DraftversionJanuary9,2012 PreprinttypesetusingLATEXstyleemulateapjv.5/2/11 DARKMATTERPOWEREDSTARS:CONSTRAINTSFROMTHEEXTRAGALACTICBACKGROUNDLIGHT A.Maurer,M.Raue,T.Kneiske,andD.Horns Institutfu¨rExperimentalphysik,Universita¨tHamburg,LuruperChaussee149,D-22761Hamburg D.Elsa¨sser Institutfu¨rTheoretischePhysikundAstrophysik,AmHubland,D-97074Wu¨rzburg and P.H.Hauschildt HamburgerSternwarte,Gojenbergsweg112,D-21029Hamburg 2 DraftversionJanuary9,2012 1 0 ABSTRACT 2 The existence of predominantly cold non-baryonic dark matter is unambiguously demonstrated by several n observations (e.g., structure formation, big bang nucleosynthesis, gravitational lensing, and rotational curves a of spiral galaxies). A candidate well motivated by particle physics is a weakly interacting massive particle J (WIMP). Self-annihilating WIMPs would affect the stellar evolution especially in the early universe. Stars 5 powered by self-annihilating WIMP dark matter should possess different properties compared with standard stars. While a direct detection of such dark matter powered stars seems very challenging, their cumulative ] emission might leave an imprint in the diffuse metagalactic radiation fields, in particular in the mid-infrared O partoftheelectromagneticspectrum.Inthisworkthepossiblecontributionsofdarkmatterpoweredstars(dark C stars;DSs)totheextragalacticbackgroundlight(EBL)arecalculated. Itisshownthatexistingdataandlimits . oftheEBLintensitycanalreadybeusedtoruleoutsomeDSparametersets. h Subject headings: dark ages, reionization, first stars – dark matter – infrared: diffuse background – stars: p - atmospheres o r t s 1. INTRODUCTION WIMPscandelayorevenpreventthenuclearhydrogenburn- a ing. Several independent observations provide compelling ev- [ Inprinciple,twomechanismscouldleadtodarkmatterac- idence for an accelerated expanding universe with a matter cretion into a star. The first one, investigated by Spolyar 1 content dominated by a non-luminous (“dark”) component v (ΛCDM cosmology). Relevant parameters for this so-called et al. (2008), is adiabatic contraction (AC) where additional 5 ΛCDM cosmology have been measured with high accuracy darkmatterfromoutsidetheformingfirststarisgravitation- 0 withWMAP(Komatsuetal.2011)andbaryonicacousticos- allypulledalongwithaccretingbaryonicgasontotheproto- 3 cillations surveys and will be further refined with upcoming star. Due to the very low surface temperature of the Dark 1 Planck data. Large sky surveys (e.g., SDSS Abazajian et al. Star compared to its enormous mass there should be no or . very little radiative feedback mechanisms preventing further 1 2009,2dFCollessetal.2003)andnumericalsimulationslike, accretion. The other possibility to replenish the dark matter 0 e.g., theMillenniumRun(Springeletal.2005)pointtoward inside a star is capture of WIMPs via scattering. The effi- 2 aconvincingpictureoflarge-scalestructureformationwithin ciency of this mechanism is depends on the product of the 1 the cosmological concordance model. A promising particle elastic scattering cross section between baryonic and dark : candidate for the dark matter (DM) content of the universe v matter and the surrounding dark matter density (Iocco et al. is the WIMP (weakly interacting massive particle; see e.g., i 2008; Iocco 2008; Freese et al. 2008a). Both mechanisms X Jungman et al. 1996; Bertone et al. 2005 for a review arti- canleadtogenericpropertiesoftheDS:lowsurfacetemper- cle). Such particles can naturally have annihilation or decay ar channelsleadingtostandardmodelparticles. atures(∼5000−10000K),highluminosities(∼106L(cid:12))and The epoch where the first stars form (z ∼ 30) is not yet presumably longer lifetimes than conventional Pop III