Radiation from early black holes - I: effects on the neutral inter-galactic medium
aa r X i v : . [ a s t r o - ph ] F e b Mon. Not. R. Astron. Soc. , 000–000 (0000) Printed 25 October 2018 (MN L A TEX style file v2.2)
Radiation from early black holes - I: effects on the neutralinter-galactic medium
E. Ripamonti , , M. Mapelli , S. Zaroubi Dipartimento di Fisica, Universit`a di Milano-Bicocca, Piazza della Scienza 3, I-20123 Milano, Italy; [email protected] Kapteyn Astronomical Institute, University of Groningen, Postbus 800, NL-9700AV, Groningen, The Netherlands Institute for Theoretical Physics, University of Z¨urich, Winterthurerstrasse 190, CH-8057 Z¨urich, Switzerland
25 October 2018
ABSTRACT
In the pre-reionization Universe, the regions of the inter-galactic medium (IGM) whichare far from luminous sources are the last to undergo reionization. Until then, theyshould be scarcely affected by stellar radiation; instead, the X-ray emission from anearly black hole (BH) population can have much larger influence. We investigate theeffects of such emission, looking at a number of BH model populations (differing forthe cosmological density evolution of BHs, the BH properties, and the spectral energydistribution of the BH emission). We find that BH radiation can easily heat the IGMto 10 − K, while achieving partial ionization. The most interesting consequence ofthis heating is that BHs are expected to induce a 21-cm signal ( δT b ∼ −
30 mK at z < ∼
12) which should be observable with forthcoming experiments (e.g. LOFAR). Wealso find that at z < ∼
10 BH emission strongly increases the critical mass separatingstar-forming and non-star-forming halos.
Key words: diffuse radiation; cosmology: theory; black hole physics; galaxies: for-mation; intergalactic medium
The Sloan Digital Sky Survey (SDSS) has unveiled theexistence of quasars at redshift z > ∼ − M ⊙ had already formedwhen the Universe was less than 1 Gyr old (Fan et al. 2001,2003).The processes which lead to the formation of such hugeblack holes (BHs) already in the early stages of the life ofthe Universe are very uncertain. A possible scenario is thatSMBHs were built up starting from a seed intermediate-mass BH (IMBH, i.e. a BH with mass of 20 − M ⊙ ), whichincreased its mass by accreting gas and/or by merging withother IMBHs.In particular, if first stars are very massive ( > M ⊙ )their fate is to directly collapse into BHs, nearly without los-ing mass (Heger & Woosley 2002). This can produce a popu-lation of IMBHs, which are expected to efficiently accrete gasin the high-density primordial Universe and eventually tocoalesce with other BHs (Volonteri, Haardt & Madau 2002,2003; Islam, Taylor & Silk 2003, 2004; Volonteri & Perna2005; Volonteri & Rees 2005, 2006). Furthermore, the accre- h tion of these IMBHs might be enhanced also during galaxymergers, which tend to drive gas into the inner regions ofthe host galaxy (Madau et al. 2004). However, recent sim-ulations by Pelupessy, Di Matteo & Ciardi (2007) suggestthat the accretion history of such seed IMBHs can hardlyaccount for the SMBHs of the SDSS.On the other hand, seed BHs can be produced alsoby the direct collapse of dense, low angular momentumgas (Haehnelt & Rees 1993; Umemura, Loeb & Turner1993; Loeb & Rasio 1994; Eisenstein & Loeb 1995; Bromm& Loeb 2003), driven by turbulence (Eisenstein & Loeb1995) or gravitational instabilities (Koushiappas, Bullock& Dekel 2004; Begelman, Volonteri & Rees 2006, hereafterBVR06; Lodato & Natarajan 2006). In particular, the so-called ’bars within bars’ mechanism (Shlosman, Frank &Begelman 1989; Shlosman, Frank & Begelman 1990) im-plies that bars, which form in self-gravitating clouds undersome assumptions, can transport angular momentum out-wards on a dynamical time-scale via gravitational and hy-drodynamical torques, allowing the radius to shrink. Thisshrinking produces greater instability and the process cas-cades. BVR06 show that this process leads to the formationof a ’quasi-star’, which rapidly collapses into a ∼ M ⊙ BHat the center of the halo. The BH should encounter veryrapid growth due to efficient gas accretion.This allows the formation of seed BHs with mass c (cid:13) E. Ripamonti, M. Mapelli, S. Zaroubi < ∼ M ⊙ (BVR06; Lodato & Natarajan 2006, 2007), de-pending on the initial parameters (e.g. the temperature ofthe gas and the spin parameter of the parent halo).If such seed BHs formed at high redshift ( z ∼ − et al. b = 0 . M = 0 .
24, Ω DM ≡ Ω M − Ω b = 0 . Λ = 0 . h = 0 . H = 100 h km s − Mpc − . First of all, we develop a formalism for estimating the totalenergy input of BHs into the neutral IGM at a given redshift,starting from basic properties of the BH population, takenfrom semi-analytic models (see next Section), such as theBH mass density ρ BH at redshift z , the average BH mass h M BH i at redshift z , and the duty cycle y of single BHs.We start from considering that the mean free path of aphoton of energy E emitted at redshift z is: λ ( E, z ) = [ n B ( z ) σ ( E )] − , (1)where n B ( z ) = n B (0)(1 + z ) is the cosmological baryonnumber density at redshift z [ n B (0) ≃ . × − cm − ;Spergel et al. 2007], and σ ( E ) is the photo-ionization crosssection per baryon of the cosmological mixture of H and He,which is approximately σ ( E ) = ( . σ H ( E ) 13 . ≤ E ≤
25 eV σ [ E/ (250 eV)] − .
25 eV ≤ E ≤
250 eV σ [ E/ (250 eV)] − .
250 eV ≤ E, (2)where σ H ( E ) is the photo-ionization cross section of hy-drogen (see eq. 2.4 of Osterbrock 1989), and σ ≃ . × − cm is the cross section for 250 eV photons (seeZdziarski & Svensson 1989 for further details on the crosssection at E >
25 eV). In this paper we will neglect theabsorption of photons with
E < . λ , but this effect is important only in the lastphases of reionization.On the other hand, the average distance between ‘ac-tive’ BHs is d = (cid:20) ρ BH ( z ) y C h M BH i ( z ) (cid:21) − / , (3)where C accounts for the clustering of BHs .The comparison of λ and d shows that for photons ofsufficiently high energy the mean free path can easily exceed d . For instance, the mean free path of a 500 eV photonemitted at z = 20 is about 9 comoving Mpc ( ∼ d in typicalmodels), but at the same redshift a 1 keV photon typicallypropagates for ∼
90 comoving Mpc. Since BHs are believedto emit a significant fraction of their luminosities at suchenergies, they will build up a roughly uniform backgroundradiation field.The BH emissivity can be estimated by assuming thatduring active phases of accretion, each primordial BH pro-duces radiation at a fraction η of the Eddington luminosity[ L Edd ≃ . × erg s − ( M BH /M ⊙ )], and that their av-erage spectrum at redshift z is described by some function F ( E, z ). Then, the proper emissivity is j ( E, z ) = L F ( E, z ) R F ( E ′ , z ) dE ′ ρ BH, ⊙ ( z ) (cid:16) η . (cid:17) y (1 + z ) , (4)where L ≃ . × − erg s − cm − M − ⊙ is a normalizationconstant , and ρ BH, ⊙ ( z ) is the BH density at redshift z ,expressed in solar masses per cubic comoving Mpc.The mean specific intensity of the radiation background If primordial BHs form in clusters (typically) of N cl BHs, theprobability that at least one of them is in an active state is 1 − (1 − y ) N cl (rather than y ); so C ≃ N cl y/ [1 − (1 − y ) N cl ]. Inthe following we will use C = 10 for models where BH clusteringshould be strong; this corresponds to N cl ≃ y =0 . . L is chosen to be the emissivity (per cm ) when the BH den-sity is equal to 1 M ⊙ per comoving Mpc and BHs are assumedto accrete with efficiency 0.1. So, it is equal to 0 . × . × (erg s − M − ⊙ ) × [3 . × (cm / Mpc)] − .c (cid:13) , 000–000 arly BH radiation - I: effects on the IGM at the observed energy E , as seen by an observer at redshift z , is then (cfr. eq. 2 of Haardt & Madau 1996) J ( E, z ) = 14 π Z ∞ z +∆ z dz ′ dldz ′ (cid:16) z z ′ (cid:17) j ( E z ′ z , z ′ ) e − τ , (5)where the cosmological proper line element at redshift z ′ is dldz ′ = cH
