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A Wide and Deep Exploration of Radio Galaxies with Subaru HSC (WERGS). I. The Optical Counterparts of FIRST Radio Sources

We report the result of optical identifications of FIRST radio sources with the Hyper Suprime-Cam Subaru Strategic Program survey (HSC-SSP). The positional cross-match within 1"between the FIRST and HSC-SSP catalogs (i ~<26) produced more than 3600 optical counterparts in the 156 deg^2 of the HSC-SSP field. The matched counterparts account for more than 50% of the FIRST sources in the search field, which substantially exceed previously reported fractions of SDSS counterparts (i ~<22) of ~30%. Among the matched sample, 9% are optically unresolved sources such as radio-loud quasars. The optically faint (i>21) radio galaxies (RGs) show that the fitting linear function of the 1.4 GHz source counts has a slope that is flatter than that of the bright RGs, while optically faint radio quasars show a slope steeper than that of bright radio quasars. The optically faint RGs show a flat slope in the i-band number counts down to 24 mag, implying either less massive or distant radio-active galactic nuclei (AGNs) beyond 24 mag. The photometric redshift and the comparison of colors with the galaxy models show that most of the matched RGs are distributed at redshifts from 0 to 1.5. The optically faint sample includes the high radio-loudness sources that are not seen in the optically bright sample. Such sources are located at redshift z>1. This study gives ~1500 radio AGNs lying at the optically faint end and high-redshift regime not probed by previous searches.


INTRODUCTION
Radio galaxies (RGs) will provide us with great opportunities for understanding galaxy formation and evolution, as well as radio-loud active galactic nuclei (AGNs) themselves. RGs prefer massive host galaxies (Seymour et al. 2007). The powerful radio jets from RGs can drive the AGN feedback to regulate star formation in massive host galaxies (McNamara et al. 2005;Fabian 2012; Morganti et al. 2013). Thus, RGs are thought to be a key population on the formation of massive galaxies. Moreover, because high-z RGs reside in over-density regions (McCarthy 1993;Miley & De Breuck 2008), RGs could be a valuable beacon to find proto-clusters.
Bright radio radiation of RGs is advantageous to probe the high-z AGNs. Such radio sources should be found by wide-area surveys in radio wavelength (NVSS, Condon et al. 1998;FIRST, Becker et al. 1995;Helfand et al. 2015;SUMSS, Bock et al. 1999; TGSS ADR, Intema et al. 2017), which follows the pioneering Cambridge Catalogue series (e.g., Edge et al. 1959). It is greatly helpful to identify optical counterparts of the radio sources to investigate the properties of host galaxies and the optical view of AGNs.
The Sloan Digital Sky Survey (SDSS, York et al. 2000) allowed identifications of the optical counterparts of radio sources, taking advantage of its large sky coverage. Ivezić et al. (2002) and subsequently Helfand et al. (2015) performed the positional cross-match between the SDSS and FIRST catalogs and identified SDSS counterparts only for ∼ 30 % of the FIRST radio core sources. Even though taking into consideration radio sources with extended complex radio morphology, which are a minority in all the FIRST sources (∼ 10 %, Ivezić et al. 2002), the matching fraction of the SDSS objects with FIRST sources was not improved (e.g., Ching et al. 2017). This means that more than half of all the FIRST sources does not have SDSS counterparts. This is likely due to the shallow depth of optical sensitivities of SDSS imaging (r < 22.2 mag).
In fact, a deep optical survey in the VVDS 1 deg 2 field showed that more than half of radio sources with a flux of > 1 mJy in 1.4 GHz, which is the same level as the FIRST sensitivity, match optically faint counterparts with I > 22.9 mag (Ciliegi et al. 2005). In a 1.4 GHz VLA survey in the 1.3 deg 2 SXDF, Simpson et al. (2006Simpson et al. ( , 2012 found a few hundred optical counterparts of highz radio-AGNs with i ′ < 26 mag up to z ∼ 4. Recently Smolčić et al. (2017a,b) performed a 3 GHz VLA deep imaging and reported more than a thousand radio-AGNs with < 26 mag in the optical bands, up to z ∼ 5 in the 2.6 deg 2 COSMOS field. Williams et al. (2018) performed an identification of radio sources in the deep 150 MHz LOFAR observation with I-band selected objects (I < 24), and they reported ∼ 2000 RGs up to z ∼ 2 in 9.2 deg 2 of the Boötes field. The previous deep optical surveys in the radio survey regions have successfully identified high-z radio-AGNs, but the number of the radio-AGNs, in particular for high radio luminosity sources, is limited to a few hundred due to their small survey areas of typically < 10 deg 2 . The Hyper Suprime-Cam (HSC) Subaru strategic program (SSP, Aihara et al. 2018a) provides a key solution for exploring the large number of radio-AGNs, which are rare and optically faint. For example, the survey of HSC-SSP in the Wide layer reaches a limiting magnitude of 25.9 in i-band in 1400 deg 2 area. This wide and deep survey has an advantage to identify rare and faint objects such as radio-AGNs.
This paper presents a new exploration for radio AGNs using a combination of the wide and deep optical catalog of the Subaru HSC-SSP and the wide-filed radio catalog of FIRST. This exploration is carried out by an ongoing project, WERGS (a Wide and Deep Exploration of Radio Galaxies with the Subaru HSC). In this paper, we particularly focus on the optical and radio properties of RGs discovered in this project. This paper is organized as follows. We introduce the two catalog data sets in Section 2. The method and statistical results of a cross-match between both the catalogs are presented in Section 3. The optical and radio properties of the whole HSC-FIRST RG sample are shown in Section 4. The properties of optically-faint RGs are discussed in Section 5. A summary is presented in Section 6. Throughout this paper, we use the AB magnitude system and a ΛCDM cosmological model with H 0 = 70 km s −1 Mpc −1 , Ω M = 0.27, and Ω Λ = 0.73.