stars. observable with today’s astronomical instruments. The cir- After a “dark phase”, the star evolves as a normal zero-age cumstances and mechanisms of stellar genesis are still top- main-sequencestar. ics of ongoing analysis and rely on sophisticated numerical Directdetection,evenofaDarkStarcluster,isachalleng- simulations (for a review see ,e.g., Bromm & Larson 2004). ingtaskwhichmayonlybepossiblewithfutureinstruments Recently, studiesdiscussedtheimpactofWIMPdarkmatter like the upcoming James Webb Space Telescope (JWST; ontheformationofthefirststars(Spolyaretal.2008;Iocco Gardner et al. 2006) and under the assumption of an opti- etal.2008;Iocco2008;Freeseetal.2008a).Duringtheepoch mistic model (Zackrisson et al. 2010). A different approach ofreionizationoftheuniverse,DMmayhaveaffectedthefor- for the search of emission in the early universe is to probe mationandevolutionofstars.Assumingthatself-annihilating thediffusemetagalacticradiationfield(MRF),see,e.g.,Raue particlesprovidethedarkmattercontentoftheuniverse,this et al. (2009). The optical to infrared part of the local MRF new source of energy injection into the first stars may alter is also known as extragalactic background light (EBL; for a their properties. The energy injection from self-annihilating reviewsee,e.g.,Hauser&Dwek2001). Itsmaincontribution comesfromintegratedstarlightandthermaldustemissionsof [email protected] all cosmic epochs (Kneiske et al. 2002, 2004; Stecker et al. 2 Maureretal. 2006;Franceschinietal.2008;Primacketal.2008;Gilmore as described in, e.g., Peebles (1993). Further details on the et al. 2009; Finke et al. 2010; Kneiske & Dole 2010). This methodandformulaeusedherecan,forexample,befoundin factmakestheEBLauniqueprobefortheintegratedstarfor- Kneiskeetal.(2002). mation history of the universe. There are different types of observational approaches to measure the EBL. Direct obser- DSspectrumwithPHOENIX:— The atmospheres and spectra vationse.g.,withtheDIRBEinstrumentonboardtheCOBE ofDarkStarsaremodeledwiththemodelatmospherepack- satellitesufferfromprominentforegroundemission, likezo- age PHOENIX, version 16. A basic description of the code diacallight,thatiscausedbyscatteredsunlightbydustinthe canbefoundinHauschildt&Baron(1999)andrecentappli- zodiacal cloud, and diffuse galactic radiation (Hauser et al. cationstostellarobjectscanbefoundinShort&Hauschildt 1998). Lower limits to the EBL are derived from integrated (2009) and inFuhrmeister et al. (2010). The current version galaxynumbercountswhichareavailableuptoaredshift≈2 16ofthePHOENIXpackage(Hauschildt&Baron2010)uses fromHubbleSpaceTelescope(Madau&Pozzetti2000)and the ACES equation of state (Barman et al., in preparation) theSpitzerinstrument(Fazioetal.2004).Apowerfulmethod to allow for a temperature range from 100K to above 106K for obtaining upper limits on the EBL density makes use of andincludesamultitudeofmolecularanddustspecies. The thespectrafromveryhighenergy(VHE)γ-raysources,espe- models presented here use the 1D mode PHOENIX/1D of ciallyblazars(see,e.g.,Mazin&Raue2007).Galaxynumber PHOENIXwithsphericalsymmetry. Themodelatmospheres countsandupperlimitsfromVHEγ-rayobservationscanbe arecomputedforradiativeandconvectiveequilibriumwitha usedtoconstrainpossibleDSscenarios. mixinglengthtopressurescaleheightratioof2,withtheas- Inthispaper,thesofarunknowncontributionofDStothe sumptionthatnoenergyisgeneratedintheatmosphere. The EBLiscalculated. ConstraintsforsomeDSscenariosarede- abundance of H was set to 0.92 by number (mass fraction: rivedaswellasaconvenientparameterizationtocalculatethe 0.75) and that of He was set to 0.08 by number (mass frac- maximum EBL density produced by a set of DS parameter tion: 0.25) for all models, all other elements (including Li) values. The paper is organized as follows: In Sect. 2 the haveanabundanceofzerointhesemodels. Modelswithef- model calculations for the EBL from DSs are described. In fectivetemperaturesfrom5000Kto7500Kwithparameters Sect. 3theresultingEBLfordifferentsetsofDSparameters (gravities,masses)takenfromSpolyaretal.