Dark stars: Implications and constraints from cosmic reionization and extragalactic background radiation

Dark stars: Implications and constraints from cosmic reionizationand extragalactic background radiation

Dominik R.G. Schleicher, Robi Banerjee, and Ralf S. Klessen*

Institute of Theoretical Astrophysics/ZAH, Albert-Ueberle-Str. 2, D-69120 Heidelberg, Germany(Received 3 September 2008; published 11 February 2009)

Dark stars powered by dark matter annihilation have been proposed as the first luminous sources in the

Universe. These stars are believed to form in the central dark matter cusp of low-mass minihalos. Recent

calculations indicate stellar masses up to �1000M� and/or have very long lifetimes. The UV photons

from these objects could therefore contribute significantly to cosmic reionization. Here we show that such

dark star models would require a somewhat artificial reionization history, based on a double-reionization

phase and a late star burst near redshift z� 6, in order to fulfill the WMAP (Wilkinson Microwave

Anisotropy Probe) constraint on the optical depth as well as the Gunn-Peterson constraint at z� 6. This

suggests that, if dark stars were common in the early universe, then models are preferred which predict a

number of UV photons similar to conventional Pop. III stars. This excludes 800M� dark stars that enter a

main-sequence phase and other models that lead to a strong increase in the number of UV photons. We

also derive constraints for massive as well as light dark matter candidates from the observed x-ray,

gamma-ray, and neutrino background, considering dark matter profiles which have been steepened during

the formation of dark stars. This increases the clumping factor at high redshift and gives rise to a higher

dark matter annihilation rate in the early universe. We furthermore estimate the potential contribution

from the annihilation products in the remnants of dark stars, which may provide a promising path to

constrain such models further, but which is currently still uncertain.

DOI: 10.1103/PhysRevD.79.043510 PACS numbers: 95.35.+d, 95.85.Pw, 95.85.Ry, 97.20.Wt

I. INTRODUCTION

Growing astrophysical evidence suggests that dark mat-ter in the Universe is self-annihilating. X-ray observationsfrom the center of our Galaxy find bright 511 keVemissionwhich cannot be attributed to single sources [1,2], but canbe well described assuming dark matter annihilation [3].Further observations indicate also an excess of GeV pho-tons [4], of microwave photons [5], and of positrons [6]. Acommon feature of these observations is that the emissionseems isotropic and not correlated to the Galactic disk.However, there is usually some discrepancy between themodel predictions and the amount of observed radiation,which may be due to uncertainties in the dark matterdistribution, astrophysical processes, and uncertainties inthe model for dark matter annihilation [7].

It is well known that weakly interacting massive darkmatter particles (WIMPs) may provide a natural explana-tion of the observed dark matter abundance [8,9].Calculations by Ahn et al. [10] indicated that the extra-galactic gamma-ray background cannot be explained fromastrophysical sources alone, but that also a contributionfrom dark matter annihilation is needed at energies be-tween 1–20 GeV. It is currently unclear whether this is infact the case or if a sufficient amount of nonthermalelectrons in active galactic nuclei (AGN) is available to

explain this background radiation [11]. Future observationswith the FERMI satellite [12] will shed more light on suchquestions and may even distinguish between such scenar-ios due to specific signatures in the anisotropic distributionof this radiation [13].The first stars have been suggested to have high masses

of the order �100M�, thus providing powerful ionizingsources in the early universe [14,15]. The effect of darkmatter annihilation on the first stars has been exploredrecently in different studies. Spolyar et al. [16] showedthat an equilibrium between cooling and energy depositionfrom dark matter annihilation can always be found duringthe collapse of the proto-stellar cloud. This has been ex-plored further by Iocco [17] and Freese et al. [18], whoconsidered the effect of scattering between baryons anddark matter particles, increasing the dark matter abundancein the star. Iocco et al. [19] considered dark star masses inthe range 5 � M� � 600M� and calculated the evolutionof the pre-main-sequence phase, finding that the dark starphase where the energy input from dark matter annihilationdominates may last up to 104 yr. Freese et al. [20] exam-ined the formation process of the star in more detail,considering polytropic equilibria and additional mass ac-cretion until the total Jeans mass of �800M� is reached.They find that this process lasts for �5� 105 yr. Theysuggest that dark stars are even more massive than what istypically assumed for the first stars, and may be the pro-genitors for the first supermassive black holes at high*[email protected]

PHYSICAL REVIEW D 79, 043510 (2009)

1550-7998=2009=79(4)=043510(15) 043510-1 � 2009 The American Physical Society

http://dx.doi.org/10.1103/PhysRevD.79.043510

redshift. Iocco et al. [19], Taoso et al. [21], and Yoon et al.[22] have calculated the stellar evolution for the case inwhich the dark matter density inside the star is enhanced bythe capture of additional WIMPs via off-scattering fromstellar baryons. Iocco et al. [19] followed the stellar evo-lution until the end of helium burning, Yoon et al. [22] untilthe end of oxygen burning, and Taoso et al. [21] until theend of hydrogen burning. Yoon et al. [22] also took theeffects of rotation into account. The calculations found apotentially very long lifetime of dark stars and correspond-ingly a strong increase in the number of UV photons thatmay contribute to reionization. Dark stars in the Galacticcenter have been discussed by Scott et al. [23,24].

Such models for the stellar population in the early uni-verse imply that the first luminous sources produce muchmore ionizing photons, and reionization starts earlier thanfor a population of conventional Pop. III stars. In fact, werecently demonstrated that reionization based on massivePop. III can well reproduce the observed reionizationoptical depth [25]. Increasing the number of ionizing pho-tons per stellar baryon may thus reionize the Universe tooearly and produce a too large reionization optical depth.This can only be avoided by introducing a transition to astellar population which produces less ionizing photons,such that the Universe can recombine after the first reio-nization phase. We therefore consider a double-reionization scenario in order to reobtain the requiredoptical depth. We discuss such models in Sec. III anddemonstrate that some models of dark stars require con-siderable fine-tuning in reionization models in order to becompatible with the reionization optical depth from theWMAP [26] 5-year data [27,28], and to complete reioni-zation at redshift z� 6 [29]. In Sec. IV, we show how suchscenarios can be tested via 21 cm measurements.

A further consequence of the formation of dark stars isthe steepening of the density profiles in minihalos [17,20],thus increasing the dark matter clumping factor with re-spect to standard Navarro-Frank-White (NFW) models. InSec. V, we estimate the increase in the clumping factorduring the formation of dark stars and compare the calcu-lation with our expectation for conventional NFW profilesand heavy dark matter candidates. In Sec. VI, we performsimilar calculations for the light dark matter scenario.Further discussion and outlook is provided in Sec. VII.

II. THE MODELS

As discussed in the introduction, various models havebeen suggested for dark stars. The main difference betweenthese models comes from considering or neglecting scat-tering between dark matter particles and baryons. In addi-tion, it is not fully clear how important a phase of darkmatter capture via off-scattering from baryons actually is,depending on further assumptions on the dark matter res-ervoir. In the following, we will thus distinguish between

main-sequence dominated models and capture-dominatedmodels.

