Redshift-distance relations from type Ia supernova observations. New constraints on grey dust models

0.57 MB·English

by  A. R. Robaina

Astronomy&Astrophysicsmanuscriptno.Robaina˙Cepa˙2006 c ESO2008
(cid:13)
February3,2008
Redshift–distance relations from type Ia supernova observations
New constraints on grey dust models
AdayR.Robaina1,2,⋆ andJordiCepa2,3
1 FacultaddeF´ısica,UniversidaddeLaLagunaE-38071,LaLaguna,Tenerife,Spain
e-mail:[email protected]
7
2 InstitutodeAstrof´ısicadeCanariasE-38200LaLaguna,Tenerife,Spain
0
3 DepartamentodeAstrof´ısica,FacultaddeF´ısica,UniversidaddeLaLaguna.E-38071LaLaguna,Tenerife,Spain
0
e-mail:[email protected]
2
n Received28March2006;accepted03August2006
a
J ABSTRACT

0
Extinctionduetointergalacticgreydusthasbeenproposedasanalternativetoacceleratedexpansiontoaccountforthedimmingof
1
SnIafluxesbeyondz 0.5.The“replenishing”greydustmodel,althoughfittingtheobservationaldata,doesnotseemtobebasedon
physicalassumptions.≃Forthisreason,inthispaperweproposeanewgreydustmodelwhosedustdistributionfollowsthecomoving
2
SFRdensityevolution,areasonablyestablishedphenomenon.Thisnewmodeliscomparedwiththeupdatedphotometricdatasample
v
fromtheHighZSupernovaSearchTeam(HZT).Also,usingpairsofsupernovaeatdifferentredshifts,thepossibilityofany“patchy”
9
distributionproposedtoexplainthediscrepanciesbetweenthe“highz”dustmodelandtheSnIaobservationsatveryhighredshift
5
(z 0.9)isruledout.Finally,thedataarecomparedwithdifferentmodelswithandwithoutdarkenergyandabestfittoauniverse
2 wit≥hadimensionalparametersΩ = 0.31andΩ = 0.69isobtained,fromwhichanageoftheuniverseoft 14.6 109 years
1 isderived.Thisageiscompatiblem0withtheageofΛt0heglobularclustersusinganequationofstateω= 1andit0o≃bviates×theneedto
0 −
resorttoanykindofphantomenergy.
7
0 Keywords. cosmology:distance–redshift–supernovae–dust
/
h
p
- 1. Introduction itseffectscanbefoundin,forexample,Bianchi&Ferrara2005;
o
Inoue&Kamaya2003;Nath,Sethi&Shchekinov1999).
tr After the discovery by Riess et al.(1998) and Perlmutter et Inanycase,greydustmodelsimplyuniverseswithΩ =1
s al.(1999)oftheexcessiveweaknessoftypeIasupernovae(SnIa m0
a or non-Euclidean geometries. The first possibility can be dis-
) at high redshift, cosmology has undergonea revolution simi-
: carded by the 2dF experiment(Peacock et al. 2001),while the
v lartothecosmicmicrowavebackground(CMB)discovery.The
secondcanberejectedbyanalysisoftheanisotropiesobserved
i cosmologicalinterpretationoftheseobservationsledtothepos-
X intheCMB(Spergeletal.2003),fromwhichatotalparameter
tulation of the accelerated expansion of the universe as a con- Ω=1isderived.
r
a sequenceofa“darkenergy”ofnegativepressureandunknown Apart from grey dust models, another effect that could
origin.Giventhedifficultphysicalinterpretationofthisdarken-
hamper the need for an accelerated expansion universe to ex-
ergy, either in terms of a cosmological constant, quintessence,
plainSnIadataistheirluminosityevolution.Observationalevi-
orevensomeformofphantomenergy,severalmechanismshave
denceshowsSnIaluminosityvariationswith galacticmorphol-
beenproposedtoexplainSnIaobservationswithoutresortingto
ogy(Hamuyetal.1996,2000;Branchetal.1996;Reindletal.
