ALMA 26 arcmin² Survey of GOODS-S at One-millimeter (ASAGAO): X-Ray AGN Properties of Millimeter-selected Galaxies

ALMA band 6 (1.2 mm) observations of the $5^{\prime} \,\times 5^{\prime}$ ($\approx 26$ arcmin²) area of the ASAGAO were conducted in 2016 September in the C40-6 array configuration for a total observing time of 45 hr (Project code: 2015.1.00098.S, PI: K. Kohno). The details of the observations and data reduction are described in B. Hatsukade et al. (2017, in preparation), and here we briefly summarize them. Two frequency tunings were adopted centered at 1.14 and 1.18 mm to cover a wider frequency range, whose central wavelength was 1.16 mm. The correlator was used in the time domain mode with a bandwidth of 2000 MHz (15.625 MHz × 128 channels). Four basebands were used for each tuning, and the total bandwidth was 16 GHz, covering the 244–248 GHz, 253–257 GHz, 259–263 GHz, and 268–272 GHz frequency ranges. The number of available antennas was 38–45.

The data were reduced with Common Astronomy Software Applications (CASA; McMullin et al. 2007). The maps were processed with the CLEAN algorithm with the task tclean.³⁰ Clean boxes were placed when a component with a peak signal-to-noise ratio (S/N) above 5.0 is identified, and CLEANed down to a $2\sigma$ level. The observations were done with a higher angular resolution ($\sim 0\buildrel{\prime\prime}\over{.} 2$) than originally requested ($0\buildrel{\prime\prime}\over{.} 8$), and we adopted a uv-taper of 160 kλ to improve the surface brightness sensitivity, which gives a final synthesized beamsize of $0\buildrel{\prime\prime}\over{.} 94\times 0\buildrel{\prime\prime}\over{.} 67$ and a typical rms noise level of 89 μJy beam⁻¹.

Source detection was conducted on the image before correcting for the primary beam attenuation. The source and noise properties were estimated with the Aegean (Hancock et al. 2012) source-finding algorithm. We find 12 sources with a peak S/N threshold of $5.0\sigma$, whereas no negative source with a peak S/N $\lt -5.0\sigma$ is found. The integrated flux density is calculated with elliptical Gaussian fitting. Table 1 (2–4th columns) lists the position of the peak intensity and the integrated flux density corrected for the primary beam attenuation with its $1\sigma$ error.

