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Marcin Sawicki

Publications and source records attributed to Marcin Sawicki.

At least 109 records · Page 6Linked to original sources

Classifying Stars, Galaxies and AGN in CLAUDS+HSC-SSP Using Gradient Boosted Decision Trees

Classifying catalog objects as stars, galaxies, or AGN is a crucial part of any statistical study of galaxies. We describe our pipeline for binary (star/galaxy) and multiclass (star/galaxy/Type I AGN/Type II AGN) classification developed for the very deep CLAUDS+HSC-SSP $u^*grizy$ dataset. Our method uses the XGBoost implementation of Gradient Boosted Trees (GBT) to train ensembles of models which take photometry, colours, maximum surface brightnesses, and effective radii from all available bands as input, and output the probability that an object belongs to each of the classes under consideration. At $i_{AB}<25$ our binary star/galaxy model has AUC=0.9974 and at the threshold that maximizes our sample's weighted F1 score, selects a sample of galaxies with 99.7% purity and 99.8% completeness. We test the model's ability to generalize to objects fainter than those seen during training and find that extrapolation of ~1-2 magnitudes is reasonable for most applications provided that the galaxies in the training sample are representative of the range of redshifts and colours of the galaxies in the target sample. We also perform an exploratory analysis of the method's ability to identify AGN using a small x-ray selected sample and find that it holds promise for classifying type I AGN, although it performs less well for type II AGN. Our results demonstrate that GBTs provide a flexible, robust and efficient method for performing classification of catalog objects in large astronomical imaging surveys.

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A giant central red disk galaxy at redshift $z=0.76$: challenge to theories of galaxy formation

We report a giant red central disk galaxy in the XMM-LSS north region. The region is covered with a rich variety of multiband photometric and spectroscopic observations. Using the photometric data of the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) and spectroscopic observation of the Baryon Oscillation Spectroscopic Survey (BOSS), we find that the galaxy has a stellar mass of $\sim 10^{11.6}$ times of the solar mass $M_\odot$. The galaxy has a red color and has an old stellar population, and thus its star formation has stopped. With the photometric image data of Hyper Suprime-Cam (HSC) Subaru Strategic Program, we demonstrate that its luminosity profile is perfectly described by a Sérsic form with $n=1.22$ indicating disk morphology. We also analyze its environment based on the VIMOS Public Extragalactic Redshift Survey (VIPERS) photometric catalog, and find that its close neighbors are all less massive, indicating that our observed galaxy is sitting at the center of its host halo. Existence of the giant red central disk galaxy seriously challenges the current standard paradigm of galaxy formation, as there is no known physical mechanism to explain the quenching of its star formation. This conclusion is supported by state-of-the-art hydrodynamical simulations of galaxy formation.

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A Large Massive Quiescent Galaxy Sample at z~1.2

In this paper we present a simple color-magnitude selection and obtain a large sample of 33,893 massive quiescent galaxies at intermediate redshifts (1 10.5, with a median of log(M*/M_sun)=11.0. A small fraction of our galaxies is also covered by the HST CANDELS. Morphological analysis in the observed H band shows that the majority of this subsample are early-type galaxies. As massive early-type galaxies trace the high density regions in the large scale structure in the universe, our study provides a quick and simple way to obtain a statistical significant sample of massive galaxies in a relative narrow redshift range. Our sample is 7-20 times larger at the massive end (log(M*/M_sun)>10.5) than any existing samples obtained in previous surveys. This is a pioneer study, and the technique introduced here can be applied to future wide-field survey to study large scale structure, and to identify high density region and clusters.

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Orphan GRB afterglow searches with the Pan-STARRS1 COSMOS survey

We present the result of a search for orphan Gamma-Ray Burst (GRB) afterglows in the Pan-STARRS1 (PS1) COSMOS survey. There is extensive theoretical and observational evidence suggesting that GRBs are collimated jets; the direct observation of orphan GRB afterglows would further support this model. An optimal survey strategy is designed by coupling the PS1 survey with the Subaru/Hyper-Suprime-Cam (HSC) survey. The PS1 COSMOS survey, one of the survey fields in the PS1 Medium Deep Survey (PS1/MDS), searches a field of 7 deg$^2$ from December 2011 to January 2014, reaching a limiting magnitude R $\sim$ 23. The dense cadence of PS1/MDS is crucial for identifying transients, and the deep magnitude reached by the HSC survey (R $\sim$ 26) is important for evaluating potential GRB hosts. A transient classification method is employed to select potential orphan GRB afterglow candidates. After a thorough analysis of the transient and host galaxy properties, we conclude that there are no candidates in this survey field. The null result implies that the consideration of jet structures is essential for further orphan GRB afterglow surveys.