THE DATA
This search for radio AGNs is based on the positional cross-match between the HSC-SSP optical source catalog and the FIRST radio source catalog. In this section, the two source catalogs are described.

Subaru HSC survey
The HSC-SSP is a multi-band (five broad band filters of g, r, i, z, and y, and four narrow band filters) imaging survey with HSC (Miyazaki et al. 2018;Komiyama et al. 2018;Furusawa et al. 2018;Kawanomoto et al. 2018, in preparation) installed on the Subaru 8.2 m telescope. Three complementary layers of the Wide, the Deep, and the UltraDeep are included in the survey. These layers are different from each other in area and depth.
We utilized the broad band forced photometry catalogs of the early data products internally released as S16A (Aihara et al. 2018b), which were obtained by observations friom March 2014 to January 2016. The typical seeing is ∼ 0. ′′ 6 in i-band. The astrometric uncertainty is ∼ 40 mas in RMS according to the comparison with the Pan-STARRS1 Surveys. The forced photometry of each band image is performed using a position of a reference band, which is mostly i-band (see Bosch et al. 2018 for details). We used the two extremes of the survey layers: the Wide layer originally covering 456 deg 2 with a 5σ depth for point sources of i = 26.4, while the UltraDeep layer of 4 deg 2 with a depth of i = 27.0 (Aihara et al. 2018b). The saturation magnitudes for point sources are 18.4 and 18.7 in i-band for the Wide layer and the UltraDeep layer, respectively. Using the two extreme layers, we investigate a dependence of a rate of optical identification on the depth of optical imaging. We do not use the Deep layer because the imaging depth of the S16A Deep layer data is still as shallow as that of the S16A Wide layer due to an incomplete observation in the Deep layer. The Wide layer is composed of six distinct areas, and the UltraDeep layer has two ares of the UD-COSMOS and the UD-SXDS. Because the UD-SXDS area in the S16A data has a shallower depth (10-40 %) than that of the UD-COSMOS, we use only the UD-COSMOS out of the UltraDeep layer. The detailed properties and the data process of the early data products are described in (Aihara et al. 2018b) and .
We produced two clean HSC-SSP samples of the HSC-SSP Wide and UltraDeep layers, respectively, from the original HSC-SSP forced catalogs. in order to exclude detector edges with low sensitivities and junk sources from the original catalogs. Here, we use a cModel magnitude for the HSC-SSP photometry data and the Galactic absorption on their magnitudes are corrected . First, we masked the edges of each area. Around the edges, a number of visits at an object position is much smaller than the central regions. Thus, striped blank gaps in which sources are absent because of CCD gaps. The blank gaps are serious for cross-matching two sources. The coordinates of the consequent areas after masking the edges are shown in Table  1. Additionally, we removed coadded patches with poor modeling of a PSF due to extremely good seeings (see section 5.8.4 in Aihara et al. 2018b for details). A patch is a minimum unit of images for the data processing. The removed patches have the color offsets with larger than 0.075 mag from the stellar sequence in either colorcolor planes of g − r and r − i, r − i and i − z, or i − z and z − y He et al. 2018). We also removed sub-regions in two patches in the XMM area, where some cModel photometries are significantly overestimated compared with aperture photometries.
Then, we imposed the following criteria. (i) a number of visits at an object position (countinputs) is more than or equal to 3 (5) for g and r (i, z, and y) bands in the Wide layer to ensure an observing depth of more than a certain sensitivity, and more than or equal to 14, 26, and 42 for g and r, i and z, and y, respectively, in the UD-COSMOS; (ii) central 3 × 3 pixels of an object are not affected by nearby bright objects (flags_pixel_bright_object_center=False, see Coupon et al. 2017 for details); (iii) an object is not deblended further (deblend_nchild=0); (iv) an object is an unique source (detect_is_primary=True); (v) central 3 × 3 pixels of an object are not saturated (flags_pixel_saturated_center = False) and (vi) not affected by cosmic rays (flags_pixel_cr_center = False); and (vii) an object is not at the edge of a CCD or a coadded patch (flags_pixel_edge = False); The following conditions were imposed only for r, i, and z bands, (viii) there are no problem with measuring cModel flux (cmodel_flux_flags = False) and (ix) centroid positions (centroid_sdss_flags = False); and (x) a signal-to-noise ratio (S/N) of an object is more than 5 in all the three bands. As a result, 23,795,523 sources in 154 deg 2 area and 643,932 sources in 1.78 deg 2 are selected as the HSC-SSP clean samples of the Wide layer and the UD-COSMOS, respectively.

FIRST radio survey
The FIRST survey (the Faint Images of the Radio Sky at Twenty-cm, Becker et al. 1995) is a wide-field survey with the Very Large Array (VLA) at 1.4 GHz. The spatial resolution is 5. ′′ 4, and the statistical astrometry error is 0. ′′ 2 for bright and compact sources (White et al. 1997). The sky coverage is 10,575 deg 2 , which nearly covers the SDSS sky area. The wide coverage and the high spatial resolution of FIRST are appropriate for finding a large number of optical counterparts of radio sources. The FIRST detection limit is 1 mJy, although only in a region at the equatorial strip the limit is 0.75 mJy. Radio sources detected with a radio flux of more than the FIRST detection limit at a redshift z 0.5 meet the definition of radio AGNs, where a radio AGN should have a 1.4 GHz luminosity of L 1.4 GHz > 10 24 W Hz −1 (Tadhunter 2016).
We use the final release catalog of FIRST (Helfand et al. 2015). To produce an uniform sample, we use only sources with a radio flux of more than 1 mJy. The FIRST catalog gives a probability P (S) that a source is a spurious detection near a bright source. We employed the probability and use only sources with P (S) < 0.05. Consequently, the FIRST clean samples in the unmasked regions of the HSC-SSP Wide layer and UD-COSMOS layer are 7,072 and 106 sources, respectively. See Appendix 6 for details about how to count FIRST sources in the un-masked HSC-SSP regions.

