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The role of internal and environmental factors in the star formation activity of galaxies is still a matter of debate, particularly at higher redshifts. Leveraging the most recent release of the COSMOS catalog, COSMOS2020, and density measurements from our previous study we disentangle the impact of environment and stellar mass on the star formation rate (SFR), and specific SFR (sSFR) of a sample of $\sim 210,000$ galaxies within redshift range $0.4< z < 4$ and present our findings in three cosmic epochs: 1) out to $z\sim 1$, the average SFR and sSFR decline at extremely dense environments and high mass end of the distribution which is mostly due to the presence of the massive quiescent population; 2) at $1

In this paper, we study the induced homological sequence and the induced merge tree of a discrete Morse function on a tree. A discrete Morse function on a tree gives rise to a sequence of Betti numbers that keep track of the number of components at each critical value. A discrete Morse function on a tree also gives rise to an induced merge tree which keeps track of component birth, death, and merging information. These topological indicators are similar but neither one contains the information of the other. We show that given a merge tree and a homological sequence along with some mild conditions on their relationship, there is a discrete Morse function on a tree that induces both the given merge tree and the given homological sequence.

We prove analogues of classical results for higher homotopy groups and singular homology groups of pseudotopological spaces. Pseudotopological spaces are a generalization of (\v{C}ech) closure spaces which are in turn a generalization of topological spaces. Pseudotopological spaces also include graphs and directed graphs as full subcategories. Thus they are a bridge that connects classical algebraic topology with the more applied side of topology. More specifically, we show the existence of a long exact sequence for homotopy groups of pairs of pseudotopological spaces and that a weak homotopy equivalence induces isomorphisms for homology groups. Our main result is the construction of weak homotopy equivalences between the geometric realizations of directed Vietoris-Rips complexes and their underlying directed graphs. This implies that singular homology groups of finite directed graphs can be efficiently calculated from finite combinatorial structures, despite their associated chain groups being infinite dimensional. This work is similar to the work of McCord for finite topological spaces but in the context of pseudotopological spaces. Our results also give a novel approach for studying (higher) homotopy groups of discrete mathematical structures such as (directed) graphs or digital images., Comment: 43 pages, fixed typos, added details to the Appendix

We develop a discrete Morse theory for open simplicial complexes $K=X\setminus T$ where $X$ is a simplicial complex and $T$ a subcomplex of $X$. A discrete Morse function $f$ on $K$ gives rise to a discrete Morse function on the order complex $S_K$ of $K$, and the topology change determined by $f$ on $K$ can be understood by analyzing the the topology change determined by the discrete Morse function on $S_K$. This topology change is given by a structure theorem on the level subcomplexes of $S_K$. Finally, we show that the Borel-Moore homology of $K$, a homology theory for locally compact spaces, is isomorphic to the homology induced by a gradient vector field on $K$ and deduce corresponding weak Morse inequalities.

We define a second (higher) homotopy group for digital images. Namely, we construct a functor from digital images to abelian groups, which closely resembles the ordinary second homotopy group from algebraic topology. We illustrate that our approach can be effective by computing this (digital) second homotopy group for a digital 2-sphere., Comment: 32 pages, 10 figures

In this paper, we extend the notion of a merge tree to that of a generalized merge tree, a merge tree that includes 1-dimensional cycle birth information. Given a discrete Morse function on a $1$-dimensional regular CW complex, we construct the induced generalized merge tree. We give several notions of equivalence of discrete Morse functions based on the induced generalized merge tree and how these notions relate to one another. As a consequence, we obtain a complete solution to the inverse problem between discrete Morse functions on $1$-dimensional regular CW complexes and generalized merge trees. After characterizing which generalized merge trees can be induced by a discrete Morse function on a simple graph, we give an algorithm based on the induced generalized merge tree of a discrete Morse function $f\colon X \to \mathbb{R}$ that cancels the critical simplices of $f$ and replaces it with an optimal discrete Morse function., Comment: 21 pages, comments welcome

Metrics for merge trees that are simultaneously stable, informative, and efficiently computable have so far eluded researchers. We show in this work that it is possible to devise such a metric when restricting merge trees to ordered domains such as the interval and the circle. We present the ``dynamic ordered persistence editing'' (DOPE) distance, which we prove is stable and informative while satisfying metric properties. We then devise a simple $O(N^2)$ dynamic programming algorithm to compute it on the interval and an $O(N^3)$ algorithm to compute it on the circle. Surprisingly, we accomplish this by ignoring all of the hierarchical information of the merge tree and simply focusing on a sequence of ordered critical points, which can be interpreted as a time series. Thus our algorithm is more similar to string edit distance and dynamic time warping than it is to more conventional merge tree comparison algorithms. In the context of time series with the interval as a domain, we show empirically on the UCR time series classification dataset that DOPE performs better than bottleneck/Wasserstein distances between persistence diagrams., Comment: 31 pages, 12 Figures