anacceleratedexpansion.Amongthemaremodelsofintergalac-
2005),whilesometheoreticalstudies(Hoflichetal.1998,2000)
ticgreydust,whichtrytoexplainthedimmingoftheobserved
suggest that SnIa luminosity could have some dependence on
brightnessatz 0.5byassumingthatanabsorbentmediumex-
redshift. Were this true, this would question the status of stan-
≃
ists in intergalacticspace whose extinctiondoesnotdependon
dard candle for this kind of objects. In any case, these studies
wavelength.Thesedustmodelshavebeendriventoevolveatthe
arebeyondthescopeofthisarticleandaremerelymentionedas
samerateasthedatasuppliedbySnIateams.
further possibilities in addition to grey dust models in order to
Thefirstmodels,proposedbyAguirre(1999a,1999b),were avoidacceleratedexpansion.
based on both a model of dust formed by carbon needles and Inthispaperwepresentobservationalevidencetorefutethe
a Draine & Lee dust model (Draine & Lee 1984), obtaining a high-zgrey dust modeleven in the case of patchydistribution.
density parameter of ΩDust 10−5. Also, Goobar, Bergstrom Wealsoproposeanewgreydustmodelwithadensitydistribu-
∼
&Mortsell(2002)havedevelopedamodelofintergalacticdust tionfollowingthatofthestarformationrate(SFR)density.This
whoseeffectsonthedistancemodulusvs.zareindistinguishable SFR-baseddistributionisbasedonobservationaldata,thusmak-
fromthosecausedbyaΛCDMuniversewithΩm0 0.3,ΩΛ0 ingthegreydustmodelbasedonphysicalassumptionsthatbest
≃ ≃
0.7(moreinformationontheintergalacticmediumamountand fits the supernova data. In Sect. 2 we give an overview of ex-
istingtheoreticalgreydustmodels,includinghigh-zandthere-
⋆ Currently at the Max-Planck-Institut fu¨r Astronomie, Heidelberg, plenishinggreydust.InthissectionthenewSFR-baseddistribu-
[email protected] tionmodelisalsodeveloped.InSect.3wederivethedust-free
2 AdayR.RobainaandJordiCepa:Redshift–distancerelationsfromtypeIasupernovaobservations
modelbybest-fittingtheSnIadata,obtainingitsdensityparam- mechanismsforpreferentialejectionofgreydustfromthegalax-
etersandtheageoftheuniverse,andcomparethedatawithdust ies and the temporal scale on which it could have been homo-
models, includingthe one developedhere. We also explorethe geneously distributed, are explained. They are partly corrobo-
possibilityofreconcilingtheobservationaldatawiththehigh-z rated by the work of Renzini (1997) on the metallicity of the
dust modelby means of a patchydust distribution. Finally, we intracumular gas. Nevertheless, it is difficult to explain how a
drawourconclusionsinSect.4. dustdistributionformedbybaryonicmattercanescapefromthe
baryoniclarge-scalestructuresobservedintheuniverse.Aguirre
himself(1999a)suggeststhatthestudyofsystematicdifferences
2. Theoreticalmodels betweenthefluxreceivedfromSnIahostedbyfieldandcluster
galaxiescoulddistinguishbetweenauniverseinacceleratedex-
The existenceof greydustwould havean enormousimpacton pansionandaneffectduetogreydust,respectively,byrestricting
the analysis of the High Z SupernovaSearch Team (HZT) and implicitlythehomogenitytotheintracumularspace.
the Supernova Cosmology Project (SCP) observations, return-
ingthestandardmodeloftheuniversetothepointwhereitwas
before1998withtheircontradictionsoftheCMBanisotropyex- 2.2.Replenishinggreydust
periments, which point to a flat universe (Ω = 1). This is the Asdifferentsurveysreachedmoreandmoredistantredshifts,it
reasonadetailedstudyofthedifferentpossibilitiesisrequired.
becameevidentthatthehigh-zdustmodelwasunabletoexplain
Anyintergalacticdustmodelproducinggreyextinctionrel- the data. However, the reasonable values obtained by Aguirre
evanttothestudyofSnIaobservationsmusthavethefollowing (1999a,1999b)forthe timescale ofthe expulsionmechanisms
characteristics: ofhisgrainmodelshavepromotedthebirthofnewmodelsthat
fitthedatamuchbetter.Agoodexampleisthereplenishinggrey
1. Large grain size, to account for the achromaticy of the ab- dustmodel,proposedbyGoobar,Bergstrom&Mortsell(2002),
sortion and to comply with the mechanism of preferential whosematchtothedataisatleastasgoodastheΩ ,0models.
