The Spectro-Photometer for the History of the Universe, Epoch of Reionization and Ices Explorer (SPHEREx) will provide all-sky spectral survey data covering optical to mid-infrared wavelengths with a spatial resolution of 6.′′2, which can be widely used to study galaxy formation and evolution. We investigate the galaxy-galaxy blending in SPHEREx datasets using the mock galaxy catalogs generated from cosmological simulations and observational data. Only ∼0.7% of the galaxies will be blended with other galaxies in all-sky survey data with a limiting magnitude of 19 AB mag. However, the fraction of blended galaxies dramatically increases to ∼7–9% in the deep survey area around the ecliptic poles, where the depth reaches ∼22 AB mag. We examine the impact of the blending in the number count and luminosity function analyses using the SPHEREx data. We find that the number count can be overestimated by up to 10–20% in the deep regions due to the flux boosting, suggesting that the impact of galaxy-galaxy blending on the number count is moderate. However, galaxy-galaxy blending can marginally change the luminosity function by up to 50% over a wide range of redshifts. As we only employ the magnitude limit at Ks-band for the source detection, the blending fractions determined in this study should be regarded as lower limits.

Using I-band images of 35 nearby (z < 0.1) type 1 active galactic nuclei (AGNs) obtained with Hubble Space Telescope, selected from the 70-month Swift-BAT X-ray source catalog, we investigate the photometric properties of the host galaxies. With a careful treatment of the point-spread function (PSF) model and imaging decomposition, we robustly measure the I-band brightness and the effective radius of bulges in our sample. Along with black hole (BH) mass estimates from single-epoch spectroscopic data, we present the relation between BH mass and I-band bulge luminosity (MBH–MI,bul relation) of our sample AGNs. We find that our sample lies offset from the MBH–MI,bul relation of inactive galaxies by 0.4 dex, i.e., at a given bulge luminosity, the BH mass of our sample is systematically smaller than that of inactive galaxies. We also demonstrate that the zero point offset in the MBH–MI,bul relation with respect to inactive galaxies is correlated with the Eddington ratio. Based on the Kormendy relation, we find that the mean surface brightness of ellipticals and classical bulges in our sample is comparable to that of normal galaxies, revealing that bulge brightness is not enhanced in our sample. As a result, we conclude that the deviation in the MBH–MI,bul relation from inactive galaxies is possibly because the scaling factor in the virial BH mass estimator depends on the Eddington ratio.

Reverberation mapping (RM) is an ecient method to investigate the physical sizes of the broad line region (BLR) and dusty torus in an active galactic nucleus (AGN). The Spectro-Photometer for the History of the Universe, Epoch of Reionization and Ices Explorer (SPHEREx) mission will provide multi-epoch spectroscopic data at optical and near-infrared wavelengths. These data can be used for RM experiments with bright AGNs. We present results of a feasibility test using SPHEREx data in the SPHEREx deep regions for torus RM measurements. We investigate the physical properties of bright AGNs in the SPHEREx deep eld. Based on this information, we compute the eciency of detecting torus time lags in simulated light curves. We demonstrate that, in combination with complementary optical data with a depth of  20 mag in B􀀀band, lags of  750 days for tori can be measured for more than  200 bright AGNs. If high signal-to-noise ratio photometric data with a depth of  21{22 mag are available, RM measurements are possible for up to  900 objects. When complemented by well-designed early optical observations, SPHEREx can provide a unique dataset for studies of the physical properties of dusty tori in bright AGNs.