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Toshinobu Takagi

Publications and source records attributed to Toshinobu Takagi.

At least 19 recordsLinked to original sources

The Calibration of Polycyclic Aromatic Hydrocarbon Dust Emission as a Star Formation Rate Indicator in the AKARI NEP Survey

Polycyclic aromatic hydrocarbon (PAH) dust emission has been proposed as an effective extinction-independent star formation rate (SFR) indicator in the mid-infrared (MIR), but this may depend on conditions in the interstellar medium. The coverage of the AKARI/Infrared Camera (IRC) allows us to study the effects of metallicity, starburst intensity, and active galactic nuclei on PAH emission in galaxies with $f_ν(L18W)\lesssim 19$ AB mag. Observations include follow-up, rest-frame optical spectra of 443 galaxies within the AKARI North Ecliptic Pole survey that have IRC detections from 7-24 $μ$m. We use optical emission line diagnostics to infer SFR based on H$α$ and [O II]$λλ3726,3729$ emission line luminosities. The PAH 6.2 $μ$m and PAH 7.7 $μ$m luminosities ($L(PAH\ 6.2\ μm)$ and $L(PAH\ 7.7\ μm)$, respectively) derived using multi-wavelength model fits are consistent with those derived from slitless spectroscopy within 0.2 dex. $L(PAH\ 6.2\ μm)$ and $L(PAH\ 7.7\ μm)$ correlate linearly with the 24 $μ$m-dust corrected H$α$ luminosity only for normal, star-forming ``main-sequence" galaxies. Assuming multi-linear correlations, we quantify the additional dependencies on metallicity and starburst intensity, which we use to correct our PAH SFR calibrations at $0<z<1.2$ for the first time. We derive the cosmic star formation rate density (SFRD) per comoving volume from $0.15 \lesssim z \lesssim 1$. The PAH SFRD is consistent with that of the far-infrared and reaches an order of magnitude higher than that of uncorrected UV observations at $z\sim1$. Starburst galaxies contribute $\gtrsim 0.7$ of the total SFRD at $z\sim1$ compared to main-sequence galaxies.

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New methods for ALMA angular-scale based observation scheduling, quality assessment, and beam shaping II: refinements

The Atacama Large Millimeter/submillimeter Array remains the largest mm radio interferometer observatory world-wide. It is now conducting its 11th observing cycle. In our previous paper presented at this conference series in 2020, we outlined a number of possible improvements to the ALMA end-to-end observing and data processing procedures which could further optimize the uv coverage and thus the image quality while at the same time improving the observing efficiency. Here we report an update of our results refining our proposed adjustments to the scheduling and quality assurance processes. In particular we present new results on ways to assess the uv coverage of a given observation efficiently, methods to define and measure the maximum recoverable angular scale, and on the robustness of the deconvolution in the final interferometric imaging process w.r.t. defects in the uv coverage. Finally we present the outline of a design for integrating uv coverage assessment into the control and processing loop of observation scheduling. The results are applicable to all radio interferometers with more than approx. 10 antennas.

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Data Combination: Interferometry and Single-dish Imaging in Radio Astronomy

Modern interferometers routinely provide radio-astronomical images down to subarcsecond resolution. However, interferometers filter out spatial scales larger than those sampled by the shortest baselines, which affects the measurement of both spatial and spectral features. Complementary single-dish data are vital for recovering the true flux distribution of spatially resolved astronomical sources with such extended emission. In this work, we provide an overview of the prominent available methods to combine single-dish and interferometric observations. We test each of these methods in the framework of the CASA data analysis software package on both synthetic continuum and observed spectral data sets. We develop a set of new assessment tools that are generally applicable to all radio-astronomical cases of data combination. Applying these new assessment diagnostics, we evaluate the methods' performance and demonstrate the significant improvement of the combined results in comparison to purely interferometric reductions. We provide combination and assessment scripts as add-on material. Our results highlight the advantage of using data combination to ensure high-quality science images of spatially resolved objects.

