Cosmic star formation history revealed by AKARI and Hyper Suprime-Cam

Cosmic star formation history revealed by AKARI and Hyper Suprime-Cam

Tomotsugu Goto    Nagisa Oi    Rieko Momose    Ece Kilerci Eser    Hideo Matsuhara    Ting-Chi Huang    Yousuke Utsumi    Yoshiki Toba    Youichi Ohyama    Toshinobu Takagi    Takehiko Wada    Matthew Malkan    Seong Jin Kim    Takao Nakagawa    the AKARI team

Understanding infrared (IR) luminosity is fundamental to understanding the cosmic star formation history and AGN evolution, since their most intense stages are often obscured by dust. Japanese infrared satellite, AKARI, provided unique data sets to probe this both at low and high redshift; the AKARI all sky survey in 6 bands (9-160 m), and the AKARI NEP survey in 9 bands (2-24m).

The AKARI performed all sky survey in 6 IR bands (9, 18, 65, 90, 140, and 160 m) with 3-10 times better sensitivity than IRAS, covering the crucial far-IR wavelengths across the peak of the dust emission. Combined with a better spatial resolution, we measure the total infrared luminosity () of individual galaxies, and thus, the total infrared luminosity density of the local Universe much more precisely than previous work.

In the AKARI NEP wide field, AKARI has obtained deep images in the mid-infrared (IR), covering 5.4 deg. However, our previous work was limited to the central area of 0.25 deg due to the lack of deep optical coverage. To rectify the situation, we used the newly advent Subaru telescope’s Hyper Suprime-Cam to obtain deep optical images over the entire 5.4 deg of the AKARI NEP wide field. With this deep and wide optical data, we, for the first time, can use the entire AKARI NEP wide data to construct restframe 8m, 12m, and total infrared (TIR) luminosity functions (LFs) at 0.152.2. A continuous 9-band filter coverage in the mid-IR wavelength (2.4, 3.2, 4.1, 7, 9, 11, 15, 18, and 24m) by the AKARI satellite allowed us to estimate restframe 8m and 12m luminosities without using a large extrapolation based on a SED fit, which was the largest uncertainty in previous work.

By combining these two results, we reveal dust-hidden cosmic star formation history and AGN evolution from z=0 to z=2.2, all probed by the AKARI satellite.


National Tsing hua University, No. 101, Section 2, Kuang-Fu Road, Hsinchu, Taiwan 30013 \move@AU\move@AF\@affiliationTokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan \move@AU\move@AF\@affiliationNational Tsing hua University, No. 101, Section 2, Kuang-Fu Road, Hsinchu, Taiwan 30013 \move@AU\move@AF\@affiliationNational Tsing hua University, No. 101, Section 2, Kuang-Fu Road, Hsinchu, Taiwan 30013 \move@AU\move@AF\@affiliationInstitute of Space and Astronautical Science, Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuo, Sagamihara, Kanagawa 252-5210, Japan \move@AU\move@AF\@affiliationNational Tsing hua University, No. 101, Section 2, Kuang-Fu Road, Hsinchu, Taiwan 30013 \move@AU\move@AF\@affiliationKavli Institute for Particle Astrophysics and Cosmology (KIPAC), SLAC National Accelerator Laboratory, Stanford University, SLAC, 2575 Sand Hill Road, Menlo Park, CA 94025, USA \move@AU\move@AF\@affiliationAcademia Sinica Institute of Astronomy and Astrophysics, P.O. Box 23-141, Taipei 10617, Taiwan \move@AU\move@AF\@affiliationAcademia Sinica Institute of Astronomy and Astrophysics, P.O. Box 23-141, Taipei 10617, Taiwan \move@AU\move@AF\@affiliationJapan Space Forum, 3-2-1, Kandasurugadai, Chiyoda-ku, Tokyo 101-0062 Japan \move@AU\move@AF\@affiliationInstitute of Space and Astronautical Science, Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuo, Sagamihara, Kanagawa 252-5210, Japan \move@AU\move@AF\@affiliationDepartment of Physics and Astronomy, UCLA, Los Angeles, CA, 90095-1547, USA \move@AU\move@AF\@affiliationNational Tsing hua University, No. 101, Section 2, Kuang-Fu Road, Hsinchu, Taiwan 30013 \move@AU\move@AF\@affiliationInstitute of Space and Astronautical Science, Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuo, Sagamihara, Kanagawa 252-5210, Japan

1 Local IR LF from AKARI all sky survey

Local infrared (IR) luminosity functions (LFs) are necessary benchmarks for high-redshift IR galaxy evolution studies. Any accurate IR LF evolution studies require accordingly accurate local IR LFs.