Positional matching
A HSC-SSP counterpart of a FIRST source is identified with the nearest neighbor by the positional crossmatch between HSC-SSP i-band and FIRST source positions. The search radius r s is set to be 1. ′′ 0 for both cross-matching in the Wide and UD-COSMOS layers, because r s = 1. ′′ 0 is an optimal condition according to an analysis on a completeness and a contamination of the cross-match as discussed below. In Figure 1, the differential distributions of the separation between HSC-SSP and FIRST sources are compared with that of chance coincidence matches. These examinations were performed in a central 15 deg 2 region of the GAMA09H Wide layer and a central 0.7 deg 2 region of the UD-COSMOS. The matches by chance coincidence are estimated from mock FIRST catalogs with random positions. Each of the mock catalogs was generated by shifting FIRST source positions from the original positions to +/−1 • or +/−2 • along R.A. direction for the Wide layer, to +/ − 0.1 • , +/ − 0.2 • , +/ − 0.3 • , or +/ − 0.4 • for the UD-COSMOS. The numbers of matches have peaks at 0. ′′ 0 < r s < 1. ′′ 0 in both of the Wide and the UD-COSMOS layers. Then at r s > 1. ′′ 0, the matches gradually increase with increasing radius, coming close to the random matches. Thus the  sources are dominated by chance coincidence at the radius of more than 1. ′′ 0.
We did not apply any particular algorithm intended for complex and extended radio sources to our crossmatch.
About 10 % of the FIRST sources have such complex and extended morphology (Ivezić et al. 2002;Ching et al. 2017). Therefore, our cross-matching method can miss radio-AGNs without a radio-core and can misidentify radio-lobes whose position matches a HSC-SSP source by chance.

Contamination and completeness
Adopting a single search radius in the positional crossmatch produces the the contamination and completeness of the source identifications, which are estimated in the following way. A total number of matches at r s < r ′ s is represented by N tot , where r ′ s is an adopted search b The matching rate is defined by a ratio of the number of the matched sources to the number of the FIRST sources. radius. The matches by chance coincidence at r s < r ′ s , N cc , were estimated by the cross-match with the mock catalogs in the way mentioned in the previous section. The contamination is defined as a ratio of N cc to N tot . For convenience, we also defined a cleanness that is defined as (1 − contamination). A number obtained by subtracting N cc from N tot is represented by N A . We furthermore define a number of matches, N B , which is a number obtained by subtracting matches by chance coincidence at r ′ s < r s < r ′′ s from a total number of matches in this radius range. We set r ′′ s of 2. ′′ 0, where the completeness is assumed to be 100 %. Finally, the completeness is defined as a ratio of N A to a sum of N A and N B . In Figure 2, we show the cleanness and completeness as a function of r s for the Wide layer. The selection of the search radius is a trade off between the both parameters. At r s ∼ 1. ′′ 0, both parameters intersect each other. At the adopted search radius of 1. ′′ 0, the contamination by chance coincidence is estimated to be 14 %, and the completeness is estimated to be 93 % in the Wide layer. In the UD-COSMOS, while the completeness is not well determined due to the small number of matches, the contamination is 16 %.
The results of the cross-matches are summarized in Table 2. The cross-matches produced 3,579 and 63 matched sources in the Wide and the UD-COMOS layers, respectively. The matching rate, a fraction of the matched FIRST sources, are 51 % in the Wide layer. The rate increases to 59 % in the UD-COSMOS. Considering the above statistics, out of 3,579 (63) matched HSC-FIRST sources in the Wide (UD-COSMOS) layer, ∼ 3078 (53) are true optical counterparts of the FIRST sources, and ∼ 501 (∼ 10) FIRST sources are likely to be random matches. The estimated completeness implies that 3310 FIRST sources have HSC-SSP counterparts in the Wide layer, suggesting a completenesscorrected matching rate of 47 %. These rates are higher than ∼ 30 % by the previous studies using the SDSS (Ivezić et al. 2002;Helfand et al. 2015). The high matching rates with the HSC-SSP data are further discussed and compared with other studies in Section 5.3.

Extended radio sources
In order to evaluate a number of sources with extended radio morphology in the HSC-FIRST matched samples, we introduce a widely-used size measure that is a ratio of the total integrated radio flux density to the peak radio flux density, or F int /F peak (e.g., Ivezić et al. 2002;Schinnerer et al. 2007;Bondi et al. 2008;Smolčić et al. 2017a). The radio F int /F peak equals to unity for a point source, while the ratio is larger than unity for an extended source or a resolved source. In Figure 3, we show the ratio as a function of the radio S/N. All the FIRST sources (grey dots), the HSC-FIRST sources in the Wide (blue dots) and the UD-COSMOS (yellow squares) are shown. The F int /F peak values of less than 1.0 are due to their low S/N.
We consider that sources simultaneously meeting the following two criteria should be extended radio sources. First one is a threshold line described by which was empirically determined for the FIRST-SDSS study by Ivezić et al. (2002), and sources above the line were classified as radio extended sources. This is how- Figure 3. Ratio of the total flux density to the peak flux density as a function of the radio S/N. All of the FIRST sources are shown as grey dots. The HSC-FIRST matched sources in the Wide are indicated by blue dots, and that in the UD-COSMOS as yellow squares. The sources above the upper red curve and the green line are considered to be extended radio sources (see main text).
ever ineffective for the low S/N sources. For a second criteria, we determine the lower envelope (the lower red curve) of the data points in Figure 3 in the following similar way to Schinnerer et al. (2007). The envelope contains 99 % of all the FIRST sources below the F int /F peak = 1 line and was mirrored above F int /F peak = 1. The mirrored upper curve (the upper red curve) is represented as where F peak /RMS is the S/N and RMS is a local RMS noise in the FIRST catalog. Finally, we considered that the sources located above both the line of Equation 1 and the curve of Equation 2 should be radio extended sources in our samples. Consequently, 10 % (374 sources) of the HSC-FIRST Wide sample and 16 % (10 sources) of the HSC-FIRST UD-COSMOS sample are selected to be the radio extended sources. These extended sources are likely radiolobes matched by chance, FR-I RGs (Fanaroff & Riley 1974), RGs with core-jet/core-halo structures, or nearby star-forming galaxies. These fractions thus are upper limits of the numbers of chance coincidence of radiolobes, and the upper limits are compatible with the contaminations estimated in Section 3.1.