Λ
destructionofsmallersizegrains(Aguirre1999b). This replenishing grey dust model is based on a grey dust
2. An efficient expulsion mechanism in the galaxy where the extinctionthatfollowsadensitydistributionoftheform:
grainsareformed.Itmustexplainwhyonlythistypeofdust
ρ =ρo (1+z)a, (2)
isfoundintheIGM. dust dust
3. Coherencewiththeexpectedmetallicityoftheintergalactic where
medium.
3 ifz<0.5
4. Thedustdistributionmustbebasedona hypothesisin turn a=
basedonreasonablyestablishedphysicalobservables. (0 ifz>0.5.
Thismodelrequiresextremelyefficientformationandexpulsion
of the dust in the range z > 0.5 so that the dilution due to the
2.1.High-zgreydust
expansionof the universe is exactly compensatedby the metal
Even though Aguirre’s (1999a, 1999b) high-z dust model im- formationingalaxiesanditsfurtherremoval.However,thisbe-
pliesauniformdustdistributionsimilartothatofnon-relativistic haviourisnotconsistentwiththecurrentknowledgeoftheover-
matter, allstarformationepisodesthattookplaceintheuniverse.Asa
consequence,a physicalexplanationofthisreplenishingmech-
ρ =ρ0 (1+z)3, (1) anism is still lacking. Moreover, the hitherto unjustified sharp
dust dust transition from a = 0 to a = 3 represents a dramatic end of
metalformationandexpulsionfromthegalaxywithoutatransi-
which fulfils the first three of the four requirementsmentioned
tionera.
above,thelatestresultspublishedbytheHZT(Riessetal.2004),
withSnIadatabeyondz=1.5,almostcertainly(atthe4σlevel)
reject the possibility of this high-zdust model. Figure 1 shows 2.3.SFR-basedmodel
the largedeviationof the Aguirre (1999a,1999b)modelin the
To avoid these features of the replenishing dust model, a grey
high-zregioncomparedtotheexperimentaldataandthebestfit.
dustmodelbasedonthestar formationrate(SFR)densityevo-
However a patchy dust distribution could render this con-
lutionisproposedhere.Itwillbeshownthattheproposedmodel
clusion unsound. If the intergalactic dust distribution were not
fits the existing SnIa data equally well, while at the same time
homogeneous,itmightbepossiblethatthelightcomingfroman
providinga dustproductionbased onthecurrentknowledgeof
SnIaathighredshift(z 0.9)propagatesthroughmoreorless
≥ starformationevolutionintheuniverse.
absorbentmedium,dependingonthesourcepositioninthesky.
FollowingtheresultscompiledbyTaniguchietal.(2005)on
The deviation of the observeddata fromthe high-zdust model
the comoving SFR density evolution (Figure 2), it can be ob-
would then be due to a bias produced by the grey dust, leav-
served that the comoving SFR density (ρc ) is approximately
ingthemagnitudeoftheabsorbedsupernovaebelowthedetec- SFR
constantintherange1 z 2.Intheregion0<z<1,theSFR
tionlimitofcurrenttelescopes.Inthiscase,thesampleobserved ≤ ≤
densitymaybereasonablyrepresentedbyasimplerelationwith
at very high redshiftwould belongto the groupof SnIa whose
redshift,withlowerSFRatrecenttimes.Forsimplerdescription,
optical path has not been very affected by the aforementioned
theSFRdensitycurveisthenrepresentedbythesetworegimes.
absortion, and for this reason its apparentbrightness would be
For our purposes this simple parameterization is adequate, but
higher than that inferred by supposing a completely homoge-
seeOda&Totani2005formorecomplexparameterization.
neousdustdistribution.
Inthiscontext,thecomovingSFRdensityisrepresentedby
The inhomogeneity in the grey dust distribution is a solid
enough possibility to take it into account in spite of Aguirre’s 101+z if 0<z<1
ρc ∝
(1999a, 1999b) arguments. In his theoretical study, possible SFR (constant if 1<z<2.
