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Mon.Not.R.Astron.Soc.000,000–000 (0000) Printed5February2008 (MNLATEXstylefilev1.4) Constraining dark matter through 21 cm observations M. Valdés1, A. Ferrara1, M. Mapelli1, E. Ripamonti2 1 SISSA/ISAS, viaBeirut 2-4, 34014 Trieste,Italy; 2KapteynAstronomical Institute, University of Groningen, Postbus 800, 9700 AV, Groningen, The Netherlands. 5February2008 7 0 ABSTRACT 0 Beyond reionization epoch cosmic hydrogen is neutral and can be directly observed 2 through its 21 cm line signal. If dark matter (DM) decays or annihilates the corre- n sponding energy input affects the hydrogen kinetic temperature and ionized fraction, a and contributes to the Lyα background. The changes induced by these processes on J the 21 cm signal can then be used to constrain the proposed DM candidates, among 0 which we select the three most popular ones: (i) 25-keV decaying sterile neutrinos, 1 (ii) 10-MeV decaying light dark matter (LDM) and (iii) 10-MeV annihilating LDM. AlthoughwefindthattheDMeffectsareconsiderablysmallerthanfoundbyprevious 1 studies(duetoamorephysicaldescriptionoftheenergytransferfromDMtothegas), v we conclude that combined observations of the 21 cm background and of its gradient 1 shouldbeabletoputconstrainsatleastonLDMcandidates.Infact,LDMdecays(an- 0 3 nihilations) induce differential brightness temperature variations with respect to the 1 non decaying/annihilating DM case up to ∆δTb =8 (22) mK at about 50 (15) MHz. 0 In principle this signal could be detected both by current single dish radio telescopes 7 and future facilities as LOFAR; however, this assumes that ionospheric, interference 0 and foreground issues can be properly taken care of. / h Key words: intergalactic medium - cosmology: theory - diffuse radiation - dark p matter - o r t s a 1 INTRODUCTION ananalysisofthefeaturesofHI21cmmapsfrom theDark : v Agescouldalsoallowtoputconstrainsontheexistenceand i Cosmic recombination at z ∼ 1000 left the gas in the Uni- nature of decaying and annihilating Dark Matter (DM). In X versein anearly uniform,dark,neutralstatewhichwecur- fact, if DM actually decays or annihilates, the injection of ar rently denote as the Dark Ages of the Universe. Gas re- highenergyphotonsintotheIGMwouldheatandionizethe mained neutral until the first luminous objects emerged at neutralgas,leavinganimprintonthe21cmbackgroundsig- z ∼ 20−30, leading to the complete reionization of the in- nalwhichcouldbedirectlyobserved(Shchekinov&Vasiliev tergalactic medium (IGM) at a later, yet unknown,epoch. 2006; Furlanetto, Oh, & Pierpaoli 2006). The investigation of the Dark Ages is one of the fron- TheimportanceofDMdecaysandannihilationsonthe tiers of modern cosmology and a new generation of radio reionization history has been analyzed in detail by several interferometersiscurrentlyindevelopmenttostudythered- authors.Mostauthorshavecometotheconclusionthatthe shifted21cmhyperfinetriplet-singletleveltransitionofthe effects of DM on the overall reionization process are rela- ground state of neutral hydrogen. Instruments such as the tively small and they cannot compete with those induced LOwFrequencyARray(LOFAR),the21CentimeterArray by more conventional ionizing sources as stars and (mini-) (21CMA), the Mileura Wide-field Array (MWA) and the quasars. However, as we will explain in detail later on, ra- Square Kilometer Array (SKA), are expected to reach the diation from decaying/annihilating DM might change the sensitivity required to map the HI distribution at angular thermal and ionization history of the gas to such an extent resolutionoftheorderofafewarcminutes(e.g.Pen,Wu,& thatdifferenceswiththecaseinwhichDMisnotconsidered Peterson 2004; Bowman, Morales, & Hewitt 2005; Kassim are large enough to produce a clear signature in observable et al. 2004; Wyithe,Loeb, & Barnes 2005). 