Table 1.  Millimeter and X-Ray Properties of ALMA Sources in GOODS-S

ID	R.A.	Decl.	${S}_{1.2\mathrm{mm}}$	${S}_{1.3\mathrm{mm}}$	${S}_{1.2\mathrm{mm}}$	$\mathrm{log}{L}_{\mathrm{IR}}$	$\mathrm{log}{M}_{* }$	CID	${S}_{{\rm{X}}}/{10}^{-17}$	$\mathrm{log}{N}_{{\rm{H}}}$	Γ	$\mathrm{log}{L}_{{\rm{X}}}$	z	AGN Flag
	(h m s)	(d m s)	(mJy)	(mJy)	(mJy)	(${L}_{\odot }$)	(${M}_{\odot }$)		(erg cm−2 s−1)	(cm−2)		(erg s−1)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)	(15)
1	03:32:28.51	–27:46:58.37	2.58 ± 0.17	⋯	⋯	12.76 ± 0.01	10.8	522	4.7	${20.0}_{-0.0}^{+4.0}$	${1.92}_{-0.02}^{+0.00}$	${42.3}_{-0.2}^{+0.7}$	2.38	NNYN
2	03:32:35.72	–27:49:16.26	2.16 ± 0.15	⋯	⋯	${12.83}_{-0.01}^{+0.04}$	11.1	666	39.0	${23.6}_{-0.2}^{+0.1}$	1.9	43.5 ± 0.1	2.582	YYYN
3 (=UDF1)	03:32:44.04	–27:46:35.90	1.53 ± 0.18	0.92 ± 0.08	⋯	12.75 ± 0.01	10.7 ± 0.10	805	107.0	20.0	${2.09}_{-0.11}^{+0.11}$	44.0 ± 0.1	3.00	NYYY
4	03:32:47.59	–27:44:52.39	1.10 ± 0.15	⋯	⋯	12.61 ± 0.01	10.7	852	8.1	22 (fixed)	1.9	42.3 ± 0.2	1.94	NNYN
5	03:32:32.90	–27:45:40.95	1.40 ± 0.19	⋯	⋯	11.00 ± 0.01	10.3	⋯	<6.9	23 (fixed)	1.9	<41.5	0.523	⋯
6 (=UDF2)	03:32:43.53	–27:46:39.27	1.44 ± 0.22	1.00 ± 0.09	⋯	${12.50}_{-0.01}^{+0.06}$	11.1 ± 0.15	⋯	<7.5	23 (fixed)	1.9	<42.8	2.92	⋯
7	03:32:29.25	–27:45:09.94	0.89 ± 0.17	⋯	⋯	${12.18}_{-0.01}^{+0.06}$	10.5	538	10.5	${24.0}_{-0.6}^{+0.0}$	1.9	${42.9}_{-0.4}^{+0.2}$	2.01	YYNN
8 (=UDF3)	03:32:38.55	–27:46:34.52	0.72 ± 0.14	0.86 ± 0.08	0.553 ± 0.014	12.75 ± 0.01	10.3 ± 0.15	718	4.5	${20.0}_{-0.0}^{+3.6}$	${2.44}_{-0.54}^{+0.00}$	42.6 ± 0.2	2.62	NYYN
9	03:32:36.75	–27:48:03.81	1.05 ± 0.25	⋯	⋯	⋯	⋯	⋯	<2.3	⋯	⋯	⋯	⋯	⋯
10	03:32:44.60	–27:48:36.18	0.62 ± 0.14	⋯	⋯	11.97 ± 0.01	10.6	818	145.0	${23.1}_{-0.1}^{+0.1}$	1.9	43.9 ± 0.1	2.593	NYYY
11	03:32:49.45	–27:49:09.21	1.34 ± 0.31	⋯	⋯	⋯	⋯	⋯	<5.7	⋯	⋯	⋯	⋯	⋯
12	03:32:31.47	–27:46:23.38	1.11 ± 0.28	⋯	⋯	12.42 ± 0.01	11.2	587	26.3	${23.3}_{-0.2}^{+0.2}$	1.9	43.1 ± 0.1	2.225	YYYN
UDF4	03:32:41.01	–27:46:31.58	⋯	0.30 ± 0.05	⋯	11.92 ± 0.02	10.5 ± 0.15	⋯	<4.6	23 (fixed)	1.9	<42.5	2.43	⋯
UDF5	03:32:36.95	–27:47:27.13	⋯	0.31 ± 0.05	⋯	11.95 ± 0.03	10.4 ± 0.15	⋯	<3.9	23 (fixed)	1.9	<42.2	1.759	⋯
UDF6	03:32:34.43	–27:46:59.77	⋯	0.24 ± 0.05	⋯	11.88 ± 0.06	10.5 ± 0.10	⋯	<5.1	23 (fixed)	1.9	<42.1	1.411	⋯
UDF7	03:32:43.32	–27:46:46.91	⋯	0.23 ± 0.05	⋯	11.69 ± 0.18	10.6 ± 0.10	797	6.6	${20.0}_{-0.0}^{+4.0}$	1.9	${42.4}_{-0.2}^{+0.7}$	2.59	NNYN
UDF8	03:32:39.74	–27:46:11.63	⋯	0.21 ± 0.05	0.223 ± 0.022	12.12 ± 0.27	11.2 ± 0.15	748	284.0	${22.6}_{-0.1}^{+0.1}$	1.9	43.7 ± 0.1	1.552	NYYY
UDF9	03:32:43.42	–27:46:34.46	⋯	0.20 ± 0.04	⋯	11.31 ± 0.48	10.0 ± 0.10	799	4.2	22 (fixed)	1.9	41.0 ± 0.2	0.667	NNNN
UDF10	03:32:40.75	–27:47:49.09	⋯	0.18 ± 0.05	⋯	11.60 ± 0.22	10.2 ± 0.15	756	2.5	${20.0}_{-0.0}^{+3.0}$	${3.00}_{-1.10}^{+0.00}$	42.4 ± 0.2	2.086	NNYN
UDF11	03:32:40.06	–27:47:55.82	⋯	0.19 ± 0.05	⋯	12.15 ± 0.26	10.8 ± 0.10	751	9.3	${21.8}_{-1.9}^{+1.0}$	${1.90}_{-0.00}^{+0.42}$	${42.4}_{-0.1}^{+0.2}$	1.996	NNYN
UDF12	03:32:41.28	–27:47:42.61	⋯	0.15 ± 0.04	⋯	11.51 ± 0.17	9.6 ± 0.15	⋯	<2.0	23 (fixed)	1.9	<42.7	5.000	⋯
UDF13	03:32:35.09	–27:46:47.78	⋯	0.17 ± 0.04	⋯	11.78 ± 0.12	10.8 ± 0.10	655	4.7	${20.0}_{-0.0}^{+3.8}$	${2.07}_{-0.17}^{+0.00}$	${42.4}_{-0.2}^{+0.5}$	2.497	NNYN
UDF14	03:32:40.96	–27:46:55.34	⋯	0.16 ± 0.04	⋯	11.59 ± 0.17	9.7 ± 0.10	⋯	<3.3	23 (fixed)	1.9	<41.5	0.769	⋯
UDF15	03:32:35.75	–27:46:54.98	⋯	0.17 ± 0.05	⋯	11.52 ± 0.31	9.9 ± 0.15	⋯	<1.8	23 (fixed)	1.9	<41.8	1.721	⋯
UDF16	03:32:42.37	–27:47:07.79	⋯	0.15 ± 0.04	⋯	11.55 ± 0.20	10.9 ± 0.10	⋯	<4.0	23 (fixed)	1.9	<42.0	1.314	⋯

