The extended ROSAT-ESO Flux-Limited X-ray Galaxy Cluster Survey (REFLEX II) VI. Effect of massive neutrinos on the cosmological constraints from clusters

0.12 MB·English

by  Hans Boehringer

Astronomy&Astrophysicsmanuscriptno.Boehringer˙15 (cid:13)c ESO2015
January21,2015
LettertotheEditor
The extended ROSAT-ESO Flux-Limited X-ray Galaxy Cluster
Survey (REFLEX II)
VI. Effect of massive neutrinos on the cosmological constraints
from clusters
HansBo¨hringer1,GayoungChon1
5
1 1Max-Planck-Institutfu¨rextraterrestrischePhysik,D-85748Garching,Germany.
0
Submitted29/11/14
2

n ABSTRACT
a
J Clustersofgalaxiesareimportantprobesforthelarge-scalestructurethatallowustotestcosmologicalmodels.WiththeREFLEX
0 IIgalaxyclustersurveywepreviouslyderivedtightconstraintsonthecosmological parametersforthematterdensity,Ωm,andthe
2 amplitude parameter of the matter density fluctuations, σ8. Whereas in these previous studies no effect of massive neutrinos was
takenintoaccount,weexploretheseeffectsinthepresentpublication.Wederivecosmologicalconstraintsforthesumoftheneutrino
] massesoftheconventionalthreeneutrinofamiliesintherange Mν = Pimνi = 0to0.6eV.TheinfluenceontheconstraintsofΩm
O andσ fortheexpectedmassrangeisweak.Interestingconstraintsontheneutrinopropertiescanbederivedbycomparingthecluster
8
C datawiththosefromthePlanckcosmicmicrowavebackground(CMB)observations.ThecurrenttensionbetweenthePlanckresults
andclusterscanformallyberesolvedwithneutrinomassesofaboutM =0.45(±0.28,1σ)eV.Whilewecautionnottoconsiderthis
. ν
h afirmmeasurementbecauseitmightalsobetheresultofunresolvedsystematics,itisinterestingthatothermeasurementsofthelocal
p large-scalestructurefluctuationamplitude,likethatofcosmiclensingshear,yieldsimilarresultsandadditionallyconfirmtheeffectof
- massiveneutrinos.Amongtheindicatorsformassiveneutrinos,galaxyclustersandinparticularourlargeandwell-controlledcluster
o surveycurrentlyprovidethebestpotentialforconstraintsofthetotalneutrinomass.
r
t Keywords.galaxies:clusters,cosmology:observations,cosmology:large-scalestructureoftheUniverse,X-rays:galaxies:clusters
s
a
[

1 1. Introduction approximately fixed, the strength of the effect depends on the
v massoftheneutrinos.Thismassisunevenlydistributedbetween
Clustersofgalaxiesformfromweakdensityfluctuationsinthe
3 the three differentneutrinospecies, but how exactly they share
early Universe on comoving scales of several Mpc in a well-
5 the massis currentlyunknown.For ourpurposesthe important
9 defined way. They can thus be used to statistically assess the parameteristhetotalmassofallneutrinofamilies,M = m ,
4 large-scalestructure.Byapplyingthisasadiagnostics,onecan andthedistributionoftheindividualmassescausesoνnlyPhiighνeir
0 constrain cosmological models that describe our Universe. We order effects that are of no concernfor our calculations. In ad-
. havebeenusing galaxyclustersfromourstatistically complete
1 dition,theeffectsofpossiblesterileneutrinosonthelarge-scale
survey of galaxy clusters, the REFLEX (ROSAT-ESO Flux-
0 structurehavebeenconsidered(e.g.Lesgourges&Pastor2006,
5 Limited X-ray) Cluster Survey (Bo¨hringer et al. 2001, 2004, 2014).Inthispaperwefocusontheeffectofthreeconventional
1 2013) to obtain constraints on cosmological model parameters neutrinos.