21 cm signal. Assessing the amplitude of these deviations The main scientific goal of such instruments is to per- from thestandard scenario requires acareful study of com- formanaccuratetomographyofmatterduringtheseremote plex physical processes, and in particular of the amount of cosmic epochs, and reconstruct in detail the latest phases energy that can be transferred from the decay/annihilation of the reionization history. However, this might not be the products to the IGM. A recent study (Ripamonti, Mapelli, only major achievement of such experiments. For example, & Ferrara2006a, hereafter RMF06a) findsthat only a rela- (cid:13)c 0000RAS 2 Valdés, Ferrara, Mapelli, Ripamonti tively small fraction of theinjected energy is effectively ab- nDM,0,τDMandhσvidependfromthepropertiesofthecho- sorbed by the IGM and goes into heating and reionization. sen DM candidate (see Secs. 2.1 and 2.3). Asaresult,theeffectsonthe21cmbackgroundsignalmight besmallerthanpreviouslypredicted(Shchekinov&Vasiliev 2006; Furlanettoetal.2006);hence,thequestionremainsif 2.1 The energy absorbed fraction theDMsignalcanstillbeobservedbynextgenerationradio The most delicate term in eq. (1) is represented by f (z), interferometers.Ifso,thisexperimentwouldconstituteasu- abs i.e. the fraction of the DM particle rest mass that is ab- perbtool todistinguish among differentDMcandidatesvia sorbed by the gas at a given redshift z; f strongly de- theirdecaying/annihilatingproperties.Inthispaperwecal- abs pendsonhowthedecay/annihilationproductsinteractwith culate the effects of DM decays/annihilations on the 21 cm theIGM. Sinceaccounting for thephysicalprocesses which background for some of the most popular DM candidates, govern such interactions is quite complicated, most of pre- such as decayingor annihilating Light Dark Matter (LDM) vious studies assume that: (i) all the energy released by and decaying sterile neutrinos. DM decays/annihilations is immediately absorbed (Hansen Therestofthepaperisorganizedasfollows.InSec.2we &Haiman2004;Pierpaoli2004;Biermann&Kusenko2006; briefly introducetheDMcandidates and their effect on the Mapellietal.2006),(ii)leavef asafreeparameter(Pad- IGM; in Sec. 3 we provide the basic equations to study the abs manabhan & Finkbeiner 2005; Zhang et al. 2006), or (iii) 21cmradiationinpresenceofdecaying/annihilatingDM.In makeapartialtreatmentoftheenergyredistribution(Chen Sec. 4 we present the results of our calculations, which are & Kamionkowski 2004; Mapelli & Ferrara 2005). then discussed in Sec. 5. Throughout thepaper we assume, Recently,RMF06ahavecalculatedbehaviouroff (z) inagreementwiththe3-yrWMAPdataanalysis(Spergelet abs in detail, for the most common case in which the deal. 2006), a ΛCDM cosmology with Ωm = 0.24, ΩΛ = 0.76, h = 0.73, Ωb = 0.042, H0 = 100hkms−1Mpc−1. cay/annihilation products are photons, active neutrinos or electron-positron pairs. Photons are affected by Compton scattering and photo-ionization; for pairs, the relevant processes are inverse Compton scattering, collisional ionizations, and positron annihilations. 2 BASIC PHYSICS RMF06afoundthat,ifthedecay/annihilationproducts We are interested in calculating the effects on HI 21 cm areeitherphotonsandactiveneutrinosorpairs,f isclose abs line signal produced by two among the most popular low- tothemaximum allowed value(equalto 0.5 for sterile neu- mass DM candidates, i.e. LDM (∼1−10 MeV) and sterile trinos, due to the active neutrino production, and equal to neutrinos (∼ 2−50 keV). In the case of sterile neutrinos 1 for LDM) only at very high redshift (z ≫ 100). At lower only the decay process is allowed; LDM particles instead redshifts,f rapidlydropstovalues<0.1;also,thehigher abs canbothdecayandannihilate.WeneglectheavierDMcan- is the mass of the progenitor DM particle, the faster is the didates (with mass larger than ∼ 100 MeV) because previ- decreaseoff .Thus,accountingforthecorrectf (z)de- abs abs ousstudies(Mapelli,Ferrara&Pierpaoli2006)havealready terminationdramaticallyreducesthepossibleeffectsofDM shown that, even assuming that all the energy released fol- decaysandannihilationsontheIGMheatingandionization lowing annihilations is immediately absorbed by the IGM, (RMF06a) with respect to previous estimates. theyrepresentanegligibleheating/ionization sourceforthe Inthispaper,forthefirsttime,wewilladoptthecorrect gas. estimate of f (z) (as given in RMF06a) in order to eval- abs Both in the case of sterile neutrinos and of LDM, the uate the impact of DM decays and annihilations on 21 cm rateofenergytransferperbaryontotheIGMcanbewritten