11 + z ′ M (1 + z ′ ) + Ω Λ ] / , (6)and τ = τ ( E, z, z ′ ) is the optical depth effectively crossedby a photon emitted at redshift z ′ and reaching redshift z with an energy E , τ ≡ τ ( E, z, z ′ ) = Z z ′ z d ˜ z dld ˜ z σ ( E z z ) n B (˜ z ) . (7)The definition of a cosmological background would re-quire that in eq. (5) ∆ z = 0; but this is not appropriatefor our purposes. In fact, as we already mentioned, we willbe looking at regions outside the ionized ‘bubbles’ producedby the first luminous sources. So, we will examine the ef-fects of the radiation background on baryons quite removedfrom any particular source (we will refer to such baryons asthe ‘neutral-IGM’ baryons), i.e. at a distance of the orderof d/
2. This is irrelevant for photons with long mean freepaths ( λ ( E, z ) > ∼ d/ λ ≪ d/
2, which are absorbed in the vicinity ofthe BHs. In short, we start the redshift integration in eq. (5)from z +∆ z (where ∆ z is chosen so as to skip the integrationover distances ≤ d/ z .From the background spectrum φ ( E, z ) we can easilyobtain the energy input per baryon due to the absorption ofbackground photons at redshift z , ǫ ( z ) = 4 π Z dE J ( E, z ) σ ( E ) . (8)It must be noted that our use of the cross section (2) inthe estimates of τ (eq. 7) and of ǫ (eq. 8) might induce twoopposite errors. First of all, τ is overestimated (and J under-estimated) when a significant fraction of the cosmic volumeis ionized. On the other hand, when the absorbing mediumis not completely neutral, we overestimate the fraction of ra-diative energy which is actually intercepted by the baryons.The former effect leads to a moderate underestimation of ǫ , starting at relatively high redshifts; the latter might leadto a large overestimation of ǫ , but only for models wherethe IGM ionized fraction becomes quite large. We neglectboth effects in our calculations: our results will generally bemild underestimates of the BH effects, except in the caseswhere the ionized fraction becomes large (a condition wherewe will significantly overestimate the BH effects).The energy input must be split into a fraction f ion goinginto ionizations, a fraction f heat going into heating, and afraction f exc going into excitations. These fractions actuallydepend on the energy E of the absorbed photon; but Shull &van Steenberg (1985) determined that, for all E > ∼
100 eV,they are reasonably fitted by the expressions f heat = 0 . − (1 − x . H ) . ] (9) We report the expressions which are given for H, and neglectthe small correction due to the presence of He.
Table 1.
Parameters of the BH growth model histories.Model ρ BH a h M BH i b y c C z s IMBH-3% 10 . − . z . − . z . − . z − . z . − . z . − . z d . − . z a In solar masses per cubic comoving Mpc. b In solar masses. c Consistent with the assumptions of the underlying models. d Fig. 2 of BVR06 does not show the ρ BH evolution for z < f ion = 0 . − x . H ) . (10) f exc = 0 . − x . H ) . . (11)where x H is the hydrogen ionization fraction ( x H = n ( H + ) / [ n ( H ) + n ( H + )]). As can be seen in Figs. 1 and 2,the contribution of photons with E <
100 eV to the back-ground is small or negligible (in the absence of reionization,the mean free path of 100 eV photons exceeds ∼ d only at z < ∼ In the above section we have seen how we can obtain anestimate of the cosmological X-ray background produced byprimordial BHs, and of the energy it can inject in the IGM.Such estimate mainly depends on three input quantities: theevolution of the cosmological density of BHs ρ BH ( z ), theduty cycle y , and the typical spectral shape of an active BH, F ( E ). The evolution of the BH average mass h M BH i ( z ), andthe clustering factor C have much smaller effects. There exist several models (e.g. RO04; BVR06; Z07+) pre-dicting the evolution of the BH mass density in the earlyUniverse. Here we will discuss three different histories whichare reasonable approximations of the models IMBH-3%,IMBH-6%, and SMBH-3% discussed in Z07+ (see their fig.8), and of one of the models in BVR06 (duty cycle 0.1, Mes-tel disk; from their fig. 2). The two IMBH models (IMBH-3% and IMBH-6%) assume that primordial BHs with mass ∼ M ⊙ form in small (10 − M ⊙ ) and numerous halos,where H cooling is efficient; the SMBH-3% and the BVR06models, instead, assume that primordial BHs of large mass( > ∼ M ⊙ ) form in larger (10 − M ⊙ ) and rarer haloscooled by atomic H. In all the four cases we will adopt thesimple power-law approximations of the Z07+ and BVR06results which are given in Table 1. Such power-laws providegood fits to all the original models for z ≥
10, whereas atlower redshifts they are either a reasonable extrapolation(for BVR06), or give a slight-to-moderate underestimate ofthe predictions of the Z07+ models. Table 1 lists also theother parameters defining the BH growth histories: the dutycycle y is by far the most important, whereas our results are c (cid:13) , 000–000 E. Ripamonti, M. Mapelli, S. Zaroubi relatively insensitive to the assumptions on h M BH i ( z ) and C . This is quite fortunate as the value of y is intrinsic in ourreference models, whereas none of them provides a simple es-timate of the other parameters. The values given in Table 1are guesses based on the general properties of the referencemodels, and on the notion that the typical BH mass shouldincrease with time (especially when ρ BH grows fast).Furthermore, we assume that before a certain redshift z s ( z s = 30 for the evolutions taken from Z07+, z s = 18 forthe one from BVR06) the BH density (and emissivity) is 0. We experiment with three different types of BH spectralenergy distributions (SEDs): simple power-laws F ( E, z ) = F α ( E ), a template F ( E, z ) = F SOS,α ( E ) introduced bySazonov, Ostriker & Sunyaev (2004), and a multi-componentspectrum which is the sum of a multi-color black body anda power-law spectrum (see Shakura & Sunyaev 1973, andSalvaterra et al. 2005), F ( E, z ) = F MC, Φ ( E, z ).Power-laws are characterized by their slope α , and areassumed to be F α ( E ) = (cid:26) E − α .
01 eV < E < eV0 otherwise . (12)In the following, we will consider the power-law with α = 1(hereafter PL1 SED) as our reference spectrum.The spectral template by Sazonov et al. (2004) is char-acterized by the slope in the 1 −
100 keV range, and its exactshape is F SOS,α ( E ) = C . < E ≤
10 eV E − .
10 eV < E ≤ eV C E − α eV < E ≤ eV C E − . eV < E < eV0 otherwise , (13)where the constants C = 10 α − . and C = 10 . − α are chosen so as to ensure continuity, and the constant C ≃ . E ≤
10 eV is the same asin the complete Sazonov et al. (2004) template (i.e. about0.85), even though we are not interested in the details oftheir model for E ≤
10 eV. In this paper we considered thecase α = 1 (SOS1 SED): we chose such a relatively steepvalue (Sazonov et al. 2004 suggest values of about 0 . − . ∝ E / and dominates up to apeak energy E p ≃ M BH /M ⊙ ) − / . (14)Above that the multi-color black body is exponentially cut-off, and the power-law component ( ∝ E − ) emerges, as de-scribed in Shakura & Sunyaev 1973 (see also Salvaterra etal. 2005 for an application to a context similar to the onewe are considering): F MC, Φ ( E, z ) = E e − E Ep .
01 eV < E ≤ E p E e − E Ep + A Φ E − E p < E ≤ eV0 otherwise . (15) -30 -28 -26 -24 S pe c i f i c f l u x [ e r g s - c m - H z - s r - ] IMBH-3% -30 -28 -26 -24 IMBH-6%10 Photon energy [eV]10 -30 -28 -26 -24 S pe c i f i c f l u x [ e r g s - c m - H z - s r - ] SMBH-3% 10 Photon energy [eV] -30 -28 -26 -24 BVR06
Figure 1.