Note. (1) ALMA source ID (those with "UDF" correspond to the D17 sources); (2) & (3) ALMA source position (J2000); (4) ALMA-integrated flux-density and 1σ error at 1.2 mm derived from the ASAGAO survey; (5) those at 1.3 mm derived from the UDF survey (D17); (6) those at 1.2 mm derived from the ASPECS (Aravena et al. 2016); (7) infrared luminosity in the rest 8–1000 μm band in units of solar luminosity (taken from D17 for the UDF sample and based on our SED fit for the ASAGAO sample) and its 1σ error; (8) stellar mass in units of solar mass (taken from D17 for the UDF sample and IDs 3, 6, and 8, and from Straatman (2016) for the rest); (9) Chandra source ID in Luo et al. (2017); (10) observed X-ray flux (or 90% confidence upper limit) in the 0.5–7 keV band converted from a count rate in the 0.5–7, 0.5–2, or 2–7 keV band with the apparent photon index ${{\rm{\Gamma }}}_{\mathrm{eff}}$; (11) X-ray absorption hydrogen column density; (12) intrinsic photon index; (13) absorption-corrected X-ray luminosity (or 90% confidence upper limit) in the rest-frame 0.5–8 keV band; (14) adopted redshift (after Straatman 2016 or D17; three decimal digits is for spectroscopic redshifts and two is for photometric redshifts); (15) AGN flags for the criteria I through IV.

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To supplement our ASAGAO sample, we also include fainter flux ALMA sources detected in the deep 1.3 mm image of the UDF ($\simeq 4.5$ arcmin² located inside the ASAGAO field) by D17. By position-matching ($\lt 0\buildrel{\prime\prime}\over{.} 2$) and flux comparison, we find that the objects with IDs 3, 6, and 8 are identical to UDF1, UDF2, and UDF3 in D17, respectively. Table 1 (5th column) lists the 1.3 mm flux density of the D17 sources. We refer to D17 for the positions of these sources except UDF1, UDF2, and UDF3 (second and third columns of Table 1). In addition, we find that ID 8 (UDF3) and UDF8 are also detected in the 1.2 mm continuum map of the ASPECS (Aravena et al. 2016). The 1.2 mm fluxes obtained by ASPECS are listed in the 6th column of Table 1 for these sources. The fluxes of UDF3 obtained from ASAGAO and ASPECS are consistent within the errors.

The ASAGAO sources are cross-matched against the ZFOURGE catalog (Straatman 2016), after correcting for systematic astrometric offsets ($-0\buildrel{\prime\prime}\over{.} 09$ in R.A. and $+0\buildrel{\prime\prime}\over{.} 28$ in decl.) with respect to the ALMA image, which are calibrated by the positions of stars in the Gaia Data Release 1 catalog (Gaia Collaboration 2016) within the ASAGAO field. The ZFOURGE fully covers the ASAGAO 26 arcmin² field, in which ∼3000 objects are cataloged with limiting magnitudes of ${K}_{{\rm{S}}}$ (AB) = 26.0–26.3 (5σ) at the 80% and 50% completeness levels with masking, respectively. We search for counterparts from the ZFOURGE catalog whose angular separation from the ALMA position is smaller than $0\buildrel{\prime\prime}\over{.} 2$, corresponding to $\approx 3\sigma$ of the statistical positional error of ALMA for a point-like source; when a counterpart is largely extended (IDs 3 and 5), we allow a larger positional offset, up to 1 arcsec. Consequently, ZFOURGE counterparts are found for 10 sources, except for IDs 9 and 11. Since the chance probability that an unrelated object falls within a radius of $0\buildrel{\prime\prime}\over{.} 2$ is only $\approx 0.004$ as calculated from the source density of the ZFOURGE catalog, we can safely assume that all of these ALMA-ZFOURGE associations are true.³¹ We adopt the best-estimated redshift (spectroscopic or photometric) in the ZFOURGE catalog but refer to D17 for the UDF sample and IDs 3, 6, and 8. The adopted redshift is listed in the 14th column of Table 1. The differences between the photometric redshifts in the ZFOURGE catalog and the spectroscopic redshifts in D17 are found to be ${\rm{\Delta }}z/(1+z)\lt 0.08$ with a median of 0.02. This indicates that the photometric redshift errors minimally affect our analysis and conclusions.

We regard the 23 sources with ZFOURGE counterparts (10 sources from the ASAGAO excluding IDs 9 and 11, and 13 sources from D17 excluding the overlapping sources UDF1, UDF2, and UDF3; hereafter the ASAGAO sample and the UDF sample, respectively) as the parent sample for our subsequent studies. All of them are also detected in FIR bands (70–160 μm) with Herschel/PACS (Elbaz et al. 2011).

To estimate the infrared luminosities (and hence SFRs) of the ASAGAO sample, we analyze their spectral energy distributions (SEDs), utilizing the MAGPHYS code (da Cunha et al. 2008, 2015). We use 43 optical-to-millimeter photometric data, including the ALMA, ZFOURGE, and de-blended Herschel/SPIRE photometries (T. Wang et al. 2017, in preparation). Checking the ALMA spectra, we have confirmed that line contamination to the 1.2 mm continuum flux is ignorable in all the targets. We use the MAGPHYS high-z excitation code for the sources at $z\gt 1$, whereas the MAGPHYS original package is applied for ID 5 (z = 0.523). In the SED fitting, the redshift is fixed to the value in Table 1. The resultant infrared luminosities in the rest-frame 8–1000 μm band (${L}_{\mathrm{IR}}$)³² are listed in the seventh column of Table 1. Further details on the SED analysis are given in Y. Yamaguchi et al. (2017, in preparation).