(2009)havebeen is calculated and compared with recent data and EBL mod- computed. For all the models a number of different variants els. ThemultidimensionalDSparameterspaceisconstrained by, for example, varying the line profiles or the equation of and a parameterization for the peak EBL contribution of DS statesetuptoinvestigatetheeffectsonthemodelsandthesyn- isderived. Sect. 4summarizestheobtainedresultsandcom- theticspectrahavebeencomputed. Foreachsetupdiscussed paresthemwithexistingdirectandindirectapproachestode- below,theindividualmodelsarerelaxedtoequilibriumbefore tect/constrainDS. computinghigh-resolutionsyntheticspectra. Throughout this paper a flat Friedmann cosmology is For a given effective temperature, the choice of line pro- adopted with Ωm = 0.3, ΩΛ = 0.7 and a Hubble constant filesproducesthelargestvariationsintheemittedspectra(see ofH =70kms−1Mpc−1. Fig. 1). The two sets of models were computed by (a) us- 0 ingStarkprofilesfortheHlinesand(b)usingvanderWaals 2. THEDSCONTRIBUTIONTOTHEEXTRAGALACTIC (vdW)broadeningfortheHlines. At Teff =5000KthevdW BACKGROUNDLIGHT(EBL) broadeningisthedominantlinebroadeningprocesswhereas InordertocalculatetheEBLproducedbydarkmatterburn- at Teff = 7500K Stark broadening is more important, de- ingstarsaforwardevolutionmodelisusedbasedonthecalcu- spite the absence of free electrons from the light metals, see lationsofKneiskeetal.(2002)andRaueetal.(2009)(seealso thecomparisontoaspectrumwithsolarabundancesinFig.2. Dweketal.1998;Salamon&Stecker1998).Inthemodel,the ThehottestmodelinFig.1clearlyshowstheelectroniclines specific intensity of the EBL I (z) is obtained by integrating of H in their UV spectra, these are also present in the DS ν 2 thespecificcomovingluminositydensityε (z)overredshiftz spectrawithlowereffectivetemperaturesbutaremuchweaker ν duetotheirhighexcitationenergies.Insolarabundancemod- c (cid:90)zmax (cid:12)(cid:12) dt (cid:12)(cid:12) els these are overwhelmed by the metal lines in the UV and Iν(z)= 4π dz(cid:48)εν(cid:48)(z(cid:48))(cid:12)(cid:12)(cid:12)dz(cid:48)(cid:12)(cid:12)(cid:12) (1) weroeudl,dthneoNt LbeTEde(tNecotnabLleo.caFloTrhtehremmaloEdqeulipliabrraiummet)eersffeccotnssaidre- z smallandappeartobeinsignificant. Athighereffectivetem- whereεν(z)isgivenby peraturesthiswilllikelybedifferent,however,thisparameter (cid:90)zmax (cid:12) (cid:12) rangeisnotconsideredhere. (cid:12) dt (cid:12) AscanbeseenfromFig.1nosignificanthydrogenionizing εν(z)= dz(cid:48)Lν(t(z)−t(z(cid:48)))ρ˙∗(z(cid:48))(cid:12)(cid:12)(cid:12)dz(cid:48)(cid:12)(cid:12)(cid:12) . (2) radiation is emitted for the stellar temperature range consid- z eredhere. L (t) is the time-dependent specific luminosity, ρ˙ (z) the co- mνoving formation rate of DSs at a given reds∗hift z, and DSformationrate:— TheformationdensityofDSsn˙∗(z)can be linked to the star formation rate ρ˙ (z) for the first stars ν(cid:48) =ν(1+z)/(1+z(cid:48))istheredshiftedfrequency. Theintegra- ∗ (PopIII).Spolyaretal.(2008,2009)proposethateveryPop tion limit z determines the maximum redshift where dark max III star that forms inside the center of an undisturbed dark matterburningstarsbegintoform. Cosmologicalparameters mater halo could establish a dark star phase ∆t . This im- enterthrough DS plies that the mass formation rate of DS can be written as: (cid:12)(cid:12)(cid:12)(cid:12)dt(cid:12)(cid:12)(cid:12)(cid:12)= 1 (3) ρ˙∗(z)=n˙∗(z)×MDS1.Thecomovingstarformationrate(SFR) (cid:12)dz(cid:12) H (1+z)E(z) 0 E(z)2 =Ωr(1+z)4+Ωm(1+z)3+Ωk(1+z)2+ΩΛ, (4) con1sTidheirsedas.sumptionholdstrueifonespecificDSmodelwithmassMDSis ConstraintsonDarkStarsfromtheEBL 3 Fig.1.