In this paper, we determine the homotopy type of the Morse complex and matching complex of multiple families of complexes by utilizing star cluster collapses and the Cluster Lemma. We compute the homotopy type of the Morse complex of an extended notion of a star graph, as well as the homotopy type of the matching complex of a Dutch windmill graph. Additionally, we provide alternate computations of the homotopy type of the Morse complex of paths, the homotopy type of the matching complex of paths, and the homotopy type of the matching complex of cycles. We then use this same method of computing homotopy types to investigate the relationship between the homotopy type of the matching complex and the generalized Morse complex.

We report CO(5$\rightarrow$4) and CO(6$\rightarrow$5) line observations in the dusty starbursting galaxy CRLE ($z = 5.667$) and the main-sequence (MS) galaxy HZ10 ($z = 5.654$) with the Northern Extended Millimeter Array (NOEMA). CRLE is the most luminous $z>5$ starburst in the COSMOS field and HZ10 is the most gas-rich "normal" galaxy currently known at $z>5$. We find line luminosities for CO(5$\rightarrow$4) and CO(6$\rightarrow$5) of (4.9 $\pm$ 0.5) and (3.8 $\pm$ 0.4) $\times$ 10$^{10}$ K km s$^{-1}$ pc$^{2}$ for CRLE and upper limits of $< 0.76$ and $< 0.60$ $\times$ 10$^{10}$ K km s$^{-1}$ pc$^{2}$ for HZ10, respectively. The CO excitation of CRLE appears comparable to other $z>5$ dusty star-forming galaxies (DSFGs). For HZ10, these line luminosity limits provide the first significant constraints of this kind for a MS galaxy at $z > 5$. We find the upper limit of $L'_{5\rightarrow4}/L'_{2\rightarrow1}$ in HZ10 could be similar to the average value for MS galaxies around $z\approx 1.5$, suggesting that MS galaxies with comparable gas excitation may already have existed one billion years after the Big Bang. For CRLE we determine the most likely values for the H$_2$ density, kinetic temperature and dust temperature based on excitation modeling of the CO line ladder. We also derive a total gas mass of $(7.1 \pm 1.3) \times 10^{10} M_\odot$. Our findings provide some of the currently most detailed constraints on the gas excitation that sets the conditions for star formation in a galaxy protocluster environment at $z > 5$., Comment: 14 pages, 6 figures, accepted to ApJ

In this paper, we study merge trees induced by a discrete Morse function on a tree. Given a discrete Morse function, we provide a method to constructing an induced merge tree and define a new notion of equivalence of discrete Morse functions based on the induced merge tree. We then relate the matching number of a tree to a certain invariant of the induced merge tree. Finally, we count the number of merge trees that can be induced on a star graph and characterize the induced merge tree.

The Morse complex $\mathcal{M}(\Delta)$ of a finite simplicial complex $\Delta$ is the complex of all gradient vector fields on $\Delta$. In this paper we study higher connectivity properties of $\mathcal{M}(\Delta)$. For example, we prove that $\mathcal{M}(\Delta)$ gets arbitrarily highly connected as the maximum degree of a vertex of $\Delta$ goes to $\infty$, and for $\Delta$ a graph additionally as the number of edges goes to $\infty$. We also classify precisely when $\mathcal{M}(\Delta)$ is connected or simply connected. Our main tool is Bestvina-Brady Morse theory, applied to a "generalized Morse complex.", Comment: 12 pages, 2 figures. v2: Substantial rewrite with stronger results, final version, accepted by Proc. Amer. Math. Soc

Various concepts and constructions in homotopy theory have been defined in the digital setting. Although there have been several attempts at a definition of a fibration in the digital setting, robust examples of these digital fibrations are few and far between. In this paper, we develop a digital Hopf fibration within the category of tolerance spaces. By widening our category to that of tolerance spaces, we are able to give a construction of this digital Hopf fibration which mimics the smooth setting.