We construct infrared galaxy LFs at redshifts of from AKARI space telescope, which performed an all-sky survey in six IR bands (9, 18, 65, 90, 140 and 160 m) with 3-10 times better sensitivity than its precursor IRAS. Availability of 160 m filter is critically important in accurately measuring total IR luminosity of galaxies, covering across the peak of the dust emission. By combining mid-IR data from Wide-field Infrared Survey Explorer (WISE), and spectroscpic redshifts from Sloan Digital Sky Survey (SDSS) Data Release 13 (DR13), 6-degree Field Galaxy Survey (6dFGS) and the 2MASS Redshift Survey (2MRS), we created a sample of 15,638 local IR galaxies with spectroscopic redshifts, by a factor of 20 larger compared with well-cited previous work based on IRAS data (Sanders et al., 2003a), which was also limited to 100 m.

After carefully correcting for volume effects in both IR and optical, we show obtained IR LFs in Fig. 1, which agree well with previous studies, but comes with much smaller errors. Especially both faint- and bright-ends of the LFs are better-determined, due to much larger size of the spectroscpic redshifts and the IR photometry.

Measured local IR luminosity density is Mpc. The contributions from luminous infrared galaxies and ultra luminous infrared galaxies to are very small, 9.3 per cent and 0.9 per cent, respectively. There exists no future all sky survey in far-infrared wavelengths in the foreseeable future. The IR LFs obtained in this work will therefore remain an important benchmark for high-redshift studies for decades. See more details in Kilerci Eser & Goto (2017).


figure \hyper@makecurrentfigure

Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefThe IR LF of 15,638 AKARISDSS6dFGS2MRS galaxies (open circles). The best-fitting double power law is shown as solid line. For comparison the total IR LF derived from the IRAS RBGS is shown (crosses Sanders et al., 2003b).The red diamonds are the data points of the RBGS sample adopted from Goto et al. (2011a).The dashed magenta line is the best-fitting double power law when the RBGS data are included in the fit.

2 High-z IR LFs from the AKARI NEP wide field

2.1 Undetected AKARI sources

The extragalactic background suggests at least half the energy generated by stars has been reprocessed into the infrared (IR) by dust (Lagache et al., 1999). At z1.3, 90% of star formation is obscured by dust (Le Floc’h et al., 2005; Goto et al., 2010a, 2015). Therefore, a full understanding of the cosmic star formation history inevitably needs an IR perspective, especially at high redshifts.

The AKARI space telescope has performed a deep mid-infrared imaging survey in the NEP region (Lee et al., 2009). We are studying the multi-band data of these mid-IR galaxies as shown in Table 1 (Takagi et al., 2010; Goto et al., 2010a). However, because very dusty objects cannot be detected in the relatively shallow CFHT imaging data (25.9ABmag; Oi et al., 2014), there remain 11,000 AKARI sources undetected in the optical. As a result, we lack understanding of the redshift and IR luminosity of these sources, i.e., they have been excluded from the past cosmic star formation history (CSFH) analysis. These sources could change our view of CSFH—if they all lie at 12, they will the cosmic star formation density at that epoch.

2.2 Uniqueness of AKARI mid-IR data

The AKARI NEP is one of the best fields for this investigation, due to the availability of continuous 9-band mid-IR filters. Spitzer lacks filters between 8 and 24m (the critical wide gap between IRAC and MIPS, excluding the tiny IRS peak up array at 16 m). Similarly WISE also has a wide gap between 4 and 12m filters. Therefore, no other telescope can provide continuous 9-band photometry in mid-IR wavelength (2-24m) over 5.4 deg, until JWST performs a similar survey. JWST will also require a large amount of telescope time to survey 5.4 deg. AKARI’s continuous 9-band photometry works as a low-resolution spectrum, which is critically important for the following key aspects:

  • Two physical processes produce the mid-IR emission: hot dust around an AGN, and PAH emission from star-formation. Quantitatively separating these is of fundamental importance. The continuous 9 filters of AKARI have made this possible through precise SED fitting (See examples in Takagi et al., 2010; Karouzos et al., 2014). Importantly, this is independent of extinction.