: (Bo¨hringer et al. 2014a). We derived in particular tight con-
v
straintsonthe matterdensityparameter,Ω , andonthe ampli- Thereis anexperimentallowerlimiton M witha valueof
i m ν
X tude parameter of the matter density fluctuations, σ from the about0.06eV(e.g.Foglietal.2012;Foreroetal.2012).Several
8
X-rayluminosityfunctionmeasuredinthenearbyUniverse. upperlimits have beenderivedfromastronomicalobservations
r
a In these calculations we assumed that neutrinos, filling the with Mν ≤ 0.93 eV from Planck alone (Planck Collaboration
Universe in large abundance, have zero mass. Modern exper- XVI2913a),Mν ≤0.9eVfromtheSDSSpowerspectrumalone
imental results from solar, atmospheric, and reactor neutrinos (Viel et al. 2010), a value of Mν = 0.36±0.14 (1σ) eV from
(e.g. Fogli et al. 2012; Forero et al. 2012; Lesgourgues et al. theSDSSIIIpowerspectrumcombinedwithWMAP(Beutleret
2013) show neutrino oscillations that imply that neutrinos are al. 2014), Mν ≤ 0.34 eV from SDSS III combined with CMB
not massless; they therefore have an effect on the large-scale and supernova data (Zhao et al. 2014), Mν ≤ 0.18 eV from
structureoftheUniverse(e.g.Lesgourges&Pastor2006,2014). thematterpowerspectrumoftheWiggleZDarkEnergySurvey
Theprocessbywhichneutrinosinfluencethe large-scalestruc- combined with data from Planck and other BAO observations
turegrowthisapartialdampingofthedensityfluctuationpower (Riemer-Sørensen 2014), and Mν ≤ 0.33 eV from a combina-
spectrumonsmallandintermediatescalesuptoaboutk≥0.02h tion of the cluster mass function, CMB, supernova, and BAO
Mpc−1(≤160h−1Mpc)incomovingunits(Lesgourges&Pastor data (Mantz et al. 2010).One of the tightest constraintscomes
2006).SincethenumberofneutrinosinthepresentUniverseis fromthelarge-scalestructureanalysisoftheLyαforesttogether
with galaxyclustering,CMB, andsupernovaobservationswith
Sendoffprintrequeststo:H.Bo¨hringer,[email protected] Mν ≤ 0.17eV (Seljak et al. 2006).In a recentpaper, Costanzi
1
Bo¨hringeretal.:REFLEXIIcosmologyconstraintswithmassiveneutrinos
etal.(2014)obtainedconstraintsonanon-zeroneutrinomassof applied an additional cut on the minimum number of detected
Mν =0.29−+00..2118(cid:16)0.22−+00..1187(cid:17)eVusingWMAP9(Planck)CMBas source photonsof 20 counts. Thishas the effect that the nomi-
nal flux cut quoted above is only reached in about 80% of the
wellasBAO,large-scalestructurelensingshearandclusterdata.
survey. In regions with lower exposure and higher interstellar
Hamann and Hasenkamp (2013) and Battye and Moss (2014)
absorption, the flux limit is accordingly higher (see Fig. 11 in
alsoconcludedonapositivesignalforneutrinomassfromCMB
Bo¨hringer et al. 2013). This effect is modelled and taken into
andlensingshearorclusterdata.
accountinthesurveyselectionfunction.
Thereforemassiveneutrinosshouldbeincludedinthemod-
ellingoftheX-rayluminosityfunctiontocomplywiththemost The flux limit imposed on the survey is for a nominal flux
recent results, which imply that neutrinos have mass. With a thathasbeencalculatedfromthedetectedphotoncountratefor
givenneutrinonumberdensitywecancalculatethecontribution a cluster X-ray spectrum characterized by a temperature of 5
ofneutrinostothematterdensityintermsofthecriticaldensity keV, a metallicity of 0.3 solar, a redshift of zero, and an inter-
andwefind(e.g.Lesgourges&Pastor2014) stellarabsorptioncolumndensitygivenbythe21cmskysurvey
described by Dickey and Lockmann (1990). The result of this
m conversionof count rate to flux is an appropriateflux estimate
Ω = P ν h2 . (1)
ν 93.14eV beforeanyredshiftinformationandisanalogoustoanobserved
objectmagnitudecorrectedforGalacticextinctionintheoptical.
