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M. J. Page

Publications and source records attributed to M. J. Page.

At least 91 records · Page 5Linked to original sources

HerMES: A Statistical Measurement of the Redshift Distribution of Herschel-SPIRE Sources Using the Cross-correlation Technique

The wide-area imaging surveys with the {\it Herschel} Space Observatory at sub-mm wavelengths have now resulted in catalogs of order one hundred thousand dusty, star-burst galaxies. We make a statistical estimate of $N(z)$ using a clustering analysis of sub-mm galaxies detected at each of 250, 350 and 500 $μ$m from the Herschel Multi-tiered Extragalactic Survey (HerMES) centered on the Boötes field. We cross-correlate {\it Herschel} galaxies against galaxy samples at optical and near-IR wavelengths from the Sloan Digital Sky Survey (SDSS), the NOAO Deep Wide Field Survey (NDWFS) and the Spitzer Deep Wide Field Survey (SDWFS). We create optical and near-IR galaxy samples based on their photometric or spectroscopic redshift distributions and test the accuracy of those redshift distributions with similar galaxy samples defined with catalogs of the Cosmological Evolution Survey (COSMOS), as the COSMOS field has superior spectroscopy coverage. We model-fit the clustering auto and cross-correlations of {\it Herschel} and optical/IR galaxy samples to estimate $N(z)$ and clustering bias factors. The $S_{350} > 20$ mJy galaxies have a bias factor varying with redshift as $b(z)=1.0^{+1.0}_{-0.5}(1+z)^{1.2^{+0.3}_{-0.7}}$. This bias and the redshift dependence is broadly in agreement with galaxies that occupy dark matter halos of mass in the range of 10$^{12}$ to 10$^{13}$ M$_{\sun}$. We find that the redshift distribution peaks around $z \sim 0.5$ to 1 for galaxies selected at 250 $μ$m with an average redshift of $< z > = 1.8 \pm 0.2$. For 350 and 500 $μ$m-selected SPIRE samples the peak shifts to higher redshift, but the average redshift remains the same with a value of $1.9 \pm 0.2$.

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Panchromatic observations of the textbook GRB 110205A: constraining physical mechanisms of prompt emission and afterglow

We present a comprehensive analysis of a bright, long duration (T90 ~ 257 s) GRB 110205A at redshift z= 2.22. The optical prompt emission was detected by Swift/UVOT, ROTSE-IIIb and BOOTES telescopes when the GRB was still radiating in the gamma-ray band. Nearly 200 s of observations were obtained simultaneously from optical, X-ray to gamma-ray, which makes it one of the exceptional cases to study the broadband spectral energy distribution across 6 orders of magnitude in energy during the prompt emission phase. By fitting the time resolved prompt spectra, we clearly identify, for the first time, an interesting two-break energy spectrum, roughly consistent with the standard GRB synchrotron emission model in the fast cooling regime. Although the prompt optical emission is brighter than the extrapolation of the best fit X/gamma-ray spectra, it traces the gamma-ray light curve shape, suggesting a relation to the prompt high energy emission. The synchrotron + SSC scenario is disfavored by the data, but the models invoking a pair of internal shocks or having two emission regions can interpret the data well. Shortly after prompt emission (~ 1100 s), a bright (R = 14.0) optical emission hump with very steep rise (alpha ~ 5.5) was observed which we interpret as the emission from the reverse shock. It is the first time that the rising phase of a reverse shock component has been closely observed. The full optical and X-ray afterglow lightcurves can be interpreted within the standard reverse shock (RS) + forward shock (FS) model. In general, the high quality prompt emission and afterglow data allow us to apply the standard fireball shock model to extract valuable information about the GRB including the radiation mechanism, radius of prompt emission R, initial Lorentz factor of the outflow, the composition of the ejecta, as well as the collimation angle and the total energy budget.