  • Accurately measuring the mid-IR emission line strength (PAH 7.7 m) and continuum luminosity. Using the 9-band photometry as a low-resolution spectra, Ohyama et al. (2017, submitted) demonstrated that photometric PAH 7.7 m line measurements agree well with spectroscopic ones.

Neither of these is possible if there is a large gap between mid-IR filters. Therefore, AKARI NEP is the only field, where the two different astrophysical power sources can be separated for thousands of IR galaxies, including those with heavy extinction.

The AKARI NEP also has been thoroughly observed in every other available waveband (Table 1), making it one of the premier large deep fields on the sky. Its large area overcomes the serious problem of cosmic variance, which hampered previous IR CSFH studies. In particular, Spitzer’s CDFS field was only deg (Le Floc’h et al., 2005), and measured an IR luminosity density nearly a factor of 10 different from other Spitzer fields (e.g., Babbedge et al., 2006). For the same reason, the single Suprime-Cam pointing in the center of the NEP deep field ( deg) is not wide enough. A large volume coverage also allows us to study environmental effects on galaxy evolution (Koyama et al., 2008; Goto et al., 2010b). AKARI was a survey telescope, which observed 5.4 deg in NEP using % of the entire pointed observations available throughout the lifetime of the mission, providing uniquely precious space-based IR data spanning a large enough area to overcome cosmic variance.

2.3 Subaru Hyper Suprime-Cam Observation

However, previously, we only had deep optical images in the central 0.25 deg, while previous AKARI’s mid-IR data exist in much larger field of 5.4 deg. Therefore, our previous work also suffered from the cosmic variance.

To rectify the situation, we carried out an optical survey of the AKARI NEP wide field using Subaru’s new Hyper Suprime-Cam (HSC; Miyazaki et al., 2012). The HSC has a field-of-view (FoV) of 1.5 deg in diameter, covered with 104 red-sensitive CCDs. It has the largest FoV among optical cameras on an 8m telescope, and can cover the AKARI NEP wide field (5.4 deg) with only 4 FoV (the left panel of Fig.2.3).

Our immediate aim of the optical survey is to detect all AKARI sources in the optical, with photometry accurate enough for reliable photometric redshifts. This allows us to determine the optical and IR luminosities (corresponding to direct and dust-obscured emission) from young stars and accreting massive black holes for a large sample representative of the cosmic history of the Universe.

Our proposal to the Subaru telescope was accepted twice (PI Goto). In 2014, we were limited to the -band observation due to unexpected unavailability of the filter stacker of HSC caused by the instrument troubles propagated from the telescope chiller trouble. We observed in in 7 FoVs with sets of 5 point dithering pattern with the seeing of 1.5”.

In 2016, we obtained data in the remaining filters in 4 FoV covering the NEP wide field. The 5 sigma limiting magnitudes are 27.18, 26.71, 26.10, 25.26, and 24.78 mag [AB] in , and -bands, respectively. See Oi et al. in this volume for more details of the observation and data reduction.


table \hyper@makecurrenttable


Table 0. \Hy@raisedlink\hyper@@anchor\@currentHrefSummary of AKARI NEP survey data

Observatory Band Sensitivity/Number of objects/exposure time Area (deg)
AKARI/IRC 2.5-24m =18.5AB 5.4
Subaru/S-Cam =27.4AB 0.25
Subaru/FOCAS optical spect., 57 sources in NEP AB
MMT6m optical spec. 1800 obj 5.4
KPNO-2.1m 21.6,21.3 5.4
Maidanak 1.5m =23.1 3.4
KPNO2m/FLAMINGOS =21.6, =21.3 5.4
WSRT 20cm 100 Jy 0.25
VLA-archive 10cm 200 Jy 5.4
GMRT 610MHz 60-80 Jy 0.25
Keck/Deimos optical spec. 1000 obj 0.25
Subaru/FMOS near-IR spec. 700 obj 0.25
Herschel 100,160 m 5-10 mJy 0.5
Herschel 250-500 m 10 mJy 7.1
Chandra X-ray 30-80ks 0.25
SCUBA2 submm 1mJy 0.25
CFHT/MegaCam AB 4
Subaru/HSC =27.2(Fig.2.3) 5.4

2.4 Cfht -band observation

Subaru telescope does not have a -band imaging capability, while it is critically important to accurately estimate photometric redshifts of low-z galaxies. Therefore, we obtained -band image of the AKARI NEP wide field using the Megaprime camera of Canada France Hawaii Telescope (CFHT, PI:T.Goto). See more details of the observation and data reduction in Appendix.

