arXiv subjects

Ryu Makiya

Publications and source records attributed to Ryu Makiya.

At least 19 recordsLinked to original sources

arXiv2025

Cosmic Infrared Background Tomography and a Census of Cosmic Dust and Star Formation

The cosmic far-infrared background (CIB) encodes dust emission from all galaxies and carries valuable information on structure formation, star formation, and chemical enrichment across cosmic time. However, its redshift-dependent spectrum remains poorly constrained due to line-of-sight projection effects. We address this by cross-correlating 11 far-infrared intensity maps spanning a 50-fold frequency range from Planck, Herschel, and IRAS, with spectroscopic galaxies and quasars from SDSS I-IV tomographically. We mitigate foregrounds using CSFD, a CIB-free Milky Way dust map. These cross-correlation amplitudes on two-halo scales trace bias-weighted CIB redshift distributions and collectively yield a $60σ$ detection of the evolving CIB spectrum, sampled across hundreds of rest-frame frequencies over $0 < z < 4$. We break the bias-intensity degeneracy by adding monopole information from FIRAS+Planck. The recovered spectrum reveals a dust temperature distribution that is broad, spanning the full range of host environments, and moderately evolving. Using low-frequency CIB amplitudes, we constrain cosmic dust density, $Ω_{\rm dust}$, which peaks at $z = 1$-$1.5$ and declines threefold to the present. Our broad spectral coverage enables a determination of the total infrared luminosity density to 0.04 dex statistical precision, tracing star-formation history with negligible cosmic variance across 90% of cosmic time. We find that cosmic star formation is 80% dust-obscured at $z = 0$ and 60% at $z = 4$. Our results, based on intensity mapping, are complete, requiring no extrapolation to faint galaxies or low-surface-brightness components. We release our tomographic CIB spectrum and redshift distributions as a public resource for future studies of the CIB, both as a cosmological matter tracer and CMB foreground.

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arXiv2023

Uchuu-$ν^2$GC galaxies and AGN: Cosmic variance forecasts of high-redshift AGN for JWST, Euclid, and LSST

Measurements of the luminosity function of active galactic nuclei (AGN) at high redshift ($z\gtrsim 6$) are expected to suffer from field-to-field variance, including cosmic and Poisson variances. Future surveys, such as those from the Euclid telescope and James Webb Space Telescope (JWST), will also be affected by field variance. We use the Uchuu simulation, a state-of-the-art cosmological $N$-body simulation with 2.1 trillion particles in a volume of $25.7~\mathrm{Gpc}^3$, combined with a semi-analytic galaxy and AGN formation model, to generate the Uchuu-$ν^2$GC catalog, publicly available, that allows us to investigate the field-to-field variance of the luminosity function of AGN. With this Uchuu-$ν^2$GC model, we quantify the cosmic variance as a function of survey area, AGN luminosity, and redshift. In general, cosmic variance decreases with increasing survey area and decreasing redshift. We find that at $z\sim6-7$, the cosmic variance depends weakly on AGN luminosity. This is because the typical mass of dark matter haloes in which AGN reside does not significantly depend on luminosity. Due to the rarity of AGN, Poisson variance dominates the total field-to-field variance, especially for bright AGN. We also examine the effect of parameters related to galaxy formation physics on the field variance. We discuss uncertainties present in the estimation of the faint-end of the AGN luminosity function from recent observations, and extend this to make predictions for the expected number of AGN and their variance for upcoming observations with Euclid, JWST, and the Legacy Survey of Space and Time (LSST).

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arXiv2022

Cosmic evolution of grain size distribution in galaxies using the $ν^2$GC semi-analytic model

We investigate the cosmological evolution of interstellar dust with a semi-analytical galaxy formation model ($ν^2$GC), focusing on the evolution of grain size distribution. The model predicts the statistical properties of dust mass and grain size distribution in galaxies across cosmic history. We confirm that the model reproduces the relation between dust-to-gas ratio and metallicity in the local Universe, and that the grain size distributions of the Milky Way (MW)-like sample become similar to the so-called MRN distribution that reproduces the observed MW extinction curve. Our model, however, tends to overpredict the dust mass function at the massive end at redshift $z\lesssim 0.8$ while it reproduces the abundance of dusty galaxies at higher redshifts. We also examine the correlation between grain size distribution and galaxy properties (metallicity, specific star formation rate, gas fraction, and stellar mass), and observe a clear trend of large-grain-dominated, small-grain-dominated, and MRN-like grain size distributions from unevolved to evolved stages. As a consequence, the extinction curve shapes are flat, steep, and intermediate (MW-like) from the unevolved to evolved phases. At a fixed metallicity, the grain size distribution tends to have larger fractions of small grains at lower redshift; accordingly, the extinction curve tends to be steeper at lower redshift. We also predict that supersolar-metallicity objects at high redshift have flat extinction curves with weak 2175 Åbump strength.