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The Herschel Multi-tiered Extragalactic Survey: HerMES

The Herschel Multi-tiered Extragalactic Survey, HerMES, is a legacy program designed to map a set of nested fields totalling ~380 deg^2. Fields range in size from 0.01 to ~20 deg^2, using Herschel-SPIRE (at 250, 350 and 500 μm), and Herschel-PACS (at 100 and 160 μm), with an additional wider component of 270 deg^2 with SPIRE alone. These bands cover the peak of the redshifted thermal spectral energy distribution from interstellar dust and thus capture the re-processed optical and ultra-violet radiation from star formation that has been absorbed by dust, and are critical for forming a complete multi-wavelength understanding of galaxy formation and evolution. The survey will detect of order 100,000 galaxies at 5σin some of the best studied fields in the sky. Additionally, HerMES is closely coordinated with the PACS Evolutionary Probe survey. Making maximum use of the full spectrum of ancillary data, from radio to X-ray wavelengths, it is designed to: facilitate redshift determination; rapidly identify unusual objects; and understand the relationships between thermal emission from dust and other processes. Scientific questions HerMES will be used to answer include: the total infrared emission of galaxies; the evolution of the luminosity function; the clustering properties of dusty galaxies; and the properties of populations of galaxies which lie below the confusion limit through lensing and statistical techniques. This paper defines the survey observations and data products, outlines the primary scientific goals of the HerMES team, and reviews some of the early results.

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The gas-to-dust mass ratio of Centaurus A as seen by Herschel

We present photometry of the nearby galaxy NGC 5128 (Centaurus A) observed with the PACS and SPIRE instruments on board the Herschel Space Observatory, at 70, 160, 250, 350 and 500 μm, as well as new CO J = 3-2 observations taken with the HARP-B instrument on the JCMT. Using a single component modified blackbody, we model the dust spectral energy distribution within the disk of the galaxy using all five Herschel wavebands, and find dust temperatures of ~30 K towards the centre of the disk and a smoothly decreasing trend to ~20 K with increasing radius. We find a total dust mass of (1.59 \pm 0.05) \times 10^7 M\odot, and a total gas mass of (2.7 \pm 0.2) \times 10^9 M\odot. The average gas-to-dust mass ratio is 103 \pm 8 but we find an interesting increase in this ratio to approximately 275 toward the centre of Cen A. We discuss several possible physical processes that may be causing this effect, including dust sputtering, jet entrainment and systematic variables such as the XCO factor. Dust sputtering by X-rays originating in the AGN or the removal of dust by the jets are our most favoured explanations.

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The Dust & Gas Properties of M83

We examine the dust and gas properties of the nearby, barred galaxy M83, which is part of the Very Nearby Galaxy Survey. Using images from the PACS and SPIRE instruments of Herschel, we examine the dust temperature and dust mass surface density distribution. We find that the nuclear, bar and spiral arm regions exhibit higher dust temperatures and masses compared to interarm regions. However, the distribution of dust temperature and mass are not spatially coincident. Assuming a trailing spiral structure, the dust temperature peaks in the spiral arms lie ahead of the dust surface density peaks. The dust mass surface density correlates well with the distribution of molecular gas as traced by CO (J=3-2) images (JCMT) and the star formation rate as traced by H?2 with a correction for obscured star formation using 24 micron emission. Using HI images from THINGS to trace the atomic gas component, we make total gas mass surface density maps and calculate the gas-to-dust ratio. We find a mean gas-to-dust ratio of 84 \pm 4 with higher values in the inner region assuming a constant CO-to-H2 conversion factor. We also examine the gas-to-dust ratio using CO-to-H2 conversion factor that varies with metallicity.

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A Multi-wavelength MOCASSIN Model of the Magellanic-type Galaxy NGC 4449

We use the photoionisation and dust radiative transfer code MOCASSIN to create a model of the dwarf irregular galaxy NGC 4449. The best-matching model reproduces the global optical emission line fluxes and the observed spectral energy distribution (SED) spanning wavelengths from the UV to sub-mm, and requires the bolometric luminosity of 6.25e9 Lsolar for the underlying stellar component, M_d/M_g of 1/680 and M_d of 2.2e6 Msolar.