2.5 Photometric redshift

Using CFHT -band, and HSC -bands data, we calculated photometric redshifts with the LePhare code (Arnouts et al., 2007). We used the COSMOS galaxy library for SED fitting (Ilbert et al., 2009). Extinction law from Calzetti et al. (2005) was applied in the SED fitting. Also, we adopted the function AUTOADAPT in LePhare to adjust magnitude zero points. In the SED fitting, we used 29 bands in maximum from the following instruments, GALEX (), CFHT (), HSC (), AKARI (), WISE ([3.4],[4.6],[12],[22]), Spitzer ([3.6],[4.5],[5.8],[8.0],[24]), Herschel (). Note not all data are available for all the AKARI sources.

By comparing with spectroscopic redshifts, we examine the accuracy of photo-z. The is defined to be the standard deviation of for ¡ 0.15, where the z is and z and z are the photometric and spectroscopic redshifts, respectively. The fraction of the objects with 0.15 is defined to be the catastrophic rate . The main result is shown in the right panel of Fig. 2.3. The (, ) are (0.038, 17.6), (0.039, 21.6), and (0.036, 12.4) for the whole sample, the sample without -band (red), and the sample with -band, respectively. The -band data improve both and .

2.6 Analysis

We compute LFs using the 1/ method, as in Goto et al. (2010a, 2015). Uncertainties of the LF values stem from various factors such as fluctuations in the number of sources in each luminosity bin, the photometric redshift uncertainties, the -correction uncertainties, and the flux errors. To compute the errors of LFs we performed Monte Carlo simulations by creating 1000 simulated catalogs. Each simulated catalog contains the same number of sources, but we assigned a new redshift to each source, by following a Gaussian distribution centered at the photometric redshift with the measured dispersion . The flux of each source is also changed; the new fluxes vary according to the measured flux error following a Gaussian distribution.

For the 8m and the 12m LFs, we can ignore the errors due to the -correction thanks to the continuous AKARI MIR filter coverage. The TIR LF errors are estimated by re-performing the SED fitting for each of the 1000 simulated catalogs.

We did not consider the uncertainty related to cosmic variance here since our field coverage has been significantly improved. For our analysis, each redshift bin covers Mpc of volume, which is large enough to avoid significant effect from the cosmic variance. See Matsuhara et al. (2006) for more discussion on the cosmic variance in the NEP field.

All the other errors described above are added to the Poisson errors for each LF bin in quadrature.

2.7 Results: High-z IR LFs

2.7.1 The 8m LF

Monochromatic 8m luminosity () is known to correlate well with the TIR luminosity (Babbedge et al., 2006; Huang et al., 2007; Goto et al., 2011c), especially for star-forming galaxies, because the rest-frame 8m flux is dominated by prominent PAH (polycyclic aromatic hydrocarbon) features such as those at 6.2, 7.7, and 8.6 m.

Since AKARI has continuous coverage in the mid-IR wavelength range, the restframe 8m luminosity can be obtained without a large uncertainty in -correction at the corresponding redshift and filter. For example, at =0.375, restframe 8m is redshifted into filter. Similarly, and cover restframe 8m at =0.775, 1.25 and 2. This filter coverage is an advantage with AKARI data. Often in previous work, SED models were used to extrapolate from Spitzer 24m fluxes, producing the largest uncertainty. This is not the case for the analysis present in this paper.

To obtain the restframe 8m LF, we used sources down to 80% completeness limits in each band as measured in Kim et al. (2012). We excluded those galaxies whose SEDs are better fit with QSO templates. This removed 2% of galaxies from the sample.