Spectrum of the background produced by primordialaccreting BHs and seen by a neutral-IGM baryon in the four BHgrowth history scenarios (IMBH-3%: top left panel; IMBH-6%:top right panel; SMBH-3%: bottom left panel; BVR06: bottomright panel) at various redshifts ( z = 8: thick dotted line; z = 10:thick solid line; z = 15: thick dashed line; z = 20: thick dot-dashed line), assuming a PL1 spectrum for the BH emission. Thethin solid line shows the spectrum we would obtain at z = 10,had we assumed that ∆ z = 0 in eq. (5). A Φ is chosen so that the energy in the power-law spectralcomponent is equal to a fraction Φ of the energy in the multi-color black body spectral component. Φ is usually taken tobe < ∼
1, and we will consider the case Φ = 0 . M BH with h M BH i ( z ) inside eq. (14), we notethat this spectral shape is slightly dependent on redshift .For all the considered spectral shapes we chose to as-sume that the BH emissivity at energies below 0 .
01 eV orabove 10 eV is 0. Such choice prevents numerical problems,and does not significantly affect our results. In Fig. 1 we show the redshift evolution of the spectrumof the background radiation produced by primordial BHsand reaching a neutral-IGM baryon. In such Figure we con-sider all the different BH growth histories, but only the PL1SED. The background level grows with time, as could be The low-energy tail of a modified blackbody spectrum is ex-pected to be ∝ E . We neglect such slope change, as only a smallfraction of the BH luminosity is emitted in this region of the spec-trum. We also note that the exponential constant was chosen tobe 3 E p in order to ensure that the multi-color black body com-ponent actually has a (broad) peak at E = E p , as described inSalvaterra et al. (2005). c (cid:13) , 000–000 arly BH radiation - I: effects on the IGM -28 -27 -26 -25 -24 S pe c i f i c f l u x [ e r g s - c m - H z - s r - ] IMBH-3% -28 -27 -26 -25 -24 IMBH-6%10 Photon energy [eV]10 -28 -27 -26 -25 -24 S pe c i f i c f l u x [ e r g s - c m - H z - s r - ] SMBH-3% 10 Photon energy [eV] -28 -27 -26 -25 -24 BVR06
Figure 2.
Spectrum of the background produced by primordialaccreting BHs, and seen by neutral-IGM baryons at z = 10.The four panels refer to the four BH growth history scenar-ios we consider (IMBH-3%: top left panel;IMBH-6%: top rightpanel; SMBH-3%: bottom left panel; BVR06: bottom right panel),whereas the different line types refer to three different SED forthe BH spectra (PL1: solid line; SOS1: dashed line; MC01: dot-dashed line). expected when we remember that the BH density, the av-erage distance among BHs, and the IGM density all evolvein a background-enhancing direction. In all the consideredgrowth scenarios, the spectra peak at E ∼ z = 0 in eq. (5): as expected, thehigh energy part of the spectrum does not change, while thesharp cutoff at low energies is replaced by a much milderpower-law decline.When comparing different BH growth histories in Fig. 1,it is clear that the normalization of the background spec-trum is related to the value of the product ( y × ρ BH ) atthe relevant z . Instead, the sharpness of the low-energy cut-off depends on the geometrical properties of the BH spatialdistribution: in models with large values of h M BH i the cut-off is very sharp, whereas it is a bit more gentle for IMBHmodels with low h M BH i . This is important because the lowenergy part of the spectrum, albeit accounting only for asmall fraction of the total energy in the background, is ab-sorbed with quite high efficiency and is a major contributorto the energy input ǫ .In Fig. 2 we show the spectrum of the background radi-ation at a fixed redshift, z = 10, while varying the BH SED.It is clear that ‘flat’ (PL1, MC01) SEDs produce larger back-
30 25 20 15 12 10 7 5 -36 -34 -32 -30 -28 -26 E ne r g y i npu t pe r ba r y on [ e r g / s ] IMBH-3%
30 25 20 15 12 10 7 510 -36 -34 -32 -30 -28 -26 IMBH-6%30 25 20 15 12 10 7 5Redshift10 -36 -34 -32 -30 -28 -26 E ne r g y i npu t pe r ba r y on [ e r g / s ] SMBH-3% 25 20 15 12 10 7 5Redshift -36 -34 -32 -30 -28 -26 BVR06
Figure 3.
Redshift evolution of the total energy input perneutral-IGM baryon due to the background produced by primor-dial BHs. As explained in the caption of Fig. 2, the four panelsrefer to the four considered BH growth histories, and each linetype refers to a different assumed BH spectrum. We also showthe energy input from BHs with a PL1 SED, had we assumedthat ∆ z = 0 in eq. (5) (thin dotted line). grounds than ‘steep’ (SOS1) SEDs, simply because a largerfraction of their luminosity is emitted in the energy range( E > ∼ − ∼ E p dependson the typical BH mass.Finally, in Fig. 3 we show the total energy input perbaryon as a function of redshift. Such a quantity is wellcorrelated with the intensity of the background spectrum,especially at low energies. Thus, it increases with time, andthe SED with the highest low energy component (MC01)gives the maximum energy input. We also compare the en-ergy input from the reference PL1 SED with that from anotherwise identical model where we assumed that ∆ z = 0 ineq. (5). This is useful to check the effects of our assumptionabout ∆ z , and also gives us a rough estimate of the level ofthe spatial fluctuations of the energy input. The differenceusually amounts to a factor of 2 −
3, even if it might belarger for the SMBH-3% and the BVR06 growth histories,especially at high z .We note that the model where the energy input fromBHs is maximum is the one where the IMBH-6% accretionhistory is combined with the MC01 SED. In the following, we c (cid:13) , 000–000 E. Ripamonti, M. Mapelli, S. Zaroubi
Table 2.
Fraction of the unresolved X-ray background which in our models is due to BH emission at z ≥ z drop , in various bands. Thenumbers in parenthesis are lower limits, obtained from the assumption that the actual X-ray background is 1 − σ higher than the centralvalues. The cases where the emission from our models exceeds the unresolved background are in bold face.Model z drop a b c d e IMBH-3%+PL1 5 0.32(0.21) 0.19(0.10) 0.37(0.26) 0.42(0.13) 0.078(0.065)IMBH-3%+SOS1 5 0.024(0.016) 0.014(0.008) 0.028(0.020) 0.031(0.010) 0.006(0.005)IMBH-3%+MC01 5 0.67(0.44) 0.043(0.023) 0.24(0.17) 0.096(0.030) 0.21(0.18)IMBH-3%+MC01 6 0.18(0.11) 0.014(0.008) 0.057(0.041) 0.031(0.010) 0.054(0.045)IMBH-3%+MC01 7 0.046(0.033) 0.005(0.003) 0.016(0.011) 0.011(0.003) 0.015(0.012)IMBH-6%+PL1 5 a Flux in the 0.5-2 keV band, normalized to a background level of 2 . . × − erg s − cm − sr − (from the combination of theB04 unresolved fraction, and the Moretti et al. 2003 total X-ray background). b Flux in the 2-8 keV band, normalized to a background level of 4 . . × − erg s − cm − sr − , (from the combination of the B04unresolved fraction, and the De Luca & Molendi 2004 total X-ray background). c Flux in the 1-2 keV band, normalized to a background level of 1 . . × − erg s − cm − sr − (from HM07). d Flux in the 2-5 keV band, normalized to a background level of 1 . . × − erg s − cm − sr − (from HM07). e Flux in the 0.65-1 keV band, normalized to a background level of 3 . . × − erg s − cm − sr − (from HM07). will refer to such combination as the ‘extreme’ model, since itleads to the strongest BH feedback effects (and is also closeto the constraints from the unresolved X-ray background;see below). On the other hand, we will also consider theIMBH-3%+PL1 model (i.e. the one combining an IMBH-3% history with a PL1 SED) as a ‘fiducial’ case. As a consistency check, we looked at whether our modelsare compatible with measurements of the unresolved X-raybackground from Bauer et al. (2004; hereafter B04), andfrom Hickox & Markevitch (2007; hereafter HM07).For such comparison, we obtained the spectrum of thebackground produced by the BH emission at a redshift z drop ,we integrated it in the relevant energy band, and we red-shifted it to z = 0 assuming no absorption.Such a calculation implies that, at z ≤ z drop , the emis-sivity due to BHs is 0. This is a quite crude assumption, butit must be remarked that observations (Steidel et al. 2002)suggest that the duty cycle declines with redshift (reaching y ∼ − at z = 0), and that several theoretical models in-clude a variation of y (e.g., in model M3 of RO04 y = 1 at z > ∼
14, but y = 10 − at z < ∼ < ∼ − z drop = 5. It can be seen thattwo of our models (IMBH-6% growth history, combinedwith either a PL1 or a MC01 SED) exceed the observedbackground in at least one band. For such cases (and alsofor the IMBH-3%+MC01 case, where the contribution fromBHs exceeds half of the unresolved X-ray background in the0 . − z drop = 6 or 7, which clearly show that the constraintsfrom the X-ray background can be easily satisfied also bythese models, provided that z drop > ∼
6. Thus, we note thatthe choice of z drop (and, in general, the fate of IMBHs inthe lower redshift range we consider) is quite crucial for ourmodels. In the rest of this paper we will use z drop = 5 forall the models, and our plots will extend to such redshift. We looked at the effects of the energy input due to the back-ground radiation produced by primordial BHs on the ther-mal and chemical evolution of the IGM. We employed a sim- c (cid:13) , 000–000 arly BH radiation - I: effects on the IGM
20 15 12 10 8 6 -5 -4 -3 -2 -1 H y d r ogen i on i z a t i on l e v e l IMBH-3%
20 15 12 10 8 610 -5 -4 -3 -2 -1 IMBH-6%20 15 12 10 8 6Redshift10 -5 -4 -3 -2 -1 H y d r ogen i on i z a t i on l e v e l SMBH-3% 20 15 12 10 8 6Redshift -5 -4 -3 -2 -1 BVR06
Figure 4.