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On the slow quenching of M* galaxies: heavily-obscured AGNs clarify the picture

We investigate the connection between X-ray and radio-loud AGNs and the physical properties of their evolved and massive host galaxies, focussing on the mass-related quenching channel followed by $\mathcal{M}^\star (\simeq 10^{10.6} M_\odot)$ galaxies in the rest-frame NUVrK colour diagram at $0.2 < z < 0.5$. While our results confirm that (1) radio-loud AGNs are predominantly hosted by already-quenched and very massive ($M_*>10^{11}M_\odot$) galaxies, ruling out their feedback as a primary driver of $\mathcal{M}^\star$ galaxy quenching, we found that (2) X-ray AGNs affected by heavy obscuration of their soft X-ray emission are mostly hosted by $\mathcal{M}^\star$ galaxies that are in the process of quenching. This is consistent with a quenching scenario that involves mergers of (gas-poor) $\mathcal{M}^\star$ galaxies $after$ the onset of the quenching process, i.e., a scenario where $\mathcal{M}^\star$ galaxy mergers are not the cause but rather an aftermath of the quenching mechanism(s). In that respect, we discuss how our results may support a picture where the slow quenching of $\mathcal{M}^\star$ galaxies happens due to halo-halo mergers along cosmic filaments.

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UV & U-band luminosity functions from CLAUDS and HSC-SSP -- I. Using four million galaxies to simultaneously constrain the very faint and bright regimes to $z \sim 3$

We constrain the rest-frame FUV (1546Å), NUV (2345Å) and U-band (3690Å) luminosity functions (LFs) and luminosity densities (LDs) with unprecedented precision from $z\sim0.2$ to $z\sim3$ (FUV, NUV) and $z\sim2$ (U-band). Our sample of over 4.3 million galaxies, selected from the CFHT Large Area $U$-band Deep Survey (CLAUDS) and HyperSuprime-Cam Subaru Strategic Program (HSC-SSP) data lets us probe the very faint regime (down to $M_\mathrm{FUV},M_\mathrm{NUV},M_\mathrm{U} \simeq -15$ at low redshift) while simultaneously detecting very rare galaxies at the bright end down to comoving densities $<10^{-5}$ Mpc$^{-3}$. Our FUV and NUV LFs are well fitted by single Schechter functions, with faint-end slopes that are very stable up to $z\sim2$. We confirm, but self-consistently and with much better precision than previous studies, that the LDs at all three wavelengths increase rapidly with lookback time to $z\sim1$, and then much more slowly at $1 1$ it is due to the evolution of both $M^\star_{UV}$ and the characteristic number density $ϕ^\star_{UV}$. In contrast, the U-band LF has an excess of faint galaxies and is fitted with a double-Schechter form; $M^\star_\mathrm{U}$, both $ϕ^\star_\mathrm{U}$ components, and the bright-end slope evolve throughout $0.2<z<2$, while the faint-end slope is constant over at least the measurable $0.05<z<0.6$. We present tables of our Schechter parameters and LD measurements that can be used for testing theoretical galaxy evolution models and forecasting future observations.

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LARgE Survey -- III. Environments of Ultra-Massive Passive Galaxies at Cosmic Noon: BCG progenitors growing through mergers

We study the environments of a sample of 61 extremely rare z~1.6 Ultra-Massive Passively Evolving Galaxies (UMPEGs: stellar masses M_stars >10^11.5 M_sun) which -- based on clustering analysis presented in Cheema et al. (2020) -- appear to be associated with very massive (M_halo ~ 10^14.1 h^-1 M_sun) dark matter halos that are likely to be the progenitors of z~0 massive (Coma- and Virgo-like) galaxy clusters. We find that UMPEGs on average have fewer than one satellite galaxy with mass ratio M_sat : M_UMPEG >~ 1:5 (i.e., M_sat >~ 10^10.8 M_sun) within 0.5 Mpc; the large mass gap that we observe between the typical UMPEG and its most massive satellite implies that the z~1.6 UMPEGs assembled through major mergers. Using observed satellite counts with merger timescales from the literature, we estimate the growth rate due to mergers with mass ratio of >~ 1:4 to be ~13% Gyr^-1 (with a ~2x systematic uncertainty). This relatively low growth rate is unlikely to significantly affect the shape of the massive end of the stellar mass function, whose evolution must instead be driven by the quenching of new cohorts of ultra-massive star-forming galaxies. However, this growth rate is high enough that, if sustained to z~0, the typical z~1.6 M_UMPEG=10^11.6 M_sun UMPEG can grow into a M_stars~10^12 M_sun brightest cluster galaxy (BCG) of a present-day massive galaxy cluster. Our observations favour a scenario in which our UMPEGs are main-branch progenitors of some of the present-day BCGs that have first assembled through major mergers at high redshifts and grown further through (likely minor) merging at later times.

