Constraint on the time variation of the fine-structure constant with the SDSS-III/BOSS DR12 quasar sample

9.4 MB·English

by  Franco D. Albareti

Mon.Not.R.Astron.Soc.000,1–15(2002) PrintedAugust17,2015 (MNLATEXstylefilev2.2)
Constraint on the time variation of the fine-structure constant
/
with the SDSS-III BOSS DR12 quasar sample
5 Franco D. Albareti,1(cid:63)† Johan Comparat,1 Carlos M. Gutie´rrez,2,3 Francisco Prada,1,4,5
1 Isabelle Paˆris,6 David Schlegel,7 Mart´ın Lo´pez-Corredoira,2,3 Donald P. Schneider,8,9
0
2 Arturo Manchado,2,3,10 D.A. Garc´ıa-Herna´ndez,2,3 Patrick Petitjean11 and Jian Ge12

g
u 1InstitutodeF´ısicaTeo´rica(UAM/CSIC),UniversidadAuto´nomadeMadrid,Cantoblanco,E-28049Madrid,Spain
A 2InstitutodeAstrof´ısicadeCanarias(IAC),LaLaguna,E-38205Tenerife,Spain
3DepartamentodeAstrof´ısica,UniversidaddeLaLaguna,LaLaguna,E-38206Tenerife,Spain
3 4CampusofInternationalExcellenceUAM+CSIC,Cantoblanco,E-28049Madrid,Spain
1 5InstitutodeAstrof´ısicadeAndaluc´ıa(CSIC),GlorietadelaAstronom´ıa,E-18080Granada,Spain
6INAF,OsservatorioAstronomicodiTrieste,ViaG.B.Tiepolo11,34131Trieste,Italy

] 7LawrenceBerkeleyNationalLaboratory,1CyclotronRoad,Berkeley,CA,94720,USA
O 8DepartmentofAstronomyandAstrophysics,ThePennsylvaniaStateUniversity,UniversityPark,PA16802,USA
C 9InstituteforGravitationandtheCosmos,ThePennsylvaniaStateUniversity,UniversityPark,PA16802,USA
10CSIC,Spain
.
h 11Institutd’AstrophysiquedeParis,CNRS-UPMC,UMR7095,98bisbdArago,75014Paris,France
p 12DepartmentofAstronomy,UniversityofFlorida,Gainesville,FL32611-2055,USA
-
o
r
t AcceptedforpublicationinMNRAS.
s
a
[

ABSTRACT
2
v
From the Sloan Digital Sky Survey (SDSS) Data Release 12, which covers the full
0
Baryonic Oscillation Spectroscopic Survey (BOSS) footprint, we investigate the possi-
6
ble variation of the fine-structure constant over cosmological time-scales. We analyse the
5
0 largest quasar sample considered so far in the literature, which contains 13175 spectra
0 (10363fromSDSS-III/BOSS DR12 + 2812 from SDSS-II DR7) with redshift z < 1. We
. applytheemission-linemethodonthe[Oiii]doublet(λλ4960,5008Å)andobtain∆α/α =
1
(0.9±1.8) × 10−5 for the relative variation of the fine-structure constant. We also investi-
0
gatethepossiblesourcesofsystematics:misidentificationofthelines,skyOHlines,Hβand
5
broadlinecontamination,GaussianandVoigtfittingprofiles,optimalwavelengthrangeforthe
1
: Gaussianfits,chosenpolynomialorderforthecontinuumspectrum,signal-to-noiseratioand
v
goodqualityofthefits.Theuncertaintyofthemeasurementisdominatedbytheskysubtrac-
Xi tion.Theresultspresentedinthiswork,beingsystematicslimited,havesufficientstatisticsto
constrainrobustlythevariationofthefine-structureconstantinredshiftbins(∆z≈0.06)over
r
a the last 7.9 Gyr. In addition, we study the [Neiii] doublet (λλ 3869,3968Å) present in 462
quasarspectraanddiscussthesystematiceffectsonusingtheseemissionlinestoconstrainthe
fine-structureconstantvariation.Betterconstraintson∆α/α(<10−6)usingtheemission-line
methodwouldbepossiblewithhigh-resolutionspectroscopyandlargegalaxy/qsosurveys.
Key words: line: profiles – quasars: emission lines – cosmology: observations – surveys –
large-scalestructureofUniverse.
1 INTRODUCTION mensionlessconstantsofphysicaltheories.Fundamentalconstants
of physics could be thought of as parameters which enter in our
Since Dirac’s philosophical argument (Dirac 1937) against the
description of Nature but they cannot be predicted with our cur-
fixed value of fundamental constants of Nature, several experi-
renttheoriesandshouldbemeasured.Dirac’sideaisbasedonthe
mentshave beenperformedto constrainpossiblevariationon di-
unlikelyfactthatthemostfundamentalconstantsoftheUniverse
haveacertainfixedvalue(atagivenenergy)withnoapparentre-
lationwiththerealworld.Itismorelikelythattheirpresentval-
(cid:63) ‘laCaixa’-SeveroOchoaScholar.
ues are the result of a dynamical process, which had yielded the
† E-mail:[email protected]
(cid:13)c 2002RAS
2 F.D.Albaretietal.
Table1.Summaryoftheresultsobtainedbyrecentworksbasedonthe[Oiii]emissionlinemethodforthepossiblevariationsofthefine-structureconstant.
Reference Quasarspectra SDSSrelease zmin zmax Timeago(Gyr)(a) ∆α/α(×10−5)
Bahcalletal.(2004) 42 EDR(Stoughtonetal.2002) 0.16 0.80 7.0 7±14
Gutie´rrez&Lo´pez-Corredoira(2010) 1568 DR6(Adelman-McCarthyetal.2008) 0.00 0.80 7.0 2.4±2.5
Rahmanietal.(2014) 2347 DR7(Abazajianetal.2009) 0.02 0.74 6.7 −2.1±1.6
Thiswork(2015) 13175 DR12(Alametal.2015) 0.04 1.00 7.9 0.9±1.8(b)
(a)ForaΛCDMcosmologywithH0=67.8kms−1Mpc−1,Ωm=0.31andΩΛ=0.69fromPlanck+WMAP-9+BAO(PlanckCollaborationetal.2014).
(b)Note:SincewehavealargersamplethanGutie´rrez&Lo´pez-Corredoira(2010),weexpectafactor≈ 2.5ofimprovementintheerrorjustfrompurely
statisticalreasons.InFigs9and10,itisshownthattheerrorisdominatedbytheskysubtractionalgorithm,whichsuggeststhattheperformedanalysishave
reachedthemaximumprecisionwiththeavailabledata.
fundamentalconstantsastheyaremeasuredtoday.Therefore,they importantonebeingionizationandchemicalhomogeneity.These
should be considered as characterizing the state of the Universe assumptionsmayinducesystematicbiasesonthevalueofα.