The infrared luminosities of the ASAGAO sample that we derive with the MAGPHYS code are found to be consistent with the ${L}_{\mathrm{IR}}$ values in D17 (for IDs 3, 6, and 8) and in Straatman (2016) within 0.1–0.2 dex in most cases; a maximum difference of $\approx 0.5$ dex is found for ID 8 (UDF3) between our result and D17, whose 1.3 mm flux density was corrected for unusually large line emission in the analysis of D17. Straatman (2016) obtained the infrared luminosities by fitting the 24, 100, and 160 μm photometry with the Wuyts et al. (2008) template. For the UDF sample we refer to D17 for ${L}_{\mathrm{IR}}$;³³ these values were obtained by a SED fit to 24 μm to 1.3 mm photometry with the spectral template by Kirkpatrick et al. (2015). The listed ${L}_{\mathrm{IR}}$ values include an estimated 20% AGN contribution.

The flux densities of the ASAGAO sample range from ∼0.6 to ∼3 mJy. It bridges the ALESS sample (Hodge et al. 2013)³⁴ and the UDF sample (D17), which contain brighter and fainter sub/millimeter galaxies than the ASAGAO sources, respectively. The majority of our sources with ZFOURGE counterparts are located at $z\simeq 2-3$. No object at $z\gt 3$ has been identified, although it is possible that the two sources (IDs 9 and 11) lacking redshift constraints are $z\gt 3$ galaxies. This result is consistent with the findings by Aravena et al. (2016) and D17 that high-z galaxies are rare in the faint ALMA populations, as expected on the basis of the selection wavelength and depth of the survey (Béthermin et al. 2015). Of the 10 identified ASAGAO sources, 8 have infrared luminosities larger than 10¹² ${L}_{\odot }$ and hence are classified as "ultra-luminous infrared galaxies" (ULIRGs). The star formation rate (SFR) estimated from the infrared luminosity after subtracting an estimated 20% AGN contribution (D17) ranges 9–600 ${M}_{\odot }$ yr⁻¹.

Figures 1 and 2 plot the relation between infrared luminosity and redshift and that between stellar mass (M_*) and SFR, respectively, for the X-ray sources in the ASAGAO and UDF samples (red circles and triangles), the ALESS-AGN sample (magenta squares), and the Herschel-AGN sample (black diamonds). We refer to Wang et al. (2013) and Straatman (2016) for the infrared luminosities of the ALESS-AGN and Herschel-AGN samples, respectively. For all the samples, we estimate the SFRs from ${L}_{\mathrm{IR}}$ after subtracting an assumed 20% AGN contribution. The stellar masses (listed in the 8th column in Table 1) are taken from the ZFOURGE catalog (Straatman 2016) for the ASAGAO (except IDs 3, 6, and 8) and Herschel-AGN samples, from D17 for the UDF sample and IDs 3, 6, and 8, and from Wang et al. (2013) for the ALESS-AGN sample (recalibrated for a Chabrier IMF). All the M_* values were derived with multiwavelength SED analyses by assuming the solar abundances, and represent the total stellar masses in the galaxies. In the figure, we draw the "main sequence" lines at z = 2.75, z = 2.25, and z = 1.75 according to Speagle et al. (2014). Figure 1 indicates that most of the ALMA-Chandra AGNs belong to main-sequence star-forming galaxies (SFGs), although a few ASAGAO objects are classified as starburst galaxies, being located more than 0.6 dex above the main-sequence line (Rodighiero et al. 2011). This is consistent with previous ALMA survey results for faint sub/millimeter galaxies (e.g., Hatsukade et al. 2015; Yamaguchi et al. 2016). The AGNs undetected by ALMA generally follow the same correlation at lower stellar-mass or SFR ranges.

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We derive the AGN fraction in the millimeter galaxies down to an X-ray flux limit of $\sim 5\times {10}^{-17}$ erg cm⁻² s⁻¹ (0.5–7 keV), which is 5 times fainter than that of the ALESS-AGN sample (Wang et al. 2013). Following Wang et al. (2013), we calculate the cumulative AGN fraction at ${f}_{{\rm{X}}}\gt {f}_{{\rm{X}},\mathrm{lim}}$ as ${\sum }_{i=1}^{N}(1/{N}_{\mathrm{MG},i})$, where the suffix i (1 through N) represents each Chandra-identified AGN with a flux of ${f}_{{\rm{X}},i}(\gt {f}_{{\rm{X}},\mathrm{lim}})$ and ${N}_{\mathrm{MG},i}$ is the total number of ALMA objects that would be detected if they had fluxes brighter than ${f}_{{\rm{X}},i}$. We find that the AGN fraction in the ASAGAO sample (with a flux-density limit of >0.6 mJy at 1.2 mm) is ${67}_{-19}^{+15}$% at ${f}_{{\rm{X}}}\,\gt \,5\,\times \,{10}^{-17}$ erg cm⁻² s⁻¹ (0.5–7 keV), whereas that in the UDF sample covering a flux-density range of 0.15–0.31 mJy at 1.3 mm (or 0.18–0.39 mJy at 1.2 mm) is ${38}_{-15}^{+18}$% at ${f}_{{\rm{X}}}\gt 4\times {10}^{-17}$ erg cm⁻² s⁻¹ (0.5–8 keV). When we limit the sample to those at $z=1.5\mbox{--}3$, we obtain AGN fractions of ${88}_{-24}^{+10}$% in the ASAGAO sample and ${63}_{-24}^{+19}$% in the UDF sample (at the same X-ray flux limits as above).