In previous work, we have defined---intrinsically, entirely within the digital setting---a fundamental group for digital images. Here, we show that this group is isomorphic to the edge group of the clique complex of the digital image considered as a graph. The clique complex is a simplicial complex and its edge group is well-known to be isomorphic to the ordinary (topological) fundamental group of its geometric realization. This identification of our intrinsic digital fundamental group with a topological fundamental group---extrinsic to the digital setting---means that many familiar facts about the ordinary fundamental group may be translated into their counterparts for the digital fundamental group: The digital fundamental group of any digital circle is $\mathbb{Z}$; a version of the Seifert-van Kampen Theorem holds for our digital fundamental group; every finitely presented group occurs as the (digital) fundamental group of some digital image. We also show that the (digital) fundamental group of every 2D digital image is a free group., Comment: 32 pages, 4 figures

In this paper, we determine the homotopy type of the Morse complex of certain collections of simplicial complexes by studying dominating vertices or strong collapses. We show that if $K$ contains two leaves that share a common vertex, then the Morse complex is strongly collapsible and hence has the homotopy type of a point. We also show that the pure Morse complex of a tree is strongly collapsible, thereby recovering as a corollary a result of Ayala et al. In addition, we prove that the Morse complex of a disjoint union $K\sqcup L$ is the Morse complex of the join $K*L$. This result is used to compute the homotopy type of the Morse complex of some families of graphs, including Caterpillar graphs, as well as the automorphism group of a disjoint union for a large collection of disjoint complexes.

We examine the role of environment on the in situ star formation (SF) hosted by the progenitors of the most massive galaxies in the present-day universe, the brightest cluster galaxies (BCGs), from $z \sim 3$ to present in the COSMOS field. Progenitors are selected from the COSMOS field using a stellar mass cut motivated by the evolving cumulative comoving number density of progenitors within the Illustris simulation, as well as the Millennium-II simulation and a constant comoving number density method for comparison. We characterize each progenitor using far-ultraviolet--far-infrared observations taken from the COSMOS field and fitting stellar, dust, and active galactic nucleus components to their spectral energy distributions. Additionally, we compare the SF rates of our progenitor sample to the local density maps of the COSMOS field to identify the effects of environment. We find that BCG progenitors evolve in three stages, starting with an in situ SF dominated phase ($z > 2.25$). This is followed by a phase until $z \sim 1.25$ where mass growth is driven by in situ SF and stellar mass deposited by mergers (both gas rich and poor) on the same order of magnitude independent of local environment. Finally, at low redshift dry mergers are the dominant stellar mass generation process. We also identify this final transition period as the time when progenitors quench, exhibiting quiescent NUV\emph{rJ} colors., Comment: 17 pages, 14 figures, 1 table, Accepted to ApJ: 2019 July 8; Published in ApJ :2019 August 22

We define a fundamental group for digital images. Namely, we construct a functor from digital images to groups, which closely resembles the ordinary fundamental group from algebraic topology. Our construction differs in several basic ways from previously established versions of a fundamental group in the digital setting. Our development gives a prominent role to subdivision of digital images. We show that our fundamental group is preserved by subdivision., Comment: 47 pages, 2 figures

With a view towards providing tools for analyzing and understanding digitized images, various notions from algebraic topology have been introduced into the setting of digital topology. In the ordinary topological setting, invariants such as the fundamental group are invariants of homotopy type. In the digital setting, however, the usual notion of homotopy leads to a very rigid invariance that does not correspond well with the topological notion of homotopy invariance. In this paper, we establish fundamental results about subdivision of maps of digital images with $1$- or $2$-dimensional domains. Our results lay the groundwork for showing that the digital fundamental group is an invariant of a much less rigid equivalence relation on digital images, that is more akin to the topological notion of homotopy invariance. Our results also lay the groundwork for defining other invariants of digital images in a way that makes them invariants of this less rigid equivalence., Comment: 40 pages, 14 figures

Digital topology is part of the ongoing endeavour to understand and analyze digitized images. With a view to supporting this endeavour, many notions from algebraic topology have been introduced into the setting of digital topology. But some of the most basic notions from homotopy theory remain largely absent from the digital topology literature. We embark on a development of homotopy theory in digital topology, and define such fundamental notions as function spaces, path spaces, and cofibrations in this setting. We establish digital analogues of basic homotopy-theoretic properties such as the homotopy extension property for cofibrations, and the homotopy lifting property for certain evaluation maps that correspond to path fibrations in the topological setting. We indicate that some depth may be achieved by using these homotopy-theoretic notions to give a preliminary treatment of Lusternik-Schnirelmann category in the digital topology setting. This topic provides a connection between digital topology and critical points of functions on manifolds, as well as other topics from topological dynamics., Comment: 45 pages, 2 figures