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arXiv2022

Mitigating the impact of fiber assignment on the measurement of galaxy-lensing cross correlation

We examine the impact of fiber assignment on the measurement of galaxy clustering and its cross correlation with weak lensing fields. Unlike the past spectroscopic galaxy surveys such as Baryon Oscillation Spectroscopic Survey (BOSS), currently ongoing spectroscopic galaxy surveys such as Prime Focus Spectrograph (PFS) and Dark Energy Spectroscopic Instrument (DESI) suffer from the fiber assignment artifacts more severely because there are more target galaxies than available fibers. The previous studies found that the fiber assignment suppresses the amplitude of the galaxy power spectrum at all scales. We newly find that the fiber assignment introduces the artificial correlation of structure at different redshifts, which suppresses the amplitude of the galaxy-lensing cross power spectrum. We show that the fiber assignment effects on the cross power spectrum can be mitigated at all scales with accuracy better than $\sim 1\%$, by up-weighting observed galaxies with the probability to be observed. This is not the case for the galaxy power spectrum, which is not fully corrected at $k \gtrsim 0.2$ [$h$/Mpc]. We find that the galaxy-lensing cross power spectrum is not affected by the pairwise probability of galaxies to be observed, and thus the correction method based on the individual probability is sufficient at all scales.

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arXiv2021

Ray-tracing log-normal simulation for weak gravitational lensing: application to the cross-correlation with galaxies

We present an algorithm to self-consistently generate mock weak gravitational lensing convergence fields and galaxy distributions in redshift space. We generate three-dimensional cosmic density fields that follow a log-normal distribution, and ray-trace them to produce convergence maps. As we generate the galaxy distribution from the same density fields in a manner consistent with ray-tracing, the galaxy-convergence cross-power spectrum measured from the mock agrees with the theoretical expectation with high precision. We use this simulation to forecast the quality of galaxy-shear cross-correlation measurements from the Subaru Hyper Suprime-Cam (HSC) and Prime Focus Spectrograph (PFS) surveys. We find that the nominal HSC and PFS surveys would detect the cross power spectra with signal-to-noise ratios of 20 and 5 at the lowest ($z = 0.7$) and highest ($z = 2.2$) redshift bins, respectively.

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arXiv2021

The thermal and gravitational energy densities in the large-scale structure of the Universe

As cosmic structures form, matter density fluctuations collapse gravitationally and baryonic matter is shock-heated and thermalized. We therefore expect a connection between the mean gravitational potential energy density of collapsed halos, $Ω_{W}^{\rm halo}$, and the mean thermal energy density of baryons, $Ω_{\rm th}$. These quantities can be obtained using two fundamentally different estimates: we compute $Ω_{W}^{\rm halo}$ using the theoretical framework of the halo model which is driven by dark matter statistics, and measure $Ω_{\rm th}$ using the Sunyaev-Zeldovich (SZ) effect which probes the mean thermal pressure of baryons. First, we derive that, at the present time, about 90% of $Ω_{W}^{\rm halo}$ originates from massive halos with $M>10^{13}\,M_\odot$. Then, using our measurements of the SZ background, we find that $Ω_{\rm th}$ accounts for about 80% of the kinetic energy of the baryons available for pressure in halos at $z\lesssim 0.5$. This constrains the amount of non-thermal pressure, e.g., due to bulk and turbulent gas motion sourced by mass accretion, to be about $Ω_{\rm non-th}\simeq 0.4\times 10^{-8}$ at $z=0$.

