THE FAINTEST X-RAY SOURCES FROM z = 0 TO 8^*,†,‡

We would like to be able to determine directly how much growth occurs in supermassive black holes in the early universe. Unfortunately, however, only the most luminous quasars at z > 6 have ever been detected individually (e.g., Fan et al. 2006; Willott et al. 2010; Mortlock et al. 2011), and these sources are so massive that their evolutionary histories are far from typical.

We would also like to know the relative contributions of the galaxy and active galactic nucleus (AGN) populations to the UV and X-ray ionizing radiation in the early universe. Estimates from optical data were that AGNs could not account for the required UV ionizing flux at z > 3 (e.g., Bolton et al. 2005; Meiksin 2005). It is now recognized that complete samples of AGNs—or at least those which are not Compton thick—are most easily obtained with X-ray observations. Direct searches for high-redshift (z = 3.5–6.5) AGNs carried out using combined deep Chandra X-ray samples and optical imaging data (e.g., Barger et al. 2003; Fontanot et al. 2007) also found that the ionization from AGNs was insufficient to maintain the observed ionization of the intergalactic medium at high redshifts. This result was conclusively established at z > 3 by Cowie et al. (2009) by measuring the contribution of AGNs to the ionizing flux as a function of redshift using X-ray, optical, and UV observations.

However, even if the space density of high-redshift, unobscured AGNs is not sufficiently high to reionize the universe, it does not rule out the possibility that substantial accretion onto supermassive black holes is occurring behind veils of obscuring material. The only way to determine this is by probing the faintest X-ray fluxes. Thus, the continued deepening of the deepest X-ray images of the sky is essential for studying this important issue. The latest of these deepenings is the now nearly 4 Ms of exposure on the Chandra Deep Field-South (CDF-S; Giacconi et al. 2002; Alexander et al. 2003, hereafter A03; Luo et al. 2008; Xue et al. 2011, hereafter X11). The 4 Ms exposure is deep enough to detect all sources above a luminosity of ∼5 × 10⁴² erg s⁻¹ in the rest-frame 3.5–14 keV band at z = 6. Thus, almost all luminous AGNs, even at very high redshifts, will be included in the catalog of directly detected sources. However, only one source with a redshift greater than z = 5 has been spectroscopically identified (Barger et al. 2003) in the Chandra Deep Field-North (CDF-N; Brandt et al. 2001; A03) and CDF-S fields.

Fainter sources are likely to be dominated by star formation, low-luminosity AGNs (LLAGNs), or highly obscured AGNs. Such sources should have strong breaks in the rest-frame UV owing to the Lyα forest of the intergalactic gas or to the intrinsic Lyman continuum break and should be included in optical or near-infrared dropout samples identified from the break properties. We can attempt to measure the properties of these fainter sources through averaging (sometimes referred to as "stacking") analyses of optically or near-infrared selected galaxy samples (e.g., Brandt et al. 2001; Nandra et al. 2002; Reddy & Steidel 2004; Lehmer et al. 2005; Worsley et al. 2006; Hickox & Markevitch 2006, 2007; Treister et al. 2011; Trouille et al. 2011). This is of particular interest for the highest redshift samples, where we may be probing supermassive black holes at times very close to their formation. However, it also allows us to examine the X-ray properties of star-forming galaxies over a wide range in redshifts (out to beyond z = 4) and to test whether the properties of these galaxies change with time.

Treister et al. (2011, hereafter T11) used the CDF-N and CDF-S data to perform sensitive X-ray stacking analyses on z > 6 galaxy candidates that could not be detected individually to look for detectable X-ray signal from the population as a whole. The high-redshift samples they used (z ∼ 6 from Bouwens et al. 2006, hereafter Bo06; and z ∼ 7 and z ∼ 8 from Bouwens et al. 2011, hereafter Bo11) were selected with the dropout technique using Hubble Space Telescope (HST) ACS and WFC3 data. For the z ∼ 6 Bo06 sample, T11 found significant detections (⩾ 5σ) in both the observed soft (0.5–2 keV) and the observed hard (2–8 keV) bands. The stacked hard-to-soft X-ray flux ratio that they found was a relatively high factor of ∼9, which they said could only be explained by very high levels of obscuration. Moreover, since the ratio was a ratio of the stacks, they inferred that there must be very few sources with significantly lower levels of obscuration. This led them to the conclusion that black holes grow significantly at early times but are heavily buried in gas and dust.

These results are rather surprising. Galaxies selected by the dropout technique are generally classic starburst galaxies, i.e., they are small, blue, and compact with high surface brightnesses (e.g., Stanway et al. 2004). Meanwhile, the masses of local supermassive black holes are generally correlated with the bulge luminosities of the host galaxies (e.g., Ferrarese & Merritt 2000; Gebhardt et al. 2000; Kormendy & Gebhardt 2001; Tremaine et al. 2002). At z ∼ 3, this would be akin to finding AGNs in Lyman break galaxies (LBGs), which is not very common (e.g., Steidel et al. 2004). Moreover, if there were a lot of gas and dust present to obscure the central black hole (T11 argue that the sources must be nearly Compton-thick along most directions), then one might expect the dust to also affect the properties of the host galaxy, unless it were somehow confined to the region around the AGN itself.