—SyntheticspectraforDSmodelsderivedwiththePHOENIXcode. Themodelparametersarefromtoptobottom: Teff = 7500K,log(g) = 1.0, M =690M(cid:12), Teff =6000K,log(g)=0.0,M =371M(cid:12), Teff =5500K,log(g)=−0.5,M =106M(cid:12)and Teff =5000K,log(g)=−0.5,M =106M(cid:12). The gravitationalaccelerationgisgiveninCGSunits. of the first stars that form in such environments are calcu- pressedasamassformationrateinunitsof M year−1Mpc−3: (cid:12) lated by Trenti & Stiavelli (2009) with a variety of radiative (cid:40) SFR forz ≤z≤z andchemical(metalenrichment)feedbackparametersandfor ρ˙ (z)= Norm min max (5) differentnumbersofstarsforming. Theyobtainvaluesforthe ∗ 0 else PopIIImassformationrateof10−5 −10−3M year−1Mpc−3 (cid:12) where SFR isanormalizationfactor,variedintheabove- up to z = 10 depending on the exact model parameters con- Norm mentionedrange,z indicatestheminimalvalueofredshift sidered. Pop III star formation rates in a similar range are min zwhereDarkStarformationcanstilloccurandz denotes also found for lower redshifts (Schneider et al. 2006; Torna- max the beginning of the Dark Star formation epoch. The ansatz tore et al. 2007; Maio et al. 2010). There exist two negative fortheSFRusedinthispaperisstronglysimplifiedandmore feedback mechanisms for Pop III star formation: radiative elaboratecalculationsoftheSFRareavailable(see,e.g.,Greif feedback from H ionizing photons and metal enrichment2. 2 &Bromm2006,Sandicketal.2011). Raueetal.(2009)have ForDSs,duetotheircoolertemperaturesandlongerlifetimes investigated the impact of a wide range of SFRs on the re- thanPopIIIstars,bothmentionedfeedbackmechanismscan sultingEBLdensityandfoundthepositionandoverallheight besuppressedandthusDSformationcan,inprinciple,been- ofthepeakthedominantfactor,whilethechoiceoftheshape hanced and prolonged. It is also possible that DS can grow onlyresultedinaweakchangeintheresultingpeakEBLden- tolargermassesthanusualfirststars(M > M )which DS PopIII sity(factor∼2).Giventherangeoftheparameterinvestigated resultsinahigherSFRρ˙ (z). Insummaryitcanbeconcluded ∗ in this work here (e.g., the overall normalization of the SFR thattheSFRofDSsuffersfromlargeuncertainties.Therefore ranges over several orders of magnitude), this simplified ap- a reasonable fiducial value is derived from the Pop III SFR proachfortheSFRissufficient. (10−5M(cid:12)year−1Mpc−3)andawiderangelimitedbyextreme AsthedurationoftheDS-formingperiodintheuniverseis models(10−7−10−3M(cid:12)year−1Mpc−3)isexplored. directly linked to the amount of photons that are emitted by Hence, as a simplification, a constant star formation rate Dark Stars the influence of z and z on the EBL is also min max over a certain redshift period is assumed which can be ex- explored. The contribution of ρ˙ (z) for large z is suppressed ∗ becauseoftheredshiftdilutionofthephotonfieldwhichgoes 2 For a detailed description of these processes please refer to Trenti & as (1+z)−3 and so the value of zmax is, in the following, set Stiavelli(2009)andreferencestherein. to 30. For z (the end of the Dark Star formation epoch) min 4 Maureretal. Fig.2.—ComparisonoftheDarkStarsyntheticspectrafor Teff = 7500K,log(g) = 1.0, M = 690M(cid:12) withasolarabundancesmodelwiththeparameters Teff =7400K,log(g)=1.0,M=1M(cid:12). values between 5 and 15 are considered. These values are etc. (foranextensivediscussionseeZackrissonetal.2010). in good agreement with assumed Pop III formation periods InthisworkawidebandofpossibleDSlifetimesisexplored, (Schneideretal.2006;Tornatoreetal.2007;Trenti&Stiavelli rangingfrom105to109years. 