(Uzan2003).Therearemanycurrenttheoreticalframeworkswhich Inthisarticle,weusethemethodbasedonthe[Oiii]emission
allowforsuchvariationofthefundamentalconstants,forinstance,
lines,firstproposedbyBahcall&Salpeter(1965),whichislessaf-
stringtheory(Maeda1988),modifiedgravityandtheorieswithex-
fectedbysystematics.Inparticular,thereisnoneedforassuming
tradimensions(e.g.Cliftonetal.2012).Moreover,theexperimental
ionizationandchemicalhomogeneity,sincethestudiedlineshave
boundsontheirvariationhavebecomeastringenttestforthosethe-
thesameprofile(thetransitionsoriginateatthesameupperenergy
oreticalmodels(e.g.Thompson2012;Lealetal.2014).Themost level).Furthermore,theemission-linemethodsuffersofmuchless
studiedfundamentalconstantsarethefine-structureconstantα,the spectral distortion, since the measurements of ∆α/α are done on
Newton gravitational constantG and the electron-to-proton mass
a spectral window ∼ 100Å as compared to ∼ 1000Å when the
ratioµ(Uzan2003,2011;Garc´ıa-Berroetal.2007). MMmethodisused.Withalargeensembleofquasarsand/orus-
Thefine-structureconstantgovernstheelectromagneticcou- ing high-resolution spectroscopy, the uncertainty can be reduced
plingbetweenphotonsandchargedparticlesα=e2/((cid:126)c).Thecur- significantly, and will compete with the absorption method when
rentconstraintonitsrelativevariation∆α/α,overgeologicaltime- usinghigh-resolutionspectroscopy.
scales,is|∆α/α| < 7×10−8 uptoz ≈ 0.15(2Gyrago);obtained
ThebeginningoftheSDSSsurveyopenedaneweraofpre-
fromtheOklophenomenon(e.g.Petrov&etal.2006).Ithasalso
cision, allowing us to use big samples of quasars; thus, reducing
beenreported|∆α/α|<3×10−7uptoz≈0.45(4−5Gyrago)from the statistical uncertainty of the measurement of ∆α/α (see Ta-
meteorites(Oliveetal.2002);whichalsoexcludespossiblevaria- ble1).Here,weextendtheseworksbyusingtheSDSS-III/BOSS
tionsonthescalesoftheSolarsystem.Ontheotherhand,thereare
Data Relase 12 (SDSS-DR12; Alam et al. 2015), which covers
also constraints, |∆α/α| (cid:46) 10−2, based on the cosmic microwave
the full Baryonic Oscillation Spectroscopic Survey (BOSS) sur-
background (CMB; Landau & Sco´ccola 2010; Planck Collabora-
veyfootprintwithanareacoverageof10000deg2.Incontrastto
tionetal.2014)atz ≈ 1100andfrombigbangnucleosynthesis,
thesepreviousinvestigations,weusespectraobtainedwiththecur-
thelatterbeingmodel-dependent.Bymeasuringfine-structuremul-
rent BOSS spectrograph (Smee et al. 2013) instead of the previ-
tipletsatdifferentredshiftintheabsorptionoremissionspectraof ousSDSS-I/IIinstrument,makingourBOSSsampletotallyinde-
galaxiesandquasars,locatedatdifferentdirectionsinthesky,one
pendentfrompreviousworks.Moreover,thespectralrangeofthe
can measure an estimate of the variation of α with time or space
BOSSspectrographallowsanextensionoftheredshiftintervalfor
overcosmologicalscales. the [Oiii] doublet from z = 0.8 to z = 1. The number of quasar
Thefirstmeasurementsonthevariationofαfromastronom- spectraisincreasedbyafactorof5withrespecttoSDSS-DR7.All
ical observations reached an accuracy of ∆α/α ≈ 10−2 − 10−3 thesespectrahavebeenvisuallyinspectedandclassifiedasquasars
(Savedoff1956;Bahcall&Salpeter1965;Bahcall&Schmidt1967; bytheBOSScollaboration,andtheirproductsareprovidedinthe
Bahcall, Sargent & Schmidt 1967). Since then, the methodology SDSS-III/BOSS Data Release 12 Quasar catalogue (DR12Q; see
andunderstandingofsystematicshasdramaticallyimproved.Cur- Paˆrisetal.2015).Forthefinalconstrainton∆α/α,wecombinein
rentmeasurementsofabsorptionmultipletsalongthelineofsight this work the BOSS sample with the previously studied SDSS-II
ofthreequasarsaroundredshift1.5,observedwithspectralresolv- DR7quasarsample.
ingpowerR≈60000atUVES/ESO-VLT,reachedthe≈ 5×10−6 There are several emission doublets, in addition to [Oiii]
level (Evans et al. 2014). Using emission lines, an accuracy of (λλ4960,5008Å),thatcanbeusedtomeasure∆α/αasnotedby
≈ 2×10−5 was achieved analysing 1500−2300 quasar spectra
Bahcalletal.(2004),andfirstusedbyGrupeetal.(2005).Gutie´rrez
at z ≈ 0.6 (Gutie´rrez & Lo´pez-Corredoira 2010; Rahmani et al. &Lo´pez-Corredoira(2010)analyseddifferentdoubletsandfound
2014),takenwiththeSloanDigitalSkySurvey(SDSS)R ≈ 2000 that the [Neiii] (λλ 3869,3968Å) and [Siii] (λλ 6719,6733Å)
spectrograph. doubletsappearinquasarspectrawithsufficientfrequencytohave
The measurements on absorption features on a quasar spec- ameaningfulsample.Resultsfor[Siii]areconsistentwithnovari-
trum are currently limited by the precision in the absolute wave- ationofthefine-structureconstant,althoughtheuncertaintyisan
lengthcalibrationofthespectra,i.e.,50−200ms−1 usingspectra order of magnitude bigger than for [Oiii] , and this doublet can
with R ≈ 60,000 (Molaro et al. 2013; Evans et al. 2014; Whit- only be used at low redshift < 0.4 for optical spectra. However,
more&Murphy2015).Furthermore,theso-calledmany-multiplet they obtained a positive variation of the fine-structure constant,
(MM)methodusedinEvansetal.(2014),althoughmoreprecise, ∆α/α=(34±1)×10−4,whenthe[Neiii]linesareused.Noexpla-
remains controversial as several assumptions are made, the most nationwasfoundforthispositivevariation.Inthiswork,wealso
(cid:13)c 2002RAS,MNRAS000,1–15
Fine-structureconstantwithBOSS 3
1400
60 S(cid:144)N >10
1200 @OIIID
50 S(cid:144)N >25
@OIIID
1000
0 40 ars S(cid:144)N@OIIID>50
200 30 uas 800
J q
Dec 20 o.of 600
N
10 400
0 200
-10 0
0 50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
RAJ2000 Redshift
Figure1.Left-handpanel:skydistributionofthefullSDSS-III/BOSSDR12Qquasars(297301)inJ2000equatorialcoordinates.Right-handpanel:number
ofquasarswith[Oiii]emissionlinesinourfiducialsample(10363quasars)in∆z = 0.05bins.S/N[Oiii]5008 > 10(10363quasars),blacksolidline;
S/N[Oiii]5008>25(4015quasars),bluedashedline;andS/N[Oiii]5008>50(1498quasars),reddottedline.
analysethe[Neiii]linestocheckwhetherthesameeffectispresent plegalaxyandquasarspectrumtemplatesforallallowedredshifts.
inourBOSSquasarsample. Then,avisually-inspectedquasarcatalogueisbuiltfromtheseob-
There are investigations which use Si iv absorption lines jects.OurfiducialsampleisobtainedfromtheDR12Qcatalogue
(λλ1394,1403Å)toobtainaprecisionof4×10−6 (Chandetal. version(Paˆrisetal.2015).