emission. Previous papers(e.g. Furlanettoet al. 2006) have as(RMF06a;Ripamonti,Mapelli&Ferrara2006b,hereafter assumedaredshift-independentf (z),whichappearstobe abs RMF06b): quite unrealistic (for a discussion, see Sec. 4) and leads to E˙x(z)=fabs(z)n˙DM(z)mDMc2, (1) oeffpeticmtsisttoic2u1pcpmermliampist.s for the contribution of DM-related wheremDMisthemassoftheDMparticleandcisthespeed Differently from Furlanetto et al. 2006, who do not se- of light. The energy absorbed fraction, f (z), is discussed lectanyspecificDMcandidateandleavethedecayrateasa abs indetailinthefollowing; n˙DM(z)isthedecreaserateofthe freeparameter,wechosetoconsiderthreespecificDMcan- numberof DM particles per baryon. didates (sterile neutrinos, decaying LDM and annihilating In the case of DMdecays, n˙DM(z) is given by LDM). This choice allows us to give predictions which can be more easily related to other DM measurements, such as n˙DM(z)≃ nDM,0, (2) the X-ray constraints on the sterile neutrino mass (Watson τDM et al. 2006; Boyarsky et al. 2006a) or the detection of the where nDM,0 and τDM are the current number of DM par- 511-keVemission linefrom theGalactic center(Knödlseder ticles per baryon and the lifetime of DM particles, respec- et al. 2005). tively. For theannihilations: 1 2 3 2.2 Sterile neutrinos n˙DM(z)≃ 2nDM,0Nb(0)hσvi(1+z) , (3) Many models of sterile neutrinos have been proposed, with whereNb(0)=2.5×10−7 cm−3 isthecurrentbaryonnum- massrangingfromeVtoTeV.Here,weareinterestedinster- berdensity(Spergeletal.2006), andhσviisthethermally- ile neutrinosaswarm DM(WDM) candidates, with masses averagedDMannihilationcrosssection.ThevaluesofmDM, of the order of a few keV (∼ 2−50 keV). These particles (cid:13)c 0000RAS,MNRAS000,000–000 Constraining DM through 21 cm observations 3 candecayintoanactiveneutrinoandaphoton(Dolgov2002 0.068 K is the temperature corresponding to the transition and references therein). energy. The mass (and thus the lifetime) of radiatively decay- In the presence of the Cosmic Microwave Background ing sterile neutrinos can be constrained by the absence of (CMB) alone, the spin temperature reaches thermal equi- any detection of X-ray lines consistent with photonsdueto librium with TCMB = 2.73(1+z) K on a short time-scale, sterile neutrinodecaysin galaxy clusters(Abazajian, Fuller making theHI undetectablein emission or absorption. & Tucker 2001; Abazajian 2006; Abazajian & Koushiappas Twomechanismscandecouple TS from TCMB:(i)colli- 2006; Boyarsky et al. 2006b) or in galaxies (Watson et al. sions,whichareeffectivemainlyatz≥70duetothehigher 2006obtainedthestrongestconstraintsfromthestudyofthe meanIGMdensity,and(ii)scatteringbyLyαphotons−the Andromedagalaxy).Otherconstraints come from thecom- so-called Wouthuysen-Field process or Lyα pumping (e.g. parison between the unresolved X-ray background and the Wouthuysen 1952; Field 1959; Hirata 2005) − which cou- expectedcontribution from sterile neutrinodecays(Mapelli plesT tothekineticgastemperatureT viathemixingof S K & Ferrara 2005; Boyarsky et al. 2006a). thehyperfinelevelsoftheHIgroundstatethroughinterme- In this paper we consider the representative case of diate transitions to the excited 2p state. m =25 keV sterile neutrinos, whose contribution to heat- The spin temperatureis thengiven by theequation: ν ing is maximum (RMF06a), due to the weakness of the T +y T +y T available constraints on lifetime for neutrinos of such mass. TS = CMB1+yα+ky c k (5) α c For such particle the upper limits on the lifetime and the where T is the kinetic temperature, and the Lyα and col- present number density number per baryon are τDM = k 9.67 × 1025 s and nDM,0 = 1.88 × 105, respectively (see lisional coupling coefficients are given by the following expressions: RMF06a, RMF06b). The contribution of other sterile neu- trinosmassestothe21cmlineisexpectedtobecomparable P10T∗ y = , (6) or smaller than for thecase considered here. α A10Tk C10T∗ y = , (7) c A10Tk 2.3 Light dark matter where We define as LDM particles all the DM candidates whose mass is 1 ≤ m /MeV ≤ 100. Such particles have been C10 =k10nHI+neγe, (8) LDM suggested as a possible source for the detected 511-keV ex- and cess from