We used the completeness curve presented in Kim et al. (2012) to correct for the incompleteness of the detections. However, this correction is 25% at maximum, since our sample is brighter than the 80% completeness limits. Our main conclusions are not affected by this incompleteness correction. To compensate for the increasing uncertainty at increasing , we use four redshift bins of 0.280.47, 0.650.90, 1.091.41, and 1.782.22. Within each redshift bin, we use the 1/ method to compensate for the flux limit in each filter.

We show the computed restframe 8m LF in the left panel of Fig. 2.7.1. The arrows mark the 8m luminosity corresponding to the flux limit at the central redshift in each redshift bin. Errorbars on each point are based on the Monte Carlo simulation, and are smaller than in our previous work (Goto et al., 2010a). To compare with previous work, the dark-yellow dot-dashed line also shows the 8m LF of star-forming galaxies at by Huang et al. (2007), using the 1/ method applied to the IRAC 8m GTO data. Compared to the local LF, our 8m LFs show strong evolution in luminosity.

2.8 12m LF

The 12m luminosity () has been well studied through ISO and IRAS. It is known to correlate closely with the TIR luminosity (Spinoglio et al., 1995; Pérez-González et al., 2005). As was the case for the 8m LF, it is advantageous that AKARI’s continuous filters in the mid-IR allow us to estimate restframe 12m luminosity without much extrapolation based on SED models.

At targeted redshifts of =0.25, 0.5, and 1, the and filters cover the restframe 12m, respectively. The methodology is the same as for the 8m LF; we used the sample down to the 80% completeness limit, corrected for the incompleteness, then used the 1/ method to compute the LF in each redshift bin. The resulting 12m LF is shown in the right panel of Fig. 2.7.1. The light green dash-dotted line shows 12m LF based on 893 galaxies at in the IRAS Faint Source Catalog (Rush et al., 1993). The dark green dash-dotted line shows 12m LF at based on 223,982 galaxies from WISE sources in Table 7 of Toba et al. (2014). Compared with these =0 LFs, the 12m LFs show steady evolution with increasing redshift.

2.9 Total IR LFs

AKARI’s continuous mid-IR coverage is also superior for SED-fitting to estimate . This is because for star-forming galaxies, the mid-IR part of the IR SED is dominated by the PAH emission lines, which reflect the SFR of galaxies (Genzel et al., 1998), and thus, correlates well with , which is also a good indicator of the galaxy SFR.

After photometric redshifts are estimated using the UV-optical-NIR photometry, we fix the redshift at the photo-, then use the same LePhare code to fit the infrared part of the SED to estimate TIR luminosity. We used Lagache et al. (2003)’s SED templates to fit the photometry using the AKARI bands at 6m ( and ).

In the mid-IR, color-correction could be large when strong PAH emissions shift into the bandpass (a factor of 3). However, during the SED fitting, we integrate the flux over the bandpass weighted by the response function. Therefore, we do not use the flux at a fixed wavelength. As such, the color-correction is negligible in our process (a few percent at most).

Galaxies in the targeted redshift range are best sampled in the 18m band due to the wide bandpass of the filter (Matsuhara et al., 2006). Therefore, we applied the 1/ method using the detection limit at . We also checked that using the flux limit does not change our main results. The same Lagache et al. (2003)’s models are also used for -corrections necessary to compute and . The redshift bins used are 0.20.5, 0.50.8, 0.81.2, and 1.21.6.

The obtained LFs are shown in the left panel of Fig. 2.9. The uncertainties are estimated through the Monte Carlo simulations (2.6). For a local benchmark, we overplot Kilerci Eser & Goto (2017) from the AKARI all sky survey in  1. The TIR LFs show a strong evolution compared to local LFs.

2.10 Total IR Luminosity density

One of the important purposes in computing IR LFs is to estimate the IR luminosity density, which in turn is an extinction-free estimator of the cosmic star formation density (Kennicutt, 1998). We estimate the total infrared luminosity density by integrating the LF weighted by the luminosity. First, we need to convert to the total infrared luminosity.

A strong correlation between and total infrared luminosity () has been reported in the literature (Caputi et al., 2007; Bavouzet et al., 2008). Using a large sample of 605 galaxies detected in the far-infrared by the AKARI all sky survey, Goto et al. (2011b) estimated the best-fit relation between and as


The is based on AKARI’s far-IR photometry in 65,90,140, and 160 m, and the measurement is based on AKARI’s 9m photometry. Given the superior statistics and availability over longer wavelengths (140 and 160m), we used this equation to convert into .