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Metallicity-PAH Relation of MIR-selected Star-forming Galaxies in AKARI North Ecliptic Pole-wide Survey

We investigate the variation in the mid-infrared spectral energy distributions of 373 low-redshift ($z<0.4$) star-forming galaxies, which reflects a variety of polycyclic aromatic hydrocarbon (PAH) emission features. The relative strength of PAH emission is parameterized as $q_\mathrm{PAH}$, which is defined as the mass fraction of PAH particles in the total dust mass. With the aid of continuous mid-infrared photometric data points covering 7-24$μ$m and far-infrared flux densities, $q_\mathrm{PAH}$ values are derived through spectral energy distribution fitting. The correlation between $q_\mathrm{PAH}$ and other physical properties of galaxies, i.e., gas-phase metallicity ($12+\mathrm{log(O/H)}$), stellar mass, and specific star-formation rate (sSFR) are explored. As in previous studies, $q_\mathrm{PAH}$ values of galaxies with high metallicity are found to be higher than those with low metallicity. The strength of PAH emission is also positively correlated with the stellar mass and negatively correlated with the sSFR. The correlation between $q_\mathrm{PAH}$ and each parameter still exists even after the other two parameters are fixed. In addition to the PAH strength, the application of metallicity-dependent gas-to-dust mass ratio appears to work well to estimate gas mass that matches the observed relationship between molecular gas and physical parameters. The result obtained will be used to calibrate the observed PAH luminosity-total infrared luminosity relation, based on the variation of MIR-FIR SED, which is used in the estimation of hidden star formation.

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ALMA [O III] and [C II] Detections of A1689-zD1 at $z=7.13$

A1689-zD1 is one of the most distant galaxies, discovered with the aid of gravitational lensing, providing us with an important opportunity to study galaxy formation in the very early Universe. In this study, we report the detection of [C II]158$μ$m and [O III]88$μ$m emission lines of A1689-zD1 in the ALMA Bands 6 and 8. We measure the redshift of this galaxy as $z_{\rm{sys}}=7.133\pm0.005$ based on the [C II] and [O III] emission lines, consistent with that adopted by Bakx et al. (2021). The observed $L_{[\rm{O\,III]}}/L_{[\rm{C\,II]}}$ ratio is $2.09\pm0.09$, higher than most of the local galaxies, but consistent with other $z\sim7$ galaxies. The moderate-spatial resolution of ALMA data provided us with a precious opportunity to investigate spatial variation of $L_{[\rm{O\,III]}}/L_{[\rm{C\,II]}}$. In contrast to the average value of 2.09, we find a much higher $L_{[\rm{O\,III]}}/L_{[\rm{C\,II]}}$ of $\sim 7$ at the center of the galaxy. This spatial variation of $L_{[\rm{O\,III]}}/L_{[\rm{C\,II]}}$ was seldom reported for other high-z galaxies. It is also interesting that the peak of the ratio does not overlap with optical peaks. Possible physical reasons include a central AGN, shock heating from merging, and starburst. Our moderate-spatial resolution data also reveals that in addition to the observed two clumps shown in previous HST images, there is a redshifted segment to the west of the northern optical clump. Such a structure is consistent with previous claims that A1689-zD1 is a merging galaxy, but with the northern redshifted part being some ejected materials, or that the northern redshifted materials being from a third more highly obscured region of the galaxy.

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The evolution of merger fraction of galaxies at z < 0.6 depending on the star formation mode in the AKARI NEP Wide field

We study the galaxy merger fraction and its dependence on star formation mode in the5.4 square degrees of the North Ecliptic Pole-Wide field. We select 6352 galaxies withAKARI 9μm detections, and identify mergers among them using the Gini coefficientand M20derived from the Subaru/HSC optical images. We obtain the total infraredluminosity and star formation rate of galaxies using the spectral energy distributiontemplates based on one band, AKARI 9μm. We classify galaxies into three differentstar formation modes (i.e. starbursts, main sequence, and quiescent galaxies) andcalculate the merger fractions for each. We find that the merger fractions of galaxiesincrease with redshift atz<0.6. The merger fractions of starbursts are higher thanthose of main sequence and quiescent galaxies in all redshift bins. We also examinethe merger fractions of far-infrared detected galaxies which have at least one detectionfromHerschel/SPIRE. We find thatHerscheldetected galaxies have higher mergerfraction compared to non-Herscheldetected galaxies, and bothHerscheldetected andnon-Herscheldetected galaxies show clearly different merger fractions depending onthe star formation modes.