The best-estimated AGN fraction obtained from the ASAGAO sample is higher than that from the UDF sample, although the sig-nificance of the difference is marginal due to the limited sample size. This is most likely related to the lower SFRs (and hence lower IR luminosities) or smaller stellar masses in the latter sample. In fact, when we divide the combined ASAGAO+UDF sample at $z=1.5\mbox{--}3$ by IR luminosity, we find AGN fractions of ${90}_{-19}^{+8}$% at ${f}_{{\rm{X}}}\gt 5\times {10}^{-17}$ erg cm⁻² s⁻¹ (0.5–7 keV) for the ULIRGs (log ${L}_{\mathrm{IR}}$ = 12–12.8), and ${57}_{-25}^{+23}$% at ${f}_{{\rm{X}}}\gt 4\times {10}^{-17}$ erg cm⁻² s⁻¹ (0.5–8 keV) for the LIRGs (log ${L}_{\mathrm{IR}}$ = 11.5–12). The trend is consistent with previous results that the AGN fraction is small among faint millimeter galaxies (Fujimoto et al. 2016) or among $z\sim 2$ galaxies with small stellar masses (Kriek et al. 2007; Yamada et al. 2009; Wang et al. 2017).

Our ASAGAO result (∼90%) is even higher than that by Wang et al. (2017), who obtained an AGN fraction of ∼50% among their green-color galaxy sample with $\mathrm{log}{M}_{* }/{M}_{\odot }\gt 10.6$. This may be related to the fact that the high-resolution observations of ALMA are biased toward more compact objects; if that is the case, these results imply that compact SFGs have remarkably high AGN fractions, as suggested by Chang et al. (2017) for $z\lt 1.5$ AGNs. On the other hand, the ALESS sources, whose stellar masses are larger than the ASAGAO sample (Figure 1), apparently shows a much smaller AGN fraction (∼20%) than ours. A primary reason is its brighter X-ray flux limit, because most of the ALESS region (E-CDFS) is covered only by ∼250 ks exposure of Chandra. Indeed, when we impose the same X-ray flux limit as that for the ALESS-AGN sample (${f}_{{\rm{X}}}\gt 2.7\times {10}^{-16}$ erg cm⁻² s⁻¹), the AGN fraction for the ASAGAO $z=1.5\mbox{--}3$ sample becomes ∼25%, consistent with the ALESS result. Namely, many AGNs in these millimeter galaxies are not X-ray luminous, and hence are only detectable with very deep X-ray data. This trend implies that even ∼90% may be a lower limit, becoming higher when the Chandra exposure increases beyond 7 Ms.

Among the 12 ALMA-Chandra sources for which the X-ray hardness ratio is available, 7 have best-fit absorption column densities of $\mathrm{log}{N}_{{\rm{H}}}/{\mathrm{cm}}^{-2}\lt 22$ (classified as "X-ray type-1 AGNs" according to Ueda et al. 2003) and 5 show $\mathrm{log}{N}_{{\rm{H}}}/{\mathrm{cm}}^{-2}\geqslant 22$ ("X-ray type-2 AGNs"). While the obscuration fraction (5 out of 12) is consistent with that found from hard(3–24 keV) X-ray-detected U/LIRGs in the COSMOS field at $z=0.3-1.9$ (12 out of 23, Matsuoka & Ueda 2017), it looks much smaller than those of local U/LIRGs; according to a recent study by Ricci et al. (2017), more than 90% of AGNs in late-merger galaxies are subject to heavy obscuration $\mathrm{log}{N}_{{\rm{H}}}/{\mathrm{cm}}^{-2}\,\gt 23$. Since the X-ray luminosity range of our ALMA-Chandra sample is similar to that of typical local U/LIRGs (Section 4.4), the difference cannot be explained by the luminosity dependence of the absorbed AGN fraction (Ueda et al. 2003). In local ULIRGs, star formation activity is concentrated at the nucleus within $\lt 0.5\,\mathrm{kpc}$ (Soifer et al. 2000). In contrast, on the basis of JVLA and ALMA imaging, Rujopakarn et al. (2016) reported that main-sequence SFGs at $z\sim 2$ with SFR ∼ 100 ${M}_{\odot }$ yr⁻¹ have extended (∼4 kpc diameter) star-forming regions, whereas the size becomes more compact in more luminous SMGs (see also Chapman et al. 2004; Biggs & Ivison 2008; Ivison et al. 2011 for the results of radio observations). The difference in the host star-forming properties between our ALMA-Chandra sample and local ULIRGs would be related to the amount of obscuring gas/dust around the nucleus.