the Galactic centre (Knödlseder et al. 2005). Ac- 16πJ σ cordingtothisscenario,theirmaximumallowedmassmLDM P10 = 27 hαν α. (9) p α should be 20 MeV, not to overproduce detectable gamma rays via internal bremsstrahlung (Beacom, Bell & Bertone In the above equations A10 = 2.85×10−15s−1 is the spon- 2004),oreven∼3MeV,ifweconsideralsotheproductionof taneous emission coefficient of the 21 cm line, P10 is the indirect de-excitation rate of the hyperfine structure levels. gamma raysforinflight annihilationsofthepositrons(Bea- com & Yu¨ksel 2006). WewriteP10 =4Pα/27;inaddition,Pα=(4πJασα)/(hpνα) is theoutcome of theequation for the Lyαscattering rate, LDMcan decay orannihilate, producingphotons,neutrinos and pairs. We will treat both channels in detail and σ(ν) 4π J σ(ν) P =c dνn(ν) = dν ν , (10) assumethattheonlydecay/annihilationproductsarepairs, α Z ν h Z ν an assumption leading to an upper limit in terms of IGM in the case that σ(ν) is a δ function. A detailed investiga- heating (RMF06a). tionofthephysicsoftheWouthuysen-Fieldprocess(Hirata We consider, as a template, the case of 10-MeV LDM 2005) finds small corrections to these expressions which we particles, which again yields the most efficient heating case neglect here for simplicity. The coefficient C10 in eq. (8) (see RMF06a). For such particles the upper limits of the is the collisional de-excitation rate by hydrogen atoms and current number (per baryon), the lifetime and the cross- 2se.4ct×ion10a−r2e8 ncmDM3,s0−∼1, r4e4s6p,ecτtDivMely=(R4M×F10062a5).s, and hσvi ∼ e(1le9c6t9r)onfso,rwdhiffereerekn1t0teismtpaebrautlautreeds; iγne,Aallcicsoonrdi&ngDtaolgLairsnzot (2001), is logγ (T )=−9.607+logT 1/2exp(−(logT )4.5/1800).(11) e k k k 3 EFFECTS ON THE 21 CM RADIATION for Tk ≤104 K,while γe(Tk >104K)=γe(Tk =104K). For the Lyα pumping to be effective, a minimum Lyα 3.1 Lyα pumping background intensity, J , is required. This is given by the α The 21 cm line is associated with the hyperfine transition condition (Ciardi & Madau 2003): between the triplet and the singlet levels of the hydrogen J ≥9×10−23(1+z)erg cm−2s−1Hz−1sr−1, (12) α ground state. This transition is governed by the spin tem- at theredshift of interest. perature, T , defined as: S n1 =3exp −T⋆ , (4) n0 (cid:16) TS(cid:17) 3.2 IGM evolution and 21 cm background. wheren0andn1arethenumberdensitiesofhydrogenatoms Next,wewanttounderstandhowDMdecays/annihilations in the singlet and triplet ground hyperfinelevels, and T = affect the thermal and ionization evolution of the IGM, ⋆ (cid:13)c 0000RAS,MNRAS000,000–000 4 Valdés, Ferrara, Mapelli, Ripamonti Figure 1.Left panel:TS andTk asafunctionofredshift(25-keV sterileneutrinodecays, fabs asinRMF06a).Thinsolidline:TCMB; thicksolid(short-dashed)line:TS with(without)25-keVneutrinodecays;dotted(long-dashed)line:Tk with(without)25-keVneutrino decays.Right:TS andTk asafunctionofredshiftfor25-keVsterileneutrinodecaysandforfabs=0.5.Thelinesarethesameasinthe leftpanel. which, in turn, determines the level of the 21 cm back- absorbed DM energy deposited into the IGM as heating ground signal. The equation that describes the evolution (Shull& van Steenberg1985) and f = 0.24 is thehelium He of the ionized fraction x is the following (see e.g. Chen & fraction by mass. The Lyα heating resulting from repeated e Kamionkowski 2004): scatterings as the photons are redshifted into the Lyman resonances is negligible as it has been recently shown (see dx 1 − dze = H(z)(1+z)[Rs(z)−Is(z)−Ix(z)], (13) e.g.Chen&MiraldaEscude´2004).Theionizationandtem- perature eqs. (13)-(16) are solved using a modified version whereIx =E˙x/E0 isthecontributiontotheionization rate of RECFAST (Seager et al. 1999). due to DM; I and R are the standard ionization and re- A third equation is needed in order to compute the s s combination rates per baryon. Considering eqs. (1)-(3) we 21 cm backgroundi: the one describing the evolution of the havethat Lyαbackgroundintensity Jα.Following Madau, Meiksin & E˙ m c2 Rees(1997) we write: I =χ (z) x =f (z)χ (z)Γ f p (14) x i E0 abs i x x E0 N2hc χ E˙ (z) for DM decays, and J (z)= H x x αeff +x x γ + α x ,(17) α 4πH(z)(cid:20) e p 22P e HI eH NHhνα (cid:21) E˙ m c2 Ix =χi(z)Ex0 =fabs(z)χi(z)fx