Indeed, Fiore et al. (2012) conducted an independent, non-optimized stacking analysis using the Bo06 sample in the CDF-S and did not confirm the T11 results. More recently, Willott (2011) provided an independent critique of T11 that parallels some of the results of the present paper.

Here we argue that the T11 result is a consequence of an incorrect background subtraction procedure. In our analysis we find a 2σ upper limit on the X-ray luminosity at z = 6.5 of 4 × 10⁴¹ erg s⁻¹, which is consistent with any X-ray production in the galaxies being solely due to star formation.

At lower redshifts we find significant weighted mean X-ray fluxes in many samples of sources over the redshift range z = 0–4. We use these to argue that (1) the relation between star formation and X-ray production remains invariant over this redshift range, (2) X-ray sources below the direct detection threshold are primarily star forming, and (3) there is full consistency between UV and X-ray estimations of the star formation history.

We use a standard H₀ = 70 km s⁻¹ Mpc⁻¹, Ω = 0.3, and Ω = 0.7 cosmology throughout. All magnitudes are in the AB magnitude system.

X11 presented the X-ray images from the 3.872 Ms total exposure of the CDF-S, which covers an area of 464.5 arcmin². They provided a main Chandra source catalog containing 740 X-ray sources detected with WAVDETECT at a false-positive probability threshold of 10⁻⁵ in at least one of three X-ray bands: full (0.5–8 keV), soft (0.5–2 keV), and hard (2–8 keV). The catalog also satisfies a binomial-probability source-selection criterion of P < 0.004, which means that the probability that the sources are not real is less than 0.004. The on-axis flux limits are ≈ 3.2 × 10⁻¹⁷, 9.1 × 10⁻¹⁸, and 5.5 × 10⁻¹⁷ erg cm⁻² s⁻¹ for the full, soft, and hard bands, respectively.

The CDF-S is now almost twice as deep as the CDF-N field, which is the only other extremely deep Chandra field. For most of our analysis we will therefore concentrate on the CDF-S alone, but in some cases we will also include similarly selected samples from the CDF-N, where these can provide an increase in the sensitivity. For the CDF-N we use the images and corresponding source catalog from A03, which contains 503 sources selected in the same three X-ray bands described above.

X11 shifted the optical positions in deep R-band imaging data—which were already matched to the HST ACS Great Observatories Origins Deep Survey-South (GOODS-S; Giavalisco et al. 2004) images—by 0175 in right ascension and −0284 in declination in order to match them to the radio positions of sources in the Very Large Array 1.4 GHz radio catalog (5σ) of Miller et al. (2008) and N. A. Miller et al. (2012, in preparation). They then matched the X-ray centroid positions to the optical sources detected in the R-band image to put them on a common astrometric frame. In this paper, we moved X11's source positions back to the GOODS-S ACS frame by shifting them by −0175 in right ascension and 0284 in declination. This allows us to work with the astrometric positions of the optical sources and spectral data in the GOODS-S samples.

In Figure 1, we show the X-ray image of the CDF-S. With small circles we show the positions of all of the X-ray sources from X11. With larger circles we show the positions of the X-ray sources that also have deep near-infrared (NIR) coverage from HST WFC3 imaging (Early Release Science or ERS, Windhorst et al. 2011; Cosmic Assembly Near-Infrared Deep Extragalactic Legacy Survey or CANDELS, Grogin et al. 2011 and Koekemoer et al. 2011). Given the X-ray positional uncertainties, we identified an X-ray source with a NIR counterpart if an F160W band counterpart brighter than F160W ∼25 (5σ) were within 2'' of the X-ray position. If more than one such NIR counterpart were within the search radius, then we identified the X-ray source with the nearest NIR neighbor. As pointed out in X11 (see also A. J. Barger et al. 2012, in preparation), nearly all of the X-ray sources have NIR counterparts. Finally, we mark with a rectangle the part of the GOODS-S region that was uniformly covered with ACS. The X-ray sensitivity degrades rapidly at large off-axis radii as the point-spread function (PSF) of the X-ray image increases, so we restrict our analysis to sources lying within an off-axis radius of 6' (very large circle). The overlap of the 6' region with the uniformly covered GOODS-S region is 101 arcmin². This region contains 360 of the 740 X-ray sources in X11 and 19,294 of the 33,955 optically selected sources given in the v2 catalog of the ACS observations of the GOODS-S. In this paper, we shall refer to this overlap region as our core region.

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We measured the weighted mean X-ray counts s⁻¹ in three types of selected galaxy samples. First, we used galaxies with secure spectroscopic redshifts. This is a relatively small sample, and the sources are bright in the rest-frame optical. Thus, if more optically luminous galaxies are X-ray brighter (e.g., Lehmer et al. 2005), then this sample may be expected to produce higher weighted mean X-ray counts s⁻¹. Second, we used a photometric redshift sample to probe fainter galaxies. Finally, we used dropout-selected samples to provide as complete a selection as possible in a given redshift range.