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The Herschel Multi-Tiered Extragalactic Survey: SPIRE-mm Photometric Redshifts

We investigate the potential of submm-mm and submm-mm-radio photometric redshifts using a sample of mm-selected sources as seen at 250, 350 and 500 μm by the SPIRE instrument on Herschel. From a sample of 63 previously identified mm-sources with reliable radio identifications in the GOODS-N and Lockman Hole North fields 46 (73 per cent) are found to have detections in at least one SPIRE band. We explore the observed submm/mm colour evolution with redshift, finding that the colours of mm-sources are adequately described by a modified blackbody with constant optical depth τ = (ν/ν0)^β where β = +1.8 and ν0 = c/100 μm. We find a tight correlation between dust temperature and IR luminosity. Using a single model of the dust temperature and IR luminosity relation we derive photometric redshift estimates for the 46 SPIRE detected mm-sources. Testing against the 22 sources with known spectroscopic, or good quality optical/near-IR photometric, redshifts we find submm/mm photometric redshifts offer a redshift accuracy of |z|/(1+z) = 0.16 (< |z| >= 0.51). Including constraints from the radio-far IR correlation the accuracy is improved to |z|/(1 + z) = 0.15 (< |z| >= 0.45). We estimate the redshift distribution of mm-selected sources finding a significant excess at z > 3 when compared to ~ 850 μm selected samples.

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Averaging the AGN X-ray spectra from deep Chandra fields

The X-ray spectra of Active Galactic Nuclei (AGN) carry the signatures of the emission from the central region, close to the Super Massive Black Hole (SMBH). For this reason, the study of deep X-ray spectra is a powerful instrument to investigate the origin of their emission. The emission line most often observed in the X-ray spectra of AGN is Fe K. It is known that it can be broadened and deformed by relativistic effects if emitted close enough to the central SMBH. In recent statistical studies of the X-ray spectra of AGN samples, it is found that a narrow Fe line is ubiquitous, while whether the broad features are as common is still uncertain. We present here the results of an investigation on the characteristics of the Fe line in the average X-ray spectra of AGN in deep Chandra fields. The average spectrum of the AGN is computed using Chandra spectra with more than 200 net counts from the AEGIS, Chandra Deep Field North and Chandra Deep Field South surveys. The sample spans a broader range of X-ray luminosities than other samples studied with stacking methods up to z=3.5. We analyze the average spectra of this sample using our own averaging method, checking the results against extensive simulations. Subsamples defined in terms of column density of the local absorber, luminosity and z are also investigated. We found a very significant Fe line with a narrow profile in all our samples and in almost all the subsamples that we constructed. The equivalent width (EW) of the narrow line estimated in the average spectrum of the full sample is 74 eV. The broad line component is significantly detected in the subsample of AGN with L<1.43 1E44 cgs and z<0.76, with EW=108 eV. We concluded that the narrow Fe line is an ubiquitous feature of the X-ray spectra of the AGN up to z=3.5.The broad line component is significant in the X-ray spectra of the AGN with low luminosity and low z.

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The Dust Extinction Curves of Gamma-Ray Burst Host Galaxies

The composition and amount of interstellar dust within gamma-ray burst (GRB) host galaxies is of key importance when addressing selection effects in the GRB redshift distribution, and when studying the properties of their host galaxies. As well as the implications for GRB research, probing the dust within the high-z hosts of GRBs also contributes to our understanding of the conditions of the interstellar medium and star-formation in the distant Universe. Nevertheless, the physical properties of dust within GRB host galaxies continues to be a highly contended issue. In this paper we explore the mean extinction properties of dust within the host galaxies of a sample of 17 GRBs with total host galaxy visual extinction Av<1 ( =0.4), covering a redshift range z=0.7-3.1. We find the average host extinction curve to have an ultraviolet slope comparable to that of the LMC, but with little evidence of a 2175Angs dust extinction feature as observed along Milky Way and LMC sightlines. We cannot at present rule out the presence of a 2175Angs feature, and both the standard SMC and LMC extinction curves also provide good fits to our data. However, we can reject an extinction curve that has a UV slope as flat as the mean Milky Way extinction curve, whilst also having a 2175Angs feature as prominent as seen in the mean Milky Way extinction curve. This is in contrast to the clear detection of a 2175Angs bump and the flatter extinction curves of some more heavily extinguished GRBs (Av>1), which may be indicative of there being a dependence between dust abundance and the wavelength dependence of dust extinction, as has been previously speculated.