Let $K$ be a finite, connected, abstract simplicial complex. The Morse complex of $K$, first introduced by Chari and Joswig, is the simplicial complex constructed from all gradient vector fields on $K$. We show that if $K$ is neither the boundary of the $n$-simplex nor a cycle, then $\mathrm{Aut}(\mathcal{M}(K))\cong \mathrm{Aut}(K)$. In the case where $K= C_n$, a cycle of length $n$, we show that $\mathrm{Aut}(\mathcal{M}(C_n))\cong \mathrm{Aut}(C_{2n})$. In the case where $K=\partial\Delta^n$, we prove that $\mathrm{Aut}(\mathcal{M}(\partial\Delta^n))\cong \mathrm{Aut}(\partial\Delta^n)\times \mathbb{Z}_2$. These results are based on recent work of Capitelli and Minian.

We report the first detailed measurement of the shape of the CO luminosity function at high redshift, based on $>$320 hr of the NSF's Karl G. Jansky Very Large Array (VLA) observations over an area of $\sim$60 arcmin$^2$ taken as part of the CO Luminosity Density at High Redshift (COLDz) survey. COLDz "blindly" selects galaxies based on their cold gas content through CO($J$=1$\to$0) emission at $z$$\sim$2-3 and CO($J$=2$\to$1) at $z$$\sim$5-7 down to a CO luminosity limit of log($L'_{\rm CO}$/K km s$^{-1}$ pc$^2$)$\simeq$9.5. We find that the characteristic luminosity and bright end of the CO luminosity function are substantially higher than predicted by semi-analytical models, but consistent with empirical estimates based on the infrared luminosity function at $z$$\sim$2. We also present the currently most reliable measurement of the cosmic density of cold gas in galaxies at early epochs, i.e., the cold gas history of the universe, as determined over a large cosmic volume of $\sim$375,000 Mpc$^3$. Our measurements are in agreement with an increase of the cold gas density from $z$$\sim$0 to $z$$\sim$2-3, followed by a possible decline towards $z$$\sim$5-7. These findings are consistent with recent surveys based on higher-$J$ CO line measurements, upon which COLDz improves in terms of statistical uncertainties by probing $\sim$50-100 times larger areas and in the reliability of total gas mass estimates by probing the low-$J$ CO lines accessible to the VLA. Our results thus appear to suggest that the cosmic star-formation rate density follows an increased cold molecular gas content in galaxies towards its peak about 10 billion years ago, and that its decline towards the earliest epochs is likely related to a lower overall amount of cold molecular gas (as traced by CO) bound in galaxies towards the first billion years after the Big Bang., Comment: 16 pages, 6 figures, 6 tables, to appear in ApJ (accepted January 04, 2019)

We describe the CO Luminosity Density at High-z (COLDz) survey, the first spectral line deep field targeting CO(1-0) emission from galaxies at $z=1.95-2.85$ and CO(2-1) at $z=4.91-6.70$. The main goal of COLDz is to constrain the cosmic density of molecular gas at the peak epoch of cosmic star formation. By targeting both a wide ($\sim$51 arcmin$^2$) and a deep area ($\sim$9 arcmin$^2$), the survey is designed to robustly constrain the bright end and the characteristic luminosity of the CO(1-0) luminosity function. An extensive analysis of the reliability of our line candidates, and new techniques provide detailed completeness and statistical corrections as necessary to determine the best constraints to date on the CO luminosity function. Our blind search for CO(1-0) uniformly selects starbursts and massive Main Sequence galaxies based on their cold molecular gas masses. Our search also detects CO(2-1) line emission from optically dark, dusty star-forming galaxies at $z>5$. We find a range of spatial sizes for the CO-traced gas reservoirs up to $\sim40$ kpc, suggesting that spatially extended cold molecular gas reservoirs may be common in massive, gas-rich galaxies at $z\sim2$. Through CO line stacking, we constrain the gas mass fraction in previously known typical star-forming galaxies at $z=2$-3. The stacked CO detection suggests lower molecular gas mass fractions than expected for massive Main Sequence galaxies by a factor of $\sim3-6$. We find total CO line brightness at $\sim34\,$GHz of $0.45\pm0.2\,\mu$K, which constrains future line intensity mapping and CMB experiments., Comment: 53 pages, 22 figures, 8 tables, ApJ in press. Full resolution images and publicly available data may be found on the survey webpage at coldz.astro.cornell.edu

We introduce a new notion of equivalence of discrete Morse functions on graphs called persistence equivalence. Two functions are considered persistence equivalent if and only if they induce the same persistence diagram. We compare this notion of equivalence to other notions of equivalent discrete Morse functions. We then compute an upper bound for the number of persistence equivalent discrete Morse functions on a fixed graph and show that this upper bound is sharp in the case where our graph is a tree. This is a version of the "realization problem" of the persistence map. We conclude with an example illustrating our construction.