We have to bear in mind, however, that the uncertainty in the column density is often quite large due to the limited photon statistics; a few objects (e.g., ID 1 and UDF7) tentatively classified as unobscured AGNs could even be Compton-thick AGNs ($\mathrm{log}{N}_{{\rm{H}}}/{\mathrm{cm}}^{-2}\sim 24$) within the error. In an extreme case, only an unabsorbed scattered component coming from outside the torus may be detected with Chandra in heavily Compton-thick AGNs; such objects would be misidentified as (low-luminosity) X-ray type-1 AGNs. In fact, according to a standard population synthesis model of the X-ray background (Ueda et al. 2014), the fraction of Compton-thick AGNs at ${f}_{{\rm{X}}}\sim 5\times {10}^{-17}$ erg cm⁻² s⁻¹ (0.5–7 keV) is predicted to be ∼20%. This corresponds to ∼3 out of the 14 Chandra objects, whereas only one object is identified as Compton-thick based on the best-fit hardness ratio. Nevertheless, considering the small number of possible additional Compton-thick AGNs (∼2), our main conclusions, discussed below, are not largely affected by this uncertainty, as long as the standard X-ray background model is correct.

In SFGs containing AGNs, the X-ray and infrared luminosities are good indicators of the mass-accretion rate onto the SMBH (${\dot{M}}_{\mathrm{BH}}$) and (dust-embedded) SFR, respectively. Figure 3 plots the relation between the infrared luminosity in the rest-frame 8–1000 μm band (${L}_{\mathrm{IR}}$) and the intrinsic X-ray luminosity (${L}_{{\rm{X}}}$) for our ALMA-Chandra (ASAGAO+UDF) objects. We also plot the Herschel-AGN sample, for which ${L}_{\mathrm{IR}}$ is taken from Straatman (2016) and ${L}_{{\rm{X}}}$ is determined from the Chandra count rates in the same way as for the ALMA-Chandra objects. Furthermore, we plot the ALESS-AGN sample from Wang et al. (2013), the NuSTAR-detected U/LIRGs in the COSMOS field from Matsuoka & Ueda (2017), and local ULIRGs for which results from hard X-ray (>10 keV) observations with NuSTAR are published. All the ${L}_{\mathrm{IR}}$ values quoted in Figure 3 are total IR luminosities that include both star-forming and AGN contributions. In the figure, we mark the ${L}_{{\rm{X}}}$–${L}_{\mathrm{IR}}$ relation expected from pure star formation activity, based on the formula by Lehmer et al. (2010) at SFR $\gt \,0.4$ ${M}_{\odot }$ yr⁻¹. We also mark the relation observed in Palomer–Green (PG) QSOs (i.e., AGN-dominant population, Teng & Veilleux 2010).

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We find that our ALMA-Chandra AGNs occupy a similar region to local ULIRGs, having a large scatter (>2 dex) in the ${L}_{{\rm{X}}}$/${L}_{\mathrm{IR}}$ ratio. Typical statistical errors in ${L}_{{\rm{X}}}$ and ${L}_{\mathrm{IR}}$ that are $\approx 0.2$ dex and $\approx 0.1$ dex, respectively (Table 1), are much smaller than the scatter. The possible systematic uncertainties in ${L}_{\mathrm{IR}}$ (0.1–0.2 dex, Section 2) also do not affect our conclusions. Figure 4 displays the histogram of log${L}_{{\rm{X}}}$/${L}_{\mathrm{IR}}$ for our ALMA-Chandra AGN and that including the Herschel-AGN sample. Bimodal distribution is strongly suggested in the latter histogram. More than half of the sources are distributed around a peak centered at log${L}_{{\rm{X}}}$/${L}_{\mathrm{IR}}$ = −3, whereas a non-negligible fraction of them show higher ${L}_{{\rm{X}}}$ /${L}_{\mathrm{IR}}$ ratios consistent with AGN-dominant populations. While such a large variation in the ${L}_{{\rm{X}}}$–${L}_{\mathrm{IR}}$ relation is known in the local universe by combining various samples with different selections (see, e.g., Figure 8 of Alexander et al. 2005), here we find a similar ${L}_{{\rm{X}}}$–${L}_{\mathrm{IR}}$ variation at $z=1.5\mbox{--}3$ by directly detecting individual objects on the basis of very deep X-ray and millimeter observations of the common survey field. The mean IR luminosities for subsamples with log${L}_{{\rm{X}}}$ = 42–43 and 43–44 are log${L}_{\mathrm{IR}}$/${M}_{\odot }$ = 12.15 ± 0.08 and 12.27 ± 0.10, respectively, which are similar to each other. This is consistent with the result by Stanley et al. (2015) utilizing stacking analysis in which the mean IR luminosities are fairly constant against X-ray luminosity at each redshift. Our result is quite different from previous studies inevitably biased for luminous AGN owing to their bright flux limits (e.g., see Figure 2 of Willott et al. 2013 for optical wide-area surveys, and Matsuoka & Ueda 2017 for a hard X-ray survey with NuSTAR in the COSMOS field), whose samples are predominantly located around the PG QSO line in Figure 3. It is interesting to compare our result with the prediction of the co-evolution scenario. We assume the relation (for a Chabrier IMF)

$$\begin{eqnarray}&&\mathrm{SFR}=1.09\times {10}^{-10}\times {L}_{\mathrm{IR}}/{L}_{\odot }\,\,\,({M}_{\odot }\,{\mathrm{yr}}^{-1}).\end{eqnarray} \tag{ 1 }$$