Optically unresolved sources
The optical morphologies on HSC images were examined to separate optically extended (resolved) sources and stellar-like unresolved objects using the procedure described in Akiyama et al. (2018) for distinguishing RGs and radio-loud quasars. We used a ratio of a second-order adaptive moment to that of a point spread function at a source position. Because i-band images were taken under good conditions in a preferential to the other bands, we use i-band images on this examination. The criteria for selecting stellar objects are The suffixes of 11 and 22 represent each perpendicular axis in a image. We adopted the adaptive moments of the HsmMoments algorithm (Hirata & Seljak 2003). Because only for fourteen sources whose HsmMoments measurements were failed, the alternative adaptive moments of the SdssShape algorithm (Lupton et al. 2001) were adopted. According to the examination of the classification by Akiyama et al. (2018), the completeness of this classification decreases and the contamination increases with increasing magnitude. At i = 23, the completeness is 80-90 % and the contamination is less than 5 %, while at i > 24, the completeness decreases down to < 70 % and the contamination is more than 40 %. Therefore, we consider that this classification of stellar objects is reliable for sources brighter than i = 24 mag. We introduce an optically bright subset sample of the HSC-FIRST matched sample, which have i < 24 mag. According to the classification, we found 326 and 2 stellar objects from the HSC-FIRST Wide sample and the UD-COSMOS sample, respectively. These correspond to 9.1 % and 3.2 % out of the both samples, respectively. For brevity, we refer to such stellar objects as quasars and to optically resolved sources as RGs or galaxies, despite the recognition of exceptions and uncertainties of the classification.

Astrometry
The large size of our sample provides us with an opportunity to inspect the astrometry between the HSC-SSP and FIRST sources. In Figure 4, we show the distributions of the residuals between source positions of HSC-SSP and FIRST. The residuals along right ascensions and declinations are a FIRST position minus a HSC-SSP position. We mention only results of the Wide layer because the UD-COSMOS sample is statistically too small to discuss the astrometry, but we just show the results of the UD-COSMOS sample.
The standard deviations of all the 3,579 HSC-FIRST Wide sample are 0. ′′ 34 in R.A. and 0. ′′ 37 in declination.  When we use only a bright and unresolved subsample whose sources are unresolved in radio morphology and have a radio peak flux of > 3 mJy and i magnitude of < 24, the standard deviations slightly moderate down to 0. ′′ 26 in R.A. and 0. ′′ 31 in declination. These uncertainties are still large compared with the positional uncertainty of the HSC-SSP catalog (0. ′′ 04 against Pan-STARRS1, Aihara et al. 2018b), and slightly larger than the uncertainty of the FIRST catalog (0. ′′ 2 for bright and compact sources, White et al. 1997). This is likely due to the galaxies composing almost the HSC-FIRST sample; we do not limit the sample for this inspection only to optically unresolved objects because of its quite small sample size.
We found a mean offset in R.A. of −0. ′′ 014 ± 0. ′′ 006 in all the HSC-FIRST Wide sources. However, when we use only the the bright and unresolved subsample, this systematic offset becomes 0. ′′ 004 ± 0. ′′ 009 and statistically not significant. On the other hand, the mean offset in declination is −0. ′′ 033 ± 0. ′′ 006 in all the HSC-FIRST Wide sample. This offset is still significant and is −0. ′′ 056 ± 0. ′′ 011, even if we use the bright and unre-solved subsample. Therefore, there is a systematic offset in declination of the HSC-SSP sources with respect to the FIRST position. Although this offset is significant but is smaller than the positional uncertainty of the FIRST catalog (0. ′′ 2) the search radius of 1. ′′ 0, and thus the offset has less effect on the cross-match in this work.
It may be valuable to compare the previous results of the FIRST sources with SDSS counterparts studied by Helfand et al. (2015). They reported that there are systematic offsets ∼ 0. ′′ 02 in R.A. and ∼ 0. ′′ 01 in declination of the FIRST positions with respect to both the SDSS sources and the FIRST sources that have been taken with JVLA not with VLA. Hence, taking this previous result into consideration, there might be offsets also between HSC-SSP and SDSS. From this simple comparison, we inferred systematic offsets of ∼ 0. ′′ 02 in R.A. and ∼ −0. ′′ 07 in declination from SDSS to HSC-SSP.

RADIO AND OPTICAL PROPERTIES OF HSC RADIO GALAXIES
In this section, radio and optical properties of the HSC-FIRST matched samples are described. In particular, we investigate differences between RGs and radioloud quasars, which were classified in Section 3.4. Moreover, we focus on differences between two sub-samples: the optically-faint HSC-FIRST sources (HSC-level), for which a optical counterpart is detected with HSC-SSP but is not with SDSS, and the optically-bright HSC-FIRST sources (SDSS-level), for which a optical counterpart is detected both with HSC-SSP and SDSS.

