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Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 2 October 2015 (MN LATEX style file v2.2)

Detecting high-z galaxies in the Near Infrared Background

Bin Yue1, Andrea Ferrara1,2, Kari Helgason31Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy2Kavli IPMU (WPI), Todai Institutes for Advanced Study, the University of Tokyo, Japan3Max Planck Institute for Astrophysics, Karl-Schwarzschild-Str. 1, 85748 Garching, Germany

2 October 2015

ABSTRACT

Emission from high-z galaxies must unquestionably contribute to the Near-InfraRedBackground (NIRB). However, this contribution has so far proven difficult to isolateeven after subtracting resolved galaxies to deep levels. Remaining NIRB fluctuationsare dominated by unresolved low-redshift galaxies on small angular scales, and byan unidentified component of unclear origin on large scales (≈ 1000′′). In this paper,by analyzing mock maps generated from semi-numerical simulations and empiricallydetermined LUV −Mh relations, we find that fluctuations associated with galaxies at5 < z < 10 amount to several percent of the unresolved NIRB flux. We investigate theproperties of this component for different survey areas and limiting magnitudes. Inall cases, we show that this signal can be efficiently, and most easily at small angularscales, isolated by cross-correlating the source-subtracted NIRB with Lyman BreakGalaxies (LBGs) detected in the same field by HST surveys. This result provides afresh insight into the properties of reionization sources.

Key words: cosmology: diffuse radiation-dark ages; reionization, first stars –infrared:diffuse-background – galaxies: high-redshift

1 INTRODUCTION

The near-infrared background (NIRB) contains a consid-erable fraction of the collective radiation emitted by starsin galaxies through cosmic times. As such, it offers aunique opportunity to study faint high-z galaxies thatremain largely undetected in deep galaxy surveys (seee.g. Salvaterra & Ferrara 2006; Fernandez & Komatsu 2006;Fernandez et al. 2010, 2012, 2013; Fernandez & Zaroubi2013). This is particularly important, as these objects arecommonly believed to provide most of the ionizing powerto drive cosmic reionization (Choudhury & Ferrara 2007;Raicevic et al. 2011; Salvaterra et al. 2011). NIRB mightalso help characterizing the stellar populations of the firstcosmic systems (Salvaterra & Ferrara 2003; Salvaterra et al.2006; Santos et al. 2002; Kashlinsky et al. 2002, 2004,2005; Magliocchetti et al. 2003; Cooray & Yoshida 2004;Cooray et al. 2004). The most recent studies have convergedon the prediction that on scales of ≈ 1000′′ the fluctuationlevel from galaxies at z >

∼ 5 is ≈ 10−3 nWm−2sr−1 at 3.6 µm(Cooray et al. 2012a; Yue et al. 2013a; Helgason et al.2015).

However, extracting such signal from available datahas been so far very challenging. Even when the deepestgalaxy subtraction from NIRB maps is applied, the domi-

nant contribution to the remaining flux fluctuations1 cannotbe associated with the known high-z galaxy population. Onsmall angular scales, most of the signal arises from unre-solved, low-z galaxies. On larger scales the measured power(see e.g. Kashlinsky et al. 2002, 2004, 2005, 2007c,b, 2012;Matsumoto et al. 2005, 2011; Seo et al. 2015; Cooray et al.2007, 2012b) is >

∼ 100 times larger than the low-redshiftgalaxies (Helgason et al. 2012), and >

∼ 1000 times largerthan that expected from early systems (Cooray et al. 2012a;Yue et al. 2013a). Therefore it must be attributed to some,yet unknown, alternative sources. Basically, two differentexplanations have been proposed for the origin of suchlarge scale (∼ 1000′′) “power excess”. They involve ei-ther early accreting black holes (Yue et al. 2013b, 2014)which could explain the detected NIRB-cosmic X-ray back-ground coherence (Cappelluti et al. 2013), or “intrahalolight” from stars ejected from their parent galaxies duringmerger events (Cooray et al. 2012b; Zemcov et al. 2014). At

1 NIRB studies usually concentrate on fluctuations rather thanabsolute flux, as the latter is difficult to measure due to thepresence of an overwhelming foreground. However, as the fore-ground is rather smooth on scales at which the NIRB ismeasured, the fluctuations analysis is more robust – see e.g.Thompson et al. 2007; Matsumoto et al. 2011; Kashlinsky et al.2012; Cooray et al. 2012b.