2005). This method also avoids the assumption of ionization and ThewavelengthcoverageoftheSDSS-III/BOSSspectrograph
chemicalhomogeneity.However,sincetheseparationbetweenboth is 3600-10400 Å and that of the SDSS-II spectrograph is 3800-
linesisonly≈9Å,thewavelengthprecisionneededinthelabora- 9200 Å. The BOSS sample is homogeneous since all the spectra
toryfortheseparationbetweenbothlinesisfivetimeshigherthan have been obtained with the same instrument, and it is indepen-
using[Oiii]lines.Nevertheless,theseconstraintsapplytothered- dentfrompreviousinvestigations.Thewidercoverageofthenew
shift interval 1.59 < z < 2.92, which does not overlap with our spectra allows consideration of higher redshifts (up to z = 1 for
range,thustheyarecomplementarytotheonesreportedinthisre- [Oiii]doublet)thaninthepreviousSDSS-IIanalysisbasedonthe
search. samemethod(seeTable1).TheBOSSspectrographhastwochan-
Finally,inthelightoftheupcominglargegalaxysurveys,like nels (blue and red) whose wavelength coverage is 3600-6350Å
eBOSSandDESI,thatwillprovidemillionsofhigh-redshiftgalaxy and5650-10400Å,respectively.Theresolvingpowerrangesfrom
spectra, we also discuss using galaxies instead of quasars to set 1560at3700Åto2270at6000Å(bluechannel)andfrom1850at
constraintsonthefine-structureconstant. 6000Åto2650at9000Å(redchannel).Foroursample,the[Oiii]
Thepaperisorganizedasfollows.First,inSection2,wede- linesfallintheredchannelfor> 96%ofthequasars.Thenum-
scribe the data set used for our analysis. Next, in Section 3, the berofpixelsofeachspectrumisabout4600fortheBOSSspectra
methodologyispresented,theemission-linemethodisexplained, and3800fortheSDSS-I/IIspectra.Thepixelspacingisuniformin
andthecodeandsimulationstoanalysethespectraaredescribed. log-wavelengths(∆logλ = 10−4dex).Morecompleteinformation
In Section 4, we study several samples to check for systematics. abouttheSDSS-I/IIandBOSSspectrographscanbefoundinSmee
Then,ourresultsarepresentedinSection5.Finally,weprovidein etal.(2013).
Section 6 a summary of the main conclusions achieved with this
researchproject.
2.1 Dataselection
The SDSS-III/BOSS DR12Q catalogue contains 297301 objects.
2 SAMPLEDESCRIPTION Fig. 1 (left-hand panel) shows the quasar distribution in the sky.
Wesummarizebelowthemainselectioncriteriainordertodefine
All the spectra used in this investigation were downloaded from ourfiducialsamplefromthiscatalogue.
the SDSS Database. This survey (York et al. 2000), which began
takingobservationsin1998,consistsofamassivecollectionofop- (i) Redshift< 1.Thislimitationisimposedbythewavelength
ticalimagesandspectrafromastronomicalobjectsincludingstars, range of the BOSS optical spectrograph and the position of the
galaxies and quasars. For this purpose, there is a dedicated 2.5- [Oiii] lines. This criterion decreases the sample down to 45802
m wide-angle optical telescope at Apache Point Observatory in quasars.
NtheirwdMpheaxsiecoof(UthSiAs;prfoojremcto(rSeDdSeSta-iIlIsI,;sEeeiseGnusnteninetetala.l2.020061)1.)Tihne- (ii) S/N[Oiii]5008 > 10. We impose a mild constraint on the
signal-to-noiseratio(S/N)ofthestronger[Oiii]line(5008Å)in
cludes BOSS (Dawson et al. 2013) among its four main surveys.
ordertopreservealargenumberofspectra.Constraintsontheex-
ThedataanalysedinthisresearchwereprovidedbyBOSS,andit
pectedwidthandamplitudesofthelineshelpinavoidingmisiden-
isusedformeasuring∆α/αforthefirsttime.TheSDSS-III/BOSS
tificationsofthe[Oiii]doublet(seeSection4).Thisselectionre-
pipeline(Boltonetal.2012)classifiestheobjectsasquasarswith
ducesthesamplefrom45802to13023objects.
aχ2minimizationproceduretofittheobservedspectrumtomulti-
(cid:13)c 2002RAS,MNRAS000,1–15
4 F.D.Albaretietal.
ΛHÞLHobservedL
6000 7000 8000 9000
4 SDSSJ112639.11+543826.5
50
z=0.612
L
-1 3 @OIIIDlines
20 Þ
-1
10 -2s 2
ÞL m
H 5 c
ΕÈÈ erg 1
2 -170 0
1
H
1 Λ
f -1
0.2 0.4 0.6 0.8 1.0 7980 8000 8020 8040 8060 8080 8100
Redshift ΛHÞLHobservedL
Figure2.Left-handpanel:datapoints(1416)forwhich|(cid:15)| = |δλz/(1+z)−δλ0|,namelytheabsolutevalueofthedifferencebetweenthemeasuredline
separationatredshiftzinrestframeandthelocalone,isbiggerthan1Åplottedasafunctionofredshift(andthewavelengthobservedfor[Oiii]4960).We
comparewithatypicalskyspectrum:the[Oiii]positionsforthesespectracorrelatewiththeskyemissionlines.Hence,thesehighvaluesof|(cid:15)|areduetobad
skysubtractionsand/orlowS/N.Thesespectraareremoved.Right-handpanel:aspectrumremovedfromthesamplebecauseoftheskyemission-linecriteria.
Forthisquasar,weget(cid:15) =1.2±0.6Å.Theweak[Oiii]lineisaffectedbythesubtractionofthe7995ÅOHskyemissionline,indicatedbytheverticalred
dashedline.
(iii) Non-converging fits. Since we analyse spectra with low Weobtainaweightedmeanfor∆α/αusingasweightstheuncer-
S/N,therearesomecaseswheretheGaussianfittothelinesdoes taintyin∆α/αcomputedwiththestandarderrorsforthepositionof
notconverge.1244spectraarediscarded,leavinguswith11779 thelinesderivedfromtheGaussianfits.ThecontaminationofHβ
spectra. isautomaticallytakenintoaccount.Forinstance,abroadHβline
nearthe[Oiii]4960linemeansabadGaussianfit.Thus,weobtain
(iv) Sky emission lines. Strong atmospheric lines, for instance
theOi5578Åline,arepoorlyornotcompletelyremovedbythe largererrorsinthepositionofthelinecentroidsand,consequently,
in∆α/α.InSection4,weanalyseseveralsampleswheretheS/N
SDSSskysubtractionalgorithm.Thismayleadtoawrongiden- Hβ
tificationofthe[Oiii]linesandtoincludelowS/N[Oiii] spectra isconstrainedtocheckthattheHβcontaminationhaslittleweight
(Gutie´rrez & Lo´pez-Corredoira 2010). Both effects will produce onthefinalconstraintvalue.
An electronic table is published along with the paper which
outliers.WeusetheSDSSskymaskforLyαforeststudieswhich
contains all the information of each spectrum from our fiducial
contains 872 lines (see Delubac et al. 2015, for more details) to
removespectrawhose[Oiii]linesliewithinaparticulardistance sampleof10363quasars(seeAppendixA).