Radio source counts
Radio properties of the Wide sample are investigated using 1.4 GHz radio source counts in Figure 5. Although radio source counts are often examined on a plane of radio flux and (dN/dS)/S −2.5 , we use another plane of radio AB magnitude and N to directly compare with the results of Ivezić et al. (2002). Here radio AB magnitude is expressed as A flux density of 1 mJy is equivalent to t = 16.4. In Figure 5, the source counts of the HSC-FIRST Wide sample, the Wide RG sample, and the Wide quasar sample are shown. Their distributions at a range of 11.5 < t < 15.5 are fitted with a linear function by minimizing the chi-square statistic. The magnitude range for fitting is the same one as the analysis by Ivezić et al. (2002), whose results are also shown in Figure 5. The parameters of the best fits are summarized in Table 3. The HSC-FIRST Wide sample (square) is roughly consistent with the FIRST sources whose SDSS counterparts are identified by Ivezić et al. (2002) (the SDSS-FIRST sample, green solid line). This is trivial because the ∼ 20 % improvement of the matching rate in this study corresponds to an increase of only ∼ 0.2 dex in log N/(mag −1 deg −2 ) and a fact that FIRST sources without SDSS counterparts draw a similar slope to those with SDSS counterparts (Ivezić et al. 2002).
The HSC-FIRST quasars have a somewhat lower number than the SDSS-FIRST quasars, while the HSC-FIRST RGs increase in number, in particular, at the bright end. To investigate where does this discrepancy stem, we separate the HSC-FIRST Wide sample into a SDSS-level subsample with i < 21.3 and a HSC-level subsample with i > 21.3. The i magnitude threshold corresponds to the limiting magnitude of the SDSS survey, where the catalog is 95 % complete for point sources (Stoughton et al. 2002). The 1.4 GHz radio source counts of the two subsamples and the fitting results are shown in Figure 6 and Table 3. The slope of the HSC-level RGs is flat compared with that of the SDSSlevel RGs, while the slope of the HSC-level quasars is steeper than that of the SDSS-level quasars. Therefore, the increased number of the HSC-FIRST RGs is likely due to the different dependences of optically-faint RGs and quasars from the optically-bright sources on radio flux.
A fraction of quasars out of the SDSS-level subsample increases with increasing radio flux, from ∼ 20 % at the faint end to ∼ 60 % at the bright end. On the other hand, in the HSC-level subsample the fraction does not strongly depend on radio flux. The fraction is approximately 5 % over the radio flux range for fitting. The results in this subsection holds even if the HSC-level subsample is limited to be sources with i < 24.

Optical number counts
Thanks to the depth of the HSC-SSP data, this study has an advantage in that it is enables us to investigate optical properties of radio-AGNs down to more than 3 mag fainter in brightness than the previous SDSS studies. The i-band number counts of the HSC-FIRST Wide sample are shown in Figure 7. A fall-off of the HSC-FIRST Wide sample at the bright end (i 18) is likely due to the saturation effect of the HSC-SSP data. An absent of the HSC-FIRST Wide quasars is likely due to not only the saturation but also the rareness of radio-loud quasars. The SDSS radio-loud quasars Note-The best fit parameters of the radio source counts in Figure 5 and 6. The fitting function is log (N/[mag −1 deg −2 ]) = a + b t [AB mag]. The numbers in the parentheses represent 1σ uncertainties in the fitting results.   are actually identified even at i 18 (White et al. 2000;Ivezić et al. 2002). The i-band number counts of the SDSS radio-loud quasars overlap with that of the HSC-FIRST quasars around 18 mag (see Figure 7 in Ivezić et al. 2002). On the other hand, at the faint end at i 25, the number counts of the HSC-FIRST sources fall. The magnitude of this fall-off coincide with that of a fall-off for the HSC galaxy sample. Both fall-offs are considered to be due to the effect of the detection incompleteness of the HSC-SSP Wide data. It is presumed that the detection completeness is close to 100 % down to brighter than ∼ 24 mag because the i-band sources were detected with a SN ratio of more than ∼ 50 at 24 mag. The number counts of the HSC-FIRST sources, which are not damped down to the detection completeness magnitude, implies a possibility that there are optically much fainter radio-AGNs.
The number counts were fitted by a linear function within the 19 < i < 24 range (magenta lines in Figure 7). The flat slope of the best fit for the HSC-FIRST RGs means that their number counts do not strongly depend on the apparent optical magnitude. The flat slope also means a decreasing fraction of the optically-faint RGs to the HSC galaxies with increasing the apparent magnitude: from 0.3 % at i = 19 to 0.01 % at i = 24. The small fraction of the faint RGs might imply a small number of distant RGs and/or RGs with a less-massive host galaxy. For the HSC-FIRST quasars, there is a turnover at ∼ 21 mag. Thus, the linear function is not well fitted to the data. The fraction to the HSC-FIRST sources drops off from 11% to < 2% over the turnover magnitude. This turnover appears at ∼ 21 mag and therefore the turnover is not due to the detection com-pleteness of HSC-SSP. The FIRST detection limit, in part, may cause the turnover because the quasar sample misses optically-faint radio-loud quasars with lower radio flux than the FIRST detection limit. However, a similar turnover is not seen in the RG sample, although the effect of the FIRST detection limit should also impinge on the RG sample. This contrast means that the dependence of the number of quasars on optical magnitude is different from RGs in optically faint regime. Jiang et al. (2007) found that the radio-loud fraction of quasars decreases with decreasing luminosity and increasing redshift although their quasar sample was basically brighter than i = 18.9. The turnover in our radio-loud quasar sample, therefore, may be partially attributed to a small number of low luminosity radio-loud quasars and/or distant radio-loud quasars.