Redshift evolution of the hydrogen ionization fraction x H . The order of the panels and the meaning of the various linetypes are the same as in Fig. 2, except for the thin dotted line,which represents the ionization evolution in a model without anyBH emission. plified version of the code described in Ripamonti, Mapelli& Ferrara (2007; hereafter RMF07; but see Ripamonti et al.2002, and Ripamonti 2007 - hereafter R07 - for more detaileddescription of this code), in order to look at the evolutionof the IGM under the influence of the energy input we cal-culated in the previous Section.Such a code follows the gas thermal and chemical evo-lution. The chemistry part deals with 12 chemical species(H , H + , H − , D , D + , He , He + , He ++ , H , H +2 , HD, ande − ), and includes all of the reactions involving these specieswhich are listed in the Galli & Palla (1998) minimal modelfor the primordial gas, plus some important extension (e.g.,it considers the ionizations and the dissociations due to theenergy input we are introducing). The thermal part includesthe cooling (or heating, if the matter temperature is lowerthan the CMB temperature) due to molecules (H and HD),to the emission from H and He atoms, to the scattering ofCMB photons off free electrons, and to bremsstrahlung radi-ation. Furthermore, it accounts for the cooling/heating dueto chemical reactions, and for the heating due to the energyinput we are considering . Other than introducing the energy input as calculated in theprevious Section, the code differs from the version described inRMF07 because we introduced the cooling through He lines andbremsstrahlung (the rates were taken from Anninos et al. 1997),and we splitted the energy input into the heating, ionization andexcitation components by using the expressions given in eq. (11),rather than the Chen & Kamionkowski (2004) approximations.
20 15 12 10 8 6 T e m pe r a t u r e [ K ] IMBH-3%
20 15 12 10 8 610100100010000
IMBH-6%20 15 12 10 8 6Redshift10100100010000 T e m pe r a t u r e [ K ] SMBH-3% 20 15 12 10 8 6Redshift
BVR06
Figure 5.
Redshift evolution of the IGM temperature T k in re-gions outside ionized bubbles. The order of the panels and themeaning of the various line types are the same as in Fig. 2, ex-cept for the thin dotted line, which represents the temperatureevolution in a model without any BH emission, and for the thickdotted line representing the CMB temperature. Figs. 4 and 5 show the effects of the BH emission upon theionization level (in particular, the hydrogen ionized fraction x H = n ( H + ) / [ n ( H ) + n ( H + )] ) and the temperature ofthe IGM T k (all these quantities are calculated outside theionized bubbles close to radiation sources). In all the modelswe consider, the BH emission starts altering the neutral IGMat z ∼ −
20. After that there is a steady increase in both x H and T k . The increase of x H stops only when the IGM iscompletely ionized (however, such condition is reached onlyin the most extreme of our models, and only at a redshift ∼ T k stops increasing once it reaches a level( ∼ K), where atomic cooling is important: in the modelswhere BH emission is assumed to be strongest (IMBH-6%with MC01 spectrum) this happens at z ∼
10, but z ∼ − z < ∼
10) our models start suffering from severalproblems. First of all, the energy input we employ is calcu-lated for a neutral medium, whereas in some of our models x H > ∼ . z ∼ −
8. Then, we are overestimat-ing the energy input . Second, we are assuming that the The situation is actually quite complicated. The reduction inthe heating rate is slower than what could naively be expected[ ǫ ∝ (1 − x H ) − ] from the increase of x H , because the bulkof the cross section is due to He, which is harder to strip ofits electrons (see e.g. Thomas & Zaroubi 2007). For example,in the ‘extreme’ model, at redshift 6 x H ≃ .
9, but x He ++ ≡ n ( He ++ ) / [ n ( He ) + n ( He + ) + n ( He ++ )] ≃ .
1, and by usingeq. (2) we are overestimating the energy input ǫ only by a fac-c (cid:13) , 000–000 E. Ripamonti, M. Mapelli, S. Zaroubi
Figure 6.
Effects of BH emission upon the CMB angular spectra.Temperature-temperature (top panel), polarization-polarization(central panel) and temperature-polarization (bottom panel)spectra are shown. Thick dotted line: CMB spectra derived as-suming Thomson optical depth τ e = 0 .
09 and a sudden reion-ization model (consistent with the 3-yr
WMAP data); thick solidand dashed lines: CMB spectra derived assuming energy injectionfrom the BHs in the ‘extreme’ (IMBH-6%+MC01, i.e. the casewhere BH energy input is strongest) and the ‘fiducial’ (IMBH-3%+PL1) cases, respectively; thin dash-dotted line: CMB spectraderived assuming no reionization and no contribution from BHs.
IGM density remains constant at its average unperturbedcosmological value, whereas this approximation becomes in-creasingly problematic as structures start to form. Third,there might be some level of metal enrichment (altering boththe heating and the cooling rates) even in regions whichare far away from the most luminous sources. Finally, weare completely neglecting the contribution to heating andreionization which is due to stars, which is likely to be sub-stantial at relatively low redshifts. However, our calculationsshould still be reasonably accurate until the end of the so-called ’overlap’ phase of reionization (probably not far from z ∼ −
8, see Section 5.1), provided that they are taken torepresent conditions in regions which were not yet ionized.
The cosmic heating and the contribution to reionization dueto BHs might also leave some imprint on the CMB spectra. tor of ∼ . − x H ) − ∼
10. Furthermore, theassumption that the IGM is completely neutral also leads to anoverestimation of the optical depth τ , and the background radia-tion (and energy input) is correspondingly underestimated. Then,our energy input rates are essentially correct, except for our ‘ex-treme’ model at z < ∼
7, where we might be overestimating ǫ by afactor of < ∼ In order to study this effect, we implement ionization andgas temperature evolution due to BHs in the version 4.5.1of the public code CMBFAST (Seljak & Zaldarriaga 1996;Seljak et al. 2003).Fig. 6 shows the temperature − temperature (TT), po-larization − polarization (EE) and temperature − polar-ization (TE) spectra of the CMB in the case in which thecontribution from BHs is accounted for. In particular the ‘ex-treme’ case (IMBH-6%+MC01, solid line) and the ’fiducial’one (IMBH-3%+PL1, dashed line) are shown. They are alsocompared with the spectra obtained without contributionsfrom stars and/or BHs (thin dot-dashed line) and with thespectra derived assuming Thomson optical depth τ e = 0 . z ≃
11, consistent with the 3-yr
Wilkinson Microwave Anisotropy Probe ( WMAP ) data.As one can expect, no significant differences appear be-tween the four cases in the TT spectrum. The ’fiducial’ andthe ’extreme’ BH model differ from the thin dot-dashed lineboth in the EE and in the TE spectra, at low multipoles( l < ∼ WMAP data (dotted line). Thus, all the scenarios consid-ered in this paper (even IMBH-6%+MC01) do not violatethe limits posed by CMB observations.Furthermore, the Thomson optical depth which can bedirectly derived from the ionization history shown in Fig. 4is τ e < .