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Instability analysis for spiral arms of local galaxies: M51, NGC3627 and NGC628

We investigate dynamical states of grand-design spiral arms in three local galaxies: M51, NGC3627 and NGC628. Based on linear perturbation analysis considering multiple components in the galaxies, we compute instability parameters of the spiral arms using their observational data and argue whether the arms will fragment by their self-gravity. Our analysis utilises observations of carbon monoxide (CO), 21-centimetre line emission and multi-band photometric images for molecular gas, atomic gas and stellar components in the arms, respectively. We find that the grand-design arms of these galaxies indicate marginally stable states, and hence they are not on the way to fragment. We consider this to be consistent with the commonness of spiral galaxies and the relative rarity of fragmented discs at low redshifts. In the analysis, molecular gas is the dominant component to determine the (in)stability of the arms, whereas atomic gas and stars are far less important. Therefore, the results of our analysis are sensitive to an assumed CO-to-H$_{\rm 2}$ conversion factor. If we assume a typical scatter of the measurements and admit nearly twice as large a conversion factor as our fiducial value, our analysis results in predicting the instability for the spiral arms. More sophisticated determination of the conversion factor is required for more accurate analysis for the (in)stability of spiral arms.

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Identification of AKARI infrared sources by Deep HSC Optical Survey: Construction of New Band-Merged Catalogue in the NEP-Wide field

The north ecliptic pole (NEP) field is a natural deep field location for many satellite observations. It has been targeted manytimes since it was surveyed by the AKARI space telescope with its unique wavelength coverage from the near- to mid-infrared(mid-IR). Many follow-up observations have been carried out and made this field one of the most frequently observed areas witha variety of facilities, accumulating abundant panchromatic data from X-ray to radio wavelength range. Recently, a deep opticalsurvey with the Hyper Suprime-Cam (HSC) at the Subaru telescope covered the NEP-Wide (NEPW) field, which enabled us toidentify faint sources in the near- and mid-IR bands, and to improve the photometric redshift (photo-z) estimation. In this work,we present newly identified AKARI sources by the HSC survey, along with multi-band photometry for 91,861 AKARI sourcesobserved over the NEPW field. We release a new band-merged catalogue combining various photometric data from GALEXUV to the submillimetre (sub-mm) bands (e.g., Herschel/SPIRE, JCMT/SCUBA-2). About 20,000 AKARI sources are newlymatched to the HSC data, most of which seem to be faint galaxies in the near- to mid-infrared AKARI bands. This cataloguemotivates a variety of current research, and will be increasingly useful as recently launched (eROSITA/ART-XC) and futurespace missions (such as JWST, Euclid, and SPHEREx) plan to take deep observations in the NEP field.

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Search for Optically Dark Infrared Galaxies without Counterparts of Subaru Hyper Suprime-Cam in the AKARI North Ecliptic Pole Wide Survey Field

We present the physical properties of AKARI sources without optical counterparts in optical images from the Hyper Suprime-Cam (HSC) on the Subaru telescope. Using the AKARI infrared (IR) source catalog and HSC optical catalog, we select 583 objects that do not have HSC counterparts in the AKARI North Ecliptic Pole (NEP) wide survey field ($\sim 5$ deg$^{2}$). Because the HSC limiting magnitude is deep ($g_{\rm AB}$ $\sim 28.6$), these are good candidates for extremely red star-forming galaxies (SFGs) and/or active galactic nuclei (AGNs), possibly at high redshifts. We compile multi-wavelength data out to 500 $μ$m and use it for Spectral Energy Distribution (SED) fitting with CIGALE to investigate the physical properties of AKARI galaxies without optical counterparts. We also compare their physical quantities with AKARI mid-IR selected galaxies with HSC counterparts. The estimated redshifts of AKARI objects without HSC counterparts range up to $z\sim 4$, significantly higher than that of AKARI objects with HSC counterparts. We find that: (i) 3.6 $-$ 4.5 $μ$m color, (ii) AGN luminosity, (iii) stellar mass, (iv) star formation rate, and (v) $V$-band dust attenuation in the interstellar medium of AKARI objects without HSC counterparts are systematically larger than those of AKARI objects with counterparts. These results suggest that our sample includes luminous, heavily dust-obscured SFGs/AGNs at $z\sim 1-4$ that are missed by previous optical surveys, providing very interesting targets for the coming James Webb Space Telescope era.