The aim of this paper is to explore how the constraints of
After the redshifts were measured, a new flux was calcu-
cosmological parameters based on the REFLEX II survey data
latedtakingtheredshiftedspectrumandanestimateforthespec-
changebyincludingmassiveneutrinos.Whiletheeffectofmas-
traltemperatureintoaccount.Thetemperaturewasestimatedby
sive neutrinos on the cluster mass function and on the derived
meansoftheX-rayluminosity-temperaturerelationfromPratt
cosmologicalconstraintshasbeenexploredbefore(e.g.Marulli
et al. (2009) determined from the REXCESS cluster sample.
etal.2011,Costanzietal.2013,Burenin2013),theapplication
This is a sample of clusters drawn from REFLEX I for deeper
of the REFLEX II cluster sample adds a new dimension to the
follow-upobservationswithXMM-Newton,whichis represen-
discussion for us. The REFLEX II galaxy cluster sample cur-
tative of the entire flux-limited survey (Bo¨hringer et al. 2007).
rentlyprovidesthemostprecisedescriptionoftheshapeofthe
The luminositywas determinedfirst fromthe observedflux by
X-rayluminosityfunction.Thebettertheshapeofthefunction
meansoftheluminositydistanceforagivenredshift.Usingthe
isconstrained,thebetterthedegeneracyoftheconstraintsonthe
X-ray luminosity mass relation given in Pratt et al. (2009), we
parameters,Ω ,σ ,and M canbebroken.Itisamaingoalof
m 8 ν thenusedthemassestimatetodetermineafiducialradiusofthe
thispapertoexplorewhatthisimpliesforourdata.Inaddition, cluster,whichistakentober 1.Weappliedabetamodelfor
500
wealso wishtostudythepossibleimplicationsontheneutrino
theclustersurfacebrightnessdistributiontocorrectforthepos-
mass that can be gained by a comparison of the cosmological
siblymissingfluxintheregionbetweenthedetectionapertureof
constraintsderivedfromourclustersamplewiththeresultsfrom
the sourcephotonsandthe radiusr . The procedureto deter-
500
thePlanckobservationsoftheCMB.
minetheflux,theluminosity,thetemperatureestimate,andr
500
The paper is structured as follows: In Sect. 2 we describe
wasperformediterativelyandisdescribedindetailinBo¨hringer
theREFLEXIIgalaxyclustersampleandinSect.3thecosmo-
etal.(2013).Inthispaperwe deduceda meanfluxuncertainty
logical modelling of these data. In Sect. 4 we then discuss the
fortheREFLEXIIclustersof20.6%,whichismostlyduetothe
effects of massive neutrinos on the X-ray luminosity function,
Poisson statistics of the source counts, but also contains some
and in Sect. 5 we compare the cosmological constraints from
systematicerrors.
clustersincludingmassiveneutrinoswiththosefromthePlanck
The X-ray source detection and selection was based on the
CMBobservationsanddrawourconclusions.Section6provides
official ROSAT All-Sky Survey source catalogue by Voges et
asummary.Todetermineallparametersthatdependondistance,
al.(1999).Weusedthepubliclyavailablefinalsourcecatalogue
we use a flatΛCDM cosmologywith a matterdensityparame- 2 as well as a preliminary source list that was created while
terΩ asrequiredbythemodel.Literaturevaluesquotedabove
m producing the public catalogue. To improve the quality of the
havea scalingby h = H /100kms−1 Mpc−1, whereasthefol-
0 source parameters for the mostly extended cluster sources, we
lowing results are scaled with h = h/0.7, if not stated other-
70 reanalysedalltheX-raysourceswiththegrowthcurveanalysis
wise. ForthecomparisonwithPlanck weuse a flatcosmology
method(Bo¨hringeretal.2000).Thefluxcutwasimposedonthe
withΩ =0.315andh=0.673.
m reanalysed data set. The process of the source identification is
describedindetailinBo¨hringeretal.(2013).