2009;Trentietal.2009;Maioetal.2010). ThetotalbolometricluminosityofasingleDSisconnected toDMparticlepropertiesvia: DSluminosity:— Independent of the exact mechanism pow- (cid:90) ering the DM burning, models predict a stable phase which L= dνL0 ∝ (cid:104)σv(cid:105)ann (8) dominates the total radiative output during the DS phase ν m χ (Spolyar et al. 2008; Iocco et al. 2008). During this phase theluminosityisnearlyconstant(seee.g. Figure2inSpolyar (Spolyaretal.2008). etal.2009,Figure4inIoccoetal.2008andFigure1inYoon Given a certain stellar mass formation rate the DS lumi- etal.2008). ThereforethefollowingansatzisadoptedforL nosity produced per mass has to be specified in the model. ν ThemassrangeofPopIIIstars,and,forthisreason,alsothe (cid:40) L0 fort(z)−t(z(cid:48))≤∆t massrangeofDSisnotverywellconstrainedbutisexpected L (t(z)−t(z(cid:48)))= ν DS (6) ν 0 else to be within roughly 10 up to a few hundred solar masses (Abel et al. 2002; Schaerer 2002). The model assumptions with∆t beingthedurationofthisstablephase(alsoreferred for the DM burning and the star formation lead to a wide DS to as DS lifetime) and L0 being the specific DS luminosity spreadintheDSluminosityperstellarmass.Thisluminosity- ν accordingtoitssyntheticspectrum(cf. Fig. 1). For∆t (cid:28) to-(stellar)mass ratio (LMR) of published DS models (Iocco DS t(z )−t(z )theemissivitycalculationreducesto et al. 2008; Spolyar et al. 2009; Freese et al. 2010) can be min max computedandusedasinputparametersfortheEBLcalcula- (cid:90)zmax tionpresentedhereandrangefrom∼102−105L /M . εν(z)≈ Lν0∆tDS dz(cid:48)ρ˙∗(z(cid:48)) (7) The influence of DM particle properties on the(cid:12)LM(cid:12)R will befurtherdiscussedinSect. 3.2. z leadingtoalinearscalingoftheresultingEBLwith∆tDS.The 3. RESULTS exactlengthoftheDSlifetimeisnotconstrainedanddepends 3.1. ConstrainingtheDSparameterspace onvariousfactors,e.g.,DMtype,DSmodel,DMhaloprofile, ConstraintsonDarkStarsfromtheEBL 5 2 10 TABLE1 DarkStarparameterrange L(cid:12)/M(cid:12) ∆tDS zmin SFRNorm min 102 105 15 10−7 fidmuacxial 110035 110079 150 1100−−53 -1sr] 101 Note.—ThemaximumvalueofLMRisclosetotheEddingtonlimitand -2m thereforeactsasanaturalupperboundaryfortheDSparameterspace. W n I [ν 100 The EBL contribution of DS is calculated using the meth- ν ods and parameters discussed in the previous section. The range of the specific parameter values is shown in table 1. Afiducialsetof“intermediate”parametervaluesisalsodis- played which acts as default when a single parameter is var- -1 10 ied. As can be seen from Eqn. 5 in combination with Eqn. 0.1 1 10 100 Wavelength [µm] 1 & Eqn. 2 the resulting EBL density scales linearly with the SFR and the LMR. In Fig. 3 the EBL contribution for Fig.3.—TwodifferentDarkStarparametersets(red-dashed:TDS=7500K, two different DS models is displayed in comparison with a M=690M(cid:12);blue-dashed:TDS=5000K,M=106M(cid:12)).Bothmodelsare strict lower limit for the guaranteed astrophysical EBL from calculatedwithSFRNorm=10−3,∆tDS=109years,zmin=5.Greymarkers: EBLmeasurements&limitsadoptedfromMazin&Raue(2007);grey:upper starsanddustingalaxies(Kneiske&Dole2010). Comparing limitsfromTeVobservations(realisticmodel)fromMazin&Raue(2007). theresultingDSEBLsignatures(reddashedandbluedashed Black:EBLlowerlimitbyKneiske&Dole(2010). ThetotalEBLshapein presenceofaDScontributionisthesumofthelowerlimitandthespecific curves)withtheirrespectiveinputspectra(seeFig. 