A. Main-sequence dominated models

After an initial phase of equilibrium between coolingand heating from dark matter annihilation [16–18], thedark star will contract further while the dark matter anni-hilates away and the heating rate thus decreases. Thisduration of this adiabatic contraction (AC) phase is cur-rently controversial: While Iocco et al. [19] find it to be inthe range of ð2–20Þ � 103 yr, Freese et al. [20] requireabout 106 yr. However, with a surface temperature of�6000 K, the stars are rather cold in this phase, and thuswill not contribute significantly to reionization. The uncer-tainty in the duration of the AC phase is therefore notcrucial in this context.If the elastic scattering cross section as well as the dark

matter density around the star are sufficiently large, the starwill enter a phase which is dominated by the capture offurther dark matter particles. Such a scenario will be dis-cussed in more detail in the next subsection. Here, weassume that the elastic scattering cross section is eithertoo small, or that the dark matter reservoir near the star isnot sufficient to maintain the capture phase for long. Then,the star will enter the main-sequence phase (MS), in whichthe luminosity is generated by nuclear burning. Stars with�1000M� are very bright in this phase, and emit�4� 104

hydrogen-ionizing photons per stellar baryon during theirlifetime [30,31]. We will refer to stars of such type, whichhave only a short or even no phase driven by dark mattercapture, as MS-dominated models.For the case of MS-dominated models, we will focus

essentially on the very massive stars suggested by Freeseet al. [20]. For stars in the typical Pop. III mass range, it hasbeen shown elsewhere [e.g. [25]] that they are consistentwith reionization constraints. A star with �800M� form-ing in a dark matter halo of �106M� corresponds to a starformation efficiency of 1%, which we adopt for this case.

B. Capture-dominated models

For a nonzero spin-dependent scattering cross sectionbetween baryons and dark matter particles, stars can cap-ture additional WIMPs which may increase the dark matterdensity inside the star. For a cross section of the order 5�10�39 cm2 and an environmental dark matter density of�1010 GeV cm�3, this contribution becomes significantand alters the stellar evolution during the main-sequencephase. We will refer to such a scenario as a capture-dominated (CD) model. These phases have been studiedin detail by Iocco et al. [19], Taoso et al. [21], and Yoonet al. [22]. They found that the number of ionizing photonsproduced by such stars may be considerably increasedwith respect to high-mass stars without dark matter anni-hilation effects, which is mostly due to a longer lifetime.

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In particular for dark matter densities of ð1–5Þ �1010 GeV cm�3, the number of produced ionizing photonsmay be increased by up to two orders of magnitude, whileit decreases rapidly for larger dark matter densities, and thenumber of ionizing photons per baryon even drops belowthe value for Pop. II stars at threshold densities of 1�1012 GeV cm�3. As Yoon et al. [22] found only a weakdependence on stellar rotation, we will not explicitly dis-tinguish between models with and without rotation in thefollowing.

For the calculation of reionization, we will focus onsome representative models of Yoon et al. [22] in thefollowing. However, we point out that there are still sig-nificant uncertainties in these models, in particular, thedark matter parameters and the lifetimes of the stars. Thelatter should be seen as upper limits, as they assume that asufficient reservoir of dark matter is available in the stellarneighborhood to allow for ongoing dark matter capture.This may however be disrupted by dynamical processes.An apparent disagreement of dark stars in the early uni-verse with our reionization model may thus indicate thatthe stellar lifetimes are indeed smaller due to suchprocesses.

III. REIONIZATION CONSTRAINTS

In this section, we briefly review our reionization modeland discuss reionization histories for main-sequence andcapture-dominated models. These calculations implicitlyassume annihilation cross sections of the order 10�26 cm2

and dark matter particle masses of the order 100 GeV, thevalues which are typically adopted in dark star models. Insuch models, dark matter annihilation does not contributeto cosmic reionization [25]. The chemistry in the preioni-zation era is thus unchanged and well described by pre-vious works [32–35], such that the initial conditions forstar formation are unchanged. Considering higher annihi-lation cross sections essentially yields an additional con-tribution to the reionization optical depth, which wouldsharpen the constraints given below.

A. General approach

Our calculation of reionization is based on the frame-work developed by Schleicher et al. [25], which we haveimplemented in the RECFAST code [36–38]. We willreview here only those ingredients which are most relevantfor this work. During reionization, the intergalactic me-dium consists of a two-phase medium, i.e. a hot ionizedphase and a rather cold and overly neutral phase. Therelative size of these phases is determined from thevolume-filling factor QHþ of the Hþ regions [39–44] as afunction of redshift, given by

dQHþ

dz¼ QHþCðzÞne;Hþ�A

HðzÞð1þ zÞ þ dnph=dz

nH; (1)

where CðzÞ ¼ 27:466 expð�0:114zþ 0:001 328z2Þ is theclumping factor [45], ne;Hþ the number density of ionized

hydrogen, �A the case A recombination coefficient [46],HðzÞ the Hubble function, nH the mean neutral hydrogendensity in regions unaffected by UV feedback, anddnph=dz the UV photon production rate. Our model con-

sists of ordinary differential equations for the evolution oftemperature T and ionized fraction xi in the overall neutralmedium. For the application considered here, the dominantcontribution to the effective ionized fraction xeff ¼ QHþ þð1�QHþÞxi and the effective temperature Teff ¼ 104 KQHþ þ Tð1�QHþÞ comes indeed from the UV feedbackof the stellar population, i.e. from the hot ionized phase.According to Gnedin and Hui [47] and Gnedin [48], weintroduce the filtering mass scale as

M2=3F ¼ 3

a

Z a

0da0M2=3

J ða0Þ�1�

�a0

a

�1=2

�; (2)

where a ¼ ð1þ zÞ�1 is the scale factor andMJ the thermalJeans mass, given as

MJ ¼ 2M��

cs0:2 km=s

�3�

n

103 cm�3

��1=2: (3)

Here, cs is the sound speed evaluated at temperature Teff , inorder to take into account the backreaction of heating onstructure formation. In this framework, the production ofUV photons can be described as

dnph=dz

nH� �

dfcolldz

; (4)

where � ¼ AHef�fescNion, with AHe ¼ 4=ð4� 3YpÞ ¼1:22, Nion the number of ionizing photons per stellarbaryon, f� is the star formation efficiency, and fesc theescape fraction of UV photons from their host galaxies.The quantity fcoll denotes the fraction of dark mattercollapsed into halos, and is given as

fcoll ¼ erfc

��cðzÞffiffiffi

2p

�ðMminÞ�; (5)

where Mmin ¼ minðMF; 105M�Þ, �c ¼ 1:69=DðzÞ is the

linearized density threshold for collapse in the sphericaltop-hat model, and�ðMminÞ describes the power associatedwith the mass scale Mmin.A relevant question in this context is also the role of

Lyman-Werner (LW) feedback, which may suppress thestar formation rate in low-mass halos. The role of suchfeedback has been addressed using different approaches.For instance, Machacek et al. [49], OShea and Norman[50], and Wise and Abel [51] have addressed this questionemploying numerical simulations in a cosmological con-text, assuming a constant LW-background radiation field.These simulations indicated that such feedback can delaystar formation considerably.More self-consistent simulations show, however, that the

above calculations overestimated the role of LW feedback.