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SCUBA-2 Ultra Deep Imaging Eao Survey (Studies) III: Multi-wavelength properties, luminosity functions and preliminary source catalog of 450-$μ$m-selected galaxies

We construct a SCUBA-2 450-$μ$m map in the COSMOS field that covers an area of 300 arcmin$^{2}$ and reaches a 1$σ$ noise level of 0.65 mJy in the deepest region. We extract 256 sources detected at 450 $μ$m with signal-to-noise ratio $>$ 4.0 and analyze the physical properties of their multi-wavelength counterparts. We find that most of the sources are at $z\lesssim3$, with a median of $z = 1.79^{+0.03}_{-0.15}$. About $35^{+32}_{-25}$% of our sources are classified as starburst galaxies based on their total star-formation rates (SFRs) and stellar masses ($M_{\ast}$). By fitting the far-infrared spectral energy distributions, we find that our 450-$μ$m-selected sample has a wide range of dust temperatures (20 K $ \lesssim T_{\rm d} \lesssim$ 60 K), with a median of ${T}_{\rm d} = 38.3^{+0.4}_{-0.9}$ K. We do not find a redshift evolution in dust temperature for sources with $L_{\rm IR}$ > $10^{12}$ $\rm L_\odot$ at $z<3$. However, we find a moderate correlation where dust temperature increases with the deviation from the SFR-$M_{\ast}$ relation. The increase in dust temperature also correlates with optical morphology, which is consistent with merger-triggered starbursts in sub-millimeter galaxies. Our galaxies do not show the tight IRX-$β_{\rm UV}$ correlation that has been observed in the local Universe. We construct the infrared luminosity functions of our 450-$μ$m sources and measure their comoving SFR densities. The contribution of the $L_{\rm IR}$ > $10^{12}$ $\rm L_\odot$ population to the SFR density rises dramatically from $z$ = 0 to 2 ($\propto$ ($1+z$)$^{3.9\pm1.1}$) and dominates the total SFR density at $z \gtrsim 2$.

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LARgE Survey -- II. The Dark Matter Halos and the Progenitors and Descendants of Ultra-Massive Passive Galaxies at Cosmic Noon

We use a 27.6 deg$^2$ survey to measure the clustering of $gzK_s$-selected quiescent galaxies at $z\sim1.6$, focusing on ultra-massive quiescent galaxies. We find that $z\sim1.6$ Ultra-Massive Passively Evolving Galaxies (UMPEGs), which have $K_s(AB)<19.75$ (stellar masses of $M_{stars}$ $>\sim 10^{11.4}M_{\odot}$ and mean $<$$M_{stars}$$>$ = $10^{11.5}M_{\odot}$), cluster more strongly than any other known galaxy population at high redshift. Comparing their correlation length, $r_0 = 29.77 \pm 2.75$ $ h^{-1}$Mpc, with the clustering of dark matter halos in the Millennium XXL N-body simulation suggests that these $z\sim1.6$ UMPEGs reside in dark matter halos of mass $M_{h}\sim10^{14.1}h^{-1}M_{\odot}$. Such very massive $z\sim1.6$ halos are associated with the ancestors of $z\sim0$ massive galaxy clusters such as the Virgo and Coma clusters. Given their extreme stellar masses and lack of companions with comparable mass, we surmise that these UMPEGs could be the already-quenched central massive galaxies of their (proto)clusters. We conclude that with only a modest amount of further growth in their stellar mass, $z\sim1.6$ UMPEGs could be the progenitors of some of the massive central galaxies of present-day massive galaxy clusters observed to be already very massive and quiescent near the peak epoch of the cosmic star formation.