The distribution of the selected quasars in redshift accord-
from the strongest sky lines. Even though we vary the distance
[Oiii]–skylines,usedifferentsetofskylines(accordingtotheir ingtotheirselectedS/N[Oiii]5008 isplottedinFig.1(right-hand
intensity),orevaluateotherconditions(S/N,fiterrors,etc.)tore- panel). Fig. 3 (left-hand panel) displays a composite image built
moveaffectedspectra;weusuallyeliminate3−5goodspectrafor withallthespectrafromourfiducialsamplesortedbyredshift.The
right-handpanelshowsthe[Oiii]doubletinrestframe.
eachbadspectraeliminated.Thus,thesetestsdecreasesignificantly
thenumberofquasarswhilenotbeingveryeffective:typically50%
oftheoutliersarenotremoved.Thus,wedecidedtoeliminateall
spectraforwhichtheseparationbetweenbothlinesdifferbymore
than1Åfromthelocalvalue(seethelastparagraphinSection3.3). 3 METHODOLOGY
Fig.2(left-handpanel)showsthatthedistributionoftheseoutliers
3.1 Measurementmethod
is correlated with a typical sky spectrum. From a visual inspec-
tion, we observed that these spectra have low S/N, and they are Tofirstorder,thedifferencebetweentheenergylevelsofanatom
in fact contaminated by sky emission line subtraction (see right- isproportionaltoα2.Transitionsbetweenenergylevelsofthesame
handpanelofFig.2).Thiseffectcausesustodiscard1416spec- atomatagivenionizationlevel,withthesameprincipalquantum
tra(12%oftheprevious11779quasars).Finally,wehave10363 number and different total angular momentum J, have an energy
quasarspectra(our‘fiducialsample’). differenceproportionaltoα4.Thesegroupsoftransitionsarecalled
fine-structuremultiplets.Savedoff(1956)firstrealizedthatthefine
The presence of broad Hβ emission line (4861 Å) near the
structureoftheseenergylevelscouldbeusedtobreakthedegener-
weak [Oiii] line 4960 Å could produce a blueshift in the deter-
acybetweentheredshifteffectandapossiblevariationofα.
mination of the [Oiii] line position. This could mimic a positive
The value of the fine-structure constant can be measured
variationonthefine-structureconstant.Therefore,aconstrainton
throughtheseparationbetweenabsorptionoremissionmultiplets
the strength and/or width of the Hβ emission line has been im-
inthespectraofdistantquasars(Uzan2003)as
posedonpreviousinvestigations(Bahcalletal.2004;Gutie´rrez&
Lo´pez-Corredoira2010;Rahmanietal.2014).However,wedonot ∆α 1(cid:40)[(λ −λ )/(λ +λ )] (cid:41)
(z)≡ 2 1 2 1 z −1 , (1)
restrict any characteristic of the Hβ line in our fiducial sample. α 2 [(λ −λ )/(λ +λ )]
2 1 2 1 0
(cid:13)c 2002RAS,MNRAS000,1–15
Fine-structureconstantwithBOSS 5
CIIID MgII @NeVD@OIID@NeIIID HΓ HΒ @OIIID @OIIID4960 @OIIID5008
0.9 0.9
0.8 0.8
0.7 0.7
hift hift
s s
d d
e e
R R
0.6 0.6
HΑ
0.5 0.5
0.4 0.4
0.3 0.3
0 0
4000 5000 6000 7000 8000 9000 10000 4940 4960 4980 5000 5020
ΛHÞLHobservedL ΛHÞLHrestframeL
Figure3.Compositeimagewithourfiducialsampleof10363BOSSquasarspectrasortedbyredshift.Left-handpanel:thewholerangeofwavelengthsis
shown.Fromrighttoleft,thestrongestemissionlinesareHα6565Å;[Oiii]λλ4960,5008Å;Hβ4861Å;Hγ4341Å;[Neiii]λλ3869,3968Å;[Oii]3730
Å;[Nev]3426Å;Mgii2796ÅandCiii]1906Å.Thenarrowstraightlineat5579Åisthestrong[Oi]atmosphericline.Right-handpanel:wavelength
intervalcentredatthe[Oiii]doubletinrestframe.
where λ (λ > λ ) are the wavelengths of the transitions and lengthseparation,indirectlywiththetheta-pinchdischargeanddi-
1,2 2 1
subscript 0 and z stand for their value at redshift zero (theoreti- rectly with the Michelson interferometer, are in good agreement,
cal/laboratoryvalues)andatredshiftz,respectively.Forillustrative being the Michelson interferometer more accurate with an error
purposes,expression(1)canbeapproximatedby <5×10−4Å.
∆α (cid:15) From equation (2), a determination of (cid:15) with a precision of
≈ , (2) 1Å allows for an uncertainty of 10−2 in ∆α/α when using the
α 2δλ
0 [Oiii] doublet. The precision from the NIST atomic data allows
whereδλ0 = [λ2−λ1]0 isthelocalz = 0separationbetweenboth for a determination of ∆α/α up to 10−5, which is a bit less than
wavelengths,and(cid:15) = δλz/(1+z)−δλ0 isthedifferencebetween the uncertainty in our result. One could perform a blind analysis
themeasuredlineseparationatredshiftzinrestframeandthelocal inordertosearchforapossiblevariationonα,wheretheabsolute
one.Thus,inprinciple,thelargerthedifferencebetweenthepairof wavelengthvaluesarenotrequired,ifonehadalargeenoughsam-
lines,thebettertheprecisionformeasuring∆α/α. pledistributedinredshift.However,theprecisionontheabsolute
Concerning emission lines, the most suitable pair of lines is wavelengthslimitstheusefulnessofhigh-resolutionspectroscopy
the[Oiii]doublet,whichisoftenpresentinquasarspectrawithrel- untilbettermeasurementsofthe[Oiii]lines(orjusttheirsepara-
ativelyhigh-S/N.Thevacuumvaluesforthe[Oiii]doubletwave- tion)areavailable.
lengthsare
λ[Oiii] =4960.295Å λ[Oiii] =5008.240Å (3)
1 2
3.2 Implementation
δλ[Oiii] =47.945Å, (4)
0 The code developed for the analysis of the quasar spectra fol-
whicharepublishedintheNISTAtomicSpectraDatabase.1These lows the one described in Gutie´rrez & Lo´pez-Corredoira (2010),
although there are some modifications and more information has
transitionsareforbidden(theycorrespondtomagneticdipoleand
beenextractedfromtheanalysis.Wedescribethemaincharacter-
electric quadrupole transitions), and they are not observed in the
isticsofourcodebelow.