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Considering single stellar sources and neglecting self-shielding, Wise and Abel [52] showed that LW feedbackonly marginally delays star formation in halos that alreadystarted collapsing before the nearby star ignites. Moredetailed simulations taking into account self-shieldingshow that the star formation rate may be changed by only20% in the presence of such feedback [53]. This is due tothe rapid reformation of molecular hydrogen in relic HIIregions, which leads to abundances of the order 10�4. Suchabundances effectively shield against LW feedback andmake it ineffective [54]. This is the point of view adoptedhere, which may translate into an uncertainty of �20% inthe star formation rate. In fact, in scenarios involving darkmatter annihilation, H2 formation and self-shielding couldbe even further enhanced compared to the standard case[55].

The models have to reproduce the reionization opticaldepth given by � ¼ 0:087� 0:017 [28] and fully ioniza-tion at z� 6 [29]. In the following, we will try to constructappropriate reionization histories for the different dark starmodels.

B. Reionization with MS-dominated dark stars

As shown previously [25], MS-dominated dark starswith �1000M� would significantly overproduce the reio-nization optical depth if this type of stars had been com-mon throughout the early universe. If, on the other hand,MS-dominated stars only had mass scales of �100M�,comparable to conventional Pop. III stars, reionizationcould not discriminate between them and conventionalPop. III stars, and dark stars would be compatible withobservations. Alternatively, as explained in the introduc-tion, a transition in the stellar population might help toalleviate the problem for high-mass dark stars. We willexplore this possibility in more detail to work out whethersuch a scenario is conceivable.

Numerical simulations by Dove et al. [56], Ciardi et al.[57], and Fujita et al. [58] indicated rather high escapefractions of order 100% for massive Pop. III stars. Woodand Loeb [59] found rather low escape fractions below10%, while radiation hydrodynamics simulations byWhalen et al. [60] show that such stars can easily photo-evaporate the minihalo. Here we adopt the point of viewthat indeed massive stars can photoevaporate small mini-halos, but that the escape fraction will be reduced to�10%in atomic cooling halos that have virial temperatures largerthan 104 K. Thus, we set fesc ¼ 1 if the filtering mass is

below the mass scale Mc ¼ 5� 107M�ð 101þzÞ3=2 that corre-

sponds to the virial temperature of 104 K [61,62], andfesc ¼ 0:1 in the other case. To reflect the expected stellarmass of�800M�, we choose a star formation efficiency off� � 1%, an order of magnitude higher than what weexpect for conventional Pop. III stars [25].

Assuming that reionization is completely due to theseMS-dominated dark stars (model MS 1), we find that the

Universe is fully ionized at redshift zreion ¼ 15:5 and thereionization optical depth is �reion � 0:22, i.e. significantlylarger than the WMAP5 optical depth (see Fig. 1). Such amodel is clearly ruled out.To reconcile the presence of such massive dark stars

with observations, one could invoke a double-reionizationscenario, assuming a transition to a different mode of starformation induced by the strong UV feedback of MS-dominated dark stars. In fact, even for conventional starformation models, it is discussed that such UV feedbackmay lead to a less massive mode of star formation [63–65].In addition, chemical enrichment should facilitate such atransition as well [44,66–70], although it is unclear howwell metals will mix with the pristine gas. We assume thatthe transition to a low-mass star formation mode with aScalo-type IMF [71] happens at redshift 15.5, when theUniverse is fully ionized and UV feedback fully effective.For the subsequent Pop. II stars, we assume a star forma-tion efficiency of f� ¼ 5� 10�3 and Nion ¼ 4� 103 UVphotons per stellar baryon.Corresponding photon escape fractions are highly un-

certain. Observations of Steidel et al. [72] indicate anescape fraction of 10% at z� 3, while others find detec-tions or upper limits in the range 5%–10% [73–76]. Weadopt the generic value of 10% for simplicity, though ourresults do not strongly depend on this assumption. For thisscenario, to which we refer as model MS 2, we find anoptical depth �reion ¼ 0:082 well within the WMAP con-straint, but the Universe does not get fully ionized untilredshift zero. This scenario is thus rejected based on theconstraint from quasar absorption spectra [29].To fulfill both the WMAP constraint as well as full

ionization at z� 6, we need to introduce an additional

FIG. 1. The evolution of the effective ionized fraction xeff , forreionization models with main-sequence dominated dark stars(see Table I). Models MS 1 and MS 2 can be ruled out byreionization constraints, while models MS 3 and MS 4 require asudden increase in the star formation rate by a factor of 30 atredshift 6.5. It appears more realistic to assume lower masses andstar formation efficiencies to reconcile dark star models withobservations.


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transition in our model. At redshift zburst ¼ 6:5, we in-crease the star formation efficiency to 15%. This mightbe considered as a sudden star burst and results in fullionization at z ¼ 6:2. In this case, we find �reion ¼ 0:116,which is within the 2� range of the WMAP data. However,we are not aware of astrophysical models that provide amotivation for such a sudden star burst that increases thestar formation rate by a factor of 30. Based on gamma-rayburst studies, Yuksel et al. [77] showed that the cosmic starformation rate does not change abruptly in the redshiftrange between redshift zero and zburst ¼ 6:5. Such a suddenburst is thus at the edge of violating observationconstraints.

To improve the agreement with WMAP, one can con-sider to shift the first transition to zPop II ¼ 18 where full

ionization is not yet reached (model MC 4), which yieldsan optical depth �reion ¼ 0:086, in good agreement withWMAP. At this redshift, 68% of the Universe is alreadyionized, so UV feedback might already be active andinduce a transition in the stellar population. The resultsare given in Fig. 1 and summarized in Table I.

However, we find that only models MS 3 and MS 4cannot be ruled out observationally. These models requiretwo severe transitions in the stellar population and cannotbe considered as ‘‘natural.’’ Improved measurements of thereionization optical depth from Planck [78] will removefurther uncertainties and may rule out model MS 3 as well.From a theoretical point of view, it must be checkedwhether strong UV feedback can lead to the requiredtransition to a low-mass stellar population, and in addition,the plausibility of a sudden star burst near redshift 6 mustbe examined as well. In summary, it seems more plausibleto conclude that MS-dominated dark stars were less mas-sive than suggested by Freese et al. [18], as already hintedby Schleicher et al. [25].