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arXiv2020

The Cosmic Thermal History Probed by Sunyaev-Zeldovich Effect Tomography

The cosmic thermal history, quantified by the evolution of the mean thermal energy density in the universe, is driven by the growth of structures as baryons get shock heated in collapsing dark matter halos. This process can be probed by redshift-dependent amplitudes of the thermal Sunyaev-Zeldovich (SZ) effect background. To do so, we cross-correlate eight sky intensity maps in the $\it{Planck}$ and Infrared Astronomical Satellite missions with two million spectroscopic redshift references in the Sloan Digital Sky Surveys. This delivers snapshot spectra for the far-infrared to microwave background light as a function of redshift up to $z\sim3$. We decompose them into the SZ and thermal dust components. Our SZ measurements directly constrain $\langle bP_{\rm e} \rangle$, the halo bias-weighted mean electron pressure, up to $z\sim 1$. This is the highest redshift achieved to date, with uncorrelated redshift bins thanks to the spectroscopic references. We detect a threefold increase in the density-weighted mean electron temperature $\bar{T}_{\rm{e}}$ from $7\times 10^5~{\rm K}$ at $z=1$ to $2\times 10^6~{\rm K}$ today. Over $z=1$-$0$, we witness the build-up of nearly $70\%$ of the present-day mean thermal energy density $ρ_{\rm{th}}$, with the corresponding density parameter $Ω_{\rm th}$ reaching $1.5 \times10^{-8}$. We find the mass bias parameter of $\it{Planck}$'s universal pressure profile of $B=1.27$ (or $1-b=1/B=0.79$), consistent with the magnitude of non-thermal pressure in gas motion and turbulence from mass assembly. We estimate the redshift-integrated mean Compton parameter $y\sim1.2\times10^{-6}$, which will be tested by future spectral distortion experiments. More than half of which originates from the large-scale structure at $z<1$, which we detect directly.

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arXiv2020

Quantifying the effect of field variance on the H$α$ luminosity function with the New Numerical Galaxy Catalogue ($ν^2$GC)

We construct a model of H$α$ emitters (HAEs) based on a semi-analytic galaxy formation model, the New Numerical Galaxy Catalog ($ν^2$GC). In this paper, we report our estimate for the field variance of the HAE distribution. By calculating the H$α$ luminosity from the star-formation rate of galaxies, our model well reproduces the observed H$α$ luminosity function (LF) at $z=0.4$. The large volume of the $ν^2$GC makes it possible to examine the spatial distribution of HAEs over a region of (411.8 Mpc)$^3$ in the comoving scale. The surface number density of $z=0.4$ HAEs with $L_{\rm Hα} \geq 10^{40}$ erg s$^{-1}$ is 308.9 deg$^{-2}$. We have confirmed that the HAE is a useful tracer for the large-scale structure of the Universe because of their significant overdensity ($>$ 5$σ$) at clusters and the filamentary structures. The H$α$ LFs within a survey area of $\sim$2 deg$^2$ (typical for previous observational studies) show a significant field variance up to $\sim$1 dex. Based on our model, one can estimate the variance on the H$α$ LFs within given survey areas.

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arXiv2020

New constraints on the mass bias of galaxy clusters from the power spectra of the thermal Sunyaev-Zeldovich effect and cosmic shear

Thermal Sunyaev-Zeldovich (tSZ) power spectrum is a powerful probe of the present-day amplitude of matter density fluctuations, and has been measured up to $\ell\approx 10^3$ from the {\it Planck} data. The largest systematic uncertainty in the interpretation of this data is the so-called "mass bias" parameter $B$, which relates the true halo mass to the mass proxy used by the {\it Planck} team as $M_{\rm 500c}^{Planck}=M_{\rm 500c}^{\rm true}/B$. Since the power spectrum of the cosmic weak lensing shear is also sensitive to the amplitude of matter density fluctuations via $S_8\equiv σ_8 Ω_m^α$ with $α\sim 0.5$, we can break the degeneracy between the mass bias and the cosmological parameters by combining the tSZ and cosmic shear power spectra. In this paper, we perform a joint likelihood analysis of the tSZ power spectrum from {\it Planck} and the cosmic shear power spectrum from Subaru Hyper Suprime-Cam. Our analysis does not use the primordial cosmic microwave background (CMB) information. We obtain a new constraint on the mass bias as $B = 1.37 ^{+0.15}_{-0.23}$ or $(1-b) = B^{-1}=0.73^{+0.08}_{-0.13}$ (68\%~C.L.), for $σ_8 < 0.9$. This value of $B$ is lower than that needed to reconcile the tSZ data with the primordial CMB and CMB lensing data, i.e., $B = 1.64 \pm 0.19$, but is consistent with the mass bias expected from hydrodynamical simulations, $B = 1.28 \pm 0.20$. Our results thus indicate that the mass bias is consistent with the non-thermal pressure support from mass accretion of galaxy clusters via the cosmic structure formation, and that the cosmologies inferred from the tSZ and the cosmic shear are consistent with each other.