Radio loudness
Radio loudness is a measure of radio activity of AGNs and is defined as a ratio of radio flux to optical flux. The radio loudness is typically defined as a ratio of 5 GHz flux to B-band flux, and AGNs and quasars with more than log R = 1 are considered to be radio-loud (Kellermann et al. 1989). Nevertheless, in this section we use the observed-frame radio loudness, R obs , according to Ivezić et al. (2002). R obs is defined as a ratio of 1.4 GHz flux and i-band flux at observed frames without k-corrections. The k-corrected radio-loudness is discussed later (Section 5.1.3). The logarithmic R obs is described as There is probably a contamination in optical flux from stellar light of a host galaxy, in particular for RGs by its definition where RGs should have extended optical components. The contamination, if any, causes an underestimate of R obs . The R obs of the HSC-FIRST Wide and UD-COSMOS samples are shown in Figure 8. The HSC-FIRST samples obviously include higher R obs sources than the SDSS-level ones owing to the deep optical observations of HSC-SSP as we have expected. In particular, radio-AGNs with more than log R obs = 3 substantially increases in number. We note the R obs could be actually higher due to the underestimate by the contamination from host galaxies. Moreover, the R obs of the HSC-level sample is biased toward high values due to the FIRST's sensitivity. At the i-band magnitude range of the SDSS-level, the quasars abound in a high R obs regime, whereas the RGs with high R obs are at the HSC-level range. The UD-COSMOS sample, as expected, includes optically fainter radio-AGNs (i 26) than the Wide sample. However, despite the deeper depth of UD-COSMOS, the highest R obs radio-AGNs are identified in the Wide layer. This means that wide optical surveys have an advantage over deeper but narrow surveys in finding rare AGNs such as the most radio-loud AGNs. 5. DISCUSSION 5.1. Properties of HSC radio galaxies as a function of photometric redshift We have successfully identified a large number of the optically-faint optical counterparts of FIRST radio sources thanks to the wide and deep HSC-SSP survey. We reported in the previous section that these optically-faint FIRST sources show apparently high radio-loudness. In this section, we further investigate optical and radio properties of the optically-faint FIRST sources in order to understand their nature. We use photometric redshift (photo-z or z photo ) of the sample but quasars have large uncertainties in photo-z, therefore we address only RGs other than quasars.

Color-color
The redshifts of the HSC-FIRST RG samples in both the Wide and UD-COSMOS layers are examined in a color-color plane as the first step. Our RG samples are shown in the r − i and i − z color-color diagram of Figure 9. As the selection criteria have been imposed on the HSC-FIRST sample to detect in these three bands of r, i, and z, the three bands photometries are available for all the HSC-FIRST sources. The colors were compared with two color tracks of two model galaxies (Bruzual & Charlot 2003) in order to estimate their redshifts. One is a passive elliptical galaxy that has star formation history with an exponential decay time of 1 Gyr, a galaxy age of 8 Gyr, and the solar metallicity. The other is a star-forming galaxy that has an instantaneous burst, a galaxy age of 0.025 Gyr, and the solar metallicity. From Figure 9, we found that most of the sources are located along the track of the model elliptical galaxy from z ∼ 0 to z ∼ 1.

Photometric redshifts
Photo-z which were estimated using the Mizuki SED fitting code and the photometries of the five HSC-SSP bands (see Tanaka  magnitudes of sources at i < 24. On the other hand, ∼ 30 % of the faint HSC-FIRST RGs with i > 24 are not included in the photo-z sample due to their low reliability of photo-z. This bias results in a lack of 36 % among RGs with log R obs > 5. The redshifts of the photo-z sample are shown in Figure 10 and range from z photo ∼ 0 to ∼ 1.5 in both layers of Wide and UD-COSMOS. The photo-z distributions of the SDSS-level and HSC-level RGs are clearly divided into low and high redshifts, respectively. This result means that the optically faint RGs or the HSC-level RGs exist at high redshifts ( 1) rather than at the local universe as intrinsically optically-faint objects. In order to inspect the photo-z for the validity, the photo-z were compared with spectroscopically measured redshifts (spec-z or z spec ) if available. We used public spec-z catalogs from SDSS DR12 (Alam et al. 2015), GAMA DR2 (Liske et al. 2015), VIPERS PDR1 (Garilli et al. 2014), VVDS (Le Fèvre et al. 2013), Wig-gleZ DR1 (Drinkwater et al. 2010), PRIMUS DR1 (Coil et al. 2011;Cool et al. 2013), and zCOSMOS DR3 (Lilly et al. 2009). We cross-matched the public spec-z sources to the HSC-FIRST photo-z sources in positions by a 1. ′′ 0 search radius. Of the HSC-FIRST photo-z sample, 404 RGs in the Wide layer and 11 RGs in the UD-COSMOS have secure spec-z where z spec > 0, an error in z spec is greater than 0, and a homogenized quality flag of z spec determinations is secure (see Tanaka et al. 2018 for details). The optical magnitudes of the spec-z sample are limited to be i < 21.8 due to the magnitude limit of spectroscopic observations. In Figure 11, the photo-z and the spec-z are compared each other. The means and standard deviations of the relative differences between both are (z photo − z spec )/(1 + z spec ) = −0.015 ± 0.057 for the Wide sources and −0.017 ± 0.012 for the UD-COSMOS sources. As the overall trend, the photo-z is good agreement with spec-z for the i < 21.8 sources.
In order to examine the photo-z of the faint sources with i > 22.0, we utilized the photo-z (z L16 ) of the COS-MOS2015 catalog in the COSMOS field, which were estimated using thirty multi-band photometric data from ultraviolet to mid-infrared (Laigle et al. 2016). The UD-COSMOS photo-z RG sub-sample includes 44 counterparts of the COSMOS2015 sources with minimum re- Color-color diagram of r − i and i − z. The HSC-FIRST Wide RGs and UD-COSMOS RGs are shown as black circles and red circles. To estimate their redshifts, color tracks of two model galaxies are over-plotted: a passive elliptical galaxy (orange curve) and a star-forming galaxy (blue curve). Each redshift of a model track is marked by large filled symbols (see the inserted legends). Minor ticks indicated by small crosses show ∆z = 0.1 steps to be eyefriendly. Only z = 0 and 3 marks are shown in the starforming galaxy track.
duced χ 2 of SED fitting being less than 5. In Figure  12, the relative differences between z photo and z L16 for 44 matched RGs are shown as a function of z L16 . Both the photo-z are consistent with each other within 10 % up to z L16 ∼ 1.7. The standard deviation of the relative difference is 0.047 in z L16 < 1.7. At z L16 > 1.7, where the sources are fainter than i ∼ 24, the relative difference is systematically negative and is −30 % at the most. This deviation at z L16 > 1.7 is attributed to a redshifted 4000Å break beyond y-band, and therefore the photo-z of these sources can not be accurately constrained only from the photometries of the five HSC-SSP bands. These examinations show that the HSC-SSP photo-z could be secure, at least, at z photo 1.7, although the photometries of the UD-COSMOS are higher than that of the Wide layer.