07 ( τ e = 0 .
027 and 0.064 in the ’fiducial’ and ’ex-treme’ case, respectively), smaller than the best fit to 3-yr
WMAP data ( τ e = 0 . ± .
03, Spergel et al. 2007). Thus,our BHs might give a partial contribution to the reioniza-tion, but are not its exclusive source, in agreement withprevious work (e.g. RO04; Ricotti et al. 2005; Z07+).
The spin temperature of the 21-cm transition can be writtenas (see e.g. Field 1958, 1959; Kuhlen, Madau & Montgomery2006; Vald`es et al. 2007; Z07+) T spin = T ∗ + T CMB + ( y k + y α ) T k y k + y α , (16)where T ∗ ≡ .
068 K corresponds to the 21-cm transition en-ergy, T CMB is the CMB temperature, T k is the IGM kinetictemperature, and y k and y α are the kinetic and Lyman α coupling terms, respectively.The kinetic coupling term is y k = T ∗ A T k ( C H + C e + C p ) , (17)where A ≃ . × − s − is the Einstein spontaneousemission rate coefficient (Wild 1952), and C H , C e and C p are the de-excitation rates due to neutral H, electrons andprotons, respectively. They are given by the fitting formulaefrom Kuhlen et al. 2006 (see also Field 1958, 1959; Smith1966; Allison & Dalgarno 1969; Zygelman 2005): C H ≃ . × − (cid:16) T k (cid:17) . e −
32 K Tk s − (18) C e ≃ n e γ e (19) C p ≃ . n p /n H ) C H , (20) c (cid:13) , 000–000 arly BH radiation - I: effects on the IGM
30 25 20 15 12 10 8 6 T e m pe r a t u r e [ K ] IMBH-3%
30 25 20 15 12 10 8 610100
IMBH-6%30 25 20 15 12 10 8 6Redshift10100 T e m pe r a t u r e [ K ] SMBH-3% 30 25 20 15 12 10 8 6Redshift
BVR06
Figure 7.
Redshift evolution of the neutral H spin temperature.The order of the panels is the same as in Fig. 2; the dotted linerepresents the CMB temperature, thick lines represent the spintemperature, and thin lines represent the IGM temperature. Con-tinuous lines refer to models with a PL1 SED, dashed lines tomodels with a SOS1 SED, and dot-dashed line to models with aMC01 SED. where n H , n e and n p are the neutral H, electron and protonnumber densities, andlog γ e s − ≃ − . . T k (cid:20) (cid:16) log T k (cid:17) . (cid:21) . (21)The Lyman α coupling term is given by y α = 16 π A T ∗ T k π e m e c f J , (22)where e and m e are the electron charge and mass, f ≃ .
416 is the oscillator strength of the Lyman α transition,and J is the intensity of Lyman α photons which are dueto collisional excitations from thermal electrons, to hydro-gen recombinations, and to collisional excitations from X-rayenergy absorption. J is then J = hc π H ( z ) h n e n H γ e,H + n e n p α eff P + n B ǫf exc hν α i , (23)where γ e,H ≃ . × − e − (118400 K) /T k cm s − is the col-lisional excitation rate of neutral H atoms by electron im-pacts, ν α ∼ . × Hz is the Lyman α frequency, and α eff P is the effective recombination coefficient to the 2 P level (including recombinations to the 2 P level, plus re-combinations to higher levels that end up in the 2 P levelthrough all possible cascade paths). We adopted a simplefit to the Pengelly (1964) results for α eff P , assuming case Arecombinations : Results for case B recombinations differ only slightly.
20 15 12 10 8 6 -505101520 δ T b [ m K ] IMBH-3%
20 15 12 10 8 6-505101520
IMBH-6%20 15 12 10 8 6Redshift-505101520 δ T b [ m K ] SMBH-3% 20 15 12 10 8 6Redshift -505101520
BVR06
Figure 8.
Redshift evolution of the brightness temperature dif-ference with respect to the CMB δT b . The order of the panelsand the meaning of the various line types are the same as in Fig.2, except for the dotted line, which represents δT b for a modelwithout any BH emission. α eff P ( T k ) ≃ . × − T − . − (2 / T , (24)where T = T k / (10 K).Once the spin temperature is known (from eq. 16), it isconvenient to express the resulting 21-cm radiation intensityas the differential brightness temperature between neutralhydrogen and the CMB, which is an observable quantity: δT b ≃ T spin − T CMB (1 + z ) τ (1 + δ ρ ) , (25)where δ ρ ≡ ( ρ − ¯ ρ ) / ¯ ρ is the cosmological density contrastin the considered region (here we will consider only the case δ ρ = 0), and τ is the IGM optical depth at an observedwavelength of 21(1 + z ) cm, τ ≃ c hA π k B ν H ( z ) n H T spin , (26)where k B is the Boltzmann constant, and ν ≃ . × Hz is the (rest-frame) frequency of the 21-cm line.
Fig. 7 shows the redshift evolution of T spin , under the as-sumption that only the radiation produced by BHs is im-portant.In all these models, T spin remains very close to T CMB (and to the predictions of models with no BH emission) un-til z ∼ −
15, i.e. until T k finally becomes much larger than T CMB . After that, the difference between T spin and T CMB becomes significant, and in models with strong BH emissionit can amount to ∼
90 K. Apart from the amplitude of thismaximum difference, the strength of BH emission also influ-ences the redshift when it is reached: in models with weak c (cid:13) , 000–000 E. Ripamonti, M. Mapelli, S. Zaroubi
BH emission (e.g. most models where a SOS1 SED is as-sumed), T spin − T CMB keeps increasing, and is largest at thelowest considered redshift (though this maximum is quitelow); whereas in models with strong BH emission (e.g. allthose where a MC01 SED is assumed) T spin − T CMB reachesa relatively high maximum at z ∼ −
9, slowly decreasingafterwards. The main reason is that in models with high BHemission the ionized fraction easily reaches the regime (at x H > ∼ .
1) where f exc (and J and y α with it, as J is domi-nated by the term due to collisional excitations from X-rayabsorption) starts dropping very fast, rather than being ap-proximately constant (see fig. 4 of Shull & Van Steenberg1985).In Fig. 8 we show the corresponding evolution of thedifferential brightness temperature δT b . Such evolution es-sentially mirrors the one of T spin − T CMB : it remains close to0 until z ∼ −
15, and then starts growing, reaching maximabetween ∼ ∼
18 mK, depending on the strength ofthe BH emission. Again, in models with weak BH emissionthe maximum is reached at the lowest considered redshift,whereas in the other models it is reached at z ∼ −
9. Themain difference with the evolution of T spin − T CMB is thatthe decline after the maximum is faster, since the high IGMionization level in models with strong BH emission reducesalso τ .It must be remarked that such an evolution of δT b inthe neutral patches of the Universe at z < ∼
12 should be de-tectable with the new generation of radio experiments, suchas LOFAR, MWA, 21CMA and SKA . For example, LOFARwill probe the 21 cm emitted from the IGM in the redshiftrange of 6–11.5 and will be sensitive to scales from a fewarcminutes up to few degrees and will be able to statisti-cally detect the 21 cm brightness temperature down to ≈ In the previous Subsection we considered the evolution ofthe 21-cm emission under the effects of BH emission only.But it is largely believed that stellar emission played a fun-damental role in the evolution of the primordial Universe:for example, most models of reionization (e.g. RO04, andreferences therein) assume that the stellar contribution wasdominant over the one from BHs. This is supported by ob-servations of the unresolved X-ray background, whose levelis difficult to reconcile with the hypothesis that reionizationis due to BH emission (e.g. Dijkstra et al. 2004). Further-more, our models do require the presence of stellar radiation,as even the ‘extreme’ one (IMBH-6%+MC01) is unable toreionize the Universe before z ∼
6, and is therefore incom-patible with observations of quasars and Lyman α emittersat z ∼ −
30 25 20 15 12 10 8 6 T e m pe r a t u r e [ K ] IMBH-3%
30 25 20 15 12 10 8 610100100010000
IMBH-6%30 25 20 15 12 10 8 6Redshift10100100010000 T e m pe r a t u r e [ K ] SMBH-3% 30 25 20 15 12 10 8 6Redshift
BVR06
Figure 9.