2 Yue et al.

present it is unclear which of the two should be preferred.To further complicate the interpretation, recent observations(Zemcov et al. 2014) show that, on large scales and at leastfor the 1.1 and 1.6 µm bands, diffuse Galactic light (DGL)might provide a non-negligible contribution, thus almost cer-tainly drowning the signal from high-z sources.

For these reasons, it is urgent to devise new strate-gies that put our understanding on firmer grounds. In prin-ciple, one could apply a brute force approach in whichgalaxies are removed from the NIRB down to increas-ingly deep magnitudes (Helgason et al. 2015) on suffi-ciently large sky areas. This is not an easy task for cur-rent instrumentation, and therefore alternative strategiesmust be pursued. Alternatively, cross-correlation studiesseem promising. The NIRB-HI 21cm line cross-correlation(Fernandez et al. 2014; Mao 2014) has the advantage thatit selectively picks up the signal from reionization sources.Also, the NIRB, if produced by sources at the epochof reionization, would be cross-correlated with the CMBthrough the thermal Sunyaev-Zeldovich effect. This corre-lation could be seen in the forthcoming Euclid all-sky sur-veys (Atrio-Barandela & Kashlinsky 2014). Additionally, arecent work (Kashlinsky et al. 2015) proposed the use ofLyman-break tomography to constrain the NIRB contribu-tion from sources above a certain redshift.

The cross-correlation between the resolved ACS-faintsources and the source-subtracted NIRB was analyzed byKashlinsky et al. (2007a); they found negligible correlatedfraction, implying that those resolved objects (or objects as-sociated to them) do not responsible for the major measuredNIRB fluctuations. This analysis did not pay particular at-tention on the high-redshift sources. It is surprising that sofar little attention has been devoted to the search for thesignatures of the high-z normal star-forming galaxies in theNIRB, given that deep galaxy surveys have made tremen-dous progresses in obtaining the UV luminosity functions ofgalaxies up to z = 10 (Bouwens et al. 2015), and the detec-tion limits of Lyman break galaxy (LBG) surveys carried outby HST have already reached H ∼ 29− 31 (Illingworth et al.2013; Bouwens et al. 2011). A simple, but mandatory step,would be to check whether the expected signal from thesehigh-redshift faint sources can be detected in the NIRB.

The idea we propose here is to cross-correlate such deepsurveys with the NIRB map so to isolate the targeted sig-nal, and show the feasibility of the statistical detection ofreionization sources via the NIRB. To this aim, we: (a)construct large scale mock maps of the source-subtractedNIRB and LBG catalogs using semi-numerical simulations;(b) perform a cross-correlation analysis between the twodata sets to extract NIRB contribution of high-z galax-ies. The paper is organized as follows. In Sec. 2 we de-scribe the steps to construct the mock maps. In Sec. 3 wepresent the analysis about the correlation coefficient andthe color differences. Conclusions and discussions are pre-sented in Sec. 4. We use Planck cosmological parameters:Ωm = 0.31,ΩΛ = 0.69,Ωb = 0.048, ns = 0.96, σ8 = 0.82 andh = 0.68 (Planck Collaboration et al. 2014). All magnitudesare in the AB-system (Oke & Gunn 1983).

2 CONSTRUCTION OF MOCK MAPS

2.1 High-z galaxies

We carry out semi-numerical simulations to get catalogs ofhalos with mass Mh

>∼ 5 × 108 M⊙ from z = 5 to 10, for

every ∆z = 0.1 using the code DexM (Mesinger & Furlanetto2007)2. We adopt a 400 Mpc box size, corresponding to anangular size of≈ 2.4 deg at z = 10. We construct a cuboid byreplicating the output boxes along the line-of-sight, addingrandom translations, rotations and reflections (Blaizot et al.2005). This is our light-cone since we assume that all line-of-sights are parallel. This assumption is convenient and safeenough when z >

∼ 5.To construct flux maps from the light-cone, we link

galaxy luminosities to halo mass Mh. The observed lumi-nosity functions (LFs) could be reproduced exactly if wederive the LUV −Mh relation through abundance matching,i.e. we force the number density of galaxies with luminos-ity > LUV to match the number of halos with mass > Mh.Formally,