We prove a discrete version of the Lusternik-Schnirelmann theorem for discrete Morse functions and the recently introduced simplicial Lusternik-Schnirelmann category of a simplicial complex. To accomplish this, a new notion of critical object of a discrete Morse function is presented, which generalizes the usual concept of critical simplex (in the sense of R. Forman). We show that the non-existence of such critical objects guarantees the strong homotopy equivalence (in the Barmak and Minian's sense) between the corresponding sublevel complexes. Finally, we establish that the number of critical objects of a discrete Morse function defined on $K$ is an upper bound for the non-normalized simplicial Lusternik-Schnirelmann category of $K$., Comment: 13 pages, 8 figures

Persistent homology has recently emerged as a powerful technique in topological data analysis for analyzing the emergence and disappearance of topological features throughout a filtered space, shown via persistence diagrams. Additionally, (co)sheaves have proven to be powerful instruments in tracking locally defined data across global systems, resulting in innovative applications to network science. In this paper, we combine the topological results of persistent homology and the quantitative data tracking capabilities of cosheaf theory to develop novel techniques in network data flow analysis. Specifically, we use cosheaf theory to construct persistent homology in a framework geared towards assessing data flow stability in hierarchical recurrent networks (HRNs). We use cosheaves to link topological information about a filtered network encoded in persistence diagrams with data associated locally to the network. From this construction, we use the homology of cosheaves as a framework to study the notion of "persistent data flow errors." That is, we generalize aspects of persistent homology to analyze the lifetime of local data flow malfunctions. We study an algorithmic construction of persistence diagrams parameterizing network data flow errors, thus enabling novel applications of statistical methods to study data flow malfunctions. We conclude with an application to network packet delivery systems.

We report interferometric measurements of [NII] 205 um fine-structure line emission from a representative sample of three galaxies at z=5-6 using the Atacama Large (sub)Millimeter Array (ALMA). These galaxies were previously detected in [CII] and far-infrared continuum emission and span almost two orders of magnitude in star formation rate (SFR). Our results show at least two different regimes of ionized inter-stellar medium properties for galaxies in the first billion years of cosmic time, separated by their L_[CII]/L_[NII] ratio. We find extremely low [NII] emission compared to [CII] (L_ [CII]/L_[NII]=68 [+200/-28]) from a "typical" L*_UV star-forming galaxy, likely directly or indirectly (by its effect on the radiation field) related to low dust abundance and low metallicity. The infrared-luminous modestly star-forming Lyman Break Galaxy (LBG) in our sample is characterized by an ionized-gas fraction (L_[CII]/L_[NII]<=20) typical of local star-forming galaxies and shows evidence for spatial variations in its ionized-gas fraction across an extended gas reservoir. The extreme SFR, warm and compact dusty starburst AzTEC-3 shows an ionized fraction higher than expected given its star-formation rate surface density (L_[CII]/L_[NII]=22+/-8) suggesting that [NII] dominantly traces a diffuse ionized medium rather than star-forming HII regions in this type of galaxy. This highest redshift sample of [NII] detections provides some of the first constraints on ionized and neutral gas modeling attempts and on the structure of the inter-stellar medium at z=5-6 in "normal" galaxies and starbursts., Comment: 12 pages, 5 figures, 2 tables, to appear in ApJ (accepted September 15, 2016)

In this paper, we study the Lusternik-Schnirelmann category of a simplicial map between simplicial complexes, generalizing the simplicial category of a complex to that of a map. Several properties of this new invariant are shown, including its relevance to products and fibrations. We relate this category of a map to the classical Lusternik-Schnirelmann category of a map between finite topological spaces. Finally, we show how the simplicial category of a map may be used to define and study a simplicial version of the essential category weight of J. Strom., Comment: 18 pages