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Torus Constraints in ANEPD-CXO245: A Compton-thick AGN with Double-Peaked Narrow Lines

We report on the torus constraints of the Compton-thick AGN with double-peaked optical narrow line region (NLR) emission lines, ANEPD-CXO245, at z=0.449 in the AKARI NEP Deep Field. The unique infrared data on this field, including those from the nine-band photometry over 2-24 $μ$m with the AKARI Infrared Camera (IRC), and the X-ray spectrum from Chandra allow us to constrain torus parameters such as the torus optical depth, X-ray absorbing column, torus angular width ($σ$) and viewing angle ($i$). We analyze the X-ray spectrum as well as the UV-optical-infrared spectral energy distribution (UOI-SED) with clumpy torus models in X-ray (XCLUMPY; Tanimoto et al. 2019) and infrared (CLUMPY; Nenkova et al. 2008) respectively. From our current data, the constraints on $σ$--$i$ from both X-rays and UOI show that the line of sight crosses the torus as expected for a type 2 AGN. We obtain a small X-ray scattering fraction (<0.1%), which suggests narrow torus openings, giving preference to the bi-polar outflow picture of the double-peaked profile. Comparing the optical depth of the torus from the UOI-SED and the absorbing column density $N_{\rm H}$ from the X-ray spectrum, we find that the gas-to-dust ratio is $\gtrsim 4$ times larger than the Galactic value.

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AGN selection in the AKARI NEP deep field with the fuzzy SVM algorithm

The aim of this work is to create a new catalog of reliable AGN candidates selected from the AKARI NEP-Deep field. Selection of the AGN candidates was done by applying a fuzzy SVM algorithm, which allows to incorporate measurement uncertainties into the classification process. The training dataset was based on the spectroscopic data available for selected objects in the NEP-Deep and NEP-Wide fields. The generalization sample was based on the AKARI NEP-Deep field data including objects without optical counterparts and making use of the infrared information only. A high quality catalog of previously unclassified 275 AGN candidates was prepared.

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Infrared luminosity functions based on 18 mid-infrared bands: revealing cosmic star formation history with AKARI and Hyper Suprime-Cam

Much of the star formation is obscured by dust. For the complete understanding of the cosmic star formation history (CSFH), infrared (IR) census is indispensable. AKARI carried out deep mid-infrared observations using its continuous 9-band filters in the North Ecliptic Pole (NEP) field (5.4 deg$^2$). This took significant amount of satellite's lifetime, $\sim$10\% of the entire pointed observations. By combining archival Spitzer (5 bands) and WISE (4 bands) mid-IR photometry, we have, in total, 18 band mid-IR photometry, which is the most comprehensive photometric coverage in mid-IR for thousands of galaxies. However previously, we only had shallow optical imaging ($\sim$25.9ABmag) in a small area of 1.0 deg$^2$. As a result, there remained thousands of AKARI's infrared sources undetected in optical. Using the new Hyper Suprime-Cam on Subaru telescope, we obtained deep enough optical images of the entire AKARI NEP field in 5 broad bands ($g\sim$27.5mag). These provided photometric redshift, and thereby IR luminosity for the previously undetected faint AKARI IR sources. Combined with the accurate mid-IR luminosity measurement, we constructed mid-IR LFs, and thereby performed a census of dust-obscured CSFH in the entire AKARI NEP field. We have measured restframe 8$μ$m, 12$μ$m luminosity functions (LFs), and estimated total infrared LFs at 0.35$<$z$<$2.2. Our results are consistent with our previous work, but with much reduced statistical errors thanks to the large area coverage of the new data. We have possibly witnessed the turnover of CSFH at $z\sim$2.

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

Understanding infrared (IR) luminosity is fundamental to understanding the cosmic star formation history and AGN evolution. 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 $μ$m), and the AKARI NEP survey in 9 bands (2-24$μ$m). The AKARI performed all sky survey in 6 IR bands (9, 18, 65, 90, 140, and 160 $μ$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 ($L_{TIR}$) 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$^2$. However, our previous work was limited to the central area of 0.25 deg$^2$ 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$^2$ 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 8$μ$m, 12$μ$m, and total infrared (TIR) luminosity functions (LFs) at 0.15$<z<$2.2. A continuous 9-band filter coverage in the mid-IR wavelength (2.4, 3.2, 4.1, 7, 9, 11, 15, 18, and 24$μ$m) by the AKARI satellite allowed us to estimate restframe 8$μ$m and 12$μ$m 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.