1)itcan DSsignature(redandbluelines). be seen that the spectral features are smoothed by the red- shift integration. The peak of the EBL is for both models 1 located at wavelengths > 2µm which differs from the value 10 (λ ∼ 1µm) for Pop III stars (Santos et al. 2002) as expected 0 z = 5 due to lower effective temperatures. The peak of both EBL -1r] 10 zmmiinn = 10 sfriagrneadtubraecskcglreoaurlnydr.eTachhisesshinotwosththeadtethteecEtaBblLeoreffgeirosnthoeftphoeteinn-- -2m s10-1 zmin = 15 tialtoconstrainDSparameterspace. ADScontributionfrom W 10-2 n thesemodelswouldresultintoatotalEBLwhichisthesum L [10-3 of the lower limit and the DS signature (red and blue lines). B E TheseEBLshapesarealreadydisfavoredbyupperlimitsfrom m 10-4 TeVobservations(greyline). u m InFig. 4thepeakEBLcontributionforthreevaluesofzmin axi10-5 withrespecttovaryingDSlifetimesisdisplayed. Asaconse- M -6 quenceofEqn. 7,forDSlifetimessmallerthantheformation 10 ipnecrrieoadstin(zgmi∆n)tD−S.t(Azmtahx)igthheerrleisfuetlitminegsEthBaLns∼ca1le0s8lyineaerasrltyhewiinth- 10-1705 106 107 108 109 1010 tensity of the EBL is increased to a greater amount as well ∆t [years] DS asthepeakvalueoftheDSsignatureisshiftedtowardlower Fig.4.—PeakEBLcontributionforthe7500KDSmodelasafunctionof wavelengths (Fig. 5). This is caused by a residual emissiv- DSlifetime,forSFRNormthefiducialvalueof10−5isused. ity at lower redshifts z < z as the end of DS formation is not the end of DS photon emminission. Due to the strong dilu- mula offers a conservative estimate as the DS lifetime only tionofthephotonnumberdensitywithredshift(1+z)−3 the enterslinearlywhichistruefor∆tDS uptovaluesaslargeas mostrecentemissiondominatestheEBLcontribution.If∆t ∼108 years. ThepossibleenhancementoftheEBLcontribu- DS is short enough the end of DS formation is roughly equal to tionduetolongerDSlifetimesisnottakenintoaccounthere, theendofDSemittingphotonsastheamountofDSdropsof butonecanestimateitfromFig. 4orithastobecalculated almost instantly. The dashed lines display a linear relation- asdescribedinthiswork. Comparinglowerwithupperlimits ship between ∆t and the maximum EBL flux. Please note ontheEBLonefindsanallowedEBLcontributionfromDS thatDSwithlifeDtiSmes∆t (cid:39)1010 years,asdisplayedinFig. in the range of 5−25nWm−2sr−1 for wavelength between DS 4 and Fig. 5, would be still present in today’s universe and 2 and 10µm (see e.g. Mazin & Raue 2007 Fig. 15). Adopt- thereforemostlikelytobedetected. ing this range limits on DS parameters can be derived. For The model results can be summarized in a formula giving example: A DS with MDS = 106M(cid:12), LDS = 9×106L(cid:12), a the peak EBL contribution at z = 0 from a DS population DS lifetime ∆tDS = 108years and minimum formation red- normalizedtothefiducialDSparameters. shiftzmin = 5resultsinaconstraintontheDSformationrate between5×10−4 and3×10−3M year−1Mpc−3. Inthisway (νI ) =2×10−5nWm−2sr−1×(cid:32) ∆tDS (cid:33) several DS parameter sets can be(cid:12)used to constrain specific ν max 107years DSscenarios. (cid:32)SFR (cid:33) (cid:32) LMR (cid:33) (cid:18)z (cid:19)−2.5 × Norm × × min (9) 3.2. Implicationsfordarkmatterproperties 10−5 103L /M 10 (cid:12) (cid:12) ThedominantfactorfortheDSluminosityduetoDMburn- ThecalculationoftheresultingEBLcontributionviathisfor- ing is the square of the DM density distribution ρ which is χ 6 Maureretal. ing EBL data. In comparison to other indirect dark matter z = 5 detection channels, the Dark Star induced EBL component min z = 10 is unique in that it is not sensitive to the exact branching ra- 10 min z = 15 tiosoftheannihilationyieldsintophotonsorchargedparticles min and their resulting spectra, as all annihilation products (with the exception of neutrinos, of course) are trapped and ther- m] malizedwithintheDarkStar. Inthisregard,thecalculations µ λ [ presentedherecanalsoserveasanindependentandcomple- mentary template for indirect dark matter searches in other wavebands. Implicationsalsoexistregardingtheelasticscatteringcross section of the Dark Matter particles. As capture via elastic 1 scattering is a dominant channel for replenishing the fuel of the Dark Star (see e.g. Iocco et al. 2008), once equilibrium 5 6 7 8 9 10 hasbeenreachedtheluminosityofsuchastarscaleslinearly 10 10 10 10 10 10 ∆t [years] with the WIMP - proton scattering cross-section3 (hydrogen DS of course being the dominant target for an assumed primor- Fig.5.