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Christopher J. Conselice

Publications and source records attributed to Christopher J. Conselice.

At least 181 records · Page 10Linked to original sources
arXiv2019

Evolution of the galaxy stellar mass functions and UV luminosity functions at $z=6-9$ in the Hubble Frontier Fields

We present new measurements of the evolution of the galaxy stellar mass functions (GSMF) and UV luminosity functions (UV LF) for galaxies from $z=6-9$ within the Frontier Field cluster MACSJ0416.1-2403 and its parallel field. To obtain these results, we derive the stellar masses of our sample by fitting synthetic stellar population models to their observed spectral energy distribution with the inclusion of nebular emission lines. This is the deepest and farthest in distance mass function measured to date and probes down to a level of M$_{*} = 10^{6.8}M_{\odot}$. The main result of this study is that the low-mass end of our GSMF to these limits and redshifts appears to become steeper from $-1.98_{-0.07}^{+0.07}$ at $z=6$ to $-2.38_{-0.88}^{+0.72}$ at $z=9$, steeper than previously observed mass functions at slightly lower redshifts, and we find no evidence of turnover in the mass range probed. We furthermore demonstrate that the UV LF for these system also appears to show a steepening at the highest redshifts, without any evidence of turnover in the luminosity range probed. Our $M_{\mathrm{UV}}-M_{*}$ relation exhibit shallower slopes than previously observed and are in accordance with a constant mass-to-light ratio. Integrating our GSMF, we find that the stellar mass density increases by a factor of $\sim15_{-6}^{+21}$ from $z=9$ to $z=6$. We estimate the dust-corrected star formation rates (SFRs) to calculate the specific star formation rates ($\mathrm{sSFR}=\mathrm{SFR/M_{*}}$) of our sample, and find that for a fixed stellar mass of $5\times10^{9}M_{\odot}$, sSFR $\propto(1+z)^{2.01\pm0.16}$. Finally, from our new measurements, we estimate the UV luminosity density ($ρ_{\textrm{UV}}$) and find that our results support a smooth decline of $ρ_{\textrm{UV}}$ towards high redshifts.

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arXiv2019

What shapes a galaxy? - Unraveling the role of mass, environment and star formation in forming galactic structure

We investigate the dependence of galaxy structure on a variety of galactic and environmental parameters for ~500,000 galaxies at z<0.2, taken from the Sloan Digital Sky Survey data release 7 (SDSS-DR7). We utilise bulge-to-total stellar mass ratio, (B/T)_*, as the primary indicator of galactic structure, which circumvents issues of morphological dependence on waveband. We rank galaxy and environmental parameters in terms of how predictive they are of galaxy structure, using an artificial neural network approach. We find that distance from the star forming main sequence (Delta_SFR), followed by stellar mass (M_*), are the most closely connected parameters to (B/T)_*, and are significantly more predictive of galaxy structure than global star formation rate (SFR), or any environmental metric considered (for both central and satellite galaxies). Additionally, we make a detailed comparison to the Illustris hydrodynamical simulation and the LGalaxies semi-analytic model. In both simulations, we find a significant lack of bulge-dominated galaxies at a fixed stellar mass, compared to the SDSS. This result highlights a potentially serious problem in contemporary models of galaxy evolution.

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arXiv2019

PLCK G165.7+67.0: Analysis of a Massive Lensing Cluster in a Hubble Space Telescope Census of Submillimeter Giant Arcs Selected Using Planck/Herschel