Ep0 nDM,0Nb(z)hσvi (15) where the first two terms are the contributions from re- forDMannihilations.InthelasttwoequationsE0=13.6eV combinationsandcollisionalexcitationsbyelectronimpacts, isthehydrogenionizationthreshold,m istheprotonmass, while the third term is theDM contribution. p χi is the fraction of the energy absorbed by the IGM from In the last equation NH=0.92Nb is the number den- DM decays/annihilations that goes into ionizations (χ ∼ sity of hydrogen atoms, αeff is the effective recombination i 22P (1−xe)/3, see Shull 1979, Shull & van Steenberg 1985), coefficient to the 22P level (Pengelly 1964), which includes fx =Ωx(z)/Ωb(z),Nb(z) is thebaryon numberdensity and direct recombinations to the 22P level and recombinations Γx =1/τDM. tohigherlevels, followed bytransitions tothe22P levelvia The equation regulating the evolution of IGM temper- all possible cascade paths. ature can be written as: Finally, γeH ≈ 2.2 × 10−8exp(−11.84/T4)cm3s−1 is dT l x the collisional excitation rate of HI atoms photons by elec- (1+z) k = 2T + γ e (T −T ) dz k H(z)(1+fHe+xe) k CMB tron impacts; χα is the net fraction of the absorbed X- ray photons from DM decays/annihilations which is con- 2χ E˙ vertedintoLyαphotons(Shull&vanSteenberg1985), and −3kbH(z)(1h+fxHe+xe) (16) T4=T/(104 K). OnceT (z)hasbeendeterminedthrougheq.(5),wecan S wherel =(8σ a T4 )/(3m c), χ is thefraction of the obtainthe21cmradiationintensity,whichcanbeexpressed γ T R CMB e h (cid:13)c 0000RAS,MNRAS000,000–000 Constraining DM through 21 cm observations 5 Figure2.Leftpanel:TS andTk asafunctionofredshift(10-MeVLDMdecays,fabsasinRMF06a).Thinsolidline:TCMB;thicksolid (short-dashed)line:TS with(without)10-MeVLDMdecays;dotted (long-dashed)line:Tk with(without) 10-MeVLDMdecays.Right: TS andTk asafunctionofredshiftfor10-MeVLDMdecays andforfabs=1.Thelinesarethesameasintheleftpanel. bythedifferentialbrightnesstemperaturebetweenaneutral possible, in principle, to constrain directly the DM nature hydrogen patch and the CMB: through 21 cm observations. To isolate the effect of DM, we will assume in the following that the entire cosmic dark T −T δTb ≃ S 1+CzMB τ, (18) matter content is constituted by particles of the considered type(sterile neutrinos or LDM), i.e. Ω =Ω −Ω . X m b where τ is the optical depth of the neutral IGM at 21(1+ z) cm: τ ≃ 32πk3Bc3νh0p2ATS10H(z)NHI. (19) 4In.1FigW. 1DwMe c:o2m5p-kaereVthseteerffileectnseouft2r5i-nkoeVdesctearyile neutrino In equation (19), hp and kB are thePlanck and Boltzmann decaysonTS assumingeitherthephysicallymotivatedvalue constants, respectively, ν0 =1420 MHz is the 21 cm hyper- offabs(leftpanel)orthecommonlyadoptedvaluefabs =0.5 fine transition frequency, and NHI is the local HI number (rightpanel),i.e.themaximumallowedvalueforsterileneu- density. If TS is higher than TCMB, the neutral IGM will trinoscorrespondingtocompleteabsorption.Inaddition,in be visible in emission against the CMB; on the contrary, if each of the panels we explore the differences between mod- TS <TCMB it will be visible in absorption. els with or without the energy injection term due to DM decays. We will refer in the following to the latter as the standard case, for brevity. With respect to thecase without DM energy injection, 4 RESULTS we find, independently of the assumption made for f , a abs In a Universe where DM does not decay or annihilate the higherkinetictemperatureandhydrogenionizationfraction. spin temperature and the kinetic temperature of the gas However, such an enhancement produces only very modest track the CMB temperature down to z ≈ 300, when the T differences with respect to thestandard case, which has S kinetic temperature starts to decrease adiabatically, T ∝ some effect on the differential brightness temperature δT . K b (1+z)2, while T ∝ (1+z). The collisions at this red- The difference T −T remains extremely small due to CMB S CMB shift are efficient at coupling T and T : the spin temper- thelimited ability of theLyαpumpingtodecouple thetwo S K ature subsequently tracks the kinetic temperature down to temperatures. z ∼ 70. At lower redshifts radiative coupling to the CMB The main difference between the results obtained from becomes dominant and