2. REFLEXIIgalaxyclustersurvey
The REFLEX II galaxy cluster survey is based on the X-ray 3. CosmologicalmodellingoftheREFLEXsurvey
detection of galaxy clusters in the ROSAT All-Sky Survey
Cosmological constraints were obtained by comparing cosmo-
(Tru¨mper1993,Vogesetal. 1999).The regionof the surveyis
logicalmodelpredictionsforthegalaxyclusterX-rayluminosity
thesouthernskybelowequatoriallatitude+2.5oandatGalactic
functionwiththeobservationsfromtheREFLEXIIproject.The
latitude|b | ≥ 20o.TheregionsoftheMagellanicCloudshave
II comparison was performed by means of a likelihood method.
beenexcised.Thesurveyregionselection,thesourcedetection,
The details of this procedure are described in Bo¨hringer et al.
the galaxy cluster sample definition and compilation, and the
constructionofthe surveyselection functionaswell astests of
1 r istheradiuswheretheaveragemassdensityinsidereachesa
thecompletenessofthesurveyaredescribedinBo¨hringeretal. 500
valueof500timesthecriticaldensityoftheUniverseattheepochof
(2013).Insummary,thesurveyareais∼4.24ster.Thenominal
observation.
fluxlimitdowntowhichgalaxyclustershavebeenidentifiedin 2 The RASS source catalogues can be found at
theROSATAll-SkySurveyinthisregionis1.8×10−12 ergs−1 http://www.xray.mpe.mpg.de/rosat/survey/rass-bsc/ for the bright
cm−2 in the 0.1 - 2.4 keV energyband,yieldinga catalogueof sources and at http://www.xray.mpe.mpg.de/rosat/survey/rass-fsc/ for
911clusters.Toassessthelarge-scalestructureinthispaper,we thefaintsources.
2
Bo¨hringeretal.:REFLEXIIcosmologyconstraintswithmassiveneutrinos
(2014a), and we here provide only a brief outline. In a first
step, the power spectrum of the matter density fluctuations for
thepresentepochiscalculatedwiththeprogramCAMB(Lewis
et al. 2000) 3. This is different to the previous calculations in
Bo¨hringer et al. (2014a), where we used the program for the
transferfunctionbyEisensteinandHu(1998).Bychangingthe
calculationsfromthelatterprogramtoCAMB,wedidnotnote
any differences larger than one percent. Based on this power
spectrum,we calculatedthe cluster massfunctionwith the for-
mulasgivenbyTinkeretal. (2008).To derivethepredictedX-
ray luminosity function from the theoretically calculated clus-
ter mass function, we used empirical scaling relations of X-
rayluminosityandmassinaccordancewiththeobservationsof
Reiprich& Bo¨hringer(2002),Prattetal.(2009),andVikhlinin
etal.(2009),withintheirconfidencelimits. Inthemarginalisa-
tions of the constraintswe allowed for a 7% uncertaintyin the
slopeofthescalingrelationandanuncertaintyof14%initsnor-
malisation(equivalenttothemasscalibration)as1σconstraints
Fig.1. Constraints on the cosmological parameters Ω and σ
oftheseparameters.Formoredetailsonthemarginalisationsee m 8
from a model fit to the observed REFLEX II X-ray luminosity
Bo¨hringer et al. (2014a). In the final likelihood fit we do not
distribution. The curves give 1 and 2σ constraints for models
compare the luminosity functions directly, but the comparison
with M =0,M =0.4,andM =0.6eVforthesetofcontours
is made between the predicted and observed X-ray luminosity ν ν ν
fromupperlefttolowerright(black,red,blue),respectively.
distribution.TotheoreticallypredicttheX-rayluminositydistri-
bution,the X-rayluminosityfunctionhasto befoldedwith the
surveyselectionfunction,whichisalsodescribedindetailinour a fixed A normalisation.Theratiobetweenthese twoparame-
S
previouspaper. tersalsodependsonthematterdensity,Ω ,sincethemaximum
m
RecentliteratureforexamplebyCostanzietal.(2014)sug- ofthepowerspectrumshiftswiththisparameter.