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HSC-XD 52: An X-ray detected AGN in a low-mass galaxy at $z\sim0.56$

The properties of low-mass galaxies hosting central black holes provide clues about the formation and evolution of the progenitors of supermassive black holes. In this letter, we present HSC-XD 52, a spectroscopically confirmed low-mass active galactic nucleus (AGN) at an intermediate redshift of $z\sim0.56$. We detect this object as a very luminous X-ray source coincident with a galaxy observed by the Hyper Suprime-Cam (HSC) as part of a broader search for low-mass AGN. We constrain its stellar mass through spectral energy distribution modeling to be LMC-like at $M_\star \approx 3 \times 10^9 M_\odot$, placing it in the dwarf regime. We estimate a central black hole mass of $M_\mathrm{BH} \sim 10^{6} M_\odot$. With an average X-ray luminosity of $L_X \approx 3.5 \times 10^{43}~\mathrm{erg}~\mathrm{s}^{-1}$, HSC-XD 52 is among the most luminous X-ray selected AGN in dwarf galaxies. The spectroscopic and photometric properties of HSC-XD 52 indicate that it is an intermediate redshift counterpart to local low-mass AGN.

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The CFHT Large Area U-band Deep Survey (CLAUDS)

The CFHT Large Area U-band Deep Survey (CLAUDS) uses data taken with the MegaCam mosaic imager on CFHT to produce images of 18.60 deg2 with median seeing of FWHM=0.92 arcsec and to a median depth of U = 27.1 AB (5 sigma in 2 arcsec apertures), with selected areas that total 1.36 deg2 reaching a median depth of U=27.7 AB. These are the deepest U-band images assembled to date over this large an area. These data are located in four fields also imaged to comparably faint levels in grizy and several narrowband filters as part of the Hyper Suprime-Cam (HSC) Subaru Strategic Program (HSC-SSP). These CFHT and Subaru datasets will remain unmatched in their combination of area and depth until the advent of the Large Synoptic Survey Telescope (LSST). This paper provides an overview of the scientific motivation for CLAUDS and gives details of the observing strategy, observations, data reduction, and data merging with the HSC-SSP. Three early applications of these deep data are used to illustrate the potential of the dataset: deep U-band galaxy number counts, z~3 Lyman break galaxy (LBG) selection, and photometric redshifts improved by adding CLAUDS U to the Subaru HSC grizy photometry.

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Two sub-millimetre bright protoclusters bounding the epoch of peak star-formation activity

We present James Clerk Maxwell Telescope Submillimetre Common-User Bolometer Array 2 (SCUBA-2) 850 & 450 $μ$m observations ($σ_{850}\sim0.5$ mJy, $σ_{450}\sim5$ mJy) of the HS1549+19 and HS1700+64 survey fields containing two of the largest known galaxy over-densities at $z=2.85$ and $2.30$, respectively. We detect 56 sub-millimetre galaxies (SMGs) with SNR $> 4$ over $\sim 50$ arcmin$^2$ at 850 $μ$m with flux densities of 3 - 17 mJy. The number counts indicate over-densities in the $3$-arcmin diameter core region ($\sim 1.5$ Mpc at $z=2.5$) of $6^{+4}_{-2}\times$ (HS1549) and $4^{+6}_{-2}\times$ (HS1700) compared to blank field surveys. Within these core regions, we spectroscopically confirm that approximately one third of the SMGs lie at the protocluster redshifts for both HS1549 and HS1700. We use statistical identifications of other SMGs in the wider fields to constrain an additional four candidate protocluster members in each system. We combine multi wavelength estimates of the star-formation rates (SFRs) from Lyman-break dropout- and narrowband-selected galaxies, and the SCUBA-2 SMGs, to estimate total SFRs of 12,$500\pm2800$ M$_\odot$ yr$^{-1}$ ($4900\pm1200$ M$_\odot$ yr$^{-1}$) in HS1549 (HS1700), and SFR densities (SFRDs) within the central 1.5-Mpc diameter of each protocluster to be $3000\pm900$ M$_\odot$ yr$^{-1}$ Mpc$^{-3}$ ($1300\pm400$ M$_\odot$ yr$^{-1}$ Mpc$^{-3}$) in the HS1549 (HS1700) protocluster, $\sim10^4\times$ larger than the global SFRDs found at their respective epochs, due to the concentration of star-forming galaxies in the small volume of the dense cluster cores. Our results suggest centrally concentrated starbursts within protoclusters may be a relatively common scenario for the build up of mass in rich clusters assembling at $z\gtrsim2$.