Optical and radio properties
The optical luminosity and radio luminosity at the rest-frame were calculated using the photo-z for the photo-z sub-sample. In Figure 13, the calculated luminosities are shown as a function of photo-z. The 1.4 GHz radio luminosity was k-corrected with radio index of −0.7. The sources at z 1 have high 1.4 GHz luminosities compared with lower redshift sources due to a bias from the FIRST sensitivity. The rest-frame g-band absolute magnitude was estimated by the SED template fitting Mizuki (Tanaka 2015;Tanaka et al. 2018). There may be two sequences of the g magnitude along the redshifts. The bright sequence with M g −21 does not strongly depend on the redshift. On the other hand, the faint sequence seems to dramatically increase with increasing redshifts. Some sources at z 0.5 may be local galaxies with strong radio radiation from active star formation. The sources with the faint absolute magnitudes are also faint in apparent magnitudes and most of them have i > 24, and therefore the faint magnitude of some sources may be from photometric uncertainties. The optical SEDs of the HSC-SSP bands show that some sources on the faint sequence have a flat SED without distinct features and thus their redshifts are probably systematically misdiagnosed as local sources. Therefore the faint sequence could be an apparent one by both the  Figure 13. The rest-frame 1.4GHz radio luminosity (upper panel) and the absolute g-band magnitude at the rest-frame (lower panel) as a function of photo-z. Only RG sources with reliable photo-z are shown. The black circles and red circles denote the Wide and UD-COSMOS RGs, respectively. effects of misdiagnosed sources and the Malmquist bias of the HSC-SSP sensitivity limits.
Intrinsic radio loudness was estimated and is defined here as a ratio of the rest frame 1.4 GHz flux to the rest frame g-band flux. The wavelength of the rest frame g-band flux is close to the rest frame B-band, which is typically used for calculating the radio loudness. The intrinsic radio loudnesses of the SDSS-and HSC-level sources as a function of apparent i-band magnitude are shown in Figure 14. We found that the RGs with intrinsically high radio-loudness (log R rest > 3) are found in the HSC-level subsample. Certainly, there are likely also low radio-loudness RGs in the HSC-level regime, but such sources are not included due to the sensitivity limit of the FIRST survey. The radio-loudness we  Radio-loudness at the rest-frame as a function of photo-z. Only the RG sources with reliable photoz are shown. Sources at the SDSS-level and the HSC-level brightness in the Wide layer (UD-COSMOS) are represented by blue circles (dark blue squares) and orange circles (pink squares), respectively. use here is obviously affected by the contamination from host galaxies into g-band flux because we used the SED templates of galaxies for estimating the rest-frame gband flux. This results in underestimate of the radioloudness.
We show each distribution of the SDSS-and HSC-level RG samples in a R rest − z photo plane in Figure 15. We distinctly found that the optically-faint RGs (the HSClevel) have higher radio-loudnesses and photo-z than the optically-bright RGs (the SDSS-level). Again, we note that optically-faint RGs with a low radio-loudness are not detected due to the FIRST sensitivity. However, we claim that our HSC-FIRST RG sample includes a large number (∼ 2000) of the optically-faint RGs which have high radio-loudness (log R rest > 3) and redshifts of more than 1. These RGs have not been probed by SDSS.