Redshift evolution of the neutral H spin temperature,when the Ly α coupling due to stellar radiation (but not the stellarradiation heating effects) is kept into account. The order of thepanels is the same as in Fig. 2. The dotted line represents theCMB temperature, thick lines represent the spin temperature,and thin lines represent the IGM temperature. Continuous linesrefer to models with a PL1 SED, dashed lines to models with aSOS1 SED, and dot-dashed line to models with a MC01 SED. et al. 2001, 2002, 2003; White et al. 2003; Kashikawa et al2006; Iye et al. 2006; Ota et al. 2007).Since we are looking at the evolution of the IGM in re-gions which are quite removed from BHs (and, consequently,from the bulk of stellar emission) and are reionized late ,the omission of the stellar contribution from our calculationsis mostly justified. In fact, the neutral IGM we are consid-ering is almost perfectly transparent to radiation with fre-quencies below the H ionization threshold (13 . α photons are the only relevant exception. Infact, although the Lyman α cross section is very high, suchphotons can scatter many times before exiting the reso-nance; more importantly, the redshifting of photons withenergies slightly higher than 10 . α radiation field also inneutral regions.Ciardi & Salvaterra (2007; hereafter CS07) found thatthe Lyman α radiation field can moderately heat the IGM: It is natural to wonder down to which redshift such neutral re-gions actually exist. Here, we will simply assume that they survivedown to z ∼
5, and look into their properties. Such hypothesiswill be discussed in Section 5.1.c (cid:13) , 000–000 arly BH radiation - I: effects on the IGM
20 15 12 10 8 6 -100102030 δ T b [ m K ] IMBH-3%
20 15 12 10 8 6-100102030
IMBH-6%20 15 12 10 8 6Redshift-100102030 δ T b [ m K ] SMBH-3% 20 15 12 10 8 6Redshift -100102030
BVR06
20 15 10 8 6-400-300-200-1000
Figure 10.
Redshift evolution of the brightness temperature dif-ference with respect to the CMB δT b , when the Ly α coupling dueto stellar radiation is kept into account. The order of the panelsand the meaning of the various line types are the same as in Fig.2. The insert in the bottom-right panel shows the same quanti-ties (for the BVR06 case; the other cases are qualitatively similar)on a much wider δT b scale. The dotted line stopping at z = 10comes from Fig. 5 (bottom panel, solid line) of CS07, and shows δT b for a model with stellar Lyman α coupling and heating, butno BH emission. This line represents an upper limit on δT b in theabsence of BH heating. the heating rate taken from their models dominates overthat of all our models at z > ∼
15, and takes the IGM tem-perature to > ∼
30 K at z ∼ −
20. On the other hand, at z < ∼
10 the Lyman α heating rate should be much smallerthan those of our models . More importantly, CS07 findthat for z < ∼
27 the intensity J α, ∗ of the Lyman α back-ground is much higher than the level [ J α,coupling ∼ − (1+ z ) erg cm − s − Hz − sr − ] which should couple T spin to T k rather than to T CMB (see Ciardi & Madau 2003).In our case, it is reasonable to neglect the heating effectsof the Lyman α background, although this will lead us tosomewhat underestimate the IGM temperature at z > ∼ α background to our estimation of T spin (and δT b ).This can be done very easily by modifying eq. (16) into T spin = T ∗ + T CMB + ( y k + y α + y α, ∗ ) T k y k + y α + y α, ∗ , (27)where y α, ∗ accounts for the additional coupling due to the The plots in CS07 actually stop at z = 10; but it is prettyclear that in their model the IGM temperature is growing at amuch slower rate than in our models. It is also worth noting thatsome of the CS07 assumptions (e.g. the values of the parameters f gas and f ∗ ) are quite extreme, and would result in a very earlycomplete reionization. More realistic assumptions would result ina significant delay in the rise of T spin . Lyman α background due to the stars , and is approxi-mately given by (see CS07): y α, ∗ ∼ J α, ∗ T ∗ A T k . (28)After approximating J α, ∗ with the expression J α, ∗ ( z )erg / (cm s Hz sr) = z ≥ − − [0 . z − > z > − z ≤ , (29)which is a moderate underestimate of the J α, ∗ curves shownin fig. 1 of CS07, we have recalculated the evolution of T spin ,and δT b . The results are shown in Figs. 9 and 10.In this case, T spin (Fig. 9) is almost perfectly coupled tothe kinetic temperature, and the difference T spin − T CMB ≃ T spin easily reaches the 10 − K range. Also δT b (Fig. 10)is affected. Here we focus on the relatively low redshiftswhich will be explored by 21-cm experiments (e.g. LOFAR),where the effects of BH emission lead to differential bright-ness temperatures which can reach 20 −
30 mK at redshifts ∼ −
15. Instead, at high redshifts (say, z > ∼ δT b canreach very high negative values (in the −
200 to −
300 mKrange); but in such redshift range the results of CS07, pre-dicting a minimum value of δT b ∼ −
170 mK at z ∼
24 arelikely more correct because they include also the the heatingeffects of the stellar Lyman α background.We point out that our results, especially those about δT b , depend only weakly from the very high level of J α, ∗ given in the CS07 paper: the effects of lowering J α, ∗ toa more realistic level, e.g. a fraction 0 . .
01) ofthe amount given by eq. (29) are a certain reduction (from ∼ − − T spin reachesa low-redshift ‘plateau’, and a much smaller change in theevolution of δT b . Then, our predictions about δT b observa-tions are quite independent from the assumptions of CS07.Instead, for the model where no BH feedback is included, areduction by a similar factor in the Lyman- α heating ratein the CS07 models would result in a much lower δT b valuethan shown by the dotted curve in Fig. 10. In the previous section we have shown that the energy inputfrom BHs can substantially heat the IGM. In turn, this islikely to affect the formation of galaxies: as the cosmologi-cal Jeans mass depends on T / k , the baryonic component ofsmall fluctuations might become unable to collapse and formstars because of the temperature increase. But the effects ofBH radiation are not limited to the heating, since the in-crease in the H ionized fraction also enhances the formationof H , which is the most important coolant in metal-freegas at temperatures < ∼ K: such enhancement would fa-cilitate the formation of stars within small halos. Then, weinvestigated the influence of BH energy input on structureformation with a method which accounts for such competing Also BHs produce a Lyman α background; but its intensityis much lower than the one due to stars, and the correspondingcoupling term is always much smaller than y α .c (cid:13) , 000–000 E. Ripamonti, M. Mapelli, S. Zaroubi
20 15 12 10 8 C r i t i c a l m a ss [ s o l a r m a ss e s ] IMBH-3%
20 15 12 10 810 IMBH-6%20 15 12 10 8Virialization redshift10 C r i t i c a l m a ss [ s o l a r m a ss e s ] SMBH-3% 20 15 12 10 8Virialization redshift BVR06
Figure 11.
Redshift evolution of the critical mass. The order ofthe panels and the meaning of the various line types are the sameas in Fig. 2, except for the thin continuous line, which represents M crit for a model without any BH emission, and for the dottedline, representing the mass M H of halos with virial temperature T vir = 10 K. effects, and which was already employed in the RMF07 andR07 papers.We used the full code (instead of the simplified versionused in the previous Section) described in Section 3, in or-der to follow the evolution of spherically symmetric halosof different masses, virializing at different redshifts. Suchevolution took into account all the physics included in thesimplified version we already described, plus the treatmentof gravity, of the hydrodynamical evolution of the gas, andof the dissociation of H molecules due to Lyman-Werner(11 . ≤ hν ≤ . . Darkmatter (DM) gravitational effects are included as describedin Sec. 2.1.3 of R07: the DM final density profile is assumedto be a truncated isothermal sphere with ξ = 0 . As in the RMF07 and R07, we classified halos as collaps-ing if they reach a maximum density larger than ρ coll =1 . × − g cm − ≃ m H cm − (a value high enough tosuggest that the formation of a luminous object is well un-der way) in less than an Hubble time after their virialization(at z vir ), i.e. at a redshift z coll > ∼ [0 . z vir )] − For this last effect we use the reaction rate given by Abel et al.1997 (reaction 27); the flux of photons at 12 .
87 eV was obtainedthrough the formalism described in Section 2.1, but assuming thatphotons at frequencies corresponding to the lines of the Lymanseries of hydrogen were completely absorbed. No stellar emissionwas assumed. R e t a i ned ga s f r a c t i on IMBH-3%
IMBH-6%5.0 5.5 6.0 6.5 7.0 7.5Halo Mass (Log)0.00.20.40.60.81.0 R e t a i ned ga s f r a c t i on SMBH-3% 5.5 6.0 6.5 7.0 7.5 8.0Halo Mass (Log)
BVR06
Figure 12.