AdayR.RobainaandJordiCepa:Redshift–distancerelationsfromtypeIasupernovaobservations 3
10−1 3. Results
3.1.Cosmologicalconstraints
)
−3 InthisworkwehaveusedthelatestpublishedHZTdata(Riess
c
p 10−2 et al. 2004; Strolger et al. 2004), since it represents the most
M
1 significantsamplewithphotometricvaluestodate.Thissample
−r hasgreatlybenefitedfromtheresultsoftheGreatObservatories
y
M Origins Deep Survey (GOODS) project, carried out using the
7 Advanced Camera for Surveys (ACS) on board the Hubble
h0. 10−3 Space Telescope (HST). The SnIa classification in the groups
(
R Gold, Silver, and Bronze used is explained in full detail by
F
ρS Strolgeretal.(2004).ThemostcertainclassificationistheGold
class,characterisedbyaclearspectroscopicconfirmationofthe
10−4 supernovatype.
0 1 2 3 4 5 6 7 In this section, the observationaldata are fitted by a model
composedofnon-relativisticmatteranddarkenergy,neglecting
z
the contributions of radiation and relativistic matter, which do
Fig.1. Comoving ρ as function of redshift. Figure taken from not play a significant role in the universe in the redshift range
SFR
Taniguchietal.(2005) considered.The magnitudeused for the fit is based on the dis-
tancemodulus,
m M =5logD +25, (4)
L
−
TheevolutionoftheSFRproperdensity(ρp )is
SFR where m and M are the apparent and absolute magnitudes, re-
spectively,andD istheluminositydistanceinMpc.Assuming
z ρc (1+z)1/2 L
ρp (z)∝ SFR· dz, (3) a flat geometry, as derived from the spectra of the CMB
SFR Z a3 H anisotropies, we have obtained, via an χ2 criterion, the best fit
zi 0· 0 with the parametersΩ = 0.31and Ω = 0.69,values simi-
m0 Λ0
wherea isthescalefactoratpresentandthevaluetakenforH lar to those found in previousstudies (Riess et al. 1998, 2004;
0 0
is65kms 1Mpc 1. Perlmutter et al. 1999),and consistentwith those derivedfrom
− −
2dFresults(Peacocketal.2001).
Nevertheless,althoughthedustdensityderivesfromtheSFR
These values are only indicative, given the fit dependence
evolution,notall thedustescapesfromthegalaxytothe IGM.
withtherejectingcriterion.InFigure2weshowtheHubbledi-
Atleastafractionofthemetalsproducedwillberetainedinlow
agramoftheentiresample,togetherwiththebestfitfound.
mass stars that never reach the core collapse supernova phase
and do not present strong stellar winds. An estimate of the re-
tained metal fraction can be obtained from the Salpeter initial
massfunction(Salpeter1955)from0.1 M to8 M .ThisSFR-
baseddistributionwilltheninclude,asexpl⊙ainedab⊙ove,atransi-
tionatz 1betweenthetworegimesofmaximumanddecreas-
≃
ingSFR:
ρ0 √π Erfi √1+z√ln10 + 101+z√1+z ifz<1
ρdust ∝ dust1(cid:18)− 2ln103/2 (cid:16) (cid:17) ln10 (cid:19)
ρ0dust2 23(1+z)3/2 ifz>1.
 (cid:16) (cid:17)
Theconstantsρ0 ,andρ0 ,whichincludetheestimationof
dust1 dust2
metals retained in low mass stars, must be fitted in the region
(0 < z < 1) to match the expected deviation at z = 0.5, while
they are chosen to guarantee the continuity of the curve in the
regionz>1.
Althoughthedustisproducedbythestarformation,therel-
evantphysicalmagnitudetoevaluateistheopacity,nottheSFR.