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LARgE Survey. I. Dead Monsters: the Massive End of the Passive Galaxy Stellar Mass Function at Cosmic Noon

We introduce the largest to date survey of massive quiescent galaxies at redshift z~1.6. With these data, which cover 27.6 deg^2, we can find significant numbers of very rare objects such as ultra-massive quiescent galaxies that populate the extreme massive end of the galaxy mass function, or dense environments that are likely to become present-day massive galaxy clusters. In this paper, the first in a series, we apply our gzK adaptation of the BzK technique to select our z~1.6 galaxy catalog and then study the quiescent galaxy stellar mass function with good statistics over M_stars ~ 10^10.2 - 10^11.7 M_sun --- a factor of 30 in mass --- including 60 ultra-massive z~1.6 quiescent galaxies with M_stars > 10^11.5 M_sun. We find that the stellar mass function of quiescent galaxies at z~1.6 is well represented by the Schechter function over this large mass range. This suggests that the mass quenching mechanism observed at lower redshifts must have already been well established by this epoch, and that it is likely due to a single physical mechanism over a wide range of mass. This close adherence to the Schechter shape also suggests that neither merging nor gravitational lensing significantly affect the observed quenched population. Finally, comparing measurements of M* parameters for quiescent and star-forming populations (ours and from the literature), we find hints of an offset (M*_SF > M*_PE), that could suggest that the efficiency of the quenching process evolves with time.

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On the fast quenching of young low-mass galaxies up to z $\sim$ 0.6: new spotlight on the lead role of environment

We investigate the connection between environment and the different quenching channels that galaxies are prone to follow in the rest-frame NUVrK colour diagram, as identified by Moutard et al. (2016b). Namely, the fast quenching channel followed by $young$ low-mass galaxies and the slow quenching channel followed by $old$ high-mass ones. We make use of the >22 deg$^2$ covered the VIPERS Multi-Lambda Survey (VIPERS-MLS) to select a galaxy sample complete down to stellar masses of $M_* > 10^{9.4} M_\odot$ at $z < 0.65$ ($M_* > 10^{8.8} M_\odot$ at $z < 0.5$) and including 33,500 (43,000) quiescent galaxies properly selected at $0.2 < z < 0.65$, while being characterized by reliable photometric redshifts ($σ_{δz/(1+z)} \leq 0.04$) that we use to measure galaxy local densities. We find that (1) the quiescence of low-mass [$M_* \leq 10^{9.7} M_\odot$] galaxies requires a strong increase of the local density, which confirms the lead role played by environment in their fast quenching and, therefore, confirms that the low-mass upturn observed in the stellar mass function of quiescent galaxies is due to $environmental$ $quenching$. We also observe that (2) the reservoir of low-mass star-forming galaxies located in very dense regions (prone to environmental quenching) has grown between $z \sim 0.6$ and $ z \sim 0.4$ whilst the share of low-mass quiescent galaxies (expected to being environmentally quenched) may have simultaneously increased, which would plead for a rising importance of $environmental$ $quenching$ with cosmic time, compared to $mass$ $quenching$. We finally discuss the composite picture of such environmental quenching of low-mass galaxies and, in particular, how this picture may be consistent with a $delayed$-$then$-$rapid$ quenching scenario.

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Gemini Infrared Multi-Object Spectrograph: Instrument Overview

The Gemini Infrared Multi-Object Spectrograph (GIRMOS) is a powerful new instrument being built to facility-class standards for the Gemini telescope. It takes advantage of the latest developments in adaptive optics and integral field spectrographs. GIRMOS will carry out simultaneous high-angular-resolution, spatially-resolved infrared ($1-2.4$ $μ$m) spectroscopy of four objects within a two-arcminute field-of-regard by taking advantage of multi-object adaptive optics. This capability does not currently exist anywhere in the world and therefore offers significant scientific gains over a very broad range of topics in astronomical research. For example, current programs for high redshift galaxies are pushing the limits of what is possible with infrared spectroscopy at $8-10$-meter class facilities by requiring up to several nights of observing time per target. Therefore, the observation of multiple objects simultaneously with adaptive optics is absolutely necessary to make effective use of telescope time and obtain statistically significant samples for high redshift science. With an expected commissioning date of 2023, GIRMOS's capabilities will also make it a key followup instrument for the James Webb Space Telescope when it is launched in 2021, as well as a true scientific and technical pathfinder for future Thirty Meter Telescope (TMT) multi-object spectroscopic instrumentation. In this paper, we will present an overview of this instrument's capabilities and overall architecture. We also highlight how this instrument lays the ground work for a future TMT early-light instrument.