3.1. Secure Spectroscopic Redshift Sample

For the GOODS-S, we started with the European Southern Observatory master redshift catalog compiled by A. Rettura in 2004 and subsequently updated by Popesso et al. (2009) and Balestra et al. (2010). This catalog includes redshifts from Cristiani et al. (2000), Croom et al. (2001), Bunker et al. (2003), Dickinson et al. (2004), Stanway et al. (2004), Strolger et al. (2004), Szokoly et al. (2004), van der Wel et al. (2004), Doherty et al. (2005), Le Fèvre et al. (2005), Mignoli et al. (2005), Ravikumar et al. (2007), and Vanzella et al. (2008). We added to this catalog 144 new redshifts for previously unidentified sources that we measured with DEIMOS in the Fall of 2010, as well as some additional redshifts obtained by S. Koposov et al. (unpublished) that were presented in Taylor et al. (2009). In our compilation we only included sources with secure redshifts. In the case of the VIMOS-VLT Deep Survey or VVDS (Le Fèvre et al. 2005), we only included sources classified as 100% secure. We included a small number of redshifts from papers that did not give a quality flag, but in these cases the spectral identifications appeared robust based on the material presented in the papers.

In our final compilation, we have secure redshifts for 1792 galaxies and 158 stars in the full GOODS-S field. In Figure 2(a) we plot the spectroscopic redshifts versus the F850LP magnitudes for the final compilation (black small squares). One thousand one hundred fifty-eight of the galaxies with secure redshifts lie in the core region. Using insecure redshifts would add a comparable number of additional redshifts, but many of these are clearly problematic based on our inspections of the spectra or on our comparisons of the redshifts given in the different catalogs, so we prefer to work only with the secure redshifts.

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For the GOODS-N, we used the catalogs of Barger et al. (2008) updated with as yet unpublished DEIMOS redshifts obtained by us and some additional redshifts from Cooper et al. (2011). The GOODS-N sample has secure redshifts for 2987 galaxies and 199 stars. The slightly larger sample in the GOODS-N as compared to the GOODS-S compensates for the shallower exposure in the CDF-N, and we use both samples in computing the weighted mean fluxes.

3.2. Photometric Redshift Sample

3.3. Dropout Samples

A fully optimally weighted determination of the mean X-ray flux in a sample from the Chandra data would involve using variable elliptical apertures that are dynamically adjusted to match the local PSFs and background. However, with optimal weightings, most of the signal—even for a set of sources that is uniformly distributed over the full Chandra field—arises at relatively small off-axis radii (less than 6'), where we may include most of the counts within the PSF with a moderately sized circular aperture (e.g., Allen et al. 2004). Even at these small off-axis angles the optimal weighting of the Chandra data involves several issues, most particularly which aperture to choose and how far out in off-axis angle to include sources (e.g., Lehmer et al. 2005; Hickox & Markevitch 2006, 2007; T11).

For faint sources, the noise level is dominated by the background. We may write the signal-to-noise ratio (S/N) in an aperture of radius r as proportional to f(r, θ)/(b^0.5 × r), where f(r, θ) is the fraction of the counts from the source contained within the aperture at off-axis radius θ (often referred to as the enclosed energy fraction) and b is the background per unit solid angle (see also T11). We show this quantity for the 2–8 keV band in Figure 3 as a function of θ (black solid: 0' or on-axis; red: 15; blue: 3'; green: 5'; black dashed: 7') and r, assuming b is roughly constant within the region. As T11 point out, the optimal r to maximize the S/N increases with increasing θ, rising from r = 04 at θ = 0' (black solid) to approximately r = 5'' at θ = 7' (black dashed). However, as can also be seen from Figure 3, the dependence on r at larger θ is very soft, so choosing a smaller aperture radius has little effect on the S/N. Moreover, using a smaller aperture radius has the advantage of minimizing contamination by neighboring sources.

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A very small aperture is optimal close to on-axis, but the use of such a small aperture places stress on the astrometry (see T11). We have therefore chosen to use a constant r = 075 aperture within an off-axis angle of θ = 3' and a constant r = 125 aperture at larger θ. This roughly brackets the optimal radius for θ = 3' (see blue curve in Figure 3 for the 2–8 keV band), namely r = 09 in the 0.5–2 keV band and r = 12 in the 2–8 keV band. The noise in typical samples computed with this procedure only differs from that computed with a fully optimized aperture as a function of radius by a few percent.

We include sources out to θ = 6', which, in conjunction with the samples lying within the well covered areas of the GOODS fields, is our definition of the core region. We stress that the results are quite insensitive to the choice of the maximum θ, because the high off-axis sources have low S/N in an optimally weighted mean. Decreasing the off-axis angle at which we include sources to θ = 5' (4') would raise the noise in typical samples by 5% (15%).

With the aperture specified, we can now compute the X-ray counts s⁻¹ as C = (S − B)/(f(r, θ) × t), where S is the number of counts in the aperture, B(= πr²b) is the number of background counts expected in the same aperture, and t is the effective exposure time at the position of this aperture. C may be negative or positive. We take the error on this quantity to be E = B^0.5/(f(r, θ) × t), since, in general, the number of background counts in the aperture, B, is high enough to justify the Gaussian approximation.