T → T again. As a result, for thetwof assumptionsisthebehaviorofT atz ∼10−70. S CMB abs K 30≤z ≤300HIisvisibleinabsorptionagainsttheCMBat Whenweusetherealisticf value,theIGMkinetictemper- abs wavelengthof21(1+z)cm.Thisscenariocouldchangecon- ature positively deviates at most by 50% from its standard siderably ifweallow forDMdecay/annihilation, depressing evolution; if instead f = 0.5 is adopted (e.g. as assumed abs orevenerasingtheabsorptionfeaturediscussedabove.Also, forexamplebyFurlanettoetal.2006),thekinetictempera- we note that different DM candidates leave different traces tureovershoots theCMB one and reaches verylarge values on the 21 cm background signal, and therefore it could be (>100 K) at low redshifts. (cid:13)c 0000RAS,MNRAS000,000–000 6 Valdés, Ferrara, Mapelli, Ripamonti Figure3.Leftpanel:TS andTk asafunctionofredshift(10-MeVLDMannihilations,fabsasinRMF06a).Thinsolidline:TCMB;thick solid(short-dashed)line:TSwith(without)10-MeVLDMannihilations;dotted(long-dashed)line:Tkwith(without)LDMannihilations. Right:TS andTk asafunctionofredshiftfor10-MeVLDMannihilationsandforfabs=1.Thelinesarethesameasintheleftpanel. 4.2 LDM: 10-MeV decay/annihilation For comparison sake, we note that this case has nearly thesamedecayrate,Γ =2.5×10−26 s−1,asthatassumed X We now turn to theanalysis of LDM candidates. Following inoneofthecasesexploredbyFurlanettoetal.(2006)(dot- the same procedure as in the previous Section we compare dashed line in Fig. 1 of that paper). Consistently, the evo- the results of the two different assumptions for f (note abs lution of T from thetwo studies is essentially thesame. K that for LDM, the constant absorbed fraction case corre- Finally we turn to the case of annihilating LDM (Fig. spondstof =1,seeSec.2.1), andalso test theeffectsof abs 3). As usual, the left panel of that figure reports the case decays/annihilation against thestandard case. in which therealistic, redshift dependent,valuesof f are abs Westartfromtheanalysisoftherealisticfabscase(Fig. assumed.Inthiscase,thekinetictemperaturedeviatesfrom 2, left panel) for decaying LDM. The most striking feature the standard adiabatic evolution at extremly high redshifts isthattheevolutionofTK decouplesfromtheadiabaticone (z >200): this is because the annihilation process depends already at z ≈ 50, and starts to increase below z ≈ 20, onthesquareofthebaryondensity.Asaresult,itscontribu- reaching TK =30 K at z =10. Such thermal history forces tionpredominantlyoccursatearlyepochsandprogressively TS toremainbelowTCMB foramuchlongerredshiftinterval vanishes with time, as realized also from the fact that be- (down to z =10) than in the standard case, in which TS ≈ low z = 100 the TK curve is simply shifted to an higher TCMB already at z ≈ 25. Interestingly, this effect extends adiabat. This fact causes the spin temperature to remain the frequency range in which the IGM can be observed in closerto(although alwayslowerthan)T ,thuspreserv- CMB absorptiontohighervalues.Themainphysicalreasonforthe ing the standard absorption feature. Quite remarkably the larger impact of LDM decays on TS with respect to sterile results assuming the realistic fabs values do not differ ap- neutrinos analyzed above basically lies in the larger fabs preciably from those obtained by imposing fabs = 1 (Fig. value (approximately a factor of 10 below z = 30) of LDM 3, right panel). As pointed out before, the effects of anni- particles;thisisontopoftheirlargerrestmass.Thehigher hilating DM are evident only at very high redshift, where heatingrateincreasesbothTK andtheLyαbackground(i.e. the detailed calculation gives fabs ≈ 1 (see RFM06a), thus yα), thuspushingTS away from TCMB. making thenon-evolvingfabs approximation acceptable. When f is instead artificially forced to be constant abs and equal to unity (Fig. 2, right panel), the physical argu- mentsgiven abovecan still beused tointerpret theresults, 4.3 Global 21 cm background. butthedeviationfromthestandardcaseismuchmoredra- matic,andresultsinanoverestimateoftheLDMdecaysim- Having obtained the evolution of T for the different DM S pact. For example, T becomes larger than T already candidates, we are now ready to compute for each case the K CMB