laboratory.Thewavelengthexperimentalvaluesareobtainedindi-
rectly by first computing the energy levels from observed wave-
lengthsusingatheta-pinchdischarge(Pettersson1982).Thewave- 3.2.1 Wavelengthsampling
lengthseparationhasdirectlybeenmeasuredintheinfraredfromH
iiregionsusingaballoon-bornetelescopeandMichelsoninterfer- Weconsideronlytheexperimentaldatatogetherwiththeirerrors
ometer(Moorwoodetal.1980).Bothmeasurementsofthewave- asprocessedbytheSDSSpipelinetoobtaintheconstraintonthe
possiblevariationofα.Wedonotresamplethewavelengthrange
by using an interpolation method. Since the pixel spacing is uni-
1 http://physics.nist.gov/PhysRefData/ASD/linesform.html forminlog-wavelengths,agivenrangeofwavelengthsinrestframe
(cid:13)c 2002RAS,MNRAS000,1–15
6 F.D.Albaretietal.
SDSSJ124144.40+601619.7 SDSSJ120839.61+340406.4 SDSSJ082251.37+455946.2
Þ-1L 15 z=0.291 Þ-1L 15 z=0.404 Þ-1L 25 z=0.679
-1s -1s -1s 20
-2cm 10 -2cm 10 -2cm 15
g g g
er er er 10
-170 5 -170 5 -170
H1 H1 H1 5
fΛ 0 H∆HΓ HΒ@OIIID HΑ fΛ 0 H∆HΓ HΒ@OIIID HΑ fΛ 0 MgII H∆ HΓ HΒ@OIIID
4 4 4
2 2 2
fΛ 0 fΛ 0 fΛ 0
D D D
-2 -2 -2
-4 -4 -4
4000 5000 6000 7000 8000 9000 10000 4000 5000 6000 7000 8000 9000 10000 4000 5000 6000 7000 8000 9000 10000
ΛHÞLHobservedL ΛHÞLHobservedL ΛHÞLHobservedL
Figure4.Seventh-orderpolynomialfits(red)tothecontinuumspectrumwiththeirresidualsforthreetypicalquasarspectraatdifferentredshift.Thegapsin
theresidualsarethemaskedregionscorrespondingto(fromrighttoleft)Hα,the[Oiii]doublet,Hβ,Hγ,HδandMgii(blackdashedlines).
(λ−,λ+)hasthesamenumberofpixelsN,i.e. emissionlinesina15Åwindowaroundtheexpectedlocationof
N ∝(cid:90) λ+(1+z)d(cid:0)logλ(cid:1)=logλ+(1+z) =logλ+ , (5) tthhee [rOedsiihi]ifltinbeass.edThoenSaDχS2Sfiptiptoelidnieffeprreonvtidteems paladteetse;rmwienarteifoenr otof
λ−(1+z) λ−(1+z) λ− Boltonetal.(2012)formoredetails.Theseredshiftestimateshave
andisindependentoftheredshiftoftheobject.Allthewavelength errors between 10−4 and 10−5, which are sufficient for our pur-
intervalswiththesamewidthinrestframewillhavethesamenum- poses. Moreover, there is also a visual redshift estimation which
berofexperimentalpoints. can be found in the quasar catalogue DR12Q (Paˆris et al. 2015).
Thedifferencebetweenbothredshiftestimates(ifany)isusually
3.2.2 Fitofthecontinuumspectrum |z −z |≈5×10−4.Wedecidedtoadoptthevisualredshifts.
vis pipe
First,wefitaseventh-orderpolynomialtosubtractthecontinuum Thecentroidpositionsofthe[Oiii]emissionlinesaredeter-
spectrumwhilemaskingregionswherestrongandwideemission minedbyfourdifferentmethods.
linesarepresent(Hα,Hβ,Hγ,Hδ,Mgiiandthe[Oiii]doublet).
OurmethoddiffersfromGutie´rrez&Lo´pez-Corredoira(2010)in (i) Gaussianprofilemethod.
that they use a cubic local spline to fit the continuum masking First, we search for the maximum flux value in an ∼ 15(1+
strongemissionlines.Thechosenorderofthepolynomialprovides z)Å window around the expected position of the line (according
enoughdegreesoffreedomtoreproducedifferentcontinuumfea- totheredshiftprovidedbytheDR12Qcatalogue).Thisprocedure
tures.InSection3,wetesthowourmeasurementfor∆α/αisaf- automaticallyerasesanybiasproducedbytheredshiftvalue.Then,
fectedbychangingthepolynomialorder.Hundredsofcontinuum wemakeaninitialGaussianfitaroundthepositionofthemaximum
spectra fits were checked by eye. The residuals from the fits are fluxvalueusingafixedwidthof∼10(1+z)Å.Fromthisfirstfit,
smallerthantheerrorsonthefluxdensities.Fig.4showsthreedif- weobtainanewpositionforthelinecentroidandaGaussianwidth.
ferentspectrawiththeircontinuumfitandresiduals. These values are used as initial parameters for the final fit of the
lines;namely,thewavelengthrangeconsideredtoperformthefinal
3.2.3 Signal-to-noiseratio
fitiscentredaroundthepositionofthelinecentroid,anditisfour
WefollowGutie´rrez&Lo´pez-Corredoira(2010)forthedetermina- timestheGaussianwidthofthelines.Thisapproachmeansthatwe
tionofS/N.Hence,wecomputethestandarddeviationoftheflux considerpixelsupto2σawayfromthecentreoftheline.Hence,
between 5040(1+z) and 5100(1+z)Å (where z is the redshift somelinesarefittedusing∼4−5pixels,whileotherswith∼15−20
of the quasar) where there are no strong emission or absorption pixelsdependingonthelinewidth.Thefittakesintoaccountthe
lines. Then, we search for the maximum of the [Oiii] 5008 line, fluxerrorsforeachpixel,i.e.,weusetheivarcolumnfoundineach
anddetermineS/N[Oiii]5008astheratiobetweenthemaximumof spectrumasweightsforthefit.Ourfinalcentroidmeasurementfor
thelineandthepreviouslycomputedstandarddeviation.Although eachconsideredlinecorrespondstothecentroidoftheGaussianfit
for a more reliable determination of the S/N, it is better to use a doneinthelaststepoftheadoptedprocedure.Wealsoderivean
Gaussianfittotheline.Thisprocedureavoidspossibleissuesre- errorfor∆α/αusingthestandarderrorsforthecentrepositionof
latedwhenfittingdatawithverylowS/N.ThisS/Nisusedinthe theGaussians.Thisisourmainmethodformeasuringα.
criterionii(Section2)tobuildourfiducialsample. (ii) Voigtprofilemethod.