For a given sample we form the optimally weighted mean X-ray counts s⁻¹, L, and the corresponding error, E_L. To do this, we first exclude all sources with a known X-ray source within 6'' or a bright (0.5–8 keV counts above 1000) X-ray source within 13'' in the existing catalogs (X11 for the CDF-S and A03 for the CDF-N) to remove any contamination from these sources. These two values (6'' and 13'') correspond to the 90% and 95% enclosed light radii, respectively, at an energy of 5 keV and an off-axis radius of 6'. This ensures that the contribution from the extended wings of the known sources is less than about a count in any aperture, even for the hard band. When averaged over the ensembles, this level of contamination is negligible. Our contamination radii are smaller than the values adopted by Hickox & Markevitch (2006, 2007) or by T11, but tests with random samples show that there is little sensitivity to increasing them, and choosing the smallest possible contamination radii minimizes the number of sources excluded by this step. The adopted procedure reduces the core area from 101 arcmin² to 86 arcmin². We form the optimally weighted mean X-ray counts s⁻¹, L = Σ(C/E²)/Σ(1/E²), by summing over the remaining sources in the sample. The corresponding error is E_L = (1/Σ(1/E²))^0.5.

The final issue is how to compute the background counts per unit solid angle, b. There are two possible approaches to this. One can compute a local background for each source using either a surrounding annulus (T11) or a wavelet approach (Hickox & Markevitch 2006, 2007), or one can compute the average background by randomizing the positions of the sources and measuring the values obtained in the blank-field apertures generated (e.g., Lehmer et al. 2005). Here we use both procedures: we use annular measurements as our primary background determination and then we use randomized position measurements to test that the procedure is not introducing offsets.

Before we continue, we note that the background we are measuring is composed of several elements: an approximately uniform instrumental background, a truly diffuse component containing contributions from hot interstellar or intergalactic gas, and contributions from individual sources below the direct detection threshold of the deep CDF images. While a local estimate of the background contributions from the instrument and the diffuse background should provide a good average measure, such estimates could be more problematic for the unresolved sources, which may be clustered. Clustering could, in principle, result in an underestimate in determining the background subtraction, since the annulus in which the background is measured lies further from the source than the aperture in which the signal is measured. However, in practice, the surface density of X-ray sources at a given redshift is small, and the average contribution of these sources to the background is also small. (Contributions from sources at other redshifts may be viewed as random with respect to the sources whose signal is being measured.)

We may use the results of Section 5.2 to estimate that the total contribution of all the sources in our photometric redshift sample is approximately 2% of the observed background in the CDF-S. In smaller redshift intervals, these contributions are correspondingly less and drop rapidly with increasing redshift (see Section 6). Thus, the redshift interval from z = 1 to 1.1 produces about 0.001 of the background, and that from z = 3–3.1 produces less than 0.0003 of the background. These contributions are too small for clustering in the galaxy population to perturb the background in any significant way.

In determining b, we use an annulus of radius 8''–22''. This choice of inner boundary avoids any contribution from the target, and this choice of outer boundary provides a large enough number of pixels. In order to eliminate any contribution to b from bright neighboring sources, we exclude 6'' regions around known sources (13'' regions around very bright sources), and we clip pixels with high counts. Considerable caution must be taken in performing the clip. Because the average number of counts in each pixel is small, the counts distribution is Poissonian. Too severe of a clip can introduce a downward bias in the estimation of the average background in the annulus, which would result in a spurious signal when that background is subtracted from the counts in the aperture. This appears to be the cause of the z ∼ 6 weighted mean signal found by T11.

To test both the present procedure and the T11 procedure, we ran 100 realizations of randomly located apertures in the GOODS-S core region for a sample with a size equal to that of the Bo06 sample of z ∼ 6 galaxies. In Figure 4 we show the two distributions of the 2–8 keV counts s⁻¹, C, that we measured. In one case we clipped the background pixels above two counts (red dashed curve; this corresponds to the T11 procedure), while in the other case we only clipped the background pixels above four counts (blue dashed curve; present procedure). The more severe clipping (red) produces a systematic offset in the measured counts, while the less severe clipping (blue) does not. The four counts clip used in the present paper is the most stringent clip possible that does not produce a significant offset. However, we note that the results are not sensitive to choosing higher values for the clipping.

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We can see this offset even more clearly when we plot the two distributions of weighted mean 2–8 keV counts s⁻¹, L. (Red solid for the T11 procedure; blue solid for the present procedure.) The offset of the red solid histogram (8.1 × 10⁻⁷ ± 2.2 × 10⁻⁷ counts s⁻¹) is almost identical to the weighted mean signal found by T11 for the Bo06 sample (downward pointing arrow). In contrast, the offset of the blue solid histogram (5 × 10⁻⁸ ± 2.2 × 10⁻⁷ counts s⁻¹) is consistent with the zero weighted mean signal expected for random realizations if the background subtraction is correct.

The error in the simulations measured from the dispersion in the realizations is about 30% higher than the formal statistical error of 1.6 × 10⁻⁷ counts s⁻¹, suggesting that systematic effects may be present. Thus, we allow for this in assessing the significance of the detections.

5.1. Secure Spectroscopic Redshift Sample

In Figure 5 we show the weighted mean counts s⁻¹ in both the 0.5–2 keV (red squares) and 2–8 keV (blue diamonds) bands versus redshift for the core samples with secure spectroscopic redshifts. In (a) and (b) we show the results, respectively, for the GOODS-S and GOODS-N fields, and in (c) we show the results for the two fields combined. The individual fields show a broadly similar pattern. As has been found in previous work (e.g., Lehmer et al. 2005), there is a strongly detected signal in the 0.5–2 keV band out to z = 4 (see also Bomans et al. 2011). Beyond this redshift, even in the combined fields, the signal falls below the 3σ threshold, even when only the formal statistical error is used.