at z ≈50 and stays above it thereafter, reaching >1000 K quantity that is most readily associated with observations, atz=10.Theincreaseissostrongthatitessentiallyerases i.e. the differential brightness temperature, δT . These are b the absorption feature expected in the standard case above shown in Fig. 4 for the realistic (left panel) and the con- z = 30. The IGM according to this prescription should be stant f (right panel) cases, respectively. In addition, to abs observed in emission up to veryhigh redshifts. facilitate thecomparison, wehavealso plottedin Fig. 5the (cid:13)c 0000RAS,MNRAS000,000–000 Constraining DM through 21 cm observations 7 Figure 4. Left panel: 21 cm differential brightness temperature as a function of redshift. The solid line shows δTb without decaying/annihilatingDM;whilethelongdashed, shortdashed anddotted linesrefertoδTb with25-keV decaying WDM,10-MeV decaying LDMand10-MeV annihilatingLDM,respectively. Calculations wereperformedassumingfabs asinRMF06a.Right:21cmdifferential brightnesstemperatureasafunctionofredshiftasintheleftpanel.Calculationswereperformedassumingfabs=0.5forsterileneutrinos andfabs=1intheothercases. brightness temperature deviation δTb−δTb,0 of thevarious ionospheric contamination become more severe at the low modelsfromthestandardone,restrictedtotherealisticf observing frequencies implied by thesehigh redshifts. abs evolution only. Although of academic interest only, it is instructive to compare the constant f cases (Fig. 4, right panel) with abs As usual, we start our analysis from the realistic f the previous results. As seen clearly form the Figure, con- abs case. For sterile neutrinos (long-dashed curves) the charac- siderablydifferentconclusionswouldbedrawn.First,sterile teristic absorption feature in the 21 cm background signal neutrino would drive δTb to positive values, resulting in an expectedat 30 ≤z≤ 300 isonly slightly modified from the emissionsignalbelowz=20;asimilartrendisalsoobtained standard case (solid line): themaximum difference is found for LDM decays, whose effects are seen in 21 cm emission to be only ≈ −2 mK in the range z ∼10−40. Yet, such a with an amplitude of about 10 mK. The results for LDM smallsignatureofWDMdecayscouldstillbeinprincipleob- annihilation instead do not show appreciable dependencies servable: even modest sized single-dish radio telescopes can on the fabs prescription, for thereasons discussed above. reach therequiredmK sensitivity in an all sky observation. The real challenge for theobservation is represented by the abilitytodisentanglethiscosmological signalfrom thevari- ousforegrounds(particularlytheGalacticsynchrotronemis- 5 DISCUSSION sion) which could be several orders of magnitude brighter. The case of decaying 10-MeV LDM (short-dashed lines in From the results obtained in this paper, we conclude that Fig.4) is more interesting, as the difference with the stan- it is in principle possible to observe the HI 21 cm signal dardcasearelarger.Forthiscasewefindthatthedeviation from the Dark Ages produced by the energy input due to is predicted to be ≈−(5−8) mK in the range 20<z <40. decays/annihilations of the most popular light/warm DM Such an amplitude could be detected by LOFAR or SKA candidates. If so, radio observations might represent one of after a 1000 hour all sky integration and by most single themostpromisingtoolstostudythenatureofDM,asdif- dish radio telescopes, provide foreground contamination is ferent particles are predicted to leave a specific signature taken care of. Finally, when LDM annihilations are consid- onthesignal.Thesensitivityrequiredtomeasurethe21cm ered,aconsiderablydifferentδT evolutionisobtainedwith backgroundsignalcanbeachievednotonlybythenextgen- b respect to the standard case. Larger deviations are present eration of radio interferometers, but also by existing radio in the entire range 40 < z < 200, where the energy in- observatories. put of LDM annihilations forces δT to values larger than However, the various foregrounds (i.e. Galactic free- b −20 mK, about two times smaller (in absolute value) than freeandsynchrotronemission,unresolvedextra-galactic ra- for the standard evolution. Such a large difference could