ner_tags: O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O B-Survey B-CelestialRegion I-CelestialRegion O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion I-CelestialRegion O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion I-CelestialRegion O B-Citation I-Citation I-Citation I-Citation O O O O O O B-CelestialRegion I-CelestialRegion O B-Citation I-Citation
tokens: Finally, we computed the cumulative number of sources, N (> S ), brighter than a given flux ( S ) in each X-ray band. To this aim, we computed the sky coverage (i.e., the sky area Ω covered as a function of the flux limit) of the J1030 field to correct the incompleteness of our catalog. We computed our sky-coverage by dividing the number of output sources flagged as “good” in our simulations by the number of input sources as a function of input flux and then multiplying for the total geometric area of the J1030 field covered by Chandra . The sky-coverage values were then fitted with a spline to obtain a smooth monotonically increasing function. The sky coverage in the full, soft, and hard bands are plotted in Fig. 11 . The derived flux limits over the central ∼1 arcmin 2 region are ∼3 × 10 −16 , 6 × 10 −17 , and 2 × 10 −16 erg cm −2 s −1 in the full, soft, and hard bands, respectively, making the deep Chandra survey in the SDSS J1030+0524 field the fifth deepest X-ray survey field achieved so far (see Fig. 1 for area-flux curve comparison with other surveys). Once the sky coverage is known, the cumulative source number was computed using the equation: Fig. 11. Sky coverage (i.e., sky area vs. flux limit relation) in the full (black solid line), soft (red dashed line), and hard (blue dash-dotted line) bands derived from our simulations. The horizontal cyan dotted line represents the total geometric area of our J1030 field (335 arcmin 2 ). where N S is the total number of detected sources in the field with fluxes higher than S , and Ω i is the sky coverage associated with the flux of the i th source. The three log( N )–log( S ) relations in the three X-ray bands are reported in Fig. 12 . The red points represent the cumulative number of sources of our J1030 field, while the log( N )–log( S ) of our mock catalog are shown as the blue dot-dashed line. For comparison, we also plotted the log( N )–log( S ) relations found in the 7 Ms (magenta line) Chandra Deep Field-South by Luo et al. (2017) , and the log( N )–log( S ) relation (green solid line) found in the COSMOS field by Civano et al. (2016) . From Fig. 12 we conclude that the log( N )–log( S ) relations derived in the J1030 field are in general agreement with those from the literature. Besides cosmic variance, we caution that some of the differences among the log( N )–log( S ) seen in Fig. 12 could be produced by systematic uncertainties in the different methods used to derive the sky coverage and the individual source fluxes in the various surveys. Fig. 12. Cumulative number counts (number of sources brighter than a given flux) for the main source catalog (red dots) in the full ( top ), soft ( middle ), and hard ( bottom ) bands. The blue dot-dashed line represents the cumulative number of sources from our mock catalog. For comparison, we plot the log( N )–log( S ) relations found in the 7 Ms Chandra Deep Field-South by Luo et al. (2017 , magenta line), and in the COSMOS field by Civano et