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The weighted mean 0.5–2 keV counts s⁻¹ in the combined fields are 5.2 ± 1.0 × 10⁻⁷ counts s⁻¹ for the redshift interval z = 3–4 and 7.2 ± 3.0 × 10⁻⁷ counts s⁻¹ for z = 4–5. The weighted mean 2–8 keV counts s⁻¹ in the combined fields are weaker and only detected out to z = 3, reflecting Chandra's poorer sensitivity at these energies.

Converting the 0.5–2 keV (2–8 keV) counts s⁻¹ to flux with an average multiplication of 6.8 × 10⁻¹² erg cm⁻² (23.9 × 10⁻¹² erg cm⁻²), where the conversion factors are taken from T11, we find the flux ratio f(0.5–2 keV)/f(2–8 keV) = 0.91 ± 0.15 at z = 0–1, 0.95 ± 0.23 at z = 1–2, and 0.65 ± 0.32 at z = 2–3. If the source spectra can be represented by power laws, then these flux ratios correspond to photon indices of 1.93 ± 0.13, 1.96 ± 0.19, and 1.69 ± 0.28, respectively, showing that the sources are quite soft on average.

5.2. Photometric Redshift Sample

In Figure 6, we show the weighted mean counts s⁻¹ in both the 0.5–2 keV (red squares) and 2–8 keV (blue diamonds) bands versus redshift for the sources in the GOODS-S core region with photometric redshifts. We give the results in tabular form in Table 1, where we compare with the GOODS-S secure spectroscopic redshift sample in the same redshift intervals. In Columns 1 and 2, we give, respectively, the minimum and maximum of the redshift interval. In Column 3, we give the number of sources in the spectroscopic redshift sample. In Columns 4 and 5, we give, respectively, the mean 0.5–2 keV and 2–8 keV counts with 1σ errors for the spectroscopic redshift sample in units of 10⁻⁷ counts s⁻¹. In Column 6, we give the number of sources in the photometric redshift sample. Finally, in Columns 7 and 8, we give, respectively, the mean 0.5–2 keV and 2–8 keV counts with 1σ errors for the photometric redshift sample in units of 10⁻⁷ counts s⁻¹.

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Table 1. Mean X-Ray Counts per Second versus Redshift: GOODS-S

		Spectroscopic Sample			Photometric Sample
zmin	zmax	Nspec	0.5–2 keV	2–8 keV	Nphotz	0.5–2 keV	2–8 keV
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
0.0	0.50	127	7.64 ± 0.83	2.59 ± 1.37	1170	1.59 ± 0.28	1.41 ± 0.46
0.50	1.0	350	9.81 ± 0.50	2.55 ± 0.81	2459	2.29 ± 0.19	0.09 ± 0.32
1.0	1.5	190	9.39 ± 0.68	3.95 ± 1.11	1500	3.35 ± 0.25	1.50 ± 0.41
1.5	2.0	25	12.2 ± 1.81	0.09 ± 2.95	817	3.76 ± 0.34	1.76 ± 0.55
2.0	2.5	38	9.66 ± 1.68	4.67 ± 2.78	835	3.00 ± 0.33	1.52 ± 0.54
2.5	3.0	32	8.00 ± 1.82	4.04 ± 3.04	697	2.10 ± 0.36	0.15 ± 0.58
3.0	3.5	24	7.82 ± 2.09	1.19 ± 3.48	430	2.46 ± 0.46	0.21 ± 0.76
3.5	4.0	14	9.00 ± 2.43	−5.86 ± 4.02	253	1.90 ± 0.61	−1.03 ± 0.99
4.0	4.5	6	−1.64 ± 4.57	−8.19 ± 7.65	145	1.00 ± 0.81	0.07 ± 1.33
4.5	5.0	0	...	...	89	1.98 ± 0.99	0.79 ± 1.62
5.0	5.5	0	...	...	46	0.50 ± 1.33	.015 ± 2.19
5.5	6.0	5	1.19 ± 4.07	11.6 ± 6.79	31	2.02 ± 1.70	0.46 ± 2.81
6.0	6.5	0	...	...	6	3.64 ± 3.59	−3.94 ± 5.83

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Figure 6 is similar to Figure 5 in that we see a strong signal out to z = 4 in the 0.5–2 keV band but no detections at higher redshifts. For example, for the redshift interval z = 4–5, the weighted mean 0.5–2 keV counts s⁻¹ is 1.38 ± 0.62 × 10⁻⁷ counts s⁻¹ or f(0.5–2 keV) = 9.4 ± 4.2 × 10⁻¹⁹ erg cm⁻² s⁻¹. We also again see a weak 2–8 keV signal with respect to the 0.5–2 keV signal; it is only detected in the redshift interval z = 1–3, where we find a flux ratio f(0.5–2 keV)/f(2–8 keV)=0.67 ± 0.15 corresponding to a photon index of Γ = 1.7.

While the overall pattern with redshift is similar in the spectroscopic redshift and photometric redshift samples, the weighted mean X-ray counts s⁻¹ are more than a factor of two lower in the photometric redshift sample than in the spectroscopic redshift sample. As we shall show in the discussion section (Section 6), this is a simple consequence of the fact that the photometric redshift sample contains sources down to fainter optical magnitudes than the spectroscopic sample. The photometric redshift sample, while containing the spectroscopically identified sources as a subsample, probes to fainter optical magnitudes, and these optically fainter sources are intrinsically fainter in the X-rays, reducing the weighted mean X-ray fluxes. However, because the photometric redshift sample contains a larger number of sources, it identifies more of the X-ray background light, as measured by the product of the number of sources per unit area and the mean counts per source, than the secure spectroscopic redshift sample. At redshifts between z = 0 and 1, the contribution to the X-ray background light by the photometric redshift sample is about twice as much as the contribution to the X-ray background light by the secure spectroscopic sample, while between z = 2 and 3, it is about six times as much.

The mean counts per source in the photometric redshift samples do not change rapidly as a function of redshift. Thus, the results are not very sensitive to catastrophic photometric redshift errors. If 4% of the sources that the photometric redshift sample placed at z = 0–1 were really at z = 2–3, then the mean counts at z = 2–3 would only change from 2.59 × 10⁻⁷ counts s⁻¹ to 2.55 × 10⁻⁷ counts s⁻¹. At z = 3–4, the change in the mean counts would be even smaller.

5.3. Dropout Samples

The X-ray fluxes probed by the optimized averaging analysis are, by construction, bounded above by the flux detection limits in the direct X-ray catalogs. As we illustrate in Figure 7, even at high redshifts, this places an upper bound on the observed-frame 0.5–2 keV luminosities of ∼10⁴² erg s⁻¹. We may therefore expect the sources in the averaging analysis to be dominated by star-forming galaxies with some contribution from LLAGNs (e.g., Bauer et al. 2004). The power-law photon indices based on the broadband X-ray colors (Γ = 1.7–2 for z = 1–3; see Section 5.1) are broadly consistent with this interpretation. Swartz et al. (2004) give an average Γ = 1.7 for the ultraluminous X-ray sources (ULXs) that dominate the X-ray contributions in strong star-forming galaxies. However, the photon indices of ULXs are poorly determined above 10 keV, which adds some uncertainty to the comparison at the highest redshifts (z ∼ 3) for which we were able to measure the weighted mean observed-frame flux ratios, f(0.5–2 keV)/f(2–8 keV). The dominance of star-forming galaxies at the low X-ray fluxes is also supported by fluctuation analyses, which show that the unresolved flux distribution is consistent with an extrapolation of the star-forming galaxy log N/log S (Hickox & Markevitch 2007; Soltan 2011).

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Dijkstra et al. (2012) predicted the X-ray sky surface brightness (i.e., the X-ray background light) from star-forming galaxies using the star formation history of Hopkins & Beacom (2006) and the star formation rate (SFR) to X-ray conversion of Mineo et al. (2012). This allows us to make a very simple comparison of the light measured from the low-luminosity X-ray sources in the averaging analysis with the X-ray prediction made from star formation histories measured at other wavelengths. In Figure 8 we compare the Dijkstra et al. calculation in the 2–8 keV band (black solid curve; we assume a photon index of Γ = 2) with the X-ray contributions determined from the results of the present photometric redshift averaging analysis in the GOODS-S core region. In Figure 8(a) we use open squares to show for the 0.5–2 keV band the quantity N × S/(A × (z₁ − z₂)), where N is the number of sources used in the averaging analysis, S is the weighted mean flux, A is the observed area in square degrees, and (z₁ − z₂) is the redshift interval. We can combine this with the contributions from the directly detected low-luminosity sources in the X11 catalog to determine the value for all sources with 0.5–2 keV luminosities less than 10⁴² erg s⁻¹ (solid circles). Figure 8(b) shows the same plot for the 2–8 keV band.

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The agreement between the averaging analysis results (open squares) and the Dijkstra et al. (2012) prediction are extremely good. As expected from the discussion of the photon indices, the 0.5–2 keV and 2–8 keV surface brightnesses are almost identical and match to the prediction for most of the z = 0–3 range over which the prediction was made, though the noise levels are much higher in the 2–8 keV sample. The only exception is at low redshifts (z < 0.5), where the upper bound on the flux excludes many of the star-forming galaxies. When the results from the directly detected low-luminosity sources in the X11 catalog are combined with the averaging analysis results (solid circles), the data also then agree with the prediction at these low redshifts. Integrating through the combined results, we find that a very large percentage of the contribution to the X-ray background from L_X < 10⁴² erg s⁻¹ star-forming galaxies comes from low-redshift objects: 79% at 0.5–2 keV and 83% at 2–8 keV arise from z ≲ 2. We also show with dashed curves the contributions from LLAGNs with L_X < 10⁴² erg s⁻¹ to the 0.5–2 keV and 2–8 keV surface brightnesses, as computed using the model of Gilli et al. (2007). These can be significant at z < 1 but drop rapidly at higher redshifts.

We may invert this procedure of constructing the X-ray surface brightness from the star formation rate and instead use the X-ray data to construct the star formation history as a function of redshift from X-ray samples (e.g., Norman et al. 2004; Lehmer et al. 2008). We converted the total X-ray surface brightness in the 0.5–2 keV band of all sources with luminosities less than 10⁴² erg s⁻¹ in each redshift interval to the corresponding comoving X-ray luminosity density in the 0.5–8 keV band, assuming a photon index of Γ = 2. We then computed the SFR per unit comoving volume using the relation in Mineo et al. (2012). For the present data, we cannot separate the various contributions to the X-ray light, so rather than adopting the Mineo et al. (2012) best-fitting linear relation obtained from only the resolved sample (their Equation (22)), we used their linear relation obtained from only the unresolved galaxies (given in their Section 8.1):

$$\begin{equation} {\rm SFR}\, ({{M}}_{\odot }\ {\rm yr}^{-1}) = 2.7\times 10^{-40} L_{0.5\hbox{--}8 {\rm \,keV}} \, ({\rm erg\ s}^{-1}) \,. \end{equation} \tag{ 1 }$$

Here the SFR is for a Salpeter (1955) initial mass function (IMF) stretching from 0.1 to 100 M_☉. (The normalization is a factor of 1.4 higher than if we had instead used their Equation 22.) We note that this calibration does depend on the star formation history. We also note that there have been numerous calibrations of the SFR with X-ray luminosity, and these vary by up to 40% (Grimm et al. 2003; Ranalli et al. 2003; Persic & Rephaeli 2007; Lehmer et al. 2010; Mineo et al. 2012). Thus, the estimated SFR will be uncertain at least at this level.

We show the star formation history determined from the X-ray data in Figure 9 (red squares), where we compare it with that derived by Hopkins & Beacom (2006) using multiwavelength data (black curve). The shapes and normalizations are in very good agreement. The normalization agreement is probably overly good, since this could be changed by any one of a number of factors, such as contamination by LLAGNs, cosmic variance, or the uncertainty in the X-ray to SFR conversion factor. As discussed above, the LLAGN contribution is probably most significant below z = 1, where it may result in the X-ray estimate of the SFR being high.

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With these data we can also address the evolution of the relation between the X-ray luminosity and the SFR as a function of redshift. This relation, L_X = c_X × SFR, depends on the IMF, the properties of binary stars, and the galaxy metallicities, among other things. One might expect that the normalization, c_X, would be higher in low-metallicity galaxies (e.g., Bookbinder et al. 1980; Dray 2006; Linden et al. 2010). There is some weak evidence for this (Kaaret et al. 2011). In turn, this might suggest that c_X could be higher at high redshifts. Mirabel et al. (2010) invoke this evolution as a possible reionization mechanism.

Dijkstra et al. (2012) tried to constrain such an evolution using the contributions to the X-ray backgrounds. Their results could only weakly constrain any evolution in c_X, but this might be due to the fact that the contributions to the backgrounds from the higher redshifts are small. We can more directly constrain any evolution in c_X as a function of redshift by comparing how the X-ray flux depends on the UV flux as a function of redshift. Since the star formation histories, particularly at the highest redshifts, are generally computed from extinction corrected UV luminosity densities, this is the most direct test we can make.

For each galaxy in the GOODS-S core region with a photometric redshift, we computed the rest-frame UV magnitude at 2500 Å by interpolating between the four ACS bands in the GOOD-S catalog and then translating this to a bolometric flux, νf_ν, evaluated at the redshifted wavelength. The rest-frame bolometric luminosity at 2500 Å is νL_ν = 4πd²_lνf_ν, where d_l is the luminosity distance. We restricted our analysis to z > 1 so that in our lower redshift intervals the above interpolation is valid. At z > 2.6 where the observed wavelength lies beyond the reddest band (F850LP) in the ACS data, we used the F850LP magnitude alone to estimate the rest-frame bolometric luminosity.

Using our optimal averaging procedure, we formed the weighted mean X-ray fluxes in unit redshift intervals from z = 1 to 6 and in νf_ν intervals stretching from 10⁻¹⁶ erg cm⁻² s⁻¹ upward in half dex intervals. We show the results in Figure 10, where we plot the weighted mean observed-frame 0.5–2 keV flux against νf_ν. For Γ = 2 there is no K-correction, and the X-ray luminosity in either the rest-frame 2–8 keV band or the rest-frame 0.5–2 keV band can be obtained from 4πd²_lf_{0.5–2 keV}. Thus, in any redshift interval the plots may be considered as luminosity-luminosity plots.

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Figure 10 illustrates a number of interesting points with regards to the X-ray fluxes. First, at any given redshift, there is a linear relation between the weighted mean X-ray flux and νf_ν(2500 Å). The linear relation only holds until we reach the flux level where we begin to exclude sources that are in the X11 catalogs (red dashed horizontal line). This only affects the high flux bins (νf_ν(2500 Å)>5 × 10⁻¹⁵ erg cm⁻² s⁻¹). Retaining in the averaging procedure the directly detected low X-ray luminosity (L_{0.5–2 keV} < 10⁴² erg s⁻¹) sources in the X11 catalog, as in Figure 10(c), extends the relation for the low-redshift sources to higher fluxes.

The underlying reason for the linear relation between the X-ray flux and νf_ν(2500 Å) is the linear relation between the X-ray flux and the SFR. However, since the conversion from the UV flux to a total SFR requires an extinction correction, it also shows that the average extinction correction is similar for all sources regardless of the near-UV flux.

Second, there is little variation in the normalization with redshift. For the full data set we find

$$\begin{equation} f_{0.5\hbox{--}2 {\rm \,keV}} = 1.57\pm 0.07\times 10^{-3} \nu f_\nu (2500 {\rm \,\AA}) \end{equation} \tag{ 2 }$$

(black solid line). However, fits to individual redshift intervals give almost identical ratios (1.48 ± 0.09 × 10⁻³ at z = 1–2, 1.62 ± 0.12 × 10⁻³ at z = 2–3, 1.89 ± 0.24 × 10⁻³ at z = 3–4, and 2.25 ± 0.75 × 10⁻³ at z = 4–5), suggesting that any increase with increasing redshift is small. More specifically, the ratio is proportional to (z)c_X(z)(1 + z)^{2 − Γ}, where (z) is the mean extinction correction for the UV flux and the (1 + z)^{2 − Γ} factor arises from the K-correction for a power-law spectrum with photon index Γ. For Γ = 2 and (z) constant, the rise in c_X(z) from z = 1.5 to z = 4.5 would be 1.5 ± 0.5, and for Γ = 1.7 and (z) constant, it would be 1.1 ± 0.4.

We may also compare the measured relation between f_{0.5–2 keV} and νf_ν(2500 Å) with that derived using local calibrations. For this derivation we use the Mineo et al. (2012) calibration of the SFR with X-ray luminosity given in Equation (1), assuming a spectral index Γ = 2 to convert the 0.5–8 keV luminosity to 0.5–2 keV luminosity:

$$\begin{equation} {\rm SFR}\, ({M}_{\odot }\ {\rm yr}^{-1}) = 5.4\times 10^{-40} L_{0.5\hbox{--}2 {\rm \,keV}} \, ({\rm erg\ s}^{-1}) \,, \end{equation} \tag{ 3 }$$

and the Kennicutt (1998) calibration of the SFR with the near-UV luminosity:

$$\begin{equation} {\rm SFR}\, ({{M}}_{\odot }\ {\rm yr}^{-1}) = 1.17\times 10^{-43} \nu L_{\nu } (2500 {\rm \,\AA})\, ({\rm erg\ s}^{-1}) \,. \end{equation} \tag{ 4 }$$

These are all computed for the same Salpeter (1955) IMF. Since we are only interested in the ratio, we only require a consistent choice of IMF. We combine Equations (3) and (4) to obtain the relation

$$\begin{equation} L_{0.5\hbox{--}2 {\rm \,keV}} = 2.2\times 10^{-4} \nu L_\nu (2500 {\rm \,\AA})\,, \end{equation} \tag{ 5 }$$

which translates to

$$\begin{equation} f_{0.5\hbox{--}2 {\rm \,keV}} = 2.2\times 10^{-4} \nu f_\nu (2500 {\rm \,\AA}) \epsilon (z) (1+z)^{2-\Gamma }\,, \end{equation} \tag{ 6 }$$

when we allow for the extinction correction, (z), to convert from the UV-derived SFR to a total SFR, and when we allow for the K-correction. In Figure 10 we show the result (black dashed line) obtained from this relation for Γ = 2 when we do not correct for extinction (i.e., (z) = 1). However, to match the observed flux, we need to assume that (z) ∼ 5, which is very similar to values estimated for the UV extinction corrections at these redshifts; e.g., Erb et al. (2006) obtained a mean correction of 4.5 for LBGs at z = 2. For Γ = 1.7, the required extinction correction is reduced to (z) ∼ 3.

We can see from Figure 10 that we can only marginally detect the most luminous star-forming galaxies at z = 5–6 with the present data. The maximum νf_ν(2500 Å) =4 × 10⁻¹⁶ erg cm⁻² s⁻¹ corresponds to f_{0.5–2 keV} = 6 × 10⁻¹⁹ erg cm⁻² s⁻¹. A substantial detection of the z = 5–6 sample using an optimal averaging analysis of the present sort would require an increase of about a factor of three in exposure time.

At higher redshifts (z = 6–8) the 2σ upper limit on νf_ν(2500 Å) corresponds to f_{0.5–2 keV} = 7 × 10⁻¹⁹ erg cm⁻² s⁻¹. This translates to an upper limit on the X-ray luminosity at z = 6.5 of 4 × 10⁴¹ erg s⁻¹ in the rest-frame 3.75–15 keV band. The highest redshift spectroscopically confirmed source in either the CDF-S or the CDF-N is at z = 5.19 (Barger et al. 2003), and there are no known sources at higher redshifts with luminosities above the threshold luminosities corresponding to the flux limits of the X-ray catalogs (see Figure 7).

Our upper limit on the X-ray luminosity at z = 6.5 of 4 × 10⁴¹ erg s⁻¹ is a factor of 20 lower than the luminosity given in T11, which was based on a supposed detection in the less sensitive 2–8 keV band. Our detection limit is consistent with the X-ray fluxes in the high-redshift sources being solely due to star formation, though contributions from LLAGNs could also be present. AGNs with luminosities above 10⁴² erg s⁻¹ thus appear to be extremely rare at high redshifts.

We thank the referee for useful comments that helped us to improve the manuscript. We thank Ezequiel Treister for numerous discussions and for providing helpful information about the T11 paper. We also thank Dominik Bomans for several stimulating conversations. We gratefully acknowledge support from NSF grant AST-0709356 (L.L.C.), the University of Wisconsin Research Committee with funds granted by the Wisconsin Alumni Research Foundation, and the David and Lucile Packard Foundation (A.J.B.). We recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain.