2347 4342hasnodetectableproximityeffectinH.
−
8 A.Dall’Aglioetal.:Theline-of-sightproximityeffectinindividualquasarspectra
thevalueofthefittingparameterashowssignificantscatterbe- Table 4. Input and results used for the photoionisation model
tweenthedifferentquasars.Thevalueofadescribesthehorizon- fits. f is the predicted Lyman limit flux of each quasar. In
LL
taloffsetofthesolidcurverelativetothedottedcurveandinthe thetreatmentofindividuallinesofsight,log(a)isthefittedpa-
following is regarded as a quantitative measure of the strength rameter used to quantify the strength of the proximity effect.
oftheproximityeffectsignal(inthesensethatalargeameans CTQ 0247 is listed twice, with and without the associated ab-
aweakproximityeffect).Thisdoesofcoursenotimplythatthe sorptionsystem.
UVbackgroundfluctuatesbyasimilaramount.Whilestatistical
errors certainly contribute to the scatter, one may also reinter-
QSO z log(f (0)) log(a)
prettheparameteraasameasureofthefluxofthequasaratthe LL
Lymanlimit.Thisfluxmayevennotalwayshavebeenconstant Q1151+0651 2.758 27.00+0.01 1.11+0.51
over the light travel time across the proximity effect zone; we Q0002 422 2.767 −26.46−+00..0015 −0.84−+∞0.49
returntothatpointinSect.5.4below. PQK1S20291−+260−91195 33..228951 −−2266..4922−−++0000....00006541 −−00..8440−−++∞0∞0..4414
Wenowbrieflycommentontwoobjectswheretheproxim- HE0940 1050 3.086 −26.16−+00..0013 −0.27−+∞0.48
ity effect appears to be extremely weak or absent. In the case HE2243−6031 3.010 −26.11−+00..0032 −0.14−+∞0.46
ofCTQ 0247,thereis a strongassociated absorptionsystem at CTQ046−0 3.139 −26.55−+00..0023 −+0.11−+∞0.41
zabs = 3.014, corresponding to logω . 1. Removing this ab- Q0347 383 3.220 −26.67−+00..0021 +0.16−+∞0.46
sorption manually from the spectrum and redoing the analysis H0055−2659 3.665 −26.61−+00..0013 +0.24−+∞0.43
yielded a proximity effect signal perfectly consistent with the CTQ10−05 3.205 −26.95−+00..0033 +0.29−+∞0.47
predictionfromthecombinedanalysis. Q0420 388 3.120 −26.37−+00..0033 +0.31−+∞0.44
Q0913−+0715 2.787 −26.74−+00..0032 +0.42−+∞0.50
CTQ0247 3.025 −26.62−+00..0022 +0.70−+∞0.40
5.2.AhiddenproximityeffectforHE2347 4342? CTQ0247 − −0.03 0.46−+∞0.49
− Q2139 4434 3.214 26.93+0.01 −+1.06−+∞0.42
ForHE2347 4342,weseenoevidenceatallofadownturnof Q1223−+1753 2.945 −27.10−+00..0021 +2.29−+∞0.44
ξ(ω).Theabs−enceofanyproximityeffectwasnoticedalreadyby Q0000 26 4.098 −26.19−+00..0014 +2.30−+∞0.24
Reimersetal. (1997) upon mere visual inspection of the spec- HE234−7 4342 2.885 −26.20−+00..0053 &+−3∞
− − 0.03
trum.Againthereisaconspicuousstrongassociatedabsorption −
system.Althoughinthiscasearemovalofthatsystemdoesnot
dramatically improve the proximity effect signal, the absorber Thelargedispersioncantoasmallpartbeexplainedbyun-
mayneverthelessplayanimportantroleinthislineofsight,as certaintiesinquasarmagnitudesandredshifts,whichbothaffect
it may attenuate the ionising radiation field towards lower red- the computation of ω. For those objects where we have rather
shifts.Thisissupportedbythefollowingsimplecalculation. accurate V magnitudes (with errors 0.1 mag), the flux scale
ThetotalmeasuredHcolumndensityintheassociatedsys- isaccuratetowithin9%.Fortherem≤ainingobjectsthefluxun-
tem is of the order of 2 1016 cm 2 (Fechneretal. 2004). We certaintiesmightbeaslargeas30%.Thedirecteffectonlog(a)
−
×
assume this to be located in an absorbing slab of matter very is an uncertainties of 0.03–0.1 dex. In addition, redshift errors
closetotheQSO.KnowingtheLymanlimitfluxoftheQSO,we (Tab. 1) might shift log(a) by 0.05–0.1 dex. We conclude that
canpredictthevalueofωatthelocationoftheslab,logω 2.1; these uncertainties cannot be the main source of spread in the
this immediatelyrelates to a predictedreductionof H co≃lumn estimatedlog(a)values.
densityin theslab of 2dex.Thus,thecolumndensityofthe We employed our Monte-Carlo simulations to estimate the
∼
same absorberwithoutthe QSO ionisingradiationwouldbe of expected scatter solely due to statistical shot noise errors (i.e.,
theorderof1018 cm 2.Thiswouldbe sufficientto renderare- cosmic variance).To this effect we first systematically reduced
−
mainingproximityeffectforthelineofsightundetectable. theopticaldepthsinthesimulatedspectrafollowingstrictlythe
We note that Fechneretal. (2004) detected evidence of a theoreticalproximityeffectprescription(Eq.4),afterwhichwe
hard radiation field from a detailed photoionisation modelling ‘remeasured’theproximityeffectanditsstrengthabyfittingthe
analysisofmetalabsorptionlinesinthissystem.Asimilartrend artificialdatainthesamewayastheobservedones.Theresult-
isapparentinourrecentinvestigationoftheHeLymanforest, ing histogramof a values is superimposedin Fig. 6; the distri-
combiningVLTandFUSEhigh-resolutionspectraofthisquasar bution is approximately Gaussian with a standard deviation of
Worsecketal. (2007). Thus,while thetraditionalH proximity σlog(a) = 0.64.Thisissubstantialandimpliesthat14ourof17
effectisclearlyabsentinHE2347 4342,mostprobablydueto ofourquasarsarelocatedwithin 2σexpectedforpurerandom
excess absorption close to the QS−O, there are clear signs of a errors.Nevertheless,3quasarsfro±moursamplearelocatedout-
‘proximityeffectinspectralhardness’(cf.Worseck&Wisotzki side of this interval,which is a bitmuch to declare them all as
2006)forthisobject.We thereforeconcludethatall17quasars outliers.
inoursampleshowevidenceofagenuineproximityeffect. This meansthat other effects play a role, and that these ef-
fectsmayleadtogrossdeviationsfromthesimpleexpectation.
Possible mechanisms might be, for example, a dispersion in
5.3.Variationsinthestrengthoftheproximityeffect spectral indices for the quasars, long time scale variability of
the quasars, or a strongly fluctuating UV background.We first
We now investigate how much of the scatter in the fitting pa- considertheeffectsofnon-uniformspectralindices.
rametera mightbe attributedto uncertainties,or shotnoise, or Inthestandardanalysisoftheproximityeffectasintroduced
intrinsicdispersionofotherrelevantproperties. by BDO88, the assumption of a uniform quasar spectral index
Figure 6 shows that formally the best-fit values of a, be- is obviously wrong, but the averaging over samples of quasars
foreandaftercontinuumcorrection(greenandblackhistograms makes the analysis very insensitive to any intrinsic dispersion.
respectively),extend over several ordersof magnitudes, with a Whenconsideringindividualquasarlinesofsightaswedohere,
standarddeviationofσ 1(blackhistogram). this assumption may be more harmful. We investigated this by
log(a)
∼
A.Dall’Aglioetal.:Theline-of-sightproximityeffectinindividualquasarspectra 9
Fig.6.Distributionoftheparameterlog(a)forthefitstothe17
individualspectrawithandwithoutcontinuumcorrection(black
andgreenhashedhistogramrespectively).Overplottedisthedis-
tributionresultingonlyfromshotnoiseinthesimulatedspectra
(solidline),andtheexpecteddistributionoflog(a)duetodisper-
sionofspectralindices(bluegaussian).
extendingtheoriginalcalculationbyBDO88,solvingtheexact
integralsfor the ratio of the photoionisationrates of the quasar
andthebackgroundandusingthephotoionisationcrosssection
forapurehydrogencloud,sothat Fig.7.Top panel:Expectedξ(ω) modelfordifferentfinite life-
timesofthequasar.ThesolidcurverepresentstheBDO88model
ω= ν∞LL 4πJhνqν(ν)σ(ν)dν =ω κ−3 (6) opfanthele:pTreonxtiamtiivtyeeaffpepclitc,awtiiothnaoQf SthOeoafbionvfienimteoldifeeltitmoet.hBeoQttSomO
Rν∞LL 4πJhνbν(ν)σ(ν)dν oldα−3 iQnfi0n0it0e2−lif4e2ti2m. eT,htehedodtotet-ddalsinheedislintheedperleindeicatteeds tξh(eωc)ucruvrevefofroar
R fiducialfinitelifetimeof68Myr.
where ω is the know expression of eq. 3 and κ 1.8
old
∼ −
is the background spectral index following the model by
Haardt&Madau (1996). Expressing everything in logarithmic 5.4.Finitequasarage
unitswearriveat
Thesimpletheoryoftheproximityeffectimplicitlyincludesthe
assumptionthatquasarsshineforaninfinitetime,oratanyrate
log(ω)=log(ω )+σ . (7)
old log(a) formuchlongerthanthelightcrossingtimeoftheproximityef-
fectzone.Thismaybewrong,andwenowaskspecificallywhat
Realquasarsshowadispersionofspectralslopesofσ = 0.25
α wouldhappenifaquasarisabruptlyswitchedonwithin,say,less
aroundα= 0.46(derivedfromtheSDSSQSOcompositespec-
than a few Myrs beforethe observation.As soon as the quasar
−
trumanditsstandarddeviationpublishedbyVandenBerketal.
startstoradiateintheUV,anover-ionised“sphere”willstartto
2001). The values of ω are therefore offset (i) by ∆log(ω) =
expand around the quasar (always assuming spherical symme-
0.142onaverage,and(ii)byarandomcomponentwithastan-
try). The new equilibriumstate with ionising photonsfrom the
darddeviationofσ =0.06(includedasthenarrowGaussian
log(a) local source and the UV background – requires at least some
in Fig. 6). Obviously, the dispersion in spectral slopes is too 104yrstoestablish,whichmeansthatforevenyoungerQSOs
small, by a long way, to account for the observed distribution ∼
theproximityeffectwillbeabsent.
oflog(a).
The light travel time between two redshifts along a single
Among the two other mentioned options, intrinsic fluctua- lineofsightcanbecalculatedforaΛ-Universeas
tionsofthe UV backgroundmightalso contribute,butnumeri-
calsimulationssuggestthatsubstantialfluctuationsareonlyex-
2 Ω
pectedfor redshiftshigherthan those coveredhere(Croftetal. t(z)= asinh Λ (8)
1999;McDonaldetal.2005). 3H0√ΩΛ sΩm(1+z)3
Thepresenceofmetaltransitionsfallingintheproximityef-
(Peacock 1999), allowing us to convert redshift intervals into
fect zone or a still imperfect continuum placement might also
light travel time differences. Switching a quasar on can be ex-
enhancethescatter.
pressed in the model by introducinga step function into the ω
A veryplausibleeffect, ontheotherhand,wouldbe signif-
profile,
icant QSO variability over timescales of the light travel time
across the proximity effect zones which is of the order of 107 0 forz<z
life
years;thereisnoreasontoexpectthatquasarsalwaysmaintain ω(z)= 2 (9)
tthheeiorbrasderiavteidveLoyumtpanutliomveitrlsuumchinloosnigtypwerililondos.tIbfeththeeysdaomneoat,stthheant  fν(λL4Lπ(J1ν+zc))(1+1zc)(cid:18)ddLL((zzqq,,z0c))(cid:19) forzlife <z<zem.
receivedby cloudsalongvariouspointsalongthe line ofsight. Far awayfromthe QSO (lowω values),the QSO hasnoeffect
Wewilldiscussaspecificaspectofthiseffectinthenextsection. yet. When passing into the over-ionised region, the theoretical
10 A.Dall’Aglioetal.:Theline-of-sightproximityeffectinindividualquasarspectra
profile ξ(ω) dropsabruptly, joining the BDO88 prescription of likelycontributorsforthisadditionaldispersionareagaingravi-
the proximity effect. This is shown in the top panel of Fig. 7, tationalclusteringofabsorbersneartheQSO,orQSOvariabil-
where we present the expected profiles for different assumed ityoververylongtimescales;fluctuationsoftheUVbackground
ages.Forpresentationpurposes,thismodelwascomputedfora arealsopossiblebutunlikelytoplayamajorroleatthisredshift
QSOatz =2.76and f (λ (1+z ))=3.46 10 27ergcm 2s 1 range.We presenteda speculative,butconceptuallysimple ob-
q ν LL q − − −
·
Hz 1. servationaltest to search for signaturesof finite quasar ages in
−
Itturnsoutthatobservablesignaturescanbeexpectedforan theopticaldepthprofilesderivedforasinglequasar,andweeven
interestingrangeofages.Uptot 4Myrtheturnoverhap- tentativelyidentifiedacandidatewheresuchapatternmightbe
QSO
penssoclosetothequasarthatevenf∼oraveryluminousQSOit visible.
willbehardtodetect,giventheinevitableshotnoiselimitations.
Aboveofatmost 500Myr,ontheotherhand,thedifferences Acknowledgements. We would like to thank Prof. Piero Rafanelli and Dr.
∼ StefanoCiroiforalltheinspiringdiscussionsandsupport.ADAisgratefulto
between the models with and without lifetime will wash out
theFondazioneIng.AldoGiniandtheUniversityofPadovaforprovidinggrants
completelybecauseξ(ω)isexpectedtobeclosetounityanyway. forthis work. ADAandGWacknowledge supportbyaHWPgrantfromthe
Therangebetweentheseextremes,4Myrs<t <400Myrs,is stateofBrandenburg,Germany.
QSO
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