The 12m is one of the most frequently used monochromatic fluxes to estimate . The total infrared luminosity can be computed from the using the conversion in Chary & Elbaz (2001); Pérez-González et al. (2005).


The 8, 12m and total LFs are weighted by the and integrated to obtain the TIR density. For integration, we first fitted an analytical function to the LFs.

In this work, a double-power law is fitted to the lowest redshift LF to determine the normalization () and slopes (). For higher redshifts we do not have enough statistics to simultaneously fit 4 parameters (, , , and ). Therefore, we fixed the slopes and normalization at the local values and varied only for the higher-redshift LFs. Fixing the faint-end slope is a common procedure with the depth of current IR satellite surveys (Babbedge et al., 2006; Caputi et al., 2007). The stronger evolution in luminosity than in density found by previous work (Pérez-González et al., 2005; Le Floc’h et al., 2005) also justifies this parametrization.

The best-fit power-laws are shown with dotted-lines in Figs. 2.7.1 and 2.9. Once the best-fit parameters are found, we integrate the double power law outside the luminosity range in which we have data to estimate the TIR luminosity density, . In the right panel of Fig. 2.9, we plot estimated from the TIR LFs (red circles), 8m LFs (brown stars), and 12m LFs (pink filled triangles). All our measurements show a strong evolution as a function of redshift.

We also plot the contributions to from LIRGs (Luminous InfraRed Galaxies; ) and ULIRGs (Ultra-Luminous InfraRed Galaxies; , measured from TIR LFs), with the blue open squares and orange filled squares, respectively. Both LIRGs and ULIRGs show a strong redshift evolution.


TG acknowledges the support by the Ministry of Science and Technology of Taiwan through grant 105-2112-M-007-003-MY3.



A Appendix: CFHT -band observation and data reduction


table \hyper@makecurrenttable

Table 0. \Hy@raisedlink\hyper@@anchor\@currentHrefThe configuration of extraction and photomety used for generating the CFHT -band catalogue

Parameter Value
FILTERNAME gauss3.07x7.conv
GAIN 0.0

Here we summarize our CFHT -band observation and data reduction. The purpose of the -band observation is to provide a -band catalogue in AKARI NEP wide field and then estimate accurate photometric redshifts with the aid of the -band magnitude. The Megaprime -band ranges from 3235Å to 4292Å with the effective wavelength at 3827.2Å. The observations were carried out in two time periods from 2015 May 22nd to 26th, and from 2016 July 6th to 7th (PI: T.Goto). There are 66 frames in total, which cover the 4.5 deg of AKARI NEP field. The exposure time is 300 second for each frame. Megaprime has 40 CCDs with 2048 4612 pixels for each. The pixel scale is 0.185 arcsec per pixel.

We used the Elixir pipeline to reduce our raw -band data. We masked bad pixels, bias structures and corrected for flat-fields. The pipeline had some problem with removing overscan regions, so we manually wrote a script to remove them. The zero point magnitude measured for camera runs are 25.188 and 25.121.

To create a coadded image, we utilized AstrOmatic softwares including SExtractor, SCAMP and SWarp. First, we used SExtractor to extract sources and performed photometry. Second, SCAMP help us with astrometric calibration. In this process, we used 2MASS -band observation as a reference catalogue for astrometry. Third, we coadd images from each frames by SWarp. Each pixel value is the median of every combined pixels. We include background subtraction with mesh size of 128 pixels. Last but not least, we ran SExtractor again on the final coadded image to obtain the -band catalogue. The configuration of extraction and photometry is listed in Table A. We cross-matched the -band catalogue with the Subaru HSC catalogue in the AKARI NEP field by matching celestial coordinate within 1 arcsec tolerance radius.

The magnitude is calculated by the following equation. {align*} m = &-2.5 ×log(data number) + 2.5 ×log(exposure time)+ m_0 + K ×(airmass -1) The is the zero point magnitude with value 25.121. The is a coefficient for airmass term correction, of which value is . Finally, we calibrated the -band magnitude with the -band of the AKARI NEP deep field, which is a 0.6 deg sub-region of the AKARI NEP field (Oi et al., 2014).


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