Theresultingextinctionisthendelayedwithrespecttodustpro-
duction owing to the time interval elapsed from production to
insertion into the IGM. This delay can be estimated from as-
sumptionsforthevelocityoftheejecta. Fig.2. Hubblediagram.DistancemoduliofobservationalSnIadatavs
z.OverplottedaretheΩ = 0.31,Ω = 0.69universe,whichisthe
Inordertofulfiltheabove-mentionedrequirements,thisgrey m0 Λ0
bestfitforaflatcosmologyobtainedfromχ2statistics.
dust model must present grain characteristics similar to those
proposed in previous models, reproducing the expected values
for R and absorptions (Goobar, Bergstrom & Mortsell 2002).
v
Finally,theinjectionmechanismandthepreferentialdestruction Itisworthnotingthatthesevaluesofmassanddark-energy
of small size grains will be assumed to be those discussed by density parameters, assuming a Hubble constant of 65 km s 1
−
Aguirre(1999b,2001). Mpc 1,yieldanageoftheuniversearoundt 14.6 109years
− 0
≃ ×
4 AdayR.RobainaandJordiCepa:Redshift–distancerelationsfromtypeIasupernovaobservations
asderivedusingCepa(2004),withtheconstraintω= 1forthe
−
equation of state of dark energy(i.e. a cosmologicalconstant).
This result is very nearly compatible with the globular cluster
ageof12.9 2.9GyfoundbyCarrettaetal.(2000)anditstimeof
±
formation,withoutresortingtoa phantomenergy(Cepa2004),
althoughtheerrormarginisstilltoolargetodeterminetheequa-
tionofstateofthedarkenergy.
3.2.Thenewdustmodel
The SnIa weakness at z 0.5 and their excess brightness at
≃
z > 0.5,representingthetransitionfromanacceleratedtoade-
celerateduniverse,are best appreciatedby representingnotthe
distancemodulibutthedistancemodulidifferenceswithrespect
totheemptyMilne’suniverseinconstantexpansion.
Thegreydustmodelsarerepresentedasthedistancemoduli
of a flat universe with Ω = 1, Ω = 0, with an atenuation
m0 Λ0
obtainedby
Fig.3.AveragedSnIadataandtheoreticalmodelsshowingthemodu-
z
lusdifferenceofdistanceswithrespecttoauniverseinconstantexpan-
∆m = 2.5log exp C ρ (z)r(z)dz (5)
dust − (cid:26) (cid:16) Z0 dust (cid:17)(cid:27) sion(Ω=0).Thehigh-zdustmodelisrejectedat4σ(dashedline).The
bestfitisgivenbyanΩ =0.31,Ω =0.69universe(solidthinline)
mo Λo
withnogreydustcontribution.TheSFR-baseddustmodelrepresented
wherer(z)isthecomovingdistancetravelledbytheSnIalight, takesintoaccountadelayof2.7Gybetweenthedustformationinthe
ρ (z)isgivenbyequations(1),(2)or(3),andC isaconstant diskanditshomogeneousdistributionintheIGM.
dust
usedfordimensionalpurposes.
In the case of the SFR-based dust model proposed in the
3.3.Furtherevidenceagainsthigh-zgreydust
presentwork(3),itwillbenecessarytoincludeadelaybetween
dustformationanditsincorporationintotheIGMtocontribute It might be argued that a non-homogeneous grey dust distri-
totheobservedextinction.Toestimatethetimeintervalinwhich bution could produce the deviation from the experimentaldata
the dust ejected could reach a homogeneousdistribution in the compared to Aguirre’s model. According to this hypothesis,at
intraclusterspace,weassumeanexpulsionvelocityforthedust highredshiftsonlytheSnIawhoselineofsighttotheobserver
grains of around 1000 km s 1, following Aguirre et al. (2001) passes through more voids (in other words: whose “beam” is
−
and Shustov & Vibe (1995). A delay of ∆t 3 109 years is emptier) can be observed,since the othersare too absorbedby
obtained,implyingthatthehomogeneityofth≈edu×stproducedat thedust.Inthisway,distantSnIaarebrighterthanexpectedac-
z 1isreachedaroundaredshiftof0.3<z<0.4. cordingtothehigh-zdustmodel,lyingsomewherebetweenthe
≃Figure3showsthedifferentuniversemodels,togetherwith high-zgreydustandtheΩm0 = 1model,wherethedatapoints
theweightedaveragedata.Fromthisfigureitcanbeconcluded arelocated(Figure4).