Fraction of gas retained by a halo at the end of oursimulations in halos virializing at z vir = 10, as a function of thetotal halo mass. The order of the panels and the meaning of thecontinuous, dashed and dot-dashed lines are the same as in Fig. 2;the dotted lines refer to the unperturbed model. The thickness ofthe line indicates whether a certain halo mass is below (thin line)or above (thick line) the critical mass. The seesaw behavior forhigh masses is purely numerical (i.e. due to the discrete numberof shells). This classification criterion is roughly comparable to thecollapse criterion of Tegmark et al. (1997): in analogy withsuch paper (and with RMF07 and R07), we define the crit-ical mass M crit ( z vir ) as the minimum mass of a collapsinghalo virializing at z vir .In Fig. 11 we compare the evolution of M crit which isobtained for each of our BH models with the same evolutionin the unperturbed ( ǫ = 0 at all redshifts) case, and withthe evolution of the mass M H ( z vir ) ≃ . × M ⊙ (1 + z vir ) − / (30)of halos with a virial temperature T vir = 10 K (assuminga mean molecular weight µ = 1 .
23, as appropriate for aneutral medium), above which the cooling due to atomic Hbecomes dominant.The BH energy injection has negligible effects upon M crit for z vir > ∼
15, but its effects become increasingly im-portant at later times: at z = 10 the BH energy input in-creases M crit by a factor between 1 . M crit can become > ∼ M H , althoughthe onset of atomic cooling slows down the increase of M crit :in such models, BH feedback prevents the formation of starsinside mini-halos cooled by molecules at z < ∼ c (cid:13) , 000–000 arly BH radiation - I: effects on the IGM F i na l c en t r a l t e m pe r a t u r e [ K ] IMBH-3%
IMBH-6%5.0 5.5 6.0 6.5 7.0 7.5Halo Mass (Log)100100010000 F i na l c en t r a l t e m pe r a t u r e [ K ] SMBH-3% 5.5 6.0 6.5 7.0 7.5 8.0Halo Mass (Log)
BVR06
Figure 13.
Central gas temperature at the end of our simulationsin halos virializing at z vir = 10, as a function of the total halomass. The order of the panels and the meaning of the continuous,dashed and dot-dashed lines are the same as in Fig. 2; the dottedlines refer to the unperturbed model. The thickness of the lineindicates whether a certain halo mass is below (thin line) or above(thick line) the critical mass. RMF07 suggested that one possible feedback effect of theenergy input from decaying/annihilating DM particles is toreduce the amount of gas which actually ends up within thepotential wells of virialized halos. As the feedback effectsof BHs are much stronger than those of DM decays andannihilations, we looked at whether these same effects areimportant in our simulations.To this purpose, we define f ret as the ratio of the massof gas which is retained inside the virial radius of a halo (atthe time when our simulations are stopped) with respect tothe baryonic mass expected from cosmology. For a halo withtotal mass M halo and baryonic mass M gas : f ret = M gas M halo Ω m Ω b . (31)In Fig. 12 we show the dependence of f ret upon M halo ,for halos virializing at z vir = 10 and for all our BH models,plus the unperturbed case.Generally, models with BH feedback exhibit a sharptransition at M halo ≃ M crit , going from f ret ∼ f ret > ∼ .
7, whereas in the unperturbed case f ret increasesquite smoothly from ∼ . ∼ . M halo < ∼ M crit ), the final gas over-density is generally < ∼
10, whereas the DMover-density is > ∼ M halo > ∼ M crit ), the heat-ing induced by the BHs cannot counteract the gravitationalpull, and the halo will retain most of its gas, which will cool,collapse and form luminous objects.This is confirmed by Fig. 13, where we show the finaltemperature of the gas at the centre of halos virializing at z vir = 10, as a function of the halo mass. In halos withmass ≤ M crit the gas temperature is much higher, if BHheating is present, than in the unperturbed case, and it isclose to the temperature T k of the IGM (1000 − ≥ M crit the final temperature in presence of BHheating is similar to the unperturbed case (200 −
400 K,much lower than the temperature of the surrounding IGM),as the gas in the centre of the halo was able to condenseand cool. The transition in the case of the gas temperatureis even sharper than in the case of f ret , probably becausethe density dependence of the cooling rate will lead to a‘runaway’ cooling as soon as the density starts to increase.Fig. 12 also shows that in models with strongBH feedback (IMBH6%+PL1, IMBH6%+MC01, andBVR06+MC01) the transition from f ret ∼ f ret ∼ . M crit ≤ M halo < ∼ M crit are relatively poor in gas, despitebeing able to form luminous objects at their centre. Such aluminous but gas-poor halo population starts developing at z ∼
12, and becomes increasingly important when lower red-shifts are considered: for instance, at z ∼ ∼
10 in mass. If such objects actually ex-ist and survive until present, they should be characterized bya high
M/L ratio, a low gas content, and a mass ∼ M ⊙ .Such properties remind us of the dwarf spheroidal galaxiesof the Local Group (see Mateo 1998), although it might justbe a coincidence. Further investigation is needed to addressthis issue. The 3-yr WMAP results (Spergel et al. 2007) for the electronscattering optical depth can be interpreted as indicating asudden reionization at z ≃
11. In such a scenario, neutralregions essentially cease to exist as soon as reionization hap-pens, and the effects of BHs at z < ∼
11 would become negli-gible: • The 21 cm brightness temperature differences would beseverely quenched because of the lack of neutral H ( δT B is proportional to the density of neutral H atoms). Even ifit were not, it is reasonable to expect that the reionization In most of the regimes we are considering, the cooling rate isdue to H molecules. An increase in density results in both anincrease in the cooling rate per molecule (which is ∝ ρ ) and anincrease in the abundance of molecules.c (cid:13) , 000–000 E. Ripamonti, M. Mapelli, S. Zaroubi takes the IGM temperature T k to ∼ K, and the BH heat-ing would be unable to drastically change T k ; the changesin T spin would be even smaller. • The high IGM temperature we just mentioned wouldprobably have important effects on structure formation; butthat is a feedback effect from stellar sources, rather thanfrom BHs.In short, the effects of BHs can be clearly observed onlyat redshifts before the end of reionization process. In thecase of a sudden reionization at z ≃
11 they would becomeextremely difficult to detect, except perhaps in our modelswith the strongest BH feedback.However, the sudden reionization scenario appears un-realistic. In fact, practically all the theoretical models pre-dict that the reionization process is quite extended in time.In particular, the most recent numerical simulations (e.g.Iliev et al. 2007; Santos et al. 2007; Zahn et al. 2007;Mesinger & Furlanetto 2007) essentially agree in the pre-diction that the end of the overlap phase (i.e., the timewhen the volume filling factor of neutral regions becomesnegligible) is at redshift 6 . < ∼ z overlap < ∼
8. Fig. 3 of Santoset al. 2007 is particularly useful for our purposes, since itincludes not only the evolution of the volume-averaged ion-ization fraction (solid line), but also a similar curve wherecomplete ionization is assumed within the ionized ‘bubbles’(dashed line): it is quite reasonable to expect the volumefilling-factor of neutral regions to drop below ∼ . . − .
9, i.e at z < ∼ − . z ≃
9, but declines below 0 . z < ∼ z overlap are usually obtained in models basedon the 3-yr WMAP data, whereas models based upon 1-yrWMAP data (Kogut et al. 2003; Spergel et al. 2003) lead tosignificantly higher values of z overlap (for instance, see Ilievet al. 2007, which presents the results of simulations basedon both sets of parameters).Furthermore, observations of the Gunn-Petersontroughs in the spectra of quasars at z > ∼ α emitters at 5 . < ∼ z < ∼ > ∼ .
1) atleast until redshift 7 −
8, and maybe even at lower redshifts;nonetheless, it is also possible (e.g. if the 3-yr WMAP resultsare underestimating τ e ) that a dearth of neutral regions at z < ∼
10 will prevent the detection of the effects we discuss.