FollowingthesameprocedurethanwhenusingaGaussianpro-
3.2.4 Measurementoftheemission-linewavelengths
file,wemakethefitwithaVoigtprofileinsteadofaGaussian.More
Tomeasurethewavelengthsofthe[Oiii]doublet,ourfittingcode precisely,weuseapseudo-Voigtprofilewhichisalinearcombi-
needs as input an accurate estimate of the redshift of the quasar, nationofaGaussianandaLorentzianprofile.Then,wehaveone
at least with an error ∆z<3×10−3. This allows a search for the moreparameter,i.e.theamplitudeoftheLorentzianfunction,while
(cid:13)c 2002RAS,MNRAS000,1–15
Fine-structureconstantwithBOSS 7
350
3500
SDSSJ121417.80+293143.4 SDSSJ121417.80+293143.4
z=0.063 300 z=0.063
3000
@OIIIDlines @NeIIIDlines
-1L 2500 -1L 250
Þ Þ
-1 -1
-2s 2000 -2s 200
m m
c c
g g
er 1500 er 150
-17 -17
0 0
1 1
H 1000 H 100
Λ Λ
f f
500 50
0 0
5260 5280 5300 5320 5340 4100 4120 4140 4160 4180 4200 4220
ΛHÞLHobservedL ΛHÞLHobservedL
Figure5.[Oiii](left-handpanel)and[Neiii](right-handpanel)linesforSDSS-J121417.80+293143.4,atredshiftz = 0.063.Themeasured∆α/αforthis
quasaris∆α/αG[Oausisii] =(2.3±7.6)×10−4,∆α/αV[Ooigitii] =(3.3±12.6)×10−4and∆α/αG[Nauessiii] =(39±8)×10−4,∆α/αV[Noigetiii] =(37±9)×10−4.The
measured∆α/αfor[Neiii]isnotconsistentwithzeroregardlessoftheprofile;seeFig.14andlastparagraphofSection4fordiscussion.Eachpanelshows
thefluxdensityforeachpixelwiththeirrespectiveerrorbars(solidsymbols),togetherwiththeGaussianfit(dottedredcurve)andthepseudo-Voigtprofile
(thickgreycurve)toeachofthelines.Thefittingprocedure(describedinthetext)onlytakesintoaccounttheexperimentaldata(solidsymbols)weightedby
theirerrorbars.NoticehowthedeviationofthelinecentroidpositionderivedfromourGaussianfit(verticalsolidline)withrespecttotheexpectedposition
oftheline(verticaldashedline)accordingtothevisualredshiftprovidedbytheDR12Qcataloguearewellcorrelatedforthesamepairof[Oiii]and[Neiii]
lines,andforthedifferentsetoflines.Thegreenshadedverticalareashighlighttheuncertaintyfortheexpectedpositionofthelinesduetothequasarredshift
error(≈ 5×10−4).Alsoshownisafourth-ordersplineinterpolationtothespectrumaftersubtractingthecontinuum(thinsolidline).The[Neiii]linesare
weakerbyoneorderofmagnitudethanthe[Oiii]lines,whichisusuallythecaseforallthespectrashowingbothpairoflines.Theweaklinenearthestronger
[Neiii]lineisblendedwithHei(3889.75Å)andHζ(3890.16Å).
its width and its position are the same as those for the Gaussian 3.3 Simulatedspectra
profile.
In Fig. 5, we depict the [Oiii] and [Neiii] lines for the In order to test the robustness and accuracy of our methodology,
we generate realizations of quasar spectra using as noise a nor-
same quasar spectrum to illustrate the Gaussian and Voigt fitting
mal distribution centred at the flux value, and taking the error in
methods.
each pixel as the standard deviation. From our fiducial sample
(iii) Integrationmethod.
(10363 quasars), we simulate 100 realizations for each spectrum
Here, the centroids of the lines are obtained by integrating
(> a million in total). This number of realizations provides rea-
around 1σ from the position of the fitted Gaussian profile. This
sonablestatisticstoderiveanerrorfromthestandarddeviationof
techniqueprovidesindicationsofwhetherthereisHβcontamina-
themeasurementsontherealizationsofeachrealspectrum,while
tion.However,duetothemid-resolutionofthespectraR ≈ 2000,
thecomputationtimeremainsreasonable(∼2d)usingastandard-
thismethodisnotveryaccurate.
size computer. The estimated error derived from the simulations
(iv) ModifiedBahcallmethod.
∆(∆α/α) includes
In Bahcall et al. (2004) the authors used a different approach sim
tocomputethelinepositions.Theyperformedathird-orderspline ∆(∆α/α)2 =∆(∆α/α)2 +∆(∆α/α)2 +∆(∆α/α)2 , (6)
interpolationtothestronger[Oiii]5008line,thenfittedthisinter- sim fit continuum code
polation to the weaker 4960 line by adjusting the amplitude and where∆(∆α/α) istheerrorderivedfromtheGaussianfits,which
fit
separationoftheprofile.Wehavemodifiedthismethodbyusinga is our error estimate for each real spectrum; ∆(∆α/α) is
continuum
Gaussianfittothestrongerlineratherthanathird-orderspline. theerrorfromdifferentcontinuumsubtractionduetotheGaussian
noise,and∆(∆α/α) isthesystematicerrorofourcode.Then,
code
Althoughwehavedescribedfourdifferentmethods,themain weexpect∆(∆α/α) >∆(∆α/α) andtheirdifferencewillbean
sim fit
resultsfor∆α/αpresentedinthisworkarebasedontheGaussian indicationofthecontinuumandsystematicerrors.
fittingmethod,whiletheotherthreeareusedonlyforcomparison Fig.6(left-handpanel)showsthecorrelationbetweentheer-
(seeSection4). rorin∆α/αfromtheGaussianfitsofeachrealspectrumandthe
Finally,ourfinalresultfor∆α/αanditserrorisobtainedinthe standard deviation for ∆α/α of its 100 realizations. The standard
samewayasinChandetal.(2005),namelywecomputeaweighted deviationsfromthesimulationsarewithinafactorof0.5−2ofthe
meanandaweightedstandarddeviation,wheretheerrorsfor∆α/α standarderrorsfromthefitsfor97%(84%)ofthecaseswhenboth
ofeachspectrumareusedasweights. quantitiesare< 5×10−3 (< 50×10−3).Thisshowsthatourcode
(cid:13)c 2002RAS,MNRAS000,1–15
8 F.D.Albaretietal.
ΛHÞLHobservedL
6000 7000 8000 9000
5
3-10DDΑΑ´H(cid:144)LHLsim 1234 DDΑΑH(cid:144)Lsim 0.00.0001.11101 ´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´
0
0 1 2 3 4 5 0.2 0.4 0.6 0.8 1.0
DHDΑ(cid:144)ΑLfitH´10-3L Redshift
Figure6.Left-handpanel:errorsfor∆α/αobtainedfromthesimulations(standarddeviationofthe∆α/αmeasurementson100realizationsofeachreal
spectrum)andstandarderrorsfromtheGaussianfitsforourfiducialsample.Thesolidlinerepresentsaone-to-onecorrespondence,whilethedashedlines
haveslopesof2and0.5.Onlythesimulationandfiterrorssmallerthan<5×10−3areshown.Right-handpanel:errorsestimatedfromthesimulationsasa
functionofredshift.Spectrawith∆(∆α/α) >5×10−3areshownasredcrosses(24%ofthetotal).Thereisacleardivisionbetweentwodifferentsetof
fit
spectrawhichcorrelateswiththeskyemissionlines(seediscussioninthemaintext).
10 10
-3DΑΑ´H(cid:144)LHL10Voigt --10505 ´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´ -3DΑΑ´H(cid:144)LHLError10Voigt 02468 ´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´´
-10 -5 0 5 10 0 2 4 6 8 10
HDΑ(cid:144)ΑL H´10-3L ErrorHDΑ(cid:144)ΑL H´10-3L
Gaussian Gaussian
Figure7.Left-handpanel:measurementsof∆α/αusingGaussianandVoigtfittingprofiles.Non-compatiblemeasurementsat1σareshownasredcrosses
(6.5%ofthetotal).Right-handpanel:errorsfromtheGaussianandVoigtfitting.Non-compatiblemeasurementsat1σareshownasredcrosses.
andthecontinuumsubtractiondonotintroducenoticeablesystem- Asafurtherproof,wealsosimulaterealizationsofthe1416
aticerrorscomparedtotheGaussianfitting.However,thereisaset dropped spectra because of sky emission lines (criterion iv, see
ofspectra(9%ofthetotal)forwhichthesimulationsprovidemuch Section 2). We found that more than 80% of the spectra have
largererrors∆(∆α/α) > 0.1.Fig.6(right-handpanel)showsthe ∆(∆α/α) > 0.1.Thisconfirmsthatthesespectrahaveverylow
sim
errorsfromthesimulationsasafunctionofredshiftforourfidu- S/N and/or large pixels error due to the proximity of the lines to
cialsample.RedcrossesstandforspectrawhoseGaussianfiterror strongskyemissionlines.