∫

MUV

Φ(M ′

UV, z)dM′

UV =

∫

Mh

dn

dM ′h

dM ′

h, (1)

where Φ is the UV LF at 1600 A. For this, we usethe Schechter parameterization with the redshift-dependentfitting parameters given in Bouwens et al. (2015). As areference, our minimum mass 5 × 108 M⊙, correspondsat z = 5, 8, 10 to an absolute magnitude MUV =−10.5,−12.1,−13.0, respectively. Luminosity at other UVwavelengths is obtained through the luminosity-dependentSpectral Energy Distribution (SED) slope β (i.e., fλ ∝ λβ)in Bouwens et al. (2014)3. However, generally speaking thispower-law only holds at λ <

∼ 2000−3000 A, while we need lu-minosities at least until 4.5/(1+z) µm, say 7500 A when z =5. Therefore at λ >2000 A we use the SED template fromStarburst994 (Leitherer et al. 1999; Vazquez & Leitherer2005; Leitherer et al. 2010), adopting a continuous star for-mation mode, with metallicity 0.1 Z⊙ and 200 Myr stellarage. The SB99 SEDs are normalized to match the power-lawform at 2000 A.

The flux received in each pixel in the map is the sum ofradiation from all galaxies seen by the pixel,

F (ν0) = ν01

(θpix)2

∑

j

Lj(ν)(1 + zj)

4πr2j (1 + zj)2, (2)

where ν = ν0(1 + zj), zj is the redshift of the j-th halos5

in the solid angle (θpix)2 (we adopt θpix = 3.6′′ for all mock

maps in this work), rj is its comoving distance. In Fig. 1we show the 3.6 µm flux map (bottom left panel) from all

2 http://homepage.sns.it/mesinger/DexM___21cmFAST.html3 β = β−19.5 + dβ

dMUV

(MUV + 19.5), the values of β−19.5 anddβ

dMUV

at z = 4, 5, 6 and 7 could be found in Bouwens et al.

(2014). For convenience of using this form at in-between red-shifts, we fit z-dependent forms (Yue et al. 2015): β−19.5 =−1.97 − 0.06(z − 6) and dβ

dMUV

= −0.18 − 0.03(z − 6). We use

these fittings anyway when 5 < z < 10.4 http://www.stsci.edu/science/starburst99/docs/default.htm5 We do not model photometric redshift uncertainties, becausethe redshift range considered here z = 5− 10 is much larger thanthe uncertainties.

Detecting high-z galaxies in the NIRB 3

galaxies between z = 5 − 10 (flux from galaxies at z > 10is negligible compared with galaxies at lower redshift, weignore it here).

Finally, we construct the flux map of 5 < z < 10 LBGs.To take into account selection effects, we assume a complete-ness function of the form

f(m) = 0.5[1 − erf(m−mlim)], (3)

where erf is the error function, and mlim is the limitingmagnitude. When constructing the flux map, for each LBGwith apparent magnitude m, we generate an uniformly dis-tributed number xr. Flux from these galaxies is added to themap only if xr 6 f(m). In Fig. 1 we show the 1.6 µm6 fluxmap constructed from the LBGs with H-band magnitudesHlim = 25 (top left) and Hlim = 27 (top right) respectively.

2.2 NIRB contamination maps

In addition to the flux from high-z (z > 5) galaxies, the ob-served NIRB also contains radiation from unresolved, low-z galaxies, and an excess radiation from unknown sources(Yue et al. 2013b, 2014; Cooray et al. 2012b; Zemcov et al.2014). We collectively refer to these two components as con-tamination, since in this work the targeted signal is the fluxfrom high-z galaxies.

We generate random maps to model this contamina-tion. The contamination maps have mean flux 1.0 (0.7)nWm−2sr−1 at 3.6 (4.5) µm. The flux fluctuations re-produce the sum of (i) the angular power spectrum ofthe power excess (see Yue et al. 2013b) matching availableobservations (Cooray et al. 2012b; Kashlinsky et al. 2012),and (ii) the angular power spectrum of low-z galaxies(Helgason et al. 2012) producing shot noise level matchingKashlinsky et al. 2012 (4.8 × 10−11nW2m−4sr−1 at 3.6 µmand 2.2 × 10−11nW2m−4sr−1 at 4.5 µm, the correspondingsubtraction magnitude is ∼ 25). Contamination maps areconstructed as follows:

• A white noise map, i.e. a Gaussian random field, is gen-erated.