We present Hubble Space Telescope WFC3-IR imaging in the fields of six apparently bright dusty star-forming galaxies (DSFGs) at $z$ = 2-4 identified by their rest-frame far-infrared colors using the Planck and Herschel space facilities. We detect near-infrared counterparts for all six submillimeter sources, allowing us to undertake strong-lensing analyses. One field in particular stands out for its prominent giant arcs, PLCK G165.7+67.0 (G165). After combining the color and morphological information, we identify 11 sets of image multiplicities in this one field. We construct a strong-lensing model constrained by this lensing evidence, which uncovers a bimodal spatial mass distribution, and from which we measure a mass of $(2.6 \pm 0.11)$ $\times$ $10^{14}$ $M_{\odot}$ within $\sim$250 kpc. The bright ($S_{350}$ $\approx$ 750 mJy) DSFG appears as two images: a giant arc with a spatial extent of 4.5" that is merging with the critical curve, and a lower-magnification counterimage that is detected in our new longer-wavelength ground- and space-based imaging data. Using our ground-based spectroscopy, we calculate a dynamical mass of $1.3^{+0.04}_{-0.70} \times 10^{15}$ $M_{\odot}$ to the same fixed radius, although this value may be inflated relative to the true value if the velocity distribution is enhanced in the line-of-sight direction. We suggest that the bimodal mass taken in combination with the weak X-ray flux and low SZ decrement may be explained as a pre-merger for which the intracluster gas is diluted along the line of sight, while the integrated surface mass density is supercritical to strong-lensing effects.

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arXiv2018

AutoSpec: Fast Automated Spectral Extraction Software for IFU Datacubes

With the ever growing popularity of integral field unit (IFU) spectroscopy, countless observations are being performed over multiple object systems such as blank fields and galaxy clusters. With this, an increasing amount of time is being spent extracting one dimensional object spectra from large three dimensional datacubes. However, a great deal of information available within these datacubes is overlooked in favor of photometrically based spatial information. Here we present a novel, yet simple approach of optimal source identification, utilizing the wealth of information available within an IFU datacube, rather than relying on ancillary imaging. Through the application of these techniques, we show that we are able to obtain object spectra comparable to deep photometry weighted extractions without the need for ancillary imaging. Further, implementing our custom designed algorithms can improve the signal-to-noise of extracted spectra and successfully deblend sources from nearby contaminants. This will be a critical tool for future IFU observations of blank and deep fields, especially over large areas where automation is necessary. We implement these techniques into the Python based spectral extraction software, AutoSpec which is available via GitHub at: https://github.com/a-griffiths/AutoSpec and Zenodo at: https://doi.org/10.5281/zenodo.1305848

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arXiv2018

Candidate Massive Galaxies at $z \sim 4$ in the Dark Energy Survey

Using stellar population models, we predicted that the Dark Energy Survey (DES) - due to its special combination of area (5000 deg. sq.) and depth ($i = 24.3$) - would be in the position to detect massive ($\gtrsim 10^{11}$ M$_{\odot}$) galaxies at $z \sim 4$. We confront those theoretical calculations with the first $\sim 150$ deg. sq. of DES data reaching nominal depth. From a catalogue containing $\sim 5$ million sources, $\sim26000$ were found to have observed-frame $g-r$ vs $r-i$ colours within the locus predicted for $z \sim 4$ massive galaxies. We further removed contamination by stars and artefacts, obtaining 606 galaxies lining up by the model selection box. We obtained their photometric redshifts and physical properties by fitting model templates spanning a wide range of star formation histories, reddening and redshift. Key to constrain the models is the addition, to the optical DES bands $g$, $r$, $i$, $z$, and $Y$, of near-IR $J$, $H$, $K_{s}$ data from the Vista Hemisphere Survey. We further applied several quality cuts to the fitting results, including goodness of fit and a unimodal redshift probability distribution. We finally select 233 candidates whose photometric redshift probability distribution function peaks around $z\sim4$, have high stellar masses ($\log($M$^{*}$/M$_{\odot})\sim 11.7$ for a Salpeter IMF) and ages around 0.1 Gyr, i.e. formation redshift around 5. These properties match those of the progenitors of the most massive galaxies in the local universe. This is an ideal sample for spectroscopic follow-up to select the fraction of galaxies which is truly at high redshift. These initial results and those at the survey completion, which we shall push to higher redshifts, will set unprecedented constraints on galaxy formation, evolution, and the re-ionisation epoch.