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Observational constraints on the physical nature of submillimetre source multiplicity: chance projections are common

Interferometric observations have demonstrated that a significant fraction of single-dish submillimetre (submm) sources are blends of multiple submm galaxies (SMGs), but the nature of this multiplicity, i.e. whether the galaxies are physically associated or chance projections, has not been determined. We performed spectroscopy of 11 SMGs in six multi-component submm sources, obtaining spectroscopic redshifts for nine of them. For an additional two component SMGs, we detected continuum emission but no obvious features. We supplement our observed sources with four sources from the literature. This sample allows us to statistically constrain the physical nature of single-dish submm source multiplicity for the first time. In three [3/7, or 43 (-33/+39) per cent at 95% confidence] of the single-dish sources for which the nature of the blending is unambiguous, the components for which spectroscopic redshifts are available are physically associated, whereas 4/7 [57 (-39/+33) per cent] have at least one unassociated component. When components whose spectra exhibit continuum but no features and for which the photometric redshift is significantly different from the spectroscopic redshift of the other component are also considered, 6/9 [67 (-37/+26) per cent] of the single-dish sources are comprised of at least one unassociated component. The nature of the multiplicity of one single-dish source is ambiguous. We conclude that physically associated systems and chance projections both contribute to the multi-component single-dish submm source population. This result contradicts the conventional wisdom that bright submm sources are solely a result of merger-induced starbursts, as blending of unassociated galaxies is also important.

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Spatially-unresolved SED fitting can underestimate galaxy masses: a solution to the missing mass problem

We perform spatially-resolved, pixel-by-pixel SED fitting on galaxies up to $z\sim2.5$ in the Hubble Extreme Deep Field (XDF). Comparing stellar mass estimates from spatially resolved and spatially unresolved photometry we find that unresolved masses can be systematically underestimated by factors of up to 5. The ratio of the unresolved to resolved mass measurement depends on the galaxy's specific star formation rate (sSFR): at low sSFRs the bias is small, but above sSFR$\ \sim 10^{-9.5}$ yr$^{-1}$ the discrepancy increases rapidly such that galaxies with sSFRs$\ \sim 10^{-8}$ yr$^{-1}$ have unresolved mass estimates of only one half to one fifth of the resolved value. This result indicates that stellar masses estimated from spatially-unresolved datasets need to be systematically corrected, in some cases by large amounts, and we provide an analytic prescription for applying this correction. We show that correcting stellar mass measurements for this bias changes the normalization and slope of the star-forming main sequence and reduces its intrinsic width; most dramatically, correcting for the mass bias increases the stellar mass density of the Universe at high redshift and can resolve the long-standing discrepancy between the directly-measured cosmic star formation rate density at $z\gtrsim1$ and that inferred from stellar mass densities ("the missing mass problem").

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SCUBA-2 Ultra Deep Imaging EAO Survey (STUDIES): Faint-End Counts at 450 um

The SCUBA-2 Ultra Deep Imaging EAO Survey (STUDIES) is a three-year JCMT Large Program aiming at reaching the 450 $μ$m confusion limit in the COSMOS-CANDELS region, to study a representative sample of the high-redshift far-infrared galaxy population that gives rise to the bulk of the far-infrared background. We present the first-year data from STUDIES. We have reached a 450 $μ$m noise level of 0.91~mJy for point sources at the map center, covered an area of 151 arcmin$^2$, and detected 98 and 141 sources at 4.0 and 3.5 $σ$, respectively. Our derived counts are best constrained in the 3.5-25 mJy regime using directly detected sources. Below the detection limits, our fluctuation analysis further constrains the slope of the counts down to 1 mJy. The resulting counts at 1-25 mJy are consistent with a power law having a slope of $-2.59$ ($\pm0.10$ for 3.5-25 mJy, and $^{+0.4}_{-0.7}$ for 1-3.5 mJy). There is no evidence of a faint-end termination or turn-over of the counts in this flux density range. Our counts are also consistent with previous SCUBA-2 blank-field and lensing cluster surveys. The integrated surface brightness from our counts down to 1 mJy is $90.0\pm17.2$ Jy deg$^{-2}$, which can account for up to $83^{+15}_{-16}\%$ of the COBE 450 $μ$m background. We show that Herschel counts at 350 and 500 $μ$m are significantly higher than our 450 $μ$m counts, likely caused by its large beam and source clustering. High-angular resolution instruments like SCUBA-2 at 450 $μ$m are therefore highly beneficial for measuring the luminosity and spatial density of high-redshift dusty galaxies.

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