thatthehigh-zdustmodelcanbediscardedtoaconfidencelevel Toevaluatethefeasibilityofthishypothesis,theSnIasample
of 4σ for a homogeneousdust distribution. Also, it can be ob- issearchedforclosepairsofSnIawith verydifferentredshifts,
servedthatthedifferencesbetweentheΩ =0.31,Ω =0.69 in whichthe low z (z 0.5)memberof the pairis fainterthan
m0 Λ0 ≃
universeandthereplenishingdustmodelarealmostnegligible. expectedfromtheMilnemodel,whilethehigh-zone(z 0.9)
≥
Finally, the differences between our model with respect to the isnot.Weresuchapairtobefound,itshouldbeconcludedthat
SnIa data are smaller than 1σ. As discussed in 2, the advan- inhomogeneitiesinthehigh-zgreydustmodelcannotbedeemed
tageofthenewmodelisthatthedustdistributio§nderivesfrom responsiblefortheobservedSnIadistancemodulusdistribution.
currentobservationalevidence. Assuminga Robertson–Walkermetric, the angle subtended
byanobjectinaflatuniverseis
InFigure4theentiresampleofphotometricdatafromSnIa
is shown superposed on the theoretical models considered so D (z)
far. It can be seen that the error bars of individual photomet- θ= T , (6)
D (z)
ricdataincludeboththeSFR-baseddustandthe‘replenishing’ P
dustmodels.Thismodelisquiteflexible:theambiguityincur- whereD isthetransversaldistanceandD theproperdistance.
T P
rentcosmicstarformationhistorystudies(expulsionvelocities, Fromthisequation,andassumingacosmologicalmodel,thean-
delaytimesandSFRcurveparameterization)doesnothaveabig glecorrespondingtoatransversaldistancecanbeevaluated.
impactonourresults,especiallyiftheconstantsareempirically Tominimizethe influenceofphotometricandmodelerrors
fittedasexplainedinSect.2.3. whenapplyingthistest,itisconvenienttolookforapparentSnIa
In all these universe models (the grey dust ones), we have pairsofverydifferentredshifts,ofwhichtheSnIaatlowzshow
assumed a flat geometry with Ω = 1.0, but this assumption the highestbrightnessdimming.This maximumSnIa dimming
m0
contradicts the results of 2dF (Peacock et al. 2001). For this isobservedaroundz = 0.5(Riessetal.1998,2004;Perlmutter
reason we have also developed an open universe (Ω = 0.3, etal.1999).Assumingacharacteristicsizeof30Mpcforavoid,
m0
Ω =0.0)withSFR-baseddustwhosedifferencesarelessthan theanglecorrespondingtothisdistanceatz=0.5willrepresent
Λ0
1σ comparedto the SnIa data (Figure 5 ). The implicationsof the highest projected angular distance to search for a suitable
thisopenuniversewillbediscussedinSect.4. pairtoapplythistest.Thisisaratherstringentrequirementsince
AdayR.RobainaandJordiCepa:Redshift–distancerelationsfromtypeIasupernovaobservations 5
Fig.5. Differences withrespect to anempty universe. Theflat (thick
line)andopen(dashedline)SFR-baseddustuniversemodelsarewithin
the1σconfidencelevel.
1. The two members of the candidate pair have to be in the
ranges0.35<z<0.65forthelowzandz 0.9forthehigh
≥
z, respectively. This requirement maximizes the difference
inbrightnessofthepairmemberstoreducethecontribution
fromphotometricerrorsasmuchaspossible.
2. For the same reason, the difference in redshift between the
membersofthepairmustbe∆z 0.4.
≥
3. Theangulardistanceontheskybetweenthetwomembersof
thepairmustbelowerthanthevalueof 1degreeassumed
≃
inTable1.
4. Bothsupernovaemustbeclassifiedwiththemaximumcon-
fidenceastypeIa.Thisrequirementrestrictsthesearchtothe
Goldsample.
ForsuchasmallSnIasample(157SnIa)itmightseemdif-
Fig.4. Top: AsinFigure 3, but representing the whole SnIasample. ficulttofulfiltheserequirements.Luckily,thesystematicsearch
TheSFR-baseddistributionfitsthedata withinthe error barsof indi-
forhigh-zsupernovaehascentredonspecificregionsofthesky,
vidualdata.Bottom:Detailofthe0<z<0.7region.
mainlyontheGOODSprojectHDFNandCDFSfields.Thesky
distribution of the SnIa sample is represented in Figure 6. The
a void size of 30 Mpc is smaller than those found by Einasto whole sample is shown in the leftpanel, while on the rightthe
et al. (1994). From their data, an average diameter of around SnIa found in the HDFN are shown, demonstrating the small
distancesthatseparatetheSnIainthesedeeplystudiedregions.