in dio sources, free-free emission from ionizing sources, syn- principle facilitate discriminating the annihilation scenario chrotron emission from cluster radio halos and relics) are fromthestandardone.Inpractice,though,foregroundsand much stronger than the cosmological signal, and will cer- (cid:13)c 0000RAS,MNRAS000,000–000 8 Valdés, Ferrara, Mapelli, Ripamonti tainly prove extremely difficult to remove. Hence, a clear detection could bechallenging to achieve. It is beyond the scope of this paper to deal in detail withtheproblemsofionosphericscintillationandforeground contamination.Anumberofstudieshavediscussedthefore- groundscomplicationsinsomedetail(e.g.Shaveretal.1999; Oh & Mack 2003; Di Matteo, Ciardi & Miniati 2004) and we refer the reader to those papers for more information. For our aims it is sufficient to say that in general the sky temperature can be roughly described as: ν −2.6 T ∼ 180 K (20) sky 180MHz (cid:16) (cid:17) (see e.g. Furlanetto, Oh & Briggs 2006) and is, at the fre- quenciesofinterest,severalordersofmagnitudehigherthan thecosmological 21 cm background signal. The success of the 21 cm background observations to constrain DM will depend on the capability of effectively removing the foregrounds and of correcting for iono- sphericvariations (e.g. Gnedin & Shaver2004; Zaldarriaga, Furlanetto&Hernquist2004;Santos,Cooray&Knox2005; Morales, Bowman & Hewitt 2005). Analternativemethodtostudythe21cmbackgrounds is by separating its spectral features from the smooth foreground spectrum (e.g. Furlanetto2006, Shaveret al. 1999). Figure 5. 21 cm differential brightness temperature difference in mK between the three DM cases considered and a non Fig. 6 shows the gradient of δT for the DM candidates b decaying−annihilating DM scenario. The dashed, solid and dot- studied here. It is clear from the figure that the gradients ted lines correspond to 25-kev sterile neutrino decays, 10-Mev are higher and easier to constrain in the frequency range LDMdecays and10-MeVannihilationscaserespectively. ν = 1420/(1+z)MHz ∼ 10−40 MHz. The foreground gradients however increase with decreasing frequency making it difficult to predict the best frequencies to get to for a ν ≥ 90 MHz, or z ≤ 15 the first luminous sources start successful detection. having a dominant impact on the IGM and thesmall mod- Discriminating among different DM cases would imply ificationsfrom decaying/annihilating DMwould not bevis- theabilitytodistinguishthedifferenceinbrightnesstemper- ible. atureand/orinitsgradientwithrespecttothestandardsce- For the 10-MeV LDM annihilations case the best ob- nario. Wedefinethesetwo quantitiesas ∆δT =δT −δT 0 serving frequencies seem to be 10−30 MHz. At these fre- b b b and∆δTb/∆ν =dδTb/dν−dδTb0/dν,wherethe0standsfor quencies ∆δTb ∼> 6 mK with a peak of over 20 mK at thestandard (i.e. non decaying/annihilating) DMscenario. 10−20 MHz. Observations at such low frequencies are par- Fig. 7 shows ∆δT versus ∆δT /∆ν for the three DM ticularly difficult and probably future radio interferometers b b models: the blue triangles correspond to 10-MeV annihila- will not reach such large wavelengths. Probably 30 MHz is tions,theredsquaresto10-MeVdecaysandtheblackstars theminimumfrequencywhichwillbeachievedbynextgen- to the 25-keV sterile neutrino decays. The points are sepa- erationinstruments,andthefrequencyatwhichitwillthen rated by 1 MHz steps in a range that goes from 5 to 130 bepossible to constrain 10-MeV annihilating LDM. MHz. As the sensitivity is somewhat uncertain for the dif- We conclude then that it is likely that future observa- ferent proposed 21 cm experiments, we assume as a guide- tions of the21 cm background radiation will allow usto ef- line that a successful detection requires ∆δT > 3 mK and fectivelyconstrainamongsomeoftheDMcandidates,which b ∆δT /∆ν >0.6 mK/MHz,respectively.Theadoptedvalue by decays or annihilations can influence deeply the proper- b for ∆δT is a conservative one given that mK sensitivities ties of the IGM. b are already achievable in all sky observations even by ex- Nevertheless our study shows that accounting for the isting single dish radio telescopes. 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