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arXiv2018

X-UDS: The Chandra Legacy Survey of the UKIDSS Ultra Deep Survey Field

We present the X-UDS survey, a set of wide and deep Chandra observations of the Subaru-XMM Deep/UKIDSS Ultra Deep Survey (SXDS/UDS) field. The survey consists of 25 observations that cover a total area of 0.33 deg$^{2}$. The observations are combined to provide a nominal depth of ~600 ksec in the central 100 arcmin$^{2}$ region of the field that has been imaged with Hubble/WFC3 by the CANDELS survey and $\sim$200 ksec in the remainder of the field. In this paper, we outline the survey's scientific goals, describe our observing strategy, and detail our data reduction and point source detection algorithms. Our analysis has resulted in a total of 868 band-merged point sources detected with a false-positive Poisson probability of $<1\times10^{-4}$. In addition, we present the results of an X-ray spectral analysis and provide best-fitting neutral hydrogen column densities, $N_{\rm H}$, as well as a sample of 51 Compton-thick active galactic nucleus candidates. Using this sample, we find the intrinsic Compton-thick fraction to be 30-35% over a wide range in redshift ($z=0.1-3$), suggesting the obscured fraction does not evolve very strongly with epoch. However, if we assume that the Compton-thick fraction is dependent on luminosity, as is seen for Compton-thin sources, then our results are consistent with a rise in the obscured fraction out to $z\sim3$. Finally, an examination of the host morphologies of our Compton-thick candidates shows a high fraction of morphological disturbances, in agreement with our previous results. All data products described in this paper are made available via a public website.

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arXiv2018

Faint Satellite Population of the NGC-3175 Group - a Local Group Analogue

In this paper we identify and study the properties of low mass dwarf satellites of a nearby Local Group analogue - the NGC-3175 galaxy group with the goal of investigating the nature of the lowest mass galaxies and the `Missing Satellites' problem. Deep imaging of nearby groups such as NGC-3175 are one of the only ways to probe these low mass galaxies which are important for problems in cosmology, dark matter and galaxy formation. We discover 553 candidate dwarf galaxies in the group, the vast majority of which have never been studied before. We obtained R and B band imaging, with the ESO 2.2m, around the central $\sim$500kpc region of NGC-3175, allowing us to detect galaxies down to $\sim$23 mag (M$_{B} \sim$-7.7 mag) in the B band. In the absence of spectroscopic information, dwarf members and likely background galaxies are separated using colour, morphology and surface brightness criteria. We compare the observed size, surface brightness and mass scaling relations to literature data. The luminosity function with a faint end slope of $α$ = -1.31, is steeper than that observed in the Local Group. In comparison with simulations, we find that our observations are between a pure $Λ$CDM model and one involving baryonic effects, removing the apparent problem of finding too few satellites as seen around the Milky Way.

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arXiv2018

SCUBA-2 Ultra Deep Imaging EAO Survey (STUDIES) II: Structural Properties and Near-Infrared Morphologies of Faint Submillimeter Galaxies

We present structural parameters and morphological properties of faint 450-um selected submillimeter galaxies (SMGs) from the JCMT Large Program, STUDIES, in the COSMOS-CANDELS region. Their properties are compared to an 850um selected and a matched star-forming samples. We investigate stellar structures of 169 faint 450-um sources (S450=2.8-29.6mJy; S/N>4) at z<3 using HST near-infrared observations. Based on our spectral energy distribution fitting, half of such faint SMGs (LIR=10^11.65+-0.98Lsun) lie above the star-formation rate (SFR)/stellar mass plane. The size-mass relation shows that these SMGs are generally similar to less-luminous star-forming galaxies selected by NUV-r vs. r-J colors. Because of the intrinsic luminosity of the sample, their rest-frame optical emission is less extended than the 850um sources (S850>2mJy), and more extended than the star-forming galaxies in the same redshift range. For the stellar mass and SFR matched sample at z~=1 and z~=2, the size differences are marginal between faint SMGs and the matched galaxies. Moreover, faint SMGs have similar Sersic indices and projected axis ratios as star-forming galaxies with the same stellar mass and SFR. Both SMGs and the matched galaxies show high fractions (~70%) of disturbed features at z~=2, and the fractions depend on the SFRs. These suggest that their star formation activity is related to galaxy merging, and the stellar structures of SMGs are similar to those of star-forming galaxies. We show that the depths of submillimeter surveys are approaching the lower luminosity end of star-forming galaxies, allowing us to detect galaxies on the main sequence.