Optical spectra and quasar/galaxy classification
We performed a quasar/galaxy classification using optical spectra in order to inspect the morphological classification based on the HSC-SSP images in Section 3.4. This inspection is based on whether a spectrum of a source that was morphologically classified as a quasar (or a galaxy) shows broad emission lines or not. We used archival spectra available from SDSS DR12 (Alam et al. 2015), GAMA PDR2 (Liske et al. 2015), and zCOSMOS (Lilly et al. 2009). In addition to the archival spectra, we also examined 18 spectra that have been recently obtained with 2dF-AAOmega installed on 3.9 m Anglo-Australian Telescope (AAO) in July 2017. See He et al. (2018, in preparation) for the details about the observation and data reduction. Finally, we inspected 622 sources in the Wide layer and 21 in the UD-COSMOS. These subsamples include sources without secure spec-z. Although this spectral inspection allows us to confirm the morphological classification using the HSC-SSP images, we should take account of the following two points. One is that the i-band magnitudes of these subsamples are biased toward a bright side and distribute from 17.4 to 22.8 in the Wide layer and from 17.7 to 21.9 in UD-COSMOS. The other is tat this spectral inspection does not distinguish between quasars and broad-line radio galaxies.
Of 622 Wide sources, we have 152 morphologically classified quasars and 470 galaxies. The inspection results show that 130 (86 %) morphologically classified quasars and 26 (5.5 %) morphologically classified galaxies show broad emission line. In the UD-COSMOS, 2 sources (100 %) among 2 morphologically classified quasars and 1 (5.3 %) among 19 morphologically classified galaxies show broad emission line. Therefore, at i 23, there could be 5 % contaminations of quasars in both the morphologically-classified RG samples of the Wide layer and UD-COSMOS. Examples of four types of spectra, a quasar with/without broad emission lines and a galaxy with/without broad emission lines, are shown in Figure 16 Figure 16.
Examples of optical spectra of HSC-FIRST sources. Four types of spectra are shown: a morphologicallyclassified quasar with broad emission lines (top left), a morphologically-classified galaxy with broad emission lines (top right), a morphologically-classified quasar without broad emission lines (bottom left), and a morphologically-classified galaxy without broad emission lines (bottom right). Two spectra were obtained with AAO (He et al. 2018, in preparation) and others were taken from SDSS DR12.
Our study using the Subaru HSC-SSP catalog has successfully identified the optical counterparts of 51 % and 59 % among the FIRST sources in the HSC-SSP Wide layer and UD-COSMOS, respectively. These matching rates are significantly higher than ∼ 30 % matching rates of the SDSS-based studies by Ivezić et al. (2002), Helfand et al. (2015), and Ching et al. (2017). Although the adopted search radii are different between the studies, even if we use the completeness-corrected matching rate, our result (47 % in the Wide layer) is still higher than the corrected-rate of 31 % in Ivezić et al. (2002). It is clear that the improved matching rate is due to the utilization of the deep optical catalog compared with the previous studies, from Figure 7, 8, and 14. This interpretation is supported by the higher matching rate of 59 % in UD-COSMOS, which have fainter HSC-SSP sources than the Wide layer.
However, approximately 40 % of FIRST sources in the HSC-SSP unmasked region still have no optical counterparts within 1 ′′ from their positions. Our sample criteria of S/N > 5 in r, i, and z likely miss a certain fraction of HSC-SSP sources with an extremely red color at the faint end, such as high-z red galaxies. Other un-matched FIRST sources are roughly grouped into two types from the inspections of their HSC-SSP images. One is a radio source with bright radio companion(s) close to it. These sources are likely radio lobes associated with low-z RGs. The other radio sources only have a single radio component. These optical counterparts may be extremely faint in optical (i < 26), such as radio-AGNs with a quite low accretion rate, obscured AGNs, radio-AGNs in less-massive host galaxies, or high redshifted objects.

SUMMARY
We presented results of the exploration of radio-AGNs using the Subaru HSC-SSP catalog and the FIRST VLA catalog. This is the initial result of the on-going project, WERGS. The positional cross-match between HSC-SSP and FIRST produced 3579 and 63 optical counterparts of the FIRST radio sources in the Wide layer and UD-COSMOS, respectively. These numbers of the matched counterparts correspond to more than 50 % of the FIRST radio sources in the search fields, showing a much higher matching rate than the previous studies of optically bright SDSS-FIRST sources (i < 21).
We reported the properties in optical and radio wavelength of the matched HSC-FIRST sources. Among the HSC-FIRST sources, 9 % in the Wide and 3 % in UD-COSMOS are optically unresolved sources, that is likely radio-loud quasars. The i-band number counts show the flat slope down to 24 mag, implying the unfalling number of either less-massive or distant radio-AGNs. The optically faint sources show the different slopes of the 1.4 GHz source counts from the bright sources with i < 21.3. Almost all the photometric redshifts of the sub-sample with available redshift data ranges up to 1.5. In particular, the optically faint sources are distributed around redshift of 1. The comparison of the color-color diagram with the galaxy model also shows the similar redshift distribution to the photometric one and most of the sources are consistent with redshifted early-type galaxies although there are the large dispersion. Thanks to the deep and wide HSC-SSP survey, we found the large number of the sources with high radioloudness (log R > 3) in the optically faint regime. Such sources are distributed at z 1.
We also showed that the rare objects such as sources with the highest radio-loudness were found in the wide and shallow field (the Wide layer) rather than the small and deep field (UD-COSMOS). Together with the result of the high matching rates, these results demonstrated the advantages of our project over the previous radio-AGN searches in terms of both sides of the deep optical depth (i < 26) and the wide search field (more than 150 deg 2 ).

COUNTING FIRST SOURCES ON THE UN-MASKED HSC-SSP REGIONS
In order to count a number of FIRST sources on the HSC-SSP regions correctly, we have to consider to FIRST sources lying on the masked HSC-SSP regions and count only the FIRST sources on the un-masked HSC-SSP regions. The masked regions result from the selection of the clean HSC-SSP sample. The flags in the masked regions are described in mask images by bitmask of a integer value (see Bosch et al. 2018 for details). Regions with the following bitmasks are considered as masked regions corresponding to the sample selection criteria described in Section 2.1: BAD (a sensor defect), BRIGHT_OBJECT (a regions near a very bright object), CR (a cosmic ray), EDGE (the edge of a CCD or coadded patch), INTRP (a interpolated pixel), SAT (a saturated pixel), and SUSPECT (a pixel value above the level where the linearity correction is reliable).
There are originally 8282 (118) FIRST sources in the HSC-SSP Wide layer (UD-COSMOS) defined in Table 1 before any masks are performed. These numbers were FIRST sources which have the nearest HSC-SSP sources within 20 ′′ for the purpose of excluding FIRST sources on the patches with poor photometries (see Section 2.1) and counting FIRST sources in UD-COSMOS. After masking, we obtained 7072 and 106 FIRST sources in the un-masked regions of the Wide layer and UD-COSMOS, respectively.