Our analysis of feedback effects from high-redshift BHs hasmany links with the former study by RO04 (and also with Ricotti et al. 2005). However, there are some crucial differ-ences between the assumptions in the two sets of models,which lead to important differences in the results. • The most important difference is likely to be in thegrowth histories of the BH densities. All of the RO04 mod-els reach ρ BH > ∼ M ⊙ Mpc − (in their notation, ω BH ∼ . × − ; cfr. the lower panel of their fig. 2) at red-shifts ≥
15, whereas at z = 15 none of our models exceeds ρ BH = 10 M ⊙ Mpc − . This difference becomes less impor-tant when going to lower redshifts. The IMBH-6% growthhistory actually overtakes the RO04 predictions at z < ∼ − z = 5. • We assume a constant dutycycle ( y = 0 . , . , or 0 .
10, depending on the model),whereas in the RO04 models this quantity strongly dependson redshift (see the bottom panel of their fig. 3): it is as-sumed to be 1 at high redshifts ( z ≥ z ≥
19, or z ≥ − when lower redshifts are considered( z ≤
13, or z ≤ • RO04 restrict their analysis to an intrinsically absorbedSazonov et al. (2004) spectrum; their treatment of radiationtransfer is more detailed than in the present paper, but asthey are not limiting themselves to the neutral-IGM, theirbackground spectrum is likely to extend to lower energiesthan ours, resembling the thin solid line in Fig. 1. • The RO04 models include also a stellar contribution.Because of all these differences, the RO04 models pre-dict a much larger energy injection into the IGM (at z > ∼ > ∼ ). Atlower redshifts ( z < ∼ −
9) such difference is erased (or evenreverted), mostly because of the reduction of the RO04 dutycycle.Taking into account these differences, the results of thecurrent paper are reasonably consistent with those of RO04.In fig. 5 of RO04, the ionized fraction and the IGM temper-ature are shown for different models. Complete ionizationis achieved already at z ∼ −
8, while in our models x HI is always less than 1 at z > K are reached at z ∼ −
10 in our paperand at z ∼ −
25 in RO04. The Thomson optical depthderived by RO04 is 0 . < ∼ τ e < ∼ .
2, but a fraction τ e ∼ . τ e ≈ . − . τ e < ∼ . τ e ≃ . ± . τ e ≃ . ± . δT b starts increasing alreadyat z ∼ −
25, because of the strong increase in the IGMtemperature due to the BH emission. The predicted peakin δT B is of the order of only a few mK, a factor of ∼ < ∼ .
2) neutral fractionin their models is the likely cause of this discrepancy, as itimplies a low τ in eq. (25). c (cid:13) , 000–000 arly BH radiation - I: effects on the IGM
15 12 10 8 6 5Redshift10 -30 -29 -28 -27 -26 E ne r g y i npu t pe r ba r y on [ e r g / s ] Figure 14.
Redshift evolution of the total energy input perbaryon due to the background produced by X-ray emission as-sociated with star formation (thick lines; the two lines refer topower-law SEDs with different photon index: Γ = 1 . . . f X = 1. For comparison, we show also the energyinput in models where BH emission was considered (IMBH-6%+ MC01: thin dot-dashed line; IMBH-3%+PL1: thin solid line;BVR06 + SOS1: thin dashed line). Observations of local star-burst galaxies (Grimm, Gilfanov& Sunyaev 2003; Ranalli, Comastri & Setti 2003; Gilfanov,Grimm & Sunyaev 2004) find a correlation between starformation and X-ray luminosity. As was noted in Glover& Brand (2003), Furlanetto (2006), Pritchard & Furlan-etto (2007) and Santos et al. (2007), it is reasonable to ex-pect that also high redshift star formation is associated withX-ray emission, although an unknown (and possibly impor-tant) correction factor f X should be introduced to quantifythe differences between the local and the primordial envi-ronment.The effects of such emission (and whether they can bedistinguished from the ones presented in this paper) will bethoroughly investigated in a companion paper (Ripamontiet al., 2008 - in preparation). Here, we just compare the en-ergy input due to BHs with the one due to X-ray emissionassociated with star formation. This was done by assumingthat the SED of such emission is a power-law with photonindex in the 1 . ≤ Γ ≤ . z < ∼
10) the expected energy input is onlya fraction of the BH contribution of most of our models, andis comparable only to the BH model with the weakest feed-back; at higher redshifts the SF-associated X-ray emissionmight be more important or even dominant, but the overallenergy input is small. In short, if the unknown factor f X is not much largerthan 1, the effects of the X-ray emission associated with starformation should be at most comparable to the ones of theweakest of our BH models (such as the BVR06+SOS1 case). We have examined how a population of accreting BHs mightaffect the pre-reionization Universe, looking in particular atthe effects upon the neutral regions outside the first ionized‘bubbles’, where stellar feedback is likely small. We exploreda number of scenarios for the growth of the cosmologicalBH density, and considered several possible SEDs. Both ofthese components are in broad agreement with observationalconstraints (e.g. the results about the X-ray background byDijkstra et al. 2004).Our analysis started from how the energy input fromthe diffuse radiation due to the BH population might af-fect the temperature and ionization level of the IGM far-away from ionized regions where local effects are important.Given the Dijkstra et al. (2004) constraints, it is not sur-prising that BH emission in our models leads only to partialionization: the main effect of BH emission is then the in-crease in the temperature of the IGM, which easily reacheslevels > ∼ K in all the cases we have considered.Then, we explored a number of possible indirect conse-quences of the energy input: • CMB measurements appear unable to constrain any ofour models, since all of them comfortably fit observationalconstraints from WMAP; • δT b should be easilydetectable with the next generation of 21-cm experiments(e.g. LOFAR), especially if stellar Lyman α coupling is reallypresent; • the critical mass for halos to be able to cool, collapseand form stars is significantly enhanced at z < ∼
10, and insome of our models it becomes ∼
100 times larger than inthe unperturbed case. This allows star formation only in ha-los with virial temperatures > ∼ K, i.e. prevents (or, inmodels with weak feedback, significantly reduces) the for-mation of PopIII objects for z < ∼ • gas depletion might occur in the models withintermediate-to-strong BH feedback, and for relatively lowvirialization redshifts: halos with masses between M crit and3 − M crit appear to be able to form stars at their centre,but their baryonic fraction is considerably lower than thecosmological average.The most relevant of our results appears to be the oneabout 21-cm observations, since it might be falsified (orconfirmed) by forthcoming observations. To our knowledge,the only mechanism which should be able to heat the IGMoutside ionized regions in a comparable way is the X-rayemission associated with star formation, as was proposedby Glover & Brand (2003), Furlanetto (2006) and Pritchard& Furlanetto (2007). We leave the detailed comparison be-tween the two models to a future paper (Ripamonti et al.2008, in preparation), where we will also investigate whetherit is possible to distinguish between the two scenarios, e.g.by using the spatial power-spectrum. c (cid:13) , 000–000 E. Ripamonti, M. Mapelli, S. Zaroubi
We stress that most of our conclusions strongly dependon the details of the reionization process, and in particularon the survival of neutral regions down to redshift ∼ − z < ∼
7. However, the scenario of an earlier reionization can-not be rejected at present: in such a case, BH signatures(such as the effects on the properties of 21-cm radiation)become difficult or impossible to detect. On the other hand,if the predictions of simulations are correct, the effects of BHemission might enhance the 21-cm contrast between neutraland ionized patches, improving our capability of studyingthe z ∼ −
12 Universe, and providing important informa-tion on the duration and the end of the reionization phase.
ACKNOWLEDGMENTS
We thank R. Salvaterra for clarifications about the CS07 re-sults, F. Haardt, G. Mellema, R. Thomas and M. Volonterifor useful discussions, and the anonymous referee for severalsuggestions about improving the manuscript. We also thankK. Visser for assistance in working with the HPC clusterof the Centre for High Performance Computing and Visu-alization of the University of Groningen, where most of ourcomputations were carried out. ER and MM thank the In-stitute for Theoretical Physics of the University of Z¨urich,and the Kapteyn Astronomical Institute of the Universityof Groningen for the hospitality during the preparation ofthis paper. ER acknowledges support from the NetherlandsOrganization for Scientific Research (NWO) under projectnumber 436016, and MM acknowledges support from theSwiss National Science Foundation, project number 200020-109581/1 (Computational Cosmology & Astrophysics). SZ isa member of the LOFAR project which is partially fundedby the European Union, European Regional DevelopmentFund, and by “Samenwerkingsverband Noord-Nederland”,EZ/KOMPAS.
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