∆(∆α/α) > 5×10−3 (24%). The errors are distributed in two
fit
clouds of points. For the cloud with ∆(∆α/α)sim ∼ 1, the virtual 3.4 GaussianversusVoigtfittingprofiles
realizationsofeachspectrumseemtodiffersignificantlyfromthe
TheresultsobtainedwhenusingVoigtprofilesinsteadofGaussian
realspectrum.Sinceweusetheerrorineachpixeltobuildthere-
onesarecomparedinFig.7.TheVoigtandGaussianmeasurements
alizations,therelativeerrorislargeforthesespectra,whichisan
indicationofalowS/Nratioorlargeabsoluteerrorsinthepixels, are1σ-compatibleforthe93.5%ofthecases(98.3%at2σ).Re-
gardingtheerrors,thereisnoclearimprovementwhenusingeither
forinstanceinwavelengthregionswithskyemissionlines.Infact,
ofbothmethods.However,Voigtprofileshaveonemoreparameter
thecloudwithbiggererrorsmimicstheskyspectrum.Notealsothe
andrestrictthenumberofdegreesoffreedom.Duetothespectral
strongcorrelationbetweenthiscloudofpointsandthespectrawith
mid-resolution and the fact that the [Oiii] lines are very narrow,
largeGaussianfittingerrors(redcrosses).Theothersetofpoints
with ∆(∆α/α) ∼ 10−3 are close to our error estimation on the thereareoftenonlyafewpixelstofit,whichfrequentlyleadtonon-
sim
measurementof∆α/αbasedontheGaussianfits. convergentfits.Thisreducesthequasarsamplein≈1000quasars.
FurtherdiscussionaboutbothprofilescanbefoundinSection4.
(cid:13)c 2002RAS,MNRAS000,1–15
Fine-structureconstantwithBOSS 9
4 SYSTEMATICS Table2.Resultsfor∆α/αconsideringseveralsampleswithdifferentcon-
straints.Thenumberofquasarspectra,themeanandstandarddeviationof
In thissection, weexamine thepossible unnoticedsystematic er-
rorsbyanalysingdifferentquasarsamples.Table2summarizesall theredshiftandthevaluefor∆α/αareshown.
thesamplesconsideredtogetherwiththeirmeanredshiftsandthe
measuredvaluefor∆α/α. σ4960/5008−1 No.ofquasarspectra Redshift ∆α/α(×10−5)
Weconsiderthefollowingsourcesofsystematicerrors. <50% 10028 0.56±0.21 1.6±2.3
<25% 8877 0.56±0.21 1.9±2.3
(i) Misidentificationofthelines.Theexpectedlinewidthsand <10% 5846 0.56±0.21 1.7±2.5
amplitudesareusefultoavoidmisidentificationofthe[Oiii]emis- <5% 3458 0.54±0.22 −0.9±3.0
sionlines.(a)Linewidths:sincebothlinesoriginateonthesame [Fλ×σ]5008/4960 No.ofquasarspectra Redshift ∆α/α(×10−5)
upperenergylevel,theirwidthmustcoincide.Wecheckthatthis
isthecasebyconsideringquasarswhose[Oiii]linewidthsarethe 2.98±0.50 8327 0.56±0.21 1.8±2.4
2.98±0.25 5761 0.55±0.21 −0.4±2.6
samewithinarelativefraction.Formorethanhalfofourfiducial
sample,the[Oiii]linewidthsdifferbylessthan10%(seeTable2). 2.98±0.10 2658 0.54±0.21 0.0±3.4
2.98±0.05 1411 0.52±0.22 5.2±4.6
(b)Amplituderatio:atomicphysicsstatesthattheamplituderatio
between the [Oiii] 5008 and [Oiii] 4960 lines is 2.98 (Storey & Fitwidth No.ofquasarspectra Redshift ∆α/α(×10−5)
Zeippen2000)(asquotedinSection5,weobtain2.96±0.02syst). 2σ 10363 0.56±0.21 1.4±2.3
Thus,weconsiderdifferentsampleswherethisratiodiffersbyless 3σ 10252 0.59±0.20 5.5±2.5
thanacertainamountfrom2.98(seeTable2).Allthesamplescon- 4σ 9978 0.59±0.20 7.1±2.7
sidered in this test yield results for ∆α/α compatible with zero. 5σ 9726 0.59±0.20 5.3±2.6
Fig.8displaystheGaussianwidthsandfluxesofboth[Oiii]emis- S/NHβ/[Oiii]4960 No.ofquasarspectra Redshift ∆α/α(×10−5)
sionlinesforourfiducialsample.
(ii) WindowsfortheGaussianfits.Weuseawavelengthrange <5 10338 0.57±0.21 1.4±2.3
of 2σ around each [Oiii] line in order to obtain the final Gaus- <2 9831 0.57±0.21 0.6±2.3
<1 8162 0.57±0.21 0.1±2.5
sian fit to the line profiles. We study how our results depend on
<0.5 5831 0.58±0.21 −0.7±2.8
thischoice.Byconsideringalargerwavelengthinterval,theresults
aremoreaffectedbytheHβcontaminationandpossibleasymme- Pol.order(cont.) No.ofquasarspectra Redshift ∆α/α(×10−5)
triesonthelinewings.Thedifferencesinthenumberofspectrafor 3 10528 0.57±0.21 1.0±2.3
thesesamples[whichareobtainedbyapplyingtheselectioncrite- 5 10550 0.57±0.21 1.3±2.3
ria (i)−(iv) discussed in Section 2.1] arise because of the criteria 7 10363 0.56±0.21 1.4±2.3
concerningthenon-convergingfitsandtheskyemissionlinesde- 9 10471 0.56±0.21 −1.1±2.3
scribedinSection2.
R2(bothfits) No.ofquasarspectra Redshift ∆α/α(×10−5)
(iii) Hβcontamination.Weanalysesampleswheretheratiobe-
tthweevenalSue/NfoHrβ∆aαnd/αS/dNec[Oreaiisi]es49a6s0wisecpolnascteraminoerde.sDtreinspgietnetthcoenfsatcrtatihnatst >>00..997 69024554 00..5566±±00..2211 12..58±±22..47
>0.99 2301 0.54±0.21 2.0±3.5
onHβ,itisalwaysconsistentwithnovariationinαwithintheer-
>0.995 845 0.51±0.22 −0.4±4.8
rors.Thisanalysisdemonstratesthatthestrengthand/orwidthof
theHβlinedonotaffectsubstantiallytheresultfor∆α/αwhena [Oiii]5008(kms−1) No.ofquasarspectra Redshift ∆α/α(×10−5)
weightedmeanisadopted. <1000 10353 0.56±0.21 1.4±2.3
(iv) Continuumsubtraction.Weuseaseventh-orderpolynomial <500 8990 0.56±0.21 0.2±2.4
tosubtractthecontinuumspectrum.Weexamineifthepolynomial <300 2798 0.52±0.22 −6.8±3.9
order has important effects on our measurements. Our values for <200 150 0.52±0.24 21±18
∆α/αandtheirerrorsareonlyslightlyaffectedbythechosenpoly-
Method No.ofquasarspectra Redshift ∆α/α(×10−5)
nomialorder.