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arXiv2019

Mitigating the impact of fiber assignment on clustering measurements from deep galaxy redshift surveys

We examine the impact of fiber assignment on clustering measurements from fiber-fed spectroscopic galaxy surveys. We identify new effects which were absent in previous, relatively shallow galaxy surveys such as Baryon Oscillation Spectroscopic Survey . Specifically, we consider deep surveys covering a wide redshift range from z=0.6 to z=2.4, as in the Subaru Prime Focus Spectrograph survey. Such surveys will have more target galaxies than we can place fibers on. This leads to two effects. First, it eliminates fluctuations with wavelengths longer than the size of the field of view, as the number of observed galaxies per field is nearly fixed to the number of available fibers. We find that we can recover the long-wavelength fluctuation by weighting galaxies in each field by the number of target galaxies. Second, it makes the preferential selection of galaxies in under-dense regions. We mitigate this effect by weighting galaxies using the so-called individual inverse probability. Correcting these two effects, we recover the underlying correlation function at better than 1 percent accuracy on scales greater than 10 Mpc/h.

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arXiv2019

A young galaxy cluster in the old Universe

Galaxies evolve from a blue star-forming phase into a red quiescent one by quenching their star formation activity. In high density environments, this galaxy evolution proceeds earlier and more efficiently. Therefore, local galaxy clusters are dominated by well-evolved red, elliptical galaxies. The fraction of blue galaxies in clusters monotonically declines with decreasing redshift, i.e., the Butcher-Oemler effect. In the local Universe, observed blue fractions of massive clusters are as small as $\lesssim$ 0.2. Here we report a discovery of a \lq \lq blue cluster\rq \rq, that is a local galaxy cluster with an unprecedentedly high fraction of blue star-forming galaxies yet hosted by a massive dark matter halo. The blue fraction is 0.57, which is 4.0 $σ$ higher than those of the other comparison clusters under the same selection and identification criteria. The velocity dispersion of the member galaxies is 510 km s$^{-1}$, which corresponds to a dark matter halo mass of 2.0$^{+1.9}_{-1.0}\times 10^{14}$ M$_{\odot}$. The blue fraction of the cluster is more than 4.7 $σ$ beyond the standard theoretical predictions including semi-analytic models of galaxy formation. The probability to find such a high blue fraction in an individual cluster is only 0.003\%, which challenges the current standard frameworks of the galaxy formation and evolution in the $Λ$CDM Universe. The spatial distribution of galaxies around the blue cluster suggests that filamentary cold gas streams can exist in massive halos even in the local Universe. However these cold streams have already disappeared in the theoretically simulated local universes.

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arXiv2018

The New Numerical Galaxy Catalogue (ν^2 GC): Properties of Active Galactic Nuclei and Their Host Galaxies

We present the latest results of a semi-analytic model of galaxy formation, "New Numerical Galaxy Catalogue", which is combined with large cosmological N-body simulations. This model can reproduce statistical properties of galaxies at z < 6.0. We focus on the properties of active galactic nuclei (AGNs) and supermassive black holes, especially on the accretion timescale onto black holes. We find that the number density of AGNs at z < 1.5 and at hard X-ray luminosity 10^{ 44 }< erg/s is underestimated compared with recent observational estimates when we assume the exponentially decreasing accretion rate and the accretion timescale which is proportional to the dynamical time of the host halo or the bulge, as is often assumed in semi-analytic models. We show that to solve this discrepancy, the accretion timescale of such less luminous AGNs instead should be a function of the black hole mass and the accreted gas mass. This timescale can be obtained from a phenomenological modelling of the gas angular momentum loss in the circumnuclear torus and/or the accretion disc. Such models predict a longer accretion timescale for less luminous AGNs at z < 1.0 than bright QSOs whose accretion timescale would be 10^{ 7-8 } yr. With this newly introduced accretion timescale, our model can explain the observed luminosity functions of AGNs at z < 6.0.