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North Ecliptic Pole multi-wavelength survey : new optical data with Hyper Suprime-Cam and near-future prospects with eROSITA

The AKARI North Ecliptic Pole (NEP) survey consists of two survey projects: NEP-Deep (0.5 sq.deg) and NEP-Wide (5.4 sq.deg), providing with tens of thousands of galaxies. A continuous filter coverage in the mid-infrared wavelengths (7, 9, 11, 15, 18 and 24 $μ$m) is unique to diagnose the contributions from dusty star-formation activity and AGNs. Here we present current status focused on the newly obtained optical images and near-future prospects with a new X-ray telescope. Hyper Suprime-Cam on Subaru telescope is a gigantic optical camera with huge Field of View (FoV). Thanks to the wide FoV, we successfully obtained deep optical images at g, r, i, z and Y-bands covering most of the NEP-Wide field. Using the deep optical images, we identified over 5000 optical counterparts of the mid-IR sources, presumably deeply obscured galaxies in NEP-Wide field. We also investigated properties of these infrared sources with SED-fitting. eROSITA, to be launched early 2018, is a new all-sky X-ray survey telescope, and expected to conduct ultra deep 2-10 keV imaging toward NEP. We expect unprecedentedly numerous Compton-thick AGN candidates when combined with the multi-wavelength data in NEP region.

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Evolution of mid-infrared galaxy luminosity functions from the entire AKARI NEP-Deep field with new CFHT photometry

We present infrared galaxy luminosity functions (LFs) in the AKARI North Ecliptic Pole (NEP) deep field using recently-obtained, wider CFHT optical/near-IR images. AKARI has obtained deep images in the mid-infrared (IR), covering 0.6 deg$^2$ of the NEP deep field. However, our previous work was limited to the central area of 0.25 deg$^2$ due to the lack of optical coverage of the full AKARI NEP survey. To rectify the situation, we recently obtained CFHT optical and near-IR images over the entire AKARI NEP deep field. These new CFHT images are used to derive accurate photometric redshifts, allowing us to fully exploit the whole AKARI NEP deep field. AKARI's deep, continuous filter coverage in the mid-IR wavelengths (2.4, 3.2, 4.1, 7, 9, 11, 15, 18, and 24$μ$m) exists nowhere else, due to filter gaps of other space telescopes. It allows us to estimate restframe 8$μ$m and 12$μ$m luminosities without using a large extrapolation based on spectral energy distribution (SED) fitting, which was the largest uncertainty in previous studies. Total infrared luminosity (TIR) is also obtained more reliably due to the superior filter coverage. The resulting restframe 8$μ$m, 12$μ$m, and TIR LFs at $0.15<z<2.2$ are consistent with previous works, but with reduced uncertainties, especially at the high luminosity-end, thanks to the wide field coverage. In terms of cosmic infrared luminosity density ($Ω_{\mathrm{IR}}$), we found that the $Ω_{\mathrm{IR}}$ evolves as $\propto (1+z)^{4.2\pm 0.4}$.

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The AKARI 2.5-5.0 Micron Spectral Atlas of Type-1 Active Galactic Nuclei: Black Hole Mass Estimator, Line Ratio, and Hot Dust Temperature

We present 2.5-5.0 $μ$m spectra of 83 nearby ($0.002\,<\,z\,<\,0.48$) and bright ($K<14$mag) type-1 active galactic nuclei (AGNs) taken with the Infrared Camera (IRC) on board $\it{AKARI}$. The 2.5-5.0 $μ$m spectral region contains emission lines such as Br$β$ (2.63 $μ$m), Br$α$ (4.05 $μ$m), and polycyclic aromatic hydrocarbons (PAH; 3.3 $μ$m), which can be used for studying the black hole (BH) masses and star formation activities in the host galaxies of AGNs. The spectral region also suffers less dust extinction than in the ultra violet (UV) or optical wavelengths, which may provide an unobscured view of dusty AGNs. Our sample is selected from bright quasar surveys of Palomar-Green (PG) and SNUQSO, and AGNs with reverberation-mapped BH masses from Peterson et al. (2004). Using 11 AGNs with reliable detection of Brackett lines, we derive the Brackett-line-based BH mass estimators. We also find that the observed Brackett line ratios can be explained with the commonly adopted physical conditions of the broad line region (BLR). Moreover, we fit the hot and warm dust components of the dust torus by adding photometric data of SDSS, 2MASS, $\it{WISE}$, and $\it{ISO}$ to the $\it{AKARI}$ spectra, finding hot and warm dust temperatures of $\sim1100\,\rm{K}$ and $\sim220\,\rm{K}$, respectively, rather than the commonly cited hot dust temperature of 1500 K.