This white paper discusses how a "next-generation" Very Large Array (ngVLA) operating in the frequency range 1-116 GHz could be a groundbreaking tool to study the detailed astrophysics of the "matter cycle" in the Milky Way and other galaxies. If optimized for high brightness sensitivity, the ngVLA would bring detailed microwave spectroscopy and modeling of the full radio spectral energy distribution into regular use as survey tools at resolutions of 0.1- 1 arcseconds. This wavelength range includes powerful diagnostics of density, excitation, and chemistry in the cold ISM, as well as multiple tracers of the rate of recent star formation, the magnetic field, shocks, and properties of the ionized ISM. We highlight design considerations that would make this facility revolutionary in this area, the foremost of which is a large amount of collecting area on ~km-length baselines. We also emphasize the strong case for harnessing the large proposed collecting area of the ngVLA for very long baseline applications as part of the core design. This would allow measurements of the three dimensional space motions of galaxies to beyond the Local Group and mapping of the Milky Way out to the far side of the disk. Finally, we discuss the gains from the proposed combination of very high resolution and sensitivity to thermal emission, which include observing the feeding of black holes and resolving forming protoclusters., Comment: 40 pages. For more information or to get involved see https://science.nrao.edu/futures/ngvla

We investigate the global cold dust properties of 85 nearby (z < 0.5) QSOs, chosen from the Palomar-Green sample of optically luminous quasars. We determine their infrared spectral energy distributions and estimate their rest-frame luminosities by combining Herschel data from 70 to 500 microns with near-infrared and mid-infrared measurements from the Two Micron All Sky Survey (2MASS) and the Wide-Field Infrared Survey Explorer (WISE). In most sources the far-infrared (FIR) emission can be attributed to thermally heated dust. Single temperature modified black body fits to the FIR photometry give an average dust temperature for the sample of 33~K, with a standard deviation of 8~K, and an average dust mass of 7E6 Solar Masses with a standard deviation of 9E6 Solar Masses. Estimates of star-formation that are based on the FIR continuum emission correlate with those based on the 11.3 microns PAH feature, however, the star-formation rates estimated from the FIR continuum are higher than those estimated from the 11.3 microns PAH emission. We attribute this result to a variety of factors including the possible destruction of the PAHs and that, in some sources, a fraction of the FIR originates from dust heated by the active galactic nucleus and by old stars., Comment: accepted for publication in ApJS

It is well-known that galaxy environment has a fundamental effect in shaping its properties. We study the environmental effects on galaxy evolution, with an emphasis on the environment defined as the local number density of galaxies. The density field is estimated with different estimators (weighted adaptive kernel smoothing, 10$^{th}$ and 5$^{th}$ nearest neighbors, Voronoi and Delaunay tessellation) for a K$_{s}<$24 sample of $\sim$190,000 galaxies in the COSMOS field at 0.1$<$z$<$3.1. The performance of each estimator is evaluated with extensive simulations. We show that overall, there is a good agreement between the estimated density fields using different methods over $\sim$2 dex in overdensity values. However, our simulations show that adaptive kernel and Voronoi tessellation outperform other methods. Using the Voronoi tessellation method, we assign surface densities to a mass complete sample of quiescent and star-forming galaxies out to z$\sim$3. We show that at a fixed stellar mass, the median color of quiescent galaxies does not depend on their host environment out to z$\sim$3. We find that the number and stellar mass density of massive ($>$10$^{11}$M$_{\odot}$) star-forming galaxies have not significantly changed since z$\sim$3, regardless of their environment. However, for massive quiescent systems at lower redshifts (z$\lesssim$1.3), we find a significant evolution in the number and stellar mass densities in denser environments compared to lower density regions. Our results suggest that the relation between stellar mass and local density is more fundamental than the color-density relation and that environment plays a significant role in quenching star formation activity in galaxies at z$\lesssim$1., Comment: 20 pages, 11 figures, main figures 4,5,8 and 10

We investigate the role of the delineated cosmic web/filaments on the star formation activity by exploring a sample of 425 narrow-band selected H{\alpha} emitters, as well as 2846 color-color selected underlying star-forming galaxies for a large scale structure (LSS) at z=0.84 in the COSMOS field from the HiZELS survey. Using the scale-independent Multi-scale Morphology Filter (MMF) algorithm, we are able to quantitatively describe the density field and disentangle it into its major components: fields, filaments and clusters. We show that the observed median star formation rate (SFR), stellar mass, specific star formation rate (sSFR), the mean SFR-Mass relation and its scatter for both H{\alpha} emitters and underlying star-forming galaxies do not strongly depend on different classes of environment, in agreement with previous studies. However, the fraction of H{\alpha} emitters varies with environment and is enhanced in filamentary structures at z~1. We propose mild galaxy-galaxy interactions as the possible physical agent for the elevation of the fraction of H{\alpha} star-forming galaxies in filaments. Our results show that filaments are the likely physical environments which are often classed as the "intermediate" densities, and that the cosmic web likely plays a major role in galaxy formation and evolution which has so far been poorly investigated., Comment: 15 pages, 11 figures, Accepted for publication in the ApJ