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arXiv2018

Joint analysis of the thermal Sunyaev-Zeldovich effect and 2MASS galaxies: Probing gas physics in the local Universe and beyond

We present a first joint analysis of the power spectra of the thermal Sunyaev-Zeldovich (tSZ) effect measured by the Planck and the number density fluctuations of galaxies in the 2MASS redshift survey (2MRS) catalog, including their cross-correlation. Combining these measurements with the cosmic microwave background (CMB) data and CMB lensing of Planck assuming a flat $Λ$CDM model, we constrain the mass bias parameter as $B = 1.54 \pm 0.098\;(1σ)$ [$(1-b) = 0.649 \pm 0.041$, where $(1-b) \equiv B^{-1}$], i.e., the Planck cluster mass should be $35\%$ lower than the true mass. The mass bias determined by the 2MRS-tSZ cross-power spectrum alone is consistent with that determined by the tSZ auto-power spectrum alone, suggesting that this large mass bias is not due to obvious systematics in the tSZ data. We find that the 2MRS-tSZ cross-power spectrum is more sensitive to less massive halos than the tSZ auto-power spectrum and it significantly improves a constraint on the mass dependence of the mass bias. The redshift dependence is not strongly constrained since the multipole range in which high redshift clusters mainly contribute to the tSZ auto is dominated by the contaminating sources. We conclude that no strong mass or redshift evolution of the mass bias is needed to explain the data.

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arXiv2018

Subaru High-z Exploration of Low-Luminosity Quasars (SHELLQs) III. Star formation properties of the host galaxies at $z \gtrsim 6$ studied with ALMA

We present our ALMA Cycle 4 measurements of the [CII] emission line and the underlying far-infrared (FIR) continuum emission from four optically low-luminosity ($M_{\rm 1450} > -25$) quasars at $z \gtrsim 6$ discovered by the Subaru Hyper Suprime Cam (HSC) survey. The [CII] line and FIR continuum luminosities lie in the ranges $L_{\rm [CII]} = (3.8-10.2) \times 10^8~L_\odot$ and $L_{\rm FIR} = (1.2-2.0) \times 10^{11}~L_\odot$, which are at least one order of magnitude smaller than those of optically-luminous quasars at $z \gtrsim 6$. We estimate the star formation rates (SFR) of our targets as $\simeq 23-40~M_\odot ~{\rm yr}^{-1}$. Their line and continuum-emitting regions are marginally resolved, and found to be comparable in size to those of optically luminous quasars, indicating that their SFR or likely gas mass surface densities (key controlling parameter of mass accretion) are accordingly different. The $L_{\rm [CII]}/L_{\rm FIR}$ ratios of the hosts, $\simeq (2.2-8.7) \times 10^{-3}$, are fully consistent with local star-forming galaxies. Using the [CII] dynamics, we derived their dynamical masses within a radius of 1.5-2.5 kpc as $\simeq (1.4-8.2) \times 10^{10}~M_\odot$. By interpreting these masses as stellar ones, we suggest that these faint quasar hosts are on or even below the star-forming main sequence at $z \sim 6$, i.e., they appear to be transforming into quiescent galaxies. This is in contrast to the optically luminous quasars at those redshifts, which show starburst-like properties. Finally, we find that the ratios of black hole mass to host galaxy dynamical mass of the most of low-luminosity quasars including the HSC ones are consistent with the local value. The mass ratios of the HSC quasars can be reproduced by a semi-analytical model that assumes merger-induced black hole-host galaxy evolution.

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arXiv2017

Generating Log-normal Mock Catalog of Galaxies in Redshift Space

We present a public code to generate a mock galaxy catalog in redshift space assuming a log-normal probability density function (PDF) of galaxy and matter density fields. We draw galaxies by Poisson-sampling the log-normal field, and calculate the velocity field from the linearised continuity equation of matter fields, assuming zero vorticity. This procedure yields a PDF of the pairwise velocity fields that is qualitatively similar to that of N-body simulations. We check fidelity of the catalog, showing that the measured two-point correlation function and power spectrum in real space agree with the input precisely. We find that a linear bias relation in the power spectrum does not guarantee a linear bias relation in the density contrasts, leading to a cross-correlation coefficient of matter and galaxies deviating from unity on small scales. We also find that linearising the Jacobian of the real-to-redshift space mapping provides a poor model for the two-point statistics in redshift space. That is, non-linear redshift-space distortion is dominated by non-linearity in the Jacobian. The power spectrum in redshift space shows a damping on small scales that is qualitatively similar to that of the well-known Fingers-of-God (FoG) effect due to random velocities, except that the log-normal mock does not include random velocities. This damping is a consequence of non-linearity in the Jacobian, and thus attributing the damping of the power spectrum solely to FoG, as commonly done in the literature, is misleading.