(v) Goodness of Gaussian fits. We quantify the quality of the Gaussian(weighted) 4537 0.58±0.20 −0.4±2.8
GaussianfitsbytheR2coefficient.Alltheconsideredsamplesshow Gaussian 4537 0.58±0.20 1.2±4.5
valuesfor∆α/αconsistentwithnovariationinα. Integration 4537 0.58±0.20 3.6±4.8
ModifiedBahcall 4537 0.58±0.20 0.8±4.4
(vi) Broadlines.Wealsostudysampleswherethewidthofboth
Median 4537 0.58±0.20 1.8±1.4
lines is less than a certain value (in kms−1). These samples are
consistentwithnovariationofα.Samplesbuiltfromnarrowlines GaussversusVoigt No.ofquasarspectra Redshift ∆α/α(×10−5)
< 300kms−1 maybemoreaffectedbymisidentificationof[Oiii] Gaussianprofiles 8485 0.55±0.19 0.4±2.5
linesasskylines. Voigtprofiles 8485 0.55±0.19 −1.1±2.8
(vii) Different methods for measuring the [Oiii] line position. Mixedprofiles 8485 0.55±0.19 1.3±2.4
We compare the results obtained by the methods to measure the
position of the [Oiii] lines described in Section 3.2.4. Since not
allthemethodsprovideanerrorforthemeasurement,wecannot (viii) Gaussian versus Voigt profiles. We compare the results
calculateaweightedmean,anditisnecessarytoselectamorere- for 8485 quasars from our fiducial sample after dropping 1878
strictedsample.Then,weconsiderasamplewherethedifference spectra with non-converging Voigt fits (this reduction increases
betweenthewidthsofthelinesislessthan25%,theamplitudera- the statistical error). We also compute a ‘mixed’ value for ∆α/α
tioisconstrainedtodifferfromthetheoreticalvalue2.98(Storey& where for each spectrum we use the value for the variation of
Zeippen2000)bylessthan0.5,andtheS/N issmallerthanhalf thefine-structureconstantwithsmallererror,either(∆α/α) or
Hβ Gauss
theS/N[Oiii]4960. (∆α/α)Voigt.
(cid:13)c 2002RAS,MNRAS000,1–15
10 F.D.Albaretietal.
1500
L
-1
s 1000
ms(cid:144)L 1000 -2cm 500
kH 700 rg
0 e
II496D 500 -17H10 15000
OI 60
@ 9
M 300 4
WH DIII 10
O
F 200 @ 5
x
u
150 Fl
150 200 300 500 700 1000 1500 10 50 100 500 1000 5000
FWHM@OIIID5008Hkm(cid:144)sL Flux@OIIID5008H10-17ergcm-2s-1L
Figure8.Left-handpanel:Gaussianwidths(inkms−1)forboth[Oiii]lines.Bothlinesoriginateonthesameupperenergylevel,thentheirwidthsmust
coincide(reddashedline).Right-handpanel:fluxesforboth[Oiii]lines.Thetheoreticalfluxratiois2.98(reddashedline).Theentirefiducialquasarsample
isshown.
Table3.DetailedinformationaboutthebinsinFig.10.
Redshiftinterval No.ofquasarspectra Redshift ∆α/α(×10−5)
0.390−0.460 817 0.42±0.02 −5.2±6.8
0.460−0.520 723 0.49±0.02 5.5±8.9
0.520−0.580 757 0.55±0.02 0.4±9.2
0.580−0.625 843 0.60±0.01 40.4±9.4
0.625−0.675 988 0.65±0.01 −3.5±7.4
0.675−0.715 1299 0.69±0.01 −8.2±7.4
0.715−0.765 1117 0.74±0.01 1.7±7.1
0.765−0.820 1444 0.79±0.02 18.1±8.3
0.820−0.880 644 0.84±0.02 4.7±9.2
0.880−1.000 580 0.93±0.03 17.0±13.3
Thisvalueisconsistentwiththepreviousresultsreportedindiffer-
entinvestigationsbasedonthesamemethod:Bahcalletal.(2004),
Figure9.Errorsfor∆α/αderivedfromtheGaussianfits(greypoints)for Gutie´rrez&Lo´pez-Corredoira(2010),andRahmanietal.(2014).
ourfiducialsample,movingmeanofthetheseerrors(blueline)usingover- TheredshiftdependenceofthemeasurementsisshowninFig.10
lappingbins(100spectraperbin,∆z≈0.025),movingstandarddeviation (left-hand panel), where several bins have been made taking into
of ∆α/α measurements using the same bins (red line) and a typical sky accounttheredshiftintervalsaffectedbythesky(shadedzones).In
spectrum.
theright-handpanel,weshowtheresultsobtainedfromthesimu-
lationsdescribedinSection3,usingthesameredshiftsintervalsfor
thebins.Themaindifferencesbetweentherealresultsandthesim-
We have also analysed the standard deviation and errors of
theresultsfor∆α/αasafunctionofredshift(Fig.9).Eventhough ulationsareintheregionswheretherearestrongskylines(shaded
regions),whilebeinginagreementintheremainingzones.Detailed
we have imposed a constraint on our initial sample based on the
informationabouteachbinfortherealdatacanbefoundinTable3.
skyemissionlines,thestandarddeviationanderrorsstillcorrelate
Our results are little affected by the specific constraints im-
withthesky.Inparticular,forthecorrelationwiththemovingstan-
posed in our sample as discussed in Section 4. For instance, we
darddeviation,thismeansthattheprecisioninourmeasurementof
∆α/αalongthewholeredshiftintervalislimitedbytheskysub- varythewidthfortheGaussianfits,thecontaminationofHβ,the
polynomialorderusedtofitthecontinuumspectrum,thequalityof
tractionalgorithm.
theGaussianfitsandtestdifferentmethodstomeasure∆α/α.The
mostimportanteffectfoundisthatbyconsideringbroaderwidths
5 RESULTS fortheGaussianfits,theresultsaremoreaffectedbythecontamina-
5.1 [Oiii]lines tionfromHβandpossibleasymmetriesinthelinewings.Wehave
alsocheckedforpossiblemisidentificationsofthe[Oiii]emission
We used a total of 10363 quasar spectra, drawn from the SDSS- linesusingtheirexpectedwidthsandamplituderatio.
III/BOSS DR12Q catalogue, after applying the selection criteria Table4containstheresultsfor∆α/αwhenthelowerbound
(i)−(iv) (see Section 2), to measure the possible variation of the on the S/N[Oiii]5008 is increased. All the results remain consis-
fine-structureconstant.Thefollowingmeasurementisobtained: tent with no variation of the fine-structure constant. In Fig. 11,
∆α the measured ∆α/α for our fiducial sample as a function of the
α =(1.4±2.3)×10−5. S/N[Oiii]5008areplottedtogetherwiththeirerrors.
(cid:13)c 2002RAS,MNRAS000,1–15