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arXiv2018

Galaxy Structure in the Ultraviolet: The Dependence of Morphological Parameters on Rest-Frame Wavelength

Evolutionary studies that compare galaxy structure as a function of redshift are complicated by the fact that any particular galaxy's appearance depends in part on the rest-frame wavelength of the observation. This leads to the necessity for a "morphological k-correction" between different pass-bands, especially when comparing the rest-frame optical or infrared (IR) to the ultraviolet (UV). This is of particular concern for high redshift studies that are conducted in the rest-frame UV. We investigate the effects of this "band-pass shifting" out of the UV by quantifying nearby galaxy structure via "CAS parameters" (concentration, asymmetry, and clumpiness). For this study we combine pan-chromatic data from the UV through the near-IR with GALEX (Galaxy Evolution Explorer) data of 2073 nearby galaxies in the "NUV" (~230 nm) and 1127 in the "FUV" (~150 nm), providing the largest study of this kind in the mid- to far-UV. We find a relationship between the CAS parameters and observed rest-frame wavelength that make galaxies appear more late-type at shorter wavelengths, particularly in the UV. The effect is strongest for E/S0 galaxies in the far-UV, which have concentrations and asymmetries that more resemble those of spiral and peculiar/merging galaxies in the optical. This may be explained by extended disks containing recent star formation. Here we also release the CAS values of the galaxies imaged in GALEX NUV and FUV for use in comparisons with deep HST imaging and JWST in the future.

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arXiv2018

The Halo Masses of Galaxies to $z\sim 3$: A Hybrid Observational and Theoretical Approach

We use a hybrid observational/theoretical approach to study the relation between galaxy kinematics and the derived stellar and halo masses of galaxies up to z=3 as a function of stellar mass, redshift and morphology. Our observational sample consists of a concatenation of 1125 galaxies with kinematic measurements at 0.4<z<3 from long-slit and integral-field studies. We investigate several ways to measure halo masses from observations based on results from semi-analytical models, showing that galaxy halo masses can be retrieved with a scatter of ~0.4 dex by using only stellar masses. We discover a third parameter, relating to the time of the formation of the halo, which reduces the scatter in the relation between the stellar and halo masses, such that systems forming earlier have a higher stellar mass to halo mass ratio, which we also find observationally. We find that this scatter correlates with morphology, such that early-type, or older stellar systems, have higher M_*/M_halo ratios. We furthermore show using this approach, and through weak lensing and abundance matching, that the ratio of stellar to halo mass does not significantly evolve with redshift at 1<z<3. This is evidence for the regulated hierarchical assembly of galaxies such that the ratio of stellar to dark matter mass remains approximately constant since $z = 2$. We use these results to show that the dark matter accretion rate evolves from $dM_{\rm halo}/d{\rm t} \sim 4000$ M_solar year$^{-1}$ at $z \sim 2.5$, to a few 100 M_solar year$^{-1}$ by $z \sim 0.5$.

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arXiv2018

Ultra Diffuse Galaxies are a Subset of Cluster Dwarf Elliptical/Spheroidal Galaxies

Since 2015 there has been a great deal of interest in a supposed new class of galaxy called Ultra Diffuse Galaxies (UDGs). These are large systems with sizes $> 1.5$ kpc and have surface brightness values which are $μ> 25$ mag arcsec$^{-2}$. Because of their low-surface brightness they are proposed to be `failed' Milky Way type galaxies given their similar size, but much lower stellar masses. As such, these systems are considered by some as a new type of galaxy, yet we show that they are a subset of a well-established and well studied population of low-surface brightness galaxies found mostly in dense areas of the universe - clusters of galaxies. We argue based on previous literature that the most likely method for forming these galaxies is through cluster processes such as `Galaxy Harassment', where through multiple high speed encounters an infalling galaxy is gradually removed of its mass, until it resembles a dwarf elliptical. Future studies of UDGs should consider the above and their more general connection to previously studied populations.

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arXiv2018

MUSE spectroscopy and deep observations of a unique compact JWST target, lensing cluster CLIO

We present the results of a VLT MUSE/FORS2 and Spitzer survey of a unique compact lensing cluster CLIO at z = 0.42, discovered through the GAMA survey using spectroscopic redshifts. Compact and massive clusters such as this are understudied, but provide a unique prospective on dark matter distributions and for finding background lensed high-z galaxies. The CLIO cluster was identified for follow up observations due to its almost unique combination of high mass and dark matter halo concentration, as well as having observed lensing arcs from ground based images. Using dual band optical and infra-red imaging from FORS2 and Spitzer, in combination with MUSE optical spectroscopy we identify 89 cluster members and find background sources out to z = 6.49. We describe the physical state of this cluster, finding a strong correlation between environment and galaxy spectral type. Under the assumption of a NFW profile, we measure the total mass of CLIO to be M$_{200} = (4.49 \pm 0.25) \times 10^{14}$ M$_\odot$. We build and present an initial strong-lensing model for this cluster, and measure a relatively low intracluster light (ICL) fraction of 7.21 $\pm$ 1.53% through galaxy profile fitting. Due to its strong potential for lensing background galaxies and its low ICL, the CLIO cluster will be a target for our 110 hour JWST 'Webb Medium-Deep Field' (WMDF) GTO program.

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arXiv2017

Major Merging History in CANDELS. I. Evolution of the Incidence of Massive Galaxy-Galaxy Pairs from z=3 to z~0

The rate of major galaxy-galaxy merging is theoretically predicted to steadily increase with redshift during the peak epoch of massive galaxy development ($1{\leq}z{\leq}3$). We use close-pair statistics to objectively study the incidence of massive galaxies (stellar $M_{1}{\geq}2{\times}10^{10}M_{\odot}$) hosting major companions ($1{\leq}M_{1}/M_{2}{\leq}4$; i.e., $<$4:1) at six epochs spanning $0{<}z{<}3$. We select companions from a nearly complete, mass-limited ($\geq5{\times}10^{9}M_{\odot}$) sample of 23,696 galaxies in the five CANDELS fields and the SDSS. Using $5-50$ kpc projected separation and close redshift proximity criteria, we find that the major companion fraction $f_{\mathrm{mc}}(z)$ based on stellar mass-ratio (MR) selection increases from 6% ($z{\sim}0$) to 16% ($z{\sim}0.8$), then turns over at $z{\sim}1$ and decreases to 7% ($z{\sim}3$). Instead, if we use a major F160W flux ratio (FR) selection, we find that $f_{\mathrm{mc}}(z)$ increases steadily until $z=3$ owing to increasing contamination from minor (MR$>$4:1) companions at $z>1$. We show that these evolutionary trends are statistically robust to changes in companion proximity. We find disagreements between published results are resolved when selection criteria are closely matched. If we compute merger rates using constant fraction-to-rate conversion factors ($C_{\mathrm{merg,pair}}{=}0.6$ and $T_{\mathrm{obs,pair}}{=}0.65\mathrm{Gyr}$), we find that MR rates disagree with theoretical predictions at $z{>}1.5$. Instead, if we use an evolving $T_{\mathrm{obs,pair}}(z){\propto}(1+z)^{-2}$ from Snyder et al., our MR-based rates agree with theory at $0{<}z{<}3$. Our analysis underscores the need for detailed calibration of $C_{\mathrm{merg,pair}}$ and $T_{\mathrm{obs,pair}}$ as a function of redshift, mass and companion selection criteria to better constrain the empirical major merger history.

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arXiv2017

Clumpy Galaxies in CANDELS. II. Physical Properties of UV-bright Clumps at $0.5\leq z<3$

Studying giant star-forming clumps in distant galaxies is important to understand galaxy formation and evolution. At present, however, observers and theorists have not reached a consensus on whether the observed "clumps" in distant galaxies are the same phenomenon that is seen in simulations. In this paper, as a step to establish a benchmark of direct comparisons between observations and theories, we publish a sample of clumps constructed to represent the commonly observed "clumps" in the literature. This sample contains 3193 clumps detected from 1270 galaxies at $0.5 \leq z < 3.0$. The clumps are detected from rest-frame UV images, as described in our previous paper. Their physical properties, e.g., rest-frame color, stellar mass (M*), star formation rate (SFR), age, and dust extinction, are measured by fitting the spectral energy distribution (SED) to synthetic stellar population models. We carefully test the procedures of measuring clump properties, especially the method of subtracting background fluxes from the diffuse component of galaxies. With our fiducial background subtraction, we find a radial clump U-V color variation, where clumps close to galactic centers are redder than those in outskirts. The slope of the color gradient (clump color as a function of their galactocentric distance scaled by the semi-major axis of galaxies) changes with redshift and M* of the host galaxies: at a fixed M*, the slope becomes steeper toward low redshift, and at a fixed redshift, it becomes slightly steeper with M*. Based on our SED-fitting, this observed color gradient can be explained by a combination of a negative age gradient, a negative E(B-V) gradient, and a positive specific star formation rate gradient of the clumps. We also find that the color gradients of clumps are steeper than those of intra-clump regions. [Abridged]

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arXiv2017

Scientific Synergy Between LSST and Euclid

Euclid and the Large Synoptic Survey Telescope (LSST) are poised to dramatically change the astronomy landscape early in the next decade. The combination of high cadence, deep, wide-field optical photometry from LSST with high resolution, wide-field optical photometry and near-infrared photometry and spectroscopy from Euclid will be powerful for addressing a wide range of astrophysical questions. We explore Euclid/LSST synergy, ignoring the political issues associated with data access to focus on the scientific, technical, and financial benefits of coordination. We focus primarily on dark energy cosmology, but also discuss galaxy evolution, transient objects, solar system science, and galaxy cluster studies. We concentrate on synergies that require coordination in cadence or survey overlap, or would benefit from pixel-level co-processing that is beyond the scope of what is currently planned, rather than scientific programs that could be accomplished only at the catalog level without coordination in data processing or survey strategies. We provide two quantitative examples of scientific synergies: the decrease in photo-z errors (benefitting many science cases) when high resolution Euclid data are used for LSST photo-z determination, and the resulting increase in weak lensing signal-to-noise ratio from smaller photo-z errors. We briefly discuss other areas of coordination, including high performance computing resources and calibration data. Finally, we address concerns about the loss of independence and potential cross-checks between the two missions and potential consequences of not collaborating.

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arXiv2017

GAMA/G10-COSMOS/3D-HST: The 0<z<5 cosmic star-formation history, stellar- and dust-mass densities

We use the energy-balance code MAGPHYS to determine stellar and dust masses, and dust corrected star-formation rates for over 200,000 GAMA galaxies, 170,000 G10-COSMOS galaxies and 200,000 3D-HST galaxies. Our values agree well with previously reported measurements and constitute a representative and homogeneous dataset spanning a broad range in stellar mass (10^8---10^12 Msol), dust mass (10^6---10^9 Msol), and star-formation rates (0.01---100 Msol per yr), and over a broad redshift range (0.0 < z < 5.0). We combine these data to measure the cosmic star-formation history (CSFH), the stellar-mass density (SMD), and the dust-mass density (DMD) over a 12 Gyr timeline. The data mostly agree with previous estimates, where they exist, and provide a quasi-homogeneous dataset using consistent mass and star-formation estimators with consistent underlying assumptions over the full time range. As a consequence our formal errors are significantly reduced when compared to the historic literature. Integrating our cosmic star-formation history we precisely reproduce the stellar-mass density with an ISM replenishment factor of 0.50 +/- 0.07, consistent with our choice of Chabrier IMF plus some modest amount of stripped stellar mass. Exploring the cosmic dust density evolution, we find a gradual increase in dust density with lookback time. We build a simple phenomenological model from the CSFH to account for the dust mass evolution, and infer two key conclusions: (1) For every unit of stellar mass which is formed 0.0065---0.004 units of dust mass is also formed; (2) Over the history of the Universe approximately 90 to 95 per cent of all dust formed has been destroyed and/or ejected.

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arXiv2017

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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