gestedthatthegalaxyclustermassfunctionshouldbemodelled The parameter σ8 was originally designed to describe the
in a particular way in the presence of massive neutrinos. The power spectrum amplitude at cluster scale. Thus to first order,
suggestedmodificationconsistsofonlyusingthematterdensity ignoringsubtlechangesintheshapeoftherenormalisedpower
withoutneutrinos,ρm −ρν,intherelationofmassandfilterra- spectrum,thevalueofσ8fixestheclusterabundance.Therefore
dius to calculate the amplitudevariance, σ(M)2, of the density looking for the best-fitting σ8 for a given cluster abundance
fluctuations.Wetestedincludingthismodificationinourcalcu- meansinthemodellingthatpowerspectrafordifferentneutrino
lations and found that the results never changed by more than masses will be rescaled such that they all give a very similar
onepercent.Sincethisisanorderofmagnitudesmallerthanthe valueofσ8.Thisisreflectedintheconstraintsweobtainforthe
systematicuncertainties,wedidnotincludethemodificationat parametercombinationof Ωm and σ8 adoptingdifferentvalues
thisstage. of Mν , as shown in Fig. 1. The subtle changesin the shape of
thepowerspectrumcausesmallmovesintheΩ andσ param-
m 8
eter plane, but the changes are much smaller than the changes
4. EffectofneutrinosontheclusterX-ray of σ8 with neutrino mass for fixed AS. While the shift in σ8
from M = 0 to M = 0.6 eV in Fig. 1 is ∆σ = 0.04, it is
luminosityfunction ν ν 8
about∆σ =0.14forfixedA .FortheresultsinFig.1wehave
8 S
Beforewedescribethederivedcosmologicalconstraints,weex- consideredextremecases.Ifthepossiblerangeoftotalneutrino
ploretheeffectofneutrinosontheclusterabundanceandtheX- massesisinsteadabout0.06to0.2eV,weexpectdifferencesin
ray luminosity function of clusters. Neutrinos damp out large- themarginalisationresultssmallerthanthepresentmarginalisa-
scale structure during the evolution of the Universe inside the tion uncertainties,if we use the σ8-normalisationof the power
horizon scale as long as they are relativistic. Thus the greatest spectrum.
length scale for which we expect damping effects is approxi- Thereisalsohardlyanydistinctioninthegoodnessoffitbe-
matelythehorizonscaleattheepochwhentheneutrinosbecome tween the fits for different Mν. The likelihood changes by less
non-relativistic.Theycanonlydampafractionoftheamplitude than∆L = 1,whichiswellwithintheone-sigmaerrors.Taking
thatcorrespondstotheirfractionofthetotalmatterdensity. the cluster results alonethereforedoesnotyield a clear prefer-
If we fix the normalisation of the power spectrum at the ence fora neutrinomass in the mass rangeshown.A discrimi-
epoch of recombination with the parameter, A , the curvature nationcanbeobtainedbycomparingthiswiththeobservations
S
power spectrum normalisation at a scale of k = 0.05 Mpc−1, oftheCMB,whichwillbediscussedinthenextsection.
0
asdoneforthePlanckpowerspectrum,weseethatthepresent
epochpowerspectrumisdepressedatsmallscalesbelowawave
5. ComparisonwiththePlanckCMBresults
vectorofabout0.014h Mpc−1 andthedepressionisstronger
70
thelargerM .Theregimethatisrelevantforclusterformationis To compare the present constraints with the Planck results,
ν
inthedepressionregion.Thisisalsotheregioninwhichthepa- we chose a power spectrum normalisation that is applicable in
rameterσ isdetermined.Thereforeweexpectthatthepresent- the same way to both surveys. For this reason, we used the
8
dayvalueforσ willchangewithchangingneutrinomassesfor parameter, A , the normalisation of the dimensionless curva-
8 S
ture power spectrum, to normalise the power spectrum for the
3 CAMB is publicly available from clusterabundancecalculation,sincethisparameterisalso used
http://www.camb.info/CAMBsubmit.html to normalise the power spectrum for the Planck data analysis
3
Bo¨hringeretal.:REFLEXIIcosmologyconstraintswithmassiveneutrinos
Fig.2.Constraintson A andσ fromtheREFLEXIIX-raylu- Fig.3.Marginalisedconstraintsfortherescaledparameterσeff
s 8 8
minosityfunctionforvaluesofM =0,0.17,0.4,and0.6eVfor and Ω for values of M = 0, 0.06, 0.17, 0.4, and 0.6 eV for
ν m ν
thecontoursfrombottomtotop,respectively.Thecontoursgive thecontoursfrombottomtotop,respectively.Thecontoursgive
the1and2σconfidenceintervals.Wealsoshowtheconstraints the1and2σconfidenceintervals.Wealsoshowtheresultofthe
derivedfromthePlanckCMBobservations(datapointwith1σ PlanckCMBobservationsasdatapointwith1σerrorbars.