We report interferometric imaging of [CII] and OH emission toward the center of the galaxy protocluster associated with the z=5.3 submillimeter galaxy (SMG) AzTEC-3, using the Atacama Large (sub)Millimeter Array (ALMA). We detect strong [CII], OH, and rest-frame 157.7 um continuum emission toward the SMG. The [CII] emission is distributed over a scale of 3.9 kpc, implying a dynamical mass of 9.7 x 10^10 Msun, and a star formation rate (SFR) surface density of Sigma_SFR = 530 Msun/yr/kpc2. This suggests that AzTEC-3 forms stars at Sigma_SFR approaching the Eddington limit for radiation pressure supported disks. We find that the OH emission is slightly blueshifted relative to the [CII] line, which may indicate a molecular outflow associated with the peak phase of the starburst. We also detect and dynamically resolve [CII] emission over a scale of 7.5 kpc toward a triplet of Lyman-break galaxies with moderate UV-based SFRs in the protocluster at ~95kpc projected distance from the SMG. These galaxies are not detected in the continuum, suggesting far-infrared SFRs of <18-54 Msun/yr, consistent with a UV-based estimate of 22 Msun/yr. The spectral energy distribution of these galaxies is inconsistent with nearby spiral and starburst galaxies, but resembles those of dwarf galaxies. This is consistent with expectations for young starbursts without significant older stellar populations. This suggests that these galaxies are significantly metal-enriched, but not heavily dust-obscured, "normal" star-forming galaxies at z>5, showing that ALMA can detect the interstellar medium in "typical" galaxies in the very early universe., Comment: 15 pages, 12 figures, 4 tables, to appear in ApJ (accepted October 15, 2014)

Galaxy interactions/mergers have been shown to dominate the population of IR luminous galaxies (log(LIR)>11.6Lsun) in the local Universe (z<0.25). Recent studies based on the relation between galaxies' star formation rates and stellar mass (the SFR-M relation or the galaxy main sequence (MS)) have suggested that galaxy interaction/mergers may only become significant when galaxies fall well above the galaxy MS. Since the typical SFR at given M increases with redshift, the existence of galaxy MS implies that massive, IR-luminous galaxies at high-z may not necessarily be driven by galaxy interactions. We examine the role of galaxy interactions in the SFR-M relation by carrying out a morphological analysis of 2084 Herschel-selected galaxies at 0.2 < z < 1.5 in the COSMOS field. Herschel-PACS and -SPIRE observations covering the full 2-deg^2 COSMOS field provide one of the largest far-IR selected samples of high-redshift galaxies with well-determined redshifts to date, with sufficient sensitivity at z ~ 1, to sample objects lying on and above the galaxy MS. Using a detailed visual classification scheme, we show that the fraction of "disk galaxies" decreases and the fraction of "irregular" galaxies increases systematically with increasing LIR out to z ~ 1.5 and z ~ 1.0, respectively. At log(LIR) > 11.5 Lsun, >50% of the objects show evident features of strongly interacting/merger systems, where this percentage is similar to the studies of local IR-luminous galaxies. The fraction of interacting/merger systems also systematically increases with the deviation from the SFR-M relation, supporting the view that galaxies fall above the MS are more dominated by mergers than the MS galaxies. Meanwhile, we find that ~18% of massive IR-luminous MS galaxies are classified as interacting systems, where this population may not evolve through the evolutionary track predicted by a simple gas exhaustion model., Comment: 14 pages, 11 figures, ApJ accepted