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arXiv2017

Imprints of the super-Eddington accretion on the quasar clustering

Super-Eddington mass accretion has been suggested as an efficient mechanism to grow supermassive black holes (SMBHs). We investigate the imprint left by the radiative efficiency of the super-Eddington accretion process on the clustering of quasars using a new semi-analytic model of galaxy and quasar formation based on large-volume cosmological $N$-body simulations. Our model includes a simple model for the radiative efficiency of a quasar, which imitates the effect of photon trapping for a high mass accretion rate. We find that the model of radiative efficiency affects the relation between the quasar luminosity and the quasar host halo mass. The quasar host halo mass has only weak dependence on quasar luminosity when there is no upper limit for quasar luminosity. On the other hand, it has significant dependence on quasar luminosity when the quasar luminosity is limited by its Eddington luminosity. In the latter case, the quasar bias also depends on the quasar luminosity, and the quasar bias of bright quasars is in agreement with observations. Our results suggest that the quasar clustering studies can provide a constraint on the accretion disc model.

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arXiv2016

The New Numerical Galaxy Catalog ($ν^2$GC): An Updated Semi-analytic Model of Galaxy and AGN with Large Cosmological N-body Simulation

We present a new cosmological galaxy formation model, $ν^2$GC, as an updated version of our previous model $ν$GC. We adopt the so-called "semi-analytic" approach, in which the formation history of dark matter halos is computed by ${\it N}$-body simulations, while the baryon physics such as gas cooling, star formation and supernova feedback are simply modeled by phenomenological equations. Major updates of the model are as follows: (1) the merger trees of dark matter halos are constructed in state-of-the-art ${\it N}$-body simulations, (2) we introduce the formation and evolution process of supermassive black holes and the suppression of gas cooling due to active galactic nucleus (AGN) activity, (3) we include heating of the intergalactic gas by the cosmic UV background, and (4) we tune some free parameters related to the astrophysical processes using a Markov chain Monte Carlo method. Our ${\it N}$-body simulations of dark matter halos have unprecedented box size and mass resolution (the largest simulation contains 550 billion particles in a 1.12 Gpc/h box), enabling the study of much smaller and rarer objects. The model was tuned to fit the luminosity functions of local galaxies and mass function of neutral hydrogen. Local observations, such as the Tully-Fisher relation, size-magnitude relation of spiral galaxies and scaling relation between the bulge mass and black hole mass were well reproduced by the model. Moreover, the model also well reproduced the cosmic star formation history and the redshift evolution of rest-frame ${\it K}$-band luminosity functions. The numerical catalog of the simulated galaxies and AGNs is publicly available on the web.

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arXiv2016

SXDF-ALMA 2-arcmin^2 Deep Survey: Stacking of Rest-Frame Near-Infrared Selected Objects

We present stacking analyses on our ALMA deep 1.1 mm imaging in the SXDF using 1.6 μm and 3.6 μm selected galaxies in the CANDELS WFC3 catalog. We detect a stacked flux of ~0.03-0.05 mJy, corresponding to LIR < 10^11 Lsun and a star formation rate (SFR) of ~ 15 Msun/yr at z = 2. We find that galaxies brighter in the rest-frame near-infrared tend to be also brighter at 1.1 mm, and galaxies fainter than m[3.6um] = 23 do not produce detectable 1.1 mm emission. This suggests a correlation between stellar mass and SFR, but outliers to this correlation are also observed, suggesting strongly boosted star formation or extremely large extinction. We also find tendencies that redder galaxies and galaxies at higher redshifts are brighter at 1.1 mm. Our field contains z ~ 2.5 H-alpha emitters and a bright single-dish source. However, we do not find evidence of bias in our results caused by the bright source. By combining the fluxes of sources detected by ALMA and fluxes of faint sources detected with stacking, we recover a 1.1 mm surface brightness of up to 20.3 +/- 1.2 Jy/deg, comparable to the extragalactic background light measured by COBE. Based on the fractions of optically faint sources in our and previous ALMA studies and the COBE measurements, we find that approximately half of the cosmic star formation may be obscured by dust and missed by deep optical surveys, Much deeper and wider ALMA imaging is therefore needed to better constrain the obscured cosmic star formation history.

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