Pareto optimality in house allocation problems

We study Pareto optimal matchings in the context of house allocation problems. We present an O(\sqrt{n}m) algorithm, based on Gales Top Trading Cycles Method, for finding a maximum cardinality Pareto optimal matching, where n is the number of agents and m is the total length of the preference lists. By contrast, we show that the problem of finding a minimum cardinality Pareto optimal matching is NP-hard, though approximable within a factor of 2. We then show that there exist Pareto optimal matchings of all sizes between a minimum and maximum cardinality Pareto optimal matching. Finally, we introduce the concept of a signature, which allows us to give a characterization, checkable in linear time, of instances that admit a unique Pareto optimal matching

UV Luminosity Function at z~4, 3, and 2

We use very deep (R_lim=27) UGRI imaging to study the evolution of the faint end of the UV-selected galaxy luminosity function from z~4 to z~2. We find that the number of sub-L* galaxies increases from z~4 to z~3 while the number of bright ones appears to remain constant. We find no evidence for continued evolution to lower redshift, z~2. If real, this differential evolution of the luminosity function suggests that differentially comparing key diagnostics of dust, stellar populations, etc. as a function of z and L may let us isolate the key mechanisms that drive galaxy evolution at high redshift and we describe several such studies currently underway.Comment: To appear in proceedings of the conference "Starbursts - from 30 Doradus to Lyman break galaxies" (IoA, Cambridge UK, Sep 2004), Astrophysics & Space Science Library, eds. de Grijs R., Gonzalez Delgado R.M. (Kluwer: Dordrecht

Are long gamma-ray bursts biased tracers of star formation? Clues from the host galaxies of the Swift/BAT6 complete sample of bright LGRBs. :III. Stellar masses, star formation rates, and metallicities at z > 1

(Abridged) Long gamma-ray bursts (LGRB) have been suggested as promising tracers of star formation owing to their association with the core-collapse of massive stars. The goal of this work is to characterise the population of host galaxies of LGRBs at 1 < z < 2, investigate the conditions in which LGRBs form at these redshifts and assess their use as tracers of star formation. We perform a spectro-photometric analysis to determine the stellar mass, star formation rate, specific star formation rate and metallicity of the complete, unbiased host galaxy sample of the Swift/BAT6 LGRB sample at 1 < z < 2. We compare the distribution of these properties to the ones of typical star-forming galaxies from the MOSDEF and COSMOS2015 Ultra Deep surveys, within the same redshift range. We find that, similarly to z < 1, LGRBs do not directly trace star formation at 1 < z < 2, and they tend to avoid high-mass, high-metallicity host galaxies. We also find evidence for an enhanced fraction of starbursts among the LGRB host sample with respect to the star-forming population of galaxies. Nonetheless we demonstrate that the driving factor ruling the LGRB efficiency is metallicity. The LGRB host distributions can be reconciled with the ones expected from galaxy surveys by imposing a metallicity upper limit of 12+logOH ~ 8.55. Metallicity rules the LGRB production efficiency, which is stifled at Z > 0.7 Zsun. Under this hypothesis we can expect LGRBs to trace star formation at z > 3, once the bulk of the star forming galaxy population are characterised by metallicities below this limit. The moderately high metallicity threshold found is in agreement with the conditions necessary to rapidly produce a fast-rotating Wolf-Rayet star a in close binary system, and could be accommodated by single star models under chemically homogeneous mixing with very rapid rotation and weak magnetic coupling.Comment: 19 pages, 17 figures, accepted for publication in Astronomy & Astrophysic

The Great Observatories Origins Deep Survey - VLT/VIMOS Spectroscopy in the GOODS-South Field: Part II

We present the full data set of the VIMOS spectroscopic campaign of the ESO/GOODS program in the CDFS, which complements the FORS2 ESO/GOODS spectroscopic campaign. The GOODS/VIMOS spectroscopic campaign is structured in two separate surveys using two different VIMOS grisms. The VIMOS Low Resolution Blue (LR-Blue) and Medium Resolution (MR) orange grisms have been used to cover different redshift ranges. The LR-Blue campaign is aimed at observing galaxies mainly at 1.8<z<3.5, while the MR campaign mainly aims at galaxies at z<1 and Lyman Break Galaxies (LBGs) at z>3.5. The full GOODS/VIMOS spectroscopic campaign consists of 20 VIMOS masks. This release adds 8 new masks to the previous release (12 masks, Popesso et al. 2009). In total we obtained 5052 spectra, 3634 from the 10 LR-Blue masks and 1418 from the 10 MR masks. A significant fraction of the extracted spectra comes from serendipitously observed sources: ~21% in the LR-Blue and ~16% in the MR masks. We obtained 2242 redshifts in the LR-Blue campaign and 976 in the MR campaign for a total success rate of 62% and 69% respectively, which increases to 66% and 73% if only primary targets are considered. The typical redshift uncertainty is estimated to be ~0.0012 (~255 km/s) for the LR-Blue grism and ~0.00040 (~120 km/s) for the MR grism. By complementing our VIMOS spectroscopic catalog with all existing spectroscopic redshifts publicly available in the CDFS, we compiled a redshift master catalog with 7332 entries, which we used to investigate large scale structures out to z~3.7. We produced stacked spectra of LBGs in a few bins of equivalent width (EW) of the Ly-alpha and found evidence for a lack of bright LBGs with high EW of the Ly-alpha. Finally, we obtained new redshifts for 12 X-ray sources of the CDFS and extended-CDFS.Comment: 22 pages, 20 figures, accepted for publication on Astronomy and Astrophysics, catalogs and data products are available at http://archive.eso.org/cms/eso-data/data-packages/goods-vimos-spectroscopy-data-release-version-2.0/, for ESO-GOODS related material consult http://www.eso.org/sci/activities/projects/goods

A preview of JWST metallicity studies at cosmic noon: the first detection of auroral [O II] emission at high redshift

Galaxie

Gas filaments of the cosmic web located around active galaxies in a protocluster

Cosmological simulations predict the Universe contains a network of intergalactic gas filaments, within which galaxies form and evolve. However, the faintness of any emission from these filaments has limited tests of this prediction. We report the detection of rest-frame ultraviolet Lyman-alpha radiation from multiple filaments extending more than one megaparsec between galaxies within the SSA 22 proto-cluster at a redshift of 3.1. Intense star formation and supermassive black-hole activity is occurring within the galaxies embedded in these structures, which are the likely sources of the elevated ionizing radiation powering the observed Lyman-alpha emission. Our observations map the gas in filamentary structures of the type thought to fuel the growth of galaxies and black holes in massive proto-clusters

Cosmic histories of star formation and reionization: An analysis with a power-law approximation

With a simple power-law approximation of high-redshift ($\gtrsim3.5$) star formation history, i.e., $\dot{\rho}_*(z)\propto [(1+z)/4.5]^{-\alpha}$, we investigate the reionization of intergalactic medium (IGM) and the consequent Thomson scattering optical depth for cosmic microwave background (CMB) photons. A constraint on the evolution index $\alpha$ is derived from the CMB optical depth measured by the {\it Wilkinson Microwave Anisotropy Probe} (WMAP) experiment, which reads $\alpha\approx2.18\lg{\mathscr{N}_{\gamma}}-3.89$, where the free parameter $\mathscr{N}_\gamma$ is the number of the escaped ionizing ultraviolet photons per baryon. Moreover, the redshift for full reionization, $z_f$, can also be expressed as a function of $\alpha$ as well as $\mathscr{N}_{\gamma}$. By further taking into account the implication of the Gunn-Peterson trough observations to quasars for the full reionization redshift, i.e., $6\lesssim z_f \lesssim7$, we obtain $0.3\lesssim\alpha\lesssim1.3$ and $80\lesssim\mathscr{N}_{\gamma}\lesssim230$. For a typical number of $\sim4000$ of ionizing photons released per baryon of normal stars, the fraction of these photons escaping from the stars, $f_{\rm esc}$, can be constrained to within the range of $(2.0-5.8)$.Comment: 10 pages, 4 figures, accepted for publication in JCA

The MOSFIRE deep evolution field survey: implications of the lack of evolution in the dust attenuation-mass relation to z ~ 2

Galaxie