errorbars).
with a neutrino mass of about M = 0.58(±0.2). We caution,
ν
however, not to interpret this result too quickly as a constraint
(Planck Collaboration 2013a). With this parameter we calcu-
ontheneutrinomassesbecauseitmightinprinciplealsobethe
lated the matter power spectrum for the present epoch, folded
resultofsystematicuncertaintiesandcalibrationproblems.But
it throughthe structureformationmodellingandfitted it to the
the results definitely illustrate the power of combiningthe two
observed REFLEX X-ray luminosity function. In this way, we
cosmologicalprobestodeterminetheneutrinomasses.
derivedconstraintsoncosmologicalparametersin the Ω - A
m S Most illustrations in the literature show constraints for the
plane as displayed in Fig. 2. The plot shows the marginali-
σ −Ω diagram. This was also made for the cluster analysis
sation results for four different total neutrino masses, M = 8 m
ν of the clusters detected through the Sunyaev-Zeldovich effect
0,0.17,0.4,and0.6eV. As forthe Ω - σ constraints, the two
m 8 withPlanckincomparisonwiththePlanckCMBresults(Planck
parametersaresomewhatdegenerate.SimilartothedatainFig.
Collaboration2013b).Thereforewetriedtofindawaytotrans-
1,thelikelihoodsoftheminimaforthedifferentcontoursetsfea-
latethedatashowninFig.2intoaplotofσ −Ω constraints.
tureadifferencelowerthan∆L≤1.Thuswithin1σuncertainty 8 m
This can be achieved by translating the Ω - A results into a
limits,wecannotdistinguishthegoodnessoffitbetweenthedif- m S
σ −Ω constraintinarepresentationthatkeepsthevalueofM
ferent models. Taking the cluster data alone, all these neutrino 8 m ν
fixedto0.06eV.Thisisanalogousto ananalysisofcosmolog-
massesarepossible.
icaldata asa functionofthe Hubbleparameter,butchoosinga
In Fig. 2 we compare the cluster constraints with the con-
representationinwhichtheresultsaretranslatedintoacosmol-
straints from the analysis of the power spectrum of CMB
ogywithafixedvalueforH .Weachievedthisbyusingforσ
anisotropiesseenbyPlanck(PlanckCollaboration2013a).The 0 8
notthevaluewewouldmeasureatpresentforthegivencosmol-
Planckdata pointthatrepresentstheresultsforPlanck+WP in
ogy and M value, but instead we used a new parameter,σeff,
Table2ofPlanckCollaboration(2013a)isshownwith1σerror ν 8
theσ valuethatwouldbepredictedonthebasesoftheA nor-
bars.ThePlanckresultshavebeenderivedforacosmologywith 8 s
M = 0.06eV,whilethevaluefor M wasvariedforthecluster malisation and the cosmological model used for the best fit of
ν ν
thePlanckresultswithh = 0.673,Ω = 0.315and M = 0.06
constraints.WecheckedthattheCMBpowerspectrumdoesnot m ν
eV.Thenewparameterisgivenby
vary in any significant way with a variation of M in the con-
ν
sideredrangeforfixed A . Thereforethe clusterconstraintsfor
s σref
differentvaluesof Mν canbecomparedwithonerepresentation σeff =σtrue× 8 , (2)
ofthePlanckdatainthisplot.Thetiltofthecrossoferrorbars 8 8 σmod
8
forPlanckfollowstheshapeoftheerrorellipse.Itsorientation
is taken from the errorellipse shown in Fig. 11 of the publica- where σref is the value from the Planck cosmology refer-
8
tionbythePlanckCollaboration(2013b)andconvertedfromthe encemodelforfixed A andσmod thevalueforasimilarmodel
Ωm−σ8 totheΩm -AS representation. withthecorrectvaluefosrMνan8dthesameAs.Theresultingplot
Formally,thetwodatasetscanbereconciledforatotalneu- is shown in Fig. 3. The position of the Planck data point with
trino mass in the range Mν = 0.45(±0.28) eV including the respecttotheclusterconstraintcontoursisequivalenttothesit-
combined 1σ uncertainties of both data sets (in a conservative uationinFig.2,andtheorientationoftheerrorellipsehasbeen
way with a direct addition of the errors instead of a Gaussian takenintoaccount.Theplotshowsthatthesamerelativelocation
addition). 4 A similar conclusion was reached by the Planck oftheerrorcontoursandthustheconclusionsontheconstraints
Collaboration(2013b):clusterandCMBdatacanbereconciled onM arethesameasgainedfromFig.2.
