Dark matter powered stars: Constraints from the extragalactic background light

1.2 MB·English

by  A. Maurer

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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