—LocationwavelengthofthepeakintheEBLSEDasafunction dialmixture). Thereisconsiderablediscussionongoingwith ofDSlifetimeforthe7500KDSmodel. For∆tDS > 109yearsthevalues regard to experimental searches for elastic WIMP - nucleon converge toward the intrinsic emission maximum indicating that DSs still emitlightatz=0. scatteringinundergroundexperiments. With respect to Dark Stars, it is interesting that, again determinedbytheoriginalDMdensityprofileinsideprimor- assuming the basic setup from Iocco et al. (2008), a spin- dialvirializedhalos,thechangeoftheprofileundertheinflu- dependent WIMP-proton cross section of the order 1pb for enceofcontractingbaryonicmaterial(adiabaticcontraction), a WIMP with a rest mass of tens of GeV would already re- andrepopulationoftheinnercuspoftheDMhaloduetoscat- sult in Dark Stars with LMRs very close to the “max” value tering processes (Freese et al. 2008, 2009). The characteris- of table 1. While backing up the constraints down to the tics(temperature,radius,luminosity)ofaDSrelyontheeffi- multiple-femtobarn level from the non-detection of annihi- ciency of the DM luminosity compared to other energy gen- lation neutrinos from the Sun (Hooper et al. 2009), the as eration mechanism like nuclear fusion. In general the more of yet definitive missing detection of a Dark Star contribu- DM contributes to the total stellar luminosity of the star, the tiontotheEBLthereforereinforcestheconclusionthatspin- cooler and bigger it grows regardless of the mechanism that dependentscatteringcanreconciletheDAMAandCoGENT producesthehighDMdensityinsidethestar. measurementsofanannualmodulationofeventrates(Bern- AsexplainedabovetheDSluminosityscaleswithρ2. The abei et al. 2010; Aalseth et al. 2011) with null-results from χ otherexperimentsonlyforcasesinwhichtheWIMP-neutron replenishmentoftheDMdensityinsideaDSispossibleeither cross-section is several orders of magnitude greater than the bythegravitationalpullofthecollapsinggasontotheDSor WIMP-proton cross section, as e.g. discussed in Ullio et al. bymultipleelasticscatteringprocessesbetweenDMandthe (2001). It should however be noted that for the case of light stellar baryons or a combination of both. The LMR of the Dark Matter particles, there exist windows where a surpris- specificdarkmatterpoweredstarspresentedinSpolyaretal. ingly high spin-independent scattering cross section of the (2009) tend to be slightly dependent on (cid:104)σv(cid:105) /m ; higher ann χ order 10−40cm2 is compatible with the DAMA/LIBRA and valuesresultinhigherDSmassesbutatthesametimealsoto CoGENT measurements (Hooper & Kelso 2011). This may higherDSluminosities. FortheearlystagesofDSformation (cid:112) againbeacasewhereDarkMatterannihilationmightsignif- theLMRisnearlyproportionalto (cid:104)σv(cid:105)ann/mχ. Inthecase icantly effect the life cycle of the first stars, and should be a ofDMcapture,asinvestigatedbyIoccoetal.(2008),theDS focusoffuturework. luminosityscaleslinearlywiththeelasticscatteringcrosssec- tionσ . ItisalsoshownthatDMburningduetoWIMPcap- 0 4. DISCUSSION&CONCLUSION tureismoreefficientinlow-massstars,butundertheassump- tion that the product σ ρ is of the order 10−26GeVcm−1 WIMPdarkmattercanhaveanimpactontheevolutionof 0 χ thefirststars. Inthiswork,thedetectabilityofDSgenerated Yoonetal.