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HerMES: point source catalogues from deep Herschel-SPIRE observations

We describe the generation of single-band point source catalogues from submillimetre Herschel-SPIRE observations taken as part of the Science Demonstration Phase of the Herschel Multi-tiered Extragalactic Survey (HerMES). Flux densities are found by means of peak-finding and the fitting of a Gaussian point-response function. With highly-confused images, careful checks must be made on the completeness and flux density accuracy of the detected sources. This is done by injecting artificial sources into the images and analysing the resulting catalogues. Measured flux densities at which 50 per cent of injected sources result in good detections at (250, 350, 500) μm range from (11.6, 13.2, 13.1) mJy to (25.7, 27.1, 35.8) mJy, depending on the depth of the observation (where a `good' detection is taken to be one with positional offset less than one full-width half-maximum of the point-response function, and with the measured flux density within a factor of 2 of the flux density of the injected source). This paper acts as a reference for the 2010 July HerMES public data release.

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Investigations of dust heating in M81, M83, and NGC 2403 with the Herschel Space Observatory

We use Spitzer Space Telescope and Herschel Space Observatory far-infrared data along with ground-based optical and near-infrared data to understand how dust heating in the nearby face-on spiral galaxies M81, M83, and NGC 2403 is affected by the starlight from all stars and by the radiation from star forming regions. We find that 70/160 micron surface brightness ratios tend to be more strongly influenced by star forming regions. However, the 250/350 micron and 350/500 micron surface brightness ratios are more strongly affected by the light from the total stellar populations, suggesting that the dust emission at >250 microns originates predominantly from a component that is colder than the dust seen at <160 microns and that is relatively unaffected by star formation activity. We conclude by discussing the implications of this for modelling the spectral energy distributions of both nearby and more distant galaxies and for using far-infrared dust emission to trace star formation.

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Herschel/HerMES: The X-ray - Infrared correlation for star-forming galaxies at z~1

For the first time, we investigate the X-ray/infrared (IR) correlation for star-forming galaxies at z~1, using SPIRE submm data from the recently-launched Herschel Space Observatory and deep X-ray data from the 2Ms Chandra deep field north (CDFN) survey. We examine the X-ray/IR correlation in the soft X-ray (SX, 0.5-2 keV) and hard X-ray (HX, 2-10 keV) bands by comparing our z~1 SPIRE-detected star-forming galaxies (SFGs) to equivalently IR-luminous (L_IR >10^10 L_sun) samples in the local/low redshift Universe. Our results suggest that the X-ray/IR properties of the SPIRE SFGs are on average similar to those of their local counterparts, as we find no evidence for evolution in the L_SX/L_IR and L_HX/L_IR ratios with redshift. We note however, that at all redshifts, both L_SX/L_IR and L_HX/L_IR are strongly dependent on IR luminosity, with luminous and ultraluminous infrared galaxies (LIRGs and ULIRGs,L_IR >10^11 L_sun) having up to an order of magnitude lower values than normal infrared galaxies (L_IR <10^11 L_sun). We derive a L_SX-L_IR relation and confirm the applicability of an existing L_HX-L_IR relation for both local and distant LIRGs and ULIRGs, consistent with a scenario where X-ray luminosity is correlated with the star-formation rate (SFR).

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The nature of X-ray absorbed QSOs

There exists a significant population of broad line, z~2 QSOs which have heavily absorbed X-ray spectra. Follow up observations in the submillimetre show that these QSOs are embedded in ultraluminous starburst galaxies, unlike most unabsorbed QSOs at the same redshifts and luminosities. Here we present X-ray spectra from XMM-Newton for a sample of 5 such X-ray absorbed QSOs that have been detected at submillimetre wavelengths. We also present spectra in the restframe ultraviolet from ground based telescopes. All 5 QSOs are found to exhibit strong C IV absorption lines in their ultraviolet spectra with equivalent width > 5 Angstroms. The X-ray spectra are inconsistent with the hypothesis that these objects show normal QSO continua absorbed by low-ionization gas. Instead, the spectra can be modelled successfully with ionized absorbers, or with cold absorbers if they posess unusually flat X-ray continuum shapes and unusual optical to X-ray spectral energy distributions. We show that the ionized absorber model provides the simplest, most self-consistent explanation for their observed properties. We estimate that the fraction of radiated power that is converted into kinetic luminosity of the outflowing winds is typically ~4 per cent, in agreement with recent estimates for the kinetic feedback from QSOs required to produce the M - sigma relation, and consistent with the hypothesis that the X-ray absorbed QSOs represent the transition phase between obscured accretion and the luminous QSO phase in the evolution of massive galaxies.