ν
4 The numerical values were obtained from the relative location of inFig.2.Forthisevaluation theexactorientationof thePlanck error
theerrorellipsesdeterminedonafinergridofM values,thanasshown ellipseiscrucial.
ν
4
Bo¨hringeretal.:REFLEXIIcosmologyconstraintswithmassiveneutrinos
6. Summaryandconclusion Acknowledgements. H.B. and G.C. acknowledge support from the DFG
Transregio Program TR33andthe Munich Excellence Cluster ”Structure and
Based on the REFLEX II galaxy cluster survey and its well- EvolutionoftheUniverse”.G.C.acknowledgessupportbytheDLRundergrant
definedX-rayluminosityfunction,we derivedtightconstraints no.50OR1405.
on the cosmologicalparametersσ and Ω and studied the in-
8 m
fluenceof massive neutrinoson these results. Within the limits
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and Hasenkamp (2013) found a similar tension in a massless Seljak,U.,Slosar,A.&McDonald,P.,2006,JCAP,10,14
neutrino cosmology for the combination of CMB and clusters Tinker,J.,Kravtsov,A.V.,Klypin,a.,etal.,2008,ApJ,688,709
as well as CMB and cosmic shear. In their analysis, they only Tru¨mper,J.,1993,Science,260,1769
Viel,M.,Haehnelt,M.G.,Springel,V.,2010,JCAP,6,15
investigated sterile neutrinos because these simultaneously de-
Vikhlinin,A.,Kravtsov,A.V.,Burenin,R.A.,etal.,2009,ApJ,692,1060
creasethetensionintheresultsfortheHubbleconstant,andthus Voges,W.,Aschenbach,B.,Boller,T.,etal.1999,A&A,349,389
their resultis notdirectly comparablewith ours.Both Hamann Zhao,G.-B.,Saito,S.,Percival,W.J.,etal.,2013,MNRAS,436,2038
and Hasenkampand Costanziet al. (2014)pointedoutthatthe
strongestdriverforapositiveneutrinomasscomesfromclusters.
Since ourresults on the cluster abundanceare amongthe most
precise results, they will contribute to the strongest constraints
forthetotalneutrinomass.
Wehereonlyconsideredclassicalneutrinos.Themaindriver
to includesterile neutrinosin recentpublications(e.g.Hamann
andHasenkamp2013)isthedifferenceontheHubbleparameter
measured by Planck and locally with calibrated distance indi-
catorssuchastheCepheides.We haveshownina recentpaper
using our cluster data that there are indications that we live in
a locally underdense region of the Universe in which one ex-
pects the Hubble parameter to be locally higher (Bo¨hringer et
al. 2014b). It is worth noting that this can resolve some of the
tension between the local and global measurementof H . This
0
also makes the results with massive non-sterile neutrinosmore
attractive.
The present marginalised constraints from the galaxy clus-
ter data take the uncertaintiesin the scaling relations, the most
serious bottle-neck preventing us from deriving tighter con-
straints,intoaccountinafairlyconservativeway(Bo¨hringeret
al.2014a).Mucheffortiscurrentlymadetobetterconstrainthe
X-ray scaling relationsof galaxyclusters with deeper observa-
tions of well-selected cluster samples with XMM-Newton and
Chandraandtoimprovetheclustermasscalibrationwithweak-
lensing studies. For the Planck data intense calibration efforts
areongoingaswell.Wethereforeexpectasignificantimprove-
mentoftheunderstandingofthesystematicsinthenearfuture,
whichwill allow usto exploitthefullpotentialof the observa-
tionaldata.
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