The X-ray luminosity ${L}_{{\rm{X}}}$ can be converted to a mass-accretion rate onto the SMBH ${\dot{M}}_{\mathrm{BH}}$ by assuming a radiative efficiency η and a bolometric correction factor ${\kappa }_{0.5-8}$ as

$$\begin{eqnarray}&&{\dot{M}}_{\mathrm{BH}}={\kappa }_{0.5-8}{L}_{{\rm{X}}}(1-\eta )/(\eta {c}^{2}),\end{eqnarray} \tag{ 2 }$$

where c is the light speed. Here, we adopt $\eta =0.05$, as estimated by comparison of the local SMBH mass density and the most updated AGN luminosity function (Ueda et al. 2014).³⁷ By analyzing the combined IR-to-mm SED of their sample, D17 estimated that the averaged fractional AGN contribution to the IR luminosity is ∼20%. Thus, assuming that 20% of ${L}_{\mathrm{IR}}$ is the intrinsic AGN bolometric luminosity, we can estimate an averaged bolometric correction factor by comparing with observed X-ray luminosities. Here, we ignore X-ray undetected objects because their intrinsic X-ray luminosities would be highly uncertain if we take into account the possibility of heavily Compton-thick obscuration. Taking a luminosity-weighted average of AGNs in the ASAGAO, UDF, and Herschel-AGN samples, we find ${\kappa }_{0.5-8}\approx 45$ (or ${\kappa }_{2-10}\approx 70$, a bolometric correction factor from the 2–10 keV luminosity, converted by assuming a photon index of 1.9).

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If the galaxy-SMBH evolution is exactly simultaneous over cosmic time, we expect the relation

$$\begin{eqnarray}&&\mathrm{SFR}\times (1-R)=A\times {\dot{M}}_{\mathrm{BH}},\end{eqnarray} \tag{ 3 }$$

where R is the return fraction (the fraction of stellar masses that are ejected back to the interstellar medium; R = 0.41 for a Chabrier IMF), and A is the mass ratio of stars to SMBHs in the local universe. Here, we consider two cases: $A={A}_{\mathrm{bul}}$ for the stellar masses only in bulge components and $A={A}_{\mathrm{tot}}$ for the total stellar masses in both bulges and disks. As a representative value, we use ${A}_{\mathrm{bul}}\sim 200$, based on the latest calibration by Kormendy & Ho (2013) at a bulge mass of ${10}^{11}\,{M}_{\odot }$. Adopting a total (bulge+disk) stellar mass density of $\mathrm{log}{\rho }_{* }/({M}_{\odot }\,{\mathrm{Mpc}}^{-3})\simeq 8.6$ (see Madau & Dickinson 2014 and references therein) and a SMBH mass density of $\mathrm{log}{\rho }_{\mathrm{BH}}/({M}_{\odot }\,{\mathrm{Mpc}}^{-3})\simeq 6.0$ (Ueda et al. 2014) in the local universe, we estimate ${A}_{\mathrm{tot}}\sim 400$. From a clustering analysis of $z\sim 2$ galaxies in the COSMOS field, Béthermin et al. (2014) suggested that most of galaxies with $\mathrm{log}{M}_{* }/{M}_{\odot }\sim 11$ (for a Salpeter IMF) at $z\sim 2$ evolve into bulge-dominated galaxies at z = 0, whereas a portion of SFGs with $\mathrm{log}{M}_{* }/{M}_{\odot }\sim 10$ at $z\sim 2$ become SFGs or passive galaxies with $\mathrm{log}{M}_{* }/{M}_{\odot }\sim 11$ at z = 0. Thus, we expect that the majority of our objects are likely the progenitors of local bulge-dominated galaxies, although a small fraction of them, with $\mathrm{log}{M}_{* }/{M}_{\odot }\sim 10$, may end up in local disk-galaxies. We therefore adopt $A={A}_{\mathrm{bul}}$ as the main assumption in the following discussions.

Combining Equations (1)–(3), we show the "simultaneous evolution" relations in the ${L}_{{\rm{X}}}$ versus ${L}_{\mathrm{IR}}$ plane by the blue solid (dashed) line in Figures 3 and 4 for the bulge (total) stellar masses. Many objects are not tightly distributed along either of these lines, suggesting that the evolution is not simultaneous in individual galaxies. The "non-coeval" nature is consistent with the finding by Yamada et al. (2009) based on K-band-selected galaxies at $z\sim 2$, although they did not use far-IR/mm data to estimate the SFR. It is seen that the majority of the $z=1.5\mbox{--}3$ sources are located above the lines; if our assumptions are correct, stars would be forming more rapidly than SMBHs in these galaxies. There is also a significant fraction of objects located below this line, in which SMBHs are growing more rapidly than the stars.