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HerMES: Lyman Break Galaxies individually detected at 0.7 < z < 2.0 in GOODS-N with Herschel/SPIRE

As part of the Herschel Multi-tiered Extragalactic Survey we have investigated the rest-frame far-infrared (FIR) properties of a sample of more than 4800 Lyman Break Galaxies (LBGs) in the Great Observatories Origins Deep Survey North field. Most LBGs are not detected individually, but we do detect a sub-sample of 12 objects at 0.7 < z < 1.6 and one object at z ~ 2.0. The ones detected by Herschel SPIRE have redder observed NUV-U and U-R colors than the others, while the undetected ones have colors consistent with average LBGs at z > 2.5. The UV-to-FIR spectral energy distributions of the objects detected in the rest-frame FIR are investigated using the code CIGALE to estimate physical parameters. We find that LBGs detected by SPIRE are high mass, luminous infrared galaxies. It appears that LBGs are located in a triangle-shaped region in the A_FUV vs. Log L_FUV diagram limited by A_FUV=0 at the bottom and by a diagonal following the temporal evolution of the most massive galaxies from the bottom-right to the top-left of the diagram. This upper envelop can be used as upper limits for the UV dust attenuation as a function of L_FUV}. The limits of this region are well explained using a closed-box model, where the chemical evolution of galaxies produces metals, which in turn lead to higher dust attenuation when the galaxies age.

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Redshift Determination and CO Line Excitation Modeling for the Multiply-Lensed Galaxy HLSW-01

We report on the redshift measurement and CO line excitation of HERMES J105751.1+573027 (HLSW-01), a strongly lensed submillimeter galaxy discovered in Herschel/SPIRE observations as part of the Herschel Multi-tiered Extragalactic Survey (HerMES). HLSW-01 is an ultra-luminous galaxy with an intrinsic far-infrared luminosity of 1.4x10^(13) solar luminosities, and is lensed by a massive group of galaxies into at least four images with a total magnification of 10.9+/-0.7. With the 100 GHz instantaneous bandwidth of the Z-Spec instrument on the Caltech Submillimeter Observatory, we robustly identify a redshift of z=2.958+/-0.007 for this source, using the simultaneous detection of four CO emission lines (J = 7-6, J = 8-7, J = 9-8, and J = 10-9). Combining the measured line fluxes for these high-J transitions with the J = 1-0, J = 3-2 and J = 5-4 line fluxes measured with the Green Bank Telescope, the Combined Array for Research in Millimeter Astronomy, and the Plateau de Bure Interferometer, respectively, we model the physical properties of the molecular gas in this galaxy. We find that the full CO spectral line energy distribution is well described by warm, moderate-density gas with Tkin = 86-235 K and n(H2) = (1.1-3.5)x10^3 cm^(-3). However, it is possible that the highest-J transitions are tracing a small fraction of very dense gas in molecular cloud cores, and two-component models that include a warm/dense molecular gas phase with Tkin ~ 200 K, n(H2) ~ 10^5 cm^(-3) are also consistent with these data. Higher signal-to-noise measurements of the J(upper) > 7 transitions with high spectral resolution, combined with high spatial resolution CO maps, are needed to improve our understanding of the gas excitation, morphology, and dynamics of this interesting high-redshift galaxy.

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Modeling of the HERMES J105751.1+573027 submillimeter source lensed by a dark matter dominated foreground group of galaxies

We present the results of a gravitational lensing analysis of the bright $\zs=2.957$ sub-millimeter galaxy (SMG), HERMES J105751.1+573027 found in {\it Herschel}/SPIRE Science Demonstration Phase data from the Herschel Multi-tiered Extragalactic Survey (HerMES) project. The high resolution imaging available in optical and Near-IR channels, along with CO emission obtained with the Plateau de Bure Interferometer, allow us to precisely estimate the intrinsic source extension and hence estimate the total lensing magnification to be $μ=10.9\pm 0.7$. We measure the half-light radius $R_{\rm eff}$ of the source in the rest-frame Near-UV and $V$ bands that characterize the unobscured light coming from stars and find $R_{\rm eff,*}= [2.0 \pm 0.1]$ kpc, in good agreement with recent studies on the Submillimeter Galaxy population. This lens model is also used to estimate the size of the gas distribution ($R_{\rm eff,gas}= [1.1\pm0.5]$) kpc by mapping back in the source plane the CO (J=5-4) transition line emission. The lens modeling yields a relatively large Einstein radius $R_{\rm Ein}= 4\farcs10 \pm 0\farcs02$, corresponding to a deflector velocity dispersion of [$483\pm 16] \,\kms$. This shows that HERMES J105751.1+573027 is lensed by a {\it galaxy group-size} dark matter halo at redshift $\zl\sim 0.6$. The projected dark matter contribution largely dominates the mass budget within the Einstein radius with $f_{\rm dm}(<R_{\rm Ein})\sim 80%$. This fraction reduces to $f_{\rm dm}(<R_{\rm eff,G1}\simeq 4.5\kpc)\sim 47%$ within the effective radius of the main deflecting galaxy of stellar mass $M_{\rm *,G1}=[8.5\pm 1.6] \times 10^{11}\msun$. At this smaller scale the dark matter fraction is consistent with results already found for massive lensing ellipticals at $z\sim0.2$ from the SLACS survey.