C. Reionization with CD dark stars

For CD dark star models, the situation is complicated bythe fact that the number of UV photons per stellar baryon,Nion, is model dependent and changes with the environ-mental dark matter density, �X. We select three represen-tative models of Yoon et al. [22], which assume a spin-dependent scattering cross section of 5� 10�39 cm2 (see

Table II). In general, stellar models depend on the productof this scattering cross section with the threshold darkmatter density at the stellar radius [21,22]. Lower elasticscattering cross sections therefore correspond to going tosmaller threshold densities at the same elastic scatteringcross section.In the models CD 1 and 2, Nion is larger than for

conventional Pop. III stars, while in the model CD 3, it iseven less than in the case of Scalo-type Pop. II stars. Such alow luminosity is unlikely to photoevaporate star-forminghalos, and we thus adopt fesc ¼ 10% for this case.However, such Scalo-type Pop. II stars are ruled out assole sources for reionization [25]. As we show in Fig. 2,even with a high star formation efficiency of f� ¼ 1%, theynever ionize the Universe completely.

TABLE I. Reionization models for MS-dominated dark stars.The parameters zPop II and zburst give the transition redshifts to a

mode of Pop. II star formation and to the sudden star burst, while�reion is the calculated reionization optical depth and zf the

redshift of full ionization.

Model zPop II zburst �reion zf

MS 1 . . . . . . 0.22 15.5

MS 2 15.8 . . . 0.078 never

MS 3 15.5 6.5 0.116 6.2

MS 4 18. 6.5 0.086 6.2

TABLE II. Reionization models for CD dark stars. The num-ber of ionizing photons was determined from the work of Yoonet al. [22]. The parameters zPop II and zburst give the transition

redshifts to a mode of Pop. II star formation and to the suddenstar burst, while �reion is the calculated reionization optical depthand zf the redshift of full ionization. The calculation assumes a

spin-dependent scattering cross section of 5� 10�39 cm2. Asstellar models depend on the product of this cross section withthe threshold dark matter density, the effect of a lower scatteringcross section is equivalent to a smaller threshold density.

Reion. model �X=1012 Nion f� zPop II �reion

CD 1a 0:01 GeV cm�3 1:75� 105 0.1% . . . 0.162

CD 1b 0:01 GeV cm�3 1:75� 105 0.1% 12.7 0.109

CD 1c 0:01 GeV cm�3 1:75� 105 0.1% 14.5 0.089

CD 2a 0:05 GeV cm�3 2:4� 106 0.1% . . . 0.283

CD 2b 0:05 GeV cm�3 2:4� 106 0.1% 21.6 0.106

CD 2c 0:05 GeV cm�3 2:4� 106 0.1% 23 0.084

CD 3 1GeV cm�3 1:1� 103 1% . . . 0.004

FIG. 2. The evolution of the effective ionized fraction xeff , forreionization models with capture-dominated dark stars (seeTable II). Models CD 1a, CD 1b, CD 2a, CD 2b, and CD 3are ruled out due to reionization constraints, while the remainingmodels require an artificial star burst.


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In principle, one could consider the presence of othersources to ionize the Universe. While dark stars of typeCD 3 may be the first stars to form, one might envision atransition to a stellar population with the power to ionizethe Universe. This transition is unlikely due to UV feed-back, as UV feedback from dark stars is rather weak in thisscenario. One thus has to rely on effective mixing of theproduced metallicity or assume that the first stellar clustersin atomic cooling halos contain a sufficient number ofmassive stars to reionize the Universe [66].

For the other two models, Nion is significantly larger andwe adopt the procedure from the previous subsection, suchthat fesc depends on the filtering mass. We adopt a starformation efficiency of f� ¼ 0:1%. We examine the reio-nization models given in Table II, which essentially followthe philosophy of the models from the previous section. Wecalculate the reionization history for the case where thesedark stars are sole sources (CD 1a, CD 2a) and find that theoptical depth is considerably too high. We then determinethe redshift where the Universe is fully ionized and assumea transition to Pop. II stars at this redshift. In addition, toobtain full ionization at redshift 6, we assume a late starburst as in the models MS 3 and MS 4. This approachcorresponds to the models CD 1b and CD 2b and yieldsoptical depths that are at least within the 2� error ofWMAP5. In the models CD 1c and CD 2c, we improvethe agreement with WMAP by introducing the Pop. IItransition at an earlier redshift.

The results are given in Fig. 2. Again, it turns out thatsomewhat artificial models are required to allow for an

initial population of CD dark stars. The best way to recon-cile these models with the constraints from reionizationmight be to focus on those models that predict a parameterNion which is closer to the Pop. III value of 4� 104. Thismay be possible, as the transition from the models CD 1and 2 to CD 3 is likely continuous, and an appropriaterange of parameters may exist to reconcile modelswith observations. This would require a �X between1011 Gev cm�3 and 1012 GeV cm�3. As mentioned earlier,the apparent violation of reionization constraints by somemodels depends also on the uncertainties in the stellarlifetime. If the dark matter reservoir near the star is de-stroyed earlier due to dynamical processes, the lifetimemay be significantly reduced. Also, we stress that theconclusions depend on the adopted elastic scattering crosssection and the dark matter density in the environment. Thediscussion here is limited to those models that have pre-viously been worked out in detail.

IV. PREDICTIONS FOR 21 CM OBSERVATIONS

While some of the models suggested above essentiallycoincide with standard reionization by mimicking the ef-fects of conventional Pop. III stars, others may have avery distinctive signature, as they consist of a double-reionization phase, and upcoming 21 cm telescopes likeLOFAR [79] or SKA [80] can thus verify or rule out suchsuggestions. The calculation shown in Fig. 3 is based onthe double-reionization model MS 4, but clearly the mod-els MS 3, CD 1b, CD 1c, CD 2b, and CD 2c yield similar

FIG. 3. 21 cm signatures of double-reionization scenarios (here MS 4 from Table I). Given is the evolution after the first reionizationphase, when the H gas is heated from the previous ionization. Top: HI gas temperature, here identical to the spin temperature. Middle:expected mean 21 cm brightness fluctuation. Bottom: frequency gradient of the mean 21 cm brightness fluctuation.


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results. In such a double-reionization scenario, the gas isheated to �104 K during the first reionization epoch.Assuming that the first reionization epoch ends at redshiftzPop II, the gas temperature in the nonionized medium will

then evolve adiabatically as

T � 104 K

�1þ z

1þ zPop II

�2: (6)

In addition, the previous reionization phase will haveestablished a radiation continuum between the Lyman �line and the Lyman limit, where the Universe is opticallythin, apart from single resonances corresponding to theLyman series. This radiation is now redshifted into theLyman series and may couple the spin temperature Tspin

of atomic hydrogen to the gas temperature T via theWouthuysen-Field effect [81,82]. In fact, a small amountof Lyman � radiation suffices to set Tspin ¼ T [83–85],

which we assume here. Also, as the Universe is opticallythin to this radiation background, even Pop. II sources willsuffice to couple the spin temperature to the gas tempera-ture. The mean 21 cm brightness temperature fluctuation isthen given as

�Tb ¼ 27xHð1þ �Þ��bh

2

0:023

��0:15

�mh2

1þ z

10

�1=2

�TS � Tr

TS

�

��HðzÞ=ð1þ zÞdvjj=drjj

�mK; (7)

where xH denotes the neutral hydrogen fraction, � thefractional overdensity, �b, �m the cosmological densityparameters for baryons and total matter, h is related to theHubble constant H0 via h ¼ H0=ð100 km=s=MpcÞ, Tr theradiation temperature, and dvjj=drjj the gradient of the

proper velocity along the line of sight, including theHubble expansion. We further calculate the frequencygradient of the mean 21 cm brightness temperature fluc-tuation to show its characteristic frequency dependence. InFig. 3, we show the evolution of the gas temperature, themean 21 cm brightness fluctuation, and its frequency gra-dient for model MS 4.