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ANIR : Atacama Near-Infrared Camera for the 1.0-m miniTAO Telescope

We have developed a near-infrared camera called ANIR (Atacama Near-InfraRed camera) for the University of Tokyo Atacama Observatory 1.0m telescope (miniTAO) installed at the summit of Cerro Chajnantor (5640 m above sea level) in northern Chile. The camera provides a field of view of 5'.1 $\times$ 5'.1 with a spatial resolution of 0".298 /pixel in the wavelength range of 0.95 to 2.4 $μ$m. Taking advantage of the dry site, the camera is capable of hydrogen Paschen-$α$ (Pa$α$, $λ=$1.8751 $μ$m in air) narrow-band imaging observations, at which wavelength ground-based observations have been quite difficult due to deep atmospheric absorption mainly from water vapor. We have been successfully obtaining Pa$α$ images of Galactic objects and nearby galaxies since the first-light observation in 2009 with ANIR. The throughputs at the narrow-band filters ($N1875$, $N191$) including the atmospheric absorption show larger dispersion (~10%) than those at broad-band filters (a few %), indicating that they are affected by temporal fluctuations in Precipitable Water Vapor (PWV) above the site. We evaluate the PWV content via the atmospheric transmittance at the narrow-band filters, and derive that the median and the dispersion of the distribution of the PWV are 0.40+/-0.30 mm for $N1875$ and 0.37+/-0.21 mm for $N191$, which are remarkably smaller (49+/-38% for $N1875$ and 59+/-26% for $N191$) than radiometry measurements at the base of Cerro Chajnantor (5100 m alt.). The decrease in PWV can be explained by the altitude of the site when we assume that the vertical distribution of the water vapor is approximated at an exponential profile with scale heights within 0.3-1.9 km (previously observed values at night). We thus conclude that miniTAO/ANIR at the summit of Cerro Chajnantor indeed provides us an excellent capability for a "ground-based" Pa$α$ observation.

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Ground-based Pa$α$ Narrow-band Imaging of Local Luminous Infrared Galaxies I: Star Formation Rates and Surface Densities

Luminous infrared galaxies (LIRGs) are enshrouded by a large amount of dust, produced by their active star formation, and it is difficult to measure their activity in the optical wavelength. We have carried out Pa$α$ narrow-band imaging observations of 38 nearby star-forming galaxies including 33 LIRGs listed in $IRAS$ RBGS catalog with the Atacama Near InfraRed camera (ANIR) on the University of Tokyo Atacama Observatory (TAO) 1.0 m telescope (miniTAO). Star formation rates (SFRs) estimated from the Pa$α$ fluxes, corrected for dust extinction using the Balmer Decrement Method (typically $A_V$ $\sim$ 4.3 mag), show a good correlation with those from the bolometric infrared luminosity of $IRAS$ data within a scatter of 0.27 dex. This suggests that the correction of dust extinction for Pa$α$ flux is sufficient in our sample. We measure the physical sizes and the surface density of infrared luminosities ($Σ_{L(\mathrm{IR})}$) and $SFR$ ($Σ_{SFR}$) of star-forming region for individual galaxies, and find that most of the galaxies follow a sequence of local ultra luminous or luminous infrared galaxies (U/LIRGs) on the $L(\mathrm{IR})$-$Σ_{L(\mathrm{IR})}$ and $SFR$-$Σ_{SFR}$ plane. We confirm that a transition of the sequence from normal galaxies to U/LIRGs is seen at $L(\mathrm{IR})=8\times10^{10}$ $L_{\odot}$. Also, we find that there is a large scatter in physical size, different from those of normal galaxies or ULIRGs. Considering the fact that most of U/LIRGs are merging or interacting galaxies, this scatter may be caused by strong external factors or differences of their merging stage.

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