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Discovery of a Multiply-Lensed Submillimeter Galaxy in Early HerMES Herschel/SPIRE Data

We report the discovery of a bright ($f(250\mum) > 400$ mJy), multiply-lensed submillimeter galaxy \obj\ in {\it Herschel}/SPIRE Science Demonstration Phase data from the HerMES project. Interferometric 880\mum\ Submillimeter Array observations resolve at least four images with a large separation of $\sim 9\arcsec$. A high-resolution adaptive optics $K_p$ image with Keck/NIRC2 clearly shows strong lensing arcs. Follow-up spectroscopy gives a redshift of $z=2.9575$, and the lensing model gives a total magnification of $μ\sim 11 \pm 1$. The large image separation allows us to study the multi-wavelength spectral energy distribution (SED) of the lensed source unobscured by the central lensing mass. The far-IR/millimeter-wave SED is well described by a modified blackbody fit with an unusually warm dust temperature, $88 \pm 3$ K. We derive a lensing-corrected total IR luminosity of $(1.43 \pm 0.09) \times 10^{13}\, \mathrm{L}_{\odot}$, implying a star formation rate of $\sim 2500\, \mathrm{M}_{\odot}\, \mathrm{yr}^{-1}$. However, models primarily developed from brighter galaxies selected at longer wavelengths are a poor fit to the full optical-to-millimeter SED. A number of other strongly lensed systems have already been discovered in early {\it Herschel} data, and many more are expected as additional data are collected.

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Dynamical Structure of the Molecular Interstellar Medium in an Extremely Bright, Multiply Lensed z~3 Submillimeter Galaxy Discovered with Herschel

We report the detection of CO 5-4, 3-2, and 1-0 emission in the strongly lensed, Herschel/SPIRE-selected submillimeter galaxy (SMG) HLSW-01 at z=2.9574+/-0.0001, using the Plateau de Bure Interferometer, the Combined Array for Research in Millimeter-wave Astronomy, and the Green Bank Telescope. The observations spatially resolve the molecular gas into four lensed images with a maximum separation of ~9", and reveal the internal gas dynamics in this system. We derive lensing-corrected CO line luminosities of L'(CO 1-0) = (4.17+/-0.41), L'(CO 3-2) = (3.96+/-0.20) and L'(CO 5-4) = (3.45+/-0.20) x 10^10 (mu_L/10.9)^-1 Kkm/s pc^2, corresponding to luminosity ratios of r_31 = 0.95+/-0.10, r_53 = 0.87+/-0.06, and r_51 = 0.83+/-0.09. This suggests a total molecular gas mass of Mgas = 3.3 x 10^10 (alpha_CO/0.8) (mu_L/10.9)^-1 Msun. The gas mass, gas mass fraction, gas depletion timescale, star formation efficiency, and specific star formation rate are typical for an SMG. The velocity structure of the gas reservoir suggests that the brightest two lensed images are dynamically resolved projections of the same dust-obscured region in the galaxy that are kinematically offset from the unresolved fainter images. The resolved kinematics appear consistent with the complex velocity structure observed in major, `wet' (i.e., gas-rich) mergers. Major mergers are commonly observed in SMGs, and are likely to be responsible for fueling their intense starbursts at high gas consumption rates. This study demonstrates the level of detail to which galaxies in the early universe can be studied by utilizing the increase in effective spatial resolution and sensitivity provided by gravitational lensing.

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