The HII region luminosity function (LF) is an important tool for deriving the birthrates and mass distribution of OB associations, and is an excellent tracer of the newly formed massive stars and associations. To date, extensive work (predominantly in H{\alpha}) has been done from the ground, which is hindered by dust extinction and the severe blending of adjacent (spatially or in projection) HII regions. Reliably measuring the properties of HII regions requires a linear resolution <40 pc, but analyses satisfying this requirement have been done only in a handful of galaxies, so far. As the first space-based work using a galaxy sample, we have selected 12 galaxies from our HST NICMOS Pa{\alpha} survey and studied the luminosity function and size distribution of HII regions both in individual galaxies and cumulatively, using a virtually extinction-free tracer of the ionizing photon rate. The high angular resolution and low sensitivity to diffuse emission of NICMOS also offer an advantage over ground-based imaging by enabling a higher degree of de-blending of the HII regions. We do not confirm the broken power-law LFs found in ground-based studies. Instead, we find that the LFs, both individual and co-added, follow a single power law dN(L)/dlnL ~ L^-1, consistent with the mass function of star clusters in nearby galaxies, and in agreement with the results of the existing analyses with HST data. The individual and co-added size distribution of HII regions are both roughly consistent with dN(D)/dlnD ~ D^-3, but the power-law scaling is probably contaminated by blended regions or complexes., Comment: 17 pages, 11 figures, 2 tables, accepted for publication in ApJ. The full catalog of the 1907 HII regions is available at: http://www.pha.jhu.edu/~liu/papers/h2lf.tab2.dat

We investigate the high-redshift quasar luminosity function (QLF) down to an apparent magnitude of I(AB) = 25 in the Cosmic Evolution Survey (COSMOS). Careful analysis of the extensive COSMOS photometry and imaging data allows us to identify and remove stellar and low-redshift contaminants, enabling a selection that is nearly complete for type-1 quasars at the redshifts of interest. We find 155 likely quasars at z > 3.1, 39 of which have prior spectroscopic confirmation. We present our sample in detail and use these confirmed and likely quasars to compute the rest-frame UV QLF in the redshift bins 3.1 < z < 3.5 and 3.5 < z < 5. The space density of faint quasars decreases by roughly a factor of four from z \sim 3.2 to z \sim 4, with faint-end slopes of {\beta} \sim -1.7 at both redshifts. The decline in space density of faint optical quasars at z > 3 is similar to what has been found for more luminous optical and X-ray quasars. We compare the rest-frame UV luminosity functions found here with the X-ray luminosity function at z > 3, and find that they evolve similarly between z \sim 3.2 and z \sim 4; however, the different normalizations imply that roughly 75% of X-ray bright active galactic nuclei (AGN) at z \sim 3 - 4 are optically obscured. This fraction is higher than found at lower redshift and may imply that the obscured, type-2 fraction continues to increase with redshift at least to z \sim 4. Finally, the implications of the results derived here for the contribution of quasars to cosmic reionization are discussed., Comment: Accepted for publication in ApJ. 17 pages, 14 figures

We present ground-based spectroscopic verification of six Y dwarfs (see Cushing et al), eighty-nine T dwarfs, eight L dwarfs, and one M dwarf identified by the Wide-field Infrared Survey Explorer (WISE). Eighty of these are cold brown dwarfs with spectral types greater than or equal to T6, six of which have been announced earlier in Mainzer et al and Burgasser et al. We present color-color and color-type diagrams showing the locus of M, L, T, and Y dwarfs in WISE color space. Near-infrared classifications as late as early Y are presented and objects with peculiar spectra are discussed. After deriving an absolute WISE 4.6 um (W2) magnitude vs. spectral type relation, we estimate spectrophotometric distances to our discoveries. We also use available astrometric measurements to provide preliminary trigonometric parallaxes to four our discoveries, which have types of L9 pec (red), T8, T9, and Y0; all of these lie within 10 pc of the Sun. The Y0 dwarf, WISE 1541-2250, is the closest at 2.8 (+1.3,-0.6) pc; if this 2.8 pc value persists after continued monitoring, WISE 1541-2250 will become the seventh closest stellar system to the Sun. Another ten objects, with types between T6 and >Y0, have spectrophotometric distance estimates also placing them within 10 pc. The closest of these, the T6 dwarf WISE 1506+7027, is believed to fall at a distance of roughly 4.9 pc. WISE multi-epoch positions supplemented with positional info primarily from Spitzer/IRAC allow us to calculate proper motions and tangential velocities for roughly one half of the new discoveries. This work represents the first step by WISE to complete a full-sky, volume-limited census of late-T and Y dwarfs. Using early results from this census, we present preliminary, lower limits to the space density of these objects and discuss constraints on both the functional form of the mass function and the low-mass limit of star formation., Comment: 147 pages with 62 figures; submitted May 30 and accepted August 22 for publication in The Astrophysical Journal Supplement Series