As pointed out above, we expect similar results for otherdouble-reionization models because of the characteristicadiabatic evolution of the gas and spin temperatures. Thedecrease of the spin temperature with increasing redshift isa unique feature that is not present in other models that likedark matter decay [86] or ambipolar diffusion heating fromprimordial magnetic fields [87–89], which may also in-crease the temperature during and before reionization.

V. COSMIC CONSTRAINTS ON MASSIVE DARKMATTER CANDIDATES

In typical dark star models, it is assumed that massivedark matter candidates like neutralinos with masses of theorder 100 GeV annihilate into gamma rays, electron-positron pairs, and neutrinos [16–20,22,90]. Similar to

the constraint on high-redshift quasars from the x-raybackground [91–93], the gamma-ray and neutrino back-grounds allow to constrain the model for and the amount ofdark matter annihilation. As detailed predictions for thedecay spectra are highly model dependent, it is typicallyassumed that roughly 1=3 of the energy goes into eachannihilation channel. Constraints on such scenarios areavailable from the Galactic center and the extragalacticgamma-ray and neutrino backgrounds [94–97]. In thissection, we consider how such constraints are affectedwhen the increase in the annihilation rate due to enhanceddark matter densities after the formation of dark stars istaken into account.

A. Gamma-ray constraints

We adopt the formalism of Mack et al. [97] who recentlyaddressed the direct annihilation of massive dark matterparticles into gamma rays. The background intensity I� isgiven from an integration along the line of sight as

I� ¼ c

4�

Z dzP�ð½1þ z��; zÞHðzÞð1þ zÞ4 ; (8)

where P�ð�; zÞ is the (proper) volume emissivity ofgamma-ray photons, which is given as

P� ¼ �b�ðð1þ zÞ��mDMÞmDMh�vin2DMC; (9)

where h�vi ¼ 3� 10�26 cm3 s�1 denotes the thermallyaveraged annihilation cross section, �b ¼ 1=3 is theadopted branching ratio to gamma rays, and mDM themass of the dark matter particle in keV. C refers to the

dark matter clumping factor. This clumping factor dependson the adopted dark matter profile and the assumptionsregarding substructure in a halo [98–101]. Here we use theclumping factor for a NFW dark matter profile [102] whichhas been derived by Ahn and Komatsu [98,103]. For z <20, it is given in the absence of adiabatic contraction as apower law of the form

CDM ¼ CDMð0Þð1þ zÞ�; (10)

where CDMð0Þ is the clumping factor at redshift zero and determines the slope. For a NFW profile [102], CDMð0Þ �105 and � 1:8. The enhancement due to adiabatic con-traction is taken into account by defining

C ¼ CDMfenh; (11)

where the factor fenh describes the enhancement of the haloclumping factor due to adiabatic contraction (AC). Wehave estimated this effect based on the results of Ioccoet al. [19], comparing a standard NFW profile with theenhanced profile that was created during dark star forma-tion. We only compare them down to the radius of the darkstar and find an enhancement of the order �103. For theNFW case, the clumping factor would be essentially un-changed when including smaller radii as well, while theAC profile is significantly steeper and the contribution


043510-7

from inside would dominate the contribution to the haloclumping factor. However, as the annihilation products aretrapped inside the star, it is natural to introduce an innercutoff at the stellar radius. In addition, we have to considerthe range of halo masses and redshifts in which dark starsmay form. We assume that the halo mass must be largerthan the filtering mass to form dark stars. However, there isalso an upper mass limit. Halos with masses above

Mc ¼ 5� 107M��

10

1þ z

�3=2

(12)

correspond to virial temperatures of 104 K [61] and arehighly turbulent [62]. It seems thus unlikely that stars willform on the very cusp of the dark matter distribution insuch halos, and more complex structures may arise. Wethus assume that dark stars form in the mass range betweenMF and Mc. Once Mc becomes larger than MF, dark starformation must end naturally. In fact, it may even endbefore, as discussed in Sec. III. To obtain the highestpossible effect, we assume that dark stars form as long aspossible. We thus have

fenh ¼�1þ 103

fcollðMFÞ � fcollðMcÞfcollðMFÞ

�: (13)

In Fig. 4, we compare the results with EGRETobservationsof the gamma-ray background [104]. In the absence ofadiabatic contraction, the predicted background peaks atthe contribution from redshift zero [97]. We find that theenhancement of annihilation due to adiabatic contractionproduces a second peak in the predicted background whichoriginates from higher redshifts. In this scenario, particlemasses smaller than 30 GeV can thus be ruled out.

B. Neutrino constraints

The contribution to the cosmic neutrino flux can beobtained in analogy to Eq. (8). As recent works [95,96],we adopt an annihilation spectrum of the form

P� ¼ �b�ðð1þ zÞ��mDMÞmDMh�vin2DMCneutrino; (14)

which is analogous to the spectrum for annihilation intogamma rays. The branching ratio to neutrinos is assumedto be 1=3 as well, and the annihilation comes from thesame dark matter distribution, thus yielding Cneutrino ¼ C.

The atmospheric neutrino background has been calculatedfrom different experiments with generally good agreement[105–109]. Iocco [17] adopted a similar atmospheric neu-trino flux for comparison with the expected neutrino fluxfrom dark stars. We adopt here the data provided by Hondaet al. [105] and compare them to the predicted backgroundin Fig. 5. The predicted background is always well belowthe observed background.

C. Emission from dark star remnants

In the previous subsections, we have included the en-hancement of the halo clumping factor down to the stellarradius, as by definition the annihilation products on smallerscales are trapped inside the star. At the end of their life-time, these stars may explode and the baryon density in thecenter may be largely depleted. The dark matter densityhas certainly been significantly reduced due to annihila-tions during the lifetime of the star, but it may still beenhanced compared to the usual NFW case. A detailedcalculation of this effect is strongly model dependent. Aswe have seen above, the strongest constraints are obtained

FIG. 4. The predicted gamma-ray background due to directannihilation into gamma rays in the presence of adiabatic con-traction during the formation of dark stars, and the backgroundmeasured by EGRET (squares) [104]. One finds two peaks in theannihilation background for a given particle mass: one corre-sponding to annihilation at redshift zero, and one correspondingto the redshift where the enhancement from adiabatic contractionwas strongest.