Φ 91Mpcisdeduced.InTable1,theanglescorresponding
void ≃ Table2summarisestheresultsofourstudyfordifferentcos-
to this distance at z = 0.5 for different models of universe are
mologies.Here,alltheSnIaat0.35 z 0.65thataremembers
shown.
≤ ≤
ofapairareweakerthanexpectedinanemptyuniverse.Arela-
tivelylargenumberofpairsisfound,consideringthatthewhole
Ω Ω θ sampleiscomposedbyonly186SnIa.
m0 Λ0
0.3 0.0 0.9502
0.3 0.7 0.8451
4. Conclusions
1.0 0.0 1.0155
WiththeavailableSnIadatawehavecalculatedthebest-fitdust-
Table1.Valuesfortheangle(indegrees)subtendedbyaD of30Mpc
T freeuniversemodel,obtainingΩ = 0.31,Ω = 0.69.These
atz = 0.5indifferentuniverses,withtheassumedHubbleconstantof m0 Λ0
65kms 1Mpc 1. resultsareverysimilartothosefoundinpreviousstudiesoflu-
− −
minositydistancetotypeIasupernovae,leadingtoareconcilia-
tionoftheageofglobularclusterswith theageoftheuniverse
(t 14.6 109years,asderivedfromthemodel,whenassum-
0
≃ ×
Withthesehypotheses,therequirementstoapplythistestto ingacosmologicalconstant-likedarkenergy,ω= 1).Phantom
−
supernovaepairsarethefollowing: energiescanthusbeavoided,aslongasthemeanvaluesdonot
6 AdayR.RobainaandJordiCepa:Redshift–distancerelationsfromtypeIasupernovaobservations
Fig.6.LocationontheskyoftheSnIasample.Left:Positionofallthesupernovaeinthesample.Right:DetailoftheHubbleDeepFieldNorth
region.Theunitsontheaxisaredegrees.
Ωm0 ΩΛ0 z1 z2 Angle Gold(A) Silver(B) galaxies are underestimated by 20%, a parameter Ωm0 = 1 is
excludedfromtheacceptablemargins.Forthisreasonwe have
0.3 0.0 0.35-0.65 0.9 θ 15 5 includedan open modelΩ = 0.3, Ω = 0.0 with our SFR-
≥ m0 Λ0
0.3 0.0 0.35-0.65 0.9 θ/2 15 3
based grey dust attenuation. Although the confidence level of
≥
0.3 0.7 0.35-0.65 0.9 θ 15 5
≥ this model with respect to the SnIa data is below 1σ, it intro-
0.3 0.7 0.35-0.65 0.9 θ/2 15 2
≥ duces a serious conflict with the interpretation of the WMAP
1.0 0.0 0.35-0.65 0.9 θ 15 5
≥ results (Spergel et al. 2003). To reconcile this model with the
1.0 0.0 0.35-0.65 0.9 θ/2 15 3
≥ CMBanisotropiesexperimentitisnecessarytoresorttoexotic
Table2.NumberofSnIapairsfoundwithanangulardistancebetween mechanisms, such as thermalization of the radiation due to the
memberslowerthantheangleθgivenbyTable1forthecorresponding intracumulardustathighz.
cosmology.A:PairsinwhichbothmembersbelongtotheGoldsample. The high-z dust model is rejected out to 4σ even if the
B:AtleastoneofthemembersbelongtotheSilversample.
grey dust presents a patchy distribution, as shown by the pair
test devised here. However, most of the data at very high red-
shift corresponds to GOODS fields, which cover a small area
on the sky (Figure 5). Pairs at other positions on the sky com-
increase.However,theuncertaintiesintheageofglobularclus-
bined with high-accuracyphotometrywould allow us to ascer-
ters are still too greatto constrainthe equationof state of dark
tain whetherthereis anysignificantamountofgreydustin the
energy.