• This map is then transformed into frequency space byFFT.

• For each complex number in frequency space, its mod-ulus is rescaled to be

√

P (q), where P is the given powerspectrum and q is the spatial frequency. The zero-frequency(q = 0) element is set to be the mean flux.

• The above map is then transformed back into real spaceby inverse FFT, resulting in a synthetic image with the same2-point clustering properties as the measured P (q).

In Fig. 1 we plot a single realization of the contaminationmap at 3.6 µm as an example (bottom right). The contami-nation is not correlated with the high-z galaxy component;however, it adds noise to the cross-correlation signal. To ac-count for the statistical variance of the contamination, wemake 30 independent realizations of the maps. In Fig. 2 we

6 In this paper we only discuss the 1.6 µm flux maps of LBGs,because we consider a redshift range from z = 5 to 10. For shorterwavelengths all procedures (and conclusions) are similar, withthe only exception of a slightly smaller signal due to the Lymandropout of z & 8 galaxies.

Figure 2. Angular power spectrum of the 3.6 µm flux map for5 < z < 10 galaxies (triangles), contamination (squares). Er-ror bars show uncertainties due to limited number of Fouriermodes in each q bin. As a comparison, in the same panel wealso plot the Helgason et al. (2012) model for z < 5 galaxies (solidline), and the observational points in Kashlinsky et al. (2012) (di-amonds) and Cooray et al. (2012b) (hourglasses). On large scales(θ >

∼ 100′′) the angular power spectrum of our co-added map(quite similar to squares in the panel) is consistent with bothobservations. Compared with K12; at θ <

∼ 100′′ our predictionfalls slightly short, probably because the non-linear clustering oflow-z galaxies is not modeled here. The C12 observations have a

shallower (i.e. ∼ 24) source subtraction, hence a higher shot-noiselevel.

show the angular power spectrum of bottom panels in Fig. 1.All maps are convolved with a circular symmetric Spitzer

PSF before further analysis.

3 CROSS-CORRELATION OF LBGs AND

NIRB

3.1 the correlation coefficient

We first analyze the correlation coefficient between the fluxmaps of LBGs and the NIRB maps. It is defined as

R(θ) =〈(δF1.6δFλ0

)θ〉√

〈(δF1.6)2θ〉 〈(δFλ0)2θ〉

. (4)

where λ0 refers to the NIR wavelength being cross-correlatedwith 1.6µm LBGs, θ is a specified smoothing scale. Thebrackets refer to the pixel-averaged fluctuations. The corre-lation coefficient indicates the fraction of sources contribut-ing to both signals. To calculate the correlation coefficienta smoothing scale must be specified. Here we smooth boththe NIRB maps and the LBG flux maps by a real spacetop-hat window function with diameter θ = 10′′, since inthe measured NIRB maps (Kashlinsky et al. 2012) the in-strumental noise is negligible at θ >

∼ 10′′. To mimic surveyswith different areas, we cut out sub-maps with differentareas from the full map. We choose three areas: (0.036)2,

4 Yue et al.

Figure 1. Upper: The 1.6 µm flux map constructed from resolved LBGs with Hlim = 25 (left) and Hlim = 27 (right) respectively. Lower:Map of the 3.6 µm flux from galaxies with 5 < z < 10 (left) and contamination map at 3.6 µm (right). The mean flux is 1 nWm−2sr−1.

(0.3)2 and (1.2)2 deg2, representing a survey region simi-lar to HUDF/XDF, UDS, and an hypothetical larger field,respectively.

Before calculating the correlation coefficient, in bothmaps we mask the pixels containing galaxies brighter than ∼25 at either 3.6 µm or 4.5 µm. From this procedure we obtainthe source-subtracted NIRB map. The correlation coefficientvs. limiting LBG magnitude is shown in Fig. 3. The filledregions are the 1σ variance of all sub-maps with the samearea however cut out from different parts of the full map.Note that for each signal map we have 30 contaminationrealizations, so even for the (1.2)2 deg2 case we have 120samples.

Fig. 3 shows that, it is indeed feasible to detect the cor-relation from the mock maps, even from a relatively shallowsurvey with Hlim ∼ 25, which is ≈ 0.04. By pushing thelimiting magnitude fainter the correlation coefficient rapidlyincreases and becomes a factor ∼ 2 higher, and then ap-proaches ≈ 0.09 more slowly towards Hlim ∼ 29. It is worthnoting that in small area fields the measured correlation co-efficient has ∼ 30− 80% relative field-by-field scatters whenHlim

>∼ 26, and even larger scatters when Hlim < 26. In some

cases there would be no cross-correlation detected, due tothe the small number of LBGs contained in the fields.

To show the differential contribution of LBGs, for a

(0.3)2deg2 field, we further show the correlation coefficientfrom galaxies with > z by Fig. 4 for Hlim = 25, 26 and 27respectively. We use the errorbars to bracket the 1σ uncer-tainty ranges. For example, LBGs with z > 8 and H <

∼ 27contribute ≈ 0.01 correlation coefficient.

3.2 The detectability vs. scales

In last sub-section we investigate the cross-correlation co-efficient by specifying a smoothing scale θ = 10′′. In thissub-section we investigate the variety of the correlation co-efficient at different angular scales. We re-define the correla-tion coefficient in frequency domain via the power spectrum

Rq(θ) =PIR×G(θ)

√

PIR(θ)× PG(θ), (5)

where P1×2(θ) is the cross-power spectrum and P1,P2 arethe auto-power spectra calculated using the 2D FFT. SinceδF 2 ≃ q2P/2π, Rq ∼ R for the same θ.

The Rq(θ) between the source-subtracted NIRB at3.6 µm, and the 1.6 µm flux map of LBGs with Hlim = 25, 26and 27 is shown by Fig. 5. The error bars are the r.m.s of30 samples each has different random contamination real-izations.

The cross-power spectrum is composed of two terms:

Detecting high-z galaxies in the NIRB 5

Figure 3. Correlation coefficient between the 3.6 µm source-subtracted NIRB and LBG flux maps vs. H-band limiting mag-nitude for three different map areas. Filled regions are the 1-σ ranges (68.3% probability). All fields are smoothed on scaleθ = 10′′. For each signal map we run 30 contamination realiza-tions: hence, for example, the (1.2)2 deg2 case uses 120 realiza-tions.

Figure 4. Contribution to correlation coefficient from LBGswith > z. The 1-σ variance is plotted by error bars. For displayingpurpose we slightly shift the x-positions.

the shot noise which dominates the small scale and the clus-tering term which dominates the large scale. The shot noiseterm is from the same sources that contribute to both thesource-subtracted NIRB and the LBG flux map. This termis dominant on small scales θ <

∼ 100′′. On larger scales, theclustering term progressively takes over. The clustering termarises from all sources sharing the same large scale struc-

Figure 5. The Rq between the source-subtracted NIRB andthe flux map constructed from LBGs down to different limitingmagnitudes. The errorbars are the r.m.s of 30 random realiza-tions. For displaying purpose we slightly shift the x-positions ofHlim = 26, 27 curves.

tures, including galaxies fainter than the limiting magnitude.As a consequence, in principle the clustering term allowsthe detection of fainter galaxies in the source-subtractedNIRB through the cross-correlation with relatively brightLBGs whose redshift is known. However, as shown by Fig. 5the cross-correlation is easiest detected at small scales. Al-though the clustering term may contain more information,the main difficulty to be overcome in order to efficiently usethis strategy is that even for a relatively large survey area of(2.4)2 deg2 (i.e. our full map), the signal-to-noise ratio neverexceeds ∼ 3 at θ >

∼ 300′′ for Hlim = 27. While increasing thelimiting magnitude to > 27 does not help much to this aim,the noise could be reduced by using larger survey areas, asexpected with, e.g. EUCLID and WFIRST.

3.3 The color

From our maps it is also possible to characterize the color,i.e. the flux ratio, of fluctuations due to unresolved galaxiesin the source-subtracted NIRB maps. With the assumption

F4.5

F3.6

≈〈(δF4.5δF1.6)θ〉

〈(δF3.6δF1.6)θ〉, (6)

we derive the [3.6] − [4.5] color as

[3.6] − [4.5] = 2.5log

(

4.5F4.5

3.6F3.6

)

≈ 2.5log

(

4.5

3.6

〈(δF4.5δF1.6)θ〉

〈(δF3.6δF1.6)θ〉

)

(7)

Such magnitude difference, which might considerably varyfor individual galaxies, represents the combined, weightedcolor of the unresolved galaxy population in these bands.In practice the PSF adds bias to the measured flux ratio,therefore before calculating the flux fluctuations we need to

6 Yue et al.

Figure 6. The magnitude difference, [3.6]− [4.5], of fluctuationsdue to unresolved galaxies in the source-subtracted NIRB mapsas a function of the survey limiting magnitude. Filled regionsindicate 1-σ ranges (68.3% probability)

deconvolve the PSF from each map. We skip this step hereand directly calculate the magnitude difference on the mapwithout PSF convolution. Again we specify θ = 10′′. Thepredicted color as a function of Hlim is reported in Fig. 6,allowing us to conclude that the magnitude difference, oforder of -0.13 mag, could be detected by cross-correlatingsurveys with area >

∼ (0.3)2 deg2. The figure reiterates thatsmaller area fields would be affected by bias effects.

4 CONCLUSIONS AND DISCUSSIONS

Motivated by the fact that LBG surveys carried out by theHST have reached detection limits much deeper than theNIRB measured by Spitzer at longer wavelengths, in thispaper we investigated the feasibility to pick the resolvedLBGs component out of the NIRB by cross-correlation anal-ysis. Our investigations were based on mock maps con-structed from semi-numerical simulations of halo formationand empirically determined LUV −Mh relations.

We found that in the source-subtracted (galaxies areremoved down to apparent magnitude ∼25) NIRB observedat 3.6 and 4.5 µm, at smallest scales where the shot noisedominates, about 10% of the flux fluctuations arises fromLBGs in 5 < z < 10 and with H <

∼ 29. Such faint galax-ies have already been resolved in the existing deep surveys.However, this fractional contribution, if measured from nar-row fields with area ∼ (0.036)2 deg2 (as the HUDF/XDF),could vary from ∼ 3% to ∼ 16%. If the limiting magnitudeis decreased to H ∼ 27, the fractional contribution decreasesto about 8%. In this case we could consider a larger field,for example with area similar to EGS, i.e. ∼ (0.3)2 deg2.The correlation coefficient now varies in a narrower range,∼ 6% − 9%. We remind that the variance at hand here isdue to both the large-scale inhomogeneity of the signal and

the contamination: it is the field-to-field variance of the cor-relation itself. We do not model errors introduced by ob-servations, for example the mask effects. However, at leasttheoretically we have shown that the contribution from thefaintest galaxies could be isolated from the NIRB throughthe cross-correlation analysis. We pointed out that it is stillchallenging to use the cross-correlation arising from clus-tering term in the cross-power spectrum to study galaxiesunresolved not only in NIRB observations, but also in LBGsurveys. This term is dominant at >

∼ 200′′, however even ifthe survey area is as large as (2.4)2 deg2, the signal still hassmall significance, with a S/N ratio <

∼ 3.Additionally, our result have interesting implications for

the color of high-z galaxy populations. For LBGs are de-tected at wavelengths< 1.6 µm while too faint to be resolvedfor existing telescopes at 3.6 and 4.5 µm, their mean colorin those band can be obtained by using the cross-correlationwith the NIRB.

It is worth noting that the predictions presented in thispaper assume a contamination in the form of NIRB fluctua-tion excess which could originate from an exotic populationof sources at even higher-z (Yue et al. 2013b). If however theexcess is found to arise more locally, we might gain the abil-ity to model or subtract it more accurately, thereby makingthe signal calculated in this paper more easily detectable,〈R〉 >

∼ 0.1.Importantly, this type of NIRB study can ultimately be

pushed further without requiring prior LBG detections, inorder to infer properties of still fainter galaxy populationsat higher-z that are inaccessible to direct detections withany current instrument. This could, for example, be accom-plished in a Lyman-break tomography study designed toisolate high-z populations via multi-band cross-correlations(Kashlinsky et al. 2015).

ACKNOWLEDGMENTS

We thank A. Kashlinsky for valuable comments on themanuscript.

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