FIG. 5. The predicted neutrino background due to direct anni-hilation into neutrinos in the presence of adiabatic contractionduring the formation of dark stars, and the atmospheric neutrinobackground [105]. One finds two peaks in the annihilationbackground for a given particle mass: one corresponding toannihilation at redshift zero, and one corresponding to theredshift where the enhancement from adiabatic contractionwas strongest.


043510-8

for direct annihilation into gamma rays, which is the casewe pursue here in more detail.

So far, we assumed that dark stars form in halos betweenthe filtering mass MF and the mass corresponding to avirial temperature of 104 K, Mc. To obtain an upper limit,it is sufficient to assume that in all halos above MF a darkstar remnant will form at some point. Such an assumptionclearly overestimates the total contribution at low redshift.When the dark star has formed, a fraction fcore � 10�6 ofthe dark matter from the total halo is in the star [20]. Forthe upper limit, we assume that the total amount of darkmatter in the star will contribute to the x-ray background(in fact, however, only the dark matter left over in the finalremnant can contribute). In this case, we have a propervolume emissivity

P� ¼ �ðð1þ zÞ��mDMÞmDMfrfanDMfcoredfcollðMFÞ

dt;

(15)

where nDM is the mean proper number density of darkmatter particles, mDM the particle mass in keV, anddfcoll=dt can be evaluated from Eq. (5). The model-dependent factor fr determines which fraction of thedark matter in the star will be left in the remnant. We adoptfr ¼ 1 to obtain an upper limit. The factor fa determinesthe fraction of the remaining dark matter which actuallyannihilates, which we set to fa ¼ 1 as well. In Fig. 6, wecompare the results with EGRET observations [104]. Wefind that the maximum contribution is clearly above theobserved background.

Whether this maximum contribution can be reached is,however, uncertain and the previous work in the literatureonly allows one to make rather crude estimates. For in-stance Iocco et al. [19] calculate the density profile for a

fiducial 100M� protostar, finding that the density withinthe star roughly scales with r�2 outside a plateau at a radiusr� 1011 cm. At the stellar radius of �1014 cm, the darkmatter density is still �1012 GeV cm�3. The time scale toremove this dark matter enhancement by annihilation is�100 Myr for 100 GeV neutralinos. We need to estimatewhich fraction of the dark matter inside the star will be leftat the end of its life, where the gas density is expelled by asupernova explosion and the dark matter annihilation fromthis region may contribute to the cosmic gamma-raybackground.Yoon et al. [22] adopted a time scale of 100 Myr, the

typical merger time scale at these redshifts, as the maxi-mum lifetime for dark stars. Depending on the scatteringcross section and the environmental density, the actual darkstar lifetime may be considerably shorter. Indeed, as weshowed in Sec. III C, it is difficult to reconcile lifetimes of�100 Myr with appropriate reionization scenarios. It istherefore reasonable to assume shorter time scales. In sucha case, a reasonable estimate is that �40% of the darkmatter inside the star would be left at the end of its life.This would still be enhanced compared to the standardNFW profile. In this case, the parameter fr is �40%, andfa may be of order 1, as the annihilation time scale iscomparable to the Hubble time. We note that these num-bers are highly uncertain, in particular, regarding the exactevolution of dark matter density during the lifetime of thestar, the effect of a supernova explosion on the dark mattercusp as well as the consequences of minor mergers.There is however also a viable possibility that the dark

matter distribution inside the star is significantly steeperthan assumed above. In the case of dark matter capture byoff-scattering from baryons, the dark matter density insidethe star follows a Gaussian shape and is highly concen-trated in a small region of r� 2� 109 cm [17,21,22,110].The implications are not entirely clear. If capture of darkmatter stops at the end of the life of the star, the densityinside the star will annihilate away quickly, and no signifi-cant contribution may come from the remnant. If, on theother hand, dark matter capture goes on until the end of thelife of the star, a contribution to the background seemsviable. In summary, this may provide a potential contribu-tion to the cosmic background, but its strength is stillhighly uncertain and should be explored further by futurework.

D. Dependence of dark star models on the neutralinomass

We conclude this section with a discussion on the con-straints from cosmic backgrounds for different neutralinomasses. As dark star models in the literature mostly con-sider neutralinos of 100 GeV, there are uncertainties thatneed to be addressed when considering different neutralinomasses. For models involving the capture of dark matter,Iocco [17] states that the mass of the neutralino does not

FIG. 6. The maximum gamma-ray background due to directannihilation into gamma rays in the remnants of dark stars, andthe background measured by EGRET [104]. The actual contri-bution to the gamma-ray background is highly model dependent(see discussion in the text).


043510-9

change the annihilation luminosity. Taoso et al. [21] findthat variations due to different neutralino masses are lessthan 5%. While these results may hold for high masses,Spergel and Press [111] showed that for neutralino massesbelow 4 GeV, they would evaporate from the star, asscattering with baryons can upscatter them as well.

In addition, the AC phase may be modified as well, asthe dark matter annihilation rate in this phase is degeneratein the parameter h�vi=mDM. Iocco et al. [19] find that theduration of the AC phase may change by almost 50% if thedark matter mass is changed by a factor of 2. The effect ofdifferent neutralino masses is therefore uncertain andshould be explored in more detail. Wewill however assumethat the general behavior involving adiabatic contraction inthe minihalo is still similar, such that the calculationsbelow are approximately correct also for different neutra-lino masses.

VI. COSMIC CONSTRAINTS ON LIGHT DARKMATTER

Observations of 511 keV emission in the center of ourGalaxy [112] provide recent motivation to models of lightdark matter [113]. Such observational signatures can beexplained assuming dark matter annihilation, while othermodels still have difficulties reproducing the observations[3]. The model assumes that dark matter annihilates intoelectron-positron pairs, which in turn annihilate into511 keV photons. Direct annihilation of dark matter intogamma rays or neutrinos is assumed to be suppressed toavoid the gamma-ray constraints and to ensure a sufficientpositron production rate. It is known that electron-positronannihilation occurs mainly via positronium formation inour galaxy [114]. In addition, it was shown [115] that darkmatter annihilation to electron-positron pairs must be ac-companied by a continuous radiation known as internalbremsstrahlung, arising from electromagnetic radiativecorrections to the dark matter annihilation process.

Motivated by these results, it was proposed that internalbremsstrahlung from dark matter annihilation may be re-sponsible for the gamma-ray background at energies of 1–20 MeV [103]. Conventional astrophysical sources cannotexplain the observed gamma-ray background at these fre-quencies [10]. A comparison of the observed and predictedbackground below 511 keV yields constraints on the darkmatter particle mass [98]. Here we examine whether andhow this scenario is affected if dark stars form in the earlyuniverse. We use a thermally averaged cross sectionh�vi � 3� 10�26 cm3 s�1 to account for the observeddark matter density [8]. This implies that h�vi is velocityindependent (S-wave annihilation). While Boehm et al. [3]argue that S-wave annihilation overpredicts the flux fromthe Galactic center, others argue that it is still consistent[98,103]. The cross section adopted here is well within theconservative constraints of Mack et al. [97]. The effect oflight dark matter annihilation on structure formation in the

early universe has been studied in various works, e.g. [116–118]. Constraints from upcoming 21 cm observations havebeen explored by Furlanetto et al. [86] and Valdes et al.[119], while constraints from background radiation havebeen considered by Mapelli and Ferrara [120]. The effectsof early dark matter halos on reionization have been ad-dressed recently by Natarajan and Schwarz [121].As in the previous section, we point out that significant

uncertainties are present when considering dark star mod-els for different dark matter masses, as this question islargely unexplored. In particular, we emphasize that nocapturing phase will be present for light dark matter, asshown in the work of Spergel and Press [111]. Anotheruncertainty is the question whether to adopt self-annihilating dark matter (i.e. Majorana particles) or parti-cles and antiparticles of dark matter. In the calculationsbelow, we assume that light dark matter is self-annihilating. Otherwise, our results would be changed bya factor of 0.5.

A. 511 keV emission

The expected x-ray background from 511 keV emissionis calculated from Eq. (8). The volume emissivity of511 keV photons is given as

P� ¼ �ðð1þ zÞ�� 511Þ511 keV�511h�vin2DMC511;

(16)

where h�vi denotes the thermally averaged annihilationcross section, �511 is the fraction producing an electron-positron pair per dark matter annihilation process, and �511

the frequency corresponding to 511 keV. In our Galaxy,this process happens via positronium formation [114], andwe assume that the same is true for other galaxies. In 25%of the cases, positronium forms in a singlet (para)statewhich decays to two 511 keV photons, whereas 75%form in a triplet (ortho)state which decays into a contin-uum. We thus adopt �511 ¼ 1=4 for 511 keV emission.C511 refers to the dark matter clumping factor, which is stillhighly uncertain. The main uncertainty is due to theadopted dark matter profile and the assumptions regardingsubstructure in a halo [98–101].Here we use the clumping factor for a NFW dark matter

profile [102] which has been derived by Ahn and Komatsu[98,103], as to our knowledge, no calculations of dark starformation are available for other dark matter profiles. Forz < 20, it is given as a power law as

CDM ¼ CDMð0Þð1þ zÞ�; (17)

where CDMð0Þ describes the clumping factor at redshiftzero and determines the slope. For a NFW profile [102],CDMð0Þ � 105 and� 1:8. The effects of different clump-ing factors will be explored in future work [122]. Ahn andKomatsu [98,103] included contributions from all haloswith masses above a minimal mass scale Mmin, which wasgiven as the maximum of the dark matter Jeans mass and


043510-10

the free-streaming mass. This approach assumes instanta-neous annihilation of the created electron-positron pairs.As pointed out by Rasera and Teyssier [123], the assump-tion of instantaneous annihilation is only valid if the darkmatter halo hosts enough baryons to provide a sufficientlyhigh annihilation probability, postulating this to happen inhalos with more than 107–1010M�, corresponding to theircalculation of the filtering mass. We also calculate thefiltering mass according to the approach of Gnedin andHui [47] and Gnedin [48], but obtain somewhat lowermasses, with �105M� halos at the beginning of reioniza-tion and �3� 107M� at the end [25]. This is also inagreement with numerical simulations of Greif et al. [62]which find efficient gas collapse in halos of 105M�. Thediscrepancy may also be due to their different reionizationmodel, which assumes reionization to start at redshift 20.

We recall that the clumping factor can be considered asthe product of the mean halo overdensity, the fraction ofcollapsed halos above a critical scale, and the mean ‘‘haloclumping factor’’ that describes dark matter clumpinesswithin a halo. To take into account that electron-positronannihilation occurs only in halos above the filtering massMF, we thus rescale the results of Ahn and Komatsu[98,103] as

C511 ¼ fcollðMFÞfcollðMminÞCDMfenh; (18)

where the factor fenh is given from Eq. (13). As above, weassume that the halo mass must be larger than the filteringmass and lower than the critical mass scale Mc that corre-sponds to virial temperatures of 104 K. For comparison, wewill also calculate 511 keV emission with fenh ¼ 1. We

note that the resulting background will be somewhat lowerthan the result of Ahn and Komatsu [98], as we adopted�511 ¼ 1=4 and include only halos above the filtering massscale in the clumping factor. In Fig. 7, we compare theresults with the observed x-ray background from theHEAO experiments [124,125] and SWIFT [126]/BATSE[127] observations [128]. In the standard NFW case, wefind a lower limit for the dark matter particle mass of7 MeV. For the case with adiabatically contracted profilesdue to dark star formation, we find a slightly higher lowerlimit of 10 MeV. This is because the enhancement iseffective only for frequencies h� < 100 keV, where theobserved background is significantly larger than at511 keV, where Ahn and Komatsu [98] obtained theirupper limit.

B. Internal bremsstrahlung

The internal bremsstrahlung is calculated according tothe approach of Ahn and Komatsu [103]. The backgroundintensity is given by Eq. (8), with a proper volume emis-sivity

P� ¼ 1

2h�h�viCbremsn

2DM

�4�

�

gð�Þ�

�; (19)

where �� 1=137 is the fine structure constant and gð�Þ isa dimensionless spectral function, defined as

gð�Þ ¼ 1

4

�ln

~s

m2e

� 1

��1þ

�~s

4m2DM

�2�; (20)

with ~s ¼ 4mDMðmDM � h�Þ. As Ahn and Komatsu [103]pointed out, bremsstrahlung is emitted in all dark matterhalos, regardless of the baryonic content. There is thus noneed to consider any shift in the minimal mass scale; theonly thing to take into account is the enhancement ofannihilation due to the AC profiles. The clumping factorCbrems is thus given as

Cbrems ¼ CDMfenh; (21)

where fenh is given by Eq. (13). In Fig. 8, we compare theresults with the observed gamma-ray background from theHEAO experiments [124] and SWIFT/BATSE observa-tions [128], as well as SMM [129,130] and Comptel[131] data [132]. We find that the signal is almost un-changed in the model taking into account dark star for-mation. The reason is that dark stars form mainly at highredshifts, in the range whereMF <Mc, while the dominantcontribution to the background comes from redshift zero.Our results agree with Ahn and Komatsu [103].

C. Emission from dark star remnants

As in Sec. VC, we consider a scenario where dark starsexplode at the end of their lifetime and dark matter anni-

FIG. 7. The predicted x-ray background due to 511 keV emis-sion for different dark matter particle masses. Solid lines:enhanced signal due from adiabatic contraction. Dotted lines:conventional NFW profiles. The observed x-ray backgroundfrom the HEAO experiments (squares) [124] and Swift/BATSE(triangles) [128] is shown as well. The comparison yields a lowerlimit of 10 MeV on the dark matter mass for the adiabaticallycontracted profiles, and 7 MeV for standard NFW halo profiles.


043510-11

hilation products in their remnants contribute to the cosmicbackground. For simplicity, we consider 511 keVemissiononly, which is also mostly sensitive to modifications at highredshift. Again, we assume that dark stars form in halosbetween the filtering massMF and the mass correspondingto a virial temperature of 104 K, Mc. In this case, thevolume emissivity is given as

P� ¼ �ðð1þ zÞ�� 511Þ511 keV�511frfanDMfcore

� dfcollðMFÞdt

; (22)

where nDM is the mean proper number density of darkmatter particles and dfcoll=dt can be evaluated fromEq. (5). The model-dependent factor fr determines whichfraction of the dark matter in the star will be left in theremnant; we adopt fr ¼ 1 to obtain an upper limit. Thefactor fa determines the fraction of the remaining darkmatter which actually annihilates, which we set to fa ¼ 1as well. As in Sec. VIA, �511 ¼ 1=4 is the fraction ofelectron-positron annihilations per one dark matter annihi-lation process, corresponding to annihilation via positro-nium formation. In Fig. 9, we compare the results with theobserved x-ray background from the HEAO experiments[124] and SWIFT/BATSE observations [128].

For dark matter particle masses below 30 MeV, theupper limit found here is higher than the observed back-ground. Again, as discussed in Sec. VC, there are signifi-cant uncertainties regarding the question whether this highcontribution can be reached, both due to uncertainties inthe dark star models, which have not been explored for

light dark matter, as well as the impact of a supernovaexplosion on the dark matter cusp. These possibilitiesshould be addressed further in future work.

VII. SUMMARYAND DISCUSSION

In this work, we have examined whether the suggestionof dark star formation in the early universe is consistentwith currently available observations. We use these obser-vations to obtain constraints on dark star models and darkmatter properties. From considering cosmic reionization,we obtain the following results:(i) Dark stars with masses of the order 800M� as sug-

gested by Freese et al. [20] can only be reconciledwith observations if somewhat artificial double-reionization scenarios are constructed. They consistof a phase of dark star formation followed by a phaseof weak Pop. II star formation and a final star burst toreionize the Universe until redshift 6.

(ii) The same is true for dark stars in which the numberof UV photons is significantly increased due to darkmatter capture, as suggested by Iocco et al. [19].

(iii) It appears more reasonable to require that darkstars, if they were common, should have similarproperties as conventional Pop. III stars. For MS-dominated models, this requires that typical darkstar masses are of order 100M� or below. For CDmodels it requires a dark matter density above1011–1012 GeV cm�3 if a spin-dependent elasticscattering cross section of t� 10�39 cm2 is as-sumed [22].

(iv) Alternatively, it may imply that the elastic scatter-ing cross section is smaller than the current upperlimits, that the dark matter cusp is destroyed by

FIG. 8. The predicted gamma-ray background due to brems-strahlung emission for different dark matter particle masses.Solid lines: enhanced signal due from adiabatic contraction.Dotted lines: conventional NFW profiles. The lines overlapalmost identically, as the main contribution comes from redshiftzero, where the clumping factor is large and dark stars areassumed not to form. The observed gamma-ray backgroundfrom the HEAO experiments (squares) [124], Swift/BATSE(triangles) [128], COMPTEL (crosses) [132], and SMM (plus-ses) [129] is shown as well.

FIG. 9. The upper limit of x-ray radiation due to dark starremnants. The observed x-ray background from the HEAOexperiments (squares) [124] and Swift/BATSE (triangles) [128]is shown as well. Only for very low dark matter particle masses,the upper limit is somewhat higher than the observed back-ground. However, the actual contribution may be lower bysome orders of magnitude (see discussion in the text).


043510-12

mergers or friction with the gas or that the star isdisplaced from the center of the cusp.

(v) A further interpretation is that dark stars are veryrare. This would require some mechanism to preventdark star formation in most minihalos.

(vi) However, if the double-reionization models areactually true, it would indicate that dark starsform only at redshifts beyond 14, which makesdirect observations difficult.

(vii) We also note that 21 cm observations may eitherconfirm or rule out double-reionization models.

We have also examined whether the formation of darkstars and the corresponding enhancement of dark matterdensity in dark matter halos due to adiabatic contractionmay increase the observed x-ray, gamma-ray, and neutrinobackground. Here we found the following results:

(i) For massive dark matter particles, direct annihilationinto gamma-rays provides significant constraints formasses less than 30 GeV.

(ii) For massive dark matter particles, the contributionfrom direct annihilation into neutrinos is well belowthe observed background.

(iii) In light dark matter scenarios, the 511 keVemissionis significantly enhanced below frequencies of100 keV in the observer’s rest frame. For a certainrange of parameters, this emission may even form asignificant contribution of the total x-ray back-ground. In this case, we derive a lower limit of10 MeV for the dark matter particle mass (whilewe find 7 MeV for standard NFW profiles).

(iv) In light dark matter scenarios, the background ra-diation due to internal bremsstrahlung is not af-fected significantly from adiabatic contraction atearly times, as the main contribution comes fromlow redshift.

(v) Both for light and massive dark matter particles, theannihilation products in the remnants of dark stars

may provide significant contributions that may beused to constrain such models in more detail.However, whether this contribution can be reachedis highly model dependent and relevant questionsregarding the death of dark stars have not beenexplored in the literature.

Future observations may provide further constraints onthis exciting suggestion. Small-scale 21 cm observationsmay directly probe the HII regions of the first stars andprovide a further test of the luminous sources at highredshift, and extremely bright stars might even be observedwith the James-Webb telescope, if they form sufficientlylate. With this work, we would like to initiate a discussionon observational tests and constraints on dark stars, whichmay tighten theoretical dark star models and provide a newlink between astronomy and particle physics.

ACKNOWLEDGMENTS

We thank Katie Freese for raising our interest in thisresearch during her visit in Heidelberg and Fabio Iocco forinteresting comments and discussions. We also thankKyungjin Ahn and Simon Glover for interesting discus-sions on dark matter annihilation and the gamma-ray back-ground, Duane Gruber for providing the HEAO andComptel-data and Ken Watanabe for providing the SMMdata. We acknowledge discussions with Arthur Hebeckeron x-ray emission from dark star remnants. D. S. thanks theHeidelberg Graduate School of Fundamental Physics(HGSFP) and the LGFG for financial support. TheHGSFP is funded by the Excellence Initiative of theGerman Government (Grant No. GSC 129/1). R. B. isfunded by the Emmy-Noether grant (DFG) BA 3607/1.R. S. K. is grateful for support from the Emmy-NoetherGrant No. KL 1358/1. All authors also acknowledge sub-sidies from the DFG SFB 439 Galaxies in the EarlyUniverse.

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