universe. Nevertheless, the consistency of the standard model
A new grey dust model based on replenishing dust but in-
and the weak basis for the alternative explanations makes the
cluding the observed comoving SFR density distribution has
possibilityofhavinganopenmodeldescribingouruniversedif-
been derived, thereby providing an alternative model based on
ficult.
observational evidence. The extinction produced by this new
SFR-based grey dust with Ωm0 = 1.0 is very close to the Acknowledgements. WewishtothankG.A.Tammann,A.TortosaAndreu,and
Ω = 0.31,Ω = 0.69modelwithnoextinction.Apartfrom A. M. Snchez Quintana for helpful comments. This work was supported by
m0 Λ0
the difficulties in providing the mass required for a flat uni- theSpanishPlanNacionaldeAstronom´ıayAstrof´ısicaundergrantAYA2005-
04149. This research made use of HZT SnIa photometric data, NASA’s
verseandtheageconflictarisingtherefrom,themodelswouldbe
Astrophysics Data System (ADS),and the Nasa/IPAC Extragalactic Database
distinguishedonly by future supernovaesurveysat high z with (NED).
higherphotometricaccuracy,suchasthosetobecarriedupwith
SNAP (Supernova Acceleration Probe) (Aldering et al. 2002)
and with the JWST (James Webb Space Telescope, Stockman References
etal.1998),whichcouldprovidetheevidencethatwillhelpto
AguirreA.N.1999a,ApJ,512,L19
decidebetweenacurrentlydarkenergy-dominateduniverseand AguirreA.N.1999b,ApJ,525,583
amatter-dominatedone.Moreover,thenextgenerationSnIasur- AguirreA.N.etal.2001,ApJ,561,521
veys,withmoreaccuratedata,willbeessentialbecausetheun- BianchiS.&FerraraA.2005,MNRAS,358,379
AlderingG.etal.2002,astro-ph/0209550
certainties in the current SnIa data, due to the contributionsof
BranchD.,RomanishinW.&BaronE.1996,ApJ,465,73.Erratum467
approximations,photometric errors, luminosity maximumesti- CepaJ.2004,A&A,422,831
mationsathighz,etc.,imposeseveralrestrictionsonthevalidity delPopoloA.2003,A&A,408,43
ofthecosmologicalresults.Onlywhencombinedwithotherex- DraineB.&LeeH.1984,ApJ,285,89
Einasto,M.etal.1994,MNRAS,269,301
perimentssuchasCMBanisotropiesorgravitationallensesisit
FujitaS.etal.2003,ApJ,586,L115
possibletoderivemorestringentconclusions. GoobarA.,BergstromL.&MortsellE.2002,A&A,384,1
All the flat grey dust models presented here consider HamuyM.etal.1996a,AJ,112,2391
Euclidean geometry with an adimensional mass parameter, HamuyM.etal.2000,AJ,120,1479
Ω = 1,ahypothesisagainstthedataobtainedsofar(Peacock HoflichP.etal.1998LIACo,34,243
m0 HoflichP.,NomotoK.,Umeda,H.&WheelerJ.C.2000,ApJ,528,590
et al. 2001). Even with the results of del Popolo (2003), who
InoueA.K.&KamayaH.2003,MNRAS,341,L7
hassuggestedthatcurrentΩm0 valuesobtainedfromclustersof NathB.B.,SethiS.K.&ShchekinovY.1999,MNRAS,303,1
AdayR.RobainaandJordiCepa:Redshift–distancerelationsfromtypeIasupernovaobservations 7
OdaT.&TotaniT.2005,ApJ,630,59
PeacockJ.A.etal.2001,Nature,410,169
PerlmutterS.etal.1999,ApJ,517,565
ReindlB.,TammannG.A.,SandageA.&SahaA.2005astro-ph/0501664
Renzini,A.1997,ApJ,488,35
RiessA.G.etal.1998,AJ,116,1009
RiessA.G.etal.2004,ApJ,607,665
SalpeterE.E.1955,ApJ,121,161
ShustovB.&VibeD.1995,Astron.Rep.,39,578
SpergelD.N.etal.2003,ApJS,148,175
StockmanH.S.etal.1998,ASPC,133,24S
StrolgerL.G.etal.2004,ApJ,613,200
TaniguchiY.etal.2005,astro-ph/0407542