(2008)haveshownthatagreatmassrangeofstars signatures in the EBL is investigated. This approach opens canundergoastableDMburningphase. a new window to search for DM effects: the near-infrared It is further worthwhile to note that, while conservative (NIR). The EBL contributions from different DS parameter models of the Dark Star contribution to the EBL do not setshavebeencalculatedand, forcertainsetsofparameters, strongly constrain WIMP properties such as mass or annihi- theresultingEBLfluxcanreachintothedetectablerangeof lation cross section, this picture can change when our prior the infrared background. A parameterization is presented to assumptionsarerelaxed: AsoutlinedinSpolyaretal.(2009), calculatethepeakEBLcontributionforavarietyofmodelin- the Dark Star luminosity-to-mass ratio - and therefore the putvalues.TheresultingEBLcanbeusedtoconstraincertain peakEBLcontribution(seeEqn. 9)-willroughlyscalewith DS scenarios by comparing the calculated peak EBL contri- the square root of the annihilation cross section and WIMP √ bution of DS with existing upper limits in the EBL density. mass as LMR ∝ (cid:104)σv(cid:105) where m is the mass of the ann/mχ χ The results of this work can be seen as complementary ap- WIMP.Assumingcross-sectionsoftheorder10−23cm3s−1for proachtoputconstraintsonDSformationscenariosasinves- TeV scale WIMPs, as have recently been invoked to explain PAMELA measurements of the cosmic-ray positron fraction 3Inthecaseofextendedadiabaticcontractionbeingthemainmechanism (Cirelli&Strumia2008),atleastthe”max”modelpresented of DM replenishment the DS luminosity scales only with the stellar mass in Table 1 would already be strongly constrained by exist- (Freeseetal.2010). ConstraintsonDarkStarsfromtheEBL 7 tigatedbySchleicheretal.(2009)wheretheinfluenceofDS AirCherenkovTelescopes,liketheCherenkovTelescopeAr- to reionization, the γ-ray and neutrino background has been ray(TheCTAConsortium2010),willradicallyimproveupon investigated. existingTeVmeasurements, hopefullyprovidingforadirect Freese et al. (2010) recently proposed a scenario in which measurementoftheEBL-inducedcutoffinAGNspectra(see Dark Stars can reach enormously high masses (107M ) due e.g. Raue & Mazin 2010). Fully self-consistent models of (cid:12) toveryefficientandlong-lastingaccretionprocessesofbary- DarkStarformation,internalstructureandevolutionarealso onicmatterontotheDarkStar,so-calledsupermassiveDark demanding to finally tackle the question whether WIMP an- Stars (SMDS). Under these conditions very long lived and nihilation played a role in the first luminous objects in the luminous SMDS can be produced. As suggested by the au- universe. thorsnearlyallbaryonicmatterinsidetheDMhalotheSMDS formsinisaccretedontothestar.Thisfacttranslatesinavery high SFR which can be used as input for Eqn. 9 to put also ThisworkwasmadepossiblewiththesupportoftheClus- constraintsontheSMDSscenarios. ter of Excellence: “Connecting Particles with the Cosmos”, Asafinalnote,itshouldbestressedthattheabilitytocon- part of the Landesexzellenzinitiative Hamburg, and the col- strain DS scenarios via EBL depends crucially on the im- laborativeresearchcenter(SFB)676“Particle,Stringsandthe provement of EBL limits and measurements. The upcoming early Universe” at the University of Hamburg. The authors JamesWebbSpaceTelescopewillprovidenewdataondeep like to thank Alessandro Mirizzi and Go¨tz Heinzelmann for field galaxy counts, as well as refined direct measurements readingofthemanuscriptandhelpfulcomments. Theauthors of the infrared background. The next generation of Imaging alsoliketothanktheanonymousrefereeforusefulcomments. 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