We note that the bolometric correction factor estimated above, ${\kappa }_{0.5\mbox{--}8}=45$, is larger than a nominal value for AGNs with similar X-ray luminosities ($\mathrm{log}{L}_{{\rm{X}}}\approx 42\,\mbox{--}\,44$), ${\kappa }_{0.5-8}\approx 5-20$ (Rigby et al. 2009). Vasudevan & Fabian (2007) showed, however, that the bolometric correction factor sharply correlates with Eddington ratio rather than luminosity: the mean value of ${\kappa }_{2-10}$ rapidly increases to ∼70 (or ${\kappa }_{0.5-8}\sim 45$) at ${\lambda }_{\mathrm{Edd}}(\equiv {L}_{\mathrm{bol}}/{L}_{\mathrm{Edd}})\gtrsim 0.1$. This would imply that the Eddington ratios of our AGNs are high, that is, they contain a rapidly growing SMBH with a relatively small black hole mass.

Figure 5 plots the correlation between X-ray luminosity and total stellar mass for the AGN in the ASAGAO, UDF, Herschel-AGN samples. Adopting a bolometric correction factor ${\kappa }_{0.5\mbox{--}8}=45$, we plot the relations that would be expected if the ratio of the stellar mass to the black hole mass were A = 200 for three assumed values of the Eddington ratio (${\lambda }_{\mathrm{Edd}}=0.01,0.1$, and 1). Apparently, the majority of the AGNs are located around the ${\lambda }_{\mathrm{Edd}}=0.01$ line, indicative of inefficient SMBH accretion. This directly contradicts the previous argument that the SMBHs in our AGN sample have high Eddington ratios (${\lambda }_{\mathrm{Edd}}\gt 0.1$) on average. Time variability in the instantaneous mass-accretion rate (hence in ${L}_{{\rm{X}}}$), which could produce a large ${L}_{{\rm{X}}}$-to-${L}_{\mathrm{IR}}$ variation (Hickox et al. 2014), cannot explain this contradiction, as long as we assume the local M_*–${M}_{\mathrm{BH}}$ relation. This discrepancy can be solved, however, if the black hole mass is ∼10 times smaller than that expected from the stellar mass with the local M_*–${M}_{\mathrm{BH}}$ relation, that is, $A\sim 2000$. In Figure 5, we also plot the ALESS-AGN sample at $z=1.5\mbox{--}3;$ assuming that their Eddington ratios are also high, they would have similarly large A values on average. This implies that these small black hole mass systems may be young galaxies, although we cannot find a clear correlation between the M_*/${L}_{{\rm{X}}}$ ratio and the galaxy age derived from the SED fit (available in the ZFOURGE catalog). We leave it to future studies to pursue this issue using a larger sample.

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We thus infer that the majority of the ALMA/Herschel- and Chandra-detected populations, a representative sample of SFGs with log ${L}_{\mathrm{IR}}$/${L}_{\odot }$ $\gt 11$ hosting AGNs at $z=1.5\mbox{--}3$, are in a star-formation-dominant phase and contain small SMBHs compared to their stellar mass. This picture is in line with earlier suggestions for more luminous (hence rare) SMGs, which are suggested to contain small SMBHs (e.g., Alexander et al. 2005, 2008; Tamura et al. 2010). This may appear to be in contrast to previous reports that luminous AGNs are in an AGN-dominant phase (e.g., Matsuoka & Ueda 2017) and have larger SMBHs than those expected from the local M_*–${M}_{\mathrm{BH}}$ relation (see Figure 38 of Kormendy & Ho 2013 for a summary). We argue that the apparent contradiction is due to selection bias for luminous AGNs in such studies. In fact, a non-negligible fraction (∼20%) of the whole sample, mostly X-ray luminous objects, is located at ${\lambda }_{\mathrm{Edd}}\gt 0.1$ lines in Figure 5. They may have SMBHs larger than those expected from the local M_*–${M}_{\mathrm{BH}}$ relation and truly be accreting with ${\lambda }_{\mathrm{Edd}}\sim 0.1$.

Recalling that the majority of our sample is likely progenitors of local bulge-dominated galaxies, the star-formation-dominant galaxies with small SMBHs must experience an AGN-dominant phase later, to make the tight M_*–${M}_{\mathrm{BH}}$ relation at z = 0. Indeed, such AGN-dominant, X-ray-luminous populations are present in our sample, and even more luminous AGNs were detected in wider and shallower surveys. Our results are consistent with an evolutionary scenario in which star formation occurs first and an AGN-dominant phase follows later (e.g., Hopkins et al. 2008; Netzer 2009), at least in objects finally evolving into galaxies with classical bulges. If this is the case, the dichotomy in the ${L}_{{\rm{X}}}$/${L}_{\mathrm{IR}}$ distribution (Figure 4) would mean that the transition time from the star formation dominant phase to the AGN-dominant one is short. It is interesting that, despite the wide diversity of populations at $z=1.5\mbox{--}3$, the mass-accretion-rate density and the SFR density appear to "co-evolve" by roughly keeping the local M_*–${M}_{\mathrm{BH}}$ relation (e.g., Mullaney et al. 2012). We suggest that the "co-evolution" view is only valid when the mass-accretion rate and SFR are averaged over a cosmological timescale for an individual galaxy, or when they